Finite Group Databasebeta

← #7686557

Subgroups — #7686557

Order 512.

5329 conjugacy classes of subgroups.

The subgroup lattice has 905 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59642C213yesmaximal, complemented
2#59454C216yesmaximal, complemented
3#59322C213yesmaximal, complemented
4#59314C213yesmaximal, complemented
5#45413C216yesmaximal, complemented
6#45086C216yesmaximal, complemented
7#39633C213yesmaximal, complemented
8#39609C213yesmaximal, complemented
9#38098C216yesmaximal, complemented
10#36577C211yesmaximal, characteristic, complemented
11#36561C213yesmaximal, complemented
12Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
13Q8×C22⋊Q8C212yesmaximal, complemented
14#36445C211yesmaximal, characteristic, complemented
15#36180C213yesmaximal, complemented
16#35868C212yesmaximal, complemented
17#35748C212yesmaximal, complemented
18#34772C213yesmaximal, complemented
19#34337C211yesmaximal, characteristic, complemented
20#34294C212yesmaximal
21#34183C211yesmaximal, characteristic, complemented
22C4×#548C211yesmaximal, characteristic
23C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
24C2×Q82C2212yes—
25C2×#557C2211yescharacteristic
26C2×#554C2216yes—
27C2×#548C2211yescharacteristic
28C2×#520C2212yes—
29C2×C4×#41C2211yescharacteristic
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2212yes—
32#2868C2213yes—
33#2857C2213yes—
34#2857C2213yes—
35#2857C2216yes—
36#2807C22112yes—
37#2792C22112yes—
38#2790C22112yes—
39#2774C22112yes—
40#2742C22112yes—
41#2729C22112yes—
42#2720C22112yes—
43#2647C2216yes—
44#2628C2216yes—
45#2589C22112yes—
46#2583C22112yes—
47#2582C2216yes—
48#2582C2213yes—
49#2580C2216yes—
50#2570C2216yes—
51#2568C2213yes—
52#2567C2216yes—
53#2567C2216yes—
54#2567C2216yes—
55#2564C22112yes—
56#2556C22112yes—
57#2552C2216yes—
58#2552C2216yes—
59#2551C2216yes—
60#2551C2213yes—
61#2551C2213yes—
62#2542C2216yes—
63#2542C2213yes—
64#2538C2213yes—
65#2522C2216yes—
66#2520C2216yes—
67#2511C2213yes—
68#2509C2216yes—
69#2507C2216yes—
70#2507C2213yes—
71#2506C2216yes—
72#2506C2216yes—
73#2505C2216yes—
74#2502C2213yes—
75#2502C2216yes—
76#2497C2213yes—
77#2492C2216yes—
78#2492C2213yes—
79#2487C2213yes—
80#2454C2216yes—
81#2453C2216yes—
82#2452C2216yes—
83#2452C2216yes—
84#2451C2216yes—
85#2451C2216yes—
86#2450C2216yes—
87#2449C22112yes—
88#2442C2216yes—
89#2441C2216yes—
90#2440C2216yes—
91#2440C2216yes—
92#2440C2216yes—
93#2440C2216yes—
94#2440C2216yes—
95#2440C2216yes—
96#2440C2216yes—
97#2440C2211yescharacteristic
98#2423C2216yes—
99#2417C2213yes—
100#2402C2216yes—
101#2396C2216yes—
102#2370C2216yes—
103#2367C2213yes—
104#2367C2216yes—
105#2365C2213yes—
106#2362C2213yes—
