Finite Group Databasebeta

← #6507601

Subgroups — #6507601

Order 512.

1876 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35045C211yesmaximal, characteristic, complemented
2#34681C211yesmaximal, characteristic
3#29572C211yesmaximal, characteristic, complemented
4#29492C211yesmaximal, characteristic, complemented
5#29481C211yesmaximal, characteristic, complemented
6#29432C211yesmaximal, characteristic, complemented
7#29192C211yesmaximal, characteristic, complemented
8#29167C211yesmaximal, characteristic, complemented
9#29068C211yesmaximal, characteristic, complemented
10#29019C211yesmaximal, characteristic, complemented
11#28952C211yesmaximal, characteristic, complemented
12#28869C211yesmaximal, characteristic, complemented
13#28365C211yesmaximal, characteristic, complemented
14#28110C211yesmaximal, characteristic, complemented
15#27706C211yesmaximal, characteristic, complemented
16#27279C211yesmaximal, characteristic, complemented
17#26987C211yesmaximal, characteristic, complemented
18#26841C211yesmaximal, characteristic, complemented
19#26499C211yesmaximal, characteristic, complemented
20#26077C211yesmaximal, characteristic, complemented
21#25676C211yesmaximal, characteristic, complemented
22#25501C211yesmaximal, characteristic, complemented
23#25263C211yesmaximal, characteristic, complemented
24#25136C211yesmaximal, characteristic, complemented
25#25045C211yesmaximal, characteristic, complemented
26#24794C211yesmaximal, characteristic, complemented
27#22191C211yesmaximal, characteristic, complemented
28#22086C211yesmaximal, characteristic, complemented
29#21453C211yesmaximal, characteristic, complemented
30#20873C211yesmaximal, characteristic, complemented
31#20568C211yesmaximal, characteristic, complemented
32C2×#532C2211yescharacteristic
33C2×#525—21no—
34C22×C4×D4C2211yescharacteristic
35C2×#501C2211yescharacteristic, complemented
36C2×#490C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#468C2211yescharacteristic, complemented
41C2×#450C2211yescharacteristic
42C2×#440C2211yescharacteristic
43C2×#440C2211yescharacteristic
44C2×#436C2211yescharacteristic
45C2×#436C2211yescharacteristic
46C2×#428C2211yescharacteristic
47C2×#418C2211yescharacteristic
48C2×#418C2211yescharacteristic
49#2863C2211yescharacteristic, complemented
50#2859C2211yescharacteristic, complemented
51#2855C2211yescharacteristic, complemented
52#2851C2211yescharacteristic, complemented
53#2652—21no—
54#2633—21no—
55#2590—21no—
56#2575—21no—
57#2517—21no—
58#2508C2211yescharacteristic, complemented
59#2499C2211yescharacteristic
60#2496C2211yescharacteristic, complemented
61#2485C2211yescharacteristic
62#2472—21no—
63#2466—21no—
64#2464—21no—
65#2461—21no—
66#2453C2211yescharacteristic, complemented
67#2452C2211yescharacteristic
68#2445C2211yescharacteristic
69#2441C2211yescharacteristic
70#2440C2211yescharacteristic
71#2433C2211yescharacteristic
72#2428C2211yescharacteristic
73#2424—21no—
74#2423C2211yescharacteristic, complemented
75#2422C2211yescharacteristic
76#2416C2211yescharacteristic
77#2415C2211yescharacteristic
78#2408C2211yescharacteristic
79#2392—21no—
80#2388—21no—
81#2336—21no—
82#2334—21no—
83C4×#127C2211yescharacteristic
84C4×C22⋊Q8C2211yescharacteristic
85C4×#121C2211yescharacteristic
86C4×#121C2211yescharacteristic
87C4×#120—21no—
88#2296C2211yescharacteristic
89#2293C2211yescharacteristic
90C42×D4C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2093C2211yescharacteristic
94#2092C2211yescharacteristic
95#2088C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2076C2211yescharacteristic, complemented
99#2072C2211yescharacteristic, complemented
100#2071C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic, complemented
108#2057C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2041C2211yescharacteristic
111#2041C2211yescharacteristic
112#2036C2211yescharacteristic, complemented
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic, complemented
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic, complemented
118#2025C2211yescharacteristic
119#2024C2211yescharacteristic, complemented
120#2014C2211yescharacteristic
121#2014C2211yescharacteristic
122#2000C2211yescharacteristic
123#1993C2211yescharacteristic, complemented
124#1973C2211yescharacteristic
125#1968C2211yescharacteristic
126#1968C2211yescharacteristic
127#1968C2211yescharacteristic, complemented
128#1961C2211yescharacteristic
129#1957C2211yescharacteristic
