Finite Group Databasebeta

← #7230693

Subgroups — #7230693

Order 512.

1676 conjugacy classes of subgroups.

The subgroup lattice has 1424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#46054C211yesmaximal, characteristic
2#36562C211yesmaximal, characteristic, complemented
3#33031C211yesmaximal, characteristic, complemented
4#33029C211yesmaximal, characteristic, complemented
5#32811C211yesmaximal, characteristic, complemented
6#32807C211yesmaximal, characteristic, complemented
7#32647C211yesmaximal, characteristic, complemented
8#32636C211yesmaximal, characteristic, complemented
9#30937C211yesmaximal, characteristic, complemented
10#30924C211yesmaximal, characteristic, complemented
11#30920C211yesmaximal, characteristic, complemented
12#30917C211yesmaximal, characteristic, complemented
13#30510C211yesmaximal, characteristic, complemented
14#30504C211yesmaximal, characteristic, complemented
15#30474C211yesmaximal, characteristic, complemented
16#30464C211yesmaximal, characteristic, complemented
17#30459C211yesmaximal, characteristic, complemented
18#30456C211yesmaximal, characteristic, complemented
19#26742C211yesmaximal, characteristic, complemented
20#26741C211yesmaximal, characteristic, complemented
21#26727C211yesmaximal, characteristic, complemented
22#26726C211yesmaximal, characteristic, complemented
23#25640C211yesmaximal, characteristic, complemented
24#25630C211yesmaximal, characteristic, complemented
25#25102C211yesmaximal, characteristic, complemented
26#25096C211yesmaximal, characteristic, complemented
27#25084C211yesmaximal, characteristic, complemented
28#25080C211yesmaximal, characteristic, complemented
29#23981C211yesmaximal, characteristic, complemented
30#23969C211yesmaximal, characteristic, complemented
31#23349C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic, complemented
33C2×#554C2211yescharacteristic
34C2×#497C2211yescharacteristic
35C2×#492C2211yescharacteristic
36C2×#479C2211yescharacteristic, complemented
37C2×#477C2211yescharacteristic, complemented
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#467C2211yescharacteristic
41C2×#465C2211yescharacteristic
42C2×#464C2211yescharacteristic
43C2×#464C2211yescharacteristic
44C2×#460C2211yescharacteristic
45C2×#460C2211yescharacteristic
46C2×#452C2211yescharacteristic, complemented
47C2×#452C2211yescharacteristic, complemented
48C2×#452C2211yescharacteristic, complemented
49C2×#450C2211yescharacteristic
50C2×#450C2211yescharacteristic
51C2×#450C2211yescharacteristic
52C2×#417C2211yescharacteristic, complemented
53C22×#102C2211yescharacteristic
54#2862C2211yescharacteristic, complemented
55#2861C2211yescharacteristic
56#2859—21no—
57#2858C2211yescharacteristic
58#2828—21no—
59#2753—21no—
60#2733—21no—
61#2712—21no—
62#2684—21no—
63#2670—21no—
64#2670—21no—
65#2592C2211yescharacteristic
66#2567C2211yescharacteristic, complemented
67#2566—21no—
68#2565—21no—
69#2556—21no—
70#2556—21no—
71#2556—21no—
72#2556—21no—
73#2548C2211yescharacteristic
74#2542C2211yescharacteristic
75#2492C2211yescharacteristic
76#2491C2211yescharacteristic
77#2490C2211yescharacteristic
78#2490C2211yescharacteristic
79#2435C2211yescharacteristic
80#2433C2211yescharacteristic
81#2431C2211yescharacteristic
82#2431C2211yescharacteristic
83#2429C2211yescharacteristic
84#2429C2211yescharacteristic
85#2429C2211yescharacteristic, complemented
86#2429C2211yescharacteristic, complemented
87#2408C2211yescharacteristic
