Finite Group Databasebeta

← #7336589

Subgroups — #7336589

Order 512.

1545 conjugacy classes of subgroups.

The subgroup lattice has 1347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#53070C211yesmaximal, characteristic, complemented
2#45187C211yesmaximal, characteristic
3#32059C211yesmaximal, characteristic, complemented
4#31579C211yesmaximal, characteristic, complemented
5#31531C211yesmaximal, characteristic, complemented
6#31226C211yesmaximal, characteristic, complemented
7#31193C211yesmaximal, characteristic, complemented
8#31012C211yesmaximal, characteristic, complemented
9#30881C211yesmaximal, characteristic, complemented
10#30854C211yesmaximal, characteristic, complemented
11#30658C211yesmaximal, characteristic, complemented
12#30562C211yesmaximal, characteristic, complemented
13#30543C211yesmaximal, characteristic, complemented
14#30520C211yesmaximal, characteristic, complemented
15#29959C211yesmaximal, characteristic, complemented
16#29674C211yesmaximal, characteristic, complemented
17#28424C211yesmaximal, characteristic, complemented
18#28350C211yesmaximal, characteristic, complemented
19#28320C211yesmaximal, characteristic, complemented
20#27800C211yesmaximal, characteristic, complemented
21#26810C211yesmaximal, characteristic, complemented
22#26595C211yesmaximal, characteristic, complemented
23#26577C211yesmaximal, characteristic, complemented
24#26543C211yesmaximal, characteristic, complemented
25#26487C211yesmaximal, characteristic, complemented
26#25959C211yesmaximal, characteristic, complemented
27#25686C211yesmaximal, characteristic, complemented
28#25171C211yesmaximal, characteristic, complemented
29#24436C211yesmaximal, characteristic
30#24247C211yesmaximal, characteristic
31#22368C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#489C2211yescharacteristic
36C2×#487C2211yescharacteristic, complemented
37C2×#485C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#485C2211yescharacteristic, complemented
40C2×#477C2211yescharacteristic, complemented
41C2×#467C2211yescharacteristic, complemented
42C2×#465C2211yescharacteristic
43C2×#464C2211yescharacteristic
44C2×#464C2211yescharacteristic
45C2×#462C2211yescharacteristic, complemented
46C2×#462C2211yescharacteristic, complemented
47C2×#452C2211yescharacteristic
48C2×#452C2211yescharacteristic
49C2×#450C2211yescharacteristic
50C2×#450C2211yescharacteristic
51C2×#441C2211yescharacteristic, complemented
52C2×C4×SD16C2211yescharacteristic
53C2×#416C2211yescharacteristic
54#2839—21no—
55#2837—21no—
56#2832—21no—
57#2831—21no—
58#2806—21no—
59#2798—21no—
60#2754—21no—
61#2754—21no—
62#2711—21no—
63#2694—21no—
64#2685—21no—
65#2685—21no—
66#2628C2211yescharacteristic
67#2621C2211yescharacteristic
68#2571C2211yescharacteristic, complemented
69#2568C2211yescharacteristic, complemented
70#2558—21no—
71#2545C2211yescharacteristic
72#2536C2211yescharacteristic
73#2499C2211yescharacteristic, complemented
74#2492C2211yescharacteristic
75#2492C2211yescharacteristic, complemented
76#2490—21no—
77#2490C2211yescharacteristic
78#2480—21no—
79#2480—21no—
80#2454C2211yescharacteristic
81#2451C2211yescharacteristic, complemented
82#2448C2211yescharacteristic
83#2446C2211yescharacteristic, complemented
84#2439C2211yescharacteristic, complemented
85#2435C2211yescharacteristic
86#2432C2211yescharacteristic
87#2429C2211yescharacteristic, complemented
88#2426C2211yescharacteristic
89#2423C2211yescharacteristic
90#2415C2211yescharacteristic
91#2415C2211yescharacteristic
92#2395C2211yescharacteristic
93#2367C2211yescharacteristic
94#2362C2211yescharacteristic
95#2341C2211yescharacteristic
96#2309C2211yescharacteristic
97#2097C2211yescharacteristic, complemented
98#2095C2211yescharacteristic, complemented
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic
103#2085C2211yescharacteristic, complemented
104#2071C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2066C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2066C2211yescharacteristic, complemented
111#2065C2211yescharacteristic
112#2065C2211yescharacteristic
113#2058C2211yescharacteristic, complemented
114#2056C2211yescharacteristic, complemented
115#2055C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic, complemented
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic, complemented
124#2035C2211yescharacteristic, complemented
125#2034C2211yescharacteristic
126#2026C2211yescharacteristic, complemented
127#2026C2211yescharacteristic, complemented
128#2023C2211yescharacteristic
129#2023C2211yescharacteristic
