Finite Group Databasebeta

← Q8×#552 #7699649

Subgroups — Q8×#552 #7699649

Order 512.

4947 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59934C216yesmaximal, complemented
2#59499C216yesmaximal, complemented
3#59445C213yesmaximal, complemented
4#59321C213yesmaximal, complemented
5#59291C216yesmaximal
6#59259C213yesmaximal, complemented
7Q8×#126C212yesmaximal, complemented
8Q8×#125C212yesmaximal, complemented
9Q8×#125C211yesmaximal, characteristic, complemented
10Q8×#123C212yesmaximal
11Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
12Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
13#36287C213yesmaximal, complemented
14#36285C213yesmaximal, complemented
15#36280C216yesmaximal, complemented
16#36193C213yesmaximal, complemented
17#36189C213yesmaximal
18C4×Q82C211yesmaximal, characteristic, complemented
19C4×#552C213yesmaximal
20C4×D4×Q8C211yesmaximal, characteristic
21Q8×#117C212yesmaximal, complemented
22Q8×#117C211yesmaximal, characteristic, complemented
23C2×Q8×C4⋊C4C211yesmaximal, characteristic, complemented
24C2×Q82C2211yescharacteristic
25C2×#552C2211yescharacteristic
26C2×D4×Q8C2211yescharacteristic
27C22×C4×Q8C2212yes—
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30#2863C2216yes—
31#2859C2213yes—
32#2859C2216yes—
33#2857C2213yes—
34#2857C2213yes—
35#2855C2216yes—
36#2791C22112yes—
37#2774C22112yes—
38#2768C22112yes—
39#2612C22112yes—
40#2606C22112yes—
41#2590C22112yes—
42#2585C22112yes—
43#2582C2213yes—
44#2582C2213yes—
45#2570C2216yes—
46#2567C2213yes—
47#2567C2213yes—
48#2565C2216yes—
49#2556C22112yes—
50#2552C2216yes—
51#2552C2213yes—
52#2552C2216yes—
53#2552C2213yes—
54#2520C22112yes—
55#2511C2216yes—
56#2511C2216yes—
57#2511C2216yes—
58#2511C2216yes—
59#2508C2216yes—
60#2507C2216yes—
61#2507C2216yes—
62#2507C2216yes—
63#2507C2216yes—
64#2507C2216yes—
65#2507C2216yes—
66#2506C2216yes—
67#2502C2216yes—
68#2497C2216yes—
69#2497C2216yes—
70#2497C2216yes—
71#2487C2216yes—
72#2473C22112yes—
73#2462C22112yes—
74#2451C2216yes—
75#2451C2216yes—
76#2446C2216yes—
77#2446C2216yes—
78#2442C2216yes—
79#2441C2216yes—
80#2440C2216yes—
81#2440C2216yes—
82#2438C22112yes—
83#2423C2216yes—
84#2423C2216yes—
85#2423C2216yes—
86#2417C2216yes—
87#2373C2216yes—
88#2371C2216yes—
89#2370C2213yes—
90#2370C2216yes—
91#2369C2216yes—
92#2369C2213yes—
93#2365C2213yes—
94#2362C2213yes—
95#2360C2216yes—
96#2360C2213yes—
97#2360C2213yes—
98#2360C2213yes—
99#2359C2216yes—
100#2356C2213yes—
101#2355C2216yes—
102#2355C2216yes—
103#2355C2213yes—
104#2355C2213yes—
105#2352C2213yes—
106Q8×C4⋊C4C2216yes—
107Q8×C4⋊C4C2213yes—
108Q8×C4⋊C4C2211yescharacteristic