88#2407C2211yescharacteristic
89#2375—21no—
90#2360C2211yescharacteristic
91#2360C2211yescharacteristic
92#2360C2211yescharacteristic, complemented
93#2360C2211yescharacteristic, complemented
94C4×#124—21no—
95C4×#124C2211yescharacteristic
96C42×Q8C2211yescharacteristic, complemented
97#2068C2211yescharacteristic, complemented
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2056C2211yescharacteristic, complemented
102#2056C2211yescharacteristic, complemented
103#2055C2211yescharacteristic
104#2055C2211yescharacteristic
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic, complemented
108#2055C2211yescharacteristic, complemented
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2036C2211yescharacteristic
114#2036C2211yescharacteristic
115#2036C2211yescharacteristic, complemented
116#2035C2211yescharacteristic, complemented
117#2026C2211yescharacteristic, complemented
118#2026C2211yescharacteristic, complemented
119#2024C2211yescharacteristic, complemented
120#2024C2211yescharacteristic, complemented
121#2024C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic, complemented
125#2016C2211yescharacteristic, complemented
126#2016C2211yescharacteristic, complemented
127#2015C2211yescharacteristic
128#2015C2211yescharacteristic
129#2014C2211yescharacteristic
130#2014C2211yescharacteristic
131#2013C2211yescharacteristic
132#2013C2211yescharacteristic
133#2013C2211yescharacteristic
134#2013C2211yescharacteristic
135#2013C2211yescharacteristic, complemented
136#2013C2211yescharacteristic, complemented
137#2001C2211yescharacteristic
138#2001C2211yescharacteristic
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#2000C2211yescharacteristic
142#2000C2211yescharacteristic
143#2000C2211yescharacteristic
144#2000C2211yescharacteristic
145#1989C2211yescharacteristic, complemented
146#1987C2211yescharacteristic, complemented
147#1985C2211yescharacteristic, complemented
148#1984C2211yescharacteristic, complemented
149#1983C2211yescharacteristic
150#1982C2211yescharacteristic
151#1981C2211yescharacteristic, complemented
152#1981C2211yescharacteristic, complemented
153#1936C2211yescharacteristic
154#1936C2211yescharacteristic, complemented
155#1934C2211yescharacteristic
156#1933C2211yescharacteristic, complemented
157#1928C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1926C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic, complemented
164#1925C2211yescharacteristic, complemented
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic, complemented
167#1923C2211yescharacteristic
168#1923C2211yescharacteristic, complemented
169#1921C2211yescharacteristic, complemented
170#1921C2211yescharacteristic, complemented
171#1919C2211yescharacteristic, complemented
172#1918C2211yescharacteristic, complemented
173#1894C2211yescharacteristic, complemented
174#1892C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic
177#1880C2211yescharacteristic
178#1880C2211yescharacteristic
179#1880C2211yescharacteristic
180#1880C2211yescharacteristic
181#1880C2211yescharacteristic, complemented
182#1880C2211yescharacteristic, complemented
183#1880C2211yescharacteristic, complemented
184#1878C2211yescharacteristic, complemented
185#1878C2211yescharacteristic, complemented
186#1878C2211yescharacteristic, complemented
187#1874C2211yescharacteristic
188#1874C2211yescharacteristic
189#1874C2211yescharacteristic
190#1872C2211yescharacteristic
191#1870C2211yescharacteristic
192#1869C2211yescharacteristic