130#2023C2211yescharacteristic
131#2016C2211yescharacteristic, complemented
132#2016C2211yescharacteristic, complemented
133#2015C2211yescharacteristic
134#2015C2211yescharacteristic
135#2015C2211yescharacteristic
136#2015C2211yescharacteristic
137#2013C2211yescharacteristic
138#2013C2211yescharacteristic
139#2001C2211yescharacteristic
140#2001C2211yescharacteristic
141#2001C2211yescharacteristic
142#2001C2211yescharacteristic
143#2001C2211yescharacteristic, complemented
144#2000C2211yescharacteristic
145#1991C2211yescharacteristic, complemented
146#1983C2211yescharacteristic
147#1973C2211yescharacteristic
148#1973C2211yescharacteristic
149#1973C2211yescharacteristic
150#1973C2211yescharacteristic
151#1971C2211yescharacteristic, complemented
152#1969C2211yescharacteristic, complemented
153#1968C2211yescharacteristic
154#1968C2211yescharacteristic
155#1960C2211yescharacteristic, complemented
156#1959C2211yescharacteristic
157#1958C2211yescharacteristic
158#1954C2211yescharacteristic
159#1948C2211yescharacteristic, complemented
160#1944C2211yescharacteristic, complemented
161#1942C2211yescharacteristic, complemented
162#1940C2211yescharacteristic, complemented
163#1928C2211yescharacteristic, complemented
164#1927C2211yescharacteristic, complemented
165#1927C2211yescharacteristic, complemented
166#1925C2211yescharacteristic
167#1924C2211yescharacteristic
168#1924C2211yescharacteristic
169#1924C2211yescharacteristic, complemented
170#1923C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1916C2211yescharacteristic, complemented
173#1880C2211yescharacteristic
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1875C2211yescharacteristic
178#1869C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1865C2211yescharacteristic, complemented
181#1865C2211yescharacteristic, complemented
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic, complemented
184#1863C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1863C2211yescharacteristic, complemented
187#1854C2211yescharacteristic
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic, complemented
190#1850C2211yescharacteristic, complemented
191#1808C2211yescharacteristic, complemented
192#1805C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1804C2211yescharacteristic
195#1798C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1776C2211yescharacteristic, complemented
200#1771C2211yescharacteristic, complemented
201#1752C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#546—42no—
215#546—42no—
216#541—42no—
217#541—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#126—21no—
223C2×#126—21no—
224C2×#125—21no—
225C2×#125—21no—
226C2×#125C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C22⋊C4—21no—
252#501—42no—
253#489—42no—
254#487—42no—
255#485—42no—
256#485—42no—
257#485—42no—
258#477—42no—
259#467—42no—
260#465—42no—
261#464—42no—
262#464—42no—
263#462—42no—
264#462—42no—
265#452—42no—
266#452—42no—
267#450—42no—
268#450—42no—
269#441—42no—
270C4×SD16—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
288#416—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×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
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#400D411yescharacteristic
342#399—21no—
343#399—21no—
344#399—21no—
345#399—21no—
346#399D411yescharacteristic
347#398—21no—
348#398—21no—
349#398—21no—
350#398—21no—
351#398—21no—
352#398—21no—
353#398—21no—
354#398D411yescharacteristic
355#397—21no—
356#397—21no—
357#397—21no—
358#397—21no—
359#397—21no—
360#397—21no—
361#397—21no—
362#397—21no—
363#397D411yescharacteristic
364#397D411yescharacteristic
365#397D411yescharacteristic
366#396—21no—
367#396—21no—
368#396—21no—
369#396—21no—
370#396—21no—
371#396—21no—
372#395—21no—
373#395—21no—
374#394—21no—
375#394—21no—
376#394—21no—
377#394—21no—
378#394—21no—
379#394—21no—
380#394—21no—
381#394—21no—
382#394—21no—
383#394D411yescharacteristic
384#394D411yescharacteristic
385#393—21no—
386#393—21no—
387#393—21no—
388#393—21no—
389#391—21no—
390#391—21no—
391#391—21no—
392#391—21no—
393#391—21no—
394#391—21no—
395#391C2311yescharacteristic
396#391C2311yescharacteristic
397#391C2311yescharacteristic
398#391C2311yescharacteristic
399#391C2311yescharacteristic
400#391C2311yescharacteristic
401#391C2311yescharacteristic
402#391C2311yescharacteristic
403#390—21no—
404#390—21no—
405#390—21no—
406#390—21no—
407#390—21no—
408#390—21no—
409#390C2311yescharacteristic
410#390C2311yescharacteristic
411#390C2311yescharacteristic
412#390C2311yescharacteristic
