Finite Group Databasebeta

← Q8×#542 #7665628

Subgroups — Q8×#542 #7665628

Order 512.

4886 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39665C216yesmaximal, complemented
2#39660C216yesmaximal, complemented
3#39657C216yesmaximal, complemented
4#39652C216yesmaximal, complemented
5#39643C213yesmaximal, complemented
6#39633C213yesmaximal, complemented
7#39609C213yesmaximal, complemented
8#39608C213yesmaximal
9Q8×C4⋊Q8C211yesmaximal, characteristic, complemented
10Q8×#126C212yesmaximal, complemented
11Q8×#124C211yesmaximal, characteristic, complemented
12Q8×#124C212yesmaximal, complemented
13Q8×#123C212yesmaximal, complemented
14Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
15Q8×C22⋊Q8C212yesmaximal, complemented
16Q8×#121C211yesmaximal, characteristic
17#35283C213yesmaximal, complemented
18#35199C213yesmaximal, complemented
19#35177C213yesmaximal, complemented
20C4×Q82C211yesmaximal, characteristic, complemented
21C4×D4×Q8C211yesmaximal, characteristic, complemented
22Q8×#117C211yesmaximal, characteristic, complemented
23C4×#542C213yesmaximal
24C2×Q82C2211yescharacteristic
25C2×Q82C2212yes—
26C2×D4×Q8C2211yescharacteristic
27C2×D4×Q8C2212yes—
28C2×#542C2211yescharacteristic
29C22×C4×Q8C2211yescharacteristic
30C22×C4×Q8C2212yes—
31#2868C2213yes—
32#2863C2216yes—
33#2862C2216yes—
34#2862C2213yes—
35#2857C2216yes—
36#2857C2213yes—
37#2857C2213yes—
38#2855C2216yes—
39#2799C22112yes—
40#2790C22112yes—
41#2774C22112yes—
42#2763C22112yes—
43#2755C22112yes—
44#2742C22112yes—
45#2729C22112yes—
46#2692C22112yes—
47#2666C22112yes—
48#2665C22112yes—
49#2647C2216yes—
50#2628C2216yes—
51#2582C2213yes—
52#2582C2216yes—
53#2568C2213yes—
54#2568C2216yes—
55#2567C2213yes—
56#2567C2216yes—
57#2567C2216yes—
58#2563C2213yes—
59#2563C2216yes—
60#2551C2213yes—
61#2551C2213yes—
62#2551C2216yes—
63#2546C2213yes—
64#2538C2213yes—
65#2520C22112yes—
66#2511C2216yes—
67#2511C2216yes—
68#2511C2216yes—
69#2511C2216yes—
70#2509C2216yes—
71#2508C2216yes—
72#2502C2216yes—
73#2497C2216yes—
74#2497C2216yes—
75#2497C2216yes—
76#2492C2216yes—
77#2492C2216yes—
78#2492C2216yes—
79#2492C2216yes—
80#2492C2216yes—
81#2492C2216yes—
82#2492C2216yes—
83#2487C2216yes—
84#2465C22112yes—
85#2452C2216yes—
86#2451C2216yes—
87#2451C2216yes—
88#2451C2216yes—
89#2451C2216yes—
90#2451C2216yes—
91#2446C2216yes—
92#2446C2216yes—
93#2440C2216yes—
94#2440C2216yes—
95#2440C2216yes—
96#2429C2216yes—
97#2423C2216yes—
98#2423C2216yes—
99#2423C2216yes—
100#2417C2216yes—
101#2369C2213yes—
102#2369C2216yes—
103#2365C2213yes—
104#2360C2216yes—
105#2355C2213yes—
106#2355C2213yes—
107Q8×C4⋊C4C2211yescharacteristic
108Q8×C4⋊C4C2211yescharacteristic
