Finite Group Databasebeta

← C22×#42951 #72299808

Subgroups — C22×#42951 #72299808

Order 1024.

103865 conjugacy classes of subgroups.

The subgroup lattice has 1914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#550C211yesmaximal, characteristic, complemented
2C23×#546C211yesmaximal, characteristic, complemented
3C2×#42951C2196yesmaximal, direct product factor
4C22×#2673C212yesmaximal, complemented
5C22×#2669C212yesmaximal, complemented
6C22×#2688C212yesmaximal, complemented
7C22×#2668C212yesmaximal, complemented
8C22×#2813C212yesmaximal, complemented
9C22×#2534C212yesmaximal, complemented
10C22×#2431C211yesmaximal, characteristic, complemented
11C22×#2407C211yesmaximal, characteristic, complemented
12C22×#2448C211yesmaximal, characteristic, complemented
13C22×#2421C211yesmaximal, characteristic, complemented
14C22×#2420C211yesmaximal, characteristic, complemented
15C22×#2445C211yesmaximal, characteristic, complemented
16C22×#2433C211yesmaximal, characteristic, complemented
17C22×#2416C211yesmaximal, characteristic, complemented
18C22×#2416C211yesmaximal, characteristic, complemented
19C22×#2408C211yesmaximal, characteristic, complemented
20C22×#2619C211yesmaximal, characteristic, complemented
21C22×#2630C212yesmaximal, complemented
22C22×#2617C212yesmaximal, complemented
23C22×#2392C211yesmaximal, characteristic, complemented
24C22×#2311C211yesmaximal, characteristic, complemented
25C24×#41C2211yescharacteristic
26C24×#41C2211yescharacteristic, complemented
27C25×D4C2211yescharacteristic
28C22×#550—232no—
29C22×#550C22148yescomplemented
30C22×#546—232no—
31C22×#546C22148yescomplemented
32C23×#127C2211yescharacteristic
33C23×#127C2211yescharacteristic
34C23×#127C2212yescomplemented
35C23×#124C2211yescharacteristic
36C23×#123C2212yes—
37C23×#123C2212yescomplemented
38C23×C22⋊Q8C2211yescharacteristic
39C23×#121C2212yes—
40C23×#121C2211yescharacteristic
41C23×#121C2211yescharacteristic
42C23×#121C2212yes—
43C23×#121C2211yescharacteristic
44C23×#121C2211yescharacteristic
45C23×#121C2212yescomplemented
46C23×#121C2211yescharacteristic, complemented
47C23×#121C2212yescomplemented
48C23×#121C2212yescomplemented
49C23×#120C2212yes—
50C23×#120C2212yes—
51C23×#120C2212yes—
52C23×#120C2212yes—
53C23×C4×Q8C2211yescharacteristic, complemented
54C23×C4×D4C2211yescharacteristic
55C23×C4×D4C2211yescharacteristic
56C23×C4×D4C2211yescharacteristic
57C23×C4×D4C2211yescharacteristic, complemented
58C23×C4×D4C2212yescomplemented
59C23×#117C2211yescharacteristic, complemented
60C24×C4⋊C4C2211yescharacteristic, complemented
61C24×C22⋊C4C2212yes—
62C2×#2688C22196yescomplemented
63C2×#2673C22196yescomplemented
64C2×#2669C22196yescomplemented
65C2×#2668C22196yescomplemented
66#42951C2211024yesdirect product factor
67C2×#2813C22196yescomplemented
68C2×#2534C22196yescomplemented
69C2×#2431C22148yescomplemented
70C2×#2407C22148yescomplemented
71C2×#2448C22148yescomplemented
72C2×#2421C22148yescomplemented
73C2×#2420C22148yescomplemented
74C2×#2445C22148yescomplemented
75C2×#2433C22148yescomplemented
76C2×#2416C22148yescomplemented
77C2×#2416C22148yescomplemented
78C2×#2408C22148yescomplemented
79C2×#2619C22148yescomplemented
80C2×#2630C22196yescomplemented
81C2×#2617C22196yescomplemented
82C22×#400C2212yescomplemented
83C22×#399C2212yescomplemented
84C2×#2392C22148yescomplemented
85C22×#398C2211yescharacteristic, complemented
86C22×#397C2212yes—
87C22×#397C2212yescomplemented
88C22×#397C2211yescharacteristic, complemented
89C22×#397C2212yescomplemented
90C22×#396C2211yescharacteristic
91C22×#396C2212yescomplemented
92C22×#396C2212yescomplemented
93C22×#396C2211yescharacteristic, complemented
94C22×#394C2211yescharacteristic
95C22×#394C2212yes—
96C22×#394C2212yes—
97C22×#394C2211yescharacteristic
98C22×#394C2212yescomplemented
99C22×#394C2212yescomplemented
100C22×#394C2212yescomplemented
101C22×#394C2211yescharacteristic, complemented
102C22×#394C2212yescomplemented
103C22×#394C2212yescomplemented
104C22×#394C2212yescomplemented
105C22×#394C2212yescomplemented
106C22×#392C2212yes—
107C22×#392C2211yescharacteristic
108C22×#392C2212yes—
109C22×#392C2212yes—
110C22×#392C2212yes—
111C22×#392C2212yescomplemented
112C22×#392C2212yescomplemented
113C22×#392C2212yescomplemented
114C22×#392C2212yescomplemented
115C2×#2311C22148yescomplemented
116C22×#391C2211yescharacteristic, complemented
117C22×#391C2211yescharacteristic, complemented
118C22×#390C2211yescharacteristic
119C22×#390C2211yescharacteristic
120C22×#390C2211yescharacteristic
121C22×#390C2211yescharacteristic
122C22×#390C2211yescharacteristic, complemented
123C22×#390C2211yescharacteristic, complemented
124C22×#389C2211yescharacteristic, complemented
125C22×#389C2211yescharacteristic, complemented
126C22×#388C2212yes—
127C22×#388C2212yescomplemented
128C22×#388C2212yescomplemented
129C22×#387C2212yescomplemented
130C22×#386C2212yes—
131C22×#386C2212yescomplemented
132C22×#386C2212yescomplemented
133C22×#386C2212yescomplemented
134C22×#386C2212yescomplemented
135C22×#386C2212yescomplemented
136C22×#386C2212yescomplemented
137C22×#386C2212yescomplemented
138C22×#386C2212yescomplemented
139C22×#385C2212yescomplemented
140C22×#382C2211yescharacteristic, complemented
141C22×#381C2212yescomplemented
142C22×#380C2211yescharacteristic
143C22×#380C2212yescomplemented
144C22×#380C2212yescomplemented
145C22×#380C2211yescharacteristic, complemented
146C22×#379C2212yes—
147C22×C4×C4⋊C4C2211yescharacteristic, complemented
148C22×C4×C22⋊C4C2211yescharacteristic
149C22×C4×C22⋊C4C2211yescharacteristic, complemented
150C27C2312yes—
151C23×#41—216no—
152C23×#41—48no—
153C23×#41—48no—
154C23×#41—48no—
155C23×#41—48no—
156C23×#41D4132yescomplemented
157C23×#41C23124yes—
158C23×#41C23124yescomplemented
159C24×Q8C2311yescharacteristic
160C24×D4—216no—
161C24×D4—48no—
162C24×D4—48no—
163C24×D4C2311yescharacteristic
164C24×D4C2311yescharacteristic
165C24×D4C2311yescharacteristic
166C24×D4C2312yes—
