Finite Group Databasebeta

← Q8×#538 #7665627

Subgroups — Q8×#538 #7665627

Order 512.

5638 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39666C216yesmaximal, complemented
2#39663C216yesmaximal, complemented
3#39659C216yesmaximal, complemented
4#39654C216yesmaximal, complemented
5#39640C213yesmaximal, complemented
6#39632C213yesmaximal, complemented
7#39605C216yesmaximal, complemented
8Q8×#126C212yesmaximal, complemented
9Q8×#124C212yesmaximal, complemented
10Q8×#123C212yesmaximal, complemented
11Q8×C22⋊Q8C211yesmaximal, characteristic, complemented
12Q8×#121C212yesmaximal, complemented
13Q8×#121C211yesmaximal, characteristic, complemented
14Q8×#120C212yesmaximal, complemented
15#35016C216yesmaximal, complemented
16#35014C213yesmaximal, complemented
17C4×D4×Q8C212yesmaximal, complemented
18C2×Q8×C22⋊C4C211yesmaximal, characteristic, complemented
19C4×#538C213yesmaximal
20C24×Q8C2211yescharacteristic
21C2×Q82C2211yescharacteristic, complemented
22C2×D4×Q8C2212yes—
23C2×D4×Q8C2212yes—
24C2×D4×Q8C2212yes—
25C2×D4×Q8C2211yescharacteristic, complemented
26C2×#538C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28C22×C4×Q8C2211yescharacteristic
29C22×C4×Q8C2212yescomplemented
30#2863C2216yescomplemented
31#2862C2216yescomplemented
32#2857C2213yes—
33#2857C2213yes—
34#2857C2216yescomplemented
35#2855C2216yescomplemented
36#2848C2216yes—
37#2806C2216yescomplemented
38#2806C2216yescomplemented
39#2805C2216yescomplemented
40#2804C2216yescomplemented
41#2788C22112yes—
42#2788C22112yescomplemented
43#2784C22112yes—
44#2780C22112yes—
45#2774C22112yescomplemented
46#2768C22112yes—
47#2666C22112yescomplemented
48#2665C22112yescomplemented
49#2646C2216yes—
50#2626C2216yes—
51#2589C22112yes—
52#2587C22112yes—
53#2586C22112yescomplemented
54#2582C2213yescomplemented
55#2574C22112yescomplemented
56#2568C2216yescomplemented
57#2567C2213yescomplemented
58#2563C2216yes—
59#2546C2216yescomplemented
60#2546C2213yescomplemented
61#2538C2216yes—
62#2538C2213yescomplemented
63#2511C2216yescomplemented
64#2511C2216yescomplemented
65#2511C2216yescomplemented
66#2505C22112yes—
67#2502C2216yescomplemented
68#2497C2216yes—
69#2497C2216yes—
70#2497C2216yes—
71#2492C2216yes—
72#2492C2216yes—
73#2492C2216yescomplemented
74#2492C2216yescomplemented
75#2487C2216yes—
76#2451C2216yescomplemented
77#2450C22112yes—
78#2446C2216yescomplemented
79#2446C2216yescomplemented
80#2440C2216yes—
81#2434C2216yes—
82#2434C2216yes—
83#2434C2216yes—
84#2429C2216yes—
85#2429C2216yescomplemented
86#2429C2216yescomplemented
87#2423C2216yes—
88#2423C2216yes—
89#2417C2216yes—
90#2417C2216yes—
91#2417C2216yescomplemented
92#2409C2216yes—
93#2409C2216yes—
94#2409C2216yes—
95#2365C2216yescomplemented
96#2360C2216yes—
