Finite Group Databasebeta

← #7699800

Subgroups — #7699800

Order 512.

5359 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59920C216yesmaximal, complemented
2#59461C216yesmaximal, complemented
3#59455C216yesmaximal, complemented
4#59429C213yesmaximal, complemented
5#59314C213yesmaximal, complemented
6#59259C213yesmaximal, complemented
7#36564C213yesmaximal, complemented
8#36555C213yesmaximal, complemented
9#36551C213yesmaximal, complemented
10Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
11#36475C212yesmaximal, complemented
12#36466C211yesmaximal, characteristic, complemented
13#36456C211yesmaximal, characteristic, complemented
14#36445C212yesmaximal, complemented
15#36435C212yesmaximal, complemented
16#36363C216yesmaximal, complemented
17#36189C213yesmaximal, complemented
18C4×Q82C211yesmaximal, characteristic, complemented
19C4×#554C213yesmaximal, complemented
20C4×#548C211yesmaximal, characteristic
21C4×#548C212yesmaximal
22C4⋊C4×#41C211yesmaximal, characteristic, complemented
23C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
24C2×Q82C2211yescharacteristic
25C2×#557C2212yes—
26C2×#554C2213yes—
27C2×#548C2211yescharacteristic
28C2×C4×#41C2211yescharacteristic
29C2×C4×#41C2212yes—
30C22×C4×Q8C2211yescharacteristic
31C22×C4×Q8C2212yes—
32#2864C2216yes—
33#2859C2213yes—
34#2857C2216yes—
35#2857C2213yes—
36#2857C2213yes—
37#2851C2216yes—
38#2788C22112yes—
39#2768C22112yes—
40#2720C22112yes—
41#2589C22112yes—
42#2587C22112yes—
43#2586C22112yes—
44#2585C22112yes—
45#2584C2216yes—
46#2582C2213yes—
47#2581C2216yes—
48#2570C2216yes—
49#2570C2216yes—
50#2567C2213yes—
51#2565C2216yes—
52#2563C2213yes—
53#2552C2213yes—
54#2551C2213yes—
55#2550C2216yes—
56#2549C22112yes—
57#2542C2216yes—
58#2538C2216yes—
59#2538C2213yes—
60#2522C22112yes—
61#2511C2216yes—
62#2509C2216yes—
63#2508C2216yes—
64#2507C2216yes—
65#2507C2216yes—
66#2506C2216yes—
67#2497C2216yes—
68#2497C2216yes—
69#2487C2216yes—
70#2465C22112yes—
71#2454C2216yes—
72#2454C2216yes—
73#2453C2216yes—
74#2452C2216yes—
75#2451C2216yes—
76#2451C2216yes—
77#2450C22112yes—
78#2449C22112yes—
79#2442C2216yes—
80#2441C2216yes—
81#2441C2216yes—
82#2440C2216yes—
83#2440C2216yes—
84#2440C2216yes—
85#2439C2216yes—
86#2423C2216yes—
87#2423C2216yes—
88#2417C2216yes—
89#2370C2216yes—
90#2369C2216yes—
91#2369C2213yes—
92#2369C2213yes—
93#2368C2216yes—
94#2368C2216yes—
95#2367C2216yes—
96#2367C2213yes—
97#2362C2213yes—
98#2362C2216yes—
99#2361C2213yes—
100#2361C2216yes—
101#2360C2216yes—
102#2360C2211yescharacteristic
103#2360C2213yes—
104#2355C2213yes—
105#2352C2213yes—
106#2352C2216yes—
107#2351C2212yes—
108#2351C2212yes—
109#2351C2212yes—