167C24×D4C2311yescharacteristic
168C24×D4C2311yescharacteristic
169C24×D4C23124yes—
170C24×D4C2312yes—
171C24×D4C2312yes—
172C24×D4C2311yescharacteristic
173C24×D4C2312yes—
174C24×D4C2312yes—
175C24×D4C2312yes—
176C24×D4C2312yes—
177C24×D4C2312yes—
178C24×D4C2312yes—
179C24×D4C2312yes—
180C24×D4C2312yes—
181C24×D4C2312yes—
182C25×C4C2311yescharacteristic
183C25×C4C2311yescharacteristic
184C25×C4C2311yescharacteristic
185C25×C4C2312yes—
186C25×C4C2312yes—
187C25×C4C2312yes—
188C25×C4C2312yes—
189C2×#550—2768no—
190C2×#550C231256yescomplemented
191C2×#546—2768no—
192C2×#546C231256yescomplemented
193C22×#127—216no—
194C22×#127—232no—
195C22×#127—48no—
196C22×#127C23124yes—
197C22×#127C23124yes—
198C22×#127C23148yescomplemented
199C22×#124—216no—
200C22×#124C23124yes—
201C22×#123—232no—
202C22×#123—416no—
203C22×#123C23148yes—
204C22×#123C23148yescomplemented
205C22×C22⋊Q8—216no—
206C22×C22⋊Q8C23124yes—
207C22×#121—232no—
208C22×#121—216no—
209C22×#121—232no—
210C22×#121—216no—
211C22×#121—216no—
212C22×#121—232no—
213C22×#121—416no—
214C22×#121—416no—
215C22×#121—48no—
216C22×#121—48no—
217C22×#121C23124yes—
218C22×#121C23124yes—
219C22×#121C23148yes—
220C22×#121C23124yes—
221C22×#121C23124yes—
222C22×#121C23148yes—
223C22×#121C23148yescomplemented
224C22×#121C23124yescomplemented
225C22×#121C23148yescomplemented
226C22×#121C23148yescomplemented
227C22×#120—232no—
228C22×#120—416no—
229C22×#120—416no—
230C22×#120—416no—
231C22×#120C23148yes—
232C22×#120C23148yes—
233C22×#120C23148yes—
234C22×#120C23148yes—
235C22×C4×Q8—216no—
236C22×C4×Q8C23124yescomplemented
237C22×C4×D4—216no—
238C22×C4×D4—216no—
239C22×C4×D4—216no—
240C22×C4×D4—232no—
241C22×C4×D4—48no—
242C22×C4×D4C23124yes—
243C22×C4×D4C23124yes—
244C22×C4×D4C23124yes—
245C22×C4×D4C23148yescomplemented
246C22×C4×D4C23124yescomplemented
247C22×#117—48no—
248C22×#117C23124yescomplemented
249C23×C4⋊C4—48no—
250C23×C4⋊C4C2311yescharacteristic
251C23×C4⋊C4C2311yescharacteristic
252C23×C4⋊C4C2311yescharacteristic
253C23×C4⋊C4C2311yescharacteristic
254C23×C4⋊C4C2311yescharacteristic
255C23×C4⋊C4C2311yescharacteristic
256C23×C4⋊C4C2312yes—
257C23×C4⋊C4C2312yes—
258C23×C4⋊C4C2312yes—
259C23×C4⋊C4C2311yescharacteristic
260C23×C4⋊C4C2312yes—
261C23×C4⋊C4C2311yescharacteristic
262C23×C4⋊C4C2311yescharacteristic
263C23×C4⋊C4C2311yescharacteristic
264C23×C4⋊C4C2312yes—
265C23×C4⋊C4C2311yescharacteristic
266C23×C4⋊C4C23124yescomplemented
267C23×C22⋊C4—232no—
268C23×C22⋊C4C23148yes—
269C23×C22⋊C4C2311yescharacteristic
270C23×C22⋊C4C2312yes—
271C23×C22⋊C4C2312yes—
272C23×C22⋊C4C2312yes—
273C23×C22⋊C4C2312yes—
274C23×C22⋊C4C2311yescharacteristic
275C23×C22⋊C4C2312yes—
276C23×C22⋊C4C2311yescharacteristic
277C23×C22⋊C4C2311yescharacteristic
278C23×C22⋊C4C2312yes—
279C23×C22⋊C4C2311yescharacteristic
280C23×C22⋊C4C2311yescharacteristic
281C23×C22⋊C4C2312yes—
282C23×C22⋊C4C2312yes—
283C23×C22⋊C4C2312yes—
284C23×C22⋊C4C2311yescharacteristic
285C23×C22⋊C4C2311yescharacteristic
286C23×C22⋊C4C2311yescharacteristic
287C23×C22⋊C4C2311yescharacteristic
288C23×C22⋊C4C2312yes—
289C23×C22⋊C4C2312yes—
290C23×C22⋊C4C2312yes—
291C23×C22⋊C4C2312yes—
292C23×C22⋊C4C2312yes—
293C23×C22⋊C4C2312yes—
294C23×C22⋊C4C2312yes—
295C23×C22⋊C4C2312yes—
296C23×C22⋊C4C2312yes—
297C23×C22⋊C4C2312yes—
298C23×C22⋊C4C2312yes—
299C23×C22⋊C4C2312yes—
300C23×C22⋊C4C2311yescharacteristic
301C23×C22⋊C4C2311yescharacteristic
302C23×C22⋊C4C2312yes—
303C23×C22⋊C4C2312yes—
304C23×C42C2311yescharacteristic
305C23×C42C2311yescharacteristic
306C23×C42C2311yescharacteristic
307C23×C42C2311yescharacteristic
308C23×C42C2312yes—
309#2813C231512yescomplemented
310#2688C231512yescomplemented
311#2673C231512yescomplemented
312#2669C231512yescomplemented
313#2668C231512yescomplemented
314#2630C231512yescomplemented
315#2619C231256yescomplemented
316#2617C231512yescomplemented
317#2534C231512yescomplemented
318#2448C231256yescomplemented
319#2445C231256yescomplemented
320#2433C231256yescomplemented
321#2431C231256yescomplemented
322#2421C231256yescomplemented
323#2420C231256yescomplemented
324#2416C231256yescomplemented
325#2416C231256yescomplemented
326#2408C231256yescomplemented
327#2407C231256yescomplemented
328C2×#400C23148yescomplemented
329C2×#399C23148yescomplemented
330#2392C231256yescomplemented
331C2×#398C23124yescomplemented
332C2×#397C23148yes—
333C2×#397C23148yescomplemented
334C2×#397C23124yescomplemented
335C2×#397C23148yescomplemented
336C2×#396C23124yes—
337C2×#396C23148yescomplemented
338C2×#396C23124yescomplemented
339C2×#396C23148yescomplemented
340C2×#394C23148yes—
341C2×#394C23148yes—
342C2×#394C23124yes—
343C2×#394C23124yes—
344C2×#394C23148yescomplemented
345C2×#394C23148yescomplemented
346C2×#394C23148yescomplemented
347C2×#394C23148yescomplemented
348C2×#394C23148yescomplemented
349C2×#394C23148yescomplemented
350C2×#394C23148yescomplemented
351C2×#394C23124yescomplemented
352C2×#392C23148yes—
353C2×#392C23148yes—
354C2×#392C23148yes—
355C2×#392C23124yes—
356C2×#392C23148yes—
357C2×#392C23148yescomplemented
358C2×#392C23148yescomplemented
359C2×#392C23148yescomplemented
360C2×#392C23148yescomplemented
361#2311C231256yescomplemented
362C2×#391C23124yescomplemented
363C2×#391C23124yescomplemented
364C2×#390C23124yes—
365C2×#390C23124yes—
366C2×#390C23124yes—
367C2×#390C23124yes—
368C2×#390C23124yescomplemented
369C2×#390C23124yescomplemented
370C2×#389C23124yescomplemented
371C2×#389C23124yescomplemented
372C2×#388C23148yes—
373C2×#388C23148yescomplemented
374C2×#388C23148yescomplemented
375C2×#387C23148yescomplemented
376C2×#386C23148yes—
377C2×#386C23148yescomplemented
378C2×#386C23148yescomplemented
379C2×#386C23148yescomplemented
380C2×#386C23148yescomplemented
381C2×#386C23148yescomplemented
382C2×#386C23148yescomplemented
383C2×#386C23148yescomplemented
384C2×#386C23148yescomplemented
385C2×#385C23148yescomplemented
386C2×#382C23124yescomplemented
387C2×#381C23148yescomplemented
388C2×#380C23124yes—
389C2×#380C23148yescomplemented
