Finite Group Databasebeta

← #7630878

Subgroups — #7630878

Order 512.

11082 conjugacy classes of subgroups.

The subgroup lattice has 928 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
4C2×#3428C211yesmaximal, characteristic, complemented
5#35831C214yesmaximal, complemented
6#35821C2112yesmaximal, complemented
7#35771C214yesmaximal, complemented
8#35761C2112yesmaximal, complemented
9#35327C213yesmaximal, complemented
10#35308C213yesmaximal, complemented
11#35306C213yesmaximal, complemented
12#35273C213yesmaximal, complemented
13#35256C213yesmaximal, complemented
14#35252C213yesmaximal, complemented
15#34633C213yesmaximal, complemented
16C2×#2620C213yesmaximal, complemented
17#34259C211yesmaximal, characteristic, complemented
18#34258C211yesmaximal, characteristic, complemented
19#34183C211yesmaximal, 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—
48#3428—216no—
49C2×#520C2211yescharacteristic
50C2×#520C2211yescharacteristic
51C2×#520C2216yescomplemented
52C2×#520C2212yescomplemented
53C2×#519C2212yescomplemented
54C2×#518C2216yescomplemented
55C2×C4×#41C2211yescharacteristic
56C2×C4×#41C2211yescharacteristic
57C2×C4×#41C2213yescomplemented
58C2×C4×#41C2213yescomplemented
59C22×#117C2213yescomplemented
60C22×#117C2213yescomplemented
61#2857C2216yescomplemented
62#2856C2216yescomplemented
63#2850C2216yescomplemented
64#2850C2216yescomplemented
65#2621C2213yescomplemented
66#2621C2213yescomplemented
67#2620C2213yescomplemented
68#2620C22112yescomplemented
69#2620C2216yescomplemented
70#2620C2216yescomplemented
71#2620C2216yescomplemented
72#2620C22112yescomplemented
73#2620C2211yescharacteristic, complemented
74#2620C2213yescomplemented
75#2620C2213yescomplemented
76#2619C2213yescomplemented
77#2619C2213yescomplemented
78#2618C22112yescomplemented
79#2617C22112yescomplemented
80#2545C22112yescomplemented
81#2544C22112yescomplemented
82#2538C22112yescomplemented
83#2537C22112yescomplemented
84#2534C22124yescomplemented
85#2429C22112yescomplemented
86#2428C22112yescomplemented
87#2427C22112yescomplemented
88#2426C22112yescomplemented
89#2425C22124yescomplemented
90#2424C22124yescomplemented
91#2417C22112yescomplemented
92#2416C22124yescomplemented
93#2416C22112yescomplemented
94#2415C22112yescomplemented
95#2414C22112yescomplemented
96#2413C22112yescomplemented
97#2412C22112yescomplemented
98#2411C22112yescomplemented
99#2410C22112yescomplemented
100#2392C22112yescomplemented
101#2392C22112yescomplemented
102C2×#396C22112yescomplemented
103C2×#394C22112yescomplemented
104Q8×C4⋊C4C2214yescomplemented
105D4×C4⋊C4C22112yescomplemented
106#2341C2214yescomplemented
107Q8×C22⋊C4C2214yescomplemented
108#2339C22112yescomplemented