110#2351C2211yescharacteristic
111Q8×C4⋊C4C2216yes—
112Q8×C4⋊C4C2213yes—
113Q8×C4⋊C4C2211yescharacteristic
114Q8×C4⋊C4C2212yes—
115Q8×C4⋊C4C2211yescharacteristic
116Q8×C4⋊C4C2213yes—
117Q8×C4⋊C4C2211yescharacteristic
118Q8×C4⋊C4C2212yes—
119Q8×C4⋊C4C2212yes—
120Q8×C4⋊C4C2213yes—
121#2349C2216yes—
122#2349C2216yes—
123D4×C4⋊C4C2213yes—
124D4×C4⋊C4C2213yes—
125D4×C4⋊C4C2213yes—
126#2345C2213yes—
127#2345C2213yes—
128#2345C2216yes—
129#2341C2211yescharacteristic
130#2341C2212yes—
131Q8×C22⋊C4C2211yescharacteristic
132Q8×C22⋊C4C2212yes—
133C4×C4⋊Q8C2216yes—
134C4×C4⋊Q8C2213yes—
135C4×C4⋊Q8C2213yes—
136C4×#125C2216yes—
137C4×#124C2213yes—
138C4×#124C2216yes—
139C4×C22⋊Q8C2216yes—
140C4×C22⋊Q8C2216yes—
141C4×C22⋊Q8C2216yes—
142C4×C22⋊Q8C2213yes—
143C4×C22⋊Q8C2213yes—
144C4×C22⋊Q8C2213yes—
145C4×#121C2216yes—
146C4×#121C2213yes—
147#2296C2216yes—
148C2×#389C2216yes—
149#2285C2213yes—
150C2×#384C2213yes—
151C42×Q8C2211yescharacteristic
152C42×Q8C2212yes—
153C42×Q8C2213yes—
154C42×D4C2216yes—
155C42×D4C2213yes—
156C2×C4×C4⋊C4C2213yes—
157C2×C4×C4⋊C4C2213yes—
158C22×#41C2311yescharacteristic
159C23×Q8C2311yescharacteristic
160Q82—28no—
161#557—48no—
162#554—224no—
163#548Q8116yescomplemented
164C2×C4⋊Q8C2313yes—
165C2×C4⋊Q8C2316yes—
166C2×C4⋊Q8C2313yes—
167C2×C4⋊Q8C2316yes—
168C2×#125C2316yes—
169C2×#125C2316yes—
170C2×#125C2316yes—
171C2×#124C2313yes—
172C2×C22⋊Q8C2313yes—
173C2×C22⋊Q8C2316yes—
174C2×C22⋊Q8C2316yes—
175C2×C22⋊Q8C2316yes—
176C2×C22⋊Q8C2316yes—
177C2×C22⋊Q8C23112yes—
178C2×C22⋊Q8C2313yes—
179C2×C22⋊Q8C2311yescharacteristic
180C2×#121C2313yes—
181C4×#41—28no—
182C4×#41—48no—
183C2×C4×Q8—28no—
184C2×C4×Q8—48no—
185C2×C4×Q8C2313yes—
186C2×C4×Q8C2313yes—
187C2×C4×Q8C2312yes—
188C2×C4×Q8C2311yescharacteristic
189C2×C4×Q8C2312yes—
190C2×C4×Q8C2311yescharacteristic
191C2×C4×Q8C2311yescharacteristic
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2312yes—
194C2×C4×Q8C2313yes—
195C2×C4×Q8C2313yes—
196C2×C4×Q8C2311yescharacteristic
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×D4C2316yes—
207C2×C4×D4C2316yes—
208C2×C4×D4C2316yes—
209C2×C4×D4C2316yes—
210C2×C4×D4C2313yes—
211C2×C4×D4C2313yes—
212C2×#117C2313yes—
213C2×#117C2316yes—
214C22×C4⋊C4C2313yes—
215C22×C4⋊C4C2313yes—
216C22×C4⋊C4C2313yes—
217C22×C4⋊C4C2311yescharacteristic
218C22×C4⋊C4C2313yes—
219C22×C4⋊C4C2316yes—
220C22×C4⋊C4C2316yes—
221C22×C42C2313yes—
222C22×C42C2313yes—
223C22×C42C2316yes—
224C22×C42C2316yes—
225#400C23112yes—
226#400C23112yes—
227#400C23112yes—
228#399C23112yes—
229#399C23112yes—
230#398C23112yes—
231#398C23112yes—
232#398C23112yes—
233#398C23112yes—
234#398C23112yes—
235#398C23112yes—
236#396C23112yes—