109Q8×C4⋊C4C2211yescharacteristic
110Q8×C4⋊C4C2213yes—
111Q8×C4⋊C4C2211yescharacteristic
112Q8×C4⋊C4C2212yes—
113Q8×C4⋊C4C2212yes—
114Q8×C4⋊C4C2212yes—
115D4×C4⋊C4C2213yes—
116#2345C2213yes—
117#2345C2213yes—
118Q8×C22⋊C4C2211yescharacteristic
119Q8×C22⋊C4C2211yescharacteristic
120Q8×C22⋊C4C2212yes—
121Q8×C22⋊C4C2212yes—
122Q8×C22⋊C4C2212yes—
123Q8×C22⋊C4C2212yes—
124Q8×C22⋊C4C2212yes—
125#2337C2216yes—
126#2335C2216yes—
127#2334C2216yes—
128#2332C2216yes—
129#2331C2213yes—
130#2331C2216yes—
131#2326C2213yes—
132#2324C2213yes—
133#2323C2213yes—
134#2320C2213yes—
135#2319C2213yes—
136#2314C2213yes—
137C4×C4⋊Q8C2213yes—
138C4×C4⋊Q8C2213yes—
139C4×C4⋊Q8C2213yes—
140C4×C4⋊Q8C2216yes—
141C4×#126C2216yes—
142C4×#124C2213yes—
143C4×#124C2216yes—
144C4×C22⋊Q8C2213yes—
145C4×C22⋊Q8C2216yes—
146C4×C22⋊Q8C2216yes—
147C4×#123C2216yes—
148C4×#121C2213yes—
149#2295C2213yes—
150#2295C2213yes—
151#2285C2213yes—
152C42×Q8C2213yes—
153C42×Q8C2211yescharacteristic
154C42×Q8C2211yescharacteristic
155C42×Q8C2212yes—
156C42×D4C2213yes—
157C4×#117C2213yes—
158C23×Q8C2311yescharacteristic
159C23×Q8C2312yes—
160Q82—28no—
161Q82—48no—
162D4×Q8—28no—
163D4×Q8—48no—
164#542Q8116yesdirect product factor
165C2×C4⋊Q8C2313yes—
166C2×C4⋊Q8C2313yes—
167C2×C4⋊Q8C2316yes—
168C2×C4⋊Q8C2316yes—
169C2×C4⋊Q8C2316yes—
170C2×C4⋊Q8C2316yes—
171C2×C4⋊Q8C2316yes—
172C2×C4⋊Q8C2316yes—
173C2×C4⋊Q8C2316yes—
174C2×C4⋊Q8C2311yescharacteristic
175C2×#126C2312yes—
176C2×#124C2311yescharacteristic
177C2×#124C2312yes—
178C2×#123C2312yes—
179C2×C22⋊Q8C2316yes—
180C2×C22⋊Q8C2316yes—
181C2×C22⋊Q8C2316yes—
182C2×C22⋊Q8C2316yes—
183C2×C22⋊Q8C23112yes—
184C2×C22⋊Q8C2311yescharacteristic
185C2×C22⋊Q8C2312yes—
186C2×#121C2311yescharacteristic
187C2×C4×Q8—28no—
188C2×C4×Q8—48no—
189C2×C4×Q8C2313yes—
190C2×C4×Q8C2313yes—
191C2×C4×Q8C2311yescharacteristic
192C2×C4×Q8C2312yes—
193C2×C4×Q8C2311yescharacteristic
194C2×C4×Q8C2311yescharacteristic
195C2×C4×Q8C2311yescharacteristic
196C2×C4×Q8C2312yes—
197C2×C4×Q8C2311yescharacteristic
198C2×C4×Q8C2312yes—
199C2×C4×Q8C2313yes—
200C2×C4×Q8C2316yes—
201C2×C4×Q8C2316yes—
202C2×C4×Q8C2316yes—
203C2×C4×Q8C2313yes—
204C2×C4×Q8C2316yes—
205C2×C4×Q8C2311yescharacteristic
206C2×C4×Q8C2311yescharacteristic
207C2×C4×D4C2313yes—
208C2×C4×D4C2316yes—
209C2×C4×D4C2313yes—
210C2×C4×D4C2311yescharacteristic
211C2×#117C2313yes—
212C2×#117C2311yescharacteristic
213C22×C4⋊C4C2313yes—
214C22×C4⋊C4C2316yes—
215C22×C42C2313yes—
216C22×C42C2316yes—
217#400C23112yes—
218#400C23112yes—
219#400C23112yes—
220#400C23112yes—
221#400C23112yes—
222#400C23112yes—
223#400C23112yes—
224#399C23112yes—
225#398C23112yes—
