Finite Group Databasebeta

← C22×#44899 #72324641

Subgroups — C22×#44899 #72324641

Order 1024.

98389 conjugacy classes of subgroups.

The subgroup lattice has 1881 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#553C211yesmaximal, characteristic, complemented
2C23×#535C211yesmaximal, characteristic, complemented
3C2×#44899C2196yesmaximal, direct product factor
4C22×#2710C212yesmaximal, complemented
5C22×#2673C212yesmaximal, complemented
6C22×#2685C212yesmaximal, complemented
7C22×#2678C212yesmaximal, complemented
8C22×#2537C211yesmaximal, characteristic, complemented
9C22×#2539C212yesmaximal, complemented
10C22×#2490C211yesmaximal, characteristic, complemented
11C22×#2521C212yesmaximal, complemented
12C22×#2501C211yesmaximal, characteristic, complemented
13C22×#2441C211yesmaximal, characteristic, complemented
14C22×#2414C211yesmaximal, characteristic, complemented
15C22×#2414C211yesmaximal, characteristic, complemented
16C22×#2445C212yesmaximal, complemented
17C22×#2422C211yesmaximal, characteristic, complemented
18C22×#2408C211yesmaximal, characteristic, complemented
19C22×#2418C212yesmaximal, complemented
20C22×#2388C211yesmaximal, characteristic, complemented
21C22×#2363C211yesmaximal, characteristic, complemented
22C22×#2354C211yesmaximal, characteristic, complemented
23C22×D4×C22⋊C4C211yesmaximal, characteristic, complemented
24C22×#2311C211yesmaximal, characteristic, complemented
25C24×#41C2211yescharacteristic
26C25×D4C2211yescharacteristic
27C22×#553—232no—
28C22×#553C22148yescomplemented
29C22×#535—232no—
30C22×#535C22148yescomplemented
31C23×#127C2212yes—
32C23×#126C2212yescomplemented
33C23×#125C2211yescharacteristic, complemented
34C23×#124C2212yes—
35C23×#123C2212yescomplemented
36C23×#123C2212yescomplemented
37C23×#123C2212yescomplemented
38C23×#123C2212yescomplemented
39C23×#121C2211yescharacteristic
40C23×#121C2211yescharacteristic
41C23×#121C2211yescharacteristic
42C23×#121C2211yescharacteristic
43C23×#121C2211yescharacteristic
44C23×#121C2211yescharacteristic
45C23×#121C2212yescomplemented
46C23×#121C2212yescomplemented
47C23×#120C2212yes—
48C23×#120C2212yes—
49C23×#120C2212yes—
50C23×C4×D4C2211yescharacteristic
51C23×C4×D4C2211yescharacteristic
52C23×C4×D4C2211yescharacteristic
53C23×C4×D4C2212yescomplemented
54C23×C4×D4C2211yescharacteristic, complemented
55C23×C4×D4C2211yescharacteristic, complemented
56C23×#117C2211yescharacteristic
57C23×#117C2211yescharacteristic, complemented
58C23×#117C2211yescharacteristic, complemented
59C24×C4⋊C4C2211yescharacteristic, complemented
60C24×C22⋊C4C2212yes—
61C2×#2710C22196yescomplemented
62C2×#2685C22196yescomplemented
63C2×#2678C22196yescomplemented
64C2×#2673C22196yescomplemented
65#44899C2211024yesdirect product factor
66C2×#2537C22148yescomplemented
67C2×#2539C22196yescomplemented
68C2×#2490C22148yescomplemented
69C2×#2521C22196yescomplemented
70C2×#2501C22148yescomplemented
71C2×#2441C22148yescomplemented
72C2×#2414C22148yescomplemented
73C2×#2414C22148yescomplemented
74C2×#2445C22196yescomplemented
75C2×#2422C22148yescomplemented
76C2×#2408C22148yescomplemented
77C2×#2418C22196yescomplemented
78C22×#399C2212yes—
79C22×#399C2212yescomplemented
80C22×#399C2212yescomplemented
81C22×#397C2212yescomplemented
82C22×#397C2212yescomplemented
83C22×#396C2212yes—
84C2×#2388C22148yescomplemented
85C22×#395C2211yescharacteristic, complemented
86C22×#394C2211yescharacteristic
87C22×#394C2211yescharacteristic
88C22×#394C2212yes—
89C22×#394C2212yescomplemented
90C22×#394C2212yescomplemented
91C22×#394C2212yescomplemented
92C22×#394C2212yescomplemented
93C22×#394C2212yescomplemented
94C22×#394C2212yescomplemented
95C22×#394C2211yescharacteristic, complemented
96C22×#393C2211yescharacteristic, complemented
97C22×#392C2211yescharacteristic
98C22×#392C2212yes—
99C22×#392C2211yescharacteristic
100C22×#392C2212yescomplemented
101C22×#392C2211yescharacteristic, complemented
102C22×#392C2212yescomplemented
103C2×#2363C22148yescomplemented
104C2×#2354C22148yescomplemented
105C2×D4×C22⋊C4C22148yescomplemented
106C2×#2311C22148yescomplemented
107C22×#391C2212yescomplemented
108C22×#390C2212yes—
109C22×#390C2212yes—
110C22×#390C2211yescharacteristic
111C22×#390C2211yescharacteristic
112C22×#390C2211yescharacteristic
113C22×#390C2211yescharacteristic
114C22×#390C2212yescomplemented
115C22×#390C2212yescomplemented
116C22×#390C2212yescomplemented
117C22×#390C2212yescomplemented
118C22×#389C2211yescharacteristic, complemented
119C22×#389C2212yescomplemented
120C22×#389C2211yescharacteristic, complemented
121C22×#388C2212yes—
122C22×#388C2212yescomplemented
123C22×#388C2212yescomplemented
124C22×#388C2212yescomplemented
125C22×#388C2212yescomplemented
126C22×#388C2212yescomplemented
127C22×#387C2212yescomplemented
128C22×#386C2212yes—
129C22×#386C2212yes—
130C22×#386C2212yes—
131C22×#386C2212yescomplemented
132C22×#386C2212yescomplemented
133C22×#385C2212yescomplemented
134C22×#384C2211yescharacteristic, complemented
135C22×#384C2211yescharacteristic, complemented
136C22×#380C2211yescharacteristic
137C22×#380C2211yescharacteristic
138C22×#380C2212yescomplemented
139C22×#380C2211yescharacteristic, complemented
140C22×#380C2211yescharacteristic, complemented
141C22×#380C2211yescharacteristic, complemented
142C22×#379C2212yes—
143C22×#379C2212yes—
144C22×C4×C4⋊C4C2212yescomplemented
145C22×C4×C4⋊C4C2211yescharacteristic, complemented
146C22×C4×C22⋊C4C2211yescharacteristic
147C22×C4×C22⋊C4C2211yescharacteristic, complemented
148C22×C4×C22⋊C4C2211yescharacteristic, complemented
149C22×C4×C22⋊C4C2212yescomplemented
150C27C2312yes—
151C23×#41—216no—
152C23×#41—216no—
153C23×#41—48no—
154C23×#41C23124yes—
155C24×Q8C2311yescharacteristic
156C24×D4—216no—
157C24×D4—216no—
158C24×D4—48no—
159C24×D4C2311yescharacteristic
160C24×D4C23124yes—
161C24×D4C2312yes—
162C24×D4C2311yescharacteristic