97#2360C2216yescomplemented
98Q8×C4⋊C4C2212yescomplemented
99Q8×C4⋊C4C2212yescomplemented
100Q8×C4⋊C4C2211yescharacteristic, complemented
101Q8×C4⋊C4C2211yescharacteristic, complemented
102D4×C4⋊C4C2216yes—
103Q8×C22⋊C4C2212yes—
104Q8×C22⋊C4C2212yes—
105Q8×C22⋊C4C2216yes—
106Q8×C22⋊C4C2216yes—
107Q8×C22⋊C4C2212yes—
108Q8×C22⋊C4C2212yes—
109Q8×C22⋊C4C2212yes—
110Q8×C22⋊C4C2212yescomplemented
111Q8×C22⋊C4C2212yescomplemented
112#2337C2216yes—
113#2335C2216yes—
114#2334C2216yes—
115#2333C2216yes—
116#2329C2213yes—
117#2329C2216yes—
118#2325C2213yes—
119#2321C2216yes—
120#2318C2216yes—
121#2312C2213yes—
122C4×C4⋊Q8C2216yescomplemented
123C4×#126C2216yes—
124C4×#124C2216yes—
125C4×C22⋊Q8C2213yes—
126C4×C22⋊Q8C2216yes—
127C4×C22⋊Q8C2216yescomplemented
128C4×#123C2216yes—
129C4×#121C2213yes—
130C4×#121C2216yes—
131C4×#120C2216yes—
132C2×#391C2213yes—
133C2×#391C2213yes—
134C2×#380C2213yes—
135C42×Q8C2212yescomplemented
136C42×D4C2216yes—
137C2×C4×C22⋊C4C2213yes—
138C23×Q8—28no—
139C23×Q8—44no—
140C23×Q8—44no—
141C23×Q8C2312yes—
142C23×Q8C2312yes—
143C23×Q8C2311yescharacteristic
144C23×Q8C2316yes—
145C23×Q8C2313yes—
146C24×C4C2313yes—
147Q82—44no—
148D4×Q8—216no—
149D4×Q8—48no—
150D4×Q8—48no—
151D4×Q8—44no—
152#538Q8116yesdirect product factor
153C2×C4⋊Q8C2316yes—
154C2×C4⋊Q8C2316yes—
155C2×C4⋊Q8C2313yes—
156C2×C4⋊Q8C2316yes—
157C2×C4⋊Q8C2313yes—
158C2×C4⋊Q8C2316yes—
159C2×#126C2312yes—
160C2×#124C2312yes—
161C2×#123C2312yes—
162C2×C22⋊Q8C2316yes—
163C2×C22⋊Q8C2316yes—
164C2×C22⋊Q8C2316yes—
165C2×C22⋊Q8C2316yes—
166C2×C22⋊Q8C2316yes—
167C2×C22⋊Q8C2316yes—
168C2×C22⋊Q8C2316yes—
169C2×C22⋊Q8C2316yes—
170C2×C22⋊Q8C2311yescharacteristic
171C2×#121C2311yescharacteristic
172C2×#121C2312yes—
173C2×#120C2312yes—
174C2×C4×Q8—44no—
175C2×C4×Q8—44no—
176C2×C4×Q8—48no—
177C2×C4×Q8C2311yescharacteristic
178C2×C4×Q8C2312yes—
179C2×C4×Q8C2312yes—
180C2×C4×Q8C2312yes—
181C2×C4×Q8C2311yescharacteristic
182C2×C4×Q8C2312yes—
183C2×C4×Q8C2316yes—
184C2×C4×Q8C2316yes—
185C2×C4×Q8C2313yes—
186C2×C4×Q8C2313yes—
187C2×C4×Q8C2313yes—
188C2×C4×Q8C2316yes—
189C2×C4×D4C2316yes—
190C2×C4×D4C2316yes—
191C2×C4×D4C2316yes—
192C2×C4×D4C2316yes—
193C2×C4×D4C2313yes—
194C2×C4×D4C2312yes—
195C22×C4⋊C4C2313yes—
196C22×C4⋊C4C2316yes—
197C22×C4⋊C4C2313yes—
198C22×C22⋊C4C2313yes—
199C22×C22⋊C4C2311yescharacteristic
200C22×C42C2316yes—
201C22×C42C2313yes—
202C22×C42C2313yes—
203#400C23112yes—
204#400C23112yes—
205#400C23112yes—
206#400C23112yes—
207#400C23112yes—
208#400C23112yes—
209#399C23112yes—
210#398C23112yes—
211#398C23112yes—
212#398C23112yes—
213#398C23112yes—
214#398C23112yes—
215#398C23112yes—
216#396C23112yes—
217#396C23112yes—
218#396C23112yes—
219#396C23112yes—
220#395C23112yes—
221#395C23112yes—
222#395C23112yes—