109Q8×C4⋊C4C2213yes—
110Q8×C4⋊C4C2211yescharacteristic
111Q8×C4⋊C4C2212yes—
112Q8×C4⋊C4C2211yescharacteristic
113Q8×C4⋊C4C2212yes—
114Q8×C4⋊C4C2212yes—
115Q8×C4⋊C4C2211yescharacteristic
116Q8×C4⋊C4C2213yes—
117Q8×C4⋊C4C2212yes—
118Q8×C4⋊C4C2212yes—
119Q8×C4⋊C4C2212yes—
120D4×C4⋊C4C2213yes—
121#2346C2213yes—
122#2345C2216yes—
123#2345C2216yes—
124#2345C2216yes—
125#2344C2213yes—
126#2343C2216yes—
127Q8×C22⋊C4C2211yescharacteristic
128Q8×C22⋊C4C2212yes—
129Q8×C22⋊C4C2212yes—
130Q8×C22⋊C4C2211yescharacteristic
131Q8×C22⋊C4C2212yes—
132C4×C4⋊Q8C2213yes—
133C4×C4⋊Q8C2213yes—
134C4×C4⋊Q8C2216yes—
135C4×#125C2216yes—
136C4×#125C2213yes—
137C4×#126C2216yes—
138C4×C22⋊Q8C2213yes—
139C4×C22⋊Q8C2213yes—
140C4×C22⋊Q8C2213yes—
141C4×C22⋊Q8C2213yes—
142C4×#123C2216yes—
143#2295C2216yes—
144#2295C2216yes—
145#2295C2216yes—
146C2×#389C2216yes—
147#2285C2213yes—
148#2285C2216yes—
149C2×#384C2213yes—
150C42×Q8C2212yes—
151C42×Q8C2212yes—
152C42×Q8C2211yescharacteristic
153C42×Q8C2213yes—
154C42×D4C2213yes—
155C4×#117C2216yes—
156C4×#117C2213yes—
157C2×C4×C4⋊C4C2213yes—
158C23×Q8C2311yescharacteristic
159C23×Q8C2311yescharacteristic
160Q82—28no—
161#552Q8116yesdirect product factor
162D4×Q8—28no—
163C2×C4⋊Q8C2313yes—
164C2×C4⋊Q8C2313yes—
165C2×C4⋊Q8C2316yes—
166C2×#126C2312yes—
167C2×#125C2316yes—
168C2×#125C23112yes—
169C2×#125C2311yescharacteristic
170C2×#125C2312yes—
171C2×#123C2312yes—
172C2×C22⋊Q8C2313yes—
173C2×C22⋊Q8C2313yes—
174C2×C22⋊Q8C2316yes—
175C2×C22⋊Q8C2316yes—
176C2×C22⋊Q8C2311yescharacteristic
177C2×C22⋊Q8C2311yescharacteristic
178C2×C4×Q8—216no—
179C2×C4×Q8—28no—
180C2×C4×Q8—28no—
181C2×C4×Q8C2313yes—
182C2×C4×Q8C2313yes—
183C2×C4×Q8C2313yes—
184C2×C4×Q8C2312yes—
185C2×C4×Q8C2312yes—
186C2×C4×Q8C2311yescharacteristic
187C2×C4×Q8C2311yescharacteristic
188C2×C4×Q8C2312yes—
189C2×C4×Q8C2311yescharacteristic
190C2×C4×Q8C2312yes—
191C2×C4×Q8C2311yescharacteristic
192C2×C4×Q8C2316yes—
193C2×C4×Q8C2313yes—
194C2×C4×Q8C2316yes—
195C2×C4×Q8C2313yes—
196C2×C4×Q8C2313yes—
197C2×C4×Q8C2316yes—
198C2×C4×Q8C2311yescharacteristic
199C2×C4×Q8C2311yescharacteristic
200C2×C4×D4C2313yes—
201C2×C4×D4C2313yes—
202C2×C4×D4C2311yescharacteristic
203C2×#117C2316yes—
204C2×#117C2313yes—
205C2×#117C2312yes—
206C2×#117C2311yescharacteristic
207C22×C4⋊C4C2313yes—
208C22×C4⋊C4C2316yes—
209C22×C4⋊C4C2313yes—
210C22×C4⋊C4C2313yes—
211C22×C4⋊C4C2316yes—
212C22×C4⋊C4C2311yescharacteristic
213C22×C42C2316yes—
214C22×C42C2313yes—
215C22×C42C2313yes—
216#400C23112yes—
217#400C23112yes—
218#400C23112yes—
219#400C23112yes—
220#399C23112yes—
221#398C23112yes—
222#398C23112yes—
223#398C23112yes—