390C2×#380C23124yescomplemented
391C2×#380C23148yescomplemented
392C2×#379C23148yes—
393C2×C4×C4⋊C4C23124yescomplemented
394C2×C4×C22⋊C4C23124yes—
395C2×C4×C22⋊C4C23124yescomplemented
396C22×#95C2311yescharacteristic
397C22×#95C2311yescharacteristic
398C22×#95C2311yescharacteristic
399C22×#95C2311yescharacteristic
400C22×#95C2311yescharacteristic
401C22×#95C2311yescharacteristic
402C22×#95C2312yes—
403C22×#95C2312yes—
404C22×#95C2312yes—
405C22×#95C2312yes—
406C22×#95C2312yes—
407C22×#95C2312yes—
408C22×#95C2312yes—
409C22×#95C2312yes—
410C22×#95C2312yes—
411C22×#95C2312yes—
412C26—216no—
413C26—216no—
414C26—48no—
415C26—48no—
416C26—48no—
417C26—48no—
418C26—48no—
419C26C2411yescharacteristic
420C26C2412yes—
421C26C2412yes—
422C26C2411yescharacteristic
423C26C2412yes—
424C26C2411yescharacteristic
425C26C24124yes—
426C22×#41—2192no—
427C22×#41—4256no—
428C22×#41—496no—
429C22×#41—496no—
430C22×#41—496no—
431C22×#41—496no—
432C22×#41—4256no—
433C22×#41C2×D41384yescomplemented
434C22×#41C24164yes—
435C22×#41C24164yescomplemented
436C23×Q8—28no—
437C23×Q8—28no—
438C23×Q8C2×D4116yes—
439C23×Q8C24112yes—
440C23×D4—216no—
441C23×D4—28no—
442C23×D4—216no—
443C23×D4—28no—
444C23×D4—28no—
445C23×D4—28no—
446C23×D4—216no—
447C23×D4—216no—
448C23×D4—216no—
449C23×D4—216no—
450C23×D4—216no—
451C23×D4—2192no—
452C23×D4—28no—
453C23×D4—216no—
454C23×D4—28no—
455C23×D4—28no—
456C23×D4—28no—
457C23×D4—28no—
458C23×D4—28no—
459C23×D4—28no—
460C23×D4—28no—
461C23×D4—216no—
462C23×D4—28no—
463C23×D4—496no—
464C23×D4—496no—
465C23×D4—48no—
466C23×D4—48no—
467C23×D4—48no—
468C23×D4—44no—
469C23×D4—44no—
470C23×D4—44no—
471C23×D4—48no—
472C23×D4—48no—
473C23×D4—48no—
474C23×D4—48no—
475C23×D4—44no—
476C23×D4—48no—
477C23×D4—48no—
478C23×D4—48no—
479C23×D4—48no—
480C23×D4—48no—
481C23×D4—48no—
482C23×D4—48no—
483C23×D4—48no—
484C23×D4—48no—
485C23×D4—48no—
486C23×D4—48no—
487C23×D4—48no—
488C23×D4—48no—
489C23×D4—48no—
490C23×D4—48no—
491C23×D4—48no—
492C23×D4—48no—
493C23×D4—48no—
494C23×D4—48no—
495C23×D4—4256no—
496C23×D4C2×D4116yes—
497C23×D4C2×D4132yes—
498C23×D4C24112yes—
499C23×D4C24112yes—
500C23×D4C24112yes—
501C23×D4C24124yes—
502C23×D4C24112yes—
503C23×D4C24112yes—
504C23×D4C24124yes—
505C23×D4C24164yes—
506C23×D4C24124yes—
507C23×D4C24112yes—
508C23×D4C24124yes—
509C23×D4C24124yes—
510C23×D4C24124yes—
511C23×D4C24124yes—
512C23×D4C24124yes—
513C23×D4C24124yes—
514C23×D4C24124yes—
515C23×D4C24124yes—
516C23×D4C24124yes—
517C24×C4—28no—
518C24×C4—28no—
519C24×C4—216no—
520C24×C4—28no—
521C24×C4—216no—
522C24×C4—28no—
523C24×C4—28no—
524C24×C4—28no—
525C24×C4—28no—
526C24×C4—28no—
527C24×C4—48no—
528C24×C4—48no—
529C24×C4—48no—
530C24×C4—48no—
531C24×C4—48no—
532C24×C4—48no—
533C24×C4—48no—
534C24×C4—48no—
535C24×C4—48no—
536C24×C4C2×D4116yes—
537C24×C4C2×D4132yes—
538C24×C4C24112yes—
539C24×C4C24112yes—
540C24×C4C2411yescharacteristic
541C24×C4C2411yescharacteristic
542C24×C4C2411yescharacteristic
543C24×C4C2412yes—
544C24×C4C2412yes—
545C24×C4C2412yes—
546C24×C4C2411yescharacteristic
547C24×C4C2412yes—
548C24×C4C2411yescharacteristic
549C24×C4C2411yescharacteristic
550C24×C4C2411yescharacteristic
551C24×C4C2411yescharacteristic
552C24×C4C2411yescharacteristic
553C24×C4C24112yes—
554C24×C4C2411yescharacteristic
555C24×C4C2412yes—
556C24×C4C2411yescharacteristic
557C24×C4C24124yes—
558C24×C4C24124yes—
559C24×C4C24124yes—
560C24×C4C24124yes—
561C24×C4C2411yescharacteristic
562#550—22048no—
563#546—22048no—
564C2×#127—2192no—
565C2×#127—2384no—
566C2×#127—496no—
567C2×#127C24164yes—
568C2×#127C24164yes—
569C2×#127C241128yescomplemented
570C2×#124—2192no—
571C2×#124C24164yes—
572C2×#123—2384no—
573C2×#123—4192no—
574C2×#123C241128yes—
575C2×#123C241128yescomplemented
576C2×C22⋊Q8—2192no—
577C2×C22⋊Q8C24164yes—
578C2×#121—2384no—
579C2×#121—2192no—
580C2×#121—2384no—
581C2×#121—2192no—
582C2×#121—2192no—
583C2×#121—2384no—
584C2×#121—4192no—
585C2×#121—4192no—
586C2×#121—496no—
587C2×#121—496no—
588C2×#121C24164yes—
589C2×#121C24164yes—
590C2×#121C241128yes—
591C2×#121C24164yes—
592C2×#121C24164yes—
593C2×#121C241128yes—
594C2×#121C241128yescomplemented
595C2×#121C24164yescomplemented
596C2×#121C241128yescomplemented
597C2×#121C241128yescomplemented
598C2×#120—2384no—
599C2×#120—4192no—
600C2×#120—4192no—
601C2×#120—4192no—
602C2×#120C241128yes—
603C2×#120C241128yes—
604C2×#120C241128yes—
605C2×#120C241128yes—
606C2×C4×Q8—2192no—
607C2×C4×Q8C24164yescomplemented
608C2×C4×D4—2192no—
609C2×C4×D4—2192no—
610C2×C4×D4—2192no—
611C2×C4×D4—2384no—
612C2×C4×D4—496no—
613C2×C4×D4C24164yes—
614C2×C4×D4C24164yes—
615C2×C4×D4C24164yes—
616C2×C4×D4C241128yescomplemented
617C2×C4×D4C24164yescomplemented
618C2×#117—496no—
619C2×#117C24164yescomplemented
620C22×C4⋊C4—28no—
621C22×C4⋊C4—28no—
622C22×C4⋊C4—28no—
623C22×C4⋊C4—216no—
624C22×C4⋊C4—28no—
625C22×C4⋊C4—216no—
626C22×C4⋊C4—28no—
627C22×C4⋊C4—28no—
628C22×C4⋊C4—216no—
629C22×C4⋊C4—28no—
630C22×C4⋊C4—496no—
631C22×C4⋊C4—48no—
632C22×C4⋊C4—44no—
633C22×C4⋊C4—44no—
634C22×C4⋊C4—44no—
635C22×C4⋊C4—44no—
636C22×C4⋊C4—48no—
637C22×C4⋊C4C24112yes—
638C22×C4⋊C4C24124yes—
639C22×C4⋊C4C24124yes—
640C22×C4⋊C4C24112yes—
641C22×C4⋊C4C24112yes—
642C22×C4⋊C4C24124yes—
643C22×C4⋊C4C24112yes—
644C22×C4⋊C4C24112yes—
645C22×C4⋊C4C24112yes—
646C22×C4⋊C4C24112yes—
647C22×C4⋊C4C24112yes—
648C22×C4⋊C4C24112yes—
649C22×C4⋊C4C24112yes—
650C22×C4⋊C4C24124yes—
651C22×C4⋊C4C24112yes—
652C22×C4⋊C4C24124yes—
653C22×C4⋊C4C24164yescomplemented
654C22×C22⋊C4—216no—
655C22×C22⋊C4—28no—
656C22×C22⋊C4—216no—
657C22×C22⋊C4—28no—
658C22×C22⋊C4—28no—
659C22×C22⋊C4—216no—
660C22×C22⋊C4—28no—
661C22×C22⋊C4—216no—
662C22×C22⋊C4—216no—
663C22×C22⋊C4—216no—
664C22×C22⋊C4—2384no—
665C22×C22⋊C4—28no—
666C22×C22⋊C4—216no—
667C22×C22⋊C4—216no—
668C22×C22⋊C4—28no—
669C22×C22⋊C4—216no—
670C22×C22⋊C4—48no—
671C22×C22⋊C4—48no—
672C22×C22⋊C4—44no—
673C22×C22⋊C4—44no—
674C22×C22⋊C4—44no—
675C22×C22⋊C4—44no—
676C22×C22⋊C4—44no—
