Finite Group Databasebeta

← #7307708

Subgroups — #7307708

Order 512.

1687 conjugacy classes of subgroups.

The subgroup lattice has 1396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59099C211yesmaximal, characteristic, complemented
2#40168C211yesmaximal, characteristic, complemented
3#32220C211yesmaximal, characteristic, complemented
4#32086C211yesmaximal, characteristic, complemented
5#31895C211yesmaximal, characteristic, complemented
6#31775C211yesmaximal, characteristic, complemented
7#31585C211yesmaximal, characteristic, complemented
8#31303C211yesmaximal, characteristic, complemented
9#31286C211yesmaximal, characteristic, complemented
10#31162C211yesmaximal, characteristic, complemented
11#31133C211yesmaximal, characteristic, complemented
12#30985C211yesmaximal, characteristic, complemented
13#30611C211yesmaximal, characteristic, complemented
14#30574C211yesmaximal, characteristic, complemented
15#29958C211yesmaximal, characteristic, complemented
16#29694C211yesmaximal, characteristic, complemented
17#28116C211yesmaximal, characteristic, complemented
18#27109C211yesmaximal, characteristic, complemented
19#26888C211yesmaximal, characteristic, complemented
20#26799C211yesmaximal, characteristic, complemented
21#26564C211yesmaximal, characteristic, complemented
22#26533C211yesmaximal, characteristic, complemented
23#26368C211yesmaximal, characteristic, complemented
24#25968C211yesmaximal, characteristic, complemented
25#25097C211yesmaximal, characteristic, complemented
26#24909C211yesmaximal, characteristic, complemented
27#24738C211yesmaximal, characteristic, complemented
28#24245C211yesmaximal, characteristic, complemented
29#24150C211yesmaximal, characteristic, complemented
30#24050C211yesmaximal, characteristic, complemented
31#23320C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#482C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic, complemented
38C2×#474C2211yescharacteristic, complemented
39C2×#469C2211yescharacteristic
40C2×#463C2211yescharacteristic
41C2×#463C2211yescharacteristic, complemented
42C2×#459C2211yescharacteristic
43C2×#449C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#442C2211yescharacteristic
46C2×C4×D8C2211yescharacteristic
47C2×#418C2211yescharacteristic
48#2851C2211yescharacteristic, complemented
49#2796—21no—
50#2750—21no—
51#2739—21no—
52#2706—21no—
53#2688—21no—
54#2678—21no—
55#2636—21no—
56#2571C2211yescharacteristic, complemented
57#2557—21no—
58#2544C2211yescharacteristic
59#2535C2211yescharacteristic
60#2517—21no—
61#2508C2211yescharacteristic, complemented
62#2497C2211yescharacteristic, complemented
63#2496C2211yescharacteristic
64#2492C2211yescharacteristic
65#2485C2211yescharacteristic
66#2481—21no—
67#2472—21no—
68#2457—21no—
69#2454C2211yescharacteristic, complemented
70#2452C2211yescharacteristic
71#2447C2211yescharacteristic
72#2441C2211yescharacteristic
73#2433C2211yescharacteristic
74#2431C2211yescharacteristic
75#2427C2211yescharacteristic
76#2422C2211yescharacteristic, complemented
77#2420C2211yescharacteristic
78#2414C2211yescharacteristic
79#2407—21no—
80#2404—21no—
81#2366C2211yescharacteristic
82#2363C2211yescharacteristic
83#2363C2211yescharacteristic
84#2358—21no—
85D4×C4⋊C4C2211yescharacteristic, complemented
86D4×C22⋊C4C2211yescharacteristic
87#2322—21no—
88C4×#123C2211yescharacteristic
89C4×#121C2211yescharacteristic, complemented
90#2297C2211yescharacteristic
91#2097C2211yescharacteristic, complemented
92#2093C2211yescharacteristic
93#2093C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2077C2211yescharacteristic
101#2072C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic, complemented
111#2058C2211yescharacteristic, complemented
112#2057C2211yescharacteristic, complemented
113#2055C2211yescharacteristic, complemented
114#2054C2211yescharacteristic
115#2054C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic, complemented
119#2042C2211yescharacteristic, complemented
120#2041C2211yescharacteristic
121#2041C2211yescharacteristic
122#2041C2211yescharacteristic