224#398C23112yes—
225#398C23112yes—
226#398C23112yes—
227#398C23112yes—
228#398C23112yes—
229#398C23112yes—
230#398C23112yes—
231#396C23112yes—
232#395C23112yes—
233#395C23112yes—
234#391C2313yes—
235#391C2313yes—
236#391C23112yes—
237#391C2316yes—
238#391C2313yes—
239#391C2313yes—
240#391C2316yes—
241#391C2316yes—
242#391C2316yes—
243#391C2316yes—
244#391C2316yes—
245#391C2313yes—
246#391C2316yes—
247#391C2313yes—
248#391C2316yes—
249#391C2316yes—
250#389C2313yes—
251#389C2313yes—
252#389C2316yes—
253#389C2316yes—
254#389C23112yes—
255#389C2316yes—
256#389C2316yes—
257#389C2316yes—
258#389C2316yes—
259#389C2316yes—
260#389C2316yes—
261#389C2313yes—
262#389C2313yes—
263#389C2316yes—
264#389C2316yes—
265#389C2316yes—
266#389C2316yes—
267#389C23112yes—
268#389C23112yes—
269#389C2316yes—
270#389C23112yes—
271#389C2316yes—
272#389C2316yes—
273#389C2316yes—
274#389C2316yes—
275#389C2316yes—
276#389C2316yes—
277#389C2313yes—
278#389C2316yes—
279#389C2316yes—
280#389C2316yes—
281#389C23112yes—
282#389C2316yes—
283#389C2316yes—
284#389C2313yes—
285#388C2316yes—
286#388C2316yes—
287#388C2316yes—
288#388C2316yes—
289#388C2316yes—
290#387C2316yes—
291#387C2316yes—
292#387C2316yes—
293#387C2316yes—
294#387C2316yes—
295#387C2316yes—
296#387C2316yes—
297#387C2316yes—
298#387C2316yes—
299#387C23112yes—
300#387C23112yes—
301#387C23112yes—
302#387C23112yes—
303#387C2316yes—
304#387C2316yes—
305#387C23112yes—
306#387C23112yes—
307#387C2316yes—
308#387C23112yes—
309#387C23112yes—
310#387C23112yes—
311#387C23112yes—
312#387C23112yes—
313#387C2316yes—
314#387C2316yes—
315#387C2316yes—
316#386C2316yes—
317#385C2316yes—
318#385C2316yes—
319#385C23112yes—
320#385C2316yes—
321#385C2316yes—
322#385C2316yes—
323#384C2313yes—
324#384C2313yes—
325#384C2316yes—
326#384C2316yes—
327#384C2316yes—
328#384C2316yes—
329#384C2313yes—
330#384C2313yes—
331#384C2316yes—
332#384C2316yes—
333#384C2316yes—
334#384C2316yes—
335#383C2316yes—
336#382C2313yes—
337#382C2316yes—
338#382C2316yes—
339#382C23112yes—
340#381C2316yes—
341#380C2316yes—
342#380C2313yes—
343#380C2316yes—
344#380C2316yes—
345#380C2313yes—
346#380C2313yes—
347#380C2316yes—
348#380C23112yes—
349#380C2313yes—
350C4×C4⋊C4C2316yes—
351C4×C4⋊C4C2316yes—
352C4×C4⋊C4C2316yes—
353C4×C4⋊C4C2313yes—
354C4×C4⋊C4C2316yes—
355C4×C4⋊C4C2313yes—
356C4×C4⋊C4C2313yes—
357C4×C4⋊C4C2316yes—
358C4×C4⋊C4C2316yes—
359C4×C4⋊C4C2313yes—
360C4×C4⋊C4C2313yes—
361C4×C4⋊C4C2316yes—
362C4×C4⋊C4C2316yes—
363C4×C4⋊C4C2313yes—
364C4×C4⋊C4C2316yes—
365C4×C4⋊C4C2316yes—
366C4×C4⋊C4C2316yes—
367C4×C4⋊C4C2316yes—
368C4×C4⋊C4C23112yes—
369C4×C4⋊C4C2313yes—
