Finite Group Databasebeta

← #7685837

Subgroups — #7685837

Order 512.

4959 conjugacy classes of subgroups.

The subgroup lattice has 891 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59871C213yesmaximal, complemented
2#59663C216yesmaximal, complemented
3#59321C213yesmaximal, complemented
4#59245C213yesmaximal, complemented
5#45279C216yesmaximal, complemented
6#45025C216yesmaximal, complemented
7#39635C213yesmaximal, complemented
8#39607C213yesmaximal, complemented
9#38099C216yesmaximal
10#36577C212yesmaximal, complemented
11#36564C213yesmaximal, complemented
12Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
13Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
14#36466C211yesmaximal, characteristic, complemented
15#36189C213yesmaximal
16#35868C212yesmaximal, complemented
17#35786C212yesmaximal, complemented
18#34772C213yesmaximal
19#34335C211yesmaximal, characteristic, complemented
20#34291C212yesmaximal
21#34182C211yesmaximal, characteristic, complemented
22C4×D4×Q8C211yesmaximal, characteristic
23C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
24C2×Q82C2211yescharacteristic
25C2×#557C2212yes—
26C2×D4×Q8C2211yescharacteristic
27C2×#519C2212yes—
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2212yes—
31#2859C2213yes—
32#2857C2213yes—
33#2857C2213yes—
34#2857C2216yes—
35#2806C22112yes—
36#2802C22112yes—
37#2802C22112yes—
38#2791C22112yes—
39#2788C22112yes—
40#2755C22112yes—
41#2704C22112yes—
42#2647C2216yes—
43#2629C2216yes—
44#2588C22112yes—
45#2586C22112yes—
46#2584C2216yes—
47#2584C22112yes—
48#2582C2216yes—
49#2582C2213yes—
50#2582C2213yes—
51#2582C2216yes—
52#2570C2216yes—
53#2568C2216yes—
54#2567C2213yes—
55#2567C2213yes—
56#2565C2216yes—
57#2552C2216yes—
58#2552C2213yes—
59#2552C2216yes—
60#2551C2213yes—
61#2550C2216yes—
62#2549C22112yes—
63#2522C2216yes—
64#2520C2216yes—
65#2511C2216yes—
66#2511C2216yes—
67#2511C2213yes—
68#2509C2216yes—
69#2507C2216yes—
70#2507C2216yes—
71#2507C2216yes—
72#2507C2213yes—
73#2506C2216yes—
74#2506C2216yes—
75#2505C2216yes—
76#2502C2213yes—
77#2497C2216yes—
78#2497C2213yes—
79#2492C2213yes—
80#2487C2213yes—
81#2473C22112yes—
82#2453C2216yes—
83#2453C2216yes—
84#2453C2216yes—
85#2451C2216yes—
86#2451C2216yes—
87#2451C2216yes—
88#2450C2216yes—
89#2442C2216yes—
90#2442C2216yes—
91#2441C2216yes—
92#2440C2216yes—
93#2440C2216yes—
94#2440C2213yes—
95#2439C2216yes—
96#2423C2216yes—
97#2417C2216yes—
98#2417C2211yescharacteristic
99#2402C2216yes—
100#2396C2216yes—
101#2369C2213yes—
102#2369C2216yes—
103#2365C2216yes—