130#1957C2211yescharacteristic
131#1944C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1943C2211yescharacteristic, complemented
134#1942C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1941C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic, complemented
139#1936C2211yescharacteristic, complemented
140#1935C2211yescharacteristic, complemented
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic, complemented
146#1933C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1926C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1895C2211yescharacteristic
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic, complemented
158#1894C2211yescharacteristic
159#1880C2211yescharacteristic, complemented
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic, complemented
163#1875C2211yescharacteristic
164#1872C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic, complemented
170#1863C2211yescharacteristic, complemented
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic, complemented
178#1862C2211yescharacteristic, complemented
179#1854C2211yescharacteristic
180#1852C2211yescharacteristic
181#1845C2211yescharacteristic, complemented
182#1834C2211yescharacteristic, complemented
183#1825C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic, complemented
186#1809C2211yescharacteristic, complemented
187#1786C2211yescharacteristic
188#1770C2211yescharacteristic, complemented
189#1770C2211yescharacteristic, complemented
190C4×C4⋊C8C2211yescharacteristic, complemented
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic
195#1753C2211yescharacteristic, complemented
196#1753C2211yescharacteristic, complemented
197#1749C2211yescharacteristic
198#1749C2211yescharacteristic, complemented
199#1744C2211yescharacteristic, complemented
200#1736C2211yescharacteristic
201#1728C2211yescharacteristic
202#1728C2211yescharacteristic, complemented
203C22×#41—21no—
204C23×D4C2311yescharacteristic
205C24×C4—21no—
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213#532—42no—
214#532—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#126—21no—
219C2×#125—21no—
220C2×#125C2311yescharacteristic
221C2×#124—21no—
222#525—48no—
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#120—21no—
237C2×#120—21no—
238C2×#120—21no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4—42no—
248C2×C4×D4—42no—
249C2×C4×D4D411yescharacteristic
250C2×C4×D4D411yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117—21no—
258C2×#117C2311yescharacteristic
259C2×#117C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—21no—
262C22×C42C2311yescharacteristic
263C22×C42C2311yescharacteristic
264#501—42no—
265#490—42no—
266#482—24no—
267#468—24no—
268#468—42no—
269#468—42no—
270#450—24no—
271#440—42no—
272#440—42no—
273#436—24no—
274#436—24no—
275#428—42no—
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291#418—24no—
292#418—42no—
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331#400—21no—
332#400—21no—
333#400—21no—
334#399—21no—
335#399—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#395—21no—
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#393—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#390—21no—
368#390—21no—
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#383—21no—
435#382—21no—
436#382—21no—
437#382C2311yescharacteristic
438#381—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4D411yescharacteristic
450C4×C4⋊C4D411yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4D411yescharacteristic
459C4×C22⋊C4D411yescharacteristic
460C4×C22⋊C4D411yescharacteristic
461C4×C22⋊C4D411yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C43C2311yescharacteristic
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#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497C25—21no—
498C2×#41—44no—
499C2×#41—44no—
500C2×#41—82no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4C2×D411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—44no—
529C23×C4—44no—
530C23×C4—82no—
531C23×C4C2×D411yescharacteristic
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16—22no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C2×M16—41no—
557C2×M16#4114yescomplemented
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—22no—
567C4⋊Q8—41no—
568#127—22no—
569#127—22no—
570#127—41no—
571#127—41no—
572#126—44no—
573#125—41no—
574#125—41no—
575#125—44no—
576#124—44no—
577#123—44no—