237#396C23112yes—
238#396C23112yes—
239#395C23112yes—
240#395C23112yes—
241#395C23112yes—
242#393C23112yes—
243#391C23112yes—
244#391C2316yes—
245#391C2316yes—
246#391C2313yes—
247#391C2316yes—
248#391C2316yes—
249#391C2313yes—
250#391C2313yes—
251#391C2316yes—
252#391C2316yes—
253#391C2316yes—
254#391C2311yescharacteristic
255#391C2316yes—
256#390C2316yes—
257#390C2316yes—
258#390C2313yes—
259#390C2313yes—
260#389C2316yes—
261#389C2316yes—
262#389C2311yescharacteristic
263#389C2316yes—
264#389C2316yes—
265#389C23112yes—
266#389C2316yes—
267#389C2313yes—
268#389C2316yes—
269#389C2316yes—
270#389C2313yes—
271#389C2316yes—
272#389C2316yes—
273#389C2316yes—
274#389C2316yes—
275#389C2316yes—
276#389C2316yes—
277#389C2316yes—
278#389C2316yes—
279#389C2316yes—
280#389C2316yes—
281#389C2316yes—
282#389C23112yes—
283#389C23112yes—
284#389C23112yes—
285#389C2316yes—
286#389C2316yes—
287#389C2313yes—
288#389C2316yes—
289#389C2316yes—
290#389C2316yes—
291#389C2316yes—
292#389C2313yes—
293#389C2313yes—
294#389C2312yes—
295#388C2316yes—
296#388C23112yes—
297#388C2316yes—
298#388C23112yes—
299#388C23112yes—
300#388C2316yes—
301#387C2312yes—
302#387C2316yes—
303#387C2316yes—
304#387C2316yes—
305#387C2316yes—
306#387C23112yes—
307#387C23112yes—
308#387C2316yes—
309#387C2316yes—
310#387C2316yes—
311#387C2316yes—
312#387C23112yes—
313#387C23112yes—
314#387C23112yes—
315#387C23112yes—
316#387C2316yes—
317#387C2316yes—
318#386C23112yes—
319#386C2316yes—
320#385C2316yes—
321#385C23112yes—
322#385C2316yes—
323#385C2316yes—
324#385C23112yes—
325#385C23112yes—
326#385C2312yes—
327#385C2316yes—
328#385C2316yes—
329#385C23112yes—
330#385C2316yes—
331#384C2316yes—
332#384C2313yes—
333#384C2313yes—
334#384C2316yes—
335#384C2316yes—
336#384C2313yes—
337#384C2313yes—
338#384C2316yes—
339#384C2316yes—
340#382C2316yes—
341#382C2316yes—
342#382C2316yes—
343#382C2313yes—
344#382C2316yes—
345#380C2313yes—
346#380C2316yes—
347#380C2313yes—
348#380C2316yes—
349#380C2316yes—
350#380C2313yes—
351#380C2313yes—
352#380C23112yes—
353#380C2316yes—
354#380C2316yes—
355#380C2316yes—
356#380C2316yes—
357C4×C4⋊C4C2313yes—
358C4×C4⋊C4C2316yes—
359C4×C4⋊C4C2316yes—
360C4×C4⋊C4C2316yes—
361C4×C4⋊C4C2316yes—
362C4×C4⋊C4C2316yes—
363C4×C4⋊C4C2316yes—
364C4×C4⋊C4C2313yes—
365C4×C4⋊C4C2313yes—
366C4×C4⋊C4C2316yes—
367C4×C4⋊C4C2313yes—
368C4×C4⋊C4C2313yes—
369C4×C4⋊C4C2313yes—
370C4×C4⋊C4C2316yes—
371C4×C4⋊C4C2316yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2316yes—
375C4×C4⋊C4C2316yes—
376C4×C4⋊C4C2313yes—
377C4×C4⋊C4C2313yes—
378C4×C4⋊C4C2313yes—
379C4×C4⋊C4C2313yes—
380C4×C4⋊C4C2313yes—
381C4×C4⋊C4C2316yes—
382C4×C4⋊C4C2316yes—
383C4×C4⋊C4C2313yes—
