Finite Group Databasebeta

← #7614220

Subgroups — #7614220

Order 512.

1678 conjugacy classes of subgroups.

The subgroup lattice has 1225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3390C211yesmaximal, characteristic
2C2×#3387C211yesmaximal, characteristic
3#45389C211yesmaximal, characteristic
4#45277C211yesmaximal, characteristic
5#31242C211yesmaximal, characteristic
6#31242C211yesmaximal, characteristic
7#31239C211yesmaximal, characteristic
8#31236C211yesmaximal, characteristic
9#28818C211yesmaximal, characteristic
10#28810C211yesmaximal, characteristic
11#28294C211yesmaximal, characteristic
12#28291C211yesmaximal, characteristic
13#28278C211yesmaximal, characteristic
14#28278C211yesmaximal, characteristic
15#26493C211yesmaximal, characteristic
16#26491C211yesmaximal, characteristic
17#26489C211yesmaximal, characteristic
18#26489C211yesmaximal, characteristic
19#26474C211yesmaximal, characteristic
20#26474C211yesmaximal, characteristic
21#26473C211yesmaximal, characteristic
22#26473C211yesmaximal, characteristic
23#24336C211yesmaximal, characteristic
24#24336C211yesmaximal, characteristic
25#24333C211yesmaximal, characteristic
26#24332C211yesmaximal, characteristic
27#23187C211yesmaximal, characteristic
28#23184C211yesmaximal, characteristic
29#21730C211yesmaximal, characteristic
30#21717C211yesmaximal, characteristic
31#21698C211yesmaximal, characteristic
32C2×Q82C2211yescharacteristic
33C2×#557C2211yescharacteristic
34C2×#557C2211yescharacteristic
35C2×#557C2211yescharacteristic
36#3390—28no—
37#3387—28no—
38C2×#501C2211yescharacteristic
39C2×#501C2211yescharacteristic
40C2×#501C2211yescharacteristic
41C2×#499C2211yescharacteristic
42C2×#498C2211yescharacteristic
43C2×#494C2211yescharacteristic
44C2×#479C2211yescharacteristic
45C2×#479C2211yescharacteristic
46C2×#479C2211yescharacteristic
47C2×#479C2211yescharacteristic
48C2×#479C2211yescharacteristic
49C2×#479C2211yescharacteristic
50C2×#477C2211yescharacteristic
51C2×#477C2211yescharacteristic
52C2×#477C2211yescharacteristic
53C2×#475C2211yescharacteristic
54C2×#475C2211yescharacteristic
55C2×#475C2211yescharacteristic
56C2×#446C2211yescharacteristic
57C2×#446C2211yescharacteristic
58C2×#441C2211yescharacteristic
59C2×#441C2211yescharacteristic
60C2×#441C2211yescharacteristic
61C2×#441C2211yescharacteristic
62C2×C4×Q16C2211yescharacteristic
63C2×C4×Q16C2211yescharacteristic
64C2×C4×Q16C2211yescharacteristic
65C2×C4×Q16C2211yescharacteristic
66#2734—21no—
67#2734—21no—
68#2726—21no—
69#2726—21no—
70#2713—21no—
71#2713—21no—
72#2713—21no—
73#2713—21no—
74#2582C2211yescharacteristic
75#2582C2211yescharacteristic
76#2581C2211yescharacteristic
77#2581C2211yescharacteristic
78#2550C2211yescharacteristic
79#2550C2211yescharacteristic
80#2550C2211yescharacteristic
81#2550C2211yescharacteristic
82#2462—21no—
83#2462—21no—
84#2462—21no—
85#2462—21no—
86#2453C2211yescharacteristic
87#2453C2211yescharacteristic
88#2453C2211yescharacteristic
89#2453C2211yescharacteristic
90#2451—21no—
91#2451—21no—
92#2451C2211yescharacteristic
93#2451C2211yescharacteristic
94#2451C2211yescharacteristic
95#2451C2211yescharacteristic
96#2446—21no—
97#2446—21no—
98#2399C2211yescharacteristic
99#2365C2211yescharacteristic
100#2365C2211yescharacteristic
101#2365C2211yescharacteristic
102#2365C2211yescharacteristic
103#2331C2211yescharacteristic
104#2330C2211yescharacteristic
105#2327C2211yescharacteristic
106#2327C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2068C2211yescharacteristic
111#2068C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2068C2211yescharacteristic
115#2066C2211yescharacteristic
