Finite Group Databasebeta

← C22×#40638 #72326013

Subgroups — C22×#40638 #72326013

Order 1024.

82973 conjugacy classes of subgroups.

The subgroup lattice has 1482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#40638C2196yesmaximal, direct product factor
2C22×#2706C212yesmaximal, complemented
3C22×#2705C212yesmaximal, complemented
4C22×#2696C212yesmaximal, complemented
5C22×#2693C212yesmaximal, complemented
6C22×#2826C211yesmaximal, characteristic, complemented
7C22×#2824C211yesmaximal, characteristic, complemented
8C22×#2505C212yesmaximal, complemented
9C22×#2480C212yesmaximal, complemented
10C22×#2405C212yesmaximal, complemented
11C22×#2405C212yesmaximal, complemented
12C22×#2463C211yesmaximal, characteristic, complemented
13C22×#2455C211yesmaximal, characteristic, complemented
14C22×#2437C212yesmaximal, complemented
15C22×#2636C212yesmaximal, complemented
16C22×#2630C212yesmaximal, complemented
17C22×#2626C211yesmaximal, characteristic, complemented
18C23×#392C211yesmaximal, characteristic
19C22×D4×C22⋊C4C212yesmaximal, complemented
20C22×#2315C211yesmaximal, characteristic, complemented
21C25×D4C2212yes—
22C25×D4C2211yescharacteristic
23C23×#126C2212yescomplemented
24C23×#123C2212yescomplemented
25C23×#123C2212yescomplemented
26C23×#123C2212yescomplemented
27C23×#123C2212yescomplemented
28C23×C22⋊Q8C2211yescharacteristic
29C23×C22⋊Q8C2212yescomplemented
30C23×C4×D4C2212yescomplemented
31C23×C4×D4C2212yescomplemented
32C24×C22⋊C4C2211yescharacteristic
33C24×C22⋊C4C2212yes—
34C24×C22⋊C4C2212yes—
35C24×C22⋊C4C2211yescharacteristic
36C24×C22⋊C4C2211yescharacteristic
37C2×#2706C22196yescomplemented
38C2×#2705C22196yescomplemented
39C2×#2696C22196yescomplemented
40C2×#2693C22196yescomplemented
41#40638C2211024yesdirect product factor
42C2×#2826C22148yescomplemented
43C2×#2824C22148yescomplemented
44C2×#2505C22196yescomplemented
45C2×#2480C22196yescomplemented
46C2×#2405C22196yescomplemented
47C2×#2405C22196yescomplemented
48C2×#2463C22148yescomplemented
49C2×#2455C22148yescomplemented
50C2×#2437C22196yescomplemented
51C2×#2636C22196yescomplemented
52C2×#2630C22196yescomplemented
53C2×#2626C22148yescomplemented
54C22×#400C2212yescomplemented
55C22×#400C2212yescomplemented
56C22×#400C2212yescomplemented
57C22×#399C2212yescomplemented
58C22×#399C2211yescharacteristic, complemented
59C22×#399C2211yescharacteristic, complemented
60C22×#398C2212yescomplemented
61C22×#397C2212yescomplemented
62C22×#397C2212yescomplemented
63C22×#397C2212yescomplemented
64C22×#396C2212yescomplemented
65C22×#396C2212yescomplemented
66C22×#396C2212yescomplemented
67C22×#396C2212yescomplemented
68C22×#396C2212yescomplemented
69C22×#394C2212yescomplemented
70C22×#394C2212yescomplemented
71C22×#394C2212yescomplemented
72C22×#394C2212yescomplemented
73C22×#394C2212yescomplemented
74C22×#394C2212yescomplemented
75C22×#394C2212yescomplemented
76C22×#394C2212yescomplemented
77C22×#393C2211yescharacteristic, complemented
78C22×#393C2212yescomplemented
79C22×#393C2211yescharacteristic, complemented
80C22×#392C2211yescharacteristic
81C22×#392C2212yes—
82C22×#392C2211yescharacteristic
83C22×#392C2211yescharacteristic
84C22×#392C22148yes—
85C22×#392C2212yes—
86C22×#392C2211yescharacteristic
87C2×D4×C22⋊C4C22196yescomplemented
88C2×#2315C22148yescomplemented
89C22×#390C2212yescomplemented
90C22×#390C2212yescomplemented
91C22×#389C2212yescomplemented
92C22×#388C2212yescomplemented
93C22×#388C2212yescomplemented
94C22×#388C2212yescomplemented
95C22×#387C2212yescomplemented
96C22×#387C2212yescomplemented
97C22×#386C2212yescomplemented
98C22×#386C2212yescomplemented
99C22×#386C2212yescomplemented
100C22×#386C2212yescomplemented
101C22×#386C2212yescomplemented
102C22×#386C2212yescomplemented
103C22×#386C2212yescomplemented
104C22×#386C2212yescomplemented
105C22×#385C2212yes—
106C22×#385C2212yes—
107C22×#385C2212yes—
108C22×#385C2212yes—
109C22×#385C2212yes—
110C22×#385C2212yescomplemented
111C22×#385C2212yescomplemented
112C22×#385C2211yescharacteristic, complemented
113C22×#385C2211yescharacteristic, complemented
114C22×#385C2211yescharacteristic, complemented
115C22×#385C2211yescharacteristic, complemented
116C22×#382C2212yescomplemented
117C22×#380C2212yes—
118C22×#380C2211yescharacteristic
119C22×#380C2212yescomplemented
120C22×#380C2212yescomplemented
121C22×#380C2212yescomplemented
122C22×#379C2212yes—
123C22×#379C2212yes—
124C22×#379C2212yes—
125C22×#379C2212yes—
126C22×C4×C22⋊C4C2212yes—
127C23×#95C2211yescharacteristic
128C27C2312yes—
129C27C2311yescharacteristic
130C24×Q8C2311yescharacteristic
131C24×D4—232no—
132C24×D4—416no—
133C24×D4—48no—
134C24×D4—416no—
135C24×D4—416no—
136C24×D4C2312yes—
137C24×D4C2311yescharacteristic
138C24×D4C2312yes—
139C24×D4C2312yes—
140C24×D4C23148yes—
