Finite Group Databasebeta

← #7026167

Subgroups — #7026167

Order 512.

1612 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45187C211yesmaximal, characteristic, complemented
2#45090C211yesmaximal, characteristic, complemented
3#32108C211yesmaximal, characteristic, complemented
4#31874C211yesmaximal, characteristic, complemented
5#31733C211yesmaximal, characteristic, complemented
6#31302C211yesmaximal, characteristic, complemented
7#31013C211yesmaximal, characteristic, complemented
8#30674C211yesmaximal, characteristic, complemented
9#30568C211yesmaximal, characteristic, complemented
10#30452C211yesmaximal, characteristic, complemented
11#28895C211yesmaximal, characteristic, complemented
12#28126C211yesmaximal, characteristic, complemented
13#27421C211yesmaximal, characteristic, complemented
14#27092C211yesmaximal, characteristic, complemented
15#27045C211yesmaximal, characteristic, complemented
16#26951C211yesmaximal, characteristic, complemented
17#26906C211yesmaximal, characteristic, complemented
18#26747C211yesmaximal, characteristic, complemented
19#26188C211yesmaximal, characteristic, complemented
20#25411C211yesmaximal, characteristic, complemented
21#25374C211yesmaximal, characteristic, complemented
22#25167C211yesmaximal, characteristic, complemented
23#25085C211yesmaximal, characteristic, complemented
24#24436C211yesmaximal, characteristic, complemented
25#24257C211yesmaximal, characteristic
26#24165C211yesmaximal, characteristic, complemented
27#23584C211yesmaximal, characteristic, complemented
28#23007C211yesmaximal, characteristic, complemented
29#22573C211yesmaximal, characteristic, complemented
30#22362C211yesmaximal, characteristic, complemented
31#22052C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#495C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#465C2211yescharacteristic
38C2×#465C2211yescharacteristic, complemented
39C2×#464C2211yescharacteristic, complemented
40C2×#462C2211yescharacteristic, complemented
41C2×#463C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#449C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#447C2211yescharacteristic
47C2×#442C2211yescharacteristic
48C2×#440C2211yescharacteristic, complemented
49C2×C4×SD16C2211yescharacteristic, complemented
50C2×#416C2211yescharacteristic
51#2796—21no—
52#2781—21no—
53#2741—21no—
54#2711—21no—
55#2711—21no—
56#2694—21no—
57#2685—21no—
58#2685—21no—
59#2591—21no—
60#2558—21no—
61#2545C2211yescharacteristic
62#2537C2211yescharacteristic
63#2531—21no—
64#2530—21no—
65#2511C2211yescharacteristic, complemented
66#2506C2211yescharacteristic, complemented
67#2497C2211yescharacteristic
68#2490—21no—
69#2490C2211yescharacteristic
70#2480—21no—
71#2480—21no—
72#2454C2211yescharacteristic
73#2448C2211yescharacteristic
74#2442—21no—
75#2435C2211yescharacteristic
76#2432C2211yescharacteristic
77#2427C2211yescharacteristic
78#2427C2211yescharacteristic, complemented
79#2426C2211yescharacteristic
80#2423C2211yescharacteristic, complemented
81#2415C2211yescharacteristic
82#2415C2211yescharacteristic
83#2395C2211yescharacteristic
84#2367C2211yescharacteristic
85#2367C2211yescharacteristic, complemented
86#2363C2211yescharacteristic, complemented
87#2362C2211yescharacteristic
88D4×C4⋊C4C2211yescharacteristic, complemented
89#2346C2211yescharacteristic, complemented
90#2341C2211yescharacteristic
91#2324C2211yescharacteristic
92#2323C2211yescharacteristic
93#2309C2211yescharacteristic
94#2095C2211yescharacteristic, complemented
95#2093C2211yescharacteristic
96#2088C2211yescharacteristic, complemented
97#2087C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2072C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2043C2211yescharacteristic, complemented
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic, complemented
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic, complemented
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic, complemented
123#2025C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic
126#2013C2211yescharacteristic, complemented
127#2012C2211yescharacteristic
128#2001C2211yescharacteristic
129#2001C2211yescharacteristic
130#2001C2211yescharacteristic, complemented
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#1999C2211yescharacteristic
134#1989C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1981C2211yescharacteristic, complemented
137#1973C2211yescharacteristic
138#1971C2211yescharacteristic, complemented
139#1968C2211yescharacteristic
140#1959C2211yescharacteristic
141#1959C2211yescharacteristic
142#1955C2211yescharacteristic
143#1948C2211yescharacteristic, complemented
144#1941C2211yescharacteristic, complemented
145#1939C2211yescharacteristic, complemented
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1935C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1928C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic
157#1925C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic, complemented
160#1924C2211yescharacteristic, complemented
161#1923C2211yescharacteristic
162#1919C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1878C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic, complemented
175#1877C2211yescharacteristic, complemented
176#1875C2211yescharacteristic