193#1851C2211yescharacteristic, complemented
194#1851C2211yescharacteristic, complemented
195#1850C2211yescharacteristic
196#1850C2211yescharacteristic
197#1831C2211yescharacteristic, complemented
198#1831C2211yescharacteristic, complemented
199#1824C2211yescharacteristic
200#1823C2211yescharacteristic, complemented
201#1763C2211yescharacteristic, complemented
202C4×#103C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#557—42no—
220#557—42no—
221#554—42no—
222#554—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×#127C2311yescharacteristic
229C2×#127C2311yescharacteristic
230C2×#125—21no—
231C2×#125—21no—
232C2×#125—21no—
233C2×#125—21no—
234C2×#125C2311yescharacteristic
235C2×#124—21no—
236C2×#124—21no—
237C2×#124—21no—
238C2×#124—21no—
239C2×#124D411yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#124C2311yescharacteristic
242C2×C22⋊Q8—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×#121C2311yescharacteristic
252C2×#121C2311yescharacteristic
253C2×#121C2311yescharacteristic
254C2×#120—21no—
255C2×#120—21no—
256C2×#120—21no—
257C2×C4×Q8—21no—
258C2×C4×Q8C2311yescharacteristic
259C2×C4×Q8C2311yescharacteristic
260C2×C4×Q8C2311yescharacteristic
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×D4—21no—
265C2×C4×D4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C4⋊C4C2311yescharacteristic
268#497—42no—
269#492—42no—
270#479—42no—
271#477—42no—
272#468—42no—
273#468—42no—
274#467—42no—
275#465—42no—
276#464—42no—
277#464—42no—
278#460—42no—
279#460—42no—
280#452—42no—
281#452—42no—
282#452—42no—
283#450—42no—
284#450—42no—
285#450—42no—
286C2×#107C2311yescharacteristic
287C2×#107C2311yescharacteristic
288C2×#107C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296#417—42no—
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#102—42no—
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×#102C2311yescharacteristic
329C2×#102C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338#400—21no—
339#399—21no—
340#399—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#395—21no—
353#395—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#393—21no—
364#393—21no—
365#393—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#391—21no—
375#391—21no—
376#391—21no—
377#391—21no—
378#391D411yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390—21no—
392#390D411yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#388D411yescharacteristic
429#388D411yescharacteristic
430#388D411yescharacteristic
431#388D411yescharacteristic
432#387—21no—
433#387—21no—
434#387—21no—
435#387—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#384—21no—
447#384—21no—
448#382—21no—
449#382—21no—
450#382D411yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455#379—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C43—21no—
473C43C2311yescharacteristic
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#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8C2×D411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×Q8C2411yescharacteristic
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4C2×D411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×Q16—22no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×Q16—41no—
546C2×Q16—41no—
547C2×Q16—41no—
548C2×Q16—41no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×SD16—41no—
566C2×SD16—41no—
567C2×SD16—41no—
568C2×SD16—41no—
569C2×SD16—41no—
570C2×SD16—41no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×SD16—41no—