370C4×C4⋊C4C2313yes—
371C4×C4⋊C4C2316yes—
372C4×C4⋊C4C2316yes—
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2316yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2313yes—
377C4×C4⋊C4C2313yes—
378C4×C4⋊C4C2313yes—
379C4×C4⋊C4C2316yes—
380C4×C4⋊C4C2313yes—
381C4×C4⋊C4C2313yes—
382C4×C4⋊C4C2316yes—
383C4×C4⋊C4C2313yes—
384C4×C4⋊C4C2316yes—
385C4×C22⋊C4C2313yes—
386C4×C22⋊C4C2316yes—
387C4×C22⋊C4C2316yes—
388C4×C22⋊C4C2313yes—
389C4×C22⋊C4C2316yes—
390C4×C22⋊C4C2313yes—
391C4×C22⋊C4C2316yes—
392C4×C22⋊C4C2313yes—
393C4×C22⋊C4C2316yes—
394C4×C22⋊C4C2316yes—
395C4×C22⋊C4C2313yes—
396C4×C22⋊C4C2313yes—
397#376C2316yes—
398#376C2316yes—
399#376C2316yes—
400C2×#95C2316yes—
401C43C2316yes—
402C43C2313yes—
403C43C2316yes—
404C22×Q8—24no—
405C22×Q8—24no—
406C22×Q8—24no—
407C22×Q8—24no—
408C22×Q8—24no—
409C22×Q8#4118yes—
410C22×Q8C2413yes—
411C22×Q8C2411yescharacteristic
412C22×Q8C2413yes—
413C22×Q8C2416yes—
414C22×Q8C2411yescharacteristic
415C22×D4C2411yescharacteristic
416C23×C4C2413yes—
417C23×C4C2413yes—
418C23×C4C2411yescharacteristic
419C23×C4C2412yes—
420C23×C4C2411yescharacteristic
421C23×C4C2413yes—
422C23×C4C2416yes—
423C23×C4C2413yes—
424C4⋊Q8—212no—
425C4⋊Q8—224no—
426C4⋊Q8—212no—
427#126C2×Q8116yescomplemented
428#125—412no—
429#125—812no—
430#125C2×Q8116yescomplemented
431#125C2×Q818yescomplemented
432#123C2×Q8116yes—
433C22⋊Q8—212no—
434C22⋊Q8—212no—
435C22⋊Q8—412no—
436C22⋊Q8—86no—
437C22⋊Q8C2×Q818yescomplemented
438C22⋊Q8C2×Q818yescomplemented
439C4×Q8—224no—
440C4×Q8—224no—
441C4×Q8—28no—
442C4×Q8—28no—
443C4×Q8—24no—
444C4×Q8—24no—
445C4×Q8—24no—
446C4×Q8—28no—
447C4×Q8—28no—
448C4×Q8—24no—
449C4×Q8—212no—
450C4×Q8—212no—
451C4×Q8—212no—
452C4×Q8—212no—
453C4×Q8—212no—
454C4×Q8—46no—
455C4×Q8—86no—
456C4×Q8C2×Q818yescomplemented
457C4×Q8#4118yes—
458C4×D4—212no—
459C4×D4—46no—
460C4×D4C2×Q818yes—
461#117—412no—
462#117—46no—
463#117C2×Q818yescomplemented
464#117C2×Q8116yescomplemented
465C2×C4⋊C4—224no—
466C2×C4⋊C4—212no—
467C2×C4⋊C4—212no—
468C2×C4⋊C4—46no—
469C2×C4⋊C4—86no—
470C2×C4⋊C4C2×Q818yescomplemented
471C2×C4⋊C4C2413yes—
472C2×C4⋊C4C2413yes—
473C2×C4⋊C4C2416yes—
474C2×C4⋊C4C2416yes—
475C2×C4⋊C4C2413yes—
476C2×C4⋊C4C24112yes—
477C2×C4⋊C4C2416yes—
478C2×C4⋊C4C2416yes—
479C2×C4⋊C4C2413yes—
480C2×C4⋊C4C2413yes—
481C2×C4⋊C4C2413yes—
482C2×C4⋊C4C2413yes—
483C2×C4⋊C4C2416yes—
484C2×C4⋊C4C2413yes—
485C2×C4⋊C4C2416yes—
486C2×C4⋊C4C2413yes—
487C2×C4⋊C4C2416yes—
488C2×C4⋊C4C2416yes—
489C2×C4⋊C4C2416yes—
490C2×C4⋊C4C2416yes—
491C2×C4⋊C4C24112yes—
492C2×C4⋊C4C2416yes—
493C2×C4⋊C4C2416yes—
494C2×C4⋊C4C2416yes—
495C2×C4⋊C4C2413yes—