109D4×C22⋊C4C22112yescomplemented
110#2317C2213yescomplemented
111#2317C2213yescomplemented
112#2311C2213yescomplemented
113#2311C2213yescomplemented
114#2310C2213yescomplemented
115#2309C2213yescomplemented
116#2297C2213yescomplemented
117#2297C2213yescomplemented
118C2×#391C2213yescomplemented
119C2×#390C2213yescomplemented
120#2285C2213yescomplemented
121C2×#384C2213yescomplemented
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—
147#550—216no—
148D4×Q8—216no—
149#548—216no—
150#548—216no—
151#548—232no—
152#547—248no—
153#546—248no—
154#546—248no—
155#546—296no—
156D42—248no—
157#537—224no—
158#537—224no—
159#536—224no—
160#536—224no—
161#535—224no—
162#535—224no—
163#532—224no—
164C2×C4⋊Q8C2313yes—
165C2×C4⋊Q8C2316yes—
166C2×#127C2313yes—
167C2×#127C2316yes—
168C2×#124—224no—
169C2×#124C2316yes—
170C2×#124C2313yes—
171C2×#124C2311yescharacteristic
172C2×#124C23112yes—
173C2×#124C2316yes—
174C2×#124C2316yes—
175#525—224no—
176#525—224no—
177C2×#123C2316yes—
178C2×#123C2316yes—
179C2×#123C23112yes—
180C2×#123C23112yes—
181C2×C22⋊Q8—224no—
182C2×C22⋊Q8C2313yes—
183C2×C22⋊Q8C2316yes—
184C2×C22⋊Q8C2313yes—
185C2×C22⋊Q8C2313yes—
186C2×C22⋊Q8C2316yes—
187C2×C22⋊Q8C2316yes—
188C2×C22⋊Q8C2311yescharacteristic
189C2×C22⋊Q8C23112yes—
190C2×C22⋊Q8C2316yes—
191C2×C22⋊Q8C2316yes—
192C2×#121—224no—
193C2×#121C2313yes—
194C2×#121C2316yes—
195C2×#121C2313yes—
196C2×#121C23112yes—
197C2×#121C2311yescharacteristic
198C2×#121C2313yes—
199C2×#121C2316yes—
200C2×#121C2316yes—
201C2×#121C23112yes—
202C2×#121C23112yes—
203C2×#121C23112yes—
204C2×#121C2316yes—
205C2×#121C2316yes—
206C2×#121C23124yes—
207C2×#120C2316yes—
208C2×#120C2316yes—
209C2×#120C23112yes—
210C2×#120C23112yes—
211#520—28no—
212#520—28no—
213#520—216no—
214#520—248no—
215#519—216no—
216#518—248no—
217C4×#41—28no—
218C4×#41—224no—
219C4×#41—224no—
220C4×#41D4116yescomplemented
221C2×C4×Q8C2312yes—
222C2×C4×Q8C2312yes—
223C2×C4×Q8C2312yes—
224C2×C4×Q8C2316yes—
225C2×C4×Q8C2316yes—
226C2×C4×Q8C2312yes—
227C2×C4×D4C2316yes—
228C2×C4×D4C2316yes—
229C2×C4×D4C2316yes—
230C2×C4×D4C2316yes—
231C2×C4×D4C2316yes—
232C2×C4×D4C2316yes—
233C2×C4×D4C2316yes—
234C2×C4×D4C23112yes—
235C2×C4×D4C23112yes—
236C2×C4×D4C23112yes—
237C2×C4×D4C2316yes—
238C2×C4×D4C2316yes—
239C2×C4×D4C2316yes—
240C2×#117—224no—
241C2×#117—224no—
242C2×#117C2313yes—
243C2×#117C2313yes—
244C2×#117C2313yes—
245C2×#117C2313yes—
246C2×#117C2313yes—
247C2×#117C2311yescharacteristic
248C2×#117C2313yes—
249C2×#117C2316yes—
250C2×#117C2316yes—
251C2×#117C2316yes—
252C2×#117C2316yes—
253C2×#117C2313yes—
254C22×C4⋊C4C2313yes—
255C22×C4⋊C4C2313yes—
256C22×C4⋊C4C2316yes—
257C22×C4⋊C4C2316yes—
258C22×C4⋊C4C2316yes—
259C22×C4⋊C4C23112yes—