163C24×D4C2311yescharacteristic
164C24×D4C2311yescharacteristic
165C24×D4C2311yescharacteristic
166C24×D4C2311yescharacteristic
167C24×D4C2311yescharacteristic
168C24×D4C2311yescharacteristic
169C24×D4C2312yes—
170C24×D4C2312yes—
171C24×D4C2312yes—
172C24×D4C2312yes—
173C24×D4C2312yes—
174C24×D4C2312yes—
175C25×C4C2311yescharacteristic
176C25×C4C2311yescharacteristic
177C25×C4C2311yescharacteristic
178C25×C4C2311yescharacteristic
179C25×C4C2312yes—
180C25×C4C2312yes—
181C25×C4C2312yes—
182C2×#553—2768no—
183C2×#553C231256yescomplemented
184C2×#535—2768no—
185C2×#535C231256yescomplemented
186C22×#127—232no—
187C22×#127C23148yes—
188C22×#126—232no—
189C22×#126C23148yescomplemented
190C22×#125—216no—
191C22×#125C23124yescomplemented
192C22×#124—232no—
193C22×#124C23148yes—
194C22×#123—232no—
195C22×#123—416no—
196C22×#123—416no—
197C22×#123—416no—
198C22×#123C23148yescomplemented
199C22×#123C23148yescomplemented
200C22×#123C23148yescomplemented
201C22×#123C23148yescomplemented
202C22×#121—216no—
203C22×#121—216no—
204C22×#121—232no—
205C22×#121—216no—
206C22×#121—216no—
207C22×#121—48no—
208C22×#121—416no—
209C22×#121D4132yescomplemented
210C22×#121C23124yes—
211C22×#121C23124yes—
212C22×#121C23124yes—
213C22×#121C23124yes—
214C22×#121C23124yes—
215C22×#121C23124yes—
216C22×#121C23148yescomplemented
217C22×#121C23148yescomplemented
218C22×#120—232no—
219C22×#120—232no—
220C22×#120—416no—
221C22×#120C23148yes—
222C22×#120C23148yes—
223C22×#120C23148yes—
224C22×C4×D4—216no—
225C22×C4×D4—232no—
226C22×C4×D4—216no—
227C22×C4×D4—216no—
228C22×C4×D4—48no—
229C22×C4×D4—48no—
230C22×C4×D4C23124yes—
231C22×C4×D4C23124yes—
232C22×C4×D4C23124yes—
233C22×C4×D4C23148yescomplemented
234C22×C4×D4C23124yescomplemented
235C22×C4×D4C23124yescomplemented
236C22×#117—216no—
237C22×#117—216no—
238C22×#117—48no—
239C22×#117C23124yes—
240C22×#117C23124yescomplemented
241C22×#117C23124yescomplemented
242C23×C4⋊C4—216no—
243C23×C4⋊C4C2311yescharacteristic
244C23×C4⋊C4C2311yescharacteristic
245C23×C4⋊C4C2312yes—
246C23×C4⋊C4C2311yescharacteristic
247C23×C4⋊C4C2311yescharacteristic
248C23×C4⋊C4C2311yescharacteristic
249C23×C4⋊C4C2311yescharacteristic
250C23×C4⋊C4C2312yes—
251C23×C4⋊C4C2311yescharacteristic
252C23×C4⋊C4C2312yes—
253C23×C4⋊C4C2312yes—
254C23×C4⋊C4C2312yes—
255C23×C4⋊C4C2311yescharacteristic
256C23×C4⋊C4C2312yes—
257C23×C4⋊C4C2312yes—
258C23×C4⋊C4C2312yes—
259C23×C4⋊C4C2312yes—
260C23×C4⋊C4C2311yescharacteristic
261C23×C4⋊C4C23124yescomplemented
262C23×C22⋊C4—416no—
263C23×C22⋊C4C2311yescharacteristic
264C23×C22⋊C4C2312yes—
265C23×C22⋊C4C2312yes—
266C23×C22⋊C4C2312yes—
267C23×C22⋊C4C2312yes—
268C23×C22⋊C4C2311yescharacteristic
269C23×C22⋊C4C2311yescharacteristic
270C23×C22⋊C4C2311yescharacteristic
271C23×C22⋊C4C2312yes—
272C23×C22⋊C4C2311yescharacteristic
273C23×C22⋊C4C2312yes—
274C23×C22⋊C4C2312yes—
275C23×C22⋊C4C2312yes—
276C23×C22⋊C4C2312yes—
277C23×C22⋊C4C2312yes—
278C23×C22⋊C4C2311yescharacteristic
279C23×C22⋊C4C2311yescharacteristic
280C23×C22⋊C4C2311yescharacteristic
281C23×C22⋊C4C23148yes—
282C23×C22⋊C4C2312yes—
283C23×C22⋊C4C2312yes—
284C23×C22⋊C4C2312yes—
285C23×C22⋊C4C2312yes—
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⋊C4C2311yescharacteristic
296C23×C22⋊C4C2311yescharacteristic
297C23×C22⋊C4C2312yes—
298C23×C22⋊C4C2312yes—
299C23×C22⋊C4C2312yes—
300C23×C42C2312yes—
301C23×C42C2312yes—
302C23×C42C2311yescharacteristic
303C23×C42C2311yescharacteristic
304C23×C42C2311yescharacteristic
305C23×C42C2312yes—
306C23×C42C2312yes—
307#2710C231512yescomplemented
308#2685C231512yescomplemented
309#2678C231512yescomplemented
310#2673C231512yescomplemented
311#2539C231512yescomplemented
312#2537C231256yescomplemented
313#2521C231512yescomplemented
314#2501C231256yescomplemented
315#2490C231256yescomplemented
316#2445C231512yescomplemented
317#2441C231256yescomplemented
318#2422C231256yescomplemented
319#2418C231512yescomplemented
320#2414C231256yescomplemented
321#2414C231256yescomplemented
322#2408C231256yescomplemented
323C2×#399C23148yes—
324C2×#399C23148yescomplemented
325C2×#399C23148yescomplemented
326C2×#397C23148yescomplemented
327C2×#397C23148yescomplemented
328C2×#396C23148yes—
329#2388C231256yescomplemented
330C2×#395C23124yescomplemented
331C2×#394C23124yes—
332C2×#394C23148yes—
333C2×#394C23124yes—
334C2×#394C23148yescomplemented
335C2×#394C23148yescomplemented
336C2×#394C23148yescomplemented
337C2×#394C23148yescomplemented
338C2×#394C23124yescomplemented
339C2×#394C23148yescomplemented
340C2×#394C23148yescomplemented
341C2×#393C23124yescomplemented
342C2×#392C23124yes—
343C2×#392C23148yes—
344C2×#392C23124yes—
345C2×#392C23148yescomplemented
346C2×#392C23124yescomplemented
347C2×#392C23148yescomplemented
348#2363C231256yescomplemented
349#2354C231256yescomplemented
350D4×C22⋊C4C231256yescomplemented
351#2311C231256yescomplemented
352C2×#391C23148yescomplemented
353C2×#390C23148yes—
354C2×#390C23148yes—
355C2×#390C23124yes—
356C2×#390C23124yes—
357C2×#390C23124yes—
358C2×#390C23124yes—
359C2×#390C23148yescomplemented
360C2×#390C23148yescomplemented
361C2×#390C23148yescomplemented
362C2×#390C23148yescomplemented
363C2×#389C23124yescomplemented
364C2×#389C23124yescomplemented
365C2×#389C23148yescomplemented
366C2×#388C23148yes—
367C2×#388C23148yescomplemented
368C2×#388C23148yescomplemented
369C2×#388C23148yescomplemented
370C2×#388C23148yescomplemented
371C2×#388C23148yescomplemented
372C2×#387C23148yescomplemented
373C2×#386C23148yes—
374C2×#386C23148yes—
375C2×#386C23148yes—
376C2×#386C23148yescomplemented
377C2×#386C23148yescomplemented
378C2×#385C23148yescomplemented
379C2×#384C23124yescomplemented
380C2×#384C23124yescomplemented
381C2×#380C23124yes—
382C2×#380C23124yes—
383C2×#380C23124yescomplemented
384C2×#380C23148yescomplemented
385C2×#380C23124yescomplemented
386C2×#380C23124yescomplemented
387C2×#379C23148yes—
388C2×#379C23148yes—