226#398C23112yes—
227#398C23112yes—
228#398C23112yes—
229#398C23112yes—
230#398C23112yes—
231#396C23112yes—
232#396C23112yes—
233#395C23112yes—
234#395C23112yes—
235#395C23112yes—
236#395C23112yes—
237#395C23112yes—
238#393C23112yes—
239#393C23112yes—
240#393C23112yes—
241#391C2316yes—
242#391C2316yes—
243#391C2316yes—
244#391C23112yes—
245#391C2316yes—
246#391C2316yes—
247#391C2316yes—
248#391C2313yes—
249#391C2316yes—
250#391C2313yes—
251#391C2316yes—
252#391C2316yes—
253#391C2316yes—
254#391C2313yes—
255#391C2316yes—
256#391C2316yes—
257#391C2316yes—
258#391C23112yes—
259#391C23112yes—
260#391C2313yes—
261#391C2313yes—
262#391C2316yes—
263#391C2313yes—
264#391C2316yes—
265#391C2316yes—
266#391C23112yes—
267#391C2316yes—
268#390C2313yes—
269#390C2316yes—
270#390C2313yes—
271#389C2316yes—
272#389C2313yes—
273#389C2313yes—
274#389C2316yes—
275#389C2316yes—
276#389C2316yes—
277#389C2316yes—
278#389C2316yes—
279#389C23112yes—
280#389C2316yes—
281#389C2313yes—
282#389C2316yes—
283#389C2316yes—
284#389C23112yes—
285#389C2316yes—
286#389C2316yes—
287#389C2316yes—
288#389C2313yes—
289#389C2313yes—
290#389C2316yes—
291#389C2316yes—
292#389C2313yes—
293#389C2313yes—
294#389C2313yes—
295#389C2316yes—
296#389C2316yes—
297#388C2316yes—
298#388C2316yes—
299#388C2316yes—
300#388C2316yes—
301#388C2316yes—
302#388C2316yes—
303#388C2316yes—
304#388C2316yes—
305#388C2316yes—
306#388C2316yes—
307#388C2316yes—
308#388C2316yes—
309#387C2316yes—
310#387C2316yes—
311#387C2316yes—
312#387C2316yes—
313#387C2316yes—
314#387C2316yes—
315#387C2316yes—
316#387C23112yes—
317#387C23112yes—
318#387C2316yes—
319#387C23112yes—
320#387C2316yes—
321#387C2316yes—
322#387C2316yes—
323#387C2316yes—
324#387C23112yes—
325#387C23112yes—
326#387C23112yes—
327#386C2316yes—
328#386C2316yes—
329#385C2316yes—
330#385C2316yes—
331#385C2316yes—
332#385C2316yes—
333#385C23112yes—
334#385C23112yes—
335#384C2316yes—
336#384C2313yes—
337#384C2313yes—
338#384C2313yes—
339#384C2313yes—
340#384C2316yes—
341#384C2316yes—
342#384C2313yes—
343#384C2316yes—
344#383C2316yes—
345#382C2316yes—
346#382C23112yes—
347#382C2313yes—
348#382C2316yes—
349#382C2316yes—
350#381C2316yes—
351#380C2313yes—
352#380C2316yes—
353#380C2316yes—
354#380C2316yes—
355#380C2316yes—
356#380C2313yes—
357#380C2313yes—
358#380C2316yes—
359#380C2313yes—
360#380C2316yes—
361#380C2316yes—
362#380C2316yes—
363C4×C4⋊C4C2313yes—
364C4×C4⋊C4C2316yes—
365C4×C4⋊C4C2316yes—
366C4×C4⋊C4C2313yes—
367C4×C4⋊C4C2313yes—
368C4×C4⋊C4C2316yes—
369C4×C4⋊C4C2313yes—
370C4×C4⋊C4C2316yes—
371C4×C4⋊C4C2313yes—
372C4×C4⋊C4C2313yes—
373C4×C4⋊C4C2316yes—
374C4×C4⋊C4C2316yes—
375C4×C4⋊C4C2313yes—