104#2365C2213yes—
105#2365C2216yes—
106#2362C2216yes—
107#2360C2216yes—
108#2360C2213yes—
109#2360C2216yes—
110#2360C2213yes—
111#2355C2213yes—
112#2352C2216yes—
113#2351C2216yes—
114#2351C2212yes—
115#2351C2212yes—
116#2351C2212yes—
117Q8×C4⋊C4C2211yescharacteristic
118Q8×C4⋊C4C2212yes—
119Q8×C4⋊C4C2212yes—
120Q8×C4⋊C4C2212yes—
121Q8×C4⋊C4C2211yescharacteristic
122Q8×C4⋊C4C2213yes—
123Q8×C4⋊C4C2211yescharacteristic
124Q8×C4⋊C4C2213yes—
125Q8×C4⋊C4C2216yes—
126Q8×C4⋊C4C2211yescharacteristic
127Q8×C4⋊C4C2213yes—
128Q8×C4⋊C4C2213yes—
129D4×C4⋊C4C2213yes—
130#2345C2216yes—
131Q8×C22⋊C4C2211yescharacteristic
132Q8×C22⋊C4C2211yescharacteristic
133Q8×C22⋊C4C2212yes—
134Q8×C22⋊C4C2212yes—
135#2331C2216yes—
136#2327C2216yes—
137#2323C2216yes—
138#2316C2216yes—
139C4×C4⋊Q8C2213yes—
140C4×C4⋊Q8C2213yes—
141C4×C4⋊Q8C2213yes—
142C4×C22⋊Q8C2216yes—
143C4×C22⋊Q8C2216yes—
144C4×C22⋊Q8C2213yes—
145C4×C22⋊Q8C2213yes—
146C4×C22⋊Q8C2213yes—
147C4×C22⋊Q8C2213yes—
148#2295C2213yes—
149C2×#389C2216yes—
150#2290C2216yes—
151#2285C2213yes—
152#2285C2213yes—
153C2×#384C2213yes—
154#2276C2212yes—
155C42×Q8C2211yescharacteristic
156C42×D4C2213yes—
157C2×C4×C4⋊C4C2213yes—
158C23×Q8C2311yescharacteristic
159C23×Q8C2311yescharacteristic
160Q82—28no—
161#557—48no—
162D4×Q8Q8116yescomplemented
163C2×C4⋊Q8C2313yes—
164C2×C4⋊Q8C2313yes—
165C2×C4⋊Q8C2316yes—
166C2×C4⋊Q8C2316yes—
167C2×C4⋊Q8C2313yes—
168C2×#125C2316yes—
169C2×#125C2316yes—
170C2×#125C23112yes—
171C2×C22⋊Q8C2311yescharacteristic
172C2×C22⋊Q8C2311yescharacteristic
173C2×C22⋊Q8C2316yes—
174C2×C22⋊Q8C2316yes—
175C2×C22⋊Q8C2316yes—
176C2×C22⋊Q8C2313yes—
177C2×C22⋊Q8C2313yes—
178#519—48no—
179C2×C4×Q8—28no—
180C2×C4×Q8—28no—
181C2×C4×Q8—48no—
182C2×C4×Q8C2313yes—
183C2×C4×Q8C2313yes—
184C2×C4×Q8C2313yes—
185C2×C4×Q8C2312yes—
186C2×C4×Q8C2311yescharacteristic
187C2×C4×Q8C2311yescharacteristic
188C2×C4×Q8C2311yescharacteristic
189C2×C4×Q8C2312yes—
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2312yes—
192C2×C4×Q8C2313yes—
193C2×C4×Q8C2313yes—
194C2×C4×Q8C2316yes—
195C2×C4×Q8C2316yes—
196C2×C4×Q8C2316yes—
197C2×C4×Q8C2316yes—
198C2×C4×Q8C2316yes—
199C2×C4×Q8C2316yes—
200C2×C4×Q8C2311yescharacteristic
201C2×C4×Q8C2311yescharacteristic
202C2×C4×D4C2311yescharacteristic
203C2×C4×D4C2313yes—
204C2×C4×D4C2313yes—
205C2×#117C2316yes—
206C2×#117C2316yes—
207C22×C4⋊C4C2313yes—
208C22×C4⋊C4C2313yes—
209C22×C4⋊C4C2313yes—
210C22×C4⋊C4C2311yescharacteristic
211C22×C4⋊C4C2316yes—
212C22×C4⋊C4C2316yes—
213C22×C42C2313yes—
214C22×C42C2313yes—
215C22×C42C2316yes—