496C2×C4⋊C4C24112yes—
497C2×C4⋊C4C2416yes—
498C2×C4⋊C4C24112yes—
499C2×C4⋊C4C2416yes—
500C2×C4⋊C4C24112yes—
501C2×C4⋊C4C2416yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C24112yes—
505C2×C4⋊C4C24112yes—
506C2×C4⋊C4C2411yescharacteristic
507C2×C4⋊C4C2411yescharacteristic
508C2×C4⋊C4C2412yes—
509C2×C4⋊C4C2412yes—
510C2×C4⋊C4C2411yescharacteristic
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2411yescharacteristic
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2412yes—
515C2×C4⋊C4C2412yes—
516C2×C4⋊C4C2413yes—
517C2×C22⋊C4C2413yes—
518C2×C22⋊C4C2416yes—
519C2×C22⋊C4C2413yes—
520C2×C22⋊C4C2413yes—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2413yes—
523C2×C22⋊C4C2416yes—
524C2×C22⋊C4C2411yescharacteristic
525C2×C22⋊C4C2412yes—
526C2×C22⋊C4C2412yes—
527C2×C22⋊C4C2411yescharacteristic
528C2×C22⋊C4C2412yes—
529C2×C42—224no—
530C2×C42—212no—
531C2×C42—212no—
532C2×C42C2413yes—
533C2×C42C2416yes—
534C2×C42C2416yes—
535C2×C42C2413yes—
536C2×C42C2413yes—
537C2×C42C2416yes—
538C2×C42C2413yes—
539C2×C42C2416yes—
540C2×C42C2413yes—
541C2×C42C2413yes—
542C2×C42C2413yes—
543C2×C42C2416yes—
544C2×C42C2413yes—
545C2×C42C2413yes—
546C2×C42C2416yes—
547C2×C42C2416yes—
548C2×C42C2416yes—
549C2×C42C2416yes—
550C2×C42C2413yes—
551C2×C42C2413yes—
552C2×C42C2416yes—
553C2×C42C2416yes—
554C2×C42C2416yes—
555C2×C42C2412yes—
556C2×C42C2412yes—
557C2×C42C2411yescharacteristic
558C2×C42C2413yes—
559#95C2416yes—
560#95C2416yes—
561#95C2416yes—
562#95C2416yes—
563#95C2413yes—
564#95C2413yes—
565#95C2416yes—
566#95C2416yes—
567#95C2416yes—
568#95C2416yes—
569#95C2416yes—
570#95C2416yes—
571#95C2416yes—
572#95C2416yes—
573#95C2416yes—
574#95C2413yes—
575#95C2413yes—
576#95C2413yes—
577#95C2413yes—
578#95C2416yes—
579#95C2416yes—
580#95C24112yes—
581#95C2416yes—
582#95C24112yes—
583#95C2416yes—
584#95C2416yes—
585#95C2416yes—
586#95C24112yes—
587#95C24112yes—
588#95C2416yes—
589#95C2416yes—
590#95C2416yes—
591#95C2416yes—
592#95C2416yes—
593#95C24112yes—
594C24C2511yescharacteristic
595C24C2511yescharacteristic
596C2×Q8—232no—
597C2×Q8—22no—
598C2×Q8—26no—
599C2×Q8—26no—
600C2×Q8—26no—
601C2×Q8—212no—
602C2×Q8—26no—
603C2×Q8—26no—
604C2×Q8—22no—
605C2×Q8—46no—
606C2×Q8—46no—
607C2×Q8—416no—
608C2×Q8C22×Q814yes—
609C2×Q8C2×#41112yes—
610C2×Q8C2×#4114yes—
611C2×Q8C2×#4114yes—
612C2×Q82−1+414yes—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4C22×Q814yes—
616C22×C4—24no—
617C22×C4—24no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—26no—
621C22×C4—26no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—26no—
625C22×C4—212no—
626C22×C4—26no—
627C22×C4—26no—