260C22×C22⋊C4C2316yes—
261C22×C22⋊C4C2316yes—
262C22×C22⋊C4C23112yes—
263C22×C22⋊C4C2316yes—
264C22×C22⋊C4C2316yes—
265C22×C22⋊C4C23112yes—
266C22×C42C2316yes—
267C22×C42C2313yes—
268C22×C42C2313yes—
269#398C23112yes—
270#398C23112yes—
271#397C23112yes—
272#397C23112yes—
273#396C2314yes—
274#396C23112yes—
275#396C23112yes—
276#396C23112yes—
277#396C23124yes—
278#396C23124yes—
279#396C23124yes—
280#394C2314yes—
281#394C23112yes—
282#394C23112yes—
283#394C23112yes—
284#394C23112yes—
285#394C23112yes—
286#394C23124yes—
287#394C23124yes—
288#394C23124yes—
289#392C23112yes—
290#392C23112yes—
291#391C2313yes—
292#391C2316yes—
293#391C23112yes—
294#391C2313yes—
295#391C23112yes—
296#391C2313yes—
297#391C2311yescharacteristic
298#390C2313yes—
299#390C2316yes—
300#390C23112yes—
301#390C2313yes—
302#390C23112yes—
303#390C23124yes—
304#390C2311yescharacteristic
305#390C2313yes—
306#389C23112yes—
307#389C23112yes—
308#389C23124yes—
309#388C23124yes—
310#388C23124yes—
311#386C23112yes—
312#386C23112yes—
313#386C23112yes—
314#386C23124yes—
315#386C23124yes—
316#386C23112yes—
317#385C23112yes—
318#385C23112yes—
319#384C2316yes—
320#384C23112yes—
321#384C2313yes—
322#384C2311yescharacteristic
323#382C2313yes—
324#382C2313yes—
325#381C23112yes—
326#380C23112yes—
327#380C23112yes—
328#380C23124yes—
329#380C23112yes—
330#379C23112yes—
331C4×C4⋊C4C23112yes—
332C4×C22⋊C4C23112yes—
333C4×C22⋊C4C23112yes—
334C2×#95C23112yes—
335C25C2416yes—
336C25C2413yes—
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—812no—
388C22×D4C2×D4124yes—
389C22×D4C2416yes—
390C22×D4C2416yes—
391C22×D4C2413yes—
392C22×D4C2416yes—
393C22×D4C2411yescharacteristic
394C22×D4C2416yes—
395C22×D4C2413yes—
396C22×D4C2412yes—
397C22×D4C2416yes—
398C22×D4C24112yes—
399C22×D4C2416yes—
400C22×D4C2416yes—
401C22×D4C24112yes—
402C22×D4C2413yes—
403C23×C4—212no—
404C23×C4—212no—
405C23×C4C2×D4124yes—
406C23×C4C2416yes—
407C23×C4C2416yes—
408C23×C4C2416yes—
409C23×C4C2413yes—
410C23×C4C2413yes—
411C23×C4C2413yes—
412C23×C4C2411yescharacteristic
413C23×C4C2413yes—
414C23×C4C2416yes—
415C23×C4C2416yes—
416C23×C4C2416yes—
417C23×C4C24112yes—
418C23×C4C2416yes—
419C23×C4C2413yes—
420C4⋊Q8—224no—
421C4⋊Q8—212no—
422#127—224no—
423#127—212no—
424#124—224no—
425#124—224no—
426#124—212no—
427#124—224no—
428#124—248no—
429#124—24no—
430#123—248no—
431#123—224no—
432#123—224no—
433#123—248no—
434C22⋊Q8—224no—
435C22⋊Q8—224no—
436C22⋊Q8—212no—
437C22⋊Q8—224no—
438C22⋊Q8—224no—
439C22⋊Q8—224no—
440C22⋊Q8—24no—
441C22⋊Q8—212no—
442C22⋊Q8—212no—
443C22⋊Q8—248no—
444#121—248no—
445#121—224no—
446#121—248no—
447#121—224no—
448#121—212no—
449#121—224no—
450#121—224no—
451#121—224no—
452#121—24no—
453#121—212no—