216#400C23112yes—
217#400C23112yes—
218#400C2316yes—
219#400C2316yes—
220#400C2316yes—
221#400C23112yes—
222#400C2316yes—
223#400C2316yes—
224#399C2316yes—
225#398C2316yes—
226#398C23112yes—
227#398C23112yes—
228#398C2316yes—
229#398C23112yes—
230#398C23112yes—
231#398C23112yes—
232#398C23112yes—
233#398C23112yes—
234#398C2316yes—
235#398C23112yes—
236#398C23112yes—
237#398C2312yes—
238#398C2316yes—
239#398C2316yes—
240#396C2316yes—
241#396C23112yes—
242#396C2312yes—
243#395C23112yes—
244#395C23112yes—
245#395C23112yes—
246#395C2316yes—
247#393C2316yes—
248#391C2313yes—
249#391C2313yes—
250#391C2316yes—
251#391C2316yes—
252#391C2313yes—
253#391C2316yes—
254#391C2316yes—
255#391C2316yes—
256#391C2316yes—
257#391C2313yes—
258#391C2316yes—
259#391C23112yes—
260#391C2313yes—
261#391C2313yes—
262#391C23112yes—
263#391C2316yes—
264#391C23112yes—
265#391C2316yes—
266#391C2313yes—
267#391C2311yescharacteristic
268#389C2311yescharacteristic
269#389C2313yes—
270#389C2316yes—
271#389C2316yes—
272#389C2316yes—
273#389C2313yes—
274#389C2316yes—
275#389C2313yes—
276#389C2313yes—
277#389C2316yes—
278#389C2316yes—
279#389C2316yes—
280#389C2316yes—
281#389C2316yes—
282#389C2316yes—
283#389C23112yes—
284#389C23112yes—
285#389C2316yes—
286#389C2316yes—
287#389C2316yes—
288#389C23112yes—
289#389C2316yes—
290#389C23112yes—
291#389C2316yes—
292#389C2316yes—
293#389C2316yes—
294#389C2316yes—
295#389C23112yes—
296#389C2316yes—
297#389C2316yes—
298#389C23112yes—
299#389C23112yes—
300#389C2316yes—
301#389C2316yes—
302#389C2316yes—
303#389C2316yes—
304#389C23112yes—
305#389C2313yes—
306#389C2313yes—
307#389C2313yes—
308#388C2316yes—
309#388C23112yes—
310#388C2316yes—
311#387C23112yes—
312#387C23112yes—
313#387C23112yes—
314#387C23112yes—
315#387C23112yes—
316#387C2316yes—
317#387C23112yes—
318#387C23112yes—
319#387C2316yes—
320#387C2316yes—
321#387C23112yes—
322#387C2316yes—
323#387C2316yes—
324#387C2316yes—
325#387C2316yes—
326#387C2316yes—
327#387C2316yes—
328#387C2316yes—
329#386C2316yes—
330#386C2312yes—
331#385C2316yes—
332#385C2316yes—
333#385C2316yes—
334#385C2316yes—
335#385C2316yes—
336#385C2316yes—
337#385C2316yes—
338#385C2316yes—
339#384C2313yes—
340#384C2313yes—
341#384C2313yes—
342#384C2316yes—
343#384C2316yes—
344#384C2316yes—
345#384C2313yes—
346#384C2313yes—
347#384C2316yes—
348#384C2313yes—
349#384C2316yes—
350#384C2313yes—
351#382C2316yes—
352#382C2316yes—
353#382C2316yes—
354#382C2316yes—
355#380C2316yes—
356#380C2316yes—
357#380C2316yes—
358#380C2313yes—
359#380C2316yes—
360#380C2313yes—