123#2036C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic, complemented
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2033C2211yescharacteristic
130#2033C2211yescharacteristic
131#2033C2211yescharacteristic, complemented
132#2033C2211yescharacteristic, complemented
133#2026C2211yescharacteristic, complemented
134#2025C2211yescharacteristic
135#2011C2211yescharacteristic
136#2000C2211yescharacteristic
137#1999C2211yescharacteristic
138#1999C2211yescharacteristic, complemented
139#1988C2211yescharacteristic, complemented
140#1982C2211yescharacteristic
141#1982C2211yescharacteristic
142#1968C2211yescharacteristic, complemented
143#1959C2211yescharacteristic, complemented
144#1958C2211yescharacteristic
145#1957C2211yescharacteristic
146#1954C2211yescharacteristic
147#1948C2211yescharacteristic, complemented
148#1944C2211yescharacteristic, complemented
149#1942C2211yescharacteristic, complemented
150#1940C2211yescharacteristic, complemented
151#1939C2211yescharacteristic, complemented
152#1936C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1926C2211yescharacteristic, complemented
159#1925C2211yescharacteristic
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic, complemented
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic, complemented
164#1921C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1894C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic, complemented
172#1879C2211yescharacteristic, complemented
173#1877C2211yescharacteristic, complemented
174#1875C2211yescharacteristic
175#1870C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic, complemented
182#1862C2211yescharacteristic, complemented
183#1862C2211yescharacteristic, complemented
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic, complemented
186#1854C2211yescharacteristic, complemented
187#1851C2211yescharacteristic
188#1851C2211yescharacteristic
189#1825C2211yescharacteristic, complemented
190#1809C2211yescharacteristic
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1797C2211yescharacteristic, complemented
196#1797C2211yescharacteristic, complemented
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1788C2211yescharacteristic
200#1786C2211yescharacteristic
201#1786C2211yescharacteristic
202C4×#107C2211yescharacteristic, complemented
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211#546—42no—
212#546—42no—
213#532—42no—
214#532—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#126—21no—
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×#123D411yescharacteristic
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×#120—21no—
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C42C2311yescharacteristic
255#485—42no—
256#482—42no—
257#478—42no—
258#478—42no—
259#474—42no—
260#469—42no—
261#463—42no—
262#463—42no—
263#459—42no—
264#449—42no—
265#447—42no—
266#442—42no—
267C4×D8—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287#418—42no—
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#399—21no—
337#399—21no—
338#398—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#393—21no—
359#393—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#392—21no—
364#392—21no—
365#392—21no—
366#391—21no—
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#389—21no—
382#389—21no—
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388D411yescharacteristic
401#388D411yescharacteristic
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387D411yescharacteristic
410#387D411yescharacteristic
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386D411yescharacteristic
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385D411yescharacteristic
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#382—21no—
441#382—21no—
442#382C2311yescharacteristic
443#382C2311yescharacteristic
444#381—21no—
445#381—21no—
446#381D411yescharacteristic
447#380—21no—
448#380—21no—
449#380—21no—
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#379—21no—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—44no—
504C2×#41—82no—