223#395C23112yes—
224#393C23112yes—
225#393C23112yes—
226#393C23112yes—
227#391C2316yes—
228#391C2316yes—
229#391C2316yes—
230#391C2316yes—
231#391C2316yes—
232#391C2316yes—
233#391C2316yes—
234#391C23112yes—
235#391C2313yes—
236#391C23112yes—
237#391C23112yes—
238#391C2316yes—
239#391C2316yes—
240#391C2316yes—
241#391C2316yes—
242#391C2316yes—
243#391C2316yes—
244#391C2316yes—
245#391C2316yes—
246#391C2316yes—
247#391C2316yes—
248#391C2316yes—
249#390C2316yes—
250#390C2316yes—
251#390C2313yes—
252#389C23112yes—
253#389C23112yes—
254#389C2313yes—
255#389C2316yes—
256#389C2316yes—
257#389C23112yes—
258#389C2316yes—
259#389C23112yes—
260#389C2316yes—
261#389C2316yes—
262#389C2313yes—
263#389C2316yes—
264#389C2316yes—
265#389C2316yes—
266#389C2316yes—
267#389C2316yes—
268#388C2316yes—
269#388C2316yes—
270#388C2316yes—
271#388C2316yes—
272#388C2316yes—
273#388C2316yes—
274#388C2316yes—
275#388C2316yes—
276#388C2316yes—
277#388C2316yes—
278#388C2316yes—
279#388C2316yes—
280#387C2316yes—
281#387C2316yes—
282#387C2316yes—
283#387C2316yes—
284#387C23112yes—
285#387C23112yes—
286#387C23112yes—
287#387C2316yes—
288#387C23112yes—
289#387C23112yes—
290#387C23112yes—
291#387C2316yes—
292#387C23112yes—
293#386C2316yes—
294#386C2316yes—
295#386C2316yes—
296#386C2316yes—
297#386C2316yes—
298#386C2316yes—
299#386C2316yes—
300#385C2316yes—
301#385C2316yes—
302#385C23112yes—
303#385C2316yes—
304#385C23112yes—
305#385C23112yes—
306#385C23112yes—
307#385C2316yes—
308#385C2316yes—
309#385C23112yes—
310#385C23112yes—
311#384C2316yes—
312#384C2316yes—
313#384C2313yes—
314#384C2313yes—
315#383C2316yes—
316#382C23112yes—
317#382C2316yes—
318#381C2316yes—
319#380C2316yes—
320#380C2316yes—
321#380C2316yes—
322#380C2316yes—
323#380C2313yes—
324#380C2313yes—
325#380C2316yes—
326#380C23112yes—
327#380C2316yes—
328#380C2316yes—
329#380C2316yes—
330#380C2316yes—
331#380C23112yes—
332#379C2316yes—
333C4×C4⋊C4C2313yes—
334C4×C4⋊C4C2316yes—
335C4×C4⋊C4C2316yes—
336C4×C4⋊C4C2316yes—
337C4×C4⋊C4C23112yes—
338C4×C4⋊C4C2316yes—
339C4×C4⋊C4C2313yes—
340C4×C4⋊C4C2316yes—
341C4×C4⋊C4C2316yes—
342C4×C4⋊C4C2316yes—
343C4×C22⋊C4C2316yes—
344C4×C22⋊C4C2316yes—
345C4×C22⋊C4C2316yes—
346C4×C22⋊C4C2316yes—
347C4×C22⋊C4C2316yes—
348C4×C22⋊C4C2316yes—
349C4×C22⋊C4C2316yes—
350C4×C22⋊C4C2316yes—
351C4×C22⋊C4C2316yes—
352C4×C22⋊C4C2316yes—
353C4×C22⋊C4C2316yes—
354C4×C22⋊C4C2316yes—
355C4×C22⋊C4C2316yes—
356C2×#95C2313yes—
357C2×#95C2313yes—
358C2×#95C2316yes—
359C43C2316yes—
360C25C2411yescharacteristic
361C22×Q8—24no—
362C22×Q8—24no—
363C22×Q8—28no—
364C22×Q8—224no—
365C22×Q8—28no—
366C22×Q8—28no—
367C22×Q8—28no—
368C22×Q8—28no—
369C22×Q8—28no—
370C22×Q8—212no—
371C22×Q8—46no—
372C22×Q8—46no—
373C22×Q8—412no—
