Finite Group Databasebeta

← #7338628

Subgroups — #7338628

Order 512.

1583 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#52975C211yesmaximal, characteristic, complemented
2#45108C211yesmaximal, characteristic, complemented
3#31853C211yesmaximal, characteristic, complemented
4#31744C211yesmaximal, characteristic, complemented
5#31722C211yesmaximal, characteristic, complemented
6#31649C211yesmaximal, characteristic, complemented
7#31455C211yesmaximal, characteristic, complemented
8#31394C211yesmaximal, characteristic, complemented
9#31170C211yesmaximal, characteristic, complemented
10#31007C211yesmaximal, characteristic, complemented
11#30917C211yesmaximal, characteristic, complemented
12#30739C211yesmaximal, characteristic, complemented
13#30545C211yesmaximal, characteristic, complemented
14#30448C211yesmaximal, characteristic, complemented
15#29729C211yesmaximal, characteristic, complemented
16#29696C211yesmaximal, characteristic, complemented
17#29120C211yesmaximal, characteristic, complemented
18#28935C211yesmaximal, characteristic, complemented
19#27764C211yesmaximal, characteristic, complemented
20#27262C211yesmaximal, characteristic, complemented
21#27245C211yesmaximal, characteristic, complemented
22#26890C211yesmaximal, characteristic, complemented
23#26826C211yesmaximal, characteristic, complemented
24#26737C211yesmaximal, characteristic, complemented
25#26674C211yesmaximal, characteristic, complemented
26#25610C211yesmaximal, characteristic, complemented
27#25337C211yesmaximal, characteristic, complemented
28#24531C211yesmaximal, characteristic, complemented
29#24426C211yesmaximal, characteristic, complemented
30#24245C211yesmaximal, characteristic
31#22368C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#495C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#489C2211yescharacteristic, complemented
37C2×#477C2211yescharacteristic, complemented
38C2×#474C2211yescharacteristic
39C2×#467C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#452C2211yescharacteristic
43C2×#449C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×C4×D8C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2831—21no—
49#2831—21no—
50#2827—21no—
51#2824—21no—
52#2750—21no—
53#2730—21no—
54#2708—21no—
55#2700—21no—
56#2695—21no—
57#2692—21no—
58#2687—21no—
59#2684—21no—
60#2628C2211yescharacteristic, complemented
61#2620C2211yescharacteristic, complemented
62#2570C2211yescharacteristic, complemented
63#2568C2211yescharacteristic, complemented
64#2547C2211yescharacteristic
65#2535C2211yescharacteristic
66#2534—21no—
67#2504C2211yescharacteristic
68#2492C2211yescharacteristic
69#2492C2211yescharacteristic
70#2491C2211yescharacteristic, complemented
71#2480—21no—
72#2452C2211yescharacteristic
73#2452C2211yescharacteristic, complemented
74#2447C2211yescharacteristic
75#2447C2211yescharacteristic, complemented
76#2440C2211yescharacteristic
77#2437—21no—
78#2435C2211yescharacteristic
79#2432C2211yescharacteristic
80#2429C2211yescharacteristic
81#2427—21no—
82#2426C2211yescharacteristic
83#2421C2211yescharacteristic, complemented
84#2417C2211yescharacteristic
85#2417C2211yescharacteristic
86#2395C2211yescharacteristic
87#2367C2211yescharacteristic
88#2361C2211yescharacteristic
89D4×C22⋊C4C2211yescharacteristic
90#2311C2211yescharacteristic
91#2101C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2076C2211yescharacteristic
95#2074C2211yescharacteristic, complemented
96#2074C2211yescharacteristic, complemented
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2072C2211yescharacteristic, complemented
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2057C2211yescharacteristic, complemented
104#2057C2211yescharacteristic, complemented
105#2056C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic, complemented
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic, complemented
119#2036C2211yescharacteristic, complemented
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2024C2211yescharacteristic, complemented
123#2024C2211yescharacteristic, complemented
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic
126#2016C2211yescharacteristic, complemented
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic, complemented
129#2013C2211yescharacteristic, complemented
130#2012C2211yescharacteristic
131#2012C2211yescharacteristic
132#2001C2211yescharacteristic
133#2001C2211yescharacteristic, complemented
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic
137#2000C2211yescharacteristic, complemented
138#1999C2211yescharacteristic
139#1990C2211yescharacteristic, complemented
140#1987C2211yescharacteristic, complemented
141#1981C2211yescharacteristic, complemented
142#1973C2211yescharacteristic
143#1973C2211yescharacteristic, complemented
144#1960C2211yescharacteristic, complemented
145#1959C2211yescharacteristic
146#1958C2211yescharacteristic
147#1954C2211yescharacteristic
148#1940C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1934C2211yescharacteristic
154#1933C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic, complemented
159#1924C2211yescharacteristic
160#1924C2211yescharacteristic, complemented