389C2×C4×C4⋊C4C23124yescomplemented
390C2×C4×C4⋊C4C23148yescomplemented
391C2×C4×C22⋊C4C23124yes—
392C2×C4×C22⋊C4C23148yescomplemented
393C2×C4×C22⋊C4C23124yescomplemented
394C2×C4×C22⋊C4C23124yescomplemented
395C22×#95C2311yescharacteristic
396C22×#95C2311yescharacteristic
397C22×#95C2311yescharacteristic
398C22×#95C2311yescharacteristic
399C22×#95C2312yes—
400C22×#95C2311yescharacteristic
401C22×#95C2311yescharacteristic
402C22×#95C2312yes—
403C22×#95C2312yes—
404C22×#95C2312yes—
405C22×#95C2312yes—
406C22×#95C2312yes—
407C22×#95C2312yes—
408C22×#95C2312yes—
409C26—216no—
410C26—216no—
411C26—48no—
412C26—48no—
413C26—48no—
414C26—48no—
415C26—48no—
416C26C2411yescharacteristic
417C26C2411yescharacteristic
418C26C2412yes—
419C26C2411yescharacteristic
420C26C2412yes—
421C26C2411yescharacteristic
422C26C24124yes—
423C22×#41—2192no—
424C22×#41—2192no—
425C22×#41—496no—
426C22×#41—4256no—
427C22×#41C24164yes—
428C23×Q8—28no—
429C23×Q8—28no—
430C23×Q8—44no—
431C23×Q8C24112yes—
432C23×D4—216no—
433C23×D4—28no—
434C23×D4—28no—
435C23×D4—28no—
436C23×D4—28no—
437C23×D4—28no—
438C23×D4—28no—
439C23×D4—216no—
440C23×D4—216no—
441C23×D4—216no—
442C23×D4—2192no—
443C23×D4—28no—
444C23×D4—28no—
445C23×D4—216no—
446C23×D4—28no—
447C23×D4—216no—
448C23×D4—2192no—
449C23×D4—28no—
450C23×D4—28no—
451C23×D4—28no—
452C23×D4—28no—
453C23×D4—28no—
454C23×D4—28no—
455C23×D4—496no—
456C23×D4—4256no—
457C23×D4—48no—
458C23×D4—48no—
459C23×D4—44no—
460C23×D4—48no—
461C23×D4—44no—
462C23×D4—44no—
463C23×D4—44no—
464C23×D4—44no—
465C23×D4—44no—
466C23×D4—44no—
467C23×D4—44no—
468C23×D4—48no—
469C23×D4—48no—
470C23×D4—48no—
471C23×D4—48no—
472C23×D4—48no—
473C23×D4—48no—
474C23×D4—48no—
475C23×D4—48no—
476C23×D4—48no—
477C23×D4—48no—
478C23×D4—48no—
479C23×D4C2×D4116yes—
480C23×D4C2×D4132yes—
481C23×D4C24112yes—
482C23×D4C24164yes—
483C23×D4C24124yes—
484C23×D4C24112yes—
485C23×D4C24112yes—
486C23×D4C24112yes—
487C23×D4C24112yes—
488C23×D4C24112yes—
489C23×D4C24112yes—
490C23×D4C24112yes—
491C23×D4C24124yes—
492C23×D4C24124yes—
493C23×D4C24124yes—
494C23×D4C24124yes—
495C23×D4C24124yes—
496C23×D4C24124yes—
497C24×C4—28no—
498C24×C4—28no—
499C24×C4—28no—
500C24×C4—28no—
501C24×C4—216no—
502C24×C4—216no—
503C24×C4—28no—
504C24×C4—28no—
505C24×C4—28no—
506C24×C4—28no—
507C24×C4—28no—
508C24×C4—28no—
509C24×C4—216no—
510C24×C4—48no—
511C24×C4—48no—
512C24×C4—48no—
513C24×C4—48no—
514C24×C4—48no—
515C24×C4—48no—
516C24×C4C2×D4116yes—
517C24×C4#41116yes—
518C24×C4C24112yes—
519C24×C4C24112yes—
520C24×C4C2411yescharacteristic
521C24×C4C2412yes—
522C24×C4C2411yescharacteristic
523C24×C4C2412yes—
524C24×C4C2411yescharacteristic
525C24×C4C2412yes—
526C24×C4C2412yes—
527C24×C4C2411yescharacteristic
528C24×C4C2412yes—
529C24×C4C2411yescharacteristic
530C24×C4C2411yescharacteristic
531C24×C4C24112yes—
532C24×C4C2411yescharacteristic
533C24×C4C2412yes—
534C24×C4C24112yes—
535C24×C4C2411yescharacteristic
536C24×C4C2411yescharacteristic
537C24×C4C2411yescharacteristic
538C24×C4C24124yes—
539C24×C4C24124yes—
540C24×C4C24124yes—
541C24×C4C2411yescharacteristic
542#553—22048no—
543#535—22048no—
544C2×#127—2384no—
545C2×#127C241128yes—
546C2×#126—2384no—
547C2×#126C241128yescomplemented
548C2×#125—2192no—
549C2×#125C24164yescomplemented
550C2×#124—2384no—
551C2×#124C241128yes—
552C2×#123—2384no—
553C2×#123—4192no—
554C2×#123—4192no—
555C2×#123—4192no—
556C2×#123C241128yescomplemented
557C2×#123C241128yescomplemented
558C2×#123C241128yescomplemented
559C2×#123C241128yescomplemented
560C2×#121—2192no—
561C2×#121—2192no—
562C2×#121—2384no—
563C2×#121—2192no—
564C2×#121—2192no—
565C2×#121—496no—
566C2×#121—4192no—
567C2×#121C2×D41384yescomplemented
568C2×#121C24164yes—
569C2×#121C24164yes—
570C2×#121C24164yes—
571C2×#121C24164yes—
572C2×#121C24164yes—
573C2×#121C24164yes—
574C2×#121C241128yescomplemented
575C2×#121C241128yescomplemented
576C2×#120—2384no—
577C2×#120—2384no—
578C2×#120—4192no—
579C2×#120C241128yes—
580C2×#120C241128yes—
581C2×#120C241128yes—
582C2×C4×D4—2192no—
583C2×C4×D4—2384no—
584C2×C4×D4—2192no—
585C2×C4×D4—2192no—
586C2×C4×D4—496no—
587C2×C4×D4—496no—
588C2×C4×D4C24164yes—
589C2×C4×D4C24164yes—
590C2×C4×D4C24164yes—
591C2×C4×D4C24164yescomplemented
592C2×C4×D4C241128yescomplemented
593C2×C4×D4C24164yescomplemented
594C2×#117—2192no—
595C2×#117—2192no—
596C2×#117—496no—
597C2×#117C24164yes—
598C2×#117C24164yescomplemented
599C2×#117C24164yescomplemented
600C22×C4⋊C4—28no—
601C22×C4⋊C4—28no—
602C22×C4⋊C4—216no—
603C22×C4⋊C4—2192no—
604C22×C4⋊C4—28no—
605C22×C4⋊C4—216no—
606C22×C4⋊C4—28no—
607C22×C4⋊C4—216no—
608C22×C4⋊C4—28no—
609C22×C4⋊C4—28no—
610C22×C4⋊C4—28no—
611C22×C4⋊C4—216no—
612C22×C4⋊C4—216no—
613C22×C4⋊C4—48no—
614C22×C4⋊C4—44no—
615C22×C4⋊C4—48no—
616C22×C4⋊C4—48no—
617C22×C4⋊C4—48no—
618C22×C4⋊C4C2×D4116yes—
619C22×C4⋊C4C24112yes—
620C22×C4⋊C4C24112yes—
621C22×C4⋊C4C24124yes—
622C22×C4⋊C4C24124yes—
623C22×C4⋊C4C24124yes—
624C22×C4⋊C4C24124yes—
625C22×C4⋊C4C24124yes—
626C22×C4⋊C4C24112yes—
627C22×C4⋊C4C24112yes—
628C22×C4⋊C4C24112yes—
629C22×C4⋊C4C24112yes—
630C22×C4⋊C4C24112yes—
631C22×C4⋊C4C24112yes—
632C22×C4⋊C4C24124yes—
633C22×C4⋊C4C24124yes—
634C22×C4⋊C4C24124yes—
635C22×C4⋊C4C24124yes—
636C22×C4⋊C4C24112yes—
637C22×C4⋊C4C24164yescomplemented
638C22×C22⋊C4—28no—
639C22×C22⋊C4—216no—
640C22×C22⋊C4—216no—
641C22×C22⋊C4—216no—
642C22×C22⋊C4—28no—
643C22×C22⋊C4—216no—
644C22×C22⋊C4—216no—
645C22×C22⋊C4—28no—
646C22×C22⋊C4—216no—
647C22×C22⋊C4—216no—
648C22×C22⋊C4—28no—
649C22×C22⋊C4—28no—
650C22×C22⋊C4—216no—
651C22×C22⋊C4—216no—
652C22×C22⋊C4—216no—
653C22×C22⋊C4—28no—
654C22×C22⋊C4—28no—
655C22×C22⋊C4—28no—
656C22×C22⋊C4—4192no—
657C22×C22⋊C4—48no—
658C22×C22⋊C4—48no—
659C22×C22⋊C4—44no—
660C22×C22⋊C4—48no—
661C22×C22⋊C4—44no—
662C22×C22⋊C4—48no—
663C22×C22⋊C4—48no—
664C22×C22⋊C4—44no—
665C22×C22⋊C4—48no—
666C22×C22⋊C4—44no—
667C22×C22⋊C4—48no—