374C22×Q8—412no—
375C22×Q8—464no—
376C22×Q8#4118yes—
377C22×Q8C2416yes—
378C22×Q8C2416yes—
379C22×Q8C2413yes—
380C22×Q8C2416yes—
381C22×Q8C2416yes—
382C22×Q8C2411yescharacteristic
383C22×Q8C2411yescharacteristic
384C22×D4C2412yes—
385C22×D4C2412yes—
386C22×D4C2412yes—
387C22×D4C2411yescharacteristic
388C23×C4—212no—
389C23×C4—46no—
390C23×C4—46no—
391C23×C4C2416yes—
392C23×C4C2416yes—
393C23×C4C2413yes—
394C23×C4C2413yes—
395C23×C4C2413yes—
396C23×C4C2413yes—
397C23×C4C2416yes—
398C23×C4C2416yes—
399C23×C4C2411yescharacteristic
400C23×C4C2411yescharacteristic
401C23×C4C2412yes—
402C4⋊Q8—224no—
403C4⋊Q8—46no—
404C4⋊Q8—412no—
405C4⋊Q8—412no—
406C4⋊Q8—46no—
407C4⋊Q8—412no—
408#126C2×Q8116yescomplemented
409#124C2×Q8116yescomplemented
410#123C2×Q8116yescomplemented
411C22⋊Q8—224no—
412C22⋊Q8—224no—
413C22⋊Q8—412no—
414C22⋊Q8—412no—
415C22⋊Q8—412no—
416C22⋊Q8—412no—
417C22⋊Q8—412no—
418C22⋊Q8—412no—
419C22⋊Q8C2×Q818yescomplemented
420#121C2×Q8116yescomplemented
421#121C2×Q818yescomplemented
422#120C2×Q8116yescomplemented
423C4×Q8—28no—
424C4×Q8—28no—
425C4×Q8—24no—
426C4×Q8—28no—
427C4×Q8—24no—
428C4×Q8—28no—
429C4×Q8—46no—
430C4×Q8—412no—
431C4×Q8—412no—
432C4×Q8—412no—
433C4×Q8—46no—
434C4×Q8—46no—
435C4×D4—224no—
436C4×D4—412no—
437C4×D4—46no—
438C4×D4—412no—
439C4×D4—412no—
440C4×D4C2×Q8116yescomplemented
441C2×C4⋊C4—46no—
442C2×C4⋊C4—412no—
443C2×C4⋊C4—46no—
444C2×C4⋊C4C2416yes—
445C2×C4⋊C4C2416yes—
446C2×C4⋊C4C2413yes—
447C2×C4⋊C4C2413yes—
448C2×C4⋊C4C2416yes—
449C2×C4⋊C4C2416yes—
450C2×C4⋊C4C2416yes—
451C2×C4⋊C4C24112yes—
452C2×C4⋊C4C2416yes—
453C2×C4⋊C4C2416yes—
454C2×C4⋊C4C24112yes—
455C2×C4⋊C4C2416yes—
456C2×C4⋊C4C2413yes—
457C2×C4⋊C4C2416yes—
458C2×C4⋊C4C2416yes—
459C2×C4⋊C4C2413yes—
460C2×C4⋊C4C2416yes—
461C2×C4⋊C4C24112yes—
462C2×C4⋊C4C2416yes—
463C2×C4⋊C4C24112yes—
464C2×C4⋊C4C24112yes—
465C2×C4⋊C4C2416yes—
466C2×C4⋊C4C2413yes—
467C2×C4⋊C4C2416yes—
468C2×C4⋊C4C2413yes—
469C2×C4⋊C4C24112yes—
470C2×C4⋊C4C2416yes—
471C2×C4⋊C4C2412yes—
472C2×C4⋊C4C2412yes—
473C2×C4⋊C4C2411yescharacteristic
474C2×C4⋊C4C2411yescharacteristic
475C2×C22⋊C4—46no—
476C2×C22⋊C4C2×Q818yescomplemented
477C2×C22⋊C4C2416yes—
478C2×C22⋊C4C2416yes—
479C2×C22⋊C4C2416yes—
480C2×C22⋊C4C2416yes—
481C2×C22⋊C4C2416yes—
482C2×C22⋊C4C2416yes—
483C2×C22⋊C4C2416yes—
484C2×C22⋊C4C2416yes—
485C2×C22⋊C4C2416yes—
486C2×C22⋊C4C2416yes—
487C2×C22⋊C4C2416yes—
488C2×C22⋊C4C2416yes—
489C2×C22⋊C4C2416yes—
490C2×C22⋊C4C2416yes—
491C2×C22⋊C4C2412yes—
492C2×C22⋊C4C2412yes—
493C2×C22⋊C4C2412yes—
494C2×C22⋊C4C2412yes—
495C2×C22⋊C4C2412yes—
496C2×C22⋊C4C2412yes—
497C2×C22⋊C4C2412yes—
498C2×C42—46no—
499C2×C42—412no—
500C2×C42—46no—
501C2×C42C2416yes—
502C2×C42C2416yes—
503C2×C42C2413yes—
504C2×C42C2416yes—
505C2×C42C2413yes—
