Finite Group Databasebeta

← #6730574

Subgroups — #6730574

Order 512.

1661 conjugacy classes of subgroups.

The subgroup lattice has 1390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42585C211yesmaximal, characteristic, complemented
2#35808C211yesmaximal, characteristic, complemented
3#33014C211yesmaximal, characteristic, complemented
4#32596C211yesmaximal, characteristic, complemented
5#32593C211yesmaximal, characteristic, complemented
6#32188C211yesmaximal, characteristic, complemented
7#31302C211yesmaximal, characteristic, complemented
8#30875C211yesmaximal, characteristic, complemented
9#30519C211yesmaximal, characteristic, complemented
10#30519C211yesmaximal, characteristic, complemented
11#30468C211yesmaximal, characteristic, complemented
12#30328C211yesmaximal, characteristic, complemented
13#30119C211yesmaximal, characteristic, complemented
14#27486C211yesmaximal, characteristic, complemented
15#27443C211yesmaximal, characteristic, complemented
16#27190C211yesmaximal, characteristic, complemented
17#27056C211yesmaximal, characteristic, complemented
18#26954C211yesmaximal, characteristic, complemented
19#26890C211yesmaximal, characteristic, complemented
20#26834C211yesmaximal, characteristic, complemented
21#26793C211yesmaximal, characteristic, complemented
22#26733C211yesmaximal, characteristic, complemented
23#26693C211yesmaximal, characteristic, complemented
24#26584C211yesmaximal, characteristic, complemented
25#26268C211yesmaximal, characteristic, complemented
26#25648C211yesmaximal, characteristic, complemented
27#25642C211yesmaximal, characteristic, complemented
28#23223C211yesmaximal, characteristic, complemented
29#23105C211yesmaximal, characteristic, complemented
30#22324C211yesmaximal, characteristic, complemented
31#21458C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#496C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#477C2211yescharacteristic, complemented
39C2×#463C2211yescharacteristic
40C2×#459C2211yescharacteristic, complemented
41C2×#447C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#442C2211yescharacteristic
44C2×C4×D8C2211yescharacteristic
45#2832—21no—
46#2718—21no—
47#2712—21no—
48#2692—21no—
49#2672—21no—
50#2662—21no—
51#2630—21no—
52#2624C2211yescharacteristic
53#2620—21no—
54#2620C2211yescharacteristic
55#2567C2211yescharacteristic, complemented
56#2548C2211yescharacteristic, complemented
57#2544C2211yescharacteristic
58#2538C2211yescharacteristic
59#2534—21no—
60#2512C2211yescharacteristic, complemented
61#2497C2211yescharacteristic
62#2491C2211yescharacteristic
63#2491C2211yescharacteristic
64#2474—21no—
65#2472—21no—
66#2461—21no—
67#2457—21no—
68#2452C2211yescharacteristic, complemented
69#2452C2211yescharacteristic, complemented
70#2447C2211yescharacteristic
71#2445C2211yescharacteristic
72#2445C2211yescharacteristic, complemented
73#2435C2211yescharacteristic
74#2433C2211yescharacteristic
75#2428C2211yescharacteristic
76#2418—21no—
77#2411—21no—
78#2396C2211yescharacteristic
79#2392—21no—
80#2369C2211yescharacteristic, complemented
81#2367C2211yescharacteristic
82#2366C2211yescharacteristic
83#2363C2211yescharacteristic
84#2362C2211yescharacteristic
85#2354C2211yescharacteristic
86#2354C2211yescharacteristic, complemented
87#2324C2211yescharacteristic
88#2100C2211yescharacteristic, complemented
89#2093C2211yescharacteristic
90#2093C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2083C2211yescharacteristic, complemented
93#2071C2211yescharacteristic, complemented
94#2071C2211yescharacteristic, complemented
95#2067C2211yescharacteristic
96#2067C2211yescharacteristic, complemented
97#2065C2211yescharacteristic, complemented
98#2058C2211yescharacteristic, complemented
99#2055C2211yescharacteristic, complemented
100#2054C2211yescharacteristic
101#2054C2211yescharacteristic
102#2054C2211yescharacteristic
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic, complemented
107#2042C2211yescharacteristic, complemented
108#2041C2211yescharacteristic, complemented
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2024C2211yescharacteristic, complemented
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2012C2211yescharacteristic
117#2012C2211yescharacteristic, complemented
118#2012C2211yescharacteristic, complemented
119#2011C2211yescharacteristic
120#2011C2211yescharacteristic
121#2011C2211yescharacteristic
122#2011C2211yescharacteristic
123#2011C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1999C2211yescharacteristic
127#1999C2211yescharacteristic
128#1987C2211yescharacteristic, complemented
129#1985C2211yescharacteristic, complemented
130#1984C2211yescharacteristic, complemented
131#1983C2211yescharacteristic
132#1982C2211yescharacteristic
133#1982C2211yescharacteristic
134#1973C2211yescharacteristic, complemented
135#1972C2211yescharacteristic, complemented
136#1970C2211yescharacteristic
137#1970C2211yescharacteristic
138#1970C2211yescharacteristic, complemented
139#1968C2211yescharacteristic, complemented
140#1959C2211yescharacteristic
141#1947C2211yescharacteristic, complemented
142#1943C2211yescharacteristic, complemented
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic, complemented
146#1934C2211yescharacteristic, complemented
147#1933C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1927C2211yescharacteristic, complemented
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic, complemented