361#380C2313yes—
362#380C23112yes—
363#380C2313yes—
364#380C2311yescharacteristic
365#380C2312yes—
366#380C2313yes—
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⋊C4C2316yes—
378C4×C4⋊C4C2313yes—
379C4×C4⋊C4C23112yes—
380C4×C4⋊C4C2316yes—
381C4×C4⋊C4C2313yes—
382C4×C4⋊C4C2316yes—
383C4×C4⋊C4C2316yes—
384C4×C4⋊C4C2313yes—
385C4×C4⋊C4C2313yes—
386C4×C4⋊C4C2316yes—
387C4×C4⋊C4C2313yes—
388C4×C4⋊C4C2316yes—
389C4×C4⋊C4C2316yes—
390C4×C4⋊C4C2316yes—
391C4×C4⋊C4C2313yes—
392C4×C4⋊C4C2313yes—
393C4×C22⋊C4C2313yes—
394C4×C22⋊C4C2316yes—
395C4×C22⋊C4C2313yes—
396C4×C22⋊C4C2316yes—
397C4×C22⋊C4C2313yes—
398C4×C22⋊C4C23112yes—
399C4×C22⋊C4C2313yes—
400C4×C22⋊C4C2313yes—
401C4×C22⋊C4C2313yes—
402#376C2316yes—
403C2×#95C2316yes—
404C43C2313yes—
405C22×Q8—24no—
406C22×Q8—24no—
407C22×Q8—24no—
408C22×Q8—24no—
409C22×Q8C2×Q818yes—
410C22×Q8C2×Q818yes—
411C22×Q8C2411yescharacteristic
412C22×Q8C2413yes—
413C22×Q8C2413yes—
414C22×Q8C2416yes—
415C22×Q8C2416yes—
416C22×Q8C2411yescharacteristic
417C22×D4C2411yescharacteristic
418C23×C4C2411yescharacteristic
419C23×C4C2413yes—
420C23×C4C2412yes—
421C23×C4C2413yes—
422C23×C4C2413yes—
423C23×C4C2411yescharacteristic
424C23×C4C2416yes—
425C23×C4C2413yes—
426C4⋊Q8—224no—
427C4⋊Q8—212no—
428C4⋊Q8—212no—
429C4⋊Q8—412no—
430C4⋊Q8C2×Q8124yes—
431#125—412no—
432#125—412no—
433#125—812no—
434C22⋊Q8—24no—
435C22⋊Q8—24no—
436C22⋊Q8—412no—
437C22⋊Q8—412no—
438C22⋊Q8—86no—
439C22⋊Q8C2×Q8124yes—
440C22⋊Q8C2×Q8124yes—
441C4×Q8—24no—
442C4×Q8—24no—
443C4×Q8—28no—
444C4×Q8—28no—
445C4×Q8—28no—
446C4×Q8—28no—
447C4×Q8—24no—
448C4×Q8—212no—
449C4×Q8—212no—
450C4×Q8—212no—
451C4×Q8—212no—
452C4×Q8—212no—
453C4×Q8—412no—
454C4×Q8—412no—
455C4×Q8—412no—
456C4×Q8—412no—
457C4×Q8—412no—
458C4×Q8—86no—
459C4×Q8C2×Q818yes—
460C4×Q8#4118yes—
461C4×D4—24no—
462C4×D4—46no—
463C4×D4C2×Q8124yes—
464#117—412no—
465#117—412no—
466C2×C4⋊C4—212no—
467C2×C4⋊C4—212no—
468C2×C4⋊C4—212no—
469C2×C4⋊C4—24no—
470C2×C4⋊C4—412no—
471C2×C4⋊C4—86no—
472C2×C4⋊C4C2416yes—
473C2×C4⋊C4C2416yes—
474C2×C4⋊C4C2413yes—
475C2×C4⋊C4C2413yes—
476C2×C4⋊C4C2416yes—
477C2×C4⋊C4C2416yes—
478C2×C4⋊C4C2413yes—
479C2×C4⋊C4C2411yescharacteristic
480C2×C4⋊C4C2412yes—
481C2×C4⋊C4C2413yes—
482C2×C4⋊C4C2416yes—
483C2×C4⋊C4C2416yes—
484C2×C4⋊C4C2411yescharacteristic
485C2×C4⋊C4C2413yes—
486C2×C4⋊C4C2416yes—
487C2×C4⋊C4C2413yes—
488C2×C4⋊C4C2416yes—
489C2×C4⋊C4C2411yescharacteristic
490C2×C4⋊C4C2412yes—
491C2×C4⋊C4C2412yes—
492C2×C4⋊C4C2413yes—
493C2×C4⋊C4C2416yes—
494C2×C4⋊C4C24112yes—
495C2×C4⋊C4C2416yes—