141C24×D4C2312yes—
142C24×D4C2312yes—
143C24×D4C23124yes—
144C24×D4C2311yescharacteristic
145C25×C4C2312yes—
146C25×C4C2311yescharacteristic
147C25×C4C2311yescharacteristic
148C25×C4C2312yes—
149C25×C4C2312yes—
150C25×C4C2311yescharacteristic
151C25×C4C2311yescharacteristic
152C25×C4C2312yes—
153C22×#126—416no—
154C22×#126C23148yescomplemented
155C22×#123—416no—
156C22×#123—416no—
157C22×#123—416no—
158C22×#123—416no—
159C22×#123C23148yescomplemented
160C22×#123C23148yescomplemented
161C22×#123C23148yescomplemented
162C22×#123C23148yescomplemented
163C22×C22⋊Q8—48no—
164C22×C22⋊Q8—416no—
165C22×C22⋊Q8C23124yes—
166C22×C22⋊Q8C23148yescomplemented
167C22×C4×D4—416no—
168C22×C4×D4—416no—
169C22×C4×D4C23148yescomplemented
170C22×C4×D4C23148yescomplemented
171C23×C4⋊C4C2312yes—
172C23×C4⋊C4C2312yes—
173C23×C4⋊C4C2312yes—
174C23×C4⋊C4C2312yes—
175C23×C4⋊C4C2312yes—
176C23×C4⋊C4C2311yescharacteristic
177C23×C4⋊C4C2312yes—
178C23×C4⋊C4C2312yes—
179C23×C4⋊C4C2312yes—
180C23×C4⋊C4C2312yes—
181C23×C4⋊C4C2312yes—
182C23×C4⋊C4C2312yes—
183C23×C4⋊C4C2312yes—
184C23×C4⋊C4C2312yes—
185C23×C4⋊C4C2312yes—
186C23×C22⋊C4—216no—
187C23×C22⋊C4—416no—
188C23×C22⋊C4—48no—
189C23×C22⋊C4—416no—
190C23×C22⋊C4—48no—
191C23×C22⋊C4C23124yes—
192C23×C22⋊C4C2312yes—
193C23×C22⋊C4C2312yes—
194C23×C22⋊C4C2312yes—
195C23×C22⋊C4C2312yes—
196C23×C22⋊C4C2312yes—
197C23×C22⋊C4C2311yescharacteristic
198C23×C22⋊C4C2311yescharacteristic
199C23×C22⋊C4C2312yes—
200C23×C22⋊C4C2312yes—
201C23×C22⋊C4C2312yes—
202C23×C22⋊C4C2312yes—
203C23×C22⋊C4C23124yes—
204C23×C22⋊C4C23124yes—
205C23×C22⋊C4C23148yes—
206C23×C22⋊C4C23148yes—
207C23×C22⋊C4C2312yes—
208C23×C22⋊C4C2311yescharacteristic
209C23×C22⋊C4C2311yescharacteristic
210C23×C22⋊C4C2312yes—
211C23×C22⋊C4C2311yescharacteristic
212C23×C22⋊C4C2311yescharacteristic
213C23×C22⋊C4C2312yes—
214C23×C22⋊C4C2312yes—
215C23×C22⋊C4C2312yes—
216C23×C22⋊C4C2312yes—
217C23×C22⋊C4C2312yes—
218C23×C22⋊C4C2312yes—
219C23×C22⋊C4C2312yes—
220C23×C22⋊C4C2312yes—
221C23×C22⋊C4C2312yes—
222C23×C22⋊C4C2312yes—
223C23×C22⋊C4C2312yes—
224C23×C22⋊C4C2312yes—
225C23×C22⋊C4C2312yes—
226C23×C22⋊C4C2312yes—
227C23×C22⋊C4C2312yes—
228C23×C22⋊C4C2312yes—
229C23×C42C2312yes—
230C23×C42C2312yes—
231#2826C231256yescomplemented
232#2824C231256yescomplemented
233#2706C231512yescomplemented
234#2705C231512yescomplemented
235#2696C231512yescomplemented
236#2693C231512yescomplemented
237#2636C231512yescomplemented
238#2630C231512yescomplemented
239#2626C231256yescomplemented
240#2505C231512yescomplemented
241#2480C231512yescomplemented
242#2463C231256yescomplemented
243#2455C231256yescomplemented
244#2437C231512yescomplemented
245#2405C231512yescomplemented
246#2405C231512yescomplemented
247C2×#400C23148yescomplemented
248C2×#400C23148yescomplemented
249C2×#400C23148yescomplemented
250C2×#399C23148yescomplemented
251C2×#399C23124yescomplemented
252C2×#399C23124yescomplemented
253C2×#398C23148yescomplemented
254C2×#397C23148yescomplemented
255C2×#397C23148yescomplemented
256C2×#397C23148yescomplemented
257C2×#396C23148yescomplemented
258C2×#396C23148yescomplemented
259C2×#396C23148yescomplemented
260C2×#396C23148yescomplemented
261C2×#396C23148yescomplemented
262C2×#394C23148yescomplemented
263C2×#394C23148yescomplemented
264C2×#394C23148yescomplemented
265C2×#394C23148yescomplemented
266C2×#394C23148yescomplemented
267C2×#394C23148yescomplemented
268C2×#394C23148yescomplemented
269C2×#394C23148yescomplemented
270C2×#393C23148yescomplemented
271C2×#393C23124yescomplemented
272C2×#393C23124yescomplemented
273C2×#392C23148yes—
274C2×#392C23124yes—
275C2×#392C23124yes—
276C2×#392C23124yes—
277C2×#392C23148yes—
278C2×#392C23124yes—
279C2×#392C231256yes—
280D4×C22⋊C4C231512yescomplemented
281#2315C231256yescomplemented
282C2×#390C23148yescomplemented
283C2×#390C23148yescomplemented
284C2×#389C23148yescomplemented
285C2×#388C23148yescomplemented
286C2×#388C23148yescomplemented
287C2×#388C23148yescomplemented
288C2×#387C23148yescomplemented
289C2×#387C23148yescomplemented
290C2×#386C23148yescomplemented
291C2×#386C23148yescomplemented
292C2×#386C23148yescomplemented
293C2×#386C23148yescomplemented
294C2×#386C23148yescomplemented
295C2×#386C23148yescomplemented
296C2×#386C23148yescomplemented
297C2×#386C23148yescomplemented
298C2×#385C23148yes—
299C2×#385C23148yes—
300C2×#385C23148yes—
301C2×#385C23148yes—
302C2×#385C23148yes—
303C2×#385C23124yescomplemented
304C2×#385C23124yescomplemented
305C2×#385C23124yescomplemented
306C2×#385C23124yescomplemented
307C2×#385C23148yescomplemented
308C2×#385C23148yescomplemented
309C2×#382C23148yescomplemented
310C2×#380C23148yes—
311C2×#380C23124yes—
312C2×#380C23148yescomplemented
313C2×#380C23148yescomplemented
314C2×#380C23148yescomplemented