677C22×C22⋊C4—44no—
678C22×C22⋊C4—48no—
679C22×C22⋊C4—48no—
680C22×C22⋊C4—48no—
681C22×C22⋊C4—48no—
682C22×C22⋊C4—48no—
683C22×C22⋊C4—48no—
684C22×C22⋊C4—48no—
685C22×C22⋊C4—48no—
686C22×C22⋊C4—48no—
687C22×C22⋊C4—48no—
688C22×C22⋊C4—48no—
689C22×C22⋊C4—48no—
690C22×C22⋊C4C241128yes—
691C22×C22⋊C4C24112yes—
692C22×C22⋊C4C24124yes—
693C22×C22⋊C4C24124yes—
694C22×C22⋊C4C24124yes—
695C22×C22⋊C4C24124yes—
696C22×C22⋊C4C24112yes—
697C22×C22⋊C4C24112yes—
698C22×C22⋊C4C24124yes—
699C22×C22⋊C4C24112yes—
700C22×C22⋊C4C24124yes—
701C22×C22⋊C4C24124yes—
702C22×C22⋊C4C24112yes—
703C22×C22⋊C4C24124yes—
704C22×C22⋊C4C24124yes—
705C22×C22⋊C4C24112yes—
706C22×C22⋊C4C24112yes—
707C22×C22⋊C4C24124yes—
708C22×C22⋊C4C24112yes—
709C22×C22⋊C4C24112yes—
710C22×C22⋊C4C24124yes—
711C22×C22⋊C4C24124yes—
712C22×C22⋊C4C24124yes—
713C22×C22⋊C4C24124yes—
714C22×C22⋊C4C24124yes—
715C22×C22⋊C4C24124yes—
716C22×C22⋊C4C24124yes—
717C22×C22⋊C4C24112yes—
718C22×C22⋊C4C24112yes—
719C22×C22⋊C4C24124yes—
720C22×C22⋊C4C24124yes—
721C22×C22⋊C4C24124yes—
722C22×C22⋊C4C24124yes—
723C22×C22⋊C4C24124yes—
724C22×C22⋊C4C24112yes—
725C22×C22⋊C4C24124yes—
726C22×C42—28no—
727C22×C42—216no—
728C22×C42—28no—
729C22×C42—28no—
730C22×C42—28no—
731C22×C42C24112yes—
732C22×C42C24112yes—
733C22×C42C24112yes—
734C22×C42C24112yes—
735C22×C42C24124yes—
736#400C241128yescomplemented
737#399C241128yescomplemented
738#398C24164yescomplemented
739#397C241128yes—
740#397C241128yescomplemented
741#397C241128yescomplemented
742#397C24164yescomplemented
743#396C24164yes—
744#396C241128yescomplemented
745#396C241128yescomplemented
746#396C24164yescomplemented
747#394C24164yes—
748#394C241128yes—
749#394C241128yes—
750#394C24164yes—
751#394C241128yescomplemented
752#394C241128yescomplemented
753#394C241128yescomplemented
754#394C241128yescomplemented
755#394C24164yescomplemented
756#394C241128yescomplemented
757#394C241128yescomplemented
758#394C241128yescomplemented
759#392C241128yes—
760#392C241128yes—
761#392C24164yes—
762#392C241128yes—
763#392C241128yes—
764#392C241128yescomplemented
765#392C241128yescomplemented
766#392C241128yescomplemented
767#392C241128yescomplemented
768#391C24164yescomplemented
769#391C24164yescomplemented
770#390C24164yes—
771#390C24164yes—
772#390C24164yes—
773#390C24164yes—
774#390C24164yescomplemented
775#390C24164yescomplemented
776#389C24164yescomplemented
777#389C24164yescomplemented
778#388C241128yes—
779#388C241128yescomplemented
780#388C241128yescomplemented
781#387C241128yescomplemented
782#386C241128yes—
783#386C241128yescomplemented
784#386C241128yescomplemented
785#386C241128yescomplemented
786#386C241128yescomplemented
787#386C241128yescomplemented
788#386C241128yescomplemented
789#386C241128yescomplemented
790#386C241128yescomplemented
791#385C241128yescomplemented
792#382C24164yescomplemented
793#381C241128yescomplemented
794#380C24164yes—
795#380C241128yescomplemented
796#380C241128yescomplemented
797#380C24164yescomplemented
798#379C241128yes—
799C4×C4⋊C4C24164yescomplemented
800C4×C22⋊C4C24164yes—
801C4×C22⋊C4C24164yescomplemented
802C2×#95C24112yes—
803C2×#95C24112yes—
804C2×#95C24124yes—
805C2×#95C24112yes—
806C2×#95C24124yes—
807C2×#95C24124yes—
808C2×#95C24124yes—
809C2×#95C24124yes—
810C2×#95C24124yes—
811C2×#95C24112yes—
812C2×#95C24112yes—
813C2×#95C24124yes—
814C2×#95C24124yes—
815C2×#95C24124yes—
816C2×#95C24112yes—
817C2×#95C24124yes—
818C25—24no—
819C25—24no—
820C25—24no—
821C25—28no—
822C25—28no—
823C25—24no—
824C25—24no—
825C25—24no—
826C25—24no—
827C25—24no—
828C25—28no—
829C25—28no—
830C25—28no—
831C25—24no—
832C25—24no—
833C25—28no—
834C25—24no—
835C25—24no—
836C25—28no—
837C25—28no—
838C25—24no—
839C25—28no—
840C25—24no—
841C25—28no—
842C25—28no—
843C25—24no—
844C25—28no—
845C25—28no—
846C25—28no—
847C25—24no—
848C25—28no—
849C25—24no—
850C25—28no—
851C25—24no—
852C25—28no—
853C25—24no—
854C25—28no—
855C25—28no—
856C25—28no—
857C25—296no—
858C25—296no—
859C25—448no—
860C25—448no—
861C25—448no—
862C25—448no—
863C25—448no—
864C25—4128no—
865C25—4128no—
866C25—864no—
867C25—864no—
868C25—864no—
869C25—864no—
870C25—864no—
871C25C22×D4116yes—
872C25C22×D418yes—
873C25H(5,𝔽2)18yes—
874C25C25112yes—
875C25C2516yes—
876C25C25112yes—
877C25C25112yes—
878C25C2516yes—
879C25C2516yes—
880C25C25132yes—
881C25C2511yescharacteristic
882C2×#41—2256no—
883C2×#41—41536no—
884C2×#41—4128no—
885C2×#41—4128no—
886C2×#41—4128no—
887C2×#41—4128no—
888C2×#41—41536no—
889C2×#41C22×D41512yescomplemented
890C22×Q8—2128no—
891C22×Q8—248no—
892C22×Q8—248no—
893C22×Q8C22×D4196yes—
894C22×Q8C25116yes—
895C22×D4—248no—
896C22×D4—296no—
897C22×D4—248no—
898C22×D4—296no—
899C22×D4—248no—
900C22×D4—248no—
901C22×D4—296no—
902C22×D4—296no—
903C22×D4—296no—
904C22×D4—296no—
905C22×D4—296no—
906C22×D4—2256no—
907C22×D4—2128no—
908C22×D4—248no—
909C22×D4—296no—
910C22×D4—248no—
911C22×D4—248no—
912C22×D4—248no—
913C22×D4—296no—
914C22×D4—248no—
915C22×D4—248no—
916C22×D4—248no—
917C22×D4—248no—
918C22×D4—248no—
919C22×D4—4128no—
920C22×D4—4128no—
921C22×D4—424no—
922C22×D4—448no—
923C22×D4—448no—
924C22×D4—4128no—
925C22×D4—448no—
926C22×D4—424no—
927C22×D4—424no—
928C22×D4—424no—
929C22×D4—448no—
930C22×D4—448no—
931C22×D4—448no—
932C22×D4—448no—
933C22×D4—4128no—
934C22×D4—464no—
935C22×D4—4128no—
936C22×D4—448no—
937C22×D4—448no—
938C22×D4—448no—
939C22×D4—448no—
940C22×D4—448no—
941C22×D4—448no—
942C22×D4—448no—
943C22×D4—448no—
944C22×D4—448no—
945C22×D4—448no—
946C22×D4—448no—
947C22×D4—448no—
948C22×D4—448no—
949C22×D4—448no—
950C22×D4—448no—
951C22×D4—448no—
952C22×D4—448no—
953C22×D4—448no—
954C22×D4—448no—
955C22×D4—41536no—
956C22×D4—464no—
957C22×D4—464no—
958C22×D4—4128no—
959C22×D4—464no—
960C22×D4—464no—
961C22×D4—864no—
962C22×D4—864no—
963C22×D4—864no—
964C22×D4—864no—
965C22×D4—864no—
966C22×D4—864no—
967C22×D4—864no—
968C22×D4—864no—
969C22×D4C22×D4196yes—
970C22×D4C22×D41192yes—
971C22×D4C25116yes—
972C22×D4C25116yes—
973C22×D4C25116yes—