376C4×C4⋊C4C2313yes—
377C4×C4⋊C4C2313yes—
378C4×C4⋊C4C2313yes—
379C4×C4⋊C4C2313yes—
380C4×C4⋊C4C2316yes—
381C4×C4⋊C4C2313yes—
382C4×C4⋊C4C2313yes—
383C4×C4⋊C4C2313yes—
384C4×C4⋊C4C2313yes—
385C4×C4⋊C4C2313yes—
386C4×C4⋊C4C2316yes—
387C4×C4⋊C4C2316yes—
388C4×C4⋊C4C2316yes—
389C4×C22⋊C4C2316yes—
390C4×C22⋊C4C2316yes—
391C4×C22⋊C4C2316yes—
392C4×C22⋊C4C2316yes—
393C4×C22⋊C4C2316yes—
394C4×C22⋊C4C2313yes—
395C4×C22⋊C4C2313yes—
396C4×C22⋊C4C2313yes—
397C4×C22⋊C4C2313yes—
398C4×C22⋊C4C2316yes—
399C4×C22⋊C4C2316yes—
400#376C2313yes—
401#376C2313yes—
402C43C2316yes—
403C43C2313yes—
404C43C2313yes—
405C22×Q8—24no—
406C22×Q8—28no—
407C22×Q8—28no—
408C22×Q8—24no—
409C22×Q8—24no—
410C22×Q8—28no—
411C22×Q8C2413yes—
412C22×Q8C2416yes—
413C22×Q8C2411yescharacteristic
414C22×Q8C2416yes—
415C22×Q8C24112yes—
416C22×Q8C2412yes—
417C22×Q8C2411yescharacteristic
418C22×D4C2411yescharacteristic
419C22×D4C2412yes—
420C23×C4C2413yes—
421C23×C4C2416yes—
422C23×C4C2411yescharacteristic
423C23×C4C2413yes—
424C23×C4C2416yes—
425C23×C4C2412yes—
426C4⋊Q8—224no—
427C4⋊Q8—212no—
428C4⋊Q8—212no—
429C4⋊Q8—412no—
430C4⋊Q8—412no—
431C4⋊Q8—412no—
432C4⋊Q8—412no—
433C4⋊Q8—412no—
434C4⋊Q8—86no—
435C4⋊Q8C2×Q818yescomplemented
436#126C2×Q8116yescomplemented
437#124C2×Q818yescomplemented
438#124C2×Q8116yescomplemented
439#123C2×Q8116yescomplemented
440C22⋊Q8—224no—
441C22⋊Q8—412no—
442C22⋊Q8—412no—
443C22⋊Q8—812no—
444C22⋊Q8—86no—
445C22⋊Q8C2×Q8116yescomplemented
446C22⋊Q8C2×Q818yescomplemented
447#121C2×Q818yes—
448C4×Q8—24no—
449C4×Q8—28no—
450C4×Q8—24no—
451C4×Q8—28no—
452C4×Q8—28no—
453C4×Q8—24no—
454C4×Q8—24no—
455C4×Q8—24no—
456C4×Q8—212no—
457C4×Q8—212no—
458C4×Q8—212no—
459C4×Q8—412no—
460C4×Q8—412no—
461C4×Q8—412no—
462C4×Q8—46no—
463C4×Q8—86no—
464C4×Q8C2×Q818yescomplemented
465C4×Q8#4118yes—
466C4×D4—212no—
467C4×D4—46no—
468C4×D4—412no—
469C4×D4C2×Q818yescomplemented
470#117—46no—
471#117C2×Q818yescomplemented
472C2×C4⋊C4—212no—
473C2×C4⋊C4—412no—
474C2×C4⋊C4C2413yes—
475C2×C4⋊C4C2416yes—
476C2×C4⋊C4C2413yes—
477C2×C4⋊C4C2416yes—
478C2×C4⋊C4C2413yes—
479C2×C4⋊C4C2413yes—
480C2×C4⋊C4C2416yes—
481C2×C4⋊C4C2413yes—
482C2×C4⋊C4C2416yes—
483C2×C4⋊C4C2413yes—
484C2×C4⋊C4C2413yes—
485C2×C4⋊C4C2416yes—
486C2×C4⋊C4C2413yes—
487C2×C4⋊C4C2413yes—
488C2×C4⋊C4C2416yes—
489C2×C4⋊C4C24112yes—
490C2×C4⋊C4C2413yes—
491C2×C4⋊C4C2413yes—
492C2×C4⋊C4C2416yes—
493C2×C4⋊C4C24112yes—
494C2×C4⋊C4C2416yes—
495C2×C4⋊C4C2416yes—
496C2×C4⋊C4C2416yes—
497C2×C4⋊C4C2416yes—
498C2×C4⋊C4C2416yes—
499C2×C4⋊C4C24112yes—
500C2×C4⋊C4C2416yes—
501C2×C4⋊C4C24112yes—
502C2×C4⋊C4C2416yes—
503C2×C4⋊C4C2416yes—
504C2×C4⋊C4C24112yes—
505C2×C4⋊C4C2416yes—