506C2×C42C2416yes—
507C2×C42C2416yes—
508C2×C42C2416yes—
509C2×C42C2413yes—
510C2×C42C2413yes—
511C2×C42C2416yes—
512C2×C42C2416yes—
513C2×C42C2416yes—
514C2×C42C2416yes—
515C2×C42C2412yes—
516#95C2416yes—
517#95C2416yes—
518#95C2416yes—
519#95C2416yes—
520#95C24112yes—
521#95C24112yes—
522#95C2416yes—
523#95C2416yes—
524#95C2416yes—
525#95C2416yes—
526#95C2416yes—
527#95C2416yes—
528#95C2416yes—
529#95C2416yes—
530#95C2416yes—
531#95C2416yes—
532#95C2416yes—
533#95C2416yes—
534#95C24112yes—
535#95C24112yes—
536#95C24112yes—
537#95C2416yes—
538#95C2416yes—
539#95C2416yes—
540#95C2416yes—
541#95C24112yes—
542#95C24112yes—
543#95C24112yes—
544C24—22no—
545C24—22no—
546C24—41no—
547C24—41no—
548C24—41no—
549C24—41no—
550C24C22×Q814yes—
551C24C2512yes—
552C24C2512yes—
553C24C2511yescharacteristic
554C2×Q8—232no—
555C2×Q8—212no—
556C2×Q8—212no—
557C2×Q8—212no—
558C2×Q8—26no—
559C2×Q8—26no—
560C2×Q8—212no—
561C2×Q8—212no—
562C2×Q8—212no—
563C2×Q8—212no—
564C2×Q8—41no—
565C2×Q8—46no—
566C2×Q8—46no—
567C2×Q8—41no—
568C2×Q8—46no—
569C2×Q8—46no—
570C2×Q8—46no—
571C2×Q8—448no—
572C2×Q8—496no—
573C2×Q8—432no—
574C2×Q8—432no—
575C2×Q8C22×Q814yescomplemented
576C2×Q8C2×#41112yes—
577C2×Q8C2×#4114yes—
578C2×Q8H(5,𝔽2)14yes—
579C2×Q8H(5,𝔽2)14yes—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—42no—
583C2×D4—41no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—41no—
588C2×D4C22×Q818yes—
589C2×D4C22×Q818yes—
590C2×D4C22×Q818yes—
591C2×D4C22×Q814yescomplemented
592C22×C4—26no—
593C22×C4—26no—
594C22×C4—26no—
595C22×C4—26no—
596C22×C4—26no—
597C22×C4—212no—
598C22×C4—212no—
599C22×C4—212no—
600C22×C4—212no—
601C22×C4—212no—
602C22×C4—212no—
603C22×C4—212no—
604C22×C4—41no—
605C22×C4—42no—
606C22×C4—41no—
607C22×C4—46no—
608C22×C4—46no—
609C22×C4—43no—
610C22×C4—43no—
611C22×C4—41no—
612C22×C4—42no—
613C22×C4—41no—
614C22×C4—43no—
615C22×C4—46no—
616C22×C4—43no—
617C22×C4—46no—
618C22×C4—43no—
619C22×C4—46no—
620C22×C4—43no—
621C22×C4—448no—
622C22×C4C22×Q814yes—
623C22×C4C22×Q814yes—
624C22×C4C22×Q818yescomplemented
625C22×C4C2×#41112yes—
626C22×C4C2516yes—
627C22×C4C2516yes—
628C22×C4C2513yes—
629C22×C4C2516yes—
630C22×C4C2516yes—
631C22×C4C2516yes—
632C22×C4C2513yes—
633C22×C4C2516yes—
634C22×C4C2512yes—
635C22×C4C2512yes—
636C22×C4C2512yes—
637C22×C4C2511yescharacteristic
638C22×C4C2511yescharacteristic
639C22×C4C2512yes—
640C22×C4C2513yes—
641C22×C4C2513yes—
642C4⋊C4—212no—
643C4⋊C4—212no—
644C4⋊C4—224no—
645C4⋊C4—212no—
646C4⋊C4—212no—
647C4⋊C4—26no—
648C4⋊C4—26no—
649C4⋊C4—212no—
650C4⋊C4—46no—
651C4⋊C4—46no—
652C4⋊C4—412no—
653C4⋊C4—43no—
654C4⋊C4—46no—
655C4⋊C4—43no—
656C4⋊C4—46no—
657C4⋊C4—412no—
658C4⋊C4—46no—
659C4⋊C4—46no—
660C4⋊C4—43no—
661C4⋊C4—46no—
662C4⋊C4—43no—