177#1873C2211yescharacteristic
178#1873C2211yescharacteristic, complemented
179#1869C2211yescharacteristic
180#1865C2211yescharacteristic, complemented
181#1864C2211yescharacteristic
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1863C2211yescharacteristic, complemented
185#1862C2211yescharacteristic, complemented
186#1854C2211yescharacteristic
187#1850C2211yescharacteristic, complemented
188#1825C2211yescharacteristic
189#1825C2211yescharacteristic, complemented
190#1808C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1798C2211yescharacteristic
193#1788C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#546—42no—
215#546—42no—
216#541—42no—
217#541—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×#126—21no—
220C2×#126—21no—
221C2×#125—21no—
222C2×#125—21no—
223C2×#125—21no—
224C2×#125C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C22×C4⋊C4—21no—
254C22×C22⋊C4—21no—
255#495—42no—
256#482—42no—
257#479—42no—
258#465—42no—
259#465—42no—
260#464—42no—
261#463—24no—
262#463—42no—
263#462—42no—
264#452—42no—
265#450—24no—
266#449—42no—
267#447—42no—
268#442—42no—
269#440—42no—
270C4×SD16—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284#416—24no—
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#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×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400D411yescharacteristic
334#399—21no—
335#399—21no—
336#399—21no—
337#399D411yescharacteristic
338#398—21no—
339#398—21no—
340#398D411yescharacteristic
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397D411yescharacteristic
348#397D411yescharacteristic
349#397D411yescharacteristic
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—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#394D411yescharacteristic
368#394D411yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#390—21no—
375#390—21no—
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390—21no—
381#390—21no—
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#389—21no—
390#389—21no—
391#389—21no—
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
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#388—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#384C2311yescharacteristic
442#384C2311yescharacteristic
443#382—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#379—21no—
455#379—21no—
456#379—21no—
457#379—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472#376—21no—
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#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2×D411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×Q16—22no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×D8—22no—
550C2×D8—22no—
551C2×D8—22no—
552C2×D8—41no—
553C2×D8—41no—
554C2×D8—41no—
555C22×C8—22no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C4⋊Q8—22no—
567C4⋊Q8—41no—
568#126—44no—
569#126—44no—
570#125—22no—
571#125—41no—
572#125—44no—
573#125—44no—
574#125—82no—
575#124—22no—
576#124—22no—
577#124—22no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#123—44no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—44no—
601#121—82no—
602#120—44no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×Q8—41no—
610C4×Q8—41no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621#117—22no—
622#117—41no—
623#117—41no—
624#117—41no—
625#117—41no—
626#117—41no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—82no—
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—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—44no—
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—41no—
737#107—41no—
738#107—41no—
739#107—41no—
740#106—22no—
741#106—22no—
742#106—41no—
743#106—41no—
744C4⋊C8—22no—
745C4⋊C8—41no—
746C4⋊C8—41no—
747C4⋊C8—41no—
748C4⋊C8—41no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—22no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102#4114yes—
781C22⋊C8—22no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788#97—41no—
789#97—41no—
790#97—41no—
791C4×C8—41no—
792C4×C8—41no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829C24—21no—
830C24—21no—
831C24—21no—
832C24—42no—
833C24—42no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24C22×D411yescharacteristic
840C24C22×D411yescharacteristic
841#41—44no—
842#41—82no—
843#41—82no—
844#41—82no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8H(5,𝔽2)12yes—
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—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—81no—
890C2×D4—82no—
891C2×D4—82no—
892C2×D4—82no—
893C2×D4—82no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4C2×#4112yes—
902C2×D4H(5,𝔽2)12yes—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—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—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
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×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
956Q16—82no—
957Q16—82no—
958SD16—44no—
959SD16—44no—
960SD16—82no—
961SD16—82no—
962D8—44no—
963D8—82no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—82no—
988C2×C8C2×#4112yes—
989C4⋊C4—24no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4C2×#4112yes—
1040C4⋊C4H(5,𝔽2)12yes—
1041C22⋊C4—24no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