506C2×C4⋊C4C2416yes—
507C2×C4⋊C4C2411yescharacteristic
508C2×C4⋊C4C2411yescharacteristic
509C2×C4⋊C4C2411yescharacteristic
510C2×C4⋊C4C2411yescharacteristic
511C2×C4⋊C4C2412yes—
512C2×C4⋊C4C2412yes—
513C2×C4⋊C4C2412yes—
514C2×C4⋊C4C2413yes—
515C2×C22⋊C4C2416yes—
516C2×C22⋊C4C2413yes—
517C2×C22⋊C4C2413yes—
518C2×C22⋊C4C2416yes—
519C2×C22⋊C4C2416yes—
520C2×C22⋊C4C2416yes—
521C2×C22⋊C4C2416yes—
522C2×C22⋊C4C2416yes—
523C2×C22⋊C4C2416yes—
524C2×C22⋊C4C2416yes—
525C2×C22⋊C4C2411yescharacteristic
526C2×C22⋊C4C2411yescharacteristic
527C2×C22⋊C4C2412yes—
528C2×C22⋊C4C2412yes—
529C2×C22⋊C4C2412yes—
530C2×C22⋊C4C2412yes—
531C2×C22⋊C4C2412yes—
532C2×C42—212no—
533C2×C42—412no—
534C2×C42C2413yes—
535C2×C42C2413yes—
536C2×C42C2416yes—
537C2×C42C2413yes—
538C2×C42C2416yes—
539C2×C42C2413yes—
540C2×C42C2416yes—
541C2×C42C2413yes—
542C2×C42C2413yes—
543C2×C42C2413yes—
544C2×C42C2413yes—
545C2×C42C2413yes—
546C2×C42C2413yes—
547C2×C42C2416yes—
548C2×C42C2416yes—
549C2×C42C2416yes—
550C2×C42C2416yes—
551C2×C42C2413yes—
552C2×C42C2413yes—
553C2×C42C2413yes—
554C2×C42C2416yes—
555C2×C42C2411yescharacteristic
556C2×C42C2411yescharacteristic
557C2×C42C2412yes—
558C2×C42C2413yes—
559#95C2413yes—
560#95C2413yes—
561#95C2413yes—
562#95C2413yes—
563#95C2413yes—
564#95C2413yes—
565#95C2413yes—
566#95C2413yes—
567#95C2416yes—
568#95C2416yes—
569#95C2416yes—
570#95C2416yes—
571#95C2416yes—
572#95C2416yes—
573#95C2416yes—
574#95C2416yes—
575#95C2416yes—
576#95C2416yes—
577#95C2416yes—
578#95C2416yes—
579#95C2416yes—
580#95C2416yes—
581#95C2416yes—
582#95C2416yes—
583#95C24112yes—
584#95C2416yes—
585#95C2416yes—
586#95C24112yes—
587#95C2416yes—
588#95C2416yes—
589#95C2416yes—
590#95C2416yes—
591#95C24112yes—
592#95C24112yes—
593#95C24112yes—
594#95C24112yes—
595C24C2512yes—
596C24C2511yescharacteristic
597C2×Q8—22no—
598C2×Q8—26no—
599C2×Q8—212no—
600C2×Q8—212no—
601C2×Q8—212no—
602C2×Q8—26no—
603C2×Q8—26no—
604C2×Q8—212no—
605C2×Q8—22no—
606C2×Q8—42no—
607C2×Q8—42no—
608C2×Q8—46no—
609C2×Q8—46no—
610C2×Q8—412no—
611C2×Q8—412no—
612C2×Q8—412no—
613C2×Q8—416no—
614C2×Q8—432no—
615C2×Q8C22×Q814yes—
616C2×Q8C22×Q818yes—
617C2×Q8C2×#4114yes—
618C2×Q8H(5,𝔽2)14yes—
619C2×Q82−1+414yes—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—42no—
623C2×D4—42no—
624C2×D4C22×Q814yes—
625C2×D4C22×Q818yes—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—26no—
629C22×C4—212no—
630C22×C4—212no—
631C22×C4—26no—
632C22×C4—26no—
633C22×C4—212no—
634C22×C4—26no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—46no—
638C22×C4—46no—
639C22×C4—43no—
640C22×C4—46no—
641C22×C4—43no—
642C22×C4C22×Q814yes—
643C22×C4C22×Q818yes—
644C22×C4C2513yes—
