Finite Group Databasebeta

← #7631258

Subgroups — #7631258

Order 512.

11448 conjugacy classes of subgroups.

The subgroup lattice has 939 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3500C211yesmaximal, characteristic, complemented
2C2×#3489C211yesmaximal, characteristic, complemented
3C2×#3488C211yesmaximal, characteristic, complemented
4C22×C4×#41C211yesmaximal, characteristic, complemented
5#36624C213yesmaximal, complemented
6C2×#2850C213yesmaximal, complemented
7#36434C214yesmaximal, complemented
8#36430C214yesmaximal, complemented
9#36218C2112yesmaximal, complemented
10#36214C2112yesmaximal, complemented
11#35328C213yesmaximal, complemented
12#35327C213yesmaximal, complemented
13#35308C213yesmaximal, complemented
14#35306C213yesmaximal, complemented
15#35256C213yesmaximal, complemented
16#35252C213yesmaximal, complemented
17#34259C211yesmaximal, characteristic, complemented
18#34258C211yesmaximal, characteristic, complemented
19#34184C211yesmaximal, characteristic, complemented
20C22×2−1+4C2211yescharacteristic
21C22×H(5,𝔽2)C2211yescharacteristic
22C23×#41C2211yescharacteristic
23#3500—216no—
24#3489—216no—
25#3488—216no—
26C2×#550C2212yes—
27C2×D4×Q8C2212yescomplemented
28C2×#548C2212yes—
29C2×#548C2212yescomplemented
30C2×#548C2214yescomplemented
31C2×#547C2216yescomplemented
32C2×#546C2216yes—
33C2×#546C2216yescomplemented
34C2×#546C22112yescomplemented
35C2×D42C2216yes—
36C2×#537C2213yes—
37C2×#537C2213yescomplemented
38C2×#536C2213yescomplemented
39C2×#536C2213yescomplemented
40C2×#535C2213yes—
41C2×#535C2213yescomplemented
42C2×#532C2213yescomplemented
43C22×#124C2213yescomplemented
44C2×#525C2213yes—
45C2×#525C2213yescomplemented
46C22×C22⋊Q8C2213yescomplemented
47C22×#121C2213yes—
48C2×#520C2211yescharacteristic
49C2×#520C2211yescharacteristic
50C2×C4×#41—216no—
51C2×C4×#41C2211yescharacteristic
52C2×C4×#41C2211yescharacteristic
53C2×C4×#41C2213yescomplemented
54C2×C4×#41C2212yescomplemented
55C2×C4×#41C2216yescomplemented
56C2×C4×#41C2213yescomplemented
57C22×C4×Q8C2212yescomplemented
58C22×C4×D4C2216yescomplemented
59C22×#117C2213yescomplemented
60C23×C42C2213yescomplemented
61#2857C2213yescomplemented
62#2857C2213yescomplemented
63#2856C2213yescomplemented
64#2856C2213yescomplemented
65#2854C22112yescomplemented
66#2850C2213yescomplemented
67#2850C2216yescomplemented
68#2850C2213yescomplemented
69#2850C22112yescomplemented
70#2850C22112yescomplemented
71#2850C2216yescomplemented
72#2850C2216yescomplemented
73#2850C2211yescharacteristic, complemented
74#2850C2213yescomplemented
75#2847C22112yescomplemented
76#2621C2216yescomplemented
77#2620C2216yescomplemented
78#2620C2216yescomplemented
79#2619C2216yescomplemented
80#2545C22112yescomplemented