663C4⋊C4—46no—
664C4⋊C4—412no—
665C4⋊C4—46no—
666C4⋊C4—412no—
667C4⋊C4—46no—
668C4⋊C4—412no—
669C4⋊C4C22×Q818yescomplemented
670C4⋊C4C22×Q818yescomplemented
671C4⋊C4C22×Q814yescomplemented
672C4⋊C4C22×Q814yescomplemented
673C22⋊C4—212no—
674C22⋊C4—212no—
675C22⋊C4—212no—
676C22⋊C4—46no—
677C22⋊C4—46no—
678C22⋊C4—46no—
679C22⋊C4—46no—
680C22⋊C4—46no—
681C22⋊C4—46no—
682C22⋊C4—46no—
683C22⋊C4—46no—
684C22⋊C4—46no—
685C22⋊C4—46no—
686C22⋊C4—46no—
687C22⋊C4C22×Q818yes—
688C22⋊C4C22×Q818yes—
689C22⋊C4C22×Q818yes—
690C22⋊C4C22×Q818yes—
691C22⋊C4C22×Q818yes—
692C22⋊C4C22×Q818yescomplemented
693C22⋊C4C22×Q818yescomplemented
694C42—212no—
695C42—212no—
696C42—212no—
697C42—26no—
698C42—26no—
699C42—212no—
700C42—46no—
701C42—46no—
702C42—43no—
703C42—46no—
704C42—43no—
705C42—46no—
706C42—46no—
707C42—46no—
708C42C22×Q818yescomplemented
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—28no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23C23×Q814yes—
733C23C23×Q814yes—
734C23C23×Q812yes—
735C23C22×#4112yes—
736C23#58512yes—
737C23C2611yescharacteristic
738Q8—224no—
739Q8—44no—
740Q8—424no—
741Q8—424no—
742Q8—424no—
743Q8—166no—
744Q8#538116yesdirect product factor
745D4—216no—
746D4—48no—
747D4—48no—
748D4—44no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—23no—
756C2×C4—23no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—224no—
764C2×C4—26no—
765C2×C4—26no—
766C2×C4—26no—
767C2×C4—26no—
768C2×C4—26no—
769C2×C4—23no—
770C2×C4—23no—
771C2×C4—26no—
772C2×C4—26no—
773C2×C4—26no—
774C2×C4—26no—
775C2×C4—26no—
776C2×C4—26no—
777C2×C4—26no—
778C2×C4—26no—
779C2×C4—23no—
780C2×C4—23no—
781C2×C4—26no—
782C2×C4—26no—
783C2×C4—26no—
784C2×C4—26no—
785C2×C4—23no—
786C2×C4—26no—
787C2×C4—23no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4—48no—
791C2×C4—424no—
792C2×C4—412no—
793C2×C4—424no—
794C2×C4—424no—
795C2×C4—86no—
796C2×C4—86no—
797C2×C4—812no—
798C2×C4C23×Q814yes—
799C2×C4C23×Q814yes—
800C2×C4C23×Q814yes—
801C2×C4C23×Q812yes—
802C2×C4C23×Q812yes—
803C2×C4C23×Q814yes—
804C2×C4C22×#4116yes—
805C2×C4C22×#4116yes—
806C2×C4C2×H(5,𝔽2)16yes—
807C2×C4C2×H(5,𝔽2)16yes—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—24no—
815C22—24no—
816C22—24no—
817C22—24no—
818C22—24no—
819C22—24no—
820C22—416no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—42no—
829C22Q8×#4114yes—
830C22C24×Q811yescharacteristic
831C22C23×#4111yescharacteristic
832C22C22×H(5,𝔽2)11yescharacteristic
833C22C22×H(5,𝔽2)11yescharacteristic
834C22C2×#58511yescharacteristic
835C222−1+611yescharacteristic
836C222−1+611yescharacteristic
837C4—24no—
838C4—22no—
839C4—24no—
840C4—22no—
841C4—24no—
842C4—26no—
843C4—24no—
844C4—46no—
845C4—46no—
846C4—46no—
847C4—43no—
848C4—43no—
849C4—46no—
850C4—46no—