107#2361C2213yes—
108#2361C2216yes—
109#2360C2216yes—
110#2360C2216yes—
111#2352C2213yes—
112#2351C2211yescharacteristic
113#2351C2212yes—
114Q8×C4⋊C4C2212yes—
115Q8×C4⋊C4C2212yes—
116Q8×C4⋊C4C2212yes—
117Q8×C4⋊C4C2212yes—
118Q8×C4⋊C4C2216yes—
119Q8×C4⋊C4C2211yescharacteristic
120Q8×C4⋊C4C2212yes—
121Q8×C4⋊C4C2213yes—
122Q8×C4⋊C4C2211yescharacteristic
123Q8×C4⋊C4C2213yes—
124Q8×C4⋊C4C2213yes—
125Q8×C4⋊C4C2211yescharacteristic
126D4×C4⋊C4C2216yes—
127D4×C4⋊C4C2216yes—
128D4×C4⋊C4C2216yes—
129D4×C4⋊C4C2213yes—
130D4×C4⋊C4C2213yes—
131#2341C2212yes—
132#2341C2211yescharacteristic
133Q8×C22⋊C4C2211yescharacteristic
134Q8×C22⋊C4C2212yes—
135#2330C2216yes—
136#2326C2216yes—
137#2323C2216yes—
138#2317C2216yes—
139C4×C4⋊Q8C2213yes—
140C4×C4⋊Q8C2213yes—
141C4×#124C2213yes—
142C4×C22⋊Q8C2216yes—
143C4×C22⋊Q8C2213yes—
144C4×C22⋊Q8C2213yes—
145C4×C22⋊Q8C2213yes—
146C4×#121C2216yes—
147C4×#121C2213yes—
148#2295C2213yes—
149C2×#389C2216yes—
150#2290C2216yes—
151#2285C2213yes—
152C2×#384C2213yes—
153C2×#384C2213yes—
154#2276C2212yes—
155C42×Q8C2211yescharacteristic
156C42×D4C2213yes—
157C2×C4×C4⋊C4C2213yes—
158C22×#41C2311yescharacteristic
159C23×Q8C2311yescharacteristic
160Q82—48no—
161#557—28no—
162#554—424no—
163#548Q8116yescomplemented
164C2×C4⋊Q8C2311yescharacteristic
165C2×C4⋊Q8C2313yes—
166C2×C4⋊Q8C2316yes—
167C2×C4⋊Q8C2316yes—
168C2×C4⋊Q8C2316yes—
169C2×C4⋊Q8C2316yes—
170C2×C4⋊Q8C2316yes—
171C2×#125C2316yes—
172C2×#125C23112yes—
173C2×#124C2313yes—
174C2×C22⋊Q8C2313yes—
175C2×C22⋊Q8C2313yes—
176C2×C22⋊Q8C2312yes—
177C2×C22⋊Q8C23112yes—
178C2×C22⋊Q8C2316yes—
179C2×C22⋊Q8C23112yes—
180C2×C22⋊Q8C23112yes—
181C2×C22⋊Q8C2313yes—
182C2×#121C2313yes—
183#520—48no—
184C4×#41—28no—
185C2×C4×Q8—28no—
186C2×C4×Q8—48no—
187C2×C4×Q8C2313yes—
188C2×C4×Q8C2313yes—
189C2×C4×Q8C2312yes—
190C2×C4×Q8C2311yescharacteristic
191C2×C4×Q8C2311yescharacteristic
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2311yescharacteristic
195C2×C4×Q8C2312yes—
196C2×C4×Q8C2313yes—
197C2×C4×Q8C2316yes—
198C2×C4×Q8C2316yes—
199C2×C4×Q8C2316yes—
200C2×C4×Q8C2316yes—
201C2×C4×Q8C2311yescharacteristic
202C2×C4×Q8C2311yescharacteristic
203C2×C4×D4C2313yes—
204C2×C4×D4C2313yes—
205C2×C4×D4C2313yes—
206C2×C4×D4C2313yes—
207C2×C4×D4C23112yes—
208C2×C4×D4C2316yes—
209C2×C4×D4C2316yes—
210C2×C4×D4C2313yes—
211C2×#117C2313yes—
212C2×#117C2316yes—
213C22×C4⋊C4C2313yes—
214C22×C4⋊C4C2311yescharacteristic
215C22×C4⋊C4C2313yes—
216C22×C4⋊C4C2316yes—
217C22×C4⋊C4C2316yes—
218C22×C4⋊C4C2316yes—
219C22×C4⋊C4C2316yes—
220C22×C4⋊C4C2316yes—
221C22×C42C2313yes—
222C22×C42C2313yes—
223C22×C42C2316yes—
224#400C23112yes—
225#400C23112yes—
226#400C2316yes—
227#400C2316yes—