315C2×#379C23148yes—
316C2×#379C23148yes—
317C2×#379C23148yes—
318C2×#379C23148yes—
319C2×C4×C22⋊C4C23148yes—
320C22×#95C23124yes—
321C22×#95C2312yes—
322C22×#95C2311yescharacteristic
323C22×#95C2311yescharacteristic
324C22×#95C2312yes—
325C22×#95C2312yes—
326C22×#95C2312yes—
327C22×#95C2312yes—
328C22×#95C2311yescharacteristic
329C22×#95C2311yescharacteristic
330C22×#95C2312yes—
331C22×#95C2312yes—
332C22×#95C2312yes—
333C22×#95C2312yes—
334C22×#95C2312yes—
335C22×#95C2312yes—
336C22×#95C2312yes—
337C22×#95C2312yes—
338C22×#95C2312yes—
339C22×#95C2312yes—
340C26—28no—
341C26—28no—
342C26—216no—
343C26—216no—
344C26—216no—
345C26—216no—
346C26—48no—
347C26—48no—
348C26—48no—
349C26—48no—
350C26—48no—
351C26#41116yes—
352C26C2412yes—
353C26C2411yescharacteristic
354C26C2411yescharacteristic
355C26C2412yes—
356C26C24124yes—
357C26C2411yescharacteristic
358C26C24112yes—
359C23×Q8—44no—
360C23×Q8—48no—
361C23×Q8C24112yes—
362C23×D4—216no—
363C23×D4—216no—
364C23×D4—216no—
365C23×D4—2384no—
366C23×D4—216no—
367C23×D4—216no—
368C23×D4—216no—
369C23×D4—216no—
370C23×D4—216no—
371C23×D4—216no—
372C23×D4—216no—
373C23×D4—4192no—
374C23×D4—48no—
375C23×D4—48no—
376C23×D4—44no—
377C23×D4—48no—
378C23×D4—48no—
379C23×D4—44no—
380C23×D4—496no—
381C23×D4—48no—
382C23×D4—48no—
383C23×D4—48no—
384C23×D4—4192no—
385C23×D4—4192no—
386C23×D4—4512no—
387C23×D4—4256no—
388C23×D4C24124yes—
389C23×D4C24112yes—
390C23×D4C24124yes—
391C23×D4C24124yes—
392C23×D4C241128yes—
393C23×D4C24124yes—
394C23×D4C24124yes—
395C23×D4C24112yes—
396C23×D4C24164yes—
397C24×C4—216no—
398C24×C4—28no—
399C24×C4—216no—
400C24×C4—28no—
401C24×C4—216no—
402C24×C4—216no—
403C24×C4—48no—
404C24×C4—48no—
405C24×C4—44no—
406C24×C4—44no—
407C24×C4—48no—
408C24×C4—48no—
409C24×C4—48no—
410C24×C4—48no—
411C24×C4—48no—
412C24×C4—48no—
413C24×C4—48no—
414C24×C4—48no—
415C24×C4—48no—
416C24×C4—48no—
417C24×C4C2412yes—
418C24×C4C2412yes—
419C24×C4C2411yescharacteristic
420C24×C4C2411yescharacteristic
421C24×C4C2412yes—
422C24×C4C2411yescharacteristic
423C24×C4C2412yes—
424C24×C4C2411yescharacteristic
425C24×C4C2412yes—
426C24×C4C2412yes—
427C24×C4C2412yes—
428C24×C4C2412yes—
429C24×C4C2412yes—
430C24×C4C24124yes—
431C24×C4C2412yes—
432C24×C4C24112yes—
433C24×C4C24112yes—
434C24×C4C24124yes—
435C24×C4C24124yes—
436C24×C4C24112yes—
437C24×C4C24112yes—
438C24×C4C24124yes—
439C2×#126—4192no—
440C2×#126C241128yescomplemented
441C2×#123—4192no—
442C2×#123—4192no—
443C2×#123—4192no—
444C2×#123—4192no—
445C2×#123C241128yescomplemented
446C2×#123C241128yescomplemented
447C2×#123C241128yescomplemented
448C2×#123C241128yescomplemented
449C2×C22⋊Q8—496no—
450C2×C22⋊Q8—4192no—
451C2×C22⋊Q8C24164yes—
452C2×C22⋊Q8C241128yescomplemented
453C2×C4×D4—4192no—
454C2×C4×D4—4192no—
455C2×C4×D4C241128yescomplemented
456C2×C4×D4C241128yescomplemented
457C22×C4⋊C4—216no—
458C22×C4⋊C4—216no—
459C22×C4⋊C4—216no—
460C22×C4⋊C4—48no—
461C22×C4⋊C4—44no—
462C22×C4⋊C4—48no—
463C22×C4⋊C4—48no—
464C22×C4⋊C4—48no—
465C22×C4⋊C4—48no—
466C22×C4⋊C4—48no—
467C22×C4⋊C4—48no—
468C22×C4⋊C4—48no—
469C22×C4⋊C4—48no—
470C22×C4⋊C4—48no—
471C22×C4⋊C4—48no—
472C22×C4⋊C4C24124yes—
473C22×C4⋊C4C24124yes—
474C22×C4⋊C4C24124yes—
475C22×C4⋊C4C24124yes—
476C22×C4⋊C4C24124yes—
477C22×C4⋊C4C24124yes—
478C22×C4⋊C4C24124yes—
479C22×C4⋊C4C24124yes—
480C22×C4⋊C4C24124yes—
481C22×C4⋊C4C24124yes—
482C22×C4⋊C4C24124yes—
483C22×C4⋊C4C24112yes—
484C22×C4⋊C4C24124yes—
485C22×C4⋊C4C24124yes—
486C22×C4⋊C4C24124yes—
487C22×C22⋊C4—28no—
488C22×C22⋊C4—28no—
489C22×C22⋊C4—216no—
490C22×C22⋊C4—2192no—
491C22×C22⋊C4—216no—
492C22×C22⋊C4—216no—
493C22×C22⋊C4—216no—
494C22×C22⋊C4—216no—
495C22×C22⋊C4—216no—
496C22×C22⋊C4—216no—
497C22×C22⋊C4—216no—
498C22×C22⋊C4—216no—
499C22×C22⋊C4—4192no—
500C22×C22⋊C4—496no—
501C22×C22⋊C4—4192no—
502C22×C22⋊C4—48no—
503C22×C22⋊C4—48no—
504C22×C22⋊C4—48no—
505C22×C22⋊C4—48no—
506C22×C22⋊C4—48no—
507C22×C22⋊C4—44no—
508C22×C22⋊C4—44no—
509C22×C22⋊C4—44no—
510C22×C22⋊C4—44no—
511C22×C22⋊C4—496no—
512C22×C22⋊C4—48no—
513C22×C22⋊C4—48no—
514C22×C22⋊C4—48no—
515C22×C22⋊C4—48no—
516C22×C22⋊C4—48no—
517C22×C22⋊C4—48no—
518C22×C22⋊C4—48no—
519C22×C22⋊C4—48no—
520C22×C22⋊C4—48no—
521C22×C22⋊C4—48no—
522C22×C22⋊C4—48no—
523C22×C22⋊C4—48no—
524C22×C22⋊C4—48no—
525C22×C22⋊C4C24164yes—
526C22×C22⋊C4C24124yes—
527C22×C22⋊C4C24124yes—
528C22×C22⋊C4C24112yes—
529C22×C22⋊C4C24112yes—
530C22×C22⋊C4C24124yes—
531C22×C22⋊C4C24124yes—
532C22×C22⋊C4C24124yes—
533C22×C22⋊C4C24124yes—
534C22×C22⋊C4C24124yes—
535C22×C22⋊C4C24124yes—
536C22×C22⋊C4C24124yes—
537C22×C22⋊C4C24164yes—
538C22×C22⋊C4C24164yes—
539C22×C22⋊C4C241128yes—
540C22×C22⋊C4C24124yes—
541C22×C22⋊C4C24112yes—
542C22×C22⋊C4C24112yes—
543C22×C22⋊C4C24112yes—
544C22×C22⋊C4C24112yes—
545C22×C22⋊C4C24124yes—
546C22×C22⋊C4C241128yes—