578#123—44no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—44no—
582C22⋊Q8—44no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—44no—
591#121—44no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—44no—
596#120—44no—
597#120—44no—
598#120—44no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—24no—
608C4×D4—42no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—44no—
616C4×D4—44no—
617C4×D4—44no—
618C4×D4—44no—
619C4×D4—44no—
620C4×D4—44no—
621C4×D4—82no—
622#117—22no—
623#117—22no—
624#117—44no—
625#117—41no—
626#117—41no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—41no—
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—44no—
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—41no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42—41no—
718C2×C42C2×D411yescharacteristic
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2×D411yescharacteristic
725C2×C42C2×D411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730C2×C42C2411yescharacteristic
731#107—22no—
732#107—22no—
733#107—22no—
734#107—22no—
735#107—41no—
736#107—41no—
737#107—41no—
738#107—41no—
739#106—22no—
740#106—22no—
741#106—41no—
742#106—41no—
743#106—41no—
744C4⋊C8—22no—
745C4⋊C8—22no—
746#103—22no—
747#103—22no—
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—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
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—22no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8#4114yescomplemented
776#97—41no—
777#97—41no—
778#97—41no—
779#97—41no—
780C4×C8—22no—
781C4×C8—22no—
782C4×C8—41no—
783C4×C8—41no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822C24—21no—
823C24—21no—
824C24—21no—
825C24—42no—
826C24—42no—
827C24—42no—
828C24—42no—
829C24—42no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834#41—816no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—42no—
842C2×Q8—42no—
843C2×Q8—81no—
844C2×D4—28no—
845C2×D4—22no—
846C2×D4—22no—
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—44no—
864C2×D4—44no—
865C2×D4—41no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—44no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
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—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4H(5,𝔽2)12yes—
895C2×D42−1+412yes—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—24no—
901C22×C4—21no—
902C22×C4—22no—
903C22×C4—22no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—41no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—816no—
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×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C2×#4112yes—
963C22×C4C2×#4112yes—
964C22×C4C2511yescharacteristic
965SD16—44no—
966SD16—44no—
967SD16—82no—
968M16—44no—
969M16—82no—
970M16—82no—
971M16—82no—
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—
993C2×C8C2×#4112yes—
994C2×C8C2×#4112yes—
995C2×C8C2×#4112yes—
996C4⋊C4—22no—
997C4⋊C4—22no—
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—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—41no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
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⋊C4H(5,𝔽2)12yes—
1050C22⋊C4—24no—
1051C22⋊C4—22no—
1052C22⋊C4—22no—
1053C22⋊C4—22no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
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—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—42no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C42—22no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—41no—
1099C42—41no—
1100C42—41no—
1101C42—41no—
1102C42—41no—
1103C42—41no—
1104C42—42no—
1105C42—42no—
1106C42—42no—
1107C42—81no—
1108C42—81no—
1109C42AGL(1,ℤ/8)14yes—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—22no—
1120C23—21no—
1121C23—22no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—48no—
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—84no—
1146C23—84no—
1147C23—84no—
1148C23—84no—
1149C23—84no—
1150C23—84no—
1151C23#53212yes—
1152C23C23×D411yescharacteristic
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—84no—
1158D4—22no—
1159D4—22no—
1160D4—22no—
1161D4—22no—
1162D4—44no—
1163D4—48no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—84no—
1173D4—84no—
1174D4—84no—
1175D4—84no—
1176D4—84no—
1177D4—84no—
1178D4—84no—
1179D4—84no—
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—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—21no—