116#2066C2211yescharacteristic
117#2066C2211yescharacteristic
118#2066C2211yescharacteristic
119#2066C2211yescharacteristic
120#2066C2211yescharacteristic
121#2066C2211yescharacteristic
122#2066C2211yescharacteristic
123#2059C2211yescharacteristic
124#2059C2211yescharacteristic
125#2059C2211yescharacteristic
126#2059C2211yescharacteristic
127#2057C2211yescharacteristic
128#2057C2211yescharacteristic
129#2057C2211yescharacteristic
130#2057C2211yescharacteristic
131#2026C2211yescharacteristic
132#2026C2211yescharacteristic
133#2026C2211yescharacteristic
134#2026C2211yescharacteristic
135#2024C2211yescharacteristic
136#2024C2211yescharacteristic
137#2024C2211yescharacteristic
138#2024C2211yescharacteristic
139#1991C2211yescharacteristic
140#1990C2211yescharacteristic
141#1984C2211yescharacteristic
142#1984C2211yescharacteristic
143#1981C2211yescharacteristic
144#1981C2211yescharacteristic
145#1981C2211yescharacteristic
146#1981C2211yescharacteristic
147#1971C2211yescharacteristic
148#1971C2211yescharacteristic
149#1971C2211yescharacteristic
150#1971C2211yescharacteristic
151#1969C2211yescharacteristic
152#1969C2211yescharacteristic
153#1969C2211yescharacteristic
154#1969C2211yescharacteristic
155#1960C2211yescharacteristic
156#1960C2211yescharacteristic
157#1949C2211yescharacteristic
158#1949C2211yescharacteristic
159#1949C2211yescharacteristic
160#1949C2211yescharacteristic
161#1944C2211yescharacteristic
162#1943C2211yescharacteristic
163#1943C2211yescharacteristic
164#1943C2211yescharacteristic
165#1942C2211yescharacteristic
166#1941C2211yescharacteristic
167#1941C2211yescharacteristic
168#1941C2211yescharacteristic
169#1940C2211yescharacteristic
170#1940C2211yescharacteristic
171#1939C2211yescharacteristic
172#1939C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1878C2211yescharacteristic
181#1865C2211yescharacteristic
182#1865C2211yescharacteristic
183#1865C2211yescharacteristic
184#1865C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1863C2211yescharacteristic
189#1847C2211yescharacteristic
190#1846C2211yescharacteristic
191#1843C2211yescharacteristic
192#1805C2211yescharacteristic
193#1805C2211yescharacteristic
194#1803C2211yescharacteristic
195#1803C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198C4×#107C2211yescharacteristic
199C4×#106C2211yescharacteristic
200#1771C2211yescharacteristic
201#1771C2211yescharacteristic
202#1770C2211yescharacteristic
203C8×C4⋊C4C2211yescharacteristic
204#1726C2211yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209Q82—24no—
210Q82—42no—
211#557—24no—
212#557—24no—
213#557—24no—
214#557—42no—
215#557—42no—
216#557—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8—21no—
220C2×C4⋊Q8—21no—
221C2×C4⋊Q8—21no—
222C2×C4⋊Q8—21no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×C4⋊Q8C2311yescharacteristic
230C2×#125—21no—
231C2×#125—21no—
232C2×#125—21no—
233C2×#125—21no—
234C2×#125—21no—
235C2×#125—21no—
236C2×#125C2311yescharacteristic
237C2×#125C2311yescharacteristic
238C2×#125C2311yescharacteristic
239C2×#125C2311yescharacteristic
240C2×#125C2311yescharacteristic
241C2×C4×Q8—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8—21no—
244C2×C4×Q8—21no—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×Q8C2311yescharacteristic
259#501—24no—
260#501—24no—
261#501D418yes—
262#499—24no—
263#498—24no—
264#494Q818yescomplemented
265#479—24no—
266#479—24no—
267#479—24no—
268#479—24no—
269#479—24no—
270#479—24no—
271#477—24no—
272#477—24no—
273#477—24no—
274#475—24no—
275#475—24no—
276#475—24no—
277#446—24no—
278#446—24no—
279#441—24no—
280#441—24no—
281#441—24no—
282#441—24no—
283C4×Q16—24no—