81#2544C22112yescomplemented
82#2543C22124yescomplemented
83#2536C22112yescomplemented
84#2535C22112yescomplemented
85#2534C22124yescomplemented
86#2429C22112yescomplemented
87#2428C22112yescomplemented
88#2427C22112yescomplemented
89#2426C22112yescomplemented
90#2425C22124yescomplemented
91#2424C22124yescomplemented
92#2417C22112yescomplemented
93#2416C22112yescomplemented
94#2415C22112yescomplemented
95#2414C22112yescomplemented
96#2413C22112yescomplemented
97#2412C22112yescomplemented
98#2411C22112yescomplemented
99#2410C22112yescomplemented
100#2351C2214yescomplemented
101#2349C22112yescomplemented
102#2341C2214yescomplemented
103Q8×C22⋊C4C2214yescomplemented
104#2339C22112yescomplemented
105D4×C22⋊C4C22112yescomplemented
106#2317C2213yescomplemented
107#2317C2213yescomplemented
108#2311C2213yescomplemented
109#2311C2213yescomplemented
110#2310C2213yescomplemented
111#2309C2213yescomplemented
112C4×#121C22112yescomplemented
113C4×#121C22112yescomplemented
114#2297C2213yescomplemented
115#2297C2213yescomplemented
116C2×#391C2213yescomplemented
117C2×#390C2213yescomplemented
118C2×#388C22112yescomplemented
119C2×#386C22112yescomplemented
120#2285C2213yescomplemented
121C2×#382C2213yescomplemented
122C2×2−1+4—28no—
123C2×2−1+4—28no—
124C2×2−1+4—28no—
125C2×H(5,𝔽2)—28no—
126C2×H(5,𝔽2)—28no—
127C2×H(5,𝔽2)—28no—
128C22×#41—28no—
129C22×#41—28no—
130C22×#41D4116yescomplemented
131C22×#41C2313yes—
132C22×#41C2313yes—
133C22×#41C2312yes—
134C22×#41C2316yes—
135C22×#41C2313yes—
136C22×#41C2313yes—
137C22×#41C2311yescharacteristic
138C22×#41C2311yescharacteristic
139C23×Q8C2313yes—
140C23×Q8C2312yes—
141C23×Q8C2311yescharacteristic
142C23×D4C2313yes—
143C23×D4C2316yes—
144C23×D4C2313yes—
145C23×D4C2316yes—
146C24×C4C2313yes—
147C24×C4C2316yes—
148#550—216no—
149D4×Q8—216no—
150#548—216no—
151#548—216no—
152#548—232no—
153#547—248no—
154#546—248no—
155#546—248no—
156#546—296no—
157D42—248no—
158#537—224no—
159#537—224no—
160#536—224no—
161#536—224no—
162#535—224no—
163#535—224no—
164#532—224no—
165C2×C4⋊Q8C2313yes—
166C2×C4⋊Q8C2316yes—
167C2×#127C2313yes—
168C2×#127C2316yes—
169C2×#124—224no—
170C2×#124C2313yes—
171C2×#124C2311yescharacteristic
172C2×#124C2316yes—
173C2×#124C23112yes—
174C2×#124C2316yes—
175C2×#124C2316yes—
176#525—224no—
177#525—224no—
178C2×#123C2316yes—
179C2×#123C2316yes—
180C2×#123C23112yes—
181C2×#123C23112yes—
182C2×C22⋊Q8—224no—
183C2×C22⋊Q8C2313yes—
184C2×C22⋊Q8C2316yes—
185C2×C22⋊Q8C2316yes—
186C2×C22⋊Q8C2316yes—
187C2×C22⋊Q8C2311yescharacteristic
188C2×C22⋊Q8C2313yes—
189C2×C22⋊Q8C2313yes—
190C2×C22⋊Q8C23112yes—
191C2×C22⋊Q8C2316yes—
192C2×C22⋊Q8C2316yes—
193C2×#121—224no—
194C2×#121C23112yes—
195C2×#121C2313yes—
196C2×#121C2316yes—