547C22×C22⋊C4C24124yes—
548C22×C22⋊C4C24124yes—
549C22×C22⋊C4C24124yes—
550C22×C22⋊C4C24124yes—
551C22×C22⋊C4C24124yes—
552C22×C22⋊C4C24124yes—
553C22×C22⋊C4C24124yes—
554C22×C22⋊C4C24124yes—
555C22×C22⋊C4C24124yes—
556C22×C22⋊C4C24124yes—
557C22×C22⋊C4C24124yes—
558C22×C22⋊C4C24124yes—
559C22×C22⋊C4C24124yes—
560C22×C22⋊C4C24124yes—
561C22×C22⋊C4C24124yes—
562C22×C22⋊C4C24124yes—
563C22×C42—216no—
564C22×C42—48no—
565C22×C42C24124yes—
566C22×C42C24124yes—
567#400C241128yescomplemented
568#400C241128yescomplemented
569#400C241128yescomplemented
570#399C24164yescomplemented
571#399C24164yescomplemented
572#399C241128yescomplemented
573#398C241128yescomplemented
574#397C241128yescomplemented
575#397C241128yescomplemented
576#397C241128yescomplemented
577#396C241128yescomplemented
578#396C241128yescomplemented
579#396C241128yescomplemented
580#396C241128yescomplemented
581#396C241128yescomplemented
582#394C241128yescomplemented
583#394C241128yescomplemented
584#394C241128yescomplemented
585#394C241128yescomplemented
586#394C241128yescomplemented
587#394C241128yescomplemented
588#394C241128yescomplemented
589#394C241128yescomplemented
590#393C24164yescomplemented
591#393C241128yescomplemented
592#393C24164yescomplemented
593#392C24164yes—
594#392C241128yes—
595#392C24164yes—
596#392C241128yes—
597#392C24164yes—
598#392C24164yes—
599#390C241128yescomplemented
600#390C241128yescomplemented
601#389C241128yescomplemented
602#388C241128yescomplemented
603#388C241128yescomplemented
604#388C241128yescomplemented
605#387C241128yescomplemented
606#387C241128yescomplemented
607#386C241128yescomplemented
608#386C241128yescomplemented
609#386C241128yescomplemented
610#386C241128yescomplemented
611#386C241128yescomplemented
612#386C241128yescomplemented
613#386C241128yescomplemented
614#386C241128yescomplemented
615#385C241128yes—
616#385C241128yes—
617#385C241128yes—
618#385C241128yes—
619#385C241128yes—
620#385C24164yescomplemented
621#385C24164yescomplemented
622#385C24164yescomplemented
623#385C24164yescomplemented
624#385C241128yescomplemented
625#385C241128yescomplemented
626#382C241128yescomplemented
627#380C241128yes—
628#380C24164yes—
629#380C241128yescomplemented
630#380C241128yescomplemented
631#380C241128yescomplemented
632#379C241128yes—
633#379C241128yes—
634#379C241128yes—
635#379C241128yes—
636C4×C22⋊C4C241128yes—
637C2×#95C24124yes—
638C2×#95C24112yes—
639C2×#95C24164yes—
640C2×#95C24112yes—
641C2×#95C24124yes—
642C2×#95C24124yes—
643C2×#95C24124yes—
644C2×#95C24112yes—
645C2×#95C24112yes—
646C2×#95C24124yes—
647C2×#95C24124yes—
648C2×#95C24124yes—
649C2×#95C24124yes—
650C2×#95C24124yes—
651C2×#95C24124yes—
652C2×#95C24124yes—
653C2×#95C24124yes—
654C2×#95C24124yes—
655C2×#95C24124yes—
656C2×#95C24124yes—
657C25—28no—
658C25—28no—
659C25—28no—
660C25—28no—
661C25—24no—
662C25—24no—
663C25—28no—
664C25—28no—
665C25—28no—
666C25—28no—
667C25—28no—
668C25—28no—
669C25—28no—
670C25—24no—
671C25—24no—
672C25—28no—
673C25—2128no—
674C25—248no—
675C25—248no—
676C25—28no—
677C25—28no—
678C25—28no—
679C25—28no—
680C25—28no—
681C25—296no—
682C25—28no—
683C25—28no—
684C25—296no—
685C25—296no—
686C25—296no—
687C25—448no—
688C25—4128no—
689C25—448no—
690C25—448no—
691C25—448no—
692C25—448no—
693C25—4128no—
694C25—4128no—
695C25—4128no—
696C25—4128no—
697C25—864no—
698C25—832no—
699C25—864no—
700C25—864no—
701C25—832no—
702C25—864no—
703C25C2×#4118yes—
704C25C2×#4118yes—
705C25C2×#4118yes—
706C25C2×#41196yes—
707C25H(5,𝔽2)116yes—
708C25H(5,𝔽2)18yes—
709C252−1+418yes—
710C25C25112yes—
711C25C2516yes—
712C25C2516yes—
713C25C25112yes—
714C25C25132yes—
715C25C2516yes—
716C25C25116yes—
717C25C2511yescharacteristic
718C22×Q8—424no—
719C22×Q8—448no—
720C22×Q8—832no—
721C22×Q8C25116yes—
722C22×D4—2256no—
723C22×D4—296no—
724C22×D4—296no—
725C22×D4—296no—
726C22×D4—2512no—
727C22×D4—296no—
728C22×D4—296no—
729C22×D4—296no—
730C22×D4—296no—
731C22×D4—296no—
732C22×D4—296no—
733C22×D4—296no—
734C22×D4—4256no—
735C22×D4—448no—
736C22×D4—448no—
737C22×D4—424no—
738C22×D4—448no—
739C22×D4—448no—
740C22×D4—424no—
741C22×D4—4128no—
742C22×D4—448no—
743C22×D4—448no—
744C22×D4—448no—
745C22×D4—4128no—
746C22×D4—4256no—
747C22×D4—4256no—
748C22×D4—43072no—
749C22×D4—4128no—
750C22×D4—464no—
751C22×D4—4128no—
752C22×D4—4128no—
753C22×D4—41536no—
754C22×D4—464no—
755C22×D4C25132yes—
756C22×D4C25116yes—
757C22×D4C25132yes—
758C22×D4C25132yes—
759C22×D4C25132yes—
760C22×D4C25132yes—
761C22×D4C25116yes—
762C23×C4—28no—
763C23×C4—28no—
764C23×C4—28no—
765C23×C4—28no—
766C23×C4—296no—
767C23×C4—28no—
768C23×C4—28no—
769C23×C4—28no—
770C23×C4—28no—
771C23×C4—28no—
772C23×C4—28no—
773C23×C4—28no—
774C23×C4—28no—
775C23×C4—28no—
776C23×C4—28no—
777C23×C4—28no—
778C23×C4—28no—