851C4—46no—
852C4C2×#538112yes—
853C2—24no—
854C2—44no—
855C2—44no—
856C2C22×#53811yescharacteristic
857C2C2×Q8×#4111yescharacteristic
858C2#6285011yescharacteristic
859C2#6289711yescharacteristic
860C2#6291911yescharacteristic
861C2Q8×H(5,𝔽2)11yescharacteristic
862C2Q8×H(5,𝔽2)11yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#538C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39666C2semidirect
2. #39663C2semidirect
3. #39659C2semidirect
4. #39654C2semidirect
5. #39640C2semidirect
6. #39632C2semidirect
7. #39605C2semidirect
8. Q8×#126C2semidirect
9. Q8×#124C2semidirect
10. Q8×#123C2semidirect
11. Q8×C22⋊Q8C2semidirect
12. Q8×#121C2semidirect
13. Q8×#121C2semidirect
14. Q8×#120C2semidirect
15. #35016C2semidirect
16. #35014C2semidirect
17. C4×D4×Q8C2semidirect
18. C2×Q8×C22⋊C4C2semidirect
21. C2×Q82C22semidirect
25. C2×D4×Q8C22semidirect
29. C22×C4×Q8C22semidirect
30. #2863C22semidirect
31. #2862C22semidirect
34. #2857C22semidirect
35. #2855C22semidirect
37. #2806C22semidirect
38. #2806C22semidirect
39. #2805C22semidirect
40. #2804C22semidirect
42. #2788C22semidirect
45. #2774C22semidirect
47. #2666C22semidirect
48. #2665C22semidirect
53. #2586C22semidirect
54. #2582C22semidirect
55. #2574C22semidirect
56. #2568C22semidirect
57. #2567C22semidirect
59. #2546C22semidirect
60. #2546C22semidirect
62. #2538C22semidirect
63. #2511C22semidirect
64. #2511C22semidirect
65. #2511C22semidirect
67. #2502C22semidirect
73. #2492C22semidirect
74. #2492C22semidirect
76. #2451C22semidirect
78. #2446C22semidirect
79. #2446C22semidirect
85. #2429C22semidirect
86. #2429C22semidirect
91. #2417C22semidirect
95. #2365C22semidirect
97. #2360C22semidirect
98. Q8×C4⋊C4C22semidirect
99. Q8×C4⋊C4C22semidirect
100. Q8×C4⋊C4C22semidirect
101. Q8×C4⋊C4C22semidirect
110. Q8×C22⋊C4C22semidirect
111. Q8×C22⋊C4C22semidirect
122. C4×C4⋊Q8C22semidirect
127. C4×C22⋊Q8C22semidirect
135. C42×Q8C22semidirect
152. #538Q8direct (N × H)
408. #126C2×Q8semidirect
409. #124C2×Q8semidirect
410. #123C2×Q8semidirect
419. C22⋊Q8C2×Q8semidirect
420. #121C2×Q8semidirect
421. #121C2×Q8semidirect
422. #120C2×Q8semidirect
440. C4×D4C2×Q8semidirect
476. C2×C22⋊C4C2×Q8semidirect
575. C2×Q8C22×Q8semidirect
591. C2×D4C22×Q8semidirect
624. C22×C4C22×Q8semidirect
669. C4⋊C4C22×Q8semidirect
670. C4⋊C4C22×Q8semidirect
671. C4⋊C4C22×Q8semidirect
672. C4⋊C4C22×Q8semidirect
692. C22⋊C4C22×Q8semidirect
693. C22⋊C4C22×Q8semidirect
708. C42C22×Q8semidirect
744. Q8#538direct (N × H)

Maximal subgroups

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

subgroupindex
#396662
#396632
#396592
#396542
#396402
#396322
#396052
Q8×#1262
Q8×#1242
Q8×#1232
Q8×C22⋊Q82
Q8×#1212
Q8×#1202
#350162
#350142
C4×D4×Q82
C2×Q8×C22⋊C42
C4×#5382