576C2×M16—41no—
577C2×M16—41no—
578C2×M16—41no—
579C22×C8—41no—
580C22×C8—41no—
581C22×C8—41no—
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C22×C8C2411yescharacteristic
589C22×C8C2411yescharacteristic
590C4⋊Q8—22no—
591C4⋊Q8—22no—
592C4⋊Q8—41no—
593C4⋊Q8—41no—
594C4⋊Q8—41no—
595C4⋊Q8—41no—
596C4⋊Q8—41no—
597C4⋊Q8—41no—
598C4⋊Q8—41no—
599C4⋊Q8—41no—
600#127—41no—
601#127—41no—
602#127—41no—
603#127—41no—
604#125—41no—
605#125—41no—
606#125—44no—
607#125—44no—
608#125—44no—
609#125—44no—
610#124—24no—
611#124—41no—
612#124—41no—
613#124—41no—
614#124—41no—
615#124—82no—
616#124—82no—
617#124—82no—
618#124—82no—
619C22⋊Q8—22no—
620C22⋊Q8—22no—
621C22⋊Q8—22no—
622C22⋊Q8—22no—
623C22⋊Q8—22no—
624C22⋊Q8—22no—
625C22⋊Q8—41no—
626C22⋊Q8—41no—
627C22⋊Q8—41no—
628C22⋊Q8—41no—
629C22⋊Q8—41no—
630C22⋊Q8—41no—
631C22⋊Q8—44no—
632C22⋊Q8—44no—
633C22⋊Q8—41no—
634C22⋊Q8—41no—
635#121—41no—
636#121—41no—
637#121—41no—
638#121—41no—
639#121—41no—
640#121—41no—
641#120—44no—
642#120—82no—
643#120—82no—
644C4×Q8—22no—
645C4×Q8—22no—
646C4×Q8—22no—
647C4×Q8—22no—
648C4×Q8—22no—
649C4×Q8—22no—
650C4×Q8—41no—
651C4×Q8—41no—
652C4×Q8—41no—
653C4×Q8—41no—
654C4×Q8—41no—
655C4×Q8—41no—
656C4×Q8—44no—
657C4×D4—41no—
658C4×D4—41no—
659C4×D4—44no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—21no—
672C2×C4⋊C4—21no—
673C2×C4⋊C4—21no—
674C2×C4⋊C4—21no—
675C2×C4⋊C4—21no—
676C2×C4⋊C4—21no—
677C2×C4⋊C4—21no—
678C2×C4⋊C4—21no—
679C2×C4⋊C4—21no—
680C2×C4⋊C4—21no—
681C2×C4⋊C4—21no—
682C2×C4⋊C4—21no—
683C2×C4⋊C4—21no—
684C2×C4⋊C4—21no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—21no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—41no—
692C2×C4⋊C4C2×D411yescharacteristic
693C2×C4⋊C4C2×D411yescharacteristic
694C2×C4⋊C4C2×D411yescharacteristic
695C2×C4⋊C4C2×D411yescharacteristic
696C2×C4⋊C4C2411yescharacteristic
697C2×C4⋊C4C2411yescharacteristic
698C2×C4⋊C4C2411yescharacteristic
699C2×C4⋊C4C2411yescharacteristic
700C2×C4⋊C4C2411yescharacteristic
701C2×C4⋊C4C2411yescharacteristic
702C2×C4⋊C4C2411yescharacteristic
703C2×C4⋊C4C2411yescharacteristic
704C2×C4⋊C4C2411yescharacteristic
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4C2×D411yescharacteristic
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C42—21no—
750C2×C42—21no—
751C2×C42—21no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42—21no—
756C2×C42—21no—
757C2×C42—21no—
758C2×C42—21no—
759C2×C42C2×D411yescharacteristic
760C2×C42C2×D411yescharacteristic
761C2×C42C2×D411yescharacteristic
762C2×C42C2×D411yescharacteristic
763C2×C42C2411yescharacteristic
764C2×C42C2411yescharacteristic
765C2×C42C2411yescharacteristic
766C2×C42C2411yescharacteristic
767C2×C42C2411yescharacteristic
768#107—22no—
769#107—22no—
770#107—22no—
771#106—22no—
772C4⋊C8—41no—
773C4⋊C8—41no—
774C4⋊C8—41no—
775C4⋊C8—41no—
776C4⋊C8—41no—
777C4⋊C8—41no—
778#103—22no—
779#103—22no—
780#103—22no—
781#103—41no—
782#103—41no—
783#103—41no—
784#103—41no—
785#103—41no—
786#103—41no—
787#103—41no—
788#103—41no—
789#103—41no—
790#103—41no—
791#103—41no—
792#103—41no—
793#103—41no—
794#103—41no—
795#102—22no—
796#102—22no—
797#102—22no—
798#102—22no—
799#102—22no—
800#102—22no—
801#102—22no—
802#102—22no—
803#102—22no—
804#102—41no—
805#102—41no—
806#102—41no—
807#102—41no—
808#102—41no—
809#102—41no—
810C22⋊C8—41no—
811C22⋊C8—41no—
812C22⋊C8—41no—
813C22⋊C8—41no—
814C22⋊C8—41no—
815C22⋊C8—41no—
816#97—41no—