197C2×#121C2316yes—
198C2×#121C2316yes—
199C2×#121C2311yescharacteristic
200C2×#121C2313yes—
201C2×#121C2313yes—
202C2×#121C23112yes—
203C2×#121C23112yes—
204C2×#121C23112yes—
205C2×#121C2316yes—
206C2×#121C2316yes—
207C2×#121C23112yes—
208C2×#121C23112yes—
209C2×#120C2316yes—
210C2×#120C2316yes—
211C2×#120C23112yes—
212C2×#120C23112yes—
213#520—28no—
214#520—28no—
215C4×#41—28no—
216C4×#41—216no—
217C4×#41—248no—
218C4×#41—224no—
219C4×#41—224no—
220C4×#41D4116yescomplemented
221C2×C4×Q8—216no—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2312yes—
225C2×C4×Q8C2316yes—
226C2×C4×Q8C2316yes—
227C2×C4×Q8C2312yes—
228C2×C4×D4—248no—
229C2×C4×D4C2316yes—
230C2×C4×D4C2316yes—
231C2×C4×D4C2316yes—
232C2×C4×D4C23112yes—
233C2×C4×D4C2316yes—
234C2×C4×D4C23112yes—
235C2×C4×D4C2316yes—
236C2×C4×D4C2316yes—
237C2×C4×D4C2316yes—
238C2×C4×D4C2316yes—
239C2×C4×D4C2316yes—
240C2×C4×D4C23112yes—
241C2×C4×D4C2316yes—
242C2×#117—224no—
243C2×#117C2313yes—
244C2×#117C2313yes—
245C2×#117C2313yes—
246C2×#117C2316yes—
247C2×#117C2316yes—
248C2×#117C2316yes—
249C2×#117C2313yes—
250C22×C4⋊C4C2313yes—
251C22×C4⋊C4C2313yes—
252C22×C4⋊C4C2316yes—
253C22×C4⋊C4C2316yes—
254C22×C22⋊C4C2316yes—
255C22×C22⋊C4C2316yes—
256C22×C22⋊C4C2316yes—
257C22×C22⋊C4C23112yes—
258C22×C22⋊C4C23112yes—
259C22×C42—224no—
260C22×C42C2311yescharacteristic
261C22×C42C2313yes—
262C22×C42C2313yes—
263C22×C42C2313yes—
264C22×C42C2316yes—
265C22×C42C2316yes—
266C22×C42C2316yes—
267C22×C42C2313yes—
268C22×C42C2313yes—
269#398C23124yes—
270#397C23124yes—
271#396C23124yes—
272#396C23124yes—
273#394C23124yes—
274#394C23124yes—
275#394C23124yes—
276#392C23124yes—
277#391C2313yes—
278#391C2316yes—
279#391C23112yes—
280#391C2313yes—
281#391C2313yes—
282#391C23112yes—
283#391C2311yescharacteristic
284#390C2313yes—
285#390C2316yes—
286#390C23112yes—
287#390C2313yes—
288#390C23112yes—
289#390C2313yes—
290#390C2311yescharacteristic
291#390C23112yes—
292#390C23112yes—
293#389C23112yes—
294#389C23112yes—
295#389C23112yes—
296#389C23112yes—
297#388C23112yes—
298#388C23124yes—
299#388C23124yes—
300#388C23124yes—
301#388C2314yes—
302#388C23112yes—
303#388C23112yes—
304#386C23112yes—
305#386C23112yes—
306#386C2314yes—
307#386C23112yes—
308#386C23112yes—
309#386C23112yes—
310#386C23112yes—
311#386C23112yes—
312#386C23124yes—
313#386C23124yes—
314#386C23124yes—
315#385C23112yes—
316#385C23112yes—
317#384C2313yes—
318#384C2313yes—
319#382C2316yes—
320#382C2313yes—
321#382C2311yescharacteristic
322#382C23112yes—
323#381C23112yes—
324#380C23112yes—
325#380C23112yes—
326#380C23112yes—
327#380C23112yes—
328#380C23112yes—
329#379C23112yes—
330C4×C4⋊C4C23112yes—
331C4×C22⋊C4C23112yes—
332C4×C22⋊C4C23112yes—
333C2×#95C23112yes—