454#121—212no—
455#121—248no—
456#121—248no—
457#121—824no—
458#120—224no—
459#120—224no—
460#120—248no—
461#120—248no—
462C4×Q8—28no—
463C4×Q8—28no—
464C4×Q8—28no—
465C4×Q8—224no—
466C4×Q8—224no—
467C4×Q8C2×D4116yescomplemented
468C4×D4—224no—
469C4×D4—224no—
470C4×D4—224no—
471C4×D4—248no—
472C4×D4—224no—
473C4×D4—224no—
474C4×D4—224no—
475C4×D4—224no—
476C4×D4—224no—
477C4×D4—248no—
478C4×D4—224no—
479C4×D4—248no—
480C4×D4C2×D4148yescomplemented
481#117—212no—
482#117—212no—
483#117—212no—
484#117—224no—
485#117—224no—
486#117—212no—
487#117—24no—
488#117—212no—
489#117—212no—
490#117—224no—
491#117—224no—
492#117C2×D4124yescomplemented
493C2×C4⋊C4—224no—
494C2×C4⋊C4—212no—
495C2×C4⋊C4—212no—
496C2×C4⋊C4—224no—
497C2×C4⋊C4—224no—
498C2×C4⋊C4—812no—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2413yes—
502C2×C4⋊C4C2413yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C2416yes—
505C2×C4⋊C4C2416yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C2416yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C24112yes—
510C2×C4⋊C4C2411yescharacteristic
511C2×C4⋊C4C2411yescharacteristic
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2416yes—
514C2×C4⋊C4C24112yes—
515C2×C4⋊C4C2416yes—
516C2×C4⋊C4C24112yes—
517C2×C4⋊C4C24124yes—
518C2×C4⋊C4C2414yes—
519C2×C4⋊C4C2416yes—
520C2×C22⋊C4—224no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4—224no—
523C2×C22⋊C4—248no—
524C2×C22⋊C4—224no—
525C2×C22⋊C4—812no—
526C2×C22⋊C4C2416yes—
527C2×C22⋊C4C2412yes—
528C2×C22⋊C4C2416yes—
529C2×C22⋊C4C2416yes—
530C2×C22⋊C4C24112yes—
531C2×C22⋊C4C2416yes—
532C2×C22⋊C4C2416yes—
533C2×C22⋊C4C2416yes—
534C2×C22⋊C4C24112yes—
535C2×C22⋊C4C24124yes—
536C2×C22⋊C4C24112yes—
537C2×C22⋊C4C2416yes—
538C2×C22⋊C4C2416yes—
539C2×C22⋊C4C2412yes—
540C2×C22⋊C4C2414yes—
541C2×C22⋊C4C2412yes—
542C2×C22⋊C4C2416yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C2416yes—
545C2×C22⋊C4C2416yes—
546C2×C22⋊C4C24112yes—
547C2×C22⋊C4C24124yes—
548C2×C22⋊C4C24112yes—
549C2×C22⋊C4C2414yes—
550C2×C22⋊C4C24112yes—
551C2×C22⋊C4C2416yes—
552C2×C42—212no—
553C2×C42—224no—
554C2×C42C2×D4124yescomplemented
555C2×C42C2413yes—
556C2×C42C2411yescharacteristic
557C2×C42C2416yes—
558C2×C42C24112yes—
559C2×C42C2416yes—
560C2×C42C2416yes—
561C2×C42C2411yescharacteristic
562C2×C42C2413yes—
563C2×C42C2416yes—
564#95C24112yes—
565#95C24124yes—
566#95C2414yes—
567#95C24112yes—
568#95C24112yes—
569#95C24112yes—
570#95C24112yes—
571C24—26no—
572C24—26no—
573C24—212no—
574C24—212no—
575C24—212no—
576C24—46no—
577C24—46no—
578C24—412no—
579C24—412no—
580C24C22×D4112yes—
581C24C2516yes—
582C24C2512yes—
583C24C2511yescharacteristic
584C24C2513yes—
585C24C2513yes—
586#41—232no—
587#41—296no—