228#400C2316yes—
229#400C2316yes—
230#400C2316yes—
231#399C23112yes—
232#399C23112yes—
233#399C2316yes—
234#398C23112yes—
235#398C23112yes—
236#398C23112yes—
237#398C23112yes—
238#398C2316yes—
239#398C23112yes—
240#398C2316yes—
241#398C2316yes—
242#398C2312yes—
243#398C2316yes—
244#398C2316yes—
245#396C2316yes—
246#396C2316yes—
247#396C23112yes—
248#395C23112yes—
249#395C23112yes—
250#395C23112yes—
251#395C23112yes—
252#395C23112yes—
253#395C2312yes—
254#393C23112yes—
255#393C2316yes—
256#391C2313yes—
257#391C2316yes—
258#391C2313yes—
259#391C2313yes—
260#391C2316yes—
261#391C2316yes—
262#391C2313yes—
263#391C2316yes—
264#391C2316yes—
265#391C2313yes—
266#391C23112yes—
267#391C2313yes—
268#390C2313yes—
269#390C2316yes—
270#390C2316yes—
271#390C2313yes—
272#389C2316yes—
273#389C2316yes—
274#389C2313yes—
275#389C2313yes—
276#389C2316yes—
277#389C2316yes—
278#389C2316yes—
279#389C23112yes—
280#389C2316yes—
281#389C23112yes—
282#389C23112yes—
283#389C2316yes—
284#389C2316yes—
285#389C2316yes—
286#389C2316yes—
287#389C2316yes—
288#389C2316yes—
289#389C2313yes—
290#389C2316yes—
291#389C23112yes—
292#389C23112yes—
293#389C2316yes—
294#389C2316yes—
295#389C2316yes—
296#389C2316yes—
297#389C2316yes—
298#389C2316yes—
299#389C2313yes—
300#389C23112yes—
301#389C2316yes—
302#389C2313yes—
303#389C2313yes—
304#389C2311yescharacteristic
305#389C2311yescharacteristic
306#388C23112yes—
307#388C23112yes—
308#388C2316yes—
309#388C2316yes—
310#388C2316yes—
311#388C2316yes—
312#388C2316yes—
313#387C23112yes—
314#387C23112yes—
315#387C23112yes—
316#387C2316yes—
317#387C2316yes—
318#387C2316yes—
319#387C2316yes—
320#387C2316yes—
321#387C2316yes—
322#387C2316yes—
323#387C2316yes—
324#387C2316yes—
325#386C2316yes—
326#386C2316yes—
327#386C2316yes—
328#385C23112yes—
329#385C23112yes—
330#385C23112yes—
331#385C23112yes—
332#385C23112yes—
333#385C23112yes—
334#385C2316yes—
335#385C2316yes—
336#385C2316yes—
337#385C2316yes—
338#385C2316yes—
339#385C2312yes—
340#385C2316yes—
341#384C2313yes—
342#384C2313yes—
343#384C2316yes—
344#384C2313yes—
345#384C2316yes—
346#384C2316yes—
347#384C2316yes—
348#384C2316yes—
349#384C2316yes—
350#384C2316yes—
351#384C2313yes—
352#384C2313yes—
353#384C2316yes—
354#384C2316yes—
355#384C2311yescharacteristic
356#382C2316yes—
357#382C2313yes—
358#382C2316yes—
359#380C2316yes—
360#380C2316yes—
361#380C2316yes—
362#380C2316yes—
363#380C2313yes—
364#380C2313yes—
365#380C2316yes—
366#380C2313yes—
367#380C2313yes—
368#380C2316yes—
369#380C2313yes—
370#380C2311yescharacteristic
371C4×C4⋊C4C2313yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2316yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2313yes—
