Finite Group Databasebeta

← #7336517

Subgroups — #7336517

Order 512.

1491 conjugacy classes of subgroups.

The subgroup lattice has 1295 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53024C211yesmaximal, characteristic
2#45322C211yesmaximal, characteristic
3#32074C211yesmaximal, characteristic, complemented
4#31595C211yesmaximal, characteristic, complemented
5#31541C211yesmaximal, characteristic, complemented
6#31213C211yesmaximal, characteristic, complemented
7#31201C211yesmaximal, characteristic
8#30990C211yesmaximal, characteristic, complemented
9#30896C211yesmaximal, characteristic, complemented
10#30853C211yesmaximal, characteristic, complemented
11#30651C211yesmaximal, characteristic, complemented
12#30562C211yesmaximal, characteristic
13#30550C211yesmaximal, characteristic, complemented
14#30550C211yesmaximal, characteristic, complemented
15#29963C211yesmaximal, characteristic, complemented
16#29674C211yesmaximal, characteristic, complemented
17#28423C211yesmaximal, characteristic, complemented
18#28333C211yesmaximal, characteristic, complemented
19#28322C211yesmaximal, characteristic, complemented
20#27789C211yesmaximal, characteristic, complemented
21#26792C211yesmaximal, characteristic, complemented
22#26607C211yesmaximal, characteristic, complemented
23#26577C211yesmaximal, characteristic, complemented
24#26527C211yesmaximal, characteristic, complemented
25#26493C211yesmaximal, characteristic, complemented
26#25965C211yesmaximal, characteristic, complemented
27#25683C211yesmaximal, characteristic, complemented
28#25173C211yesmaximal, characteristic, complemented
29#24437C211yesmaximal, characteristic
30#24255C211yesmaximal, characteristic
31#22362C211yesmaximal, characteristic
32C2×D4×Q8C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#491C2211yescharacteristic
36C2×#491C2211yescharacteristic
37C2×#484C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#485C2211yescharacteristic
40C2×#479C2211yescharacteristic
41C2×#467C2211yescharacteristic
42C2×#467C2211yescharacteristic
43C2×#462C2211yescharacteristic
44C2×#462C2211yescharacteristic
45C2×#462C2211yescharacteristic
46C2×#462C2211yescharacteristic
47C2×#451C2211yescharacteristic
48C2×#451C2211yescharacteristic
49C2×#451C2211yescharacteristic
50C2×#451C2211yescharacteristic
51C2×#441C2211yescharacteristic
52C2×#441C2211yescharacteristic
53C22×#103C2211yescharacteristic
54#2845—21no—
55#2839—21no—
56#2836—21no—
57#2827—21no—
58#2781—21no—
59#2772—21no—
60#2768—21no—
61#2747—21no—
62#2713—21no—
63#2698—21no—
64#2690—21no—
65#2689—21no—
66#2629C2211yescharacteristic
67#2621C2211yescharacteristic
68#2571C2211yescharacteristic
69#2565C2211yescharacteristic
70#2556—21no—
71#2550—21no—
72#2546C2211yescharacteristic
73#2536C2211yescharacteristic
74#2502C2211yescharacteristic
75#2489C2211yescharacteristic
76#2489C2211yescharacteristic
77#2489C2211yescharacteristic
78#2468—21no—
79#2466—21no—
80#2453C2211yescharacteristic
81#2453C2211yescharacteristic
82#2446C2211yescharacteristic
83#2446C2211yescharacteristic
84#2442C2211yescharacteristic
85#2434C2211yescharacteristic
86#2434C2211yescharacteristic
87#2429C2211yescharacteristic
88#2429C2211yescharacteristic
89#2423C2211yescharacteristic
90#2417C2211yescharacteristic
91#2415C2211yescharacteristic
92#2395C2211yescharacteristic
93#2365C2211yescharacteristic
94#2362C2211yescharacteristic
95Q8×C22⋊C4C2211yescharacteristic
96#2310C2211yescharacteristic
97#2097C2211yescharacteristic
98#2097C2211yescharacteristic
99#2097C2211yescharacteristic
100#2096C2211yescharacteristic
101#2095C2211yescharacteristic
102#2095C2211yescharacteristic
103#2085C2211yescharacteristic