384C4×C4⋊C4C2313yes—
385C4×C4⋊C4C2311yescharacteristic
386C4×C4⋊C4C2313yes—
387C4×C4⋊C4C2316yes—
388C4×C22⋊C4C23112yes—
389C4×C22⋊C4C2316yes—
390C4×C22⋊C4C2313yes—
391C4×C22⋊C4C2316yes—
392C4×C22⋊C4C2313yes—
393C4×C22⋊C4C2311yescharacteristic
394C4×C22⋊C4C2316yes—
395C4×C22⋊C4C2313yes—
396C4×C22⋊C4C2316yes—
397C4×C22⋊C4C2316yes—
398C4×C22⋊C4C2313yes—
399C4×C22⋊C4C2312yes—
400C4×C22⋊C4C2316yes—
401C4×C22⋊C4C2313yes—
402C2×#95C2316yes—
403C2×#95C2316yes—
404C43C2316yes—
405C43C2313yes—
406C2×#41—24no—
407C2×#41—24no—
408C2×#41C2×Q818yes—
409C22×Q8—24no—
410C22×Q8—24no—
411C22×Q8C2×Q818yes—
412C22×Q8C2413yes—
413C22×Q8C2411yescharacteristic
414C22×Q8C2416yes—
415C22×Q8C2416yes—
416C22×Q8C2411yescharacteristic
417C22×D4C2413yes—
418C22×D4C2413yes—
419C23×C4C2413yes—
420C23×C4C2413yes—
421C23×C4C2412yes—
422C23×C4C2413yes—
423C23×C4C2413yes—
424C23×C4C2411yescharacteristic
425C23×C4C2416yes—
426C23×C4C2416yes—
427C23×C4C2416yes—
428C23×C4C2413yes—
429C4⋊Q8—212no—
430C4⋊Q8—224no—
431C4⋊Q8—212no—
432C4⋊Q8—412no—
433#125—224no—
434#125—412no—
435#125—412no—
436#124C2×Q8124yes—
437C22⋊Q8—212no—
438C22⋊Q8—224no—
439C22⋊Q8—224no—
440C22⋊Q8—412no—
441C22⋊Q8—812no—
442C22⋊Q8—86no—
443C22⋊Q8C2×Q8124yes—
444C22⋊Q8#4118yescomplemented
445#121C2×Q8124yes—
446C4×Q8—24no—
447C4×Q8—24no—
448C4×Q8—212no—
449C4×Q8—28no—
450C4×Q8—28no—
451C4×Q8—28no—
452C4×Q8—28no—
453C4×Q8—24no—
454C4×Q8—212no—
455C4×Q8—24no—
456C4×Q8—212no—
457C4×Q8—212no—
458C4×Q8—412no—
459C4×Q8—412no—
460C4×Q8—412no—
461C4×Q8—86no—
462C4×Q8C2×Q818yes—
463C4×Q8#4118yes—
464C4×D4—212no—
465C4×D4—212no—
466C4×D4—224no—
467C4×D4—212no—
468C4×D4—412no—
469C4×D4—412no—
470C4×D4—46no—
471C4×D4—412no—
472C4×D4C2×Q8124yes—
473#117—212no—
474#117—412no—
475C2×C4⋊C4—212no—
476C2×C4⋊C4—212no—
477C2×C4⋊C4—212no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—212no—
480C2×C4⋊C4—412no—
481C2×C4⋊C4—86no—
482C2×C4⋊C4C2413yes—
483C2×C4⋊C4C2416yes—
484C2×C4⋊C4C2416yes—
485C2×C4⋊C4C2413yes—
486C2×C4⋊C4C2416yes—
487C2×C4⋊C4C2416yes—
488C2×C4⋊C4C2416yes—
489C2×C4⋊C4C2413yes—
490C2×C4⋊C4C2411yescharacteristic
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2413yes—
493C2×C4⋊C4C2416yes—
494C2×C4⋊C4C2416yes—
495C2×C4⋊C4C2413yes—
496C2×C4⋊C4C2413yes—
497C2×C4⋊C4C2416yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2413yes—
500C2×C4⋊C4C2413yes—
501C2×C4⋊C4C2416yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C2412yes—
504C2×C4⋊C4C2416yes—
505C2×C4⋊C4C24112yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C24112yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2413yes—
510C2×C4⋊C4C2416yes—
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C24112yes—
