Finite Group Databasebeta

← #7160950

Subgroups — #7160950

Order 512.

1632 conjugacy classes of subgroups.

The subgroup lattice has 1376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45049C211yesmaximal, characteristic
2#42669C211yesmaximal, characteristic, complemented
3#31957C211yesmaximal, characteristic, complemented
4#31939C211yesmaximal, characteristic, complemented
5#31558C211yesmaximal, characteristic, complemented
6#31556C211yesmaximal, characteristic, complemented
7#31401C211yesmaximal, characteristic, complemented
8#31390C211yesmaximal, characteristic, complemented
9#30422C211yesmaximal, characteristic, complemented
10#30404C211yesmaximal, characteristic, complemented
11#28600C211yesmaximal, characteristic, complemented
12#28153C211yesmaximal, characteristic, complemented
13#28144C211yesmaximal, characteristic, complemented
14#27740C211yesmaximal, characteristic, complemented
15#26534C211yesmaximal, characteristic, complemented
16#26314C211yesmaximal, characteristic, complemented
17#25769C211yesmaximal, characteristic, complemented
18#25613C211yesmaximal, characteristic, complemented
19#25319C211yesmaximal, characteristic, complemented
20#25128C211yesmaximal, characteristic, complemented
21#25113C211yesmaximal, characteristic, complemented
22#24924C211yesmaximal, characteristic, complemented
23#24901C211yesmaximal, characteristic, complemented
24#24766C211yesmaximal, characteristic, complemented
25#24534C211yesmaximal, characteristic, complemented
26#24527C211yesmaximal, characteristic, complemented
27#23766C211yesmaximal, characteristic, complemented
28#23192C211yesmaximal, characteristic, complemented
29#22991C211yesmaximal, characteristic, complemented
30#22414C211yesmaximal, characteristic, complemented
31#21896C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#497C2211yescharacteristic
35C2×#487C2211yescharacteristic, complemented
36C2×#468C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#461C2211yescharacteristic
39C2×#452C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#441C2211yescharacteristic, complemented
44C2×C4×SD16C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×C8×D4C2211yescharacteristic
47C2×C8×D4C2211yescharacteristic, complemented
48C2×#424C2211yescharacteristic, complemented
49C2×#416C2211yescharacteristic
50C22×#102C2211yescharacteristic
51#2837—21no—
52#2793—21no—
53#2791—21no—
54#2752—21no—
55#2740—21no—
56#2703—21no—
57#2691—21no—
58#2687—21no—
59#2670—21no—
60#2667—21no—
61#2654—21no—
62#2621C2211yescharacteristic, complemented
63#2570C2211yescharacteristic, complemented
64#2563C2211yescharacteristic
65#2557—21no—
66#2547C2211yescharacteristic
67#2542C2211yescharacteristic
68#2538C2211yescharacteristic
69#2536C2211yescharacteristic
70#2536C2211yescharacteristic, complemented
71#2535C2211yescharacteristic
72#2516—21no—
73#2503C2211yescharacteristic
74#2499C2211yescharacteristic, complemented
75#2480—21no—
76#2472—21no—
77#2423C2211yescharacteristic
78#2423C2211yescharacteristic, complemented
79#2421C2211yescharacteristic
80#2420C2211yescharacteristic
81#2417C2211yescharacteristic
82#2415C2211yescharacteristic, complemented
83#2412—21no—
84#2408C2211yescharacteristic
85#2407C2211yescharacteristic
86#2392C2211yescharacteristic
87#2367C2211yescharacteristic
88#2365C2211yescharacteristic, complemented
89#2352C2211yescharacteristic
90#2341C2211yescharacteristic
91D4×C22⋊C4C2211yescharacteristic
92#2324C2211yescharacteristic
93#2314C2211yescharacteristic, complemented
94#2101C2211yescharacteristic, complemented
95#2101C2211yescharacteristic, complemented
96#2099C2211yescharacteristic, complemented
97#2097C2211yescharacteristic, complemented
98#2094C2211yescharacteristic
99#2094C2211yescharacteristic
100#2085C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic, complemented
104#2077C2211yescharacteristic, complemented
105#2077C2211yescharacteristic, complemented
106#2076C2211yescharacteristic, complemented
107#2074C2211yescharacteristic, complemented
108#2074C2211yescharacteristic, complemented
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2071C2211yescharacteristic
112#2068C2211yescharacteristic, complemented
113#2067C2211yescharacteristic
114#2066C2211yescharacteristic, complemented
115#2066C2211yescharacteristic, complemented
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2055C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2035C2211yescharacteristic, complemented