505C2×#41—82no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×D411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C2×D411yescharacteristic
539C23×C4C2×D411yescharacteristic
540C23×C4C2411yescharacteristic
541C23×C4C2411yescharacteristic
542C2×SD16—22no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—22no—
549C2×D8—22no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—41no—
553C2×D8—41no—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16—41no—
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C4⋊Q8—22no—
566C4⋊Q8—41no—
567#127—22no—
568#127—22no—
569#127—41no—
570#127—41no—
571#126—82no—
572#125—41no—
573#125—41no—
574#124—22no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—44no—
579#123—42no—
580#123—44no—
581#123—44no—
582C22⋊Q8—22no—
583C22⋊Q8—41no—
584C22⋊Q8—82no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—44no—
594#121—44no—
595#121—41no—
596#121—41no—
597#120—44no—
598#120—44no—
599#120—82no—
600C4×D4—22no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—44no—
617C4×D4—82no—
618C4×D4—82no—
619#117—41no—
620#117—41no—
621#117—41no—
622#117—41no—
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—82no—
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
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—44no—
698C2×C22⋊C4—82no—
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—41no—
713C2×C42—41no—
714C2×C42C2×D411yescharacteristic
715C2×C42C2×D411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721#107—22no—
722#107—22no—
723#107—41no—
724#107—41no—
725#107—41no—
726#107—41no—
727#107—41no—
728#106—22no—
729#106—41no—
730#106—41no—
731#106—41no—
732#106—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779#97—41no—
780C4×C8—41no—
781C4×C8—41no—
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#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—42no—
826C24—42no—
827C24—42no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834#41—82no—
835#41—82no—
836#41—82no—
837#41—82no—
838#41—816no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—42no—
846C2×Q8—42no—
847C2×Q8—81no—
848C2×D4—24no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—41no—
871C2×D4—41no—
872C2×D4—41no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—44no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—82no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4H(5,𝔽2)12yes—
910C2×D4H(5,𝔽2)12yes—
911C2×D42−1+412yes—
912C22×C4—21no—
913C22×C4—22no—
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—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—41no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C2511yescharacteristic
979SD16—82no—
980D8—44no—
981D8—44no—
982D8—82no—
983M16—82no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C4⋊C4—22no—
1009C4⋊C4—22no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4H(5,𝔽2)12yes—
1053C22⋊C4—24no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—41no—
1111C42—41no—
1112C42—42no—
1113C42—81no—
1114C42—81no—
1115C42—81no—
1116C42—81no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—22no—
1122C23—21no—
1123C23—21no—
1124C23—22no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—22no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—84no—
1160C23—84no—
1161C23—84no—
1162C23—162no—
1163C23—162no—
1164C23—162no—
1165C23—162no—
1166C23C23×D411yescharacteristic
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—84no—
1172D4—22no—
1173D4—22no—
1174D4—22no—
1175D4—22no—
1176D4—22no—
1177D4—22no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—84no—
1189D4—84no—
1190D4—84no—
1191D4—82no—
1192D4—84no—
1193D4—84no—
1194D4—84no—
1195D4—84no—
1196D4—84no—
1197D4—162no—
1198D4—162no—
1199D4—162no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—44no—
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—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—82no—
1280C2×C4—84no—
1281C2×C4—84no—
1282C2×C4—84no—
1283C2×C4—84no—
1284C2×C4—162no—
1285C2×C4—162no—
1286C2×C4—162no—
1287C2×C4—162no—
1288C2×C4#57512yes—
1289C2×C4#57612yes—
1290C2×C4C2×H(5,𝔽2)11yescharacteristic
1291C2×C4C2×H(5,𝔽2)11yescharacteristic
1292C2×C4C2×H(5,𝔽2)11yescharacteristic