779C23×C4—28no—
780C23×C4—28no—
781C23×C4—28no—
782C23×C4—28no—
783C23×C4—28no—
784C23×C4—28no—
785C23×C4—28no—
786C23×C4—28no—
787C23×C4—24no—
788C23×C4—24no—
789C23×C4—248no—
790C23×C4—28no—
791C23×C4—24no—
792C23×C4—24no—
793C23×C4—28no—
794C23×C4—28no—
795C23×C4—28no—
796C23×C4—28no—
797C23×C4—28no—
798C23×C4—28no—
799C23×C4—28no—
800C23×C4—28no—
801C23×C4—296no—
802C23×C4—248no—
803C23×C4—296no—
804C23×C4—296no—
805C23×C4—448no—
806C23×C4—448no—
807C23×C4—424no—
808C23×C4—424no—
809C23×C4—448no—
810C23×C4—448no—
811C23×C4—448no—
812C23×C4—448no—
813C23×C4—448no—
814C23×C4—448no—
815C23×C4—448no—
816C23×C4—448no—
817C23×C4—448no—
818C23×C4—448no—
819C23×C4—4128no—
820C23×C4—464no—
821C23×C4—864no—
822C23×C4—864no—
823C23×C4—832no—
824C23×C4—832no—
825C23×C4—832no—
826C23×C4—864no—
827C23×C4H(5,𝔽2)116yes—
828C23×C4C25112yes—
829C23×C4C25112yes—
830C23×C4C2516yes—
831C23×C4C25112yes—
832C23×C4C25112yes—
833C23×C4C25112yes—
834C23×C4C2516yes—
835C23×C4C25112yes—
836C23×C4C25112yes—
837C23×C4C25112yes—
838C23×C4C2516yes—
839C23×C4C2516yes—
840C23×C4C25112yes—
841C23×C4C25132yes—
842C23×C4C25112yes—
843C23×C4C25116yes—
844C23×C4C25132yes—
845C23×C4C25132yes—
846C23×C4C25116yes—
847C23×C4C25116yes—
848C23×C4C25116yes—
849C23×C4C25132yes—
850#126—4256no—
851#123—4256no—
852#123—4256no—
853#123—4256no—
854#123—4256no—
855C22⋊Q8—4128no—
856C22⋊Q8—4256no—
857C4×D4—4256no—
858C4×D4—4256no—
859C2×C4⋊C4—296no—
860C2×C4⋊C4—296no—
861C2×C4⋊C4—296no—
862C2×C4⋊C4—448no—
863C2×C4⋊C4—424no—
864C2×C4⋊C4—448no—
865C2×C4⋊C4—448no—
866C2×C4⋊C4—448no—
867C2×C4⋊C4—448no—
868C2×C4⋊C4—448no—
869C2×C4⋊C4—448no—
870C2×C4⋊C4—448no—
871C2×C4⋊C4—448no—
872C2×C4⋊C4—448no—
873C2×C4⋊C4—448no—
874C2×C4⋊C4C25132yes—
875C2×C4⋊C4C25132yes—
876C2×C4⋊C4C25132yes—
877C2×C4⋊C4C25132yes—
878C2×C4⋊C4C25132yes—
879C2×C4⋊C4C25116yes—
880C2×C4⋊C4C25132yes—
881C2×C4⋊C4C25132yes—
882C2×C4⋊C4C25132yes—
883C2×C4⋊C4C25132yes—
884C2×C4⋊C4C25132yes—
885C2×C4⋊C4C25132yes—
886C2×C4⋊C4C25132yes—
887C2×C4⋊C4C25132yes—
888C2×C4⋊C4C25132yes—
889C2×C22⋊C4—248no—
890C2×C22⋊C4—248no—
891C2×C22⋊C4—296no—
892C2×C22⋊C4—2256no—
893C2×C22⋊C4—296no—
894C2×C22⋊C4—296no—
895C2×C22⋊C4—296no—
896C2×C22⋊C4—296no—
897C2×C22⋊C4—296no—
898C2×C22⋊C4—296no—
899C2×C22⋊C4—296no—
900C2×C22⋊C4—296no—
901C2×C22⋊C4—4256no—
902C2×C22⋊C4—4128no—
903C2×C22⋊C4—4256no—
904C2×C22⋊C4—448no—
905C2×C22⋊C4—448no—
906C2×C22⋊C4—448no—
907C2×C22⋊C4—448no—
908C2×C22⋊C4—448no—
909C2×C22⋊C4—424no—
910C2×C22⋊C4—424no—
911C2×C22⋊C4—424no—
912C2×C22⋊C4—424no—
913C2×C22⋊C4—4128no—
914C2×C22⋊C4—448no—
915C2×C22⋊C4—448no—
916C2×C22⋊C4—448no—
917C2×C22⋊C4—448no—
918C2×C22⋊C4—448no—
919C2×C22⋊C4—448no—
920C2×C22⋊C4—448no—
921C2×C22⋊C4—448no—
922C2×C22⋊C4—448no—
923C2×C22⋊C4—448no—
924C2×C22⋊C4—448no—
925C2×C22⋊C4—448no—
926C2×C22⋊C4—448no—
927C2×C22⋊C4C25132yes—
928C2×C22⋊C4C25132yes—
929C2×C22⋊C4C25132yes—
930C2×C22⋊C4C25132yes—
931C2×C22⋊C4C25132yes—
932C2×C22⋊C4C25116yes—
933C2×C22⋊C4C25116yes—
934C2×C22⋊C4C25132yes—
935C2×C22⋊C4C25132yes—
936C2×C22⋊C4C25132yes—
937C2×C22⋊C4C25132yes—
938C2×C22⋊C4C25132yes—
939C2×C22⋊C4C25116yes—
940C2×C22⋊C4C25116yes—
941C2×C22⋊C4C25132yes—
942C2×C22⋊C4C25116yes—
943C2×C22⋊C4C25116yes—
944C2×C22⋊C4C25132yes—
945C2×C22⋊C4C25132yes—
946C2×C22⋊C4C25132yes—
947C2×C22⋊C4C25132yes—
948C2×C22⋊C4C25132yes—
949C2×C22⋊C4C25132yes—
950C2×C22⋊C4C25132yes—
951C2×C22⋊C4C25132yes—
952C2×C22⋊C4C25132yes—
953C2×C22⋊C4C25132yes—
954C2×C22⋊C4C25132yes—
955C2×C22⋊C4C25132yes—
956C2×C22⋊C4C25132yes—
957C2×C22⋊C4C25132yes—
958C2×C22⋊C4C25132yes—
959C2×C22⋊C4C25132yes—
960C2×C42—296no—
961C2×C42—448no—
962C2×C42C25132yes—
963C2×C42C25132yes—
964#95C25132yes—
965#95C25116yes—
966#95C25116yes—
967#95C25132yes—
968#95C25132yes—
969#95C25132yes—
970#95C25132yes—
971#95C25116yes—
972#95C25116yes—
973#95C25132yes—
974#95C25132yes—
975#95C25132yes—
976#95C25132yes—
977#95C25132yes—
978#95C25132yes—
979#95C25132yes—
980#95C25132yes—
981#95C25132yes—
982#95C25132yes—
983C24—224no—
984C24—224no—
985C24—264no—
986C24—232no—
987C24—264no—
988C24—232no—
989C24—224no—
990C24—224no—
991C24—212no—
992C24—212no—
993C24—224no—
994C24—224no—
995C24—224no—
996C24—224no—
997C24—224no—
998C24—224no—
999C24—224no—
1000C24—224no—
1001C24—212no—
1002C24—212no—
1003C24—232no—
1004C24—232no—
1005C24—264no—
1006C24—264no—
1007C24—264no—
1008C24—264no—
1009C24—264no—
1010C24—232no—
1011C24—232no—
1012C24—2384no—
1013C24—224no—
1014C24—224no—
1015C24—224no—
1016C24—224no—
1017C24—224no—
1018C24—264no—
1019C24—224no—
1020C24—224no—
1021C24—264no—
1022C24—264no—
1023C24—264no—
1024C24—432no—
1025C24—4384no—
1026C24—432no—
1027C24—432no—
1028C24—432no—
1029C24—432no—
1030C24—4384no—
1031C24—4384no—
1032C24—4384no—
1033C24—432no—
1034C24—432no—
1035C24—416no—
1036C24—416no—
1037C24—432no—
