Finite Group Databasebeta

← #7073033

Subgroups — #7073033

Order 512.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1387 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59812C211yesmaximal, characteristic
2#39664C211yesmaximal, characteristic, complemented
3#32009C211yesmaximal, characteristic, complemented
4#31878C211yesmaximal, characteristic, complemented
5#31788C211yesmaximal, characteristic, complemented
6#31722C211yesmaximal, characteristic, complemented
7#31678C211yesmaximal, characteristic, complemented
8#31215C211yesmaximal, characteristic, complemented
9#31024C211yesmaximal, characteristic, complemented
10#30504C211yesmaximal, characteristic, complemented
11#29465C211yesmaximal, characteristic, complemented
12#29020C211yesmaximal, characteristic, complemented
13#28934C211yesmaximal, characteristic, complemented
14#27346C211yesmaximal, characteristic, complemented
15#26979C211yesmaximal, characteristic, complemented
16#26946C211yesmaximal, characteristic, complemented
17#26845C211yesmaximal, characteristic, complemented
18#26675C211yesmaximal, characteristic, complemented
19#25582C211yesmaximal, characteristic, complemented
20#25176C211yesmaximal, characteristic, complemented
21#25112C211yesmaximal, characteristic, complemented
22#24781C211yesmaximal, characteristic, complemented
23#24511C211yesmaximal, characteristic, complemented
24#24426C211yesmaximal, characteristic, complemented
25#24259C211yesmaximal, characteristic, complemented
26#24092C211yesmaximal, characteristic, complemented
27#23710C211yesmaximal, characteristic, complemented
28#23084C211yesmaximal, characteristic, complemented
29#23032C211yesmaximal, characteristic, complemented
30#22566C211yesmaximal, characteristic, complemented
31#22042C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#491C2211yescharacteristic, complemented
35C2×#481C2211yescharacteristic
36C2×#467C2211yescharacteristic
37C2×#467C2211yescharacteristic, complemented
38C2×#465C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#461C2211yescharacteristic
41C2×#452C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C2×#440C2211yescharacteristic
47C2×C8×D4C2211yescharacteristic
48C2×#432C2211yescharacteristic, complemented
49C22×#107C2211yescharacteristic, complemented
50C22×#102C2211yescharacteristic
51#2855C2211yescharacteristic, complemented
52#2791—21no—
53#2780—21no—
54#2748—21no—
55#2748—21no—
56#2708—21no—
57#2668—21no—
58#2667—21no—
59#2553—21no—
60#2542C2211yescharacteristic, complemented
61#2538C2211yescharacteristic
62#2535—21no—
63#2534—21no—
64#2522—21no—
65#2507C2211yescharacteristic, complemented
66#2497—21no—
67#2489C2211yescharacteristic
68#2487C2211yescharacteristic, complemented
69#2485C2211yescharacteristic
70#2480—21no—
71#2457—21no—
72#2454C2211yescharacteristic
73#2447C2211yescharacteristic
74#2446C2211yescharacteristic, complemented
75#2429C2211yescharacteristic
76#2427C2211yescharacteristic
77#2423C2211yescharacteristic, complemented
78#2417C2211yescharacteristic
79#2417C2211yescharacteristic
80#2417C2211yescharacteristic
81#2417C2211yescharacteristic
82#2408C2211yescharacteristic
83#2407C2211yescharacteristic
84#2361C2211yescharacteristic
85#2360C2211yescharacteristic, complemented
86#2358—21no—
87#2345C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2333—21no—
90C4×C22⋊Q8C2211yescharacteristic, complemented
91C4×#121C2211yescharacteristic
92C4×#121C2211yescharacteristic
93#2297C2211yescharacteristic
94#2099C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2087C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic, complemented
100#2075C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic
104#2066C2211yescharacteristic, complemented
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic, complemented
109#2059C2211yescharacteristic, complemented
110#2056C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2042C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2036C2211yescharacteristic, complemented
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic, complemented
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic
123#2033C2211yescharacteristic