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—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
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—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—42no—
1102C42—42no—
1103C42—42no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—22no—
1122C23—21no—
1123C23—21no—
1124C23—22no—
1125C23—21no—
1126C23—21no—
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—84no—
1147C23—84no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23C23×D411yescharacteristic
1154Q8—22no—
1155Q8—22no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166D4—22no—
1167D4—22no—
1168D4—22no—
1169D4—22no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—82no—
1179D4—84no—
1180D4—84no—
1181D4—162no—
1182D4—162no—
1183D4—162no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
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—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—22no—
1216C2×C4—22no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
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—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—162no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4C22×#4111yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4C2×H(5,𝔽2)11yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4#58511yescharacteristic
1277C2×C4#58511yescharacteristic
1278C8—22no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C22—41no—
1287C22—41no—
1288C22—42no—
1289C22—41no—
1290C22—41no—
1291C22—42no—
1292C22—41no—
1293C22—41no—
1294C22—42no—
1295C22—41no—
1296C22—41no—
1297C22—42no—
1298C22—41no—
1299C22—41no—
1300C22—42no—
1301C22—42no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—81no—
1307C22—81no—
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—168no—
1322C22D4×#4111yescharacteristic
1323C22#348411yescharacteristic
1324C22#348811yescharacteristic
1325C22#358411yescharacteristic
1326C22#358411yescharacteristic
1327C22#358511yescharacteristic
1328C22#358611yescharacteristic
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—42no—
1334C4—41no—
1335C4—41no—
1336C4—42no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—42no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4#349411yescharacteristic
1355C4#351911yescharacteristic
1356C4#353411yescharacteristic
1357C4#356211yescharacteristic
1358C2—81no—
1359C2—81no—
1360C2—82no—
1361C2—82no—
1362C2—161no—
1363C2#4310711yescharacteristic
1364C2#6148611yescharacteristic
1365C2#6151011yescharacteristic
1366C2#6161611yescharacteristic
1367C2#6169111yescharacteristic
1368C2#6201111yescharacteristic
1369C2#6201211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24257C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45187C2semidirect
2. #45090C2semidirect
3. #32108C2semidirect
4. #31874C2semidirect
5. #31733C2semidirect
6. #31302C2semidirect
7. #31013C2semidirect
8. #30674C2semidirect
9. #30568C2semidirect
10. #30452C2semidirect
11. #28895C2semidirect
12. #28126C2semidirect
13. #27421C2semidirect
14. #27092C2semidirect
15. #27045C2semidirect
16. #26951C2semidirect
17. #26906C2semidirect
18. #26747C2semidirect
19. #26188C2semidirect
20. #25411C2semidirect
21. #25374C2semidirect
22. #25167C2semidirect
23. #25085C2semidirect
24. #24436C2semidirect
26. #24165C2semidirect
27. #23584C2semidirect
28. #23007C2semidirect
29. #22573C2semidirect
30. #22362C2semidirect
31. #22052C2semidirect
36. C2×#479C22semidirect
38. C2×#465C22semidirect
39. C2×#464C22semidirect
40. C2×#462C22semidirect
48. C2×#440C22semidirect
49. C2×C4×SD16C22semidirect
65. #2511C22semidirect
66. #2506C22semidirect
78. #2427C22semidirect
80. #2423C22semidirect
85. #2367C22semidirect
86. #2363C22semidirect
88. D4×C4⋊C4C22semidirect
89. #2346C22semidirect
94. #2095C22semidirect
96. #2088C22semidirect
97. #2087C22semidirect
98. #2084C22semidirect
99. #2072C22semidirect
102. #2066C22semidirect
104. #2059C22semidirect
105. #2056C22semidirect
109. #2043C22semidirect
114. #2042C22semidirect
117. #2036C22semidirect
120. #2035C22semidirect
122. #2033C22semidirect
123. #2025C22semidirect
126. #2013C22semidirect
130. #2001C22semidirect
134. #1989C22semidirect
136. #1981C22semidirect
138. #1971C22semidirect
143. #1948C22semidirect
144. #1941C22semidirect
145. #1939C22semidirect
148. #1935C22semidirect
149. #1935C22semidirect
152. #1928C22semidirect
159. #1924C22semidirect
160. #1924C22semidirect
162. #1919C22semidirect
163. #1918C22semidirect
164. #1917C22semidirect
165. #1917C22semidirect
171. #1878C22semidirect
172. #1878C22semidirect
174. #1877C22semidirect
175. #1877C22semidirect
178. #1873C22semidirect
180. #1865C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
184. #1863C22semidirect
185. #1862C22semidirect
187. #1850C22semidirect
189. #1825C22semidirect
190. #1808C22semidirect
196. #1771C22semidirect
197. #1763C22semidirect
198. #1762C22semidirect
199. C4×#103C22semidirect
200. C4×#103C22semidirect
201. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#451872
#450902
#321082
#318742
#317332
#313022
#310132
#306742
#305682
#304522
#288952
#281262
#274212
#270922
#270452
#269512
#269062
#267472
#261882
#254112
#253742
#251672
#250852
#244362
#242572
#241652
#235842
#230072
#225732
#223622
#220522