1038C24—432no—
1039C24—432no—
1040C24—432no—
1041C24—416no—
1042C24—416no—
1043C24—4384no—
1044C24—432no—
1045C24—432no—
1046C24—432no—
1047C24—432no—
1048C24—432no—
1049C24—432no—
1050C24—432no—
1051C24—8192no—
1052C24—8192no—
1053C24—896no—
1054C24—8192no—
1055C24—8192no—
1056C24—8512no—
1057C24—896no—
1058C24—81024no—
1059C24#539164yes—
1060C24C22×#41124yes—
1061C24C22×#41124yes—
1062C24C22×#41124yes—
1063C24C22×#41164yes—
1064C24C22×#4114yes—
1065C24C2×H(5,𝔽2)148yes—
1066C24C2×H(5,𝔽2)124yes—
1067C24C2×H(5,𝔽2)14yes—
1068C24C2×H(5,𝔽2)18yes—
1069C24C2×H(5,𝔽2)18yes—
1070C24C2×2−1+4124yes—
1071C24C2×2−1+414yes—
1072C24C2618yes—
1073C24C2614yes—
1074C24C2614yes—
1075C24C2618yes—
1076C24C2614yes—
1077C24C2613yes—
1078C2×Q8—416no—
1079C2×Q8—432no—
1080C2×Q8—896no—
1081C2×D4—2768no—
1082C2×D4—264no—
1083C2×D4—264no—
1084C2×D4—264no—
1085C2×D4—264no—
1086C2×D4—264no—
1087C2×D4—264no—
1088C2×D4—264no—
1089C2×D4—264no—
1090C2×D4—264no—
1091C2×D4—264no—
1092C2×D4—432no—
1093C2×D4—432no—
1094C2×D4—416no—
1095C2×D4—432no—
1096C2×D4—432no—
1097C2×D4—416no—
1098C2×D4—432no—
1099C2×D4—432no—
1100C2×D4—432no—
1101C2×D4—4384no—
1102C2×D4—42048no—
1103C2×D4—4384no—
1104C2×D4—4192no—
1105C2×D4—4384no—
1106C2×D4—4384no—
1107C2×D4—41024no—
1108C2×D4—4192no—
1109C22×C4—224no—
1110C22×C4—224no—
1111C22×C4—264no—
1112C22×C4—224no—
1113C22×C4—224no—
1114C22×C4—264no—
1115C22×C4—224no—
1116C22×C4—224no—
1117C22×C4—224no—
1118C22×C4—224no—
1119C22×C4—224no—
1120C22×C4—224no—
1121C22×C4—224no—
1122C22×C4—224no—
1123C22×C4—224no—
1124C22×C4—224no—
1125C22×C4—224no—
1126C22×C4—224no—
1127C22×C4—224no—
1128C22×C4—224no—
1129C22×C4—224no—
1130C22×C4—224no—
1131C22×C4—224no—
1132C22×C4—224no—
1133C22×C4—224no—
1134C22×C4—224no—
1135C22×C4—224no—
1136C22×C4—212no—
1137C22×C4—224no—
1138C22×C4—212no—
1139C22×C4—232no—
1140C22×C4—224no—
1141C22×C4—212no—
1142C22×C4—212no—
1143C22×C4—224no—
1144C22×C4—224no—
1145C22×C4—224no—
1146C22×C4—224no—
1147C22×C4—224no—
1148C22×C4—224no—
1149C22×C4—264no—
1150C22×C4—232no—
1151C22×C4—264no—
1152C22×C4—264no—
1153C22×C4—432no—
1154C22×C4—432no—
1155C22×C4—416no—
1156C22×C4—416no—
1157C22×C4—432no—
1158C22×C4—432no—
1159C22×C4—432no—
1160C22×C4—432no—
1161C22×C4—432no—
1162C22×C4—432no—
1163C22×C4—432no—
1164C22×C4—432no—
1165C22×C4—432no—
1166C22×C4—432no—
1167C22×C4—4384no—
1168C22×C4—4192no—
1169C22×C4—432no—
1170C22×C4—432no—
1171C22×C4—432no—
1172C22×C4—416no—
1173C22×C4—416no—
1174C22×C4—432no—
1175C22×C4—432no—
1176C22×C4—432no—
1177C22×C4—432no—
1178C22×C4—416no—
1179C22×C4—432no—
1180C22×C4—416no—
1181C22×C4—432no—
1182C22×C4—896no—
1183C22×C4—8192no—
1184C22×C4—8192no—
1185C22×C4—896no—
1186C22×C4—8192no—
1187C22×C4—896no—
1188C22×C4C2×H(5,𝔽2)148yes—
1189C22×C4C2618yes—
1190C22×C4C2614yes—
1191C22×C4C2614yes—
1192C22×C4C2618yes—
1193C22×C4C2618yes—
1194C22×C4C2618yes—
1195C22×C4C2618yes—
1196C22×C4C2618yes—
1197C22×C4C2618yes—
1198C22×C4C2614yes—
1199C22×C4C2618yes—
1200C22×C4C2618yes—
1201C22×C4C2614yes—
1202C22×C4C2618yes—
1203C4⋊C4—264no—
1204C4⋊C4—264no—
1205C4⋊C4—264no—
1206C4⋊C4—432no—
1207C4⋊C4—416no—
1208C4⋊C4—432no—
1209C4⋊C4—432no—
1210C4⋊C4—432no—
1211C4⋊C4—432no—
1212C4⋊C4—432no—
1213C4⋊C4—432no—
1214C4⋊C4—432no—
1215C4⋊C4—432no—
1216C4⋊C4—432no—
1217C4⋊C4—432no—
1218C22⋊C4—232no—
1219C22⋊C4—232no—
1220C22⋊C4—264no—
1221C22⋊C4—264no—
1222C22⋊C4—264no—
1223C22⋊C4—264no—
1224C22⋊C4—264no—
1225C22⋊C4—264no—
1226C22⋊C4—264no—
1227C22⋊C4—264no—
1228C22⋊C4—264no—
1229C22⋊C4—432no—
1230C22⋊C4—432no—
1231C22⋊C4—432no—
1232C22⋊C4—432no—
1233C22⋊C4—432no—
1234C22⋊C4—416no—
1235C22⋊C4—416no—
1236C22⋊C4—416no—
1237C22⋊C4—416no—
1238C22⋊C4—432no—
1239C22⋊C4—432no—
1240C22⋊C4—432no—
1241C22⋊C4—432no—
1242C22⋊C4—432no—
1243C22⋊C4—432no—
1244C22⋊C4—432no—
1245C22⋊C4—432no—
1246C22⋊C4—432no—
1247C22⋊C4—432no—
1248C22⋊C4—432no—
1249C22⋊C4—432no—
1250C22⋊C4—432no—
1251C42—264no—
1252C42—432no—
1253C23—296no—
1254C23—248no—
1255C23—296no—
1256C23—28no—
1257C23—28no—
1258C23—2256no—
1259C23—248no—
1260C23—296no—
1261C23—296no—
1262C23—296no—
1263C23—296no—
1264C23—28no—
1265C23—28no—
1266C23—24no—
1267C23—24no—
1268C23—28no—
1269C23—28no—
1270C23—28no—
1271C23—28no—
1272C23—28no—
1273C23—28no—
1274C23—28no—
1275C23—28no—
1276C23—24no—
1277C23—24no—
1278C23—248no—
1279C23—248no—
1280C23—296no—
1281C23—2128no—
1282C23—28no—
1283C23—28no—
1284C23—28no—
1285C23—28no—
1286C23—28no—
1287C23—28no—
1288C23—28no—
1289C23—4128no—
1290C23—4128no—
1291C23—4128no—
1292C23—4128no—
1293C23—448no—
1294C23—448no—
1295C23—448no—
1296C23—448no—
1297C23—424no—
1298C23—424no—
1299C23—448no—
1300C23—4128no—
1301C23—4128no—
1302C23—4256no—
1303C23—448no—
1304C23—424no—
1305C23—424no—
1306C23—448no—
1307C23—448no—
1308C23—448no—
1309C23—448no—
1310C23—448no—