124#2016C2211yescharacteristic, complemented
125#2015C2211yescharacteristic
126#2013C2211yescharacteristic
127#2001C2211yescharacteristic
128#2001C2211yescharacteristic, complemented
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1989C2211yescharacteristic, complemented
135#1973C2211yescharacteristic
136#1971C2211yescharacteristic, complemented
137#1969C2211yescharacteristic, complemented
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic
140#1959C2211yescharacteristic
141#1955C2211yescharacteristic
142#1955C2211yescharacteristic, complemented
143#1954C2211yescharacteristic
144#1944C2211yescharacteristic, complemented
145#1942C2211yescharacteristic, complemented
146#1939C2211yescharacteristic, complemented
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1935C2211yescharacteristic, complemented
150#1935C2211yescharacteristic, complemented
151#1935C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1933C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic
161#1924C2211yescharacteristic
162#1924C2211yescharacteristic, complemented
163#1919C2211yescharacteristic, complemented
164#1893C2211yescharacteristic
165#1892C2211yescharacteristic
166#1880C2211yescharacteristic
167#1878C2211yescharacteristic, complemented
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1874C2211yescharacteristic
171#1873C2211yescharacteristic, complemented
172#1873C2211yescharacteristic, complemented
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic, complemented
175#1872C2211yescharacteristic, complemented
176#1872C2211yescharacteristic, complemented
177#1869C2211yescharacteristic
178#1869C2211yescharacteristic, complemented
179#1865C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1854C2211yescharacteristic, complemented
186#1854C2211yescharacteristic, complemented
187#1853C2211yescharacteristic
188#1824C2211yescharacteristic
189#1824C2211yescharacteristic, complemented
190#1808C2211yescharacteristic
191#1802C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1786C2211yescharacteristic
195#1776C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1752C2211yescharacteristic
201#1752C2211yescharacteristic, complemented
202C4×C22⋊C8C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#553—42no—
214#553—42no—
215#546—42no—
216#546—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#125C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121—21no—
233C2×#121D411yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×#120—21no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C42C2311yescharacteristic
257#491—42no—
258#481—42no—
259#467—42no—
260#467—42no—
261#465—24no—
262#464—42no—
263#461—42no—
264#452—24no—
265#452—42no—
266#450—42no—
267#450—42no—
268#440—42no—
269#440—42no—
270C8×D4—42no—
271#432—42no—
272C2×#107—42no—
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#102—24no—
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×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332#400—21no—
333#400—21no—
334#400—21no—
335#399—21no—
336#399—21no—
337#399—21no—
338#399—21no—
339#399—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#396—21no—
355#396—21no—
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#392—21no—
367#392—21no—
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#390—21no—
376#390—21no—
377#390D411yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389D411yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388D411yescharacteristic
403#388D411yescharacteristic
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#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386D411yescharacteristic
429#386D411yescharacteristic
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#384—21no—
439#384C2311yescharacteristic
440#382—21no—
441#381—21no—
442#381—21no—
443#380—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380D411yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#379—21no—
459#379—21no—
460C4×C4⋊C4—21no—
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⋊C4—21no—
470C4×C22⋊C4—21no—
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×Q16—22no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571#126—44no—
572#125—22no—