334C2×#95C23112yes—
335C25C2413yes—
336C25C2416yes—
3372−1+4—464no—
338H(5,𝔽2)—464no—
339C2×#41—2128no—
340C2×#41—24no—
341C2×#41—28no—
342C2×#41—28no—
343C2×#41—24no—
344C2×#41—28no—
345C2×#41—212no—
346C2×#41—224no—
347C2×#41—224no—
348C2×#41—212no—
349C2×#41—224no—
350C2×#41—212no—
351C2×#41—212no—
352C2×#41—212no—
353C2×#41—212no—
354C2×#41—212no—
355C2×#41—212no—
356C2×#41—212no—
357C2×#41—212no—
358C2×#41C2×D4124yes—
359C2×#41C2×D4124yes—
360C2×#41C2×D418yes—
361C2×#41C2×D418yes—
362C2×#41C2×D418yes—
363C2×#41#4118yes—
364C22×Q8—24no—
365C22×Q8—24no—
366C22×Q8—28no—
367C22×Q8—28no—
368C22×Q8—28no—
369C22×Q8—212no—
370C22×Q8—212no—
371C22×Q8—212no—
372C22×Q8C2×D418yes—
373C22×Q8C2413yes—
374C22×Q8C2416yes—
375C22×Q8C2411yescharacteristic
376C22×Q8C2413yes—
377C22×Q8C2411yescharacteristic
378C22×D4—212no—
379C22×D4—212no—
380C22×D4—224no—
381C22×D4—224no—
382C22×D4—224no—
383C22×D4—224no—
384C22×D4—212no—
385C22×D4—212no—
386C22×D4—212no—
387C22×D4—424no—
388C22×D4C2×D4124yes—
389C22×D4C2412yes—
390C22×D4C2416yes—
391C22×D4C2416yes—
392C22×D4C2416yes—
393C22×D4C2413yes—
394C22×D4C2416yes—
395C22×D4C2411yescharacteristic
396C22×D4C2416yes—
397C22×D4C2413yes—
398C22×D4C2416yes—
399C22×D4C24112yes—
400C22×D4C2416yes—
401C22×D4C24112yes—
402C22×D4C2413yes—
403C23×C4—212no—
404C23×C4—212no—
405C23×C4—224no—
406C23×C4—412no—
407C23×C4—412no—
408C23×C4C2×D4124yes—
409C23×C4C2416yes—
410C23×C4C2416yes—
411C23×C4C2416yes—
412C23×C4C2412yes—
413C23×C4C2416yes—
414C23×C4C2416yes—
415C23×C4C2416yes—
416C23×C4C2413yes—
417C23×C4C2413yes—
418C23×C4C2413yes—
419C23×C4C2413yes—
420C23×C4C2411yescharacteristic
421C23×C4C2416yes—
422C23×C4C2416yes—
423C23×C4C2416yes—
424C23×C4C2416yes—
425C23×C4C2413yes—
426C4⋊Q8—224no—
427C4⋊Q8—212no—
428#127—224no—
429#127—212no—
430#124—224no—
431#124—224no—
432#124—212no—
433#124—224no—
434#124—248no—
435#124—24no—
436#123—248no—
437#123—224no—
438#123—224no—
439#123—248no—
440C22⋊Q8—224no—
441C22⋊Q8—224no—
442C22⋊Q8—212no—
443C22⋊Q8—224no—
444C22⋊Q8—224no—
445C22⋊Q8—224no—
446C22⋊Q8—24no—
447C22⋊Q8—212no—
448C22⋊Q8—212no—
449C22⋊Q8—248no—
450#121—248no—
451#121—224no—
452#121—248no—
453#121—224no—
454#121—212no—
455#121—224no—
456#121—224no—
457#121—224no—
458#121—24no—
459#121—212no—
460#121—212no—
461#121—248no—
462#121—248no—
463#121—424no—
464#121—424no—
465#120—224no—
466#120—224no—
467#120—248no—
468#120—248no—
469C4×Q8—28no—
470C4×Q8—28no—
471C4×Q8—28no—
472C4×Q8—224no—
473C4×Q8—224no—
474C4×Q8C2×D4116yescomplemented
475C4×D4—224no—
476C4×D4—224no—
477C4×D4—224no—
478C4×D4—248no—
479C4×D4—224no—
480C4×D4—224no—
481C4×D4—224no—
482C4×D4—224no—
483C4×D4—224no—
484C4×D4—248no—
485C4×D4—224no—
486C4×D4—248no—
487C4×D4C2×D4148yescomplemented