668C22×C22⋊C4—48no—
669C22×C22⋊C4—48no—
670C22×C22⋊C4—48no—
671C22×C22⋊C4—48no—
672C22×C22⋊C4—48no—
673C22×C22⋊C4—48no—
674C22×C22⋊C4C2×D4132yes—
675C22×C22⋊C4C24112yes—
676C22×C22⋊C4C24112yes—
677C22×C22⋊C4C24112yes—
678C22×C22⋊C4C24112yes—
679C22×C22⋊C4C24112yes—
680C22×C22⋊C4C24112yes—
681C22×C22⋊C4C24124yes—
682C22×C22⋊C4C24124yes—
683C22×C22⋊C4C24112yes—
684C22×C22⋊C4C24112yes—
685C22×C22⋊C4C24124yes—
686C22×C22⋊C4C24124yes—
687C22×C22⋊C4C24124yes—
688C22×C22⋊C4C24124yes—
689C22×C22⋊C4C24124yes—
690C22×C22⋊C4C24124yes—
691C22×C22⋊C4C24124yes—
692C22×C22⋊C4C24124yes—
693C22×C22⋊C4C241128yes—
694C22×C22⋊C4C24112yes—
695C22×C22⋊C4C24112yes—
696C22×C22⋊C4C24124yes—
697C22×C22⋊C4C24124yes—
698C22×C22⋊C4C24112yes—
699C22×C22⋊C4C24124yes—
700C22×C22⋊C4C24124yes—
701C22×C22⋊C4C24124yes—
702C22×C22⋊C4C24124yes—
703C22×C22⋊C4C24112yes—
704C22×C22⋊C4C24124yes—
705C22×C22⋊C4C24124yes—
706C22×C22⋊C4C24124yes—
707C22×C22⋊C4C24124yes—
708C22×C22⋊C4C24124yes—
709C22×C22⋊C4C24124yes—
710C22×C22⋊C4C24124yes—
711C22×C22⋊C4C24124yes—
712C22×C42—216no—
713C22×C42—216no—
714C22×C42—28no—
715C22×C42—28no—
716C22×C42—28no—
717C22×C42—48no—
718C22×C42—48no—
719C22×C42C24124yes—
720C22×C42C24124yes—
721C22×C42C24112yes—
722C22×C42C24112yes—
723C22×C42C24112yes—
724C22×C42C24124yes—
725C22×C42C24124yes—
726#399C241128yes—
727#399C241128yescomplemented
728#399C241128yescomplemented
729#397C241128yescomplemented
730#397C241128yescomplemented
731#396C241128yes—
732#395C24164yescomplemented
733#394C24164yes—
734#394C24164yes—
735#394C241128yes—
736#394C24164yescomplemented
737#394C241128yescomplemented
738#394C241128yescomplemented
739#394C241128yescomplemented
740#394C241128yescomplemented
741#394C241128yescomplemented
742#394C241128yescomplemented
743#393C24164yescomplemented
744#392C24164yes—
745#392C24164yes—
746#392C241128yes—
747#392C24164yescomplemented
748#392C241128yescomplemented
749#392C241128yescomplemented
750#391C241128yescomplemented
751#390C241128yes—
752#390C24164yes—
753#390C24164yes—
754#390C241128yes—
755#390C24164yes—
756#390C24164yes—
757#390C241128yescomplemented
758#390C241128yescomplemented
759#390C241128yescomplemented
760#390C241128yescomplemented
761#389C24164yescomplemented
762#389C24164yescomplemented
763#389C241128yescomplemented
764#388C241128yes—
765#388C241128yescomplemented
766#388C241128yescomplemented
767#388C241128yescomplemented
768#388C241128yescomplemented
769#388C241128yescomplemented
770#387C241128yescomplemented
771#386C241128yes—
772#386C241128yes—
773#386C241128yes—
774#386C241128yescomplemented
775#386C241128yescomplemented
776#385C241128yescomplemented
777#384C24164yescomplemented
778#384C24164yescomplemented
779#380C24164yes—
780#380C24164yes—
781#380C24164yescomplemented
782#380C24164yescomplemented
783#380C24164yescomplemented
784#380C241128yescomplemented
785#379C241128yes—
786#379C241128yes—
787C4×C4⋊C4C24164yescomplemented
788C4×C4⋊C4C241128yescomplemented
789C4×C22⋊C4C24164yes—
790C4×C22⋊C4C24164yescomplemented
791C4×C22⋊C4C241128yescomplemented
792C4×C22⋊C4C24164yescomplemented
793C2×#95C24124yes—
794C2×#95C24112yes—
795C2×#95C24112yes—
796C2×#95C24124yes—
797C2×#95C24112yes—
798C2×#95C24124yes—
799C2×#95C24112yes—
800C2×#95C24112yes—
801C2×#95C24112yes—
802C2×#95C24124yes—
803C2×#95C24124yes—
804C2×#95C24124yes—
805C2×#95C24124yes—
806C2×#95C24124yes—
807C25—24no—
808C25—24no—
809C25—28no—
810C25—24no—
811C25—24no—
812C25—24no—
813C25—28no—
814C25—24no—
815C25—24no—
816C25—28no—
817C25—28no—
818C25—24no—
819C25—28no—
820C25—24no—
821C25—28no—
822C25—24no—
823C25—24no—
824C25—24no—
825C25—24no—
826C25—28no—
827C25—24no—
828C25—24no—
829C25—24no—
830C25—28no—
831C25—24no—
832C25—28no—
833C25—28no—
834C25—24no—
835C25—24no—
836C25—24no—
837C25—24no—
838C25—28no—
839C25—24no—
840C25—24no—
841C25—28no—
842C25—24no—
843C25—24no—
844C25—24no—
845C25—28no—
846C25—296no—
847C25—296no—
848C25—448no—
849C25—448no—
850C25—448no—
851C25—448no—
852C25—448no—
853C25—4128no—
854C25—4128no—
855C25—864no—
856C25—864no—
857C25—864no—
858C25—864no—
859C25—864no—
860C25C22×D4116yes—
861C25C22×D418yes—
862C25C2×#4118yes—
863C25C25112yes—
864C25C2516yes—
865C25C2516yes—
866C25C25112yes—
867C25C2516yes—
868C25C2516yes—
869C25C25132yes—
870C25C2511yescharacteristic
871C2×#41—2256no—
872C2×#41—2256no—
873C2×#41—4128no—
874C2×#41—41536no—
875C22×Q8—248no—
876C22×Q8—248no—
877C22×Q8—424no—
878C22×Q8—464no—
879C22×Q8C25116yes—
880C22×D4—248no—
881C22×D4—248no—
882C22×D4—296no—
883C22×D4—248no—
884C22×D4—248no—
885C22×D4—248no—
886C22×D4—248no—
887C22×D4—296no—
888C22×D4—296no—
889C22×D4—296no—
890C22×D4—2256no—
891C22×D4—2128no—
892C22×D4—248no—
893C22×D4—248no—
894C22×D4—296no—
895C22×D4—248no—
896C22×D4—296no—
897C22×D4—2256no—
898C22×D4—248no—
899C22×D4—248no—
900C22×D4—248no—
901C22×D4—248no—
902C22×D4—248no—
903C22×D4—248no—
904C22×D4—4128no—
905C22×D4—41536no—
906C22×D4—424no—
907C22×D4—448no—
908C22×D4—4128no—
909C22×D4—424no—
910C22×D4—448no—
911C22×D4—448no—
912C22×D4—424no—
913C22×D4—424no—
914C22×D4—424no—
915C22×D4—424no—
916C22×D4—424no—
917C22×D4—424no—
918C22×D4—464no—
919C22×D4—4128no—
920C22×D4—464no—
921C22×D4—464no—
922C22×D4—464no—
923C22×D4—448no—
924C22×D4—448no—
925C22×D4—448no—
926C22×D4—448no—
927C22×D4—448no—
928C22×D4—448no—
929C22×D4—448no—
930C22×D4—448no—
931C22×D4—448no—
932C22×D4—448no—
933C22×D4—448no—
934C22×D4—464no—
935C22×D4—464no—
936C22×D4—464no—
937C22×D4—864no—
938C22×D4—864no—
939C22×D4—864no—
940C22×D4—864no—
941C22×D4—864no—
942C22×D4C22×D4196yes—
943C22×D4C22×D41192yes—
944C22×D4C25116yes—
945C22×D4C25116yes—
946C22×D4C25116yes—
947C22×D4C25116yes—
948C22×D4C25132yes—
949C22×D4C25116yes—
950C22×D4C25116yes—
951C22×D4C25116yes—
952C22×D4C25116yes—
953C22×D4C25132yes—
954C22×D4C25132yes—
955C22×D4C25132yes—
956C22×D4C25132yes—
957C22×D4C25132yes—
958C22×D4C25132yes—
959C23×C4—24no—