1311C23—4128no—
1312C23—448no—
1313C23—448no—
1314C23—832no—
1315C23—864no—
1316C23—864no—
1317C23—832no—
1318C23—864no—
1319C23—864no—
1320C23—8768no—
1321C23—81536no—
1322C23—8128no—
1323C23C2×#539196yes—
1324C23C2×#539116yes—
1325C23#3490132yes—
1326C23#3532116yes—
1327C23#3536132yes—
1328C23#3543116yes—
1329C23C23×#4118yes—
1330C23C23×#4118yes—
1331C23C23×#4118yes—
1332C23C23×#4116yes—
1333C23C22×H(5,𝔽2)116yes—
1334C23C22×H(5,𝔽2)18yes—
1335C23C22×H(5,𝔽2)112yes—
1336C23C22×H(5,𝔽2)112yes—
1337C23C22×H(5,𝔽2)16yes—
1338C23C22×2−1+418yes—
1339C23C22×2−1+416yes—
1340C23C2711yescharacteristic
1341Q8—832no—
1342D4—2256no—
1343D4—4128no—
1344D4—464no—
1345D4—4128no—
1346D4—4128no—
1347D4—4128no—
1348D4—464no—
1349C2×C4—296no—
1350C2×C4—28no—
1351C2×C4—28no—
1352C2×C4—28no—
1353C2×C4—28no—
1354C2×C4—28no—
1355C2×C4—28no—
1356C2×C4—28no—
1357C2×C4—28no—
1358C2×C4—28no—
1359C2×C4—28no—
1360C2×C4—28no—
1361C2×C4—28no—
1362C2×C4—28no—
1363C2×C4—28no—
1364C2×C4—28no—
1365C2×C4—28no—
1366C2×C4—28no—
1367C2×C4—28no—
1368C2×C4—28no—
1369C2×C4—28no—
1370C2×C4—28no—
1371C2×C4—28no—
1372C2×C4—28no—
1373C2×C4—28no—
1374C2×C4—28no—
1375C2×C4—28no—
1376C2×C4—24no—
1377C2×C4—24no—
1378C2×C4—24no—
1379C2×C4—24no—
1380C2×C4—28no—
1381C2×C4—28no—
1382C2×C4—28no—
1383C2×C4—28no—
1384C2×C4—28no—
1385C2×C4—28no—
1386C2×C4—28no—
1387C2×C4—4128no—
1388C2×C4—464no—
1389C2×C4—448no—
1390C2×C4—448no—
1391C2×C4—424no—
1392C2×C4—448no—
1393C2×C4—424no—
1394C2×C4—448no—
1395C2×C4—448no—
1396C2×C4—448no—
1397C2×C4—448no—
1398C2×C4—424no—
1399C2×C4—424no—
1400C2×C4—448no—
1401C2×C4—448no—
1402C2×C4—864no—
1403C2×C4—832no—
1404C2×C4—864no—
1405C2×C4—832no—
1406C2×C4—832no—
1407C2×C4—864no—
1408C2×C4C22×H(5,𝔽2)116yes—
1409C22—28no—
1410C22—216no—
1411C22—28no—
1412C22—216no—
1413C22—2192no—
1414C22—216no—
1415C22—216no—
1416C22—28no—
1417C22—28no—
1418C22—216no—
1419C22—216no—
1420C22—216no—
1421C22—44no—
1422C22—44no—
1423C22—48no—
1424C22—48no—
1425C22—48no—
1426C22—48no—
1427C22—44no—
1428C22—44no—
1429C22—48no—
1430C22—48no—
1431C22—4192no—
1432C22—496no—
1433C22—496no—
1434C22—48no—
1435C22—48no—
1436C22—48no—
1437C22—48no—
1438C22—48no—
1439C22—48no—
1440C22—48no—
1441C22—8128no—
1442C22—8256no—
1443C22—896no—
1444C22#40638164yesdirect product factor
1445C22C22×#539116yes—
1446C22C22×#539112yes—
1447C22C2×#3532112yes—
1448C22C2×#3536124yes—
1449C22C2×#3543112yes—
1450C22C2×#3490124yes—
1451C22C24×#4111yescharacteristic
1452C22C23×H(5,𝔽2)12yes—
1453C22C23×H(5,𝔽2)11yescharacteristic
1454C22C23×H(5,𝔽2)12yes—
1455C22C23×2−1+411yescharacteristic
1456C4—216no—
1457C4—44no—
1458C4—44no—
1459C4—48no—
1460C4—48no—
1461C4—48no—
1462C4—48no—
1463C4—44no—
1464C4—48no—
1465C4—44no—
1466C4—48no—
1467C4—48no—
1468C4—48no—
1469C4—48no—
1470C2—216no—
1471C2—416no—
1472C2—48no—
1473C2—48no—
1474C2—88no—
1475C2C2×#40638124yesdirect product factor
1476C2C23×#53911yescharacteristic
1477C2C22×#349012yes—
1478C2C22×#353211yescharacteristic
1479C2C22×#353612yes—
1480C2C22×#354311yescharacteristic
subgroupG/H
center, socleC25C25
commutator, Frattini, cosocleC23C27
prime radicalC23×#392C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C25 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#40638C2direct (N × H)
2. C22×#2706C2semidirect
3. C22×#2705C2semidirect
4. C22×#2696C2semidirect
5. C22×#2693C2semidirect
6. C22×#2826C2semidirect
7. C22×#2824C2semidirect
8. C22×#2505C2semidirect
9. C22×#2480C2semidirect
10. C22×#2405C2semidirect
11. C22×#2405C2semidirect
12. C22×#2463C2semidirect
13. C22×#2455C2semidirect
14. C22×#2437C2semidirect
15. C22×#2636C2semidirect
16. C22×#2630C2semidirect
17. C22×#2626C2semidirect
19. C22×D4×C22⋊C4C2semidirect
20. C22×#2315C2semidirect
23. C23×#126C22semidirect
24. C23×#123C22semidirect
25. C23×#123C22semidirect
26. C23×#123C22semidirect
27. C23×#123C22semidirect
29. C23×C22⋊Q8C22semidirect
30. C23×C4×D4C22semidirect
31. C23×C4×D4C22semidirect
37. C2×#2706C22semidirect
38. C2×#2705C22semidirect
39. C2×#2696C22semidirect
40. C2×#2693C22semidirect
41. #40638C22direct (N × H)
42. C2×#2826C22semidirect
43. C2×#2824C22semidirect
44. C2×#2505C22semidirect
45. C2×#2480C22semidirect
46. C2×#2405C22semidirect
47. C2×#2405C22semidirect
48. C2×#2463C22semidirect
49. C2×#2455C22semidirect
50. C2×#2437C22semidirect
51. C2×#2636C22semidirect
52. C2×#2630C22semidirect
53. C2×#2626C22semidirect
54. C22×#400C22semidirect
55. C22×#400C22semidirect
56. C22×#400C22semidirect
57. C22×#399C22semidirect
58. C22×#399C22semidirect
59. C22×#399C22semidirect
60. C22×#398C22semidirect
61. C22×#397C22semidirect
62. C22×#397C22semidirect
63. C22×#397C22semidirect
64. C22×#396C22semidirect
65. C22×#396C22semidirect
66. C22×#396C22semidirect
67. C22×#396C22semidirect
68. C22×#396C22semidirect
69. C22×#394C22semidirect