645C22×C4C2513yes—
646C22×C4C2513yes—
647C22×C4C2516yes—
648C22×C4C2516yes—
649C22×C4C2513yes—
650C22×C4C2513yes—
651C22×C4C2516yes—
652C22×C4C2513yes—
653C22×C4C2516yes—
654C22×C4C2511yescharacteristic
655C22×C4C2511yescharacteristic
656C22×C4C2511yescharacteristic
657C22×C4C2512yes—
658C22×C4C2511yescharacteristic
659C22×C4C2512yes—
660C22×C4C2511yescharacteristic
661C22×C4C2512yes—
662C22×C4C2513yes—
663C22×C4C2511yescharacteristic
664C22×C4C2513yes—
665C4⋊C4—26no—
666C4⋊C4—212no—
667C4⋊C4—26no—
668C4⋊C4—212no—
669C4⋊C4—212no—
670C4⋊C4—26no—
671C4⋊C4—212no—
672C4⋊C4—26no—
673C4⋊C4—212no—
674C4⋊C4—212no—
675C4⋊C4—26no—
676C4⋊C4—26no—
677C4⋊C4—26no—
678C4⋊C4—26no—
679C4⋊C4—26no—
680C4⋊C4—412no—
681C4⋊C4—46no—
682C4⋊C4—46no—
683C4⋊C4—43no—
684C4⋊C4—43no—
685C4⋊C4—46no—
686C4⋊C4—46no—
687C4⋊C4—46no—
688C4⋊C4—46no—
689C4⋊C4—46no—
690C4⋊C4—412no—
691C4⋊C4—46no—
692C4⋊C4—412no—
693C4⋊C4—412no—
694C4⋊C4—46no—
695C4⋊C4—46no—
696C4⋊C4—412no—
697C4⋊C4—46no—
698C4⋊C4C22×Q814yes—
699C4⋊C4C22×Q814yes—
700C4⋊C4C22×Q814yes—
701C4⋊C4C22×Q814yes—
702C4⋊C4C22×Q818yes—
703C4⋊C4C22×Q818yes—
704C4⋊C4C22×Q818yes—
705C4⋊C4C2×#41112yes—
706C22⋊C4—212no—
707C22⋊C4—46no—
708C22⋊C4—43no—
709C22⋊C4—43no—
710C22⋊C4—46no—
711C22⋊C4—46no—
712C22⋊C4—46no—
713C22⋊C4—46no—
714C22⋊C4—46no—
715C22⋊C4—46no—
716C22⋊C4C22×Q814yes—
717C22⋊C4C22×Q814yes—
718C22⋊C4C22×Q818yes—
719C22⋊C4C22×Q818yes—
720C22⋊C4C22×Q818yes—
721C22⋊C4C22×Q818yes—
722C22⋊C4C22×Q818yes—
723C42—26no—
724C42—26no—
725C42—26no—
726C42—212no—
727C42—26no—
728C42—212no—
729C42—212no—
730C42—26no—
731C42—26no—
732C42—26no—
733C42—26no—
734C42—26no—
735C42—46no—
736C42—46no—
737C42—43no—
738C42—46no—
739C42—43no—
740C42—46no—
741C42—43no—
742C42—46no—
743C42—43no—
744C42C22×Q814yes—
745C42C22×Q814yes—
746C42C22×Q818yes—
747C42C2×#41112yes—
748C23—22no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—22no—
753C23—21no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—22no—
758C23—22no—
759C23—21no—
760C23C23×Q814yes—
761C23C23×Q812yes—
762C23C2611yescharacteristic
763Q8—28no—
764Q8—48no—
765Q8—412no—
766Q8—424no—
767Q8—812no—
768Q8—1612no—
769Q8#542116yesdirect product factor
770D4—28no—
771D4—48no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—23no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—23no—
789C2×C4—22no—
790C2×C4—28no—
791C2×C4—23no—
792C2×C4—23no—
793C2×C4—26no—
794C2×C4—26no—
795C2×C4—23no—
796C2×C4—26no—
797C2×C4—26no—
798C2×C4—23no—
799C2×C4—26no—
800C2×C4—23no—
801C2×C4—23no—
802C2×C4—23no—
803C2×C4—23no—
804C2×C4—26no—
805C2×C4—23no—
806C2×C4—23no—
807C2×C4—23no—
808C2×C4—23no—
809C2×C4—26no—
810C2×C4—26no—