161#1924C2211yescharacteristic, complemented
162#1923C2211yescharacteristic
163#1921C2211yescharacteristic, complemented
164#1921C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic, complemented
179#1874C2211yescharacteristic, complemented
180#1872C2211yescharacteristic
181#1872C2211yescharacteristic
182#1872C2211yescharacteristic, complemented
183#1869C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic, complemented
186#1850C2211yescharacteristic
187#1824C2211yescharacteristic
188#1824C2211yescharacteristic, complemented
189#1823C2211yescharacteristic, complemented
190#1805C2211yescharacteristic, complemented
191#1804C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1798C2211yescharacteristic, complemented
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1771C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200#1762C2211yescharacteristic
201#1752C2211yescharacteristic
202#1750C2211yescharacteristic, complemented
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#542—42no—
217#542—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#126—21no—
223C2×#124—21no—
224C2×#124—21no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×#121—21no—
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C22⋊C4—21no—
257C22×C22⋊C4—21no—
258#495—42no—
259#489—42no—
260#489—42no—
261#477—42no—
262#474—42no—
263#467—42no—
264#464—42no—
265#463—42no—
266#452—42no—
267#450—42no—
268#449—42no—
269#447—42no—
270C4×D8—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#102—42no—
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400D411yescharacteristic
333#399—21no—
334#399D411yescharacteristic
335#398—21no—
336#398—21no—
337#398—21no—
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#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397D411yescharacteristic
352#397D411yescharacteristic
353#397D411yescharacteristic
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#395—21no—
363#395—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394D411yescharacteristic
373#394D411yescharacteristic
374#393—21no—
375#393—21no—
376#393—21no—
377#393—21no—
378#393—21no—
379#393—21no—
380#392—21no—
381#391—21no—
382#391—21no—
383#391—21no—
384#391—21no—
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#390—21no—
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#389—21no—
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#387—21no—
417#387—21no—
418#387—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#386—21no—
429#386—21no—
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#385—21no—
439#384C2311yescharacteristic
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#381—21no—
444#381—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#379—21no—
456#379—21no—
457#379—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8—21no—
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×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C22×D4C2411yescharacteristic
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×D8—22no—
552C2×D8—22no—
553C2×D8—41no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—22no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576#126—44no—
577#124—22no—
578#124—22no—
579#124—22no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—44no—
586#124—82no—
587#123—44no—
588#123—44no—
589C22⋊Q8—22no—
590C22⋊Q8—44no—
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—
600C22⋊Q8—82no—
601C22⋊Q8—82no—
602C22⋊Q8—82no—
603#121—22no—
604#121—22no—
605#121—44no—
606#121—41no—
607#121—41no—
608#121—41no—
609#121—41no—
610#120—44no—
611C4×Q8—22no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—82no—
626#117—41no—
627#117—41no—
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—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4—41no—
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⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—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—44no—
710C2×C22⋊C4—82no—
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×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729C2×C42C2411yescharacteristic
730#107—22no—
731#107—22no—
732#107—41no—
733#107—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778#97—41no—
779#97—41no—
780#97—41no—
781C4×C8—41no—
782C4×C8—41no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—21no—
828C24—42no—
829C24—42no—
830C24—42no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837#41—82no—
838#41—82no—
839#41—82no—
840#41—82no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
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—42no—
860C2×Q8—42no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—81no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×Q8—81no—
868C2×D4—24no—
869C2×D4—22no—
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—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—41no—
887C2×D4—41no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—81no—
895C2×D4—82no—
896C2×D4—82no—
897C2×D4—82no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4H(5,𝔽2)12yes—
907C2×D4H(5,𝔽2)12yes—
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—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