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C24112yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C2413yes—
501C2×C4⋊C4C2412yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C2416yes—
505C2×C4⋊C4C24112yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C2416yes—
508C2×C4⋊C4C2416yes—
509C2×C4⋊C4C2416yes—
510C2×C4⋊C4C24112yes—
511C2×C4⋊C4C24112yes—
512C2×C4⋊C4C2416yes—
513C2×C4⋊C4C2416yes—
514C2×C4⋊C4C2416yes—
515C2×C4⋊C4C2416yes—
516C2×C4⋊C4C2413yes—
517C2×C4⋊C4C2413yes—
518C2×C4⋊C4C2416yes—
519C2×C4⋊C4C2413yes—
520C2×C4⋊C4C2411yescharacteristic
521C2×C22⋊C4C2413yes—
522C2×C22⋊C4C2411yescharacteristic
523C2×C22⋊C4C2411yescharacteristic
524C2×C22⋊C4C2416yes—
525C2×C22⋊C4C2412yes—
526C2×C22⋊C4C2412yes—
527C2×C22⋊C4C2416yes—
528C2×C22⋊C4C2412yes—
529C2×C22⋊C4C2413yes—
530C2×C22⋊C4C2416yes—
531C2×C22⋊C4C2413yes—
532C2×C22⋊C4C2413yes—
533C2×C42—212no—
534C2×C42—212no—
535C2×C42—412no—
536C2×C42C2416yes—
537C2×C42C2416yes—
538C2×C42C2411yescharacteristic
539C2×C42C2413yes—
540C2×C42C2416yes—
541C2×C42C2416yes—
542C2×C42C2413yes—
543C2×C42C2413yes—
544C2×C42C2413yes—
545C2×C42C2413yes—
546C2×C42C2413yes—
547C2×C42C2413yes—
548C2×C42C2413yes—
549C2×C42C24112yes—
550C2×C42C2413yes—
551C2×C42C2413yes—
552C2×C42C2416yes—
553C2×C42C2416yes—
554C2×C42C24112yes—
555C2×C42C2413yes—
556C2×C42C2413yes—
557#95C2416yes—
558#95C2416yes—
559#95C2416yes—
560#95C2416yes—
561#95C2412yes—
562#95C2416yes—
563#95C2416yes—
564#95C2416yes—
565#95C2413yes—
566#95C2413yes—
567#95C2413yes—
568#95C2413yes—
569#95C2413yes—
570#95C2413yes—
571#95C2416yes—
572#95C24112yes—
573#95C24112yes—
574#95C2416yes—
575#95C2416yes—
576#95C2416yes—
577#95C2412yes—
578#95C2416yes—
579#95C2412yes—
580#95C2416yes—
581#95C2412yes—
582#95C24112yes—
583#95C2416yes—
584#95C24112yes—
585#95C2416yes—
586#95C2416yes—
587#95C2416yes—
588#95C2416yes—
589#95C24112yes—
590#95C2416yes—
591#95C2416yes—
592#95C2416yes—
593#95C2416yes—
594C24C2511yescharacteristic
595C24C2511yescharacteristic
596C2×Q8—232no—
597C2×Q8—232no—
598C2×Q8—26no—
599C2×Q8—26no—
600C2×Q8—22no—
601C2×Q8—212no—
602C2×Q8—26no—
603C2×Q8—26no—
604C2×Q8—22no—
605C2×Q8—22no—
606C2×Q8—212no—
607C2×Q8—46no—
608C2×Q8—46no—
609C2×Q8—46no—
610C2×Q8—46no—
611C2×Q8C22×Q8112yes—
612C2×Q8C22×Q8112yes—
613C2×Q8C22×Q814yes—
614C2×Q8C2×#4114yes—
615C2×Q8H(5,𝔽2)14yes—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4C22×Q814yes—
619C22×C4—22no—
620C22×C4—26no—
621C22×C4—26no—
622C22×C4—26no—
623C22×C4—26no—
624C22×C4—22no—
625C22×C4—26no—
626C22×C4—24no—
627C22×C4—212no—