413#390C2311yescharacteristic
414#390C2311yescharacteristic
415#389—21no—
416#389—21no—
417#389—21no—
418#389—21no—
419#389C2311yescharacteristic
420#389C2311yescharacteristic
421#389C2311yescharacteristic
422#389C2311yescharacteristic
423#389C2311yescharacteristic
424#389C2311yescharacteristic
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#388—21no—
434#388—21no—
435#388—21no—
436#388—21no—
437#388—21no—
438#388—21no—
439#388—21no—
440#388—21no—
441#388—21no—
442#388—21no—
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#385—21no—
452#385—21no—
453#385—21no—
454#385—21no—
455#384C2311yescharacteristic
456#382—21no—
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#382C2311yescharacteristic
460#380—21no—
461#380—21no—
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#379—21no—
467#379—21no—
468#379—21no—
469#379—21no—
470C4×C4⋊C4—21no—
471C4×C4⋊C4C2311yescharacteristic
472C4×C4⋊C4C2311yescharacteristic
473C4×C4⋊C4C2311yescharacteristic
474C4×C4⋊C4C2311yescharacteristic
475C4×C22⋊C4—21no—
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
502C25—21no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2×D411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—22no—
533C2×Q16—41no—
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×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C22×C8—22no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—22no—
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574#126—44no—
575#126—44no—
576#125—22no—
577#125—41no—
578#125—44no—
579#125—44no—
580#124—22no—
581#124—22no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#123—44no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
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—
601#121—22no—
602#121—41no—
603#121—44no—
604#120—44no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×D4—22no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619#117—41no—
620#117—41no—
621#117—41no—
622#117—41no—
623#117—41no—
624#117—41no—
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⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
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⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—44no—
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728#107—22no—
729#107—22no—
730#107—41no—
731#107—41no—
732#107—41no—
733#107—41no—
734#106—22no—
735#106—22no—
736#106—41no—
737#106—41no—
738#106—41no—
739#106—41no—
740C4⋊C8—22no—
741C4⋊C8—41no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744C4⋊C8—41no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
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#102—22no—
766#102—22no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777C22⋊C8—22no—
778C22⋊C8—22no—
779C22⋊C8—22no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784#97—22no—
785#97—41no—
786#97—41no—
787C4×C8—41no—
788C4×C8—41no—
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
833C24—21no—
834C24—21no—
835C24—42no—
836C24—42no—
837C24—81no—
838C24—81no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24C22×D411yescharacteristic
843C24C22×D411yescharacteristic
844#41—44no—
845#41—82no—
846#41—82no—
847#41—82no—
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—21no—
870C2×Q8—21no—
871C2×Q8—42no—
872C2×Q8—81no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8H(5,𝔽2)12yes—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—41no—
890C2×D4—41no—
891C2×D4—41no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—81no—
898C2×D4—82no—
899C2×D4—82no—
900C2×D4—82no—
901C2×D4—82no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D42−1+412yes—
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—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C2511yescharacteristic
951Q16—44no—
952Q16—82no—
953Q16—82no—
954Q16—82no—
955SD16—44no—
956SD16—82no—
957SD16—82no—
958SD16—82no—
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—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—82no—
982C2×C8H(5,𝔽2)12yes—
983C2×C8H(5,𝔽2)12yes—
984C4⋊C4—24no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—41no—
1005C4⋊C4—41no—
1006C4⋊C4—41no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
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—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
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—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—42no—
1093C42—42no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—22no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—84no—