154#1925C2211yescharacteristic, complemented
155#1925C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic
159#1923C2211yescharacteristic
160#1923C2211yescharacteristic
161#1921C2211yescharacteristic, complemented
162#1918C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1880C2211yescharacteristic, complemented
169#1880C2211yescharacteristic, complemented
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic, complemented
178#1879C2211yescharacteristic, complemented
179#1877C2211yescharacteristic, complemented
180#1875C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic, complemented
188#1862C2211yescharacteristic, complemented
189#1854C2211yescharacteristic
190#1825C2211yescharacteristic
191#1818C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194C4×#107C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic, complemented
199#1762C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic
202#1750C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212#559—42no—
213#559—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#126—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×#120—21no—
241#518—42no—
242#518—42no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×#117—21no—
257C2×#117—21no—
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C22⋊C4—21no—
261C22×C22⋊C4—21no—
262#496—42no—
263#486—24no—
264#486—42no—
265#482—42no—
266#477—42no—
267#463—24no—
268#459—42no—
269#447—24no—
270#447—42no—
271#442—42no—
272C4×D8—42no—
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#400—21no—
328#400D411yescharacteristic
329#399—21no—
330#399D411yescharacteristic
331#398D411yescharacteristic
332#398D411yescharacteristic
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396D411yescharacteristic
346#396D411yescharacteristic
347#395—21no—
348#395—21no—
349#395D411yescharacteristic
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#393—21no—
368#393—21no—
369#393—21no—
370#393—21no—
371#393D411yescharacteristic
372#392—21no—
373#392—21no—
374#392—21no—
375#391—21no—
376#391—21no—
377#391—21no—
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#389—21no—
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#387—21no—
422#387—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#384—21no—
438#384C2311yescharacteristic
439#384C2311yescharacteristic
440#381—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447#379—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2411yescharacteristic
527C2×SD16—22no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C4⋊Q8—22no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563#127—22no—
564#127—22no—
565#127—41no—
566#127—41no—
567#127—41no—
568#127—41no—
569#126—82no—
570#124—22no—
571#124—22no—
572#124—41no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—44no—
577#124—82no—
578#124—82no—
579#124—82no—
580#123—44no—
581#123—44no—
582#123—82no—
583#123—82no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—82no—
587C22⋊Q8—82no—
588C22⋊Q8—82no—
589#121—22no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—82no—
596#120—82no—
597#120—82no—
598C4×Q8—22no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
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—44no—
618C4×D4—44no—
619C4×D4—82no—
620#117—22no—
621#117—41no—
622#117—41no—
623#117—41no—
624#117—82no—
625#117—82no—
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⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
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—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—44no—
712C2×C22⋊C4—44no—
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733#107—22no—
734#107—22no—
735#107—41no—
736#107—41no—
737#107—41no—
738#107—41no—
739#106—41no—
740#106—41no—
741C4⋊C8—22no—
742C4⋊C8—41no—
743C4⋊C8—41no—
744C4⋊C8—41no—
745#103—22no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
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—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102#4114yes—
777C22⋊C8—22no—
778C22⋊C8—41no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781#97—41no—
782#97—41no—
783#97—41no—
784C4×C8—22no—
785C4×C8—41no—
786C4×C8—41no—
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#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817C24—21no—
818C24—21no—
819C24—21no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830C2×Q8—22no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—41no—
838C2×Q8—41no—
839C2×Q8—42no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
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—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—44no—
883C2×D4—44no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
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×D4C2×#4112yes—
908C2×D4H(5,𝔽2)12yes—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—24no—
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—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C2511yescharacteristic
961SD16—82no—
962SD16—82no—
963D8—44no—
964D8—44no—
965D8—82no—
966D8—82no—
967D8—82no—
968D8—82no—
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—21no—
982C2×C8—21no—
983C2×C8—21no—
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×C8C2×#4112yes—
993C4⋊C4—22no—
994C4⋊C4—22no—
995C4⋊C4—22no—
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—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
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⋊C4C2×#4112yes—