628C22×C4—22no—
629C22×C4—26no—
630C22×C4—24no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—26no—
634C22×C4—42no—
635C22×C4—43no—
636C22×C4—46no—
637C22×C4—46no—
638C22×C4—43no—
639C22×C4—43no—
640C22×C4C22×Q8112yes—
641C22×C4C22×Q8112yes—
642C22×C42−1+414yes—
643C22×C4C2511yescharacteristic
644C22×C4C2512yes—
645C22×C4C2513yes—
646C22×C4C2512yes—
647C22×C4C2516yes—
648C22×C4C2516yes—
649C22×C4C2516yes—
650C22×C4C2513yes—
651C22×C4C2513yes—
652C22×C4C2516yes—
653C22×C4C2511yescharacteristic
654C22×C4C2512yes—
655C22×C4C2511yescharacteristic
656C22×C4C2513yes—
657C22×C4C2513yes—
658C22×C4C2513yes—
659C22×C4C2513yes—
660C22×C4C2511yescharacteristic
661C22×C4C2512yes—
662C22×C4C2513yes—
663C22×C4C2511yescharacteristic
664C4⋊C4—212no—
665C4⋊C4—212no—
666C4⋊C4—26no—
667C4⋊C4—26no—
668C4⋊C4—212no—
669C4⋊C4—212no—
670C4⋊C4—26no—
671C4⋊C4—212no—
672C4⋊C4—212no—
673C4⋊C4—212no—
674C4⋊C4—26no—
675C4⋊C4—24no—
676C4⋊C4—212no—
677C4⋊C4—22no—
678C4⋊C4—26no—
679C4⋊C4—26no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—24no—
683C4⋊C4—24no—
684C4⋊C4—212no—
685C4⋊C4—26no—
686C4⋊C4—412no—
687C4⋊C4—46no—
688C4⋊C4—46no—
689C4⋊C4—412no—
690C4⋊C4—46no—
691C4⋊C4—46no—
692C4⋊C4—43no—
693C4⋊C4—42no—
694C4⋊C4—46no—
695C4⋊C4—46no—
696C4⋊C4—46no—
697C4⋊C4—46no—
698C4⋊C4—46no—
699C4⋊C4—46no—
700C4⋊C4—46no—
701C4⋊C4—412no—
702C4⋊C4—412no—
703C4⋊C4—412no—
704C4⋊C4—46no—
705C4⋊C4—46no—
706C4⋊C4—46no—
707C4⋊C4—46no—
708C4⋊C4C22×Q8112yes—
709C4⋊C4C22×Q8112yes—
710C4⋊C4C22×Q8124yes—
711C4⋊C4C2×#41112yes—
712C4⋊C42−1+414yes—
713C22⋊C4—22no—
714C22⋊C4—24no—
715C22⋊C4—26no—
716C22⋊C4—212no—
717C22⋊C4—22no—
718C22⋊C4—24no—
719C22⋊C4—42no—
720C22⋊C4—46no—
721C22⋊C4—43no—
722C22⋊C4—46no—
723C22⋊C4C22×Q8112yes—
724C22⋊C4C22×Q8112yes—
725C42—26no—
726C42—26no—
727C42—26no—
728C42—26no—
729C42—26no—
730C42—26no—
731C42—212no—
732C42—212no—
733C42—212no—
734C42—212no—
735C42—26no—
736C42—22no—
737C42—26no—
738C42—46no—
739C42—46no—
740C42—412no—
741C42—43no—
742C42—43no—
743C42—412no—
744C42C22×Q8112yes—
745C42C2×#41112yes—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23C23×Q812yes—
757C23C23×Q812yes—
758C23C2×2−1+412yes—
759C23#58512yes—
760C23C2611yescharacteristic
761Q8—224no—
762Q8—224no—
763Q8—44no—
764Q8—812no—
765Q8—812no—
766Q8#554116yes—
767D4—28no—
768C2×C4—21no—
769C2×C4—23no—
770C2×C4—23no—
771C2×C4—22no—
772C2×C4—23no—
773C2×C4—23no—
774C2×C4—23no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—23no—
779C2×C4—22no—
780C2×C4—23no—
781C2×C4—23no—
782C2×C4—224no—
783C2×C4—224no—