513C2×C4⋊C4C2416yes—
514C2×C4⋊C4C2416yes—
515C2×C4⋊C4C2416yes—
516C2×C4⋊C4C2416yes—
517C2×C4⋊C4C2416yes—
518C2×C4⋊C4C24112yes—
519C2×C4⋊C4C24112yes—
520C2×C4⋊C4C2413yes—
521C2×C4⋊C4C2413yes—
522C2×C4⋊C4C2411yescharacteristic
523C2×C4⋊C4C2413yes—
524C2×C4⋊C4C2412yes—
525C2×C4⋊C4C2411yescharacteristic
526C2×C22⋊C4C2416yes—
527C2×C22⋊C4C2411yescharacteristic
528C2×C22⋊C4C2416yes—
529C2×C22⋊C4C2413yes—
530C2×C22⋊C4C2416yes—
531C2×C22⋊C4C2413yes—
532C2×C22⋊C4C24112yes—
533C2×C22⋊C4C2416yes—
534C2×C22⋊C4C2413yes—
535C2×C22⋊C4C24112yes—
536C2×C22⋊C4C2416yes—
537C2×C22⋊C4C2411yescharacteristic
538C2×C22⋊C4C2413yes—
539C2×C22⋊C4C2416yes—
540C2×C22⋊C4C2412yes—
541C2×C42—212no—
542C2×C42—212no—
543C2×C42—412no—
544C2×C42—412no—
545C2×C42C2413yes—
546C2×C42C2416yes—
547C2×C42C2416yes—
548C2×C42C2416yes—
549C2×C42C2413yes—
550C2×C42C2413yes—
551C2×C42C2413yes—
552C2×C42C2416yes—
553C2×C42C2416yes—
554C2×C42C2413yes—
555C2×C42C2413yes—
556C2×C42C2413yes—
557C2×C42C2412yes—
558C2×C42C2411yescharacteristic
559C2×C42C2411yescharacteristic
560C2×C42C2416yes—
561C2×C42C2416yes—
562C2×C42C2413yes—
563C2×C42C2416yes—
564C2×C42C2413yes—
565C2×C42C2416yes—
566C2×C42C2416yes—
567C2×C42C2412yes—
568C2×C42C2413yes—
569C2×C42C2413yes—
570#95C2412yes—
571#95C2416yes—
572#95C2416yes—
573#95C2416yes—
574#95C2416yes—
575#95C2416yes—
576#95C2416yes—
577#95C2411yescharacteristic
578#95C2411yescharacteristic
579#95C2412yes—
580#95C2412yes—
581#95C2413yes—
582#95C2416yes—
583#95C2413yes—
584#95C2416yes—
585#95C2416yes—
586#95C2413yes—
587#95C2413yes—
588#95C2416yes—
589#95C2416yes—
590#95C24112yes—
591#95C2416yes—
592#95C24112yes—
593#95C2416yes—
594#95C2416yes—
595#95C2412yes—
596#95C2416yes—
597#95C24112yes—
598#95C2416yes—
599#95C24112yes—
600#95C2416yes—
601#95C2416yes—
602#95C24112yes—
603C24C2513yes—
604C24C2511yescharacteristic
605#41—232no—
606C2×Q8—232no—
607C2×Q8—22no—
608C2×Q8—26no—
609C2×Q8—212no—
610C2×Q8—212no—
611C2×Q8—26no—
612C2×Q8—22no—
613C2×Q8—46no—
614C2×Q8—46no—
615C2×Q8—46no—
616C2×Q8—46no—
617C2×Q8C22×Q8112yes—
618C2×Q8C22×Q814yes—
619C2×Q8C2×#4114yes—
620C2×Q8C2×#4114yes—
621C2×Q8H(5,𝔽2)14yes—
622C2×D4—26no—
623C2×D4—26no—
624C2×D4—26no—
625C2×D4—26no—
626C2×D4C22×Q8112yes—
627C2×D4C22×Q8112yes—
628C22×C4—22no—
629C22×C4—26no—
630C22×C4—26no—
631C22×C4—26no—
632C22×C4—26no—
633C22×C4—22no—
634C22×C4—24no—
635C22×C4—26no—
636C22×C4—212no—
637C22×C4—26no—
638C22×C4—26no—
639C22×C4—26no—
640C22×C4—24no—
641C22×C4—26no—
642C22×C4—26no—
643C22×C4—212no—
644C22×C4—212no—
645C22×C4—42no—
646C22×C4—43no—
647C22×C4—46no—
648C22×C4—46no—
649C22×C4—46no—
650C22×C4—46no—
651C22×C4—46no—
652C22×C4—43no—