1039C4⋊C4H(5,𝔽2)12yes—
1040C22⋊C4—24no—
1041C22⋊C4—22no—
1042C22⋊C4—22no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
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—
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—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—42no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42—81no—
1112C42—81no—
1113C42—81no—
1114C23—21no—
1115C23—21no—
1116C23—22no—
1117C23—21no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—48no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
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—162no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23—162no—
1162C23—162no—
1163C23C23×D411yescharacteristic
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—82no—
1169Q8—162no—
1170Q8—162no—
1171D4—22no—
1172D4—22no—
1173D4—22no—
1174D4—22no—
1175D4—48no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—84no—
1193D4—84no—
1194D4—162no—
1195D4—162no—
1196D4—162no—
1197D4—162no—
1198D4—162no—
1199D4—162no—
1200D4—162no—
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—22no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—22no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
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—84no—
1276C2×C4—84no—
1277C2×C4—162no—
1278C2×C4—162no—
1279C2×C4—162no—
1280C2×C4—162no—
1281C2×C4—162no—
1282C2×C4#57612yes—
1283C2×C4#57612yes—
1284C2×C4C22×#4111yescharacteristic
1285C2×C4C2×H(5,𝔽2)11yescharacteristic
1286C2×C4C2×H(5,𝔽2)11yescharacteristic
1287C2×C4#58511yescharacteristic
1288C2×C4#58511yescharacteristic
1289C2×C4#58511yescharacteristic
1290C8—22no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C8—41no—
1296C8—41no—
1297C8—41no—
1298C22—42no—
1299C22—41no—
1300C22—41no—
1301C22—42no—
1302C22—41no—
1303C22—42no—
1304C22—42no—
1305C22—42no—
1306C22—41no—
1307C22—41no—
1308C22—42no—
1309C22—41no—
1310C22—41no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
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—168no—
1341C22D4×#4111yescharacteristic
1342C22#348411yescharacteristic
1343C22#348711yescharacteristic
1344C22C2×#57611yescharacteristic
1345C22C2×#57611yescharacteristic
1346C22#358511yescharacteristic
1347C22#358611yescharacteristic
1348C4—22no—
1349C4—22no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—42no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—41no—
1361C4—41no—
1362C4—42no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4#346011yescharacteristic
1373C4#351311yescharacteristic
1374C4#353311yescharacteristic
1375C4#354011yescharacteristic
1376C2—81no—
1377C2—82no—
1378C2—82no—
1379C2—161no—
1380C2—161no—
1381C2—161no—
1382C2#3780311yescharacteristic
1383C2#6152311yescharacteristic
1384C2#6153911yescharacteristic
1385C2#6162411yescharacteristic
1386C2#6167911yescharacteristic
1387C2#6193211yescharacteristic
1388C2#6194411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42585C2semidirect
2. #35808C2semidirect
3. #33014C2semidirect
4. #32596C2semidirect
5. #32593C2semidirect
6. #32188C2semidirect
7. #31302C2semidirect
8. #30875C2semidirect
9. #30519C2semidirect
10. #30519C2semidirect
11. #30468C2semidirect
12. #30328C2semidirect
13. #30119C2semidirect
14. #27486C2semidirect
15. #27443C2semidirect
16. #27190C2semidirect
17. #27056C2semidirect
18. #26954C2semidirect
19. #26890C2semidirect
20. #26834C2semidirect
21. #26793C2semidirect
22. #26733C2semidirect
23. #26693C2semidirect
24. #26584C2semidirect
25. #26268C2semidirect
26. #25648C2semidirect
27. #25642C2semidirect
28. #23223C2semidirect
29. #23105C2semidirect
30. #22324C2semidirect
31. #21458C2semidirect
38. C2×#477C22semidirect
40. C2×#459C22semidirect
55. #2567C22semidirect
56. #2548C22semidirect
60. #2512C22semidirect
68. #2452C22semidirect
69. #2452C22semidirect
72. #2445C22semidirect
80. #2369C22semidirect
86. #2354C22semidirect
88. #2100C22semidirect
90. #2093C22semidirect
91. #2088C22semidirect
92. #2083C22semidirect
93. #2071C22semidirect
94. #2071C22semidirect
96. #2067C22semidirect
97. #2065C22semidirect
98. #2058C22semidirect
99. #2055C22semidirect
106. #2042C22semidirect
107. #2042C22semidirect
108. #2041C22semidirect
113. #2024C22semidirect
117. #2012C22semidirect
118. #2012C22semidirect
128. #1987C22semidirect
129. #1985C22semidirect
130. #1984C22semidirect
134. #1973C22semidirect
135. #1972C22semidirect
138. #1970C22semidirect
139. #1968C22semidirect
141. #1947C22semidirect
142. #1943C22semidirect
145. #1936C22semidirect
146. #1934C22semidirect
147. #1933C22semidirect
148. #1928C22semidirect
149. #1927C22semidirect
153. #1925C22semidirect
154. #1925C22semidirect
155. #1925C22semidirect
156. #1925C22semidirect
161. #1921C22semidirect
162. #1918C22semidirect
163. #1918C22semidirect
164. #1917C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
167. #1916C22semidirect
168. #1880C22semidirect
169. #1880C22semidirect
177. #1879C22semidirect
178. #1879C22semidirect
179. #1877C22semidirect
187. #1862C22semidirect
188. #1862C22semidirect
194. C4×#107C22semidirect
195. #1771C22semidirect
196. #1770C22semidirect
198. #1762C22semidirect
199. #1762C22semidirect
200. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#425852
#358082
#330142
#325962
#325932
#321882
#313022
#308752
#305192
#304682
#303282
#301192
#274862
#274432
#271902
#270562
#269542
#268902
#268342
#267932
#267332
#266932
#265842
#262682
#256482
#256422
#232232
#231052
#223242
#214582