488#117—212no—
489#117—212no—
490#117—212no—
491#117—224no—
492#117—224no—
493#117—224no—
494#117C2×D4124yescomplemented
495C2×C4⋊C4—212no—
496C2×C4⋊C4—212no—
497C2×C4⋊C4—224no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4C2413yes—
500C2×C4⋊C4C2413yes—
501C2×C4⋊C4C2416yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C24112yes—
504C2×C4⋊C4C2416yes—
505C2×C4⋊C4C2416yes—
506C2×C4⋊C4C24112yes—
507C2×C4⋊C4C2411yescharacteristic
508C2×C4⋊C4C2411yescharacteristic
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C24112yes—
512C2×C4⋊C4C2416yes—
513C2×C4⋊C4C24112yes—
514C2×C4⋊C4C24112yes—
515C2×C4⋊C4C2416yes—
516C2×C22⋊C4—224no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—248no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—424no—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2416yes—
523C2×C22⋊C4C24112yes—
524C2×C22⋊C4C24112yes—
525C2×C22⋊C4C2416yes—
526C2×C22⋊C4C24112yes—
527C2×C22⋊C4C24112yes—
528C2×C22⋊C4C24124yes—
529C2×C22⋊C4C24112yes—
530C2×C22⋊C4C2416yes—
531C2×C22⋊C4C2416yes—
532C2×C22⋊C4C2412yes—
533C2×C22⋊C4C2414yes—
534C2×C22⋊C4C2412yes—
535C2×C22⋊C4C2416yes—
536C2×C22⋊C4C2416yes—
537C2×C22⋊C4C2416yes—
538C2×C22⋊C4C2416yes—
539C2×C22⋊C4C2414yes—
540C2×C22⋊C4C24124yes—
541C2×C22⋊C4C24112yes—
542C2×C22⋊C4C24112yes—
543C2×C22⋊C4C2416yes—
544C2×C42—224no—
545C2×C42—212no—
546C2×C42—212no—
547C2×C42—224no—
548C2×C42—224no—
549C2×C42—212no—
550C2×C42—212no—
551C2×C42—24no—
552C2×C42C2×D4124yescomplemented
553C2×C42C2416yes—
554C2×C42C2413yes—
555C2×C42C2416yes—
556C2×C42C2416yes—
557C2×C42C2416yes—
558C2×C42C2416yes—
559C2×C42C2416yes—
560C2×C42C2412yes—
561C2×C42C2411yescharacteristic
562C2×C42C2413yes—
563C2×C42C2416yes—
564C2×C42C2411yescharacteristic
565#95C24112yes—
566#95C24112yes—
567#95C24124yes—
568#95C24124yes—
569#95C2414yes—
570#95C24112yes—
571#95C24112yes—
572#95C2414yes—
573C24—26no—
574C24—26no—
575C24—212no—
576C24—212no—
577C24—212no—
578C24—212no—
579C24—46no—
580C24—412no—
581C24—412no—
582C24C22×D4112yes—
583C24C2516yes—
584C24C2512yes—
585C24C2513yes—
586C24C2513yes—
587C24C2511yescharacteristic
588#41—232no—
589#41—296no—
590#41—296no—
591#41—432no—
592#41—496no—
593#41—448no—
594#41—448no—
595#41#121164yescomplemented
596C2×Q8—232no—
597C2×Q8—26no—
598C2×Q8—26no—
599C2×Q8—22no—
600C2×Q8—212no—
601C2×Q8—212no—
602C2×Q8—26no—
603C2×Q8—22no—
604C2×Q8—26no—
605C2×Q8—212no—
606C2×Q8—26no—
607C2×Q8—22no—
608C2×Q8—432no—
609C2×Q8—448no—
610C2×Q8C22×D4112yes—
611C2×Q8C22×D414yes—
612C2×Q8C22×D414yes—
613C2×Q8C2×#4114yes—
614C2×D4—212no—
615C2×D4—212no—
616C2×D4—296no—
617C2×D4—24no—
618C2×D4—212no—
619C2×D4—212no—
620C2×D4—212no—
621C2×D4—212no—
622C2×D4—212no—
623C2×D4—212no—
624C2×D4—212no—
625C2×D4—28no—