123#2035C2211yescharacteristic, complemented
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic
126#2001C2211yescharacteristic
127#2001C2211yescharacteristic
128#2001C2211yescharacteristic, complemented
129#2001C2211yescharacteristic, complemented
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1993C2211yescharacteristic, complemented
135#1988C2211yescharacteristic, complemented
136#1987C2211yescharacteristic, complemented
137#1983C2211yescharacteristic
138#1983C2211yescharacteristic
139#1981C2211yescharacteristic, complemented
140#1973C2211yescharacteristic
141#1969C2211yescharacteristic, complemented
142#1958C2211yescharacteristic
143#1955C2211yescharacteristic
144#1949C2211yescharacteristic, complemented
145#1939C2211yescharacteristic, complemented
146#1936C2211yescharacteristic
147#1934C2211yescharacteristic
148#1924C2211yescharacteristic, complemented
149#1923C2211yescharacteristic
150#1895C2211yescharacteristic
151#1894C2211yescharacteristic, complemented
152#1894C2211yescharacteristic, complemented
153#1893C2211yescharacteristic
154#1893C2211yescharacteristic
155#1892C2211yescharacteristic
156#1892C2211yescharacteristic
157#1892C2211yescharacteristic
158#1892C2211yescharacteristic, complemented
159#1892C2211yescharacteristic, complemented
160#1892C2211yescharacteristic, complemented
161#1892C2211yescharacteristic, complemented
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1878C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1878C2211yescharacteristic, complemented
168#1878C2211yescharacteristic, complemented
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1875C2211yescharacteristic
173#1872C2211yescharacteristic
174#1870C2211yescharacteristic, complemented
175#1869C2211yescharacteristic
176#1865C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1854C2211yescharacteristic, complemented
179#1852C2211yescharacteristic
180#1850C2211yescharacteristic
181#1850C2211yescharacteristic, complemented
182#1836C2211yescharacteristic, complemented
183#1835C2211yescharacteristic, complemented
184#1825C2211yescharacteristic, complemented
185#1823C2211yescharacteristic
186#1805C2211yescharacteristic, complemented
187#1805C2211yescharacteristic, complemented
188#1805C2211yescharacteristic, complemented
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1804C2211yescharacteristic
192#1803C2211yescharacteristic, complemented
193#1803C2211yescharacteristic, complemented
194#1802C2211yescharacteristic
195#1788C2211yescharacteristic
196#1786C2211yescharacteristic
197#1776C2211yescharacteristic, complemented
198C4×#106C2211yescharacteristic, complemented
199#1771C2211yescharacteristic, complemented
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202#1750C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#546—24no—
216#546—42no—
217#542—24no—
218#542—42no—
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#126—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#123—21no—
226C2×#123—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257#497—24no—
258#487—42no—
259#468—42no—
260#465—42no—
261#461—42no—
262#452—42no—
263#452—42no—
264#450—42no—
265#450—42no—
266#441—42no—
267C4×SD16—42no—
268#435—42no—
269C8×D4—42no—
270C8×D4—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277#424—42no—
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284#416—42no—
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×#102—42no—
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×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#399—21no—
331#399—21no—
332#399—21no—
333#399—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398D411yescharacteristic
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397D411yescharacteristic
354#396—21no—
355#396—21no—
356#396—21no—
357#396D411yescharacteristic
358#396D411yescharacteristic
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394D411yescharacteristic
366#394D411yescharacteristic
367#394D411yescharacteristic
368#393—21no—
369#393—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392D411yescharacteristic
374#391—21no—
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#390—21no—
381#390—21no—
382#390—21no—
383#390—21no—
384#390—21no—
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#389—21no—
390#389—21no—
391#389—21no—
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