104#2072C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2068C2211yescharacteristic
108#2068C2211yescharacteristic
109#2068C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2059C2211yescharacteristic
114#2056C2211yescharacteristic
115#2056C2211yescharacteristic
116#2043C2211yescharacteristic
117#2043C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic
126#2026C2211yescharacteristic
127#2026C2211yescharacteristic
128#2026C2211yescharacteristic
129#2026C2211yescharacteristic
130#2026C2211yescharacteristic
131#2016C2211yescharacteristic
132#2016C2211yescharacteristic
133#2016C2211yescharacteristic
134#2016C2211yescharacteristic
135#2016C2211yescharacteristic
136#2016C2211yescharacteristic
137#2016C2211yescharacteristic
138#2016C2211yescharacteristic
139#2001C2211yescharacteristic
140#2001C2211yescharacteristic
141#2001C2211yescharacteristic
142#2001C2211yescharacteristic
143#2001C2211yescharacteristic
144#2001C2211yescharacteristic
145#1992C2211yescharacteristic
146#1981C2211yescharacteristic
147#1971C2211yescharacteristic
148#1971C2211yescharacteristic
149#1971C2211yescharacteristic
150#1971C2211yescharacteristic
151#1969C2211yescharacteristic
152#1969C2211yescharacteristic
153#1969C2211yescharacteristic
154#1969C2211yescharacteristic
155#1960C2211yescharacteristic
156#1956C2211yescharacteristic
157#1956C2211yescharacteristic
158#1955C2211yescharacteristic
159#1948C2211yescharacteristic
160#1944C2211yescharacteristic
161#1943C2211yescharacteristic
162#1939C2211yescharacteristic
163#1927C2211yescharacteristic
164#1927C2211yescharacteristic
165#1927C2211yescharacteristic
166#1927C2211yescharacteristic
167#1924C2211yescharacteristic
168#1924C2211yescharacteristic
169#1924C2211yescharacteristic
170#1923C2211yescharacteristic
171#1917C2211yescharacteristic
172#1917C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1872C2211yescharacteristic
178#1869C2211yescharacteristic
179#1865C2211yescharacteristic
180#1865C2211yescharacteristic
181#1865C2211yescharacteristic
182#1863C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1854C2211yescharacteristic
188#1854C2211yescharacteristic
189#1853C2211yescharacteristic
190#1850C2211yescharacteristic
191#1808C2211yescharacteristic
192#1805C2211yescharacteristic
193#1805C2211yescharacteristic
194#1805C2211yescharacteristic
195#1798C2211yescharacteristic
196#1787C2211yescharacteristic
197#1787C2211yescharacteristic
198#1787C2211yescharacteristic
199C4×#107C2211yescharacteristic
200#1771C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1750C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×Q16C2311yescharacteristic
211C22×Q16C2311yescharacteristic
212C22×Q16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214D4×Q8—42no—
215D4×Q8—42no—
216#541—42no—
217#541—42no—
218C2×C4⋊Q8—21no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×#126—21no—
225C2×#126—21no—
226C2×#125—21no—
227C2×#125—21no—
228C2×#125C2311yescharacteristic
229C2×#125C2311yescharacteristic
230C2×#125C2311yescharacteristic
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252#499—42no—
253#491—42no—
254#491—42no—
255#485—42no—
256#485—42no—
257#484—42no—
258#479—42no—
259#467—42no—
260#467—42no—
261#462—42no—
262#462—42no—
263#462—42no—
264#462—42no—
265#451—42no—
266#451—42no—
267#451—42no—
268#451—42no—
269#441—42no—
270#441—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×#103—42no—
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#103C2311yescharacteristic
316C2×#103C2311yescharacteristic
317C2×#103C2311yescharacteristic
318C2×#103C2311yescharacteristic
319C2×#103C2311yescharacteristic
320C2×#103C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#400—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#400—21no—