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—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—22no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—44no—
1217C2×C4—48no—
1218C2×C4—44no—
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—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—84no—
1262C2×C4—84no—
1263C2×C4—82no—
1264C2×C4—82no—
1265C2×C4—84no—
1266C2×C4—84no—
1267C2×C4—84no—
1268C2×C4#53212yes—
1269C2×C4C2×AGL(1,ℤ/8)12yes—
1270C2×C4C2×AGL(1,ℤ/8)12yes—
1271C2×C4C2×AGL(1,ℤ/8)12yes—
1272C2×C4#57512yes—
1273C2×C4C22×#4111yescharacteristic
1274C2×C4C22×#4111yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4C2×2−1+411yescharacteristic
1278C2×C4#58511yescharacteristic
1279C8—22no—
1280C8—22no—
1281C8—22no—
1282C8—22no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22—41no—
1301C22—41no—
1302C22—42no—
1303C22—41no—
1304C22—42no—
1305C22—42no—
1306C22—41no—
1307C22—816no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22C2×#53211yescharacteristic
1324C22#348411yescharacteristic
1325C22#348911yescharacteristic
1326C22C22×AGL(1,ℤ/8)11yescharacteristic
1327C22C2×#57511yescharacteristic
1328C22#358511yescharacteristic
1329C22#358611yescharacteristic
1330C4—22no—
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—22no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—42no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4#349211yescharacteristic
1356C4#350511yescharacteristic
1357C4#351311yescharacteristic
1358C4#352011yescharacteristic
1359C2—42no—
1360C2—81no—
1361C2—82no—
1362C2—82no—
1363C2—161no—
1364C2#3539311yescharacteristic
1365C2#6069711yescharacteristic
1366C2#6070011yescharacteristic
1367C2#6158211yescharacteristic
1368C2#6158911yescharacteristic
1369C2#6210911yescharacteristic
1370C2#6211911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#34681C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35045C2semidirect
3. #29572C2semidirect
4. #29492C2semidirect
5. #29481C2semidirect
6. #29432C2semidirect
7. #29192C2semidirect
8. #29167C2semidirect
9. #29068C2semidirect
10. #29019C2semidirect
11. #28952C2semidirect
12. #28869C2semidirect
13. #28365C2semidirect
14. #28110C2semidirect
15. #27706C2semidirect
16. #27279C2semidirect
17. #26987C2semidirect
18. #26841C2semidirect
19. #26499C2semidirect
20. #26077C2semidirect
21. #25676C2semidirect
22. #25501C2semidirect
23. #25263C2semidirect
24. #25136C2semidirect
25. #25045C2semidirect
26. #24794C2semidirect
27. #22191C2semidirect
28. #22086C2semidirect
29. #21453C2semidirect
30. #20873C2semidirect
31. #20568C2semidirect
35. C2×#501C22semidirect
40. C2×#468C22semidirect
49. #2863C22semidirect
50. #2859C22semidirect
51. #2855C22semidirect
52. #2851C22semidirect
58. #2508C22semidirect
60. #2496C22semidirect
66. #2453C22semidirect
74. #2423C22semidirect
91. #2101C22semidirect
92. #2099C22semidirect
95. #2088C22semidirect
96. #2084C22semidirect
97. #2083C22semidirect
98. #2076C22semidirect
99. #2072C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
105. #2066C22semidirect
107. #2059C22semidirect
108. #2057C22semidirect
112. #2036C22semidirect
115. #2034C22semidirect
117. #2033C22semidirect
119. #2024C22semidirect
123. #1993C22semidirect
127. #1968C22semidirect
131. #1944C22semidirect
132. #1944C22semidirect
133. #1943C22semidirect
134. #1942C22semidirect
135. #1942C22semidirect
136. #1941C22semidirect
138. #1936C22semidirect
139. #1936C22semidirect
140. #1935C22semidirect
145. #1934C22semidirect
146. #1933C22semidirect
147. #1927C22semidirect
148. #1926C22semidirect
149. #1921C22semidirect
150. #1920C22semidirect
151. #1918C22semidirect
152. #1918C22semidirect
157. #1895C22semidirect
159. #1880C22semidirect
162. #1877C22semidirect
169. #1864C22semidirect
170. #1863C22semidirect
177. #1862C22semidirect
178. #1862C22semidirect
181. #1845C22semidirect
182. #1834C22semidirect
185. #1809C22semidirect
186. #1809C22semidirect
188. #1770C22semidirect
189. #1770C22semidirect
190. C4×C4⋊C8C22semidirect
195. #1753C22semidirect
196. #1753C22semidirect
198. #1749C22semidirect
199. #1744C22semidirect
202. #1728C22semidirect
557. C2×M16#41semidirect
775. C22⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
#350452
#346812
#295722
#294922
#294812
#294322
#291922
#291672
#290682
#290192
#289522
#288692
#283652
#281102
#277062
#272792
#269872
#268412
#264992
#260772
#256762
#255012
#252632
#251362
#250452
#247942
#221912
#220862
#214532
#208732
#205682