960C23×C4—24no—
961C23×C4—24no—
962C23×C4—24no—
963C23×C4—24no—
964C23×C4—24no—
965C23×C4—28no—
966C23×C4—24no—
967C23×C4—28no—
968C23×C4—24no—
969C23×C4—2128no—
970C23×C4—2128no—
971C23×C4—248no—
972C23×C4—248no—
973C23×C4—248no—
974C23×C4—248no—
975C23×C4—24no—
976C23×C4—24no—
977C23×C4—28no—
978C23×C4—24no—
979C23×C4—24no—
980C23×C4—28no—
981C23×C4—28no—
982C23×C4—24no—
983C23×C4—24no—
984C23×C4—24no—
985C23×C4—24no—
986C23×C4—24no—
987C23×C4—28no—
988C23×C4—24no—
989C23×C4—28no—
990C23×C4—28no—
991C23×C4—24no—
992C23×C4—28no—
993C23×C4—24no—
994C23×C4—24no—
995C23×C4—28no—
996C23×C4—28no—
997C23×C4—28no—
998C23×C4—28no—
999C23×C4—28no—
1000C23×C4—24no—
1001C23×C4—28no—
1002C23×C4—24no—
1003C23×C4—24no—
1004C23×C4—24no—
1005C23×C4—24no—
1006C23×C4—28no—
1007C23×C4—28no—
1008C23×C4—296no—
1009C23×C4—296no—
1010C23×C4—248no—
1011C23×C4—248no—
1012C23×C4—248no—
1013C23×C4—248no—
1014C23×C4—248no—
1015C23×C4—248no—
1016C23×C4—296no—
1017C23×C4—448no—
1018C23×C4—448no—
1019C23×C4—448no—
1020C23×C4—448no—
1021C23×C4—448no—
1022C23×C4—448no—
1023C23×C4—464no—
1024C23×C4—464no—
1025C23×C4—864no—
1026C23×C4—864no—
1027C23×C4—864no—
1028C23×C4C22×D418yes—
1029C23×C4C22×D4116yes—
1030C23×C4C22×D4196yes—
1031C23×C4C22×D418yes—
1032C23×C4C2×#4118yes—
1033C23×C4C2×#41196yes—
1034C23×C4C2×#4118yes—
1035C23×C4H(5,𝔽2)18yes—
1036C23×C4H(5,𝔽2)18yes—
1037C23×C4H(5,𝔽2)18yes—
1038C23×C4C2516yes—
1039C23×C4C2516yes—
1040C23×C4C2516yes—
1041C23×C4C25112yes—
1042C23×C4C2516yes—
1043C23×C4C25112yes—
1044C23×C4C2516yes—
1045C23×C4C25112yes—
1046C23×C4C25112yes—
1047C23×C4C2516yes—
1048C23×C4C25112yes—
1049C23×C4C25116yes—
1050C23×C4C25116yes—
1051C23×C4C2516yes—
1052C23×C4C25112yes—
1053C23×C4C25116yes—
1054C23×C4C2516yes—
1055C23×C4C25116yes—
1056C23×C4C2516yes—
1057C23×C4C2516yes—
1058C23×C4C25132yes—
1059C23×C4C25132yes—
1060C23×C4C25132yes—
1061C23×C4C2516yes—
1062#127—2512no—
1063#126—2512no—
1064#125—2256no—
1065#124—2512no—
1066#123—2512no—
1067#123—4256no—
1068#123—4256no—
1069#123—4256no—
1070#121—2256no—
1071#121—2256no—
1072#121—2512no—
1073#121—2256no—
1074#121—2256no—
1075#121—4128no—
1076#121—4256no—
1077#121C22×D41512yescomplemented
1078#120—2512no—
1079#120—2512no—
1080#120—4256no—
1081C4×D4—2256no—
1082C4×D4—2512no—
1083C4×D4—2256no—
1084C4×D4—2256no—
1085C4×D4—4128no—
1086C4×D4—4128no—
1087#117—2256no—
1088#117—2256no—
1089#117—4128no—
1090C2×C4⋊C4—248no—
1091C2×C4⋊C4—248no—
1092C2×C4⋊C4—296no—
1093C2×C4⋊C4—2256no—
1094C2×C4⋊C4—248no—
1095C2×C4⋊C4—296no—
1096C2×C4⋊C4—248no—
1097C2×C4⋊C4—296no—
1098C2×C4⋊C4—248no—
1099C2×C4⋊C4—248no—
1100C2×C4⋊C4—248no—
1101C2×C4⋊C4—296no—
1102C2×C4⋊C4—296no—
1103C2×C4⋊C4—448no—
1104C2×C4⋊C4—424no—
1105C2×C4⋊C4—448no—
1106C2×C4⋊C4—448no—
1107C2×C4⋊C4—448no—
1108C2×C4⋊C4C22×D4196yes—
1109C2×C4⋊C4C25116yes—
1110C2×C4⋊C4C25116yes—
1111C2×C4⋊C4C25132yes—
1112C2×C4⋊C4C25116yes—
1113C2×C4⋊C4C25116yes—
1114C2×C4⋊C4C25116yes—
1115C2×C4⋊C4C25116yes—
1116C2×C4⋊C4C25132yes—
1117C2×C4⋊C4C25116yes—
1118C2×C4⋊C4C25132yes—
1119C2×C4⋊C4C25132yes—
1120C2×C4⋊C4C25132yes—
1121C2×C4⋊C4C25116yes—
1122C2×C4⋊C4C25132yes—
1123C2×C4⋊C4C25132yes—
1124C2×C4⋊C4C25132yes—
1125C2×C4⋊C4C25132yes—
1126C2×C4⋊C4C25116yes—
1127C2×C22⋊C4—248no—
1128C2×C22⋊C4—296no—
1129C2×C22⋊C4—296no—
1130C2×C22⋊C4—296no—
1131C2×C22⋊C4—248no—
1132C2×C22⋊C4—296no—
1133C2×C22⋊C4—296no—
1134C2×C22⋊C4—248no—
1135C2×C22⋊C4—296no—
1136C2×C22⋊C4—296no—
1137C2×C22⋊C4—248no—
1138C2×C22⋊C4—248no—
1139C2×C22⋊C4—296no—
1140C2×C22⋊C4—296no—
1141C2×C22⋊C4—296no—
1142C2×C22⋊C4—248no—
1143C2×C22⋊C4—248no—
1144C2×C22⋊C4—248no—
1145C2×C22⋊C4—4256no—
1146C2×C22⋊C4—448no—
1147C2×C22⋊C4—448no—
1148C2×C22⋊C4—448no—
1149C2×C22⋊C4—424no—
1150C2×C22⋊C4—448no—
1151C2×C22⋊C4—424no—
1152C2×C22⋊C4—448no—
1153C2×C22⋊C4—448no—
1154C2×C22⋊C4—424no—
1155C2×C22⋊C4—424no—
1156C2×C22⋊C4—448no—
1157C2×C22⋊C4—448no—
1158C2×C22⋊C4—448no—
1159C2×C22⋊C4—448no—
1160C2×C22⋊C4—448no—
1161C2×C22⋊C4—448no—
1162C2×C22⋊C4—448no—
1163C2×C22⋊C4C22×D41192yes—
1164C2×C22⋊C4C25116yes—
1165C2×C22⋊C4C25132yes—
1166C2×C22⋊C4C25132yes—
1167C2×C22⋊C4C25132yes—
1168C2×C22⋊C4C25132yes—
1169C2×C22⋊C4C25116yes—
1170C2×C22⋊C4C25116yes—
1171C2×C22⋊C4C25116yes—
1172C2×C22⋊C4C25132yes—
1173C2×C22⋊C4C25116yes—
1174C2×C22⋊C4C25132yes—
1175C2×C22⋊C4C25132yes—
1176C2×C22⋊C4C25132yes—
1177C2×C22⋊C4C25132yes—
1178C2×C22⋊C4C25132yes—
1179C2×C22⋊C4C25116yes—
1180C2×C22⋊C4C25116yes—
1181C2×C22⋊C4C25116yes—
1182C2×C22⋊C4C25132yes—
1183C2×C22⋊C4C25132yes—
1184C2×C22⋊C4C25132yes—
1185C2×C22⋊C4C25132yes—
1186C2×C22⋊C4C25116yes—
1187C2×C22⋊C4C25116yes—
1188C2×C22⋊C4C25132yes—
1189C2×C22⋊C4C25132yes—
1190C2×C22⋊C4C25132yes—
1191C2×C22⋊C4C25132yes—
1192C2×C22⋊C4C25132yes—
1193C2×C22⋊C4C25132yes—
1194C2×C22⋊C4C25132yes—
1195C2×C22⋊C4C25116yes—
1196C2×C22⋊C4C25116yes—
1197C2×C22⋊C4C25132yes—
1198C2×C22⋊C4C25132yes—
1199C2×C22⋊C4C25132yes—
1200C2×C42—296no—
1201C2×C42—296no—
1202C2×C42—248no—
1203C2×C42—248no—
1204C2×C42—248no—
1205C2×C42—448no—
1206C2×C42—448no—
1207C2×C42C25132yes—
1208C2×C42C25132yes—
1209C2×C42C25116yes—
1210C2×C42C25116yes—
1211C2×C42C25116yes—
1212C2×C42C25132yes—
1213C2×C42C25132yes—
1214#95C25116yes—
1215#95C25116yes—
1216#95C25116yes—
1217#95C25116yes—
1218#95C25132yes—
1219#95C25116yes—
1220#95C25116yes—
1221#95C25132yes—
1222#95C25132yes—
1223#95C25132yes—
1224#95C25132yes—
1225#95C25132yes—
1226#95C25132yes—
1227#95C25132yes—
1228C24—212no—
1229C24—212no—
1230C24—224no—
1231C24—212no—
1232C24—212no—
1233C24—212no—
1234C24—224no—
1235C24—212no—
1236C24—212no—
1237C24—224no—
1238C24—224no—
1239C24—212no—
1240C24—224no—
1241C24—212no—
1242C24—224no—
1243C24—212no—
1244C24—212no—
1245C24—212no—
1246C24—232no—
1247C24—232no—
1248C24—264no—
1249C24—232no—
1250C24—264no—
1251C24—232no—
1252C24—232no—
1253C24—264no—
1254C24—232no—
1255C24—212no—
1256C24—224no—
1257C24—212no—
1258C24—212no—
1259C24—212no—
1260C24—224no—