341#400—21no—
342#400—21no—
343#400D411yescharacteristic
344#399—21no—
345#399D411yescharacteristic
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#398—21no—
355#398—21no—
356#398—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#398D411yescharacteristic
367#397—21no—
368#397—21no—
369#397—21no—
370#397—21no—
371#397—21no—
372#397—21no—
373#397D411yescharacteristic
374#397D411yescharacteristic
375#397D411yescharacteristic
376#396—21no—
377#396—21no—
378#396—21no—
379#396—21no—
380#396—21no—
381#395—21no—
382#395—21no—
383#395—21no—
384#395—21no—
385#394—21no—
386#394—21no—
387#394D411yescharacteristic
388#394D411yescharacteristic
389#391—21no—
390#391—21no—
391#391—21no—
392#391—21no—
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#391C2311yescharacteristic
404#391C2311yescharacteristic
405#391C2311yescharacteristic
406#391C2311yescharacteristic
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389—21no—
412#389—21no—
413#389—21no—
414#389—21no—
415#389—21no—
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388—21no—
429#388—21no—
430#388—21no—
431#388—21no—
432#388—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387—21no—
440#387—21no—
441#387—21no—
442#387—21no—
443#387—21no—
444#387—21no—
445#386—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#385—21no—
452#385—21no—
453#384C2311yescharacteristic
454#384C2311yescharacteristic
455#382—21no—
456#382—21no—
457#382—21no—
458#382—21no—
459#382C2311yescharacteristic
460#382C2311yescharacteristic
461#381—21no—
462#381—21no—
463#380—21no—
464#380—21no—
465#380—21no—
466#380C2311yescharacteristic
467#380C2311yescharacteristic
468#380C2311yescharacteristic
469#380C2311yescharacteristic
470C4×C4⋊C4—21no—
471C4×C4⋊C4—21no—
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C4⋊C4C2311yescharacteristic
476C4×C22⋊C4—21no—
477C4×C22⋊C4C2311yescharacteristic
478C4×C22⋊C4C2311yescharacteristic
479C4×C22⋊C4C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C22×Q8—21no—
503C22×Q8—21no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8—41no—
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×Q8C2411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C2×Q16—22no—
529C2×Q16—22no—
530C2×Q16—22no—
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×Q16—41no—
550C2×Q16—41no—
551C2×Q16—41no—
552C22×C8—22no—
553C22×C8—41no—
554C22×C8—41no—
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C4⋊Q8—22no—
564C4⋊Q8—22no—
565C4⋊Q8—22no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573C4⋊Q8—44no—
574#126—44no—
575#126—44no—
576#125—22no—
577#125—41no—
578#125—41no—
579#125—41no—
580#125—41no—
581#125—41no—
582#125—44no—
583#125—44no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—44no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—44no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C4×Q8—22no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—44no—
617#117—41no—
618#117—41no—
619#117—41no—
620#117—41no—
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⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
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⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718#107—22no—
719#107—22no—
720#107—22no—
721#107—41no—
722#107—41no—
723#107—41no—
724#106—22no—
725#106—41no—
726#106—41no—
727#106—41no—
728#106—41no—
729#106—41no—
730C4⋊C8—22no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735#103—22no—
736#103—22no—
737#103—22no—
738#103—22no—
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—41no—
748#103—41no—
749#103—41no—
750#103—41no—
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#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767C22⋊C8—22no—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774#97—22no—