573#125—41no—
574#124—22no—
575#124—41no—
576#123—44no—
577#123—44no—
578C22⋊Q8—22no—
579C22⋊Q8—22no—
580C22⋊Q8—22no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594#121—24no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#121—44no—
603#120—44no—
604#120—44no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×Q8—41no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—44no—
622C4×D4—82no—
623C4×D4—82no—
624#117—41no—
625#117—41no—
626C2×C4⋊C4—22no—
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—21no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
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—44no—
709C2×C22⋊C4—82no—
710C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—41no—
727C2×C42—41no—
728C2×C42C2×D411yescharacteristic
729C2×C42C2×D411yescharacteristic
730C2×C42C2411yescharacteristic
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734#107—22no—
735#107—22no—
736#107—41no—
737#107—41no—
738#107—41no—
739#107—41no—
740#106—22no—
741#106—41no—
742#106—41no—
743#106—41no—
744C4⋊C8—22no—
745C4⋊C8—41no—
746C4⋊C8—41no—
747C4⋊C8—41no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#103—22no—
754#103—41no—
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#102—22no—
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#4114yes—
776C22⋊C8—22no—
777C22⋊C8—22no—
778C22⋊C8—22no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784C22⋊C8—41no—
785C22⋊C8—41no—
786#97—22no—
787#97—41no—
788#97—41no—
789#97—41no—
790C4×C8—41no—
791C4×C8—41no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831C24—21no—
832C24—21no—
833C24—42no—
834C24—42no—
835C24—42no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24—81no—
840C24C22×D411yescharacteristic
841C24C22×D411yescharacteristic
842C24C22×D411yescharacteristic
843#41—82no—
844#41—82no—
845#41—82no—
846#41—82no—
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×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×D4—24no—
866C2×D4—22no—
867C2×D4—22no—
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—41no—
879C2×D4—41no—
880C2×D4—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—44no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—81no—
894C2×D4—82no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4#13714yes—
903C2×D4C2×#4112yes—
904C2×D4H(5,𝔽2)12yes—
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—22no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—41no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C2511yescharacteristic
976Q16—82no—
977Q16—82no—
978SD16—44no—
979SD16—44no—
980SD16—82no—
981SD16—82no—
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×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—44no—
1005C2×C8—82no—
1006C2×C8C2×#4112yes—
1007C2×C8H(5,𝔽2)12yes—
1008C4⋊C4—22no—
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—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—41no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
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⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4C2×#4112yes—
1062C4⋊C4H(5,𝔽2)12yes—
1063C22⋊C4—24no—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—41no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—41no—
1114C42—41no—
1115C42—42no—
1116C42—42no—
1117C42—81no—
1118C42—81no—
1119C42—81no—
1120C42—81no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—22no—
1138C23—22no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
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—84no—
1155C23—84no—
1156C23—84no—
1157C23—162no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23C2×#13712yes—
1162C23C2×#13712yes—
1163C23C23×D411yescharacteristic
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176D4—22no—
1177D4—22no—
1178D4—22no—
1179D4—22no—
1180D4—44no—
1181D4—41no—
1182D4—41no—
1183D4—41no—
1184D4—41no—
1185D4—82no—
1186D4—82no—
1187D4—84no—
1188D4—84no—
1189D4—84no—
1190D4—84no—
1191D4—84no—
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—22no—
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—22no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
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—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—82no—