377C4×C4⋊C4C2313yes—
378C4×C4⋊C4C2316yes—
379C4×C4⋊C4C2316yes—
380C4×C4⋊C4C2313yes—
381C4×C4⋊C4C2313yes—
382C4×C4⋊C4C2316yes—
383C4×C4⋊C4C2313yes—
384C4×C4⋊C4C2316yes—
385C4×C4⋊C4C2313yes—
386C4×C4⋊C4C2316yes—
387C4×C4⋊C4C2316yes—
388C4×C4⋊C4C2313yes—
389C4×C4⋊C4C2316yes—
390C4×C4⋊C4C2313yes—
391C4×C4⋊C4C2316yes—
392C4×C4⋊C4C2313yes—
393C4×C22⋊C4C23112yes—
394C4×C22⋊C4C2313yes—
395C4×C22⋊C4C2316yes—
396C4×C22⋊C4C2316yes—
397C4×C22⋊C4C2313yes—
398C4×C22⋊C4C2313yes—
399C4×C22⋊C4C2316yes—
400C4×C22⋊C4C2313yes—
401C4×C22⋊C4C2311yescharacteristic
402C4×C22⋊C4C2313yes—
403#376C2316yes—
404C2×#95C2316yes—
405C43C2313yes—
406C2×#41—24no—
407C2×#41—24no—
408C2×#41C2×Q818yes—
409C22×Q8—24no—
410C22×Q8—24no—
411C22×Q8C2×Q818yes—
412C22×Q8C2413yes—
413C22×Q8C2412yes—
414C22×Q8C2413yes—
415C22×Q8C24112yes—
416C22×Q8C2411yescharacteristic
417C22×D4C2413yes—
418C22×D4C2413yes—
419C23×C4C2413yes—
420C23×C4C2413yes—
421C23×C4C2413yes—
422C23×C4C2412yes—
423C23×C4C2413yes—
424C23×C4C2413yes—
425C23×C4C2411yescharacteristic
426C23×C4C2416yes—
427C23×C4C24112yes—
428C4⋊Q8—24no—
429C4⋊Q8—212no—
430C4⋊Q8—412no—
431C4⋊Q8—412no—
432C4⋊Q8—412no—
433C4⋊Q8—412no—
434C4⋊Q8—86no—
435#125—224no—
436#125—424no—
437#124C2×Q8124yes—
438C22⋊Q8—212no—
439C22⋊Q8—212no—
440C22⋊Q8—28no—
441C22⋊Q8—424no—
442C22⋊Q8—424no—
443C22⋊Q8—412no—
444C22⋊Q8—812no—
445C22⋊Q8C2×Q8124yes—
446#121C2×Q8124yes—
447C4×Q8—24no—
448C4×Q8—24no—
449C4×Q8—28no—
450C4×Q8—28no—
451C4×Q8—28no—
452C4×Q8—28no—
453C4×Q8—24no—
454C4×Q8—212no—
455C4×Q8—212no—
456C4×Q8—212no—
457C4×Q8—412no—
458C4×Q8—412no—
459C4×Q8—412no—
460C4×Q8—412no—
461C4×Q8C2×Q818yes—
462C4×Q8#4118yes—
463C4×D4—212no—
464C4×D4—212no—
465C4×D4—212no—
466C4×D4—212no—
467C4×D4—412no—
468C4×D4—412no—
469C4×D4—424no—
470C4×D4C2×Q8124yes—
471#117—212no—
472#117—412no—
473C2×C4⋊C4—212no—
474C2×C4⋊C4—212no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—412no—
477C2×C4⋊C4—412no—
478C2×C4⋊C4—412no—
479C2×C4⋊C4—86no—
480C2×C4⋊C4—86no—
481C2×C4⋊C4C2413yes—
482C2×C4⋊C4C2416yes—
483C2×C4⋊C4C2413yes—
484C2×C4⋊C4C2416yes—
485C2×C4⋊C4C2416yes—
486C2×C4⋊C4C2413yes—
487C2×C4⋊C4C2416yes—
488C2×C4⋊C4C2416yes—
489C2×C4⋊C4C2413yes—
490C2×C4⋊C4C2411yescharacteristic
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2413yes—
493C2×C4⋊C4C2413yes—
494C2×C4⋊C4C2413yes—
495C2×C4⋊C4C2411yescharacteristic
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C2416yes—
498C2×C4⋊C4C2413yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C2412yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2412yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C2416yes—
505C2×C4⋊C4C2411yescharacteristic
506C2×C4⋊C4C2412yes—