70. C22×#394C22semidirect
71. C22×#394C22semidirect
72. C22×#394C22semidirect
73. C22×#394C22semidirect
74. C22×#394C22semidirect
75. C22×#394C22semidirect
76. C22×#394C22semidirect
77. C22×#393C22semidirect
78. C22×#393C22semidirect
79. C22×#393C22semidirect
87. C2×D4×C22⋊C4C22semidirect
88. C2×#2315C22semidirect
89. C22×#390C22semidirect
90. C22×#390C22semidirect
91. C22×#389C22semidirect
92. C22×#388C22semidirect
93. C22×#388C22semidirect
94. C22×#388C22semidirect
95. C22×#387C22semidirect
96. C22×#387C22semidirect
97. C22×#386C22semidirect
98. C22×#386C22semidirect
99. C22×#386C22semidirect
100. C22×#386C22semidirect
101. C22×#386C22semidirect
102. C22×#386C22semidirect
103. C22×#386C22semidirect
104. C22×#386C22semidirect
110. C22×#385C22semidirect
111. C22×#385C22semidirect
112. C22×#385C22semidirect
113. C22×#385C22semidirect
114. C22×#385C22semidirect
115. C22×#385C22semidirect
116. C22×#382C22semidirect
119. C22×#380C22semidirect
120. C22×#380C22semidirect
121. C22×#380C22semidirect
154. C22×#126C23semidirect
159. C22×#123C23semidirect
160. C22×#123C23semidirect
161. C22×#123C23semidirect
162. C22×#123C23semidirect
166. C22×C22⋊Q8C23semidirect
169. C22×C4×D4C23semidirect
170. C22×C4×D4C23semidirect
231. #2826C23semidirect
232. #2824C23semidirect
233. #2706C23semidirect
234. #2705C23semidirect
235. #2696C23semidirect
236. #2693C23semidirect
237. #2636C23semidirect
238. #2630C23semidirect
239. #2626C23semidirect
240. #2505C23semidirect
241. #2480C23semidirect
242. #2463C23semidirect
243. #2455C23semidirect
244. #2437C23semidirect
245. #2405C23semidirect
246. #2405C23semidirect
247. C2×#400C23semidirect
248. C2×#400C23semidirect
249. C2×#400C23semidirect
250. C2×#399C23semidirect
251. C2×#399C23semidirect
252. C2×#399C23semidirect
253. C2×#398C23semidirect
254. C2×#397C23semidirect
255. C2×#397C23semidirect
256. C2×#397C23semidirect
257. C2×#396C23semidirect
258. C2×#396C23semidirect
259. C2×#396C23semidirect
260. C2×#396C23semidirect
261. C2×#396C23semidirect
262. C2×#394C23semidirect
263. C2×#394C23semidirect
264. C2×#394C23semidirect
265. C2×#394C23semidirect
266. C2×#394C23semidirect
267. C2×#394C23semidirect
268. C2×#394C23semidirect
269. C2×#394C23semidirect
270. C2×#393C23semidirect
271. C2×#393C23semidirect
272. C2×#393C23semidirect
280. D4×C22⋊C4C23semidirect
281. #2315C23semidirect
282. C2×#390C23semidirect
283. C2×#390C23semidirect
284. C2×#389C23semidirect
285. C2×#388C23semidirect
286. C2×#388C23semidirect
287. C2×#388C23semidirect
288. C2×#387C23semidirect
289. C2×#387C23semidirect
290. C2×#386C23semidirect
291. C2×#386C23semidirect
292. C2×#386C23semidirect
293. C2×#386C23semidirect
294. C2×#386C23semidirect
295. C2×#386C23semidirect
296. C2×#386C23semidirect
297. C2×#386C23semidirect
303. C2×#385C23semidirect
304. C2×#385C23semidirect
305. C2×#385C23semidirect
306. C2×#385C23semidirect
307. C2×#385C23semidirect
308. C2×#385C23semidirect
309. C2×#382C23semidirect
312. C2×#380C23semidirect
313. C2×#380C23semidirect
314. C2×#380C23semidirect
440. C2×#126C24semidirect
445. C2×#123C24semidirect
446. C2×#123C24semidirect
447. C2×#123C24semidirect
448. C2×#123C24semidirect
452. C2×C22⋊Q8C24semidirect
455. C2×C4×D4C24semidirect
456. C2×C4×D4C24semidirect
567. #400C24semidirect
568. #400C24semidirect
569. #400C24semidirect
570. #399C24semidirect
571. #399C24semidirect
572. #399C24semidirect
573. #398C24semidirect
574. #397C24semidirect
575. #397C24semidirect
576. #397C24semidirect
577. #396C24semidirect
578. #396C24semidirect
579. #396C24semidirect
580. #396C24semidirect
581. #396C24semidirect
582. #394C24semidirect
583. #394C24semidirect
584. #394C24semidirect
585. #394C24semidirect
586. #394C24semidirect
587. #394C24semidirect
588. #394C24semidirect
589. #394C24semidirect
590. #393C24semidirect
591. #393C24semidirect
592. #393C24semidirect
599. #390C24semidirect
600. #390C24semidirect
601. #389C24semidirect
602. #388C24semidirect
603. #388C24semidirect
604. #388C24semidirect
605. #387C24semidirect
606. #387C24semidirect
607. #386C24semidirect
608. #386C24semidirect
609. #386C24semidirect
610. #386C24semidirect
611. #386C24semidirect
612. #386C24semidirect
613. #386C24semidirect
614. #386C24semidirect
620. #385C24semidirect
621. #385C24semidirect
622. #385C24semidirect
623. #385C24semidirect
624. #385C24semidirect
625. #385C24semidirect
626. #382C24semidirect
629. #380C24semidirect
630. #380C24semidirect
631. #380C24semidirect
1444. C22#40638direct (N × H)
1475. C2C2×#40638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#406382
C22×#27062
C22×#27052
C22×#26962
C22×#26932
C22×#28262
C22×#28242
C22×#25052
C22×#24802
C22×#24052
C22×#24632
C22×#24552
C22×#24372
C22×#26362
C22×#26302
C22×#26262
C23×#3922
C22×D4×C22⋊C42
C22×#23152