653C22×C4—43no—
654C22×C4—46no—
655C22×C4C22×Q8112yes—
656C22×C4C22×Q8112yes—
657C22×C4C2×#4114yes—
658C22×C4C2513yes—
659C22×C4C2511yescharacteristic
660C22×C4C2512yes—
661C22×C4C2516yes—
662C22×C4C2516yes—
663C22×C4C2511yescharacteristic
664C22×C4C2513yes—
665C22×C4C2516yes—
666C22×C4C2513yes—
667C22×C4C2516yes—
668C22×C4C2511yescharacteristic
669C22×C4C2511yescharacteristic
670C22×C4C2513yes—
671C22×C4C2513yes—
672C22×C4C2512yes—
673C22×C4C2511yescharacteristic
674C22×C4C2513yes—
675C22×C4C2512yes—
676C22×C4C2512yes—
677C22×C4C2513yes—
678C22×C4C2511yescharacteristic
679C4⋊C4—26no—
680C4⋊C4—212no—
681C4⋊C4—26no—
682C4⋊C4—212no—
683C4⋊C4—212no—
684C4⋊C4—26no—
685C4⋊C4—26no—
686C4⋊C4—26no—
687C4⋊C4—212no—
688C4⋊C4—212no—
689C4⋊C4—212no—
690C4⋊C4—212no—
691C4⋊C4—26no—
692C4⋊C4—212no—
693C4⋊C4—212no—
694C4⋊C4—212no—
695C4⋊C4—212no—
696C4⋊C4—26no—
697C4⋊C4—24no—
698C4⋊C4—212no—
699C4⋊C4—22no—
700C4⋊C4—26no—
701C4⋊C4—24no—
702C4⋊C4—412no—
703C4⋊C4—46no—
704C4⋊C4—46no—
705C4⋊C4—412no—
706C4⋊C4—46no—
707C4⋊C4—43no—
708C4⋊C4—42no—
709C4⋊C4—46no—
710C4⋊C4—46no—
711C4⋊C4—412no—
712C4⋊C4—46no—
713C4⋊C4—412no—
714C4⋊C4—46no—
715C4⋊C4—46no—
716C4⋊C4—412no—
717C4⋊C4C22×Q8112yes—
718C4⋊C4C22×Q8112yes—
719C4⋊C4C2×#4114yes—
720C4⋊C4C2×#41112yes—
721C4⋊C4C2×#4118yes—
722C4⋊C42−1+414yes—
723C22⋊C4—26no—
724C22⋊C4—22no—
725C22⋊C4—212no—
726C22⋊C4—212no—
727C22⋊C4—26no—
728C22⋊C4—212no—
729C22⋊C4—412no—
730C22⋊C4—43no—
731C22⋊C4—46no—
732C22⋊C4—46no—
733C22⋊C4—412no—
734C22⋊C4C22×Q814yes—
735C22⋊C4C22×Q8112yes—
736C22⋊C4C22×Q8124yes—
737C22⋊C4C2×#4118yes—
738C42—22no—
739C42—26no—
740C42—26no—
741C42—26no—
742C42—26no—
743C42—26no—
744C42—212no—
745C42—26no—
746C42—212no—
747C42—212no—
748C42—212no—
749C42—212no—
750C42—26no—
751C42—24no—
752C42—22no—
753C42—42no—
754C42—46no—
755C42—46no—
756C42—46no—
757C42—46no—
758C42—43no—
759C42—43no—
760C42—46no—
761C42C22×Q8112yes—
762C42C2×#41112yes—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—23no—
768C23—23no—
769C23—23no—
770C23—23no—
771C23—23no—
772C23—23no—
773C23C23×Q816yes—
774C23C23×Q812yes—
775C23C22×#4112yes—
776C23#58512yes—
777C23C2611yescharacteristic
778Q8—224no—
779Q8—28no—
780Q8—812no—
781Q8—812no—
782Q8#554116yescomplemented
783D4—224no—
784D4—224no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—23no—
788C2×C4—22no—
789C2×C4—23no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—23no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—23no—
798C2×C4—22no—
799C2×C4—23no—
800C2×C4—21no—
801C2×C4—23no—
802C2×C4—22no—
803C2×C4—224no—
804C2×C4—224no—
805C2×C4—28no—
806C2×C4—21no—
807C2×C4—23no—
808C2×C4—23no—
809C2×C4—23no—
810C2×C4—26no—