284C4×Q16—24no—
285C4×Q16—42no—
286C4×Q16—42no—
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#107C2311yescharacteristic
290C2×#107C2311yescharacteristic
291C2×#107C2311yescharacteristic
292C2×#107C2311yescharacteristic
293C2×#107C2311yescharacteristic
294C2×#107C2311yescharacteristic
295C2×#107C2311yescharacteristic
296C2×#107C2311yescharacteristic
297C2×#106C2311yescharacteristic
298C2×#106C2311yescharacteristic
299C2×#106C2311yescharacteristic
300C2×#106C2311yescharacteristic
301C2×#106C2311yescharacteristic
302C2×#106C2311yescharacteristic
303C2×#106C2311yescharacteristic
304C2×#106C2311yescharacteristic
305C2×#106C2311yescharacteristic
306C2×#106C2311yescharacteristic
307C2×C4⋊C8C2311yescharacteristic
308C2×C4⋊C8C2311yescharacteristic
309C2×C4⋊C8C2311yescharacteristic
310C2×C4⋊C8C2311yescharacteristic
311C2×C4⋊C8C2311yescharacteristic
312C2×C4⋊C8C2311yescharacteristic
313C2×C4⋊C8C2311yescharacteristic
314C2×C4⋊C8C2311yescharacteristic
315C2×C4⋊C8C2311yescharacteristic
316C2×C4⋊C8C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×#103C2311yescharacteristic
322C2×#103C2311yescharacteristic
323C2×#103C2311yescharacteristic
324C2×#103C2311yescharacteristic
325C2×#103C2311yescharacteristic
326C2×#103C2311yescharacteristic
327C2×#103C2311yescharacteristic
328C2×#103C2311yescharacteristic
329C2×#103C2311yescharacteristic
330C2×#103C2311yescharacteristic
331C2×#103C2311yescharacteristic
332C2×#103C2311yescharacteristic
333C2×#103C2311yescharacteristic
334C2×#103C2311yescharacteristic
335C2×#103C2311yescharacteristic
336C2×#103C2311yescharacteristic
337C2×#103C2311yescharacteristic
338C2×#103C2311yescharacteristic
339C2×#103C2311yescharacteristic
340C2×#103C2311yescharacteristic
341C2×#97C2311yescharacteristic
342C2×#97C2311yescharacteristic
343C2×#97C2311yescharacteristic
344C2×#97C2311yescharacteristic
345C2×#97C2311yescharacteristic
346C2×C4×C8C2311yescharacteristic
347C2×C4×C8C2311yescharacteristic
348C2×C4×C8C2311yescharacteristic
349C2×C4×C8C2311yescharacteristic
350C2×C4×C8C2311yescharacteristic
351#400—21no—
352#400—21no—
353#400—21no—
354#400—21no—
355#400—21no—
356#400—21no—
357#398—21no—
358#398—21no—
359#398—21no—
360#398—21no—
361#398—21no—
362#398—21no—
363#398—21no—
364#398—21no—
365#398—21no—
366#398—21no—
367#398—21no—
368#398—21no—
369#398—21no—
370#398—21no—
371#398—21no—
372#398—21no—
373#398D411yescharacteristic
374#398D411yescharacteristic
375#398D411yescharacteristic
376#398D411yescharacteristic
377#395—21no—
378#395—21no—
379#395—21no—
380#395—21no—
381#395—21no—
382#395—21no—
383#395—21no—
384#395—21no—
385#395—21no—
386#395—21no—
387#395D411yescharacteristic
388#395D411yescharacteristic
389#395D411yescharacteristic
390#395D411yescharacteristic
391#391—21no—
392#391—21no—
393#391—21no—
394#391—21no—
395#391—21no—
396#391—21no—
397#391—21no—
398#391—21no—
399#391—21no—
400#391—21no—
401#391—21no—
402#391—21no—
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#391C2311yescharacteristic
408#391C2311yescharacteristic
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389—21no—
420#389—21no—
421#389—21no—
422#389—21no—
423#389—21no—
424#389—21no—
425#389—21no—
426#389—21no—
427#389—21no—
428#389—21no—
429#389—21no—
430#389—21no—
431#389C2311yescharacteristic
432#389C2311yescharacteristic
433#389C2311yescharacteristic
434#389C2311yescharacteristic
435#389C2311yescharacteristic
436#389C2311yescharacteristic
437#389C2311yescharacteristic
438#389C2311yescharacteristic
439#389C2311yescharacteristic
440#389C2311yescharacteristic
441#389C2311yescharacteristic
442#389C2311yescharacteristic
443#387—21no—
444#387—21no—