507C2×C4⋊C4C2416yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2416yes—
510C2×C4⋊C4C24112yes—
511C2×C4⋊C4C24112yes—
512C2×C4⋊C4C24112yes—
513C2×C4⋊C4C2416yes—
514C2×C4⋊C4C2416yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C24112yes—
517C2×C4⋊C4C24112yes—
518C2×C4⋊C4C2416yes—
519C2×C4⋊C4C2416yes—
520C2×C4⋊C4C2416yes—
521C2×C4⋊C4C24112yes—
522C2×C4⋊C4C2416yes—
523C2×C4⋊C4C2416yes—
524C2×C4⋊C4C2416yes—
525C2×C4⋊C4C2413yes—
526C2×C4⋊C4C2413yes—
527C2×C4⋊C4C2413yes—
528C2×C4⋊C4C2411yescharacteristic
529C2×C22⋊C4C2416yes—
530C2×C22⋊C4C2416yes—
531C2×C22⋊C4C2413yes—
532C2×C22⋊C4C2413yes—
533C2×C22⋊C4C2413yes—
534C2×C22⋊C4C2412yes—
535C2×C22⋊C4C2416yes—
536C2×C22⋊C4C2416yes—
537C2×C22⋊C4C2416yes—
538C2×C22⋊C4C24112yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2416yes—
541C2×C22⋊C4C2411yescharacteristic
542C2×C22⋊C4C2413yes—
543C2×C22⋊C4C2416yes—
544C2×C22⋊C4C2411yescharacteristic
545C2×C42—212no—
546C2×C42—212no—
547C2×C42—412no—
548C2×C42C2413yes—
549C2×C42C2416yes—
550C2×C42C2416yes—
551C2×C42C2413yes—
552C2×C42C2413yes—
553C2×C42C2413yes—
554C2×C42C2413yes—
555C2×C42C2416yes—
556C2×C42C2416yes—
557C2×C42C2413yes—
558C2×C42C2413yes—
559C2×C42C2413yes—
560C2×C42C2411yescharacteristic
561C2×C42C2411yescharacteristic
562C2×C42C24112yes—
563C2×C42C2416yes—
564C2×C42C2416yes—
565C2×C42C2413yes—
566C2×C42C2413yes—
567C2×C42C2413yes—
568#95C2416yes—
569#95C2416yes—
570#95C2416yes—
571#95C2416yes—
572#95C2412yes—
573#95C2416yes—
574#95C2416yes—
575#95C2416yes—
576#95C2411yescharacteristic
577#95C2411yescharacteristic
578#95C2412yes—
579#95C2413yes—
580#95C2413yes—
581#95C2413yes—
582#95C2416yes—
583#95C2413yes—
584#95C2416yes—
585#95C24112yes—
586#95C2416yes—
587#95C2416yes—
588#95C2416yes—
589#95C2416yes—
590#95C2412yes—
591#95C2416yes—
592#95C2416yes—
593#95C2416yes—
594#95C2416yes—
595#95C2416yes—
596#95C2416yes—
597#95C2416yes—
598#95C2416yes—
599#95C2416yes—
600#95C2416yes—
601#95C24112yes—
602C24C2513yes—
603C24C2511yescharacteristic
604#41—232no—
605C2×Q8—232no—
606C2×Q8—26no—
607C2×Q8—26no—
608C2×Q8—26no—
609C2×Q8—26no—
610C2×Q8—24no—
611C2×Q8—26no—
612C2×Q8—24no—
613C2×Q8—42no—
614C2×Q8—412no—
615C2×Q8—412no—
616C2×Q8—412no—
617C2×Q8C22×Q8112yes—
618C2×Q8C22×Q814yes—
619C2×Q8C2×#4114yes—
620C2×Q8H(5,𝔽2)14yes—
621C2×D4—26no—
622C2×D4—26no—
623C2×D4—26no—
624C2×D4—26no—
625C2×D4C22×Q8112yes—
626C2×D4C22×Q8112yes—
627C22×C4—22no—
628C22×C4—26no—
629C22×C4—26no—
630C22×C4—26no—
631C22×C4—26no—
632C22×C4—22no—
633C22×C4—26no—
634C22×C4—24no—
635C22×C4—212no—
636C22×C4—26no—
637C22×C4—26no—
638C22×C4—26no—
639C22×C4—26no—
640C22×C4—24no—
641C22×C4—26no—
642C22×C4—26no—
643C22×C4—42no—
644C22×C4—43no—