974C22×D4C25132yes—
975C22×D4C25116yes—
976C22×D4C25116yes—
977C22×D4C25116yes—
978C22×D4C25132yes—
979C22×D4C25132yes—
980C22×D4C25132yes—
981C22×D4C25132yes—
982C22×D4C25132yes—
983C22×D4C25132yes—
984C22×D4C25132yes—
985C22×D4C25132yes—
986C22×D4C25132yes—
987C22×D4C25132yes—
988C22×D4C25132yes—
989C23×C4—24no—
990C23×C4—24no—
991C23×C4—24no—
992C23×C4—28no—
993C23×C4—28no—
994C23×C4—24no—
995C23×C4—2128no—
996C23×C4—248no—
997C23×C4—248no—
998C23×C4—24no—
999C23×C4—24no—
1000C23×C4—28no—
1001C23×C4—24no—
1002C23×C4—24no—
1003C23×C4—28no—
1004C23×C4—24no—
1005C23×C4—28no—
1006C23×C4—28no—
1007C23×C4—24no—
1008C23×C4—24no—
1009C23×C4—24no—
1010C23×C4—28no—
1011C23×C4—24no—
1012C23×C4—24no—
1013C23×C4—24no—
1014C23×C4—24no—
1015C23×C4—28no—
1016C23×C4—28no—
1017C23×C4—24no—
1018C23×C4—28no—
1019C23×C4—24no—
1020C23×C4—24no—
1021C23×C4—28no—
1022C23×C4—28no—
1023C23×C4—24no—
1024C23×C4—24no—
1025C23×C4—24no—
1026C23×C4—24no—
1027C23×C4—24no—
1028C23×C4—24no—
1029C23×C4—24no—
1030C23×C4—24no—
1031C23×C4—24no—
1032C23×C4—28no—
1033C23×C4—28no—
1034C23×C4—24no—
1035C23×C4—24no—
1036C23×C4—24no—
1037C23×C4—296no—
1038C23×C4—296no—
1039C23×C4—248no—
1040C23×C4—248no—
1041C23×C4—248no—
1042C23×C4—248no—
1043C23×C4—248no—
1044C23×C4—248no—
1045C23×C4—4128no—
1046C23×C4—448no—
1047C23×C4—448no—
1048C23×C4—448no—
1049C23×C4—448no—
1050C23×C4—448no—
1051C23×C4—448no—
1052C23×C4—448no—
1053C23×C4—448no—
1054C23×C4—448no—
1055C23×C4—4128no—
1056C23×C4—464no—
1057C23×C4—464no—
1058C23×C4—864no—
1059C23×C4—864no—
1060C23×C4C22×D418yes—
1061C23×C4C22×D4116yes—
1062C23×C4C22×D4196yes—
1063C23×C4C22×D41192yes—
1064C23×C4C22×D418yes—
1065C23×C4H(5,𝔽2)18yes—
1066C23×C4H(5,𝔽2)18yes—
1067C23×C4H(5,𝔽2)18yes—
1068C23×C4C2516yes—
1069C23×C4C2516yes—
1070C23×C4C2516yes—
1071C23×C4C2516yes—
1072C23×C4C25112yes—
1073C23×C4C25112yes—
1074C23×C4C25112yes—
1075C23×C4C2516yes—
1076C23×C4C2516yes—
1077C23×C4C25112yes—
1078C23×C4C2516yes—
1079C23×C4C2516yes—
1080C23×C4C2516yes—
1081C23×C4C25116yes—
1082C23×C4C25116yes—
1083C23×C4C2516yes—
1084C23×C4C25112yes—
1085C23×C4C25116yes—
1086C23×C4C2516yes—
1087C23×C4C25132yes—
1088C23×C4C25132yes—
1089C23×C4C25132yes—
1090C23×C4C25132yes—
1091C23×C4C2516yes—
1092#127—2256no—
1093#127—2512no—
1094#127—4128no—
1095#124—2256no—
1096#123—2512no—
1097#123—4256no—
1098C22⋊Q8—2256no—
1099#121—2512no—
1100#121—2256no—
1101#121—2512no—
1102#121—2256no—
1103#121—2256no—
1104#121—2512no—
1105#121—4256no—
1106#121—4256no—
1107#121—4128no—
1108#121—4128no—
1109#120—2512no—
1110#120—4256no—
1111#120—4256no—
1112#120—4256no—
1113C4×Q8—2256no—
1114C4×D4—2256no—
1115C4×D4—2256no—
1116C4×D4—2256no—
1117C4×D4—2512no—
1118C4×D4—4128no—
1119#117—4128no—
1120C2×C4⋊C4—248no—
1121C2×C4⋊C4—248no—
1122C2×C4⋊C4—248no—
1123C2×C4⋊C4—296no—
1124C2×C4⋊C4—248no—
1125C2×C4⋊C4—296no—
1126C2×C4⋊C4—248no—
1127C2×C4⋊C4—248no—
1128C2×C4⋊C4—296no—
1129C2×C4⋊C4—248no—
1130C2×C4⋊C4—4128no—
1131C2×C4⋊C4—448no—
1132C2×C4⋊C4—424no—
1133C2×C4⋊C4—424no—
1134C2×C4⋊C4—424no—
1135C2×C4⋊C4—424no—
1136C2×C4⋊C4—448no—
1137C2×C4⋊C4C25116yes—
1138C2×C4⋊C4C25116yes—
1139C2×C4⋊C4C25116yes—
1140C2×C4⋊C4C25116yes—
1141C2×C4⋊C4C25116yes—
1142C2×C4⋊C4C25116yes—
1143C2×C4⋊C4C25132yes—
1144C2×C4⋊C4C25132yes—
1145C2×C4⋊C4C25132yes—
1146C2×C4⋊C4C25116yes—
1147C2×C4⋊C4C25132yes—
1148C2×C4⋊C4C25116yes—
1149C2×C4⋊C4C25116yes—
1150C2×C4⋊C4C25116yes—
1151C2×C4⋊C4C25132yes—
1152C2×C4⋊C4C25116yes—
1153C2×C22⋊C4—296no—
1154C2×C22⋊C4—248no—
1155C2×C22⋊C4—296no—
1156C2×C22⋊C4—248no—
1157C2×C22⋊C4—248no—
1158C2×C22⋊C4—296no—
1159C2×C22⋊C4—248no—
1160C2×C22⋊C4—296no—
1161C2×C22⋊C4—296no—
1162C2×C22⋊C4—296no—
1163C2×C22⋊C4—2512no—
1164C2×C22⋊C4—296no—
1165C2×C22⋊C4—248no—
1166C2×C22⋊C4—296no—
1167C2×C22⋊C4—248no—
1168C2×C22⋊C4—296no—
1169C2×C22⋊C4—448no—
1170C2×C22⋊C4—448no—
1171C2×C22⋊C4—424no—
1172C2×C22⋊C4—424no—
1173C2×C22⋊C4—424no—
1174C2×C22⋊C4—424no—
1175C2×C22⋊C4—424no—
1176C2×C22⋊C4—424no—
1177C2×C22⋊C4—448no—
1178C2×C22⋊C4—448no—
1179C2×C22⋊C4—448no—
1180C2×C22⋊C4—448no—
1181C2×C22⋊C4—448no—
1182C2×C22⋊C4—448no—
1183C2×C22⋊C4—448no—
1184C2×C22⋊C4—448no—
1185C2×C22⋊C4—448no—
1186C2×C22⋊C4—448no—
1187C2×C22⋊C4—448no—
1188C2×C22⋊C4—448no—
1189C2×C22⋊C4C25116yes—
1190C2×C22⋊C4C25132yes—
1191C2×C22⋊C4C25132yes—
1192C2×C22⋊C4C25132yes—
1193C2×C22⋊C4C25132yes—
1194C2×C22⋊C4C25116yes—
1195C2×C22⋊C4C25132yes—
1196C2×C22⋊C4C25116yes—
1197C2×C22⋊C4C25132yes—
1198C2×C22⋊C4C25116yes—
1199C2×C22⋊C4C25116yes—
1200C2×C22⋊C4C25116yes—
1201C2×C22⋊C4C25132yes—
1202C2×C22⋊C4C25132yes—
1203C2×C22⋊C4C25132yes—
1204C2×C22⋊C4C25116yes—
1205C2×C22⋊C4C25116yes—
1206C2×C22⋊C4C25116yes—
1207C2×C22⋊C4C25116yes—
1208C2×C22⋊C4C25132yes—
1209C2×C22⋊C4C25132yes—
1210C2×C22⋊C4C25132yes—
1211C2×C22⋊C4C25132yes—
1212C2×C22⋊C4C25132yes—
1213C2×C22⋊C4C25132yes—
1214C2×C22⋊C4C25132yes—
1215C2×C22⋊C4C25132yes—
1216C2×C22⋊C4C25132yes—
1217C2×C22⋊C4C25132yes—
1218C2×C22⋊C4C25132yes—
1219C2×C22⋊C4C25132yes—
1220C2×C22⋊C4C25116yes—
1221C2×C22⋊C4C25116yes—
1222C2×C22⋊C4C25132yes—
1223C2×C22⋊C4C25132yes—
1224C2×C42—248no—
1225C2×C42—296no—
1226C2×C42—248no—
1227C2×C42—248no—
1228C2×C42—248no—
1229C2×C42C25116yes—
1230C2×C42C25116yes—
1231C2×C42C25116yes—
1232C2×C42C25116yes—
1233C2×C42C25132yes—
1234#95C25116yes—
1235#95C25116yes—
1236#95C25116yes—
1237#95C25116yes—
1238#95C25116yes—
1239#95C25116yes—
1240#95C25132yes—
1241#95C25132yes—
1242#95C25132yes—
1243#95C25132yes—
1244#95C25132yes—
1245#95C25132yes—
1246#95C25132yes—
1247#95C25132yes—
1248#95C25132yes—
1249#95C25132yes—
1250C24—212no—
1251C24—212no—
1252C24—212no—
1253C24—224no—
1254C24—224no—
1255C24—212no—
1256C24—212no—
1257C24—212no—
1258C24—212no—
1259C24—212no—
1260C24—224no—
1261C24—224no—
1262C24—224no—
1263C24—212no—
1264C24—212no—
1265C24—224no—
1266C24—212no—
1267C24—212no—
1268C24—232no—
1269C24—264no—
1270C24—264no—
1271C24—232no—
1272C24—232no—
1273C24—232no—
1274C24—264no—
1275C24—232no—
1276C24—232no—
1277C24—224no—
1278C24—224no—