1279C2×C4—82no—
1280C2×C4—84no—
1281C2×C4—162no—
1282C2×C4—162no—
1283C2×C4—162no—
1284C2×C4—162no—
1285C2×C4—162no—
1286C2×C4—162no—
1287C2×C4C2×#13712yes—
1288C2×C4C22×#4111yescharacteristic
1289C2×C4C2×H(5,𝔽2)11yescharacteristic
1290C2×C4C2×H(5,𝔽2)11yescharacteristic
1291C2×C4C2×H(5,𝔽2)11yescharacteristic
1292C2×C4#58511yescharacteristic
1293C2×C4#58511yescharacteristic
1294C8—22no—
1295C8—22no—
1296C8—41no—
1297C8—41no—
1298C8—41no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—42no—
1317C22—41no—
1318C22—41no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22—41no—
1323C22—42no—
1324C22—42no—
1325C22—41no—
1326C22—42no—
1327C22—42no—
1328C22—41no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—168no—
1338C22D4×#4111yescharacteristic
1339C22#348411yescharacteristic
1340C22#349611yescharacteristic
1341C22C22×#13711yescharacteristic
1342C22#358411yescharacteristic
1343C22#358411yescharacteristic
1344C22#358511yescharacteristic
1345C4—22no—
1346C4—41no—
1347C4—42no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—42no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4#349411yescharacteristic
1371C4#351911yescharacteristic
1372C4#354211yescharacteristic
1373C4#356211yescharacteristic
1374C2—42no—
1375C2—42no—
1376C2—81no—
1377C2—82no—
1378C2—82no—
1379C2#4392311yescharacteristic
1380C2#6145311yescharacteristic
1381C2#6148711yescharacteristic
1382C2#6160711yescharacteristic
1383C2#6167811yescharacteristic
1384C2#6225411yescharacteristic
1385C2#6231311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#59812C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39664C2semidirect
3. #32009C2semidirect
4. #31878C2semidirect
5. #31788C2semidirect
6. #31722C2semidirect
7. #31678C2semidirect
8. #31215C2semidirect
9. #31024C2semidirect
10. #30504C2semidirect
11. #29465C2semidirect
12. #29020C2semidirect
13. #28934C2semidirect
14. #27346C2semidirect
15. #26979C2semidirect
16. #26946C2semidirect
17. #26845C2semidirect
18. #26675C2semidirect
19. #25582C2semidirect
20. #25176C2semidirect
21. #25112C2semidirect
22. #24781C2semidirect
23. #24511C2semidirect
24. #24426C2semidirect
25. #24259C2semidirect
26. #24092C2semidirect
27. #23710C2semidirect
28. #23084C2semidirect
29. #23032C2semidirect
30. #22566C2semidirect
31. #22042C2semidirect
34. C2×#491C22semidirect
37. C2×#467C22semidirect
48. C2×#432C22semidirect
49. C22×#107C22semidirect
51. #2855C22semidirect
60. #2542C22semidirect
65. #2507C22semidirect
68. #2487C22semidirect
74. #2446C22semidirect
77. #2423C22semidirect
85. #2360C22semidirect
90. C4×C22⋊Q8C22semidirect
94. #2099C22semidirect
95. #2088C22semidirect
96. #2087C22semidirect
97. #2083C22semidirect
99. #2077C22semidirect
100. #2075C22semidirect
101. #2068C22semidirect
102. #2068C22semidirect
104. #2066C22semidirect
105. #2066C22semidirect
108. #2059C22semidirect
109. #2059C22semidirect
110. #2056C22semidirect
117. #2036C22semidirect
118. #2036C22semidirect
120. #2035C22semidirect
124. #2016C22semidirect
128. #2001C22semidirect
134. #1989C22semidirect
136. #1971C22semidirect
137. #1969C22semidirect
142. #1955C22semidirect
144. #1944C22semidirect
145. #1942C22semidirect
146. #1939C22semidirect
149. #1935C22semidirect
150. #1935C22semidirect
151. #1935C22semidirect
154. #1933C22semidirect
155. #1933C22semidirect
156. #1928C22semidirect
157. #1927C22semidirect
158. #1927C22semidirect
162. #1924C22semidirect
163. #1919C22semidirect
167. #1878C22semidirect
171. #1873C22semidirect
172. #1873C22semidirect
174. #1872C22semidirect
175. #1872C22semidirect
176. #1872C22semidirect
178. #1869C22semidirect
179. #1865C22semidirect
180. #1863C22semidirect
185. #1854C22semidirect
186. #1854C22semidirect
189. #1824C22semidirect
195. #1776C22semidirect
196. #1770C22semidirect
197. #1763C22semidirect
201. #1752C22semidirect
202. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#598122
#396642
#320092
#318782
#317882
#317222
#316782
#312152
#310242
#305042
#294652
#290202
#289342
#273462
#269792
#269462
#268452
#266752
#255822
#251762
#251122
#247812
#245112
#244262
#242592
#240922
#237102
#230842
#230322
#225662
#220422