1261C24—212no—
1262C24—224no—
1263C24—224no—
1264C24—212no—
1265C24—212no—
1266C24—212no—
1267C24—212no—
1268C24—224no—
1269C24—212no—
1270C24—212no—
1271C24—224no—
1272C24—212no—
1273C24—212no—
1274C24—212no—
1275C24—224no—
1276C24—264no—
1277C24—264no—
1278C24—432no—
1279C24—432no—
1280C24—432no—
1281C24—432no—
1282C24—432no—
1283C24—4384no—
1284C24—4384no—
1285C24—416no—
1286C24—416no—
1287C24—432no—
1288C24—416no—
1289C24—416no—
1290C24—432no—
1291C24—432no—
1292C24—416no—
1293C24—416no—
1294C24—416no—
1295C24—432no—
1296C24—416no—
1297C24—416no—
1298C24—416no—
1299C24—432no—
1300C24—416no—
1301C24—416no—
1302C24—432no—
1303C24—416no—
1304C24—416no—
1305C24—432no—
1306C24—416no—
1307C24—416no—
1308C24—432no—
1309C24—416no—
1310C24—416no—
1311C24—432no—
1312C24—416no—
1313C24—416no—
1314C24—432no—
1315C24—416no—
1316C24—432no—
1317C24—416no—
1318C24—8192no—
1319C24—8192no—
1320C24—8192no—
1321C24—8192no—
1322C24—8192no—
1323C24—81024no—
1324C24C23×D4148yes—
1325C24C23×D4124yes—
1326C24C23×D414yes—
1327C24C22×#41124yes—
1328C24C22×#4114yes—
1329C24C2×H(5,𝔽2)14yes—
1330C24C2×H(5,𝔽2)14yes—
1331C24C2×H(5,𝔽2)14yes—
1332C24#58514yes—
1333C24#58514yes—
1334C24C2618yes—
1335C24C2614yes—
1336C24C2614yes—
1337C24C2618yes—
1338C24C2614yes—
1339C24C2614yes—
1340C24C2613yes—
1341#41—41024no—
1342C2×Q8—232no—
1343C2×Q8—232no—
1344C2×Q8—416no—
1345C2×Q8—4192no—
1346C2×D4—232no—
1347C2×D4—232no—
1348C2×D4—264no—
1349C2×D4—232no—
1350C2×D4—232no—
1351C2×D4—232no—
1352C2×D4—232no—
1353C2×D4—264no—
1354C2×D4—264no—
1355C2×D4—264no—
1356C2×D4—232no—
1357C2×D4—232no—
1358C2×D4—264no—
1359C2×D4—232no—
1360C2×D4—264no—
1361C2×D4—232no—
1362C2×D4—232no—
1363C2×D4—232no—
1364C2×D4—232no—
1365C2×D4—232no—
1366C2×D4—232no—
1367C2×D4—2384no—
1368C2×D4—41024no—
1369C2×D4—416no—
1370C2×D4—432no—
1371C2×D4—4384no—
1372C2×D4—416no—
1373C2×D4—432no—
1374C2×D4—432no—
1375C2×D4—416no—
1376C2×D4—416no—
1377C2×D4—416no—
1378C2×D4—416no—
1379C2×D4—416no—
1380C2×D4—416no—
1381C2×D4—4192no—
1382C2×D4—4384no—
1383C2×D4—4192no—
1384C2×D4—4192no—
1385C2×D4—4192no—
1386C2×D4—432no—
1387C2×D4—432no—
1388C2×D4—432no—
1389C2×D4—432no—
1390C2×D4—432no—
1391C2×D4—432no—
1392C2×D4—432no—
1393C2×D4—432no—
1394C2×D4—432no—
1395C2×D4—432no—
1396C2×D4—432no—
1397C2×D4—4192no—
1398C2×D4—4192no—
1399C2×D4—4192no—
1400C2×D4—8192no—
1401C2×D4—8192no—
1402C2×D4—8192no—
1403C2×D4—8192no—
1404C2×D4—8192no—
1405C2×D4C23×D4164yes—
1406C2×D4C23×D41128yes—
1407C22×C4—212no—
1408C22×C4—212no—
1409C22×C4—212no—
1410C22×C4—212no—
1411C22×C4—212no—
1412C22×C4—212no—
1413C22×C4—212no—
1414C22×C4—224no—
1415C22×C4—224no—
1416C22×C4—212no—
1417C22×C4—232no—
1418C22×C4—232no—
1419C22×C4—264no—
1420C22×C4—232no—
1421C22×C4—232no—
1422C22×C4—232no—
1423C22×C4—232no—
1424C22×C4—232no—
1425C22×C4—232no—
1426C22×C4—2384no—
1427C22×C4—2384no—
1428C22×C4—212no—
1429C22×C4—224no—
1430C22×C4—212no—
1431C22×C4—224no—
1432C22×C4—212no—
1433C22×C4—212no—
1434C22×C4—224no—
1435C22×C4—212no—
1436C22×C4—212no—
1437C22×C4—212no—
1438C22×C4—212no—
1439C22×C4—224no—
1440C22×C4—224no—
1441C22×C4—212no—
1442C22×C4—212no—
1443C22×C4—224no—
1444C22×C4—212no—
1445C22×C4—224no—
1446C22×C4—224no—
1447C22×C4—212no—
1448C22×C4—224no—
1449C22×C4—212no—
1450C22×C4—224no—
1451C22×C4—224no—
1452C22×C4—224no—
1453C22×C4—212no—
1454C22×C4—224no—
1455C22×C4—224no—
1456C22×C4—212no—
1457C22×C4—212no—
1458C22×C4—212no—
1459C22×C4—212no—
1460C22×C4—224no—
1461C22×C4—264no—
1462C22×C4—264no—
1463C22×C4—232no—
1464C22×C4—232no—
1465C22×C4—232no—
1466C22×C4—232no—
1467C22×C4—232no—
1468C22×C4—232no—
1469C22×C4—264no—
1470C22×C4—432no—
1471C22×C4—432no—
1472C22×C4—432no—
1473C22×C4—432no—
1474C22×C4—432no—
1475C22×C4—432no—
1476C22×C4—416no—
1477C22×C4—416no—
1478C22×C4—416no—
1479C22×C4—416no—
1480C22×C4—432no—
1481C22×C4—432no—
1482C22×C4—432no—
1483C22×C4—416no—
1484C22×C4—432no—
1485C22×C4—416no—
1486C22×C4—432no—
1487C22×C4—4192no—
1488C22×C4—4192no—
1489C22×C4—8192no—
1490C22×C4—8192no—
1491C22×C4—8192no—
1492C22×C4#546164yes—
1493C22×C4C23×D4148yes—
1494C22×C4C23×D4124yes—
1495C22×C4C23×D4164yes—
1496C22×C4C23×D4124yes—
1497C22×C4C22×#41124yes—
1498C22×C4C22×#41164yes—
1499C22×C4C22×#41124yes—
1500C22×C4C2×H(5,𝔽2)124yes—
1501C22×C4C2×H(5,𝔽2)124yes—
1502C22×C4C2×H(5,𝔽2)124yes—
1503C22×C4C2614yes—
1504C22×C4C2618yes—
1505C22×C4C2614yes—
1506C22×C4C2614yes—
1507C22×C4C2618yes—
1508C22×C4C2614yes—
1509C22×C4C2614yes—
1510C22×C4C2614yes—
1511C22×C4C2618yes—
1512C22×C4C2618yes—
1513C22×C4C2618yes—
1514C22×C4C2618yes—
1515C22×C4C2614yes—
1516C22×C4C2614yes—
1517C22×C4C2614yes—
1518C22×C4C2614yes—
1519C22×C4C2614yes—
1520C4⋊C4—232no—
1521C4⋊C4—232no—
1522C4⋊C4—264no—
1523C4⋊C4—232no—
1524C4⋊C4—264no—
1525C4⋊C4—232no—
1526C4⋊C4—264no—
1527C4⋊C4—232no—
1528C4⋊C4—232no—
1529C4⋊C4—232no—
1530C4⋊C4—264no—
1531C4⋊C4—264no—
1532C4⋊C4—432no—
1533C4⋊C4—416no—
1534C4⋊C4—432no—
1535C4⋊C4—432no—
1536C4⋊C4—432no—
1537C4⋊C4C23×D4164yes—
1538C22⋊C4—232no—
1539C22⋊C4—264no—
1540C22⋊C4—264no—
1541C22⋊C4—264no—
1542C22⋊C4—232no—
1543C22⋊C4—264no—
1544C22⋊C4—264no—
1545C22⋊C4—232no—
1546C22⋊C4—264no—
1547C22⋊C4—264no—
1548C22⋊C4—232no—
1549C22⋊C4—232no—
1550C22⋊C4—264no—
1551C22⋊C4—264no—
1552C22⋊C4—264no—
1553C22⋊C4—232no—
1554C22⋊C4—232no—
1555C22⋊C4—232no—
1556C22⋊C4—432no—
1557C22⋊C4—432no—
1558C22⋊C4—432no—
1559C22⋊C4—416no—
1560C22⋊C4—432no—
1561C22⋊C4—416no—
1562C22⋊C4—432no—
1563C22⋊C4—432no—
1564C22⋊C4—416no—
1565C22⋊C4—416no—
1566C22⋊C4—432no—
1567C22⋊C4—432no—
1568C22⋊C4—432no—
1569C22⋊C4—432no—
1570C22⋊C4—432no—
1571C22⋊C4—432no—
1572C22⋊C4—432no—
1573C22⋊C4C23×D41128yes—
1574C42—264no—
1575C42—264no—
1576C42—232no—
1577C42—232no—
1578C42—232no—
1579C42—432no—
1580C42—432no—
1581C23—248no—
1582C23—248no—
1583C23—296no—
1584C23—248no—
1585C23—296no—
1586C23—248no—
1587C23—24no—
1588C23—24no—
1589C23—28no—
1590C23—24no—
1591C23—24no—
1592C23—24no—