1279C24—212no—
1280C24—224no—
1281C24—212no—
1282C24—224no—
1283C24—224no—
1284C24—212no—
1285C24—224no—
1286C24—224no—
1287C24—224no—
1288C24—212no—
1289C24—224no—
1290C24—212no—
1291C24—224no—
1292C24—212no—
1293C24—212no—
1294C24—224no—
1295C24—224no—
1296C24—224no—
1297C24—224no—
1298C24—264no—
1299C24—264no—
1300C24—432no—
1301C24—432no—
1302C24—432no—
1303C24—432no—
1304C24—432no—
1305C24—4384no—
1306C24—4384no—
1307C24—416no—
1308C24—416no—
1309C24—416no—
1310C24—432no—
1311C24—416no—
1312C24—432no—
1313C24—416no—
1314C24—432no—
1315C24—416no—
1316C24—416no—
1317C24—432no—
1318C24—416no—
1319C24—432no—
1320C24—416no—
1321C24—432no—
1322C24—416no—
1323C24—432no—
1324C24—432no—
1325C24—416no—
1326C24—432no—
1327C24—432no—
1328C24—416no—
1329C24—432no—
1330C24—432no—
1331C24—416no—
1332C24—432no—
1333C24—432no—
1334C24—432no—
1335C24—432no—
1336C24—416no—
1337C24—432no—
1338C24—416no—
1339C24—432no—
1340C24—8192no—
1341C24—8192no—
1342C24—8192no—
1343C24—8192no—
1344C24—8192no—
1345C24—81024no—
1346C24C23×D4148yes—
1347C24C23×D4124yes—
1348C24C23×D414yes—
1349C24C2×H(5,𝔽2)124yes—
1350C24C2×H(5,𝔽2)14yes—
1351C24C2×H(5,𝔽2)14yes—
1352C24C2×H(5,𝔽2)14yes—
1353C24C2×H(5,𝔽2)14yes—
1354C24#58514yes—
1355C24#58514yes—
1356C24C2618yes—
1357C24C2614yes—
1358C24C2618yes—
1359C24C2618yes—
1360C24C2614yes—
1361C24C2614yes—
1362C24C2613yes—
1363#41—41024no—
1364#41—41024no—
1365C2×Q8—232no—
1366C2×Q8—232no—
1367C2×Q8—2384no—
1368C2×Q8C23×D4164yes—
1369C2×D4—232no—
1370C2×D4—264no—
1371C2×D4—232no—
1372C2×D4—264no—
1373C2×D4—232no—
1374C2×D4—232no—
1375C2×D4—264no—
1376C2×D4—264no—
1377C2×D4—264no—
1378C2×D4—264no—
1379C2×D4—264no—
1380C2×D4—232no—
1381C2×D4—264no—
1382C2×D4—232no—
1383C2×D4—232no—
1384C2×D4—232no—
1385C2×D4—264no—
1386C2×D4—232no—
1387C2×D4—232no—
1388C2×D4—232no—
1389C2×D4—232no—
1390C2×D4—232no—
1391C2×D4—2384no—
1392C2×D4—416no—
1393C2×D4—432no—
1394C2×D4—432no—
1395C2×D4—4384no—
1396C2×D4—432no—
1397C2×D4—416no—
1398C2×D4—416no—
1399C2×D4—416no—
1400C2×D4—432no—
1401C2×D4—432no—
1402C2×D4—432no—
1403C2×D4—432no—
1404C2×D4—4384no—
1405C2×D4—4192no—
1406C2×D4—4384no—
1407C2×D4—432no—
1408C2×D4—432no—
1409C2×D4—432no—
1410C2×D4—432no—
1411C2×D4—432no—
1412C2×D4—432no—
1413C2×D4—432no—
1414C2×D4—432no—
1415C2×D4—432no—
1416C2×D4—432no—
1417C2×D4—432no—
1418C2×D4—432no—
1419C2×D4—432no—
1420C2×D4—432no—
1421C2×D4—432no—
1422C2×D4—432no—
1423C2×D4—432no—
1424C2×D4—432no—
1425C2×D4—432no—
1426C2×D4—41024no—
1427C2×D4—4192no—
1428C2×D4—4192no—
1429C2×D4—4384no—
1430C2×D4—4192no—
1431C2×D4—4192no—
1432C2×D4—8192no—
1433C2×D4—8192no—
1434C2×D4—8192no—
1435C2×D4—8192no—
1436C2×D4—8192no—
1437C2×D4—8192no—
1438C2×D4—8192no—
1439C2×D4—8192no—
1440C2×D4C23×D4164yes—
1441C2×D4C23×D41128yes—
1442C22×C4—212no—
1443C22×C4—212no—
1444C22×C4—212no—
1445C22×C4—224no—
1446C22×C4—224no—
1447C22×C4—212no—
1448C22×C4—232no—
1449C22×C4—264no—
1450C22×C4—232no—
1451C22×C4—232no—
1452C22×C4—232no—
1453C22×C4—2384no—
1454C22×C4—212no—
1455C22×C4—212no—
1456C22×C4—212no—
1457C22×C4—224no—
1458C22×C4—224no—
1459C22×C4—212no—
1460C22×C4—212no—
1461C22×C4—212no—
1462C22×C4—212no—
1463C22×C4—212no—
1464C22×C4—212no—
1465C22×C4—224no—
1466C22×C4—224no—
1467C22×C4—212no—
1468C22×C4—212no—
1469C22×C4—212no—
1470C22×C4—224no—
1471C22×C4—212no—
1472C22×C4—212no—
1473C22×C4—212no—
1474C22×C4—224no—
1475C22×C4—224no—
1476C22×C4—212no—
1477C22×C4—224no—
1478C22×C4—212no—
1479C22×C4—212no—
1480C22×C4—224no—
1481C22×C4—224no—
1482C22×C4—212no—
1483C22×C4—212no—
1484C22×C4—212no—
1485C22×C4—212no—
1486C22×C4—212no—
1487C22×C4—212no—
1488C22×C4—224no—
1489C22×C4—212no—
1490C22×C4—224no—
1491C22×C4—212no—
1492C22×C4—212no—
1493C22×C4—264no—
1494C22×C4—264no—
1495C22×C4—232no—
1496C22×C4—232no—
1497C22×C4—232no—
1498C22×C4—232no—
1499C22×C4—232no—
1500C22×C4—232no—
1501C22×C4—4384no—
1502C22×C4—432no—
1503C22×C4—432no—
1504C22×C4—432no—
1505C22×C4—432no—
1506C22×C4—432no—
1507C22×C4—432no—
1508C22×C4—432no—
1509C22×C4—432no—
1510C22×C4—432no—
1511C22×C4—4384no—
1512C22×C4—416no—
1513C22×C4—416no—
1514C22×C4—416no—
1515C22×C4—432no—
1516C22×C4—416no—
1517C22×C4—416no—
1518C22×C4—432no—
1519C22×C4—416no—
1520C22×C4—416no—
1521C22×C4—432no—
1522C22×C4—432no—
1523C22×C4—416no—
1524C22×C4—416no—
1525C22×C4—4192no—
1526C22×C4—4192no—
1527C22×C4—8192no—
1528C22×C4—8192no—
1529C22×C4#534164yes—
1530C22×C4C23×D4148yes—
1531C22×C4C23×D4124yes—
1532C22×C4C23×D4164yes—
1533C22×C4C23×D41128yes—
1534C22×C4C23×D4124yes—
1535C22×C4C2×H(5,𝔽2)124yes—
1536C22×C4C2×H(5,𝔽2)124yes—
1537C22×C4C2×H(5,𝔽2)124yes—
1538C22×C4C2614yes—
1539C22×C4C2614yes—
1540C22×C4C2614yes—
1541C22×C4C2614yes—
1542C22×C4C2614yes—
1543C22×C4C2618yes—
1544C22×C4C2618yes—
1545C22×C4C2618yes—
1546C22×C4C2618yes—
1547C22×C4C2614yes—
1548C22×C4C2614yes—
1549C22×C4C2614yes—
1550C22×C4C2614yes—
1551C22×C4C2618yes—
1552C22×C4C2614yes—
1553C22×C4C2614yes—
1554C22×C4C2614yes—
1555C4⋊C4—232no—
1556C4⋊C4—232no—
1557C4⋊C4—232no—
1558C4⋊C4—264no—
1559C4⋊C4—232no—
1560C4⋊C4—264no—
1561C4⋊C4—232no—
1562C4⋊C4—232no—
1563C4⋊C4—264no—
1564C4⋊C4—232no—
1565C4⋊C4—432no—
1566C4⋊C4—416no—
1567C4⋊C4—416no—
1568C4⋊C4—416no—
1569C4⋊C4—416no—
1570C4⋊C4—432no—
1571C22⋊C4—264no—
1572C22⋊C4—232no—
1573C22⋊C4—264no—
1574C22⋊C4—232no—
1575C22⋊C4—232no—
1576C22⋊C4—264no—
1577C22⋊C4—232no—
1578C22⋊C4—264no—
1579C22⋊C4—264no—
1580C22⋊C4—264no—
1581C22⋊C4—264no—
1582C22⋊C4—232no—
1583C22⋊C4—264no—
1584C22⋊C4—232no—
1585C22⋊C4—264no—
1586C22⋊C4—432no—
1587C22⋊C4—432no—
1588C22⋊C4—416no—
1589C22⋊C4—416no—
1590C22⋊C4—416no—
1591C22⋊C4—416no—
1592C22⋊C4—416no—
1593C22⋊C4—416no—
1594C22⋊C4—432no—
1595C22⋊C4—432no—
1596C22⋊C4—432no—
1597C22⋊C4—432no—
1598C22⋊C4—432no—
1599C22⋊C4—432no—
1600C22⋊C4—432no—
1601C22⋊C4—432no—
1602C22⋊C4—432no—
1603C22⋊C4—432no—
1604C22⋊C4—432no—
1605C22⋊C4—432no—
1606C42—232no—
1607C42—264no—
1608C42—232no—
1609C42—232no—
1610C42—232no—
1611C23—248no—
1612C23—296no—
1613C23—248no—
1614C23—248no—
1615C23—248no—