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#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#384—21no—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#381—21no—
442#381—21no—
443#381—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#379—21no—
458#379—21no—
459C4×C4⋊C4—21no—
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4C2311yescharacteristic
468C4×C22⋊C4C2311yescharacteristic
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#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—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C22×D4C2×D411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C23×C4C2411yescharacteristic
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—22no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C2×M16—41no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8—41no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8—41no—
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C4⋊Q8—22no—
573C4⋊Q8—22no—
574C4⋊Q8—22no—
575C4⋊Q8—22no—
576#126—44no—
577#124—22no—
578#124—44no—
579#124—82no—
580#124#4114yes—
581#123—44no—
582#123—44no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—44no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—44no—
604#121—41no—
605#121—41no—
606#121—41no—
607#120—44no—
608#120—82no—
609C4×Q8—22no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629#117—22no—
630#117—22no—
631#117—41no—
632#117—41no—
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⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
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—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—44no—
711C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—41no—
737#107—41no—
738#106—22no—
739#106—41no—
740#106—41no—
741#106—41no—
742C4⋊C8—22no—
743C4⋊C8—22no—
744C4⋊C8—41no—
745C4⋊C8—41no—
746C4⋊C8—41no—
747C4⋊C8—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
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—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776C22⋊C8—22no—
777C22⋊C8—22no—
778C22⋊C8—22no—
779C22⋊C8—41no—
780C22⋊C8—41no—
781C22⋊C8—41no—
782C22⋊C8—41no—
783C22⋊C8—41no—
784#97—22no—
785#97—22no—
786C4×C8—22no—
787C4×C8—22no—
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#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829C24—21no—
830C24—21no—
831C24—42no—
832C24—42no—
833C24—42no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24C22×D411yescharacteristic
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×Q8—42no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8C2×#4112yes—
866C2×D4—22no—
867C2×D4—22no—
868C2×D4—22no—
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—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—44no—
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—81no—
903C2×D4—81no—
904C2×D4C2×#4112yes—
905C2×D4H(5,𝔽2)12yes—
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—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—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
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×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C2511yescharacteristic
965Q16—44no—
966Q16—82no—
967SD16—44no—
968SD16—82no—
969SD16—82no—
970SD16—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×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—82no—
996C2×C8—82no—
997C2×C8—82no—
998C2×C8H(5,𝔽2)12yes—
999C4⋊C4—22no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
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—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—41no—
1027C4⋊C4—41no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C22⋊C4—22no—
1052C22⋊C4—24no—
1053C22⋊C4—24no—
1054C22⋊C4—22no—
1055C22⋊C4—22no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
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—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—42no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C42C2×#4112yes—
1112C42H(5,𝔽2)12yes—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—22no—
1126C23—21no—
1127C23—21no—
1128C23—22no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—84no—
1148C23—84no—
1149C23—84no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23—162no—
1154C23#57712yes—
1155C23C23×D411yescharacteristic
1156Q8—22no—
1157Q8—22no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—162no—
1169D4—22no—
1170D4—22no—
1171D4—22no—