1130C23—84no—
1131C23—162no—
1132C23—162no—
1133C23—162no—
1134C23—162no—
1135C23—162no—
1136C23C23×D411yescharacteristic
1137Q8—22no—
1138Q8—22no—
1139Q8—41no—
1140Q8—41no—
1141Q8—41no—
1142Q8—41no—
1143Q8—41no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—162no—
1154Q8—162no—
1155D4—22no—
1156D4—22no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—82no—
1164D4—84no—
1165D4—84no—
1166D4—162no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
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—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—84no—
1254C2×C4—162no—
1255C2×C4C2×H(5,𝔽2)11yescharacteristic
1256C2×C4C2×H(5,𝔽2)11yescharacteristic
1257C2×C4C2×H(5,𝔽2)11yescharacteristic
1258C2×C4C2×H(5,𝔽2)11yescharacteristic
1259C2×C4C2×2−1+411yescharacteristic
1260C2×C4#58511yescharacteristic
1261C8—22no—
1262C8—22no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C8—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—42no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—42no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—41no—
1283C22—42no—
1284C22—41no—
1285C22—41no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—168no—
1298C22#348411yescharacteristic
1299C22#348911yescharacteristic
1300C22#349811yescharacteristic
1301C22#358411yescharacteristic
1302C22#358411yescharacteristic
1303C22#358611yescharacteristic
1304C22#358611yescharacteristic
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—42no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—42no—
1317C4—41no—
1318C4—41no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4#353611yescharacteristic
1332C4#353611yescharacteristic
1333C4#354211yescharacteristic
1334C4#355811yescharacteristic
1335C2—81no—
1336C2—81no—
1337C2—82no—
1338C2—161no—
1339C2#4795111yescharacteristic
1340C2#6163811yescharacteristic
1341C2#6167411yescharacteristic
1342C2#6217211yescharacteristic
1343C2#6219611yescharacteristic
1344C2#6246211yescharacteristic
1345C2#6246711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
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
1. #53070C2semidirect
3. #32059C2semidirect
4. #31579C2semidirect
5. #31531C2semidirect
6. #31226C2semidirect
7. #31193C2semidirect
8. #31012C2semidirect
9. #30881C2semidirect
10. #30854C2semidirect
11. #30658C2semidirect
12. #30562C2semidirect
13. #30543C2semidirect
14. #30520C2semidirect
15. #29959C2semidirect
16. #29674C2semidirect
17. #28424C2semidirect
18. #28350C2semidirect
19. #28320C2semidirect
20. #27800C2semidirect
21. #26810C2semidirect
22. #26595C2semidirect
23. #26577C2semidirect
24. #26543C2semidirect
25. #26487C2semidirect
26. #25959C2semidirect
27. #25686C2semidirect
28. #25171C2semidirect
31. #22368C2semidirect
34. C2×#501C22semidirect
36. C2×#487C22semidirect
39. C2×#485C22semidirect
40. C2×#477C22semidirect
41. C2×#467C22semidirect
45. C2×#462C22semidirect
46. C2×#462C22semidirect
51. C2×#441C22semidirect
68. #2571C22semidirect
69. #2568C22semidirect
73. #2499C22semidirect
75. #2492C22semidirect
81. #2451C22semidirect
83. #2446C22semidirect
84. #2439C22semidirect
87. #2429C22semidirect
97. #2097C22semidirect
98. #2095C22semidirect
103. #2085C22semidirect
108. #2066C22semidirect
109. #2066C22semidirect
110. #2066C22semidirect
113. #2058C22semidirect
114. #2056C22semidirect
120. #2036C22semidirect
123. #2035C22semidirect
124. #2035C22semidirect
126. #2026C22semidirect
127. #2026C22semidirect
131. #2016C22semidirect
132. #2016C22semidirect
143. #2001C22semidirect
145. #1991C22semidirect
151. #1971C22semidirect
152. #1969C22semidirect
155. #1960C22semidirect
159. #1948C22semidirect
160. #1944C22semidirect
161. #1942C22semidirect
162. #1940C22semidirect
163. #1928C22semidirect
164. #1927C22semidirect
165. #1927C22semidirect
169. #1924C22semidirect
170. #1923C22semidirect
171. #1916C22semidirect
172. #1916C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
179. #1865C22semidirect
180. #1865C22semidirect
181. #1865C22semidirect
183. #1863C22semidirect
184. #1863C22semidirect
185. #1863C22semidirect
186. #1863C22semidirect
189. #1854C22semidirect
190. #1850C22semidirect
191. #1808C22semidirect
192. #1805C22semidirect
193. #1805C22semidirect
199. #1776C22semidirect
200. #1771C22semidirect
201. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#530702
#451872
#320592
#315792
#315312
#312262
#311932
#310122
#308812
#308542
#306582
#305622
#305432
#305202
#299592
#296742
#284242
#283502
#283202
#278002
#268102
#265952
#265772
#265432
#264872
#259592
#256862
#251712
#244362
#242472
#223682