1616C23—296no—
1617C23—24no—
1618C23—24no—
1619C23—24no—
1620C23—28no—
1621C23—28no—
1622C23—24no—
1623C23—24no—
1624C23—24no—
1625C23—24no—
1626C23—24no—
1627C23—28no—
1628C23—28no—
1629C23—28no—
1630C23—24no—
1631C23—24no—
1632C23—28no—
1633C23—24no—
1634C23—24no—
1635C23—248no—
1636C23—296no—
1637C23—248no—
1638C23—28no—
1639C23—28no—
1640C23—24no—
1641C23—28no—
1642C23—24no—
1643C23—28no—
1644C23—28no—
1645C23—24no—
1646C23—28no—
1647C23—28no—
1648C23—28no—
1649C23—24no—
1650C23—28no—
1651C23—24no—
1652C23—28no—
1653C23—24no—
1654C23—28no—
1655C23—24no—
1656C23—28no—
1657C23—28no—
1658C23—28no—
1659C23—4128no—
1660C23—4128no—
1661C23—424no—
1662C23—448no—
1663C23—424no—
1664C23—424no—
1665C23—448no—
1666C23—424no—
1667C23—448no—
1668C23—424no—
1669C23—424no—
1670C23—4128no—
1671C23—4256no—
1672C23—4128no—
1673C23—424no—
1674C23—424no—
1675C23—448no—
1676C23—448no—
1677C23—424no—
1678C23—448no—
1679C23—424no—
1680C23—448no—
1681C23—448no—
1682C23—448no—
1683C23—448no—
1684C23—424no—
1685C23—424no—
1686C23—448no—
1687C23—448no—
1688C23—424no—
1689C23—448no—
1690C23—448no—
1691C23—448no—
1692C23—424no—
1693C23—448no—
1694C23—424no—
1695C23—448no—
1696C23—448no—
1697C23—864no—
1698C23—864no—
1699C23—864no—
1700C23—864no—
1701C23—864no—
1702C23—81536no—
1703C23—864no—
1704C23—8128no—
1705C23—8128no—
1706C23C2×#534116yes—
1707C23#3488116yes—
1708C23#3488116yes—
1709C23#3542116yes—
1710C23#3543116yes—
1711C23#3546116yes—
1712C23#3562116yes—
1713C23C24×D4116yes—
1714C23C24×D418yes—
1715C23C24×D416yes—
1716C23C22×H(5,𝔽2)18yes—
1717C23C22×H(5,𝔽2)16yes—
1718C23C22×H(5,𝔽2)16yes—
1719C23C22×H(5,𝔽2)16yes—
1720C23C22×H(5,𝔽2)16yes—
1721C23C2×#58516yes—
1722C23C2×#58516yes—
1723C23C2711yescharacteristic
1724Q8—2128no—
1725D4—2128no—
1726D4—4128no—
1727D4—4128no—
1728D4—464no—
1729D4—4128no—
1730D4—464no—
1731D4—464no—
1732D4—4128no—
1733D4—464no—
1734D4—464no—
1735D4—864no—
1736D4—864no—
1737D4—864no—
1738D4—864no—
1739D4—864no—
1740D4—864no—
1741D4—864no—
1742D4—864no—
1743C2×C4—248no—
1744C2×C4—24no—
1745C2×C4—24no—
1746C2×C4—24no—
1747C2×C4—28no—
1748C2×C4—28no—
1749C2×C4—24no—
1750C2×C4—248no—
1751C2×C4—296no—
1752C2×C4—2128no—
1753C2×C4—24no—
1754C2×C4—24no—
1755C2×C4—24no—
1756C2×C4—28no—
1757C2×C4—28no—
1758C2×C4—24no—
1759C2×C4—24no—
1760C2×C4—24no—
1761C2×C4—24no—
1762C2×C4—24no—
1763C2×C4—24no—
1764C2×C4—28no—
1765C2×C4—28no—
1766C2×C4—24no—
1767C2×C4—24no—
1768C2×C4—24no—
1769C2×C4—28no—
1770C2×C4—24no—
1771C2×C4—24no—
1772C2×C4—24no—
1773C2×C4—28no—
1774C2×C4—28no—
1775C2×C4—24no—
1776C2×C4—28no—
1777C2×C4—24no—
1778C2×C4—24no—
1779C2×C4—28no—
1780C2×C4—28no—
1781C2×C4—24no—
1782C2×C4—24no—
1783C2×C4—24no—
1784C2×C4—24no—
1785C2×C4—24no—
1786C2×C4—24no—
1787C2×C4—28no—
1788C2×C4—24no—
1789C2×C4—24no—
1790C2×C4—28no—
1791C2×C4—24no—
1792C2×C4—4128no—
1793C2×C4—4128no—
1794C2×C4—448no—
1795C2×C4—448no—
1796C2×C4—424no—
1797C2×C4—424no—
1798C2×C4—424no—
1799C2×C4—448no—
1800C2×C4—424no—
1801C2×C4—424no—
1802C2×C4—448no—
1803C2×C4—424no—
1804C2×C4—424no—
1805C2×C4—424no—
1806C2×C4—424no—
1807C2×C4—464no—
1808C2×C4—464no—
1809C2×C4—864no—
1810C2×C4—864no—
1811C2×C4C2×#534196yes—
1812C2×C4C24×D4116yes—
1813C2×C4C24×D418yes—
1814C2×C4C24×D418yes—
1815C2×C4C22×H(5,𝔽2)18yes—
1816C2×C4C22×H(5,𝔽2)18yes—
1817C2×C4C22×H(5,𝔽2)18yes—
1818C22—28no—
1819C22—28no—
1820C22—28no—
1821C22—216no—
1822C22—216no—
1823C22—28no—
1824C22—28no—
1825C22—28no—
1826C22—216no—
1827C22—44no—
1828C22—48no—
1829C22—496no—
1830C22—4192no—
1831C22—496no—
1832C22—44no—
1833C22—48no—
1834C22—44no—
1835C22—44no—
1836C22—48no—
1837C22—44no—
1838C22—48no—
1839C22—44no—
1840C22—44no—
1841C22—44no—
1842C22—44no—
1843C22—48no—
1844C22—48no—
1845C22—48no—
1846C22—44no—
1847C22—48no—
1848C22—44no—
1849C22—48no—
1850C22—48no—
1851C22—48no—
1852C22—48no—
1853C22—44no—
1854C22—48no—
1855C22—44no—
1856C22—48no—
1857C22—44no—
1858C22—48no—
1859C22—48no—
1860C22—44no—
1861C22—48no—
1862C22—48no—
1863C22—8256no—
1864C22—848no—
1865C22—896no—
1866C22—896no—
1867C22#42951164yesdirect product factor
1868C22C22×#534112yes—
1869C22C2×#3542112yes—
1870C22C2×#3562112yes—
1871C22C2×#3543112yes—
1872C22C2×#3546112yes—
1873C22C2×#3488112yes—
1874C22C2×#3488112yes—
1875C22C25×D411yescharacteristic
1876C22C23×H(5,𝔽2)11yescharacteristic
1877C22C23×H(5,𝔽2)11yescharacteristic
1878C22C23×H(5,𝔽2)11yescharacteristic
1879C22C23×H(5,𝔽2)11yescharacteristic
1880C22C22×#58511yescharacteristic
1881C22C22×#58511yescharacteristic
1882C4—28no—
1883C4—216no—
1884C4—28no—
1885C4—44no—
1886C4—44no—
1887C4—48no—
1888C4—48no—
1889C4—44no—
1890C4—44no—
1891C4—44no—
1892C4—44no—
1893C4—44no—
1894C4—48no—
1895C4—44no—
1896C4—44no—
1897C4—48no—
1898C4C22×#534116yes—
1899C2—48no—
1900C2—416no—
1901C2—48no—
1902C2—84no—
1903C2—88no—
1904C2—88no—
1905C2C2×#42951124yesdirect product factor
1906C2C23×#53411yescharacteristic
1907C2C22×#348811yescharacteristic
1908C2C22×#348811yescharacteristic
1909C2C22×#354211yescharacteristic
1910C2C22×#356211yescharacteristic
1911C2C22×#354311yescharacteristic
1912C2C22×#354611yescharacteristic
subgroupG/H
center, socleC25C25
commutator, Frattini, cosocleC23C27
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C23×#550C2semidirect
2. C23×#546C2semidirect
3. C2×#42951C2direct (N × H)
4. C22×#2673C2semidirect
5. C22×#2669C2semidirect
6. C22×#2688C2semidirect
7. C22×#2668C2semidirect
8. C22×#2813C2semidirect
9. C22×#2534C2semidirect
10. C22×#2431C2semidirect
11. C22×#2407C2semidirect
12. C22×#2448C2semidirect
13. C22×#2421C2semidirect
14. C22×#2420C2semidirect
15. C22×#2445C2semidirect
16. C22×#2433C2semidirect
17. C22×#2416C2semidirect
18. C22×#2416C2semidirect
19. C22×#2408C2semidirect
20. C22×#2619C2semidirect
21. C22×#2630C2semidirect
22. C22×#2617C2semidirect
23. C22×#2392C2semidirect
24. C22×#2311C2semidirect
26. C24×#41C22semidirect
29. C22×#550C22semidirect
31. C22×#546C22semidirect
34. C23×#127C22semidirect
37. C23×#123C22semidirect
45. C23×#121C22semidirect