1293C2×C4C2×2−1+411yescharacteristic
1294C2×C4#58511yescharacteristic
1295C2×C4#58511yescharacteristic
1296C8—41no—
1297C8—41no—
1298C8—41no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C22—42no—
1305C22—41no—
1306C22—41no—
1307C22—42no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—42no—
1312C22—41no—
1313C22—42no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—41no—
1318C22—42no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—42no—
1325C22—42no—
1326C22—42no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—168no—
1347C22#348411yescharacteristic
1348C22#348811yescharacteristic
1349C22#348911yescharacteristic
1350C22C2×#57511yescharacteristic
1351C22C2×#57611yescharacteristic
1352C22#358411yescharacteristic
1353C22#358511yescharacteristic
1354C4—22no—
1355C4—22no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—41no—
1363C4—41no—
1364C4—42no—
1365C4—41no—
1366C4—41no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4—81no—
1373C4—81no—
1374C4—81no—
1375C4—81no—
1376C4—81no—
1377C4—81no—
1378C4#353411yescharacteristic
1379C4#353511yescharacteristic
1380C4#353611yescharacteristic
1381C4#356211yescharacteristic
1382C2—81no—
1383C2—81no—
1384C2—82no—
1385C2—82no—
1386C2—82no—
1387C2—161no—
1388C2#4784311yescharacteristic
1389C2#6160811yescharacteristic
1390C2#6160911yescharacteristic
1391C2#6199511yescharacteristic
1392C2#6202411yescharacteristic
1393C2#6211911yescharacteristic
1394C2#6221511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59099C2semidirect
2. #40168C2semidirect
3. #32220C2semidirect
4. #32086C2semidirect
5. #31895C2semidirect
6. #31775C2semidirect
7. #31585C2semidirect
8. #31303C2semidirect
9. #31286C2semidirect
10. #31162C2semidirect
11. #31133C2semidirect
12. #30985C2semidirect
13. #30611C2semidirect
14. #30574C2semidirect
15. #29958C2semidirect
16. #29694C2semidirect
17. #28116C2semidirect
18. #27109C2semidirect
19. #26888C2semidirect
20. #26799C2semidirect
21. #26564C2semidirect
22. #26533C2semidirect
23. #26368C2semidirect
24. #25968C2semidirect
25. #25097C2semidirect
26. #24909C2semidirect
27. #24738C2semidirect
28. #24245C2semidirect
29. #24150C2semidirect
30. #24050C2semidirect
31. #23320C2semidirect
35. C2×#482C22semidirect
37. C2×#478C22semidirect
38. C2×#474C22semidirect
41. C2×#463C22semidirect
48. #2851C22semidirect
56. #2571C22semidirect
61. #2508C22semidirect
62. #2497C22semidirect
69. #2454C22semidirect
76. #2422C22semidirect
85. D4×C4⋊C4C22semidirect
89. C4×#121C22semidirect
91. #2097C22semidirect
95. #2092C22semidirect
96. #2088C22semidirect
97. #2088C22semidirect
98. #2085C22semidirect
99. #2083C22semidirect
101. #2072C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
104. #2068C22semidirect
106. #2066C22semidirect
110. #2065C22semidirect
111. #2058C22semidirect
112. #2057C22semidirect
113. #2055C22semidirect
118. #2042C22semidirect
119. #2042C22semidirect
125. #2034C22semidirect
131. #2033C22semidirect
132. #2033C22semidirect
133. #2026C22semidirect
138. #1999C22semidirect
139. #1988C22semidirect
142. #1968C22semidirect
143. #1959C22semidirect
147. #1948C22semidirect
148. #1944C22semidirect
149. #1942C22semidirect
150. #1940C22semidirect
151. #1939C22semidirect
154. #1934C22semidirect
155. #1928C22semidirect
156. #1927C22semidirect
158. #1926C22semidirect
161. #1924C22semidirect
163. #1923C22semidirect
164. #1921C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
171. #1879C22semidirect
172. #1879C22semidirect
173. #1877C22semidirect
181. #1862C22semidirect
182. #1862C22semidirect
183. #1862C22semidirect
185. #1854C22semidirect
186. #1854C22semidirect
189. #1825C22semidirect
193. #1804C22semidirect
195. #1797C22semidirect
196. #1797C22semidirect
202. C4×#107C22semidirect

Maximal subgroups

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

subgroupindex
#590992
#401682
#322202
#320862
#318952
#317752
#315852
#313032
#312862
#311622
#311332
#309852
#306112
#305742
#299582
#296942
#281162
#271092
#268882
#267992
#265642
#265332
#263682
#259682
#250972
#249092
#247382
#242452
#241502
#240502
#233202