626C2×D4—224no—
627C2×D4—212no—
628C2×D4—212no—
629C2×D4—224no—
630C2×D4—26no—
631C2×D4—26no—
632C2×D4—22no—
633C2×D4—212no—
634C2×D4—212no—
635C2×D4—26no—
636C2×D4—22no—
637C2×D4—224no—
638C2×D4—26no—
639C2×D4—212no—
640C2×D4—26no—
641C2×D4—22no—
642C2×D4—412no—
643C2×D4—412no—
644C2×D4—412no—
645C2×D4—412no—
646C2×D4—424no—
647C2×D4—496no—
648C2×D4—448no—
649C2×D4—848no—
650C2×D4C22×D4124yes—
651C2×D4C22×D4112yes—
652C2×D4C22×D4112yes—
653C2×D4C22×D4112yes—
654C2×D4C2×#41112yes—
655C22×C4—26no—
656C22×C4—26no—
657C22×C4—24no—
658C22×C4—296no—
659C22×C4—24no—
660C22×C4—22no—
661C22×C4—26no—
662C22×C4—26no—
663C22×C4—26no—
664C22×C4—22no—
665C22×C4—26no—
666C22×C4—26no—
667C22×C4—26no—
668C22×C4—24no—
669C22×C4—212no—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—212no—
673C22×C4—212no—
674C22×C4—212no—
675C22×C4—212no—
676C22×C4—212no—
677C22×C4—212no—
678C22×C4—212no—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—212no—
682C22×C4—212no—
683C22×C4—212no—
684C22×C4—212no—
685C22×C4—212no—
686C22×C4—212no—
687C22×C4—46no—
688C22×C4—46no—
689C22×C4—46no—
690C22×C4—46no—
691C22×C4—46no—
692C22×C4—46no—
693C22×C4—46no—
694C22×C4—412no—
695C22×C4—412no—
696C22×C4—496no—
697C22×C4C22×D4112yes—
698C22×C4C22×D4112yes—
699C22×C4C22×D4112yes—
700C22×C4C22×D414yes—
701C22×C4C22×D4112yes—
702C22×C4C22×D4124yes—
703C22×C4C22×D4112yes—
704C22×C4C22×D4112yes—
705C22×C4C2×#41112yes—
706C22×C4C2516yes—
707C22×C4C2516yes—
708C22×C4C2512yes—
709C22×C4C2516yes—
710C22×C4C2516yes—
711C22×C4C2512yes—
712C22×C4C2512yes—
713C22×C4C2512yes—
714C22×C4C2516yes—
715C22×C4C2511yescharacteristic
716C22×C4C2513yes—
717C22×C4C2512yes—
718C22×C4C2511yescharacteristic
719C22×C4C2513yes—
720C4⋊C4—26no—
721C4⋊C4—26no—
722C4⋊C4—212no—
723C4⋊C4—224no—
724C4⋊C4—212no—
725C4⋊C4—212no—
726C4⋊C4—212no—
727C4⋊C4—224no—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—24no—
731C4⋊C4—212no—
732C4⋊C4—224no—
733C4⋊C4—212no—
734C4⋊C4—412no—
735C4⋊C4—412no—
736C4⋊C4C22×D4124yes—
737C22⋊C4—212no—
738C22⋊C4—212no—
739C22⋊C4—224no—
740C22⋊C4—212no—
741C22⋊C4—212no—
742C22⋊C4—24no—
743C22⋊C4—212no—
744C22⋊C4—212no—
745C22⋊C4—212no—
746C22⋊C4—224no—
747C22⋊C4—224no—
748C22⋊C4—224no—
749C22⋊C4—248no—
750C22⋊C4—28no—
751C22⋊C4—24no—
752C22⋊C4—212no—
753C22⋊C4—212no—
754C22⋊C4—224no—
755C22⋊C4—28no—
756C22⋊C4—424no—
757C22⋊C4—412no—
758C22⋊C4—412no—
759C22⋊C4C22×D4124yes—
760C42—24no—
761C42—22no—
762C42—212no—
763C42—26no—
764C42—212no—
765C42—212no—
766C42—212no—
767C42—212no—
768C42—212no—
769C42C22×D414yes—
770C42C22×D4112yes—
771C42C22×D4124yes—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—26no—
776C23—26no—
777C23—23no—
778C23—23no—
779C23—26no—
780C23—26no—
781C23—224no—
782C23—224no—