1593C23—28no—
1594C23—24no—
1595C23—24no—
1596C23—28no—
1597C23—28no—
1598C23—24no—
1599C23—28no—
1600C23—24no—
1601C23—28no—
1602C23—24no—
1603C23—24no—
1604C23—24no—
1605C23—248no—
1606C23—248no—
1607C23—296no—
1608C23—24no—
1609C23—28no—
1610C23—24no—
1611C23—24no—
1612C23—24no—
1613C23—28no—
1614C23—24no—
1615C23—28no—
1616C23—28no—
1617C23—24no—
1618C23—24no—
1619C23—24no—
1620C23—24no—
1621C23—28no—
1622C23—24no—
1623C23—24no—
1624C23—28no—
1625C23—24no—
1626C23—24no—
1627C23—24no—
1628C23—28no—
1629C23—4128no—
1630C23—4128no—
1631C23—424no—
1632C23—448no—
1633C23—424no—
1634C23—424no—
1635C23—448no—
1636C23—424no—
1637C23—424no—
1638C23—424no—
1639C23—448no—
1640C23—4128no—
1641C23—4256no—
1642C23—4128no—
1643C23—448no—
1644C23—424no—
1645C23—424no—
1646C23—424no—
1647C23—448no—
1648C23—424no—
1649C23—424no—
1650C23—424no—
1651C23—448no—
1652C23—424no—
1653C23—424no—
1654C23—448no—
1655C23—424no—
1656C23—424no—
1657C23—448no—
1658C23—424no—
1659C23—424no—
1660C23—448no—
1661C23—424no—
1662C23—424no—
1663C23—448no—
1664C23—424no—
1665C23—424no—
1666C23—448no—
1667C23—864no—
1668C23—864no—
1669C23—864no—
1670C23—864no—
1671C23—864no—
1672C23—81536no—
1673C23—864no—
1674C23—864no—
1675C23—8128no—
1676C23C2×#546116yes—
1677C23#3485116yes—
1678C23#3494116yes—
1679C23#3498116yes—
1680C23#3506116yes—
1681C23#3542116yes—
1682C23#3546116yes—
1683C23C24×D4116yes—
1684C23C24×D418yes—
1685C23C24×D416yes—
1686C23C23×#4118yes—
1687C23C23×#4116yes—
1688C23C22×H(5,𝔽2)16yes—
1689C23C22×H(5,𝔽2)16yes—
1690C23C22×H(5,𝔽2)16yes—
1691C23C2×#58516yes—
1692C23C2×#58516yes—
1693C23C2711yescharacteristic
1694Q8—464no—
1695D4—2128no—
1696D4—4128no—
1697D4—464no—
1698D4—4128no—
1699D4—464no—
1700D4—464no—
1701D4—464no—
1702D4—464no—
1703D4—464no—
1704D4—464no—
1705D4—864no—
1706D4—864no—
1707D4—864no—
1708D4—864no—
1709D4—864no—
1710C2×C4—296no—
1711C2×C4—248no—
1712C2×C4—24no—
1713C2×C4—24no—
1714C2×C4—24no—
1715C2×C4—24no—
1716C2×C4—24no—
1717C2×C4—24no—
1718C2×C4—24no—
1719C2×C4—28no—
1720C2×C4—28no—
1721C2×C4—24no—
1722C2×C4—248no—
1723C2×C4—248no—
1724C2×C4—248no—
1725C2×C4—2128no—
1726C2×C4—2128no—
1727C2×C4—24no—
1728C2×C4—28no—
1729C2×C4—24no—
1730C2×C4—28no—
1731C2×C4—24no—
1732C2×C4—24no—
1733C2×C4—28no—
1734C2×C4—24no—
1735C2×C4—24no—
1736C2×C4—24no—
1737C2×C4—24no—
1738C2×C4—28no—
1739C2×C4—28no—
1740C2×C4—24no—
1741C2×C4—24no—
1742C2×C4—28no—
1743C2×C4—24no—
1744C2×C4—28no—
1745C2×C4—28no—
1746C2×C4—24no—
1747C2×C4—28no—
1748C2×C4—24no—
1749C2×C4—28no—
1750C2×C4—28no—
1751C2×C4—28no—
1752C2×C4—24no—
1753C2×C4—28no—
1754C2×C4—28no—
1755C2×C4—24no—
1756C2×C4—24no—
1757C2×C4—24no—
1758C2×C4—24no—
1759C2×C4—28no—
1760C2×C4—424no—
1761C2×C4—448no—
1762C2×C4—424no—
1763C2×C4—424no—
1764C2×C4—424no—
1765C2×C4—448no—
1766C2×C4—448no—
1767C2×C4—448no—
1768C2×C4—424no—
1769C2×C4—424no—
1770C2×C4—448no—
1771C2×C4—464no—
1772C2×C4—464no—
1773C2×C4—864no—
1774C2×C4—864no—
1775C2×C4—864no—
1776C2×C4C2×#546196yes—
1777C2×C4C24×D4116yes—
1778C2×C4C24×D418yes—
1779C2×C4C24×D418yes—
1780C2×C4C23×#4118yes—
1781C2×C4C23×#4118yes—
1782C2×C4C22×H(5,𝔽2)18yes—
1783C2×C4C22×H(5,𝔽2)18yes—
1784C2×C4C22×H(5,𝔽2)18yes—
1785C22—28no—
1786C22—28no—
1787C22—216no—
1788C22—28no—
1789C22—28no—
1790C22—216no—
1791C22—28no—
1792C22—216no—
1793C22—28no—
1794C22—48no—
1795C22—44no—
1796C22—44no—
1797C22—44no—
1798C22—48no—
1799C22—44no—
1800C22—44no—
1801C22—48no—
1802C22—44no—
1803C22—44no—
1804C22—44no—
1805C22—48no—
1806C22—496no—
1807C22—4192no—
1808C22—496no—
1809C22—44no—
1810C22—44no—
1811C22—48no—
1812C22—44no—
1813C22—48no—
1814C22—44no—
1815C22—44no—
1816C22—44no—
1817C22—48no—
1818C22—44no—
1819C22—44no—
1820C22—48no—
1821C22—44no—
1822C22—44no—
1823C22—48no—
1824C22—44no—
1825C22—44no—
1826C22—48no—
1827C22—44no—
1828C22—44no—
1829C22—48no—
1830C22—8256no—
1831C22—848no—
1832C22—848no—
1833C22—896no—
1834C22#44899164yesdirect product factor
1835C22C22×#546112yes—
1836C22C2×#3542112yes—
1837C22C2×#3546112yes—
1838C22C2×#3506112yes—
1839C22C2×#3485112yes—
1840C22C2×#3498112yes—
1841C22C2×#3494112yes—
1842C22C25×D411yescharacteristic
1843C22C24×#4111yescharacteristic
1844C22C23×H(5,𝔽2)11yescharacteristic
1845C22C23×H(5,𝔽2)11yescharacteristic
1846C22C23×H(5,𝔽2)11yescharacteristic
1847C22C22×#58511yescharacteristic
1848C22C22×#58511yescharacteristic
1849C4—28no—
1850C4—28no—
1851C4—28no—
1852C4—216no—
1853C4—28no—
1854C4—48no—
1855C4—44no—
1856C4—48no—
1857C4—44no—
1858C4—44no—
1859C4—44no—
1860C4—44no—
1861C4—44no—
1862C4—48no—
1863C4—48no—
1864C4—48no—
1865C4C22×#546116yes—
1866C2—48no—
1867C2—416no—
1868C2—48no—
1869C2—84no—
1870C2—84no—
1871C2—88no—
1872C2C2×#44899124yesdirect product factor
1873C2C23×#54611yescharacteristic
1874C2C22×#350611yescharacteristic
1875C2C22×#348511yescharacteristic
1876C2C22×#349811yescharacteristic
1877C2C22×#349411yescharacteristic
1878C2C22×#354211yescharacteristic
1879C2C22×#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×#553C2semidirect
2. C23×#535C2semidirect
3. C2×#44899C2direct (N × H)
4. C22×#2710C2semidirect
5. C22×#2673C2semidirect
6. C22×#2685C2semidirect
7. C22×#2678C2semidirect
8. C22×#2537C2semidirect
9. C22×#2539C2semidirect
10. C22×#2490C2semidirect
11. C22×#2521C2semidirect
12. C22×#2501C2semidirect
13. C22×#2441C2semidirect
14. C22×#2414C2semidirect
15. C22×#2414C2semidirect
16. C22×#2445C2semidirect
17. C22×#2422C2semidirect
18. C22×#2408C2semidirect
19. C22×#2418C2semidirect
20. C22×#2388C2semidirect
21. C22×#2363C2semidirect
22. C22×#2354C2semidirect
23. C22×D4×C22⋊C4C2semidirect
24. C22×#2311C2semidirect
28. C22×#553C22semidirect
30. C22×#535C22semidirect
32. C23×#126C22semidirect
33. C23×#125C22semidirect
35. C23×#123C22semidirect
36. C23×#123C22semidirect
37. C23×#123C22semidirect
38. C23×#123C22semidirect
45. C23×#121C22semidirect
46. C23×#121C22semidirect
53. C23×C4×D4C22semidirect
54. C23×C4×D4C22semidirect