445#387—21no—
446#387—21no—
447#387—21no—
448#387—21no—
449#387—21no—
450#387—21no—
451#387—21no—
452#387—21no—
453#387—21no—
454#387—21no—
455#387—21no—
456#387—21no—
457#387—21no—
458#387—21no—
459#387—21no—
460#387—21no—
461#387—21no—
462#387—21no—
463#387—21no—
464#387—21no—
465#387—21no—
466#387—21no—
467#387—21no—
468#387—21no—
469#387—21no—
470#387—21no—
471#387—21no—
472#387—21no—
473#387—21no—
474#387—21no—
475#384C2311yescharacteristic
476#382C2311yescharacteristic
477#382C2311yescharacteristic
478#382C2311yescharacteristic
479C4×C4⋊C4—21no—
480C4×C4⋊C4—21no—
481C4×C4⋊C4—21no—
482C4×C4⋊C4—21no—
483C4×C4⋊C4C2311yescharacteristic
484C4×C4⋊C4C2311yescharacteristic
485C4×C4⋊C4C2311yescharacteristic
486C4×C4⋊C4C2311yescharacteristic
487C4×C4⋊C4C2311yescharacteristic
488C4×C4⋊C4C2311yescharacteristic
489C4×C4⋊C4C2311yescharacteristic
490C4×C4⋊C4C2311yescharacteristic
491#376C2311yescharacteristic
492#340C2311yescharacteristic
493#340C2311yescharacteristic
494#340C2311yescharacteristic
495#340C2311yescharacteristic
496#340C2311yescharacteristic
497#340C2311yescharacteristic
498#340C2311yescharacteristic
499#340C2311yescharacteristic
500#340C2311yescharacteristic
501#340C2311yescharacteristic
502#340C2311yescharacteristic
503#340C2311yescharacteristic
504#340C2311yescharacteristic
505#340C2311yescharacteristic
506#340C2311yescharacteristic
507#340C2311yescharacteristic
508#336C2311yescharacteristic
509#336C2311yescharacteristic
510#336C2311yescharacteristic
511#336C2311yescharacteristic
512#336C2311yescharacteristic
513#336C2311yescharacteristic
514#336C2311yescharacteristic
515#336C2311yescharacteristic
516C22×Q8—21no—
517C22×Q8—21no—
518C22×Q8—21no—
519C22×Q8—21no—
520C22×Q8—21no—
521C22×Q8C2×D411yescharacteristic
522C22×Q8C2×D411yescharacteristic
523C22×Q8C2411yescharacteristic
524C22×Q8C2411yescharacteristic
525C22×Q8C2411yescharacteristic
526C22×Q8C2411yescharacteristic
527C2×Q16—22no—
528C2×Q16—22no—
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16C2×Q814yes—
536C2×Q16C2×Q814yes—
537C2×Q16C2×Q814yes—
538C2×Q16C2×Q814yes—
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C4⋊Q8—22no—
548C4⋊Q8—22no—
549C4⋊Q8—22no—
550C4⋊Q8—22no—
551C4⋊Q8—22no—
552C4⋊Q8—22no—
553C4⋊Q8—22no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—44no—
559C4⋊Q8—44no—
560C4⋊Q8—44no—
561C4⋊Q8—44no—
562C4⋊Q8—44no—
563C4⋊Q8—44no—
564C4⋊Q8C2×D414yes—
565C4⋊Q8C2×Q814yes—
566C4⋊Q8C2×Q814yes—
567#125—22no—
568#125—22no—
569#125—22no—
570#125—22no—
571#125—22no—
572#125—41no—
573#125—41no—
574#125—41no—
575#125—41no—
576#125—44no—
577#125—44no—
578#125—44no—
579#125—44no—
580#125—44no—
581#125—44no—
582#125C2×D414yes—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—22no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—22no—
595C4×Q8—22no—
596C4×Q8—22no—
597C4×Q8—22no—
598C4×Q8—22no—
599C4×Q8—22no—
600C4×Q8—22no—
601C4×Q8—22no—
602C4×Q8—22no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—44no—
612C4×Q8—44no—
613C4×Q8—44no—
614C4×Q8—44no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709#107—22no—
710#107—22no—
711#107—22no—
712#107—22no—
713#107—22no—
714#107—41no—
715#107—41no—
716#107—41no—
717#107C2×D414yes—
718#107C2×D414yes—
719#106—22no—
720#106—22no—
721#106—22no—
722#106—22no—
723#106—22no—
724#106—22no—
725#106—22no—
726#106—41no—
727#106C2×D414yes—
728#106C2×D414yes—
729C4⋊C8—22no—
730C4⋊C8—22no—
731C4⋊C8—22no—
732C4⋊C8—22no—
733C4⋊C8—22no—
734C4⋊C8—22no—
735C4⋊C8—22no—
736C4⋊C8—22no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#97—22no—
764#97—22no—
765#97—22no—
766#97—22no—
767#97C2×D414yes—
768C4×C8—22no—
769C4×C8—22no—