783C23—26no—
784C23—22no—
785C23—26no—
786C23—22no—
787C23—22no—
788C23—26no—
789C23—212no—
790C23—24no—
791C23—24no—
792C23—212no—
793C23—412no—
794C23—424no—
795C23—424no—
796C23—424no—
797C23—812no—
798C23—824no—
799C23—824no—
800C23—812no—
801C23C23×D416yes—
802C23C23×D416yes—
803C23C23×D416yes—
804C23C23×D412yes—
805C23C22×#4116yes—
806C23#58514yes—
807C23C2611yescharacteristic
808Q8—224no—
809Q8—412no—
810Q8—424no—
811Q8—44no—
812Q8C2×#121116yes—
813D4—248no—
814D4—224no—
815D4—424no—
816D4—424no—
817D4—48no—
818D4—424no—
819D4—412no—
820D4—424no—
821D4—44no—
822D4—824no—
823D4—812no—
824D4—812no—
825D4—824no—
826D4C2×#121148yes—
827C2×C4—216no—
828C2×C4—22no—
829C2×C4—21no—
830C2×C4—23no—
831C2×C4—21no—
832C2×C4—23no—
833C2×C4—26no—
834C2×C4—26no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—224no—
839C2×C4—28no—
840C2×C4—224no—
841C2×C4—224no—
842C2×C4—224no—
843C2×C4—26no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—26no—
847C2×C4—26no—
848C2×C4—26no—
849C2×C4—22no—
850C2×C4—26no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—26no—
854C2×C4—212no—
855C2×C4—24no—
856C2×C4—26no—
857C2×C4—26no—
858C2×C4—24no—
859C2×C4—212no—
860C2×C4—424no—
861C2×C4—424no—
862C2×C4—424no—
863C2×C4—424no—
864C2×C4—424no—
865C2×C4—424no—
866C2×C4—424no—
867C2×C4—424no—
868C2×C4—812no—
869C2×C4—812no—
870C2×C4C2×#121148yes—
871C2×C4C23×D414yes—
872C2×C4C23×D4112yes—
873C2×C4C23×D412yes—
874C2×C4C23×D416yes—
875C2×C4C23×D412yes—
876C2×C4C23×D416yes—
877C2×C4C23×D416yes—
878C2×C4C23×D412yes—
879C2×C4C22×#4116yes—
880C2×C4C22×#4112yes—
881C2×C4#58514yes—
882C22—26no—
883C22—24no—
884C22—212no—
885C22—24no—
886C22—212no—
887C22—26no—
888C22—22no—
889C22—22no—
890C22—26no—
891C22—26no—
892C22—26no—
893C22—448no—
894C22—46no—
895C22—46no—
896C22—46no—
897C22—42no—
898C22—44no—
899C22—412no—
900C22—44no—
901C22—412no—
902C22—42no—
903C22—46no—
904C22—42no—
905C22—46no—
906C22—1624no—
907C22C22×#121112yes—
908C22#350014yescomplemented
909C22C24×D411yescharacteristic
910C22C24×D411yescharacteristic
911C22C23×#4111yescharacteristic
912C22C2×#58512yes—
913C22C2×#58512yes—
914C4—24no—
915C4—24no—
916C4—212no—
917C4—22no—
918C4—26no—
919C4—46no—
920C4—42no—
921C4—46no—
922C4—46no—
923C4—42no—
924C4—42no—
925C4—46no—
926C4C22×#12114yes—
927C4C22×#121112yes—
928C2—24no—
929C2—212no—
930C2—46no—
931C2—82no—
932C2—86no—
933C2C23×#12111yescharacteristic
934C2C2×#350011yescharacteristic
935C2#6281012yes—
936C2#6281112yes—
937C2#6281211yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3500C2semidirect
2. C2×#3489C2semidirect
3. C2×#3488C2semidirect
4. C22×C4×#41C2semidirect
5. #36624C2semidirect
6. C2×#2850C2semidirect
7. #36434C2semidirect
8. #36430C2semidirect