55. C23×C4×D4C22semidirect
57. C23×#117C22semidirect
58. C23×#117C22semidirect
59. C24×C4⋊C4C22semidirect
61. C2×#2710C22semidirect
62. C2×#2685C22semidirect
63. C2×#2678C22semidirect
64. C2×#2673C22semidirect
65. #44899C22direct (N × H)
66. C2×#2537C22semidirect
67. C2×#2539C22semidirect
68. C2×#2490C22semidirect
69. C2×#2521C22semidirect
70. C2×#2501C22semidirect
71. C2×#2441C22semidirect
72. C2×#2414C22semidirect
73. C2×#2414C22semidirect
74. C2×#2445C22semidirect
75. C2×#2422C22semidirect
76. C2×#2408C22semidirect
77. C2×#2418C22semidirect
79. C22×#399C22semidirect
80. C22×#399C22semidirect
81. C22×#397C22semidirect
82. C22×#397C22semidirect
84. C2×#2388C22semidirect
85. C22×#395C22semidirect
89. C22×#394C22semidirect
90. C22×#394C22semidirect
91. C22×#394C22semidirect
92. C22×#394C22semidirect
93. C22×#394C22semidirect
94. C22×#394C22semidirect
95. C22×#394C22semidirect
96. C22×#393C22semidirect
100. C22×#392C22semidirect
101. C22×#392C22semidirect
102. C22×#392C22semidirect
103. C2×#2363C22semidirect
104. C2×#2354C22semidirect
105. C2×D4×C22⋊C4C22semidirect
106. C2×#2311C22semidirect
107. C22×#391C22semidirect
114. C22×#390C22semidirect
115. C22×#390C22semidirect
116. C22×#390C22semidirect
117. C22×#390C22semidirect
118. C22×#389C22semidirect
119. C22×#389C22semidirect
120. C22×#389C22semidirect
122. C22×#388C22semidirect
123. C22×#388C22semidirect
124. C22×#388C22semidirect
125. C22×#388C22semidirect
126. C22×#388C22semidirect
127. C22×#387C22semidirect
131. C22×#386C22semidirect
132. C22×#386C22semidirect
133. C22×#385C22semidirect
134. C22×#384C22semidirect
135. C22×#384C22semidirect
138. C22×#380C22semidirect
139. C22×#380C22semidirect
140. C22×#380C22semidirect
141. C22×#380C22semidirect
144. C22×C4×C4⋊C4C22semidirect
145. C22×C4×C4⋊C4C22semidirect
147. C22×C4×C22⋊C4C22semidirect
148. C22×C4×C22⋊C4C22semidirect
149. C22×C4×C22⋊C4C22semidirect
183. C2×#553C23semidirect
185. C2×#535C23semidirect
189. C22×#126C23semidirect
191. C22×#125C23semidirect
198. C22×#123C23semidirect
199. C22×#123C23semidirect
200. C22×#123C23semidirect
201. C22×#123C23semidirect
209. C22×#121D4semidirect
216. C22×#121C23semidirect
217. C22×#121C23semidirect
233. C22×C4×D4C23semidirect
234. C22×C4×D4C23semidirect
235. C22×C4×D4C23semidirect
240. C22×#117C23semidirect
241. C22×#117C23semidirect
261. C23×C4⋊C4C23semidirect
307. #2710C23semidirect
308. #2685C23semidirect
309. #2678C23semidirect
310. #2673C23semidirect
311. #2539C23semidirect
312. #2537C23semidirect
313. #2521C23semidirect
314. #2501C23semidirect
315. #2490C23semidirect
316. #2445C23semidirect
317. #2441C23semidirect
318. #2422C23semidirect
319. #2418C23semidirect
320. #2414C23semidirect
321. #2414C23semidirect
322. #2408C23semidirect
324. C2×#399C23semidirect
325. C2×#399C23semidirect
326. C2×#397C23semidirect
327. C2×#397C23semidirect
329. #2388C23semidirect
330. C2×#395C23semidirect
334. C2×#394C23semidirect
335. C2×#394C23semidirect
336. C2×#394C23semidirect
337. C2×#394C23semidirect
338. C2×#394C23semidirect
339. C2×#394C23semidirect
340. C2×#394C23semidirect
341. C2×#393C23semidirect
345. C2×#392C23semidirect
346. C2×#392C23semidirect
347. C2×#392C23semidirect
348. #2363C23semidirect
349. #2354C23semidirect
350. D4×C22⋊C4C23semidirect
351. #2311C23semidirect
352. C2×#391C23semidirect
359. C2×#390C23semidirect
360. C2×#390C23semidirect
361. C2×#390C23semidirect
362. C2×#390C23semidirect
363. C2×#389C23semidirect
364. C2×#389C23semidirect
365. C2×#389C23semidirect
367. C2×#388C23semidirect
368. C2×#388C23semidirect
369. C2×#388C23semidirect
370. C2×#388C23semidirect
371. C2×#388C23semidirect
372. C2×#387C23semidirect
376. C2×#386C23semidirect
377. C2×#386C23semidirect
378. C2×#385C23semidirect
379. C2×#384C23semidirect
380. C2×#384C23semidirect
383. C2×#380C23semidirect
384. C2×#380C23semidirect
385. C2×#380C23semidirect
386. C2×#380C23semidirect
389. C2×C4×C4⋊C4C23semidirect
390. C2×C4×C4⋊C4C23semidirect
392. C2×C4×C22⋊C4C23semidirect
393. C2×C4×C22⋊C4C23semidirect
394. C2×C4×C22⋊C4C23semidirect
547. C2×#126C24semidirect
549. C2×#125C24semidirect
556. C2×#123C24semidirect
557. C2×#123C24semidirect
558. C2×#123C24semidirect
559. C2×#123C24semidirect
567. C2×#121C2×D4semidirect
574. C2×#121C24semidirect
575. C2×#121C24semidirect
591. C2×C4×D4C24semidirect
592. C2×C4×D4C24semidirect
593. C2×C4×D4C24semidirect
598. C2×#117C24semidirect
599. C2×#117C24semidirect
637. C22×C4⋊C4C24semidirect
727. #399C24semidirect
728. #399C24semidirect
729. #397C24semidirect
730. #397C24semidirect
732. #395C24semidirect
736. #394C24semidirect
737. #394C24semidirect
738. #394C24semidirect
739. #394C24semidirect
740. #394C24semidirect
741. #394C24semidirect
742. #394C24semidirect
743. #393C24semidirect
747. #392C24semidirect
748. #392C24semidirect
749. #392C24semidirect
750. #391C24semidirect
757. #390C24semidirect
758. #390C24semidirect
759. #390C24semidirect
760. #390C24semidirect
761. #389C24semidirect
762. #389C24semidirect
763. #389C24semidirect
765. #388C24semidirect
766. #388C24semidirect
767. #388C24semidirect
768. #388C24semidirect
769. #388C24semidirect
770. #387C24semidirect
774. #386C24semidirect
775. #386C24semidirect
776. #385C24semidirect
777. #384C24semidirect
778. #384C24semidirect
781. #380C24semidirect
782. #380C24semidirect
783. #380C24semidirect
784. #380C24semidirect
787. C4×C4⋊C4C24semidirect
788. C4×C4⋊C4C24semidirect
790. C4×C22⋊C4C24semidirect
791. C4×C22⋊C4C24semidirect
792. C4×C22⋊C4C24semidirect
1077. #121C22×D4semidirect
1834. C22#44899direct (N × H)
1872. C2C2×#44899direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#5532
C23×#5352
C2×#448992
C22×#27102
C22×#26732
C22×#26852
C22×#26782
C22×#25372
C22×#25392
C22×#24902
C22×#25212
C22×#25012
C22×#24412
C22×#24142
C22×#24452
C22×#24222
C22×#24082
C22×#24182
C22×#23882
C22×#23632
C22×#23542
C22×D4×C22⋊C42
C22×#23112