770C4×C8—22no—
771C4×C8—41no—
772C4×C8C2×Q814yes—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831C2×Q8—22no—
832C2×Q8—22no—
833C2×Q8—24no—
834C2×Q8—22no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—41no—
856C2×Q8—41no—
857C2×Q8—41no—
858C2×Q8—42no—
859C2×Q8—42no—
860C2×Q8—42no—
861C2×Q8—42no—
862C2×Q8—42no—
863C2×Q8—42no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×Q8—81no—
871C2×Q8—81no—
872C2×Q8C22×Q812yes—
873C2×Q8C22×Q812yes—
874C2×Q8C22×Q812yes—
875C2×Q8C22×Q812yes—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C2511yescharacteristic
907Q16—28no—
908Q16—28no—
909Q16—44no—
910Q16—44no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8C22×D412yes—
931C2×C8C22×D412yes—
932C2×C8C22×Q812yes—
933C2×C8C22×Q812yes—
934C2×C82−1+412yes—
935C4⋊C4—24no—
936C4⋊C4—24no—
937C4⋊C4—24no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—24no—
945C4⋊C4—24no—
946C4⋊C4—24no—
947C4⋊C4—24no—
948C4⋊C4—22no—
949C4⋊C4—22no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—41no—
975C4⋊C4—41no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4C22×D412yes—
1015C4⋊C4C22×D412yes—
1016C4⋊C4C22×D412yes—
1017C4⋊C4C22×D412yes—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—42no—
1029C42—42no—
1030C42—42no—
1031C42—42no—
1032C42—42no—
1033C42—42no—
1034C42—42no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C42—42no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42C22×D412yes—
1045C42C22×Q812yes—
1046C42H(5,𝔽2)12yes—
1047C422−1+412yes—
1048C23C23×D411yescharacteristic
1049Q8—22no—
1050Q8—22no—
1051Q8—22no—
1052Q8—22no—
1053Q8—22no—
1054Q8—22no—
1055Q8—22no—
1056Q8—22no—
1057Q8—44no—
1058Q8—41no—
1059Q8—41no—
1060Q8—41no—
1061Q8—41no—
1062Q8—41no—
1063Q8—41no—
1064Q8—41no—
1065Q8—41no—
1066Q8—82no—
1067Q8—84no—
1068Q8—84no—
1069Q8—84no—
1070Q8—162no—
1071Q8—162no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—22no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4D4212yes—
1158C2×C4D4212yes—
1159C2×C4D4×Q812yes—
1160C2×C4D4×Q812yes—
1161C2×C4#57812yes—
1162C2×C4C23×D411yescharacteristic
1163C2×C4C23×Q811yescharacteristic
1164C2×C4C2×H(5,𝔽2)11yescharacteristic
1165C2×C4C2×2−1+411yescharacteristic
1166C2×C4C2×2−1+411yescharacteristic
1167C2×C4#58511yescharacteristic
1168C8—22no—
1169C8—22no—
1170C8—41no—
1171C8—41no—
1172C8—41no—
1173C8—41no—
1174C8—41no—
1175C8D4×Q814yes—
1176C22C2×D4211yescharacteristic
1177C22C2×D4×Q811yescharacteristic
1178C22#349711yescharacteristic
1179C22C2×#57811yescharacteristic
1180C22#358411yescharacteristic
1181C22#358611yescharacteristic
1182C22#358611yescharacteristic
1183C4—22no—
1184C4—22no—
1185C4—22no—
1186C4—22no—
1187C4—22no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—42no—
1193C4—42no—
1194C4—42no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—42no—
1199C4—42no—
1200C4—42no—
1201C4—42no—
1202C4—42no—
1203C4—41no—
1204C4—41no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4C2×D4×Q811yescharacteristic
1214C4#349711yescharacteristic
1215C4#350111yescharacteristic
1216C4#355011yescharacteristic
1217C2#5981711yescharacteristic
1218C2#6107311yescharacteristic
1219C2#6107611yescharacteristic
1220C2#6137211yescharacteristic
1221C2#6137911yescharacteristic
1222C2#6240611yescharacteristic
1223C2#6241211yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2399 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
264. #494Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#33902
C2×#33872
#453892
#452772
#312422
#312392
#312362
#288182
#288102
#282942
#282912
#282782
#264932
#264912
#264892
#264742
#264732
#243362
#243332
#243322
#231872
#231842
#217302
#217172
#216982