628C22×C4—26no—
629C22×C4—26no—
630C22×C4—26no—
631C22×C4—43no—
632C22×C4—46no—
633C22×C4—46no—
634C22×C4—43no—
635C22×C4—43no—
636C22×C4C22×Q818yes—
637C22×C4C22×Q814yes—
638C22×C4C22×Q814yes—
639C22×C4C2×#41112yes—
640C22×C4C2513yes—
641C22×C4C2513yes—
642C22×C4C2516yes—
643C22×C4C2516yes—
644C22×C4C2513yes—
645C22×C4C2516yes—
646C22×C4C2513yes—
647C22×C4C2516yes—
648C22×C4C2513yes—
649C22×C4C2511yescharacteristic
650C22×C4C2512yes—
651C22×C4C2511yescharacteristic
652C22×C4C2512yes—
653C22×C4C2512yes—
654C22×C4C2511yescharacteristic
655C22×C4C2512yes—
656C22×C4C2511yescharacteristic
657C22×C4C2513yes—
658C22×C4C2513yes—
659C22×C4C2511yescharacteristic
660C22×C4C2513yes—
661C4⋊C4—212no—
662C4⋊C4—224no—
663C4⋊C4—212no—
664C4⋊C4—212no—
665C4⋊C4—26no—
666C4⋊C4—26no—
667C4⋊C4—212no—
668C4⋊C4—26no—
669C4⋊C4—26no—
670C4⋊C4—212no—
671C4⋊C4—212no—
672C4⋊C4—26no—
673C4⋊C4—212no—
674C4⋊C4—26no—
675C4⋊C4—212no—
676C4⋊C4—26no—
677C4⋊C4—26no—
678C4⋊C4—26no—
679C4⋊C4—46no—
680C4⋊C4—46no—
681C4⋊C4—46no—
682C4⋊C4—412no—
683C4⋊C4—46no—
684C4⋊C4—46no—
685C4⋊C4—43no—
686C4⋊C4—46no—
687C4⋊C4—412no—
688C4⋊C4—46no—
689C4⋊C4—412no—
690C4⋊C4—412no—
691C4⋊C4—412no—
692C4⋊C4—412no—
693C4⋊C4—46no—
694C4⋊C4—46no—
695C4⋊C4—46no—
696C4⋊C4C22×Q814yes—
697C4⋊C4C22×Q814yes—
698C4⋊C4C22×Q818yes—
699C4⋊C4C22×Q818yes—
700C4⋊C4C22×Q814yes—
701C4⋊C4C22×Q818yes—
702C4⋊C4C22×Q814yes—
703C4⋊C4C22×Q818yes—
704C4⋊C4C22×Q818yes—
705C4⋊C4C22×Q818yes—
706C4⋊C4C2×#41112yes—
707C22⋊C4—26no—
708C22⋊C4—26no—
709C22⋊C4—212no—
710C22⋊C4—26no—
711C22⋊C4—46no—
712C22⋊C4—43no—
713C22⋊C4—46no—
714C22⋊C4C22×Q814yes—
715C22⋊C4C22×Q818yes—
716C22⋊C4C22×Q818yes—
717C22⋊C4C22×Q814yes—
718C22⋊C4C22×Q818yes—
719C42—26no—
720C42—212no—
721C42—212no—
722C42—212no—
723C42—212no—
724C42—26no—
725C42—26no—
726C42—26no—
727C42—26no—
728C42—26no—
729C42—26no—
730C42—212no—
731C42—26no—
732C42—212no—
733C42—26no—
734C42—46no—
735C42—46no—
736C42—46no—
737C42—43no—
738C42—46no—
739C42—43no—
740C42—46no—
741C42—46no—
742C42C22×Q818yes—
743C42C22×Q818yes—
744C42C22×Q814yes—
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—
758C23C22×#4112yes—
759C23#58512yes—
760C23C2611yescharacteristic
761Q8—224no—
762Q8—28no—
763Q8—412no—
764Q8—812no—
765Q8#552116yesdirect product factor
766D4—28no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—23no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—23no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—23no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—23no—
787C2×C4—216no—
788C2×C4—224no—
789C2×C4—28no—
790C2×C4—28no—
791C2×C4—26no—
792C2×C4—26no—
793C2×C4—23no—