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×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C2511yescharacteristic
967Q16—82no—
968Q16—82no—
969SD16—82no—
970SD16—82no—
971SD16—82no—
972SD16—82no—
973D8—44no—
974D8—82no—
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—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—82no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
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⋊C4H(5,𝔽2)12yes—
1049C22⋊C4—24no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—41no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—42no—
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—22no—
1121C23—21no—
1122C23—22no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—84no—
1146C23—84no—
1147C23—84no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23#57812yes—
1153C23C23×D411yescharacteristic
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—162no—
1167Q8—162no—
1168Q8—162no—
1169D4—22no—
1170D4—22no—
1171D4—22no—
1172D4—22no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—82no—
1182D4—84no—
1183D4—84no—
1184D4—84no—
1185D4—162no—
1186D4—162no—
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—21no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
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—162no—
1276C2×C4—162no—
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4C2×H(5,𝔽2)11yescharacteristic
1280C2×C4#58511yescharacteristic
1281C2×C4#58511yescharacteristic
1282C2×C4#58511yescharacteristic
1283C8—41no—
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—42no—
1302C22—42no—
1303C22—41no—
1304C22—42no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—42no—
1309C22—42no—
1310C22—41no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—168no—
1327C22#348411yescharacteristic
1328C22#348811yescharacteristic
1329C22#350011yescharacteristic
1330C22C2×#57811yescharacteristic
1331C22#358411yescharacteristic
1332C22#358511yescharacteristic
1333C22#358511yescharacteristic
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—42no—
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#353411yescharacteristic
1360C4#354211yescharacteristic
1361C4#354511yescharacteristic
1362C4#356211yescharacteristic
1363C2—42no—
1364C2—81no—
1365C2—82no—
1366C2—82no—
1367C2—161no—
1368C2#4795511yescharacteristic
1369C2#6164211yescharacteristic
1370C2#6166911yescharacteristic
1371C2#6201711yescharacteristic
1372C2#6204711yescharacteristic
1373C2#6260411yescharacteristic
1374C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24245C2
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. #52975C2semidirect
2. #45108C2semidirect
3. #31853C2semidirect
4. #31744C2semidirect
5. #31722C2semidirect
6. #31649C2semidirect
7. #31455C2semidirect
8. #31394C2semidirect
9. #31170C2semidirect
10. #31007C2semidirect
11. #30917C2semidirect
12. #30739C2semidirect
13. #30545C2semidirect
14. #30448C2semidirect
15. #29729C2semidirect
16. #29696C2semidirect
17. #29120C2semidirect
18. #28935C2semidirect
19. #27764C2semidirect
20. #27262C2semidirect
21. #27245C2semidirect
22. #26890C2semidirect
23. #26826C2semidirect
24. #26737C2semidirect
25. #26674C2semidirect
26. #25610C2semidirect
27. #25337C2semidirect
28. #24531C2semidirect
29. #24426C2semidirect
31. #22368C2semidirect
36. C2×#489C22semidirect
37. C2×#477C22semidirect
60. #2628C22semidirect
61. #2620C22semidirect
62. #2570C22semidirect
63. #2568C22semidirect
70. #2491C22semidirect
73. #2452C22semidirect
75. #2447C22semidirect
83. #2421C22semidirect
91. #2101C22semidirect
92. #2101C22semidirect
93. #2087C22semidirect
95. #2074C22semidirect
96. #2074C22semidirect
99. #2072C22semidirect
101. #2068C22semidirect
102. #2068C22semidirect
103. #2057C22semidirect
104. #2057C22semidirect
105. #2056C22semidirect
106. #2056C22semidirect
108. #2055C22semidirect
118. #2036C22semidirect
119. #2036C22semidirect
122. #2024C22semidirect
123. #2024C22semidirect
126. #2016C22semidirect
128. #2015C22semidirect
129. #2013C22semidirect
133. #2001C22semidirect
137. #2000C22semidirect
139. #1990C22semidirect
140. #1987C22semidirect
141. #1981C22semidirect
143. #1973C22semidirect
144. #1960C22semidirect
148. #1940C22semidirect
151. #1936C22semidirect
152. #1935C22semidirect
154. #1933C22semidirect
155. #1933C22semidirect
156. #1933C22semidirect
158. #1925C22semidirect
160. #1924C22semidirect
161. #1924C22semidirect
163. #1921C22semidirect
164. #1921C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
170. #1880C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
178. #1877C22semidirect
179. #1874C22semidirect
182. #1872C22semidirect
185. #1862C22semidirect
188. #1824C22semidirect
189. #1823C22semidirect
190. #1805C22semidirect
194. #1798C22semidirect
198. #1771C22semidirect
199. #1763C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#529752
#451082
#318532
#317442
#317222
#316492
#314552
#313942
#311702
#310072
#309172
#307392
#305452
#304482
#297292
#296962
#291202
#289352
#277642
#272622
#272452
#268902
#268262
#267372
#266742
#256102
#253372
#245312
#244262
#242452
#223682