811C2×C4—26no—
812C2×C4—23no—
813C2×C4—26no—
814C2×C4—23no—
815C2×C4—23no—
816C2×C4—26no—
817C2×C4—23no—
818C2×C4—23no—
819C2×C4—26no—
820C2×C4—23no—
821C2×C4—48no—
822C2×C4—412no—
823C2×C4—424no—
824C2×C4—86no—
825C2×C4—812no—
826C2×C4C23×Q812yes—
827C2×C4C23×Q812yes—
828C2×C4C23×Q814yes—
829C2×C4C23×Q812yes—
830C2×C4C23×Q812yes—
831C2×C4C23×Q814yes—
832C2×C4C23×Q812yes—
833C2×C4C23×Q814yes—
834C2×C4C23×Q812yes—
835C2×C4C22×#4116yes—
836C2×C4C22×#4116yes—
837C2×C4C22×#4112yes—
838C2×C4C2×H(5,𝔽2)16yes—
839C2×C4C2×2−1+416yes—
840C2×C4#58512yes—
841C22—24no—
842C22—22no—
843C22—24no—
844C22—22no—
845C22—22no—
846C22—24no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—41no—
851C22—42no—
852C22—41no—
853C22—41no—
854C22—42no—
855C22C24×Q811yescharacteristic
856C22C23×#4111yescharacteristic
857C22C22×H(5,𝔽2)11yescharacteristic
858C22C22×2−1+411yescharacteristic
859C22C2×#58511yescharacteristic
860C22H(7,𝔽2)11yescharacteristic
861C222−1+611yescharacteristic
862C4—22no—
863C4—24no—
864C4—24no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—26no—
869C4—22no—
870C4—24no—
871C4—43no—
872C4—46no—
873C4—43no—
874C4—46no—
875C4—46no—
876C4—43no—
877C4—43no—
878C4—46no—
879C4—43no—
880C4—43no—
881C4C2×#542112yes—
882C4Q8×#4114yes—
883C2—44no—
884C2—42no—
885C2C22×#54211yescharacteristic
886C2C2×Q8×#4111yescharacteristic
887C2#6285711yescharacteristic
888C2#6292311yescharacteristic
889C2#6295311yescharacteristic
890C2Q8×H(5,𝔽2)11yescharacteristic
891C2Q8×2−1+411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#121C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39665C2semidirect
2. #39660C2semidirect
3. #39657C2semidirect
4. #39652C2semidirect
5. #39643C2semidirect
6. #39633C2semidirect
7. #39609C2semidirect
9. Q8×C4⋊Q8C2semidirect
10. Q8×#126C2semidirect
11. Q8×#124C2semidirect
12. Q8×#124C2semidirect
13. Q8×#123C2semidirect
14. Q8×C22⋊Q8C2semidirect
15. Q8×C22⋊Q8C2semidirect
17. #35283C2semidirect
18. #35199C2semidirect
19. #35177C2semidirect
20. C4×Q82C2semidirect
21. C4×D4×Q8C2semidirect
22. Q8×#117C2semidirect
164. #542Q8direct (N × H)
435. C4⋊Q8C2×Q8semidirect
436. #126C2×Q8semidirect
437. #124C2×Q8semidirect
438. #124C2×Q8semidirect
439. #123C2×Q8semidirect
445. C22⋊Q8C2×Q8semidirect
446. C22⋊Q8C2×Q8semidirect
464. C4×Q8C2×Q8semidirect
469. C4×D4C2×Q8semidirect
471. #117C2×Q8semidirect
769. Q8#542direct (N × H)

Maximal subgroups

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

subgroupindex
#396652
#396602
#396572
#396522
#396432
#396332
#396092
#396082
Q8×C4⋊Q82
Q8×#1262
Q8×#1242
Q8×#1232
Q8×C22⋊Q82
Q8×#1212
#352832
#351992
#351772
C4×Q822
C4×D4×Q82
Q8×#1172
C4×#5422