784C2×C4—28no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—23no—
788C2×C4—23no—
789C2×C4—26no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—26no—
794C2×C4—26no—
795C2×C4—26no—
796C2×C4—23no—
797C2×C4—21no—
798C2×C4—23no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—21no—
805C2×C4—26no—
806C2×C4—26no—
807C2×C4—26no—
808C2×C4—23no—
809C2×C4—23no—
810C2×C4—26no—
811C2×C4—26no—
812C2×C4—23no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—26no—
816C2×C4—26no—
817C2×C4—26no—
818C2×C4—22no—
819C2×C4—23no—
820C2×C4—23no—
821C2×C4—412no—
822C2×C4—48no—
823C2×C4—44no—
824C2×C4—86no—
825C2×C4—812no—
826C2×C4C23×Q812yes—
827C2×C4C23×Q816yes—
828C2×C4C23×Q816yes—
829C2×C4C23×Q816yes—
830C2×C4C23×Q816yes—
831C2×C4C22×#4116yes—
832C2×C4C22×#4116yes—
833C2×C4C22×#4112yes—
834C2×C4C2×H(5,𝔽2)16yes—
835C2×C4C2×2−1+412yes—
836C2×C4C2×2−1+414yes—
837C2×C4C2×2−1+412yes—
838C2×C4C2×2−1+412yes—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22#350214yes—
853C22C24×Q811yescharacteristic
854C22C23×#4111yescharacteristic
855C22C22×H(5,𝔽2)11yescharacteristic
856C22C22×2−1+411yescharacteristic
857C22C22×2−1+411yescharacteristic
858C22C2×#58511yescharacteristic
859C22H(7,𝔽2)11yescharacteristic
860C4—26no—
861C4—26no—
862C4—24no—
863C4—22no—
864C4—22no—
865C4—26no—
866C4—26no—
867C4—43no—
868C4—43no—
869C4—46no—
870C4—42no—
871C4—46no—
872C4—43no—
873C4—41no—
874C4—42no—
875C4—42no—
876C4—41no—
877C4—46no—
878C4—46no—
879C4C2×#554112yes—
880C4#352314yes—
881C2—24no—
882C2—42no—
883C2C22×#55411yescharacteristic
884C2C2×#350211yescharacteristic
885C2C2×#352311yescharacteristic
886C2#6291711yescharacteristic
887C2Q8×2−1+411yescharacteristic
888C2#6300811yescharacteristic
889C2#6301511yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC22×D4C24
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59871C2semidirect
2. #59663C2semidirect
3. #59321C2semidirect
4. #59245C2semidirect
5. #45279C2semidirect
6. #45025C2semidirect
7. #39635C2semidirect
8. #39607C2semidirect
10. #36577C2semidirect
11. #36564C2semidirect
12. Q8×C22⋊Q8C2semidirect
13. Q8×C22⋊Q8C2semidirect
14. #36466C2semidirect
16. #35868C2semidirect
17. #35786C2semidirect
19. #34335C2semidirect
21. #34182C2semidirect
23. C2×Q8×C4⋊C4C2semidirect
162. D4×Q8Q8semidirect

Maximal subgroups

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

subgroupindex
#598712
#596632
#593212
#592452
#452792
#450252
#396352
#396072
#380992
#365772
#365642
Q8×C22⋊Q82
#364662
#361892
#358682
#357862
#347722
#343352
#342912
#341822
C4×D4×Q82
C2×Q8×C4⋊C42