645C22×C4—43no—
646C22×C4—46no—
647C22×C4—46no—
648C22×C4—412no—
649C22×C4—412no—
650C22×C4—412no—
651C22×C4C22×Q8112yes—
652C22×C4C22×Q8112yes—
653C22×C4H(5,𝔽2)14yes—
654C22×C4C2512yes—
655C22×C4C2512yes—
656C22×C4C2513yes—
657C22×C4C2512yes—
658C22×C4C2516yes—
659C22×C4C2513yes—
660C22×C4C2513yes—
661C22×C4C2516yes—
662C22×C4C2516yes—
663C22×C4C2516yes—
664C22×C4C2511yescharacteristic
665C22×C4C2513yes—
666C22×C4C2513yes—
667C22×C4C2511yescharacteristic
668C22×C4C2513yes—
669C22×C4C2511yescharacteristic
670C22×C4C2511yescharacteristic
671C22×C4C2512yes—
672C22×C4C2511yescharacteristic
673C22×C4C2513yes—
674C22×C4C2511yescharacteristic
675C4⋊C4—212no—
676C4⋊C4—26no—
677C4⋊C4—26no—
678C4⋊C4—22no—
679C4⋊C4—212no—
680C4⋊C4—212no—
681C4⋊C4—212no—
682C4⋊C4—26no—
683C4⋊C4—212no—
684C4⋊C4—26no—
685C4⋊C4—212no—
686C4⋊C4—26no—
687C4⋊C4—212no—
688C4⋊C4—212no—
689C4⋊C4—26no—
690C4⋊C4—26no—
691C4⋊C4—212no—
692C4⋊C4—24no—
693C4⋊C4—22no—
694C4⋊C4—26no—
695C4⋊C4—24no—
696C4⋊C4—24no—
697C4⋊C4—212no—
698C4⋊C4—24no—
699C4⋊C4—24no—
700C4⋊C4—22no—
701C4⋊C4—46no—
702C4⋊C4—412no—
703C4⋊C4—412no—
704C4⋊C4—46no—
705C4⋊C4—46no—
706C4⋊C4—412no—
707C4⋊C4—46no—
708C4⋊C4—46no—
709C4⋊C4—42no—
710C4⋊C4—412no—
711C4⋊C4—412no—
712C4⋊C4—46no—
713C4⋊C4—46no—
714C4⋊C4—46no—
715C4⋊C4—412no—
716C4⋊C4—46no—
717C4⋊C4—46no—
718C4⋊C4—46no—
719C4⋊C4C22×Q8112yes—
720C4⋊C4C22×Q8112yes—
721C4⋊C4C2×#41112yes—
722C4⋊C42−1+414yes—
723C22⋊C4—26no—
724C22⋊C4—212no—
725C22⋊C4—24no—
726C22⋊C4—212no—
727C22⋊C4—26no—
728C22⋊C4—26no—
729C22⋊C4—212no—
730C22⋊C4—46no—
731C22⋊C4—46no—
732C22⋊C4—412no—
733C22⋊C4—46no—
734C22⋊C4—46no—
735C22⋊C4C22×Q814yes—
736C22⋊C4C22×Q8112yes—
737C22⋊C4C22×Q8124yes—
738C22⋊C42−1+414yes—
739C42—22no—
740C42—26no—
741C42—26no—
742C42—26no—
743C42—26no—
744C42—26no—
745C42—212no—
746C42—212no—
747C42—212no—
748C42—212no—
749C42—26no—
750C42—26no—
751C42—26no—
752C42—22no—
753C42—46no—
754C42—46no—
755C42—412no—
756C42—43no—
757C42C22×Q8112yes—
758C42C2×#41112yes—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—23no—
764C23—23no—
765C23—23no—
766C23—23no—
767C23—23no—
768C23—23no—
769C23C23×Q816yes—
770C23C23×Q812yes—
771C23C2×H(5,𝔽2)12yes—
772C23C2×2−1+412yes—
773C23C2611yescharacteristic
774Q8—224no—
775Q8—48no—
776Q8—412no—
777Q8—1612no—
778Q8#554116yescomplemented
779D4—224no—
780D4—224no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—23no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—23no—
788C2×C4—23no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—23no—
792C2×C4—23no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—23no—
798C2×C4—21no—
799C2×C4—224no—
800C2×C4—224no—
801C2×C4—28no—
802C2×C4—22no—