46. C23×#121C22semidirect
47. C23×#121C22semidirect
48. C23×#121C22semidirect
53. C23×C4×Q8C22semidirect
57. C23×C4×D4C22semidirect
58. C23×C4×D4C22semidirect
59. C23×#117C22semidirect
60. C24×C4⋊C4C22semidirect
62. C2×#2688C22semidirect
63. C2×#2673C22semidirect
64. C2×#2669C22semidirect
65. C2×#2668C22semidirect
66. #42951C22direct (N × H)
67. C2×#2813C22semidirect
68. C2×#2534C22semidirect
69. C2×#2431C22semidirect
70. C2×#2407C22semidirect
71. C2×#2448C22semidirect
72. C2×#2421C22semidirect
73. C2×#2420C22semidirect
74. C2×#2445C22semidirect
75. C2×#2433C22semidirect
76. C2×#2416C22semidirect
77. C2×#2416C22semidirect
78. C2×#2408C22semidirect
79. C2×#2619C22semidirect
80. C2×#2630C22semidirect
81. C2×#2617C22semidirect
82. C22×#400C22semidirect
83. C22×#399C22semidirect
84. C2×#2392C22semidirect
85. C22×#398C22semidirect
87. C22×#397C22semidirect
88. C22×#397C22semidirect
89. C22×#397C22semidirect
91. C22×#396C22semidirect
92. C22×#396C22semidirect
93. C22×#396C22semidirect
98. C22×#394C22semidirect
99. C22×#394C22semidirect
100. C22×#394C22semidirect
101. C22×#394C22semidirect
102. C22×#394C22semidirect
103. C22×#394C22semidirect
104. C22×#394C22semidirect
105. C22×#394C22semidirect
111. C22×#392C22semidirect
112. C22×#392C22semidirect
113. C22×#392C22semidirect
114. C22×#392C22semidirect
115. C2×#2311C22semidirect
116. C22×#391C22semidirect
117. C22×#391C22semidirect
122. C22×#390C22semidirect
123. C22×#390C22semidirect
124. C22×#389C22semidirect
125. C22×#389C22semidirect
127. C22×#388C22semidirect
128. C22×#388C22semidirect
129. C22×#387C22semidirect
131. C22×#386C22semidirect
132. C22×#386C22semidirect
133. C22×#386C22semidirect
134. C22×#386C22semidirect
135. C22×#386C22semidirect
136. C22×#386C22semidirect
137. C22×#386C22semidirect
138. C22×#386C22semidirect
139. C22×#385C22semidirect
140. C22×#382C22semidirect
141. C22×#381C22semidirect
143. C22×#380C22semidirect
144. C22×#380C22semidirect
145. C22×#380C22semidirect
147. C22×C4×C4⋊C4C22semidirect
149. C22×C4×C22⋊C4C22semidirect
156. C23×#41D4semidirect
158. C23×#41C23semidirect
190. C2×#550C23semidirect
192. C2×#546C23semidirect
198. C22×#127C23semidirect
204. C22×#123C23semidirect
223. C22×#121C23semidirect
224. C22×#121C23semidirect
225. C22×#121C23semidirect
226. C22×#121C23semidirect
236. C22×C4×Q8C23semidirect
245. C22×C4×D4C23semidirect
246. C22×C4×D4C23semidirect
248. C22×#117C23semidirect
266. C23×C4⋊C4C23semidirect
309. #2813C23semidirect
310. #2688C23semidirect
311. #2673C23semidirect
312. #2669C23semidirect
313. #2668C23semidirect
314. #2630C23semidirect
315. #2619C23semidirect
316. #2617C23semidirect
317. #2534C23semidirect
318. #2448C23semidirect
319. #2445C23semidirect
320. #2433C23semidirect
321. #2431C23semidirect
322. #2421C23semidirect
323. #2420C23semidirect
324. #2416C23semidirect
325. #2416C23semidirect
326. #2408C23semidirect
327. #2407C23semidirect
328. C2×#400C23semidirect
329. C2×#399C23semidirect
330. #2392C23semidirect
331. C2×#398C23semidirect
333. C2×#397C23semidirect
334. C2×#397C23semidirect
335. C2×#397C23semidirect
337. C2×#396C23semidirect
338. C2×#396C23semidirect
339. C2×#396C23semidirect
344. C2×#394C23semidirect
345. C2×#394C23semidirect
346. C2×#394C23semidirect
347. C2×#394C23semidirect
348. C2×#394C23semidirect
349. C2×#394C23semidirect
350. C2×#394C23semidirect
351. C2×#394C23semidirect
357. C2×#392C23semidirect
358. C2×#392C23semidirect
359. C2×#392C23semidirect
360. C2×#392C23semidirect
361. #2311C23semidirect
362. C2×#391C23semidirect
363. C2×#391C23semidirect
368. C2×#390C23semidirect
369. C2×#390C23semidirect
370. C2×#389C23semidirect
371. C2×#389C23semidirect
373. C2×#388C23semidirect
374. C2×#388C23semidirect
375. C2×#387C23semidirect
377. C2×#386C23semidirect
378. C2×#386C23semidirect
379. C2×#386C23semidirect
380. C2×#386C23semidirect
381. C2×#386C23semidirect
382. C2×#386C23semidirect
383. C2×#386C23semidirect
384. C2×#386C23semidirect
385. C2×#385C23semidirect
386. C2×#382C23semidirect
387. C2×#381C23semidirect
389. C2×#380C23semidirect
390. C2×#380C23semidirect
391. C2×#380C23semidirect
393. C2×C4×C4⋊C4C23semidirect
395. C2×C4×C22⋊C4C23semidirect
433. C22×#41C2×D4semidirect
435. C22×#41C24semidirect
569. C2×#127C24semidirect
575. C2×#123C24semidirect
594. C2×#121C24semidirect
595. C2×#121C24semidirect
596. C2×#121C24semidirect
597. C2×#121C24semidirect
607. C2×C4×Q8C24semidirect
616. C2×C4×D4C24semidirect
617. C2×C4×D4C24semidirect
619. C2×#117C24semidirect
653. C22×C4⋊C4C24semidirect
736. #400C24semidirect
737. #399C24semidirect
738. #398C24semidirect
740. #397C24semidirect
741. #397C24semidirect
742. #397C24semidirect
744. #396C24semidirect
745. #396C24semidirect
746. #396C24semidirect
751. #394C24semidirect
752. #394C24semidirect
753. #394C24semidirect
754. #394C24semidirect
755. #394C24semidirect
756. #394C24semidirect
757. #394C24semidirect
758. #394C24semidirect
764. #392C24semidirect
765. #392C24semidirect
766. #392C24semidirect
767. #392C24semidirect
768. #391C24semidirect
769. #391C24semidirect
774. #390C24semidirect
775. #390C24semidirect
776. #389C24semidirect
777. #389C24semidirect
779. #388C24semidirect
780. #388C24semidirect
781. #387C24semidirect
783. #386C24semidirect
784. #386C24semidirect
785. #386C24semidirect
786. #386C24semidirect
787. #386C24semidirect
788. #386C24semidirect
789. #386C24semidirect
790. #386C24semidirect
791. #385C24semidirect
792. #382C24semidirect
793. #381C24semidirect
795. #380C24semidirect
796. #380C24semidirect
797. #380C24semidirect
799. C4×C4⋊C4C24semidirect
801. C4×C22⋊C4C24semidirect
889. C2×#41C22×D4semidirect
1867. C22#42951direct (N × H)
1905. C2C2×#42951direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C23×#5502
C23×#5462
C2×#429512
C22×#26732
C22×#26692
C22×#26882
C22×#26682
C22×#28132
C22×#25342
C22×#24312
C22×#24072
C22×#24482
C22×#24212
C22×#24202
C22×#24452
C22×#24332
C22×#24162
C22×#24082
C22×#26192
C22×#26302
C22×#26172
C22×#23922
C22×#23112