588#41—296no—
589#41—432no—
590#41—496no—
591#41—448no—
592#41—448no—
593#41#121164yescomplemented
594C2×Q8—232no—
595C2×Q8—26no—
596C2×Q8—26no—
597C2×Q8—22no—
598C2×Q8—212no—
599C2×Q8—212no—
600C2×Q8—26no—
601C2×Q8—22no—
602C2×Q8—26no—
603C2×Q8—212no—
604C2×Q8—26no—
605C2×Q8—22no—
606C2×Q8—432no—
607C2×Q8—448no—
608C2×Q8C22×D4112yes—
609C2×Q8C22×D414yes—
610C2×Q8C22×D414yes—
611C2×Q8C2×#4114yes—
612C2×D4—212no—
613C2×D4—212no—
614C2×D4—296no—
615C2×D4—24no—
616C2×D4—212no—
617C2×D4—212no—
618C2×D4—212no—
619C2×D4—212no—
620C2×D4—212no—
621C2×D4—212no—
622C2×D4—212no—
623C2×D4—212no—
624C2×D4—212no—
625C2×D4—224no—
626C2×D4—26no—
627C2×D4—26no—
628C2×D4—22no—
629C2×D4—212no—
630C2×D4—212no—
631C2×D4—26no—
632C2×D4—22no—
633C2×D4—224no—
634C2×D4—26no—
635C2×D4—212no—
636C2×D4—26no—
637C2×D4—22no—
638C2×D4—412no—
639C2×D4—44no—
640C2×D4—412no—
641C2×D4—412no—
642C2×D4—424no—
643C2×D4—412no—
644C2×D4—412no—
645C2×D4—496no—
646C2×D4—448no—
647C2×D4—848no—
648C2×D4C22×D4124yes—
649C2×D4C22×D4112yes—
650C2×D4C22×D4112yes—
651C2×D4C22×D4112yes—
652C2×D4C2×#41112yes—
653C22×C4—26no—
654C22×C4—26no—
655C22×C4—296no—
656C22×C4—26no—
657C22×C4—26no—
658C22×C4—22no—
659C22×C4—26no—
660C22×C4—22no—
661C22×C4—26no—
662C22×C4—26no—
663C22×C4—26no—
664C22×C4—212no—
665C22×C4—212no—
666C22×C4—212no—
667C22×C4—212no—
668C22×C4—212no—
669C22×C4—212no—
670C22×C4—212no—
671C22×C4—212no—
672C22×C4—212no—
673C22×C4—212no—
674C22×C4—212no—
675C22×C4—212no—
676C22×C4—224no—
677C22×C4—46no—
678C22×C4—46no—
679C22×C4—46no—
680C22×C4—412no—
681C22×C4—412no—
682C22×C4—412no—
683C22×C4—412no—
684C22×C4—46no—
685C22×C4C22×D4112yes—
686C22×C4C22×D4112yes—
687C22×C4C22×D4112yes—
688C22×C4C22×D414yes—
689C22×C4C22×D4112yes—
690C22×C4C22×D4124yes—
691C22×C4C22×D4112yes—
692C22×C4C22×D4112yes—
693C22×C4C2×#41112yes—
694C22×C4C2512yes—
695C22×C4C2512yes—
696C22×C4C2516yes—
697C22×C4C2512yes—
698C22×C4C2516yes—
699C22×C4C2516yes—
700C22×C4C2512yes—
701C22×C4C2516yes—
702C22×C4C2516yes—
703C22×C4C2512yes—
704C22×C4C2513yes—
705C22×C4C2511yescharacteristic
706C22×C4C2511yescharacteristic
707C22×C4C2513yes—
708C4⋊C4—212no—
709C4⋊C4—24no—
710C4⋊C4—26no—
711C4⋊C4—26no—
712C4⋊C4—212no—
713C4⋊C4—212no—
714C4⋊C4—212no—
715C4⋊C4—212no—
716C4⋊C4—212no—
717C4⋊C4—212no—
718C4⋊C4—224no—
719C4⋊C4—22no—
720C4⋊C4—22no—
721C4⋊C4—24no—
722C4⋊C4—212no—
723C4⋊C4—224no—
724C4⋊C4—212no—
725C4⋊C4—412no—
726C4⋊C4—424no—
727C4⋊C4—44no—
728C4⋊C4C22×D4124yes—
729C22⋊C4—212no—
730C22⋊C4—212no—
731C22⋊C4—224no—
732C22⋊C4—212no—
733C22⋊C4—212no—
734C22⋊C4—24no—
735C22⋊C4—212no—
736C22⋊C4—212no—
737C22⋊C4—212no—
738C22⋊C4—24no—
739C22⋊C4—212no—
740C22⋊C4—224no—
741C22⋊C4—212no—
742C22⋊C4—212no—
743C22⋊C4—224no—