803C2×C4—23no—
804C2×C4—23no—
805C2×C4—26no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—26no—
809C2×C4—26no—
810C2×C4—23no—
811C2×C4—26no—
812C2×C4—23no—
813C2×C4—26no—
814C2×C4—26no—
815C2×C4—26no—
816C2×C4—23no—
817C2×C4—26no—
818C2×C4—22no—
819C2×C4—23no—
820C2×C4—22no—
821C2×C4—26no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—23no—
825C2×C4—22no—
826C2×C4—23no—
827C2×C4—22no—
828C2×C4—23no—
829C2×C4—26no—
830C2×C4—26no—
831C2×C4—26no—
832C2×C4—412no—
833C2×C4—412no—
834C2×C4—48no—
835C2×C4—412no—
836C2×C4—812no—
837C2×C4—1612no—
838C2×C4C23×Q812yes—
839C2×C4C23×Q816yes—
840C2×C4C23×Q816yes—
841C2×C4C23×Q812yes—
842C2×C4C23×Q816yes—
843C2×C4C22×#4116yes—
844C2×C4C22×#4116yes—
845C2×C4C22×#4112yes—
846C2×C4C2×H(5,𝔽2)12yes—
847C2×C4C2×H(5,𝔽2)16yes—
848C2×C4C2×H(5,𝔽2)12yes—
849C2×C4C2×2−1+412yes—
850C2×C4C2×2−1+414yes—
851C2×C4C2×2−1+412yes—
852C2×C4C2×2−1+412yes—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—26no—
860C22—26no—
861C22—26no—
862C22—43no—
863C22—43no—
864C22—43no—
865C22—43no—
866C22#350314yes—
867C22C24×Q811yescharacteristic
868C22C23×#4111yescharacteristic
869C22C22×H(5,𝔽2)11yescharacteristic
870C22C22×H(5,𝔽2)11yescharacteristic
871C22C22×2−1+411yescharacteristic
872C22C22×2−1+411yescharacteristic
873C22H(7,𝔽2)11yescharacteristic
874C4—22no—
875C4—22no—
876C4—26no—
877C4—24no—
878C4—22no—
879C4—22no—
880C4—26no—
881C4—22no—
882C4—26no—
883C4—42no—
884C4—43no—
885C4—42no—
886C4—42no—
887C4—43no—
888C4—46no—
889C4—46no—
890C4—46no—
891C4—46no—
892C4—43no—
893C4C2×#554112yes—
894C4#352214yes—
895C2—24no—
896C2—46no—
897C2C22×#55411yescharacteristic
898C2C2×#352211yescharacteristic
899C2C2×#350311yescharacteristic
900C2#6291611yescharacteristic
901C2Q8×2−1+411yescharacteristic
902C2#6300011yescharacteristic
903C2#6301611yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59642C2semidirect
2. #59454C2semidirect
3. #59322C2semidirect
4. #59314C2semidirect
5. #45413C2semidirect
6. #45086C2semidirect
7. #39633C2semidirect
8. #39609C2semidirect
9. #38098C2semidirect
10. #36577C2semidirect
11. #36561C2semidirect
12. Q8×C4⋊Q8C2semidirect
13. Q8×C22⋊Q8C2semidirect
14. #36445C2semidirect
15. #36180C2semidirect
16. #35868C2semidirect
17. #35748C2semidirect
18. #34772C2semidirect
19. #34337C2semidirect
21. #34183C2semidirect
23. C2×Q8×C4⋊C4C2semidirect
163. #548Q8semidirect
778. Q8#554semidirect

Maximal subgroups

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

subgroupindex
#596422
#594542
#593222
#593142
#454132
#450862
#396332
#396092
#380982
#365772
#365612
Q8×C4⋊Q82
Q8×C22⋊Q82
#364452
#361802
#358682
#357482
#347722
#343372
#342942
#341832
C4×#5482
C2×Q8×C4⋊C42