794C2×C4—23no—
795C2×C4—23no—
796C2×C4—23no—
797C2×C4—26no—
798C2×C4—23no—
799C2×C4—23no—
800C2×C4—26no—
801C2×C4—23no—
802C2×C4—23no—
803C2×C4—23no—
804C2×C4—23no—
805C2×C4—23no—
806C2×C4—26no—
807C2×C4—26no—
808C2×C4—26no—
809C2×C4—26no—
810C2×C4—23no—
811C2×C4—26no—
812C2×C4—26no—
813C2×C4—23no—
814C2×C4—26no—
815C2×C4—23no—
816C2×C4—26no—
817C2×C4—23no—
818C2×C4—412no—
819C2×C4—412no—
820C2×C4—86no—
821C2×C4—812no—
822C2×C4C23×Q812yes—
823C2×C4C23×Q812yes—
824C2×C4C23×Q814yes—
825C2×C4C23×Q814yes—
826C2×C4C23×Q814yes—
827C2×C4C23×Q812yes—
828C2×C4C23×Q812yes—
829C2×C4C23×Q814yes—
830C2×C4C23×Q812yes—
831C2×C4C22×#4116yes—
832C2×C4C22×#4116yes—
833C2×C4C22×#4116yes—
834C2×C4C22×#4116yes—
835C2×C4C22×#4112yes—
836C2×C4C2×2−1+416yes—
837C2×C4#58512yes—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22Q8×#4114yes—
852C22C24×Q811yescharacteristic
853C22C23×#4111yescharacteristic
854C22C23×#4111yescharacteristic
855C22C22×2−1+411yescharacteristic
856C22C2×#58511yescharacteristic
857C22C2×#58511yescharacteristic
858C22H(7,𝔽2)11yescharacteristic
859C4—22no—
860C4—24no—
861C4—26no—
862C4—26no—
863C4—24no—
864C4—24no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—43no—
870C4—46no—
871C4—46no—
872C4—43no—
873C4—43no—
874C4—46no—
875C4—43no—
876C4—46no—
877C4—43no—
878C4C2×#552112yes—
879C4Q8×#4114yes—
880C2—24no—
881C2—42no—
882C2C22×#55211yescharacteristic
883C2C2×Q8×#4111yescharacteristic
884C2C2×Q8×#4111yescharacteristic
885C2Q8×2−1+411yescharacteristic
886C2#6300611yescharacteristic
887C2#6300811yescharacteristic
888C2#6303311yescharacteristic
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. #59934C2semidirect
2. #59499C2semidirect
3. #59445C2semidirect
4. #59321C2semidirect
6. #59259C2semidirect
7. Q8×#126C2semidirect
8. Q8×#125C2semidirect
9. Q8×#125C2semidirect
11. Q8×C22⋊Q8C2semidirect
12. Q8×C22⋊Q8C2semidirect
13. #36287C2semidirect
14. #36285C2semidirect
15. #36280C2semidirect
16. #36193C2semidirect
18. C4×Q82C2semidirect
21. Q8×#117C2semidirect
22. Q8×#117C2semidirect
23. C2×Q8×C4⋊C4C2semidirect
161. #552Q8direct (N × H)
427. #126C2×Q8semidirect
430. #125C2×Q8semidirect
431. #125C2×Q8semidirect
437. C22⋊Q8C2×Q8semidirect
438. C22⋊Q8C2×Q8semidirect
456. C4×Q8C2×Q8semidirect
463. #117C2×Q8semidirect
464. #117C2×Q8semidirect
470. C2×C4⋊C4C2×Q8semidirect
765. Q8#552direct (N × H)

Maximal subgroups

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

subgroupindex
#599342
#594992
#594452
#593212
#592912
#592592
Q8×#1262
Q8×#1252
Q8×#1232
Q8×C22⋊Q82
#362872
#362852
#362802
#361932
#361892
C4×Q822
C4×#5522
C4×D4×Q82
Q8×#1172
C2×Q8×C4⋊C42