744C22⋊C4—248no—
745C22⋊C4—28no—
746C22⋊C4—24no—
747C22⋊C4—212no—
748C22⋊C4—212no—
749C22⋊C4—412no—
750C22⋊C4—424no—
751C22⋊C4—412no—
752C22⋊C4—44no—
753C22⋊C4—412no—
754C22⋊C4C22×D4124yes—
755C42—22no—
756C42—26no—
757C42—224no—
758C42—212no—
759C42—212no—
760C42—212no—
761C42C22×D4112yes—
762C42C22×D414yes—
763C42C22×D4124yes—
764C23—26no—
765C23—26no—
766C23—21no—
767C23—23no—
768C23—21no—
769C23—23no—
770C23—26no—
771C23—22no—
772C23—26no—
773C23—22no—
774C23—224no—
775C23—26no—
776C23—22no—
777C23—26no—
778C23—22no—
779C23—22no—
780C23—26no—
781C23—24no—
782C23—212no—
783C23—24no—
784C23—212no—
785C23—412no—
786C23—412no—
787C23—424no—
788C23—812no—
789C23—812no—
790C23—812no—
791C23—824no—
792C23—824no—
793C23—812no—
794C23C23×D412yes—
795C23C23×D416yes—
796C23C23×D416yes—
797C23C23×D416yes—
798C23C22×#4116yes—
799C23C2611yescharacteristic
800Q8—224no—
801Q8—412no—
802Q8—424no—
803Q8—44no—
804Q8C2×#121116yes—
805D4—248no—
806D4—224no—
807D4—48no—
808D4—424no—
809D4—424no—
810D4—424no—
811D4—412no—
812D4—424no—
813D4—44no—
814D4—824no—
815D4—812no—
816D4—812no—
817D4—824no—
818D4C2×#121148yes—
819C2×C4—23no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—23no—
823C2×C4—22no—
824C2×C4—26no—
825C2×C4—22no—
826C2×C4—26no—
827C2×C4—224no—
828C2×C4—28no—
829C2×C4—224no—
830C2×C4—224no—
831C2×C4—224no—
832C2×C4—26no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—26no—
837C2×C4—26no—
838C2×C4—26no—
839C2×C4—22no—
840C2×C4—26no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—26no—
844C2×C4—22no—
845C2×C4—26no—
846C2×C4—212no—
847C2×C4—212no—
848C2×C4—24no—
849C2×C4—26no—
850C2×C4—22no—
851C2×C4—24no—
852C2×C4—424no—
853C2×C4—424no—
854C2×C4—424no—
855C2×C4—424no—
856C2×C4—824no—
857C2×C4—812no—
858C2×C4—812no—
859C2×C4—812no—
860C2×C4C2×#121148yes—
861C2×C4C23×D4112yes—
862C2×C4C23×D414yes—
863C2×C4C23×D412yes—
864C2×C4C23×D416yes—
865C2×C4C23×D412yes—
866C2×C4C23×D416yes—
867C2×C4C23×D416yes—
868C2×C4C23×D412yes—
869C2×C4C22×#4116yes—
870C2×C4C22×#4112yes—
871C22—26no—
872C22—212no—
873C22—212no—
874C22—26no—
875C22—22no—
876C22—26no—
877C22—22no—
878C22—26no—
879C22—22no—
880C22—26no—
881C22—46no—
882C22—42no—
883C22—46no—
884C22—42no—
885C22—46no—
886C22—42no—
887C22—44no—
888C22—412no—
889C22—44no—
890C22—412no—
891C22—42no—
892C22—46no—
893C22—42no—
894C22—46no—
895C22—824no—
896C22—1624no—
897C22C22×#121112yes—
898C22C24×D411yescharacteristic
899C22C24×D411yescharacteristic
900C22C23×#4111yescharacteristic
901C22H(7,𝔽2)12yes—
902C222−1+612yes—
903C4—24no—
904C4—212no—
905C4—22no—
906C4—26no—
907C4—46no—
908C4—46no—
909C4—46no—
910C4—42no—
911C4—42no—
912C4—42no—
913C4—42no—
914C4—46no—
915C4C22×#12114yes—
916C4C22×#121112yes—