811C2×C4—26no—
812C2×C4—23no—
813C2×C4—26no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—26no—
817C2×C4—26no—
818C2×C4—26no—
819C2×C4—23no—
820C2×C4—21no—
821C2×C4—22no—
822C2×C4—26no—
823C2×C4—23no—
824C2×C4—21no—
825C2×C4—26no—
826C2×C4—26no—
827C2×C4—21no—
828C2×C4—22no—
829C2×C4—23no—
830C2×C4—23no—
831C2×C4—26no—
832C2×C4—26no—
833C2×C4—23no—
834C2×C4—26no—
835C2×C4—21no—
836C2×C4—412no—
837C2×C4—48no—
838C2×C4—412no—
839C2×C4—812no—
840C2×C4—86no—
841C2×C4—812no—
842C2×C4—812no—
843C2×C4C23×Q812yes—
844C2×C4C23×Q816yes—
845C2×C4C23×Q816yes—
846C2×C4C23×Q812yes—
847C2×C4C23×Q816yes—
848C2×C4C22×#4114yes—
849C2×C4C22×#4116yes—
850C2×C4C22×#4112yes—
851C2×C4C22×#4114yes—
852C2×C4C22×#4116yes—
853C2×C4C22×#4112yes—
854C2×C4C22×#4112yes—
855C2×C4C2×H(5,𝔽2)16yes—
856C2×C4C2×2−1+414yes—
857C2×C4C2×2−1+412yes—
858C22—22no—
859C22—22no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—26no—
865C22—26no—
866C22—26no—
867C22—43no—
868C22—43no—
869C22—43no—
870C22—43no—
871C22Q8×#4114yes—
872C22C24×Q811yescharacteristic
873C22C23×#4111yescharacteristic
874C22C23×#4111yescharacteristic
875C22C22×H(5,𝔽2)11yescharacteristic
876C22C22×2−1+411yescharacteristic
877C22C2×#58511yescharacteristic
878C22H(7,𝔽2)11yescharacteristic
879C4—24no—
880C4—22no—
881C4—26no—
882C4—24no—
883C4—22no—
884C4—26no—
885C4—26no—
886C4—22no—
887C4—24no—
888C4—46no—
889C4—46no—
890C4—43no—
891C4—43no—
892C4—41no—
893C4—46no—
894C4—41no—
895C4—42no—
896C4—46no—
897C4—43no—
898C4C2×#554112yes—
899C4#348214yes—
900C2—24no—
901C2—46no—
902C2C22×#55411yescharacteristic
903C2C2×Q8×#4111yescharacteristic
904C2C2×#348211yescharacteristic
905C2#6298611yescharacteristic
906C2Q8×2−1+411yescharacteristic
907C2#6300811yescharacteristic
908C2#6301511yescharacteristic
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. #59920C2semidirect
2. #59461C2semidirect
3. #59455C2semidirect
4. #59429C2semidirect
5. #59314C2semidirect
6. #59259C2semidirect
7. #36564C2semidirect
8. #36555C2semidirect
9. #36551C2semidirect
10. Q8×C22⋊Q8C2semidirect
11. #36475C2semidirect
12. #36466C2semidirect
13. #36456C2semidirect
14. #36445C2semidirect
15. #36435C2semidirect
16. #36363C2semidirect
17. #36189C2semidirect
18. C4×Q82C2semidirect
19. C4×#554C2semidirect
22. C4⋊C4×#41C2semidirect
23. C2×Q8×C4⋊C4C2semidirect
163. #548Q8semidirect
444. C22⋊Q8#41semidirect
782. Q8#554semidirect

Maximal subgroups

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

subgroupindex
#599202
#594612
#594552
#594292
#593142
#592592
#365642
#365552
#365512
Q8×C22⋊Q82
#364752
#364662
#364562
#364452
#364352
#363632
#361892
C4×Q822
C4×#5542
C4×#5482
C4⋊C4×#412
C2×Q8×C4⋊C42