9. #36218C2semidirect
10. #36214C2semidirect
11. #35328C2semidirect
12. #35327C2semidirect
13. #35308C2semidirect
14. #35306C2semidirect
15. #35256C2semidirect
16. #35252C2semidirect
17. #34259C2semidirect
18. #34258C2semidirect
19. #34184C2semidirect
27. C2×D4×Q8C22semidirect
29. C2×#548C22semidirect
30. C2×#548C22semidirect
31. C2×#547C22semidirect
33. C2×#546C22semidirect
34. C2×#546C22semidirect
37. C2×#537C22semidirect
38. C2×#536C22semidirect
39. C2×#536C22semidirect
41. C2×#535C22semidirect
42. C2×#532C22semidirect
43. C22×#124C22semidirect
45. C2×#525C22semidirect
46. C22×C22⋊Q8C22semidirect
53. C2×C4×#41C22semidirect
54. C2×C4×#41C22semidirect
55. C2×C4×#41C22semidirect
56. C2×C4×#41C22semidirect
57. C22×C4×Q8C22semidirect
58. C22×C4×D4C22semidirect
59. C22×#117C22semidirect
60. C23×C42C22semidirect
61. #2857C22semidirect
62. #2857C22semidirect
63. #2856C22semidirect
64. #2856C22semidirect
65. #2854C22semidirect
66. #2850C22semidirect
67. #2850C22semidirect
68. #2850C22semidirect
69. #2850C22semidirect
70. #2850C22semidirect
71. #2850C22semidirect
72. #2850C22semidirect
73. #2850C22semidirect
74. #2850C22semidirect
75. #2847C22semidirect
76. #2621C22semidirect
77. #2620C22semidirect
78. #2620C22semidirect
79. #2619C22semidirect
80. #2545C22semidirect
81. #2544C22semidirect
82. #2543C22semidirect
83. #2536C22semidirect
84. #2535C22semidirect
85. #2534C22semidirect
86. #2429C22semidirect
87. #2428C22semidirect
88. #2427C22semidirect
89. #2426C22semidirect
90. #2425C22semidirect
91. #2424C22semidirect
92. #2417C22semidirect
93. #2416C22semidirect
94. #2415C22semidirect
95. #2414C22semidirect
96. #2413C22semidirect
97. #2412C22semidirect
98. #2411C22semidirect
99. #2410C22semidirect
100. #2351C22semidirect
101. #2349C22semidirect
102. #2341C22semidirect
103. Q8×C22⋊C4C22semidirect
104. #2339C22semidirect
105. D4×C22⋊C4C22semidirect
106. #2317C22semidirect
107. #2317C22semidirect
108. #2311C22semidirect
109. #2311C22semidirect
110. #2310C22semidirect
111. #2309C22semidirect
112. C4×#121C22semidirect
113. C4×#121C22semidirect
114. #2297C22semidirect
115. #2297C22semidirect
116. C2×#391C22semidirect
117. C2×#390C22semidirect
118. C2×#388C22semidirect
119. C2×#386C22semidirect
120. #2285C22semidirect
121. C2×#382C22semidirect
130. C22×#41D4semidirect
220. C4×#41D4semidirect
474. C4×Q8C2×D4semidirect
487. C4×D4C2×D4semidirect
494. #117C2×D4semidirect
552. C2×C42C2×D4semidirect
595. #41#121semidirect
908. C22#3500semidirect

Maximal subgroups

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

subgroupindex
C2×#35002
C2×#34892
C2×#34882
C22×C4×#412
#366242
C2×#28502
#364342
#364302
#362182
#362142
#353282
#353272
#353082
#353062
#352562
#352522
#342592
#342582
#341842