917C2—212no—
918C2—46no—
919C2—42no—
920C2—82no—
921C2—86no—
922C2C23×#12111yescharacteristic
923C2#6285211yescharacteristic
924C2#6285312yes—
925C2#6285712yes—
926C2#6285911yescharacteristic
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. C2×#3428C2semidirect
5. #35831C2semidirect
6. #35821C2semidirect
7. #35771C2semidirect
8. #35761C2semidirect
9. #35327C2semidirect
10. #35308C2semidirect
11. #35306C2semidirect
12. #35273C2semidirect
13. #35256C2semidirect
14. #35252C2semidirect
15. #34633C2semidirect
16. C2×#2620C2semidirect
17. #34259C2semidirect
18. #34258C2semidirect
19. #34183C2semidirect
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
51. C2×#520C22semidirect
52. C2×#520C22semidirect
53. C2×#519C22semidirect
54. C2×#518C22semidirect
57. C2×C4×#41C22semidirect
58. C2×C4×#41C22semidirect
59. C22×#117C22semidirect
60. C22×#117C22semidirect
61. #2857C22semidirect
62. #2856C22semidirect
63. #2850C22semidirect
64. #2850C22semidirect
65. #2621C22semidirect
66. #2621C22semidirect
67. #2620C22semidirect
68. #2620C22semidirect
69. #2620C22semidirect
70. #2620C22semidirect
71. #2620C22semidirect
72. #2620C22semidirect
73. #2620C22semidirect
74. #2620C22semidirect
75. #2620C22semidirect
76. #2619C22semidirect
77. #2619C22semidirect
78. #2618C22semidirect
79. #2617C22semidirect
80. #2545C22semidirect
81. #2544C22semidirect
82. #2538C22semidirect
83. #2537C22semidirect
84. #2534C22semidirect
85. #2429C22semidirect
86. #2428C22semidirect
87. #2427C22semidirect
88. #2426C22semidirect
89. #2425C22semidirect
90. #2424C22semidirect
91. #2417C22semidirect
92. #2416C22semidirect
93. #2416C22semidirect
94. #2415C22semidirect
95. #2414C22semidirect
96. #2413C22semidirect
97. #2412C22semidirect
98. #2411C22semidirect
99. #2410C22semidirect
100. #2392C22semidirect
101. #2392C22semidirect
102. C2×#396C22semidirect
103. C2×#394C22semidirect
104. Q8×C4⋊C4C22semidirect
105. D4×C4⋊C4C22semidirect
106. #2341C22semidirect
107. Q8×C22⋊C4C22semidirect
108. #2339C22semidirect
109. D4×C22⋊C4C22semidirect
110. #2317C22semidirect
111. #2317C22semidirect
112. #2311C22semidirect
113. #2311C22semidirect
114. #2310C22semidirect
115. #2309C22semidirect
116. #2297C22semidirect
117. #2297C22semidirect
118. C2×#391C22semidirect
119. C2×#390C22semidirect
120. #2285C22semidirect
121. C2×#384C22semidirect
130. C22×#41D4semidirect
220. C4×#41D4semidirect
467. C4×Q8C2×D4semidirect
480. C4×D4C2×D4semidirect
492. #117C2×D4semidirect
554. C2×C42C2×D4semidirect
593. #41#121semidirect

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
C2×#34282
#358312
#358212
#357712
#357612
#353272
#353082
#353062
#352732
#352562
#352522
#346332
C2×#26202
#342592
#342582
#341832