775#97—41no—
776#97—41no—
777C4×C8—41no—
778C4×C8—41no—
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#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833C24C22×D411yescharacteristic
834C24C22×D411yescharacteristic
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—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—42no—
870C2×Q8—42no—
871C2×Q8—42no—
872C2×Q8—42no—
873C2×Q8—44no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8—82no—
877C2×Q8—82no—
878C2×Q8—82no—
879C2×Q8—82no—
880C2×Q8—82no—
881C2×Q8—82no—
882C2×Q8—82no—
883C2×Q8H(5,𝔽2)12yes—
884C2×Q82−1+412yes—
885C2×D4—22no—
886C2×D4—41no—
887C2×D4—41no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C2511yescharacteristic
938Q16—44no—
939Q16—44no—
940Q16—82no—
941Q16—82no—
942Q16—82no—
943Q16—82no—
944Q16—82no—
945Q16—82no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—82no—
969C2×C8H(5,𝔽2)12yes—
970C2×C8H(5,𝔽2)12yes—
971C4⋊C4—24no—
972C4⋊C4—22no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4H(5,𝔽2)12yes—
1039C22⋊C4—24no—
1040C22⋊C4—22no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—42no—
1073C42—42no—
1074C42—42no—
1075C42—42no—
1076C42—42no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23#57812yes—
1095C23C23×D411yescharacteristic
1096Q8—22no—
1097Q8—22no—
1098Q8—22no—
1099Q8—22no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—41no—
1110Q8—41no—
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—84no—
1121Q8—84no—
1122D4—44no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—84no—
1215C2×C4—84no—
1216C2×C4—162no—
1217C2×C4#57812yes—
1218C2×C4C2×H(5,𝔽2)11yescharacteristic
1219C2×C4C2×H(5,𝔽2)11yescharacteristic
1220C2×C4C2×H(5,𝔽2)11yescharacteristic
1221C2×C4C2×H(5,𝔽2)11yescharacteristic
1222C2×C4C2×2−1+411yescharacteristic
1223C2×C4#58511yescharacteristic
1224C8—22no—
1225C8—22no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—41no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22#348411yescharacteristic
1247C22#348911yescharacteristic
1248C22#349811yescharacteristic
1249C22C2×#57811yescharacteristic
1250C22C2×#57811yescharacteristic
1251C22#358611yescharacteristic
1252C22#358611yescharacteristic
1253C4—22no—
1254C4—41no—
1255C4—41no—
1256C4—42no—
1257C4—42no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—42no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4#353611yescharacteristic
1282C4#353611yescharacteristic
1283C4#354211yescharacteristic
1284C4#355811yescharacteristic
1285C2—42no—
1286C2—81no—
1287C2#4795111yescharacteristic
1288C2#6161211yescharacteristic
1289C2#6169311yescharacteristic
1290C2#6216811yescharacteristic
1291C2#6216811yescharacteristic
1292C2#6243211yescharacteristic
1293C2#6244211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32074C2semidirect
4. #31595C2semidirect
5. #31541C2semidirect
6. #31213C2semidirect
8. #30990C2semidirect
9. #30896C2semidirect
10. #30853C2semidirect
11. #30651C2semidirect
13. #30550C2semidirect
14. #30550C2semidirect
15. #29963C2semidirect
16. #29674C2semidirect
17. #28423C2semidirect
18. #28333C2semidirect
19. #28322C2semidirect
20. #27789C2semidirect
21. #26792C2semidirect
22. #26607C2semidirect
23. #26577C2semidirect
24. #26527C2semidirect
25. #26493C2semidirect
26. #25965C2semidirect
27. #25683C2semidirect
28. #25173C2semidirect

Maximal subgroups

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

subgroupindex
#530242
#453222
#320742
#315952
#315412
#312132
#312012
#309902
#308962
#308532
#306512
#305622
#305502
#299632
#296742
#284232
#283332
#283222
#277892
#267922
#266072
#265772
#265272
#264932
#259652
#256832
#251732
#244372
#242552
#223622