1172D4—22no—
1173D4—44no—
1174D4—44no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—82no—
1180D4—84no—
1181D4—84no—
1182D4—162no—
1183D4—162no—
1184D4—162no—
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—22no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—41no—
1218C2×C4—41no—
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—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—84no—
1271C2×C4—162no—
1272C2×C4—162no—
1273C2×C4—162no—
1274C2×C4—162no—
1275C2×C4#54612yes—
1276C2×C4#54612yes—
1277C2×C4C22×#4111yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4C2×H(5,𝔽2)11yescharacteristic
1280C2×C4C2×H(5,𝔽2)11yescharacteristic
1281C2×C4#58511yescharacteristic
1282C2×C4#58511yescharacteristic
1283C8—22no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—42no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—42no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—42no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—41no—
1317C22—41no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—168no—
1327C22C2×#54611yescharacteristic
1328C22#348811yescharacteristic
1329C22#349611yescharacteristic
1330C22C2×#57711yescharacteristic
1331C22#358411yescharacteristic
1332C22#358411yescharacteristic
1333C22#358611yescharacteristic
1334C4—22no—
1335C4—22no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—42no—
1345C4—41no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4#351311yescharacteristic
1360C4#351311yescharacteristic
1361C4#354311yescharacteristic
1362C4#356211yescharacteristic
1363C2—42no—
1364C2—81no—
1365C2—81no—
1366C2—82no—
1367C2—82no—
1368C2#4500211yescharacteristic
1369C2#6117211yescharacteristic
1370C2#6120711yescharacteristic
1371C2#6202311yescharacteristic
1372C2#6206311yescharacteristic
1373C2#6228211yescharacteristic
1374C2#6230711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45049C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42669C2semidirect
3. #31957C2semidirect
4. #31939C2semidirect
5. #31558C2semidirect
6. #31556C2semidirect
7. #31401C2semidirect
8. #31390C2semidirect
9. #30422C2semidirect
10. #30404C2semidirect
11. #28600C2semidirect
12. #28153C2semidirect
13. #28144C2semidirect
14. #27740C2semidirect
15. #26534C2semidirect
16. #26314C2semidirect
17. #25769C2semidirect
18. #25613C2semidirect
19. #25319C2semidirect
20. #25128C2semidirect
21. #25113C2semidirect
22. #24924C2semidirect
23. #24901C2semidirect
24. #24766C2semidirect
25. #24534C2semidirect
26. #24527C2semidirect
27. #23766C2semidirect
28. #23192C2semidirect
29. #22991C2semidirect
30. #22414C2semidirect
31. #21896C2semidirect
35. C2×#487C22semidirect
43. C2×#441C22semidirect
47. C2×C8×D4C22semidirect
48. C2×#424C22semidirect
62. #2621C22semidirect
63. #2570C22semidirect
70. #2536C22semidirect
74. #2499C22semidirect
78. #2423C22semidirect
82. #2415C22semidirect
88. #2365C22semidirect
93. #2314C22semidirect
94. #2101C22semidirect
95. #2101C22semidirect
96. #2099C22semidirect
97. #2097C22semidirect
100. #2085C22semidirect
103. #2077C22semidirect
104. #2077C22semidirect
105. #2077C22semidirect
106. #2076C22semidirect
107. #2074C22semidirect
108. #2074C22semidirect
112. #2068C22semidirect
114. #2066C22semidirect
115. #2066C22semidirect
122. #2035C22semidirect
123. #2035C22semidirect
128. #2001C22semidirect
129. #2001C22semidirect
134. #1993C22semidirect
135. #1988C22semidirect
136. #1987C22semidirect
139. #1981C22semidirect
141. #1969C22semidirect
144. #1949C22semidirect
145. #1939C22semidirect
148. #1924C22semidirect
151. #1894C22semidirect
152. #1894C22semidirect
158. #1892C22semidirect
159. #1892C22semidirect
160. #1892C22semidirect
161. #1892C22semidirect
165. #1878C22semidirect
166. #1878C22semidirect
167. #1878C22semidirect
168. #1878C22semidirect
174. #1870C22semidirect
176. #1865C22semidirect
178. #1854C22semidirect
181. #1850C22semidirect
182. #1836C22semidirect
183. #1835C22semidirect
184. #1825C22semidirect
186. #1805C22semidirect
187. #1805C22semidirect
188. #1805C22semidirect
192. #1803C22semidirect
193. #1803C22semidirect
197. #1776C22semidirect
198. C4×#106C22semidirect
199. #1771C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#450492
#426692
#319572
#319392
#315582
#315562
#314012
#313902
#304222
#304042
#286002
#281532
#281442
#277402
#265342
#263142
#257692
#256132
#253192
#251282
#251132
#249242
#249012
#247662
#245342
#245272
#237662
#231922
#229912
#224142
#218962