817C4×C8—41no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836#95—21no—
837#95—21no—
838#95—21no—
839#95—21no—
840#95—21no—
841#95—21no—
842#95—21no—
843#95C2×D411yescharacteristic
844#95C2×D411yescharacteristic
845#95C2×D411yescharacteristic
846#95C2×D411yescharacteristic
847#95C2×D411yescharacteristic
848#95C2×D411yescharacteristic
849#95C2×D411yescharacteristic
850#95C2×D411yescharacteristic
851C24—21no—
852C24—21no—
853C24—21no—
854C24—42no—
855C24—81no—
856C24—81no—
857C24—81no—
858C24—81no—
859C24—81no—
860C24—81no—
861C24C22×D411yescharacteristic
862C24C22×D411yescharacteristic
863#41—44no—
864#41—82no—
865#41—82no—
866#41—82no—
867C2×Q8—22no—
868C2×Q8—22no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—21no—
881C2×Q8—21no—
882C2×Q8—21no—
883C2×Q8—21no—
884C2×Q8—21no—
885C2×Q8—21no—
886C2×Q8—21no—
887C2×Q8—21no—
888C2×Q8—21no—
889C2×Q8—21no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—41no—
893C2×Q8—42no—
894C2×Q8—42no—
895C2×Q8—81no—
896C2×Q8—81no—
897C2×Q8—81no—
898C2×Q8—81no—
899C2×Q8H(5,𝔽2)12yes—
900C2×D4—22no—
901C2×D4—22no—
902C2×D4—21no—
903C2×D4—21no—
904C2×D4—21no—
905C2×D4—21no—
906C2×D4—21no—
907C2×D4—21no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—21no—
912C2×D4—21no—
913C2×D4—21no—
914C2×D4—21no—
915C2×D4—21no—
916C2×D4—21no—
917C2×D4—21no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—41no—
921C2×D4—42no—
922C2×D4—44no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—42no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—82no—
939C2×D4—82no—
940C2×D4—82no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4—81no—
947C2×D4—81no—
948C2×D4—81no—
949C2×D4—81no—
950C2×D4—81no—
951C2×D4—81no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4C22×D411yescharacteristic
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C2511yescharacteristic
999Q16—82no—
1000Q16—82no—
1001Q16—82no—
1002SD16—82no—
1003SD16—82no—
1004SD16—82no—
1005SD16—82no—
1006SD16—82no—
1007SD16—82no—
1008SD16—82no—
1009SD16—82no—
1010SD16—82no—
1011M16—82no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—82no—
1037C4⋊C4—24no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—41no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4H(5,𝔽2)12yes—
1085C4⋊C4H(5,𝔽2)12yes—
1086C4⋊C4H(5,𝔽2)12yes—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4#13714yes—
1131C42—24no—
1132C42—22no—
1133C42—22no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—41no—
1145C42—41no—
1146C42—42no—
1147C42—42no—
1148C42—42no—
1149C42—42no—
1150C42—42no—
1151C42—81no—
1152C42—81no—
1153C42—81no—
1154C42—81no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—84no—
1190C23—162no—
1191C23—162no—
1192C23—162no—
1193C23—162no—
1194C23—162no—
1195C23—162no—
1196C23C2×#13712yes—
1197C23C23×D411yescharacteristic
1198Q8—22no—
1199Q8—22no—
1200Q8—44no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—41no—
1210Q8—41no—
1211Q8—41no—
1212Q8—41no—
1213Q8—41no—
1214Q8—41no—
1215Q8—162no—
1216Q8—162no—
1217D4—44no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—84no—
1231D4—84no—
1232D4—162no—
1233D4—162no—
1234D4—162no—
1235D4—162no—
1236D4—162no—
1237D4—162no—
1238D4—162no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—22no—
1256C2×C4—21no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—22no—
1266C2×C4—22no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—84no—
1320C2×C4—162no—
1321C2×C4—162no—
1322C2×C4C2×#13712yes—
1323C2×C4C2×#13712yes—
1324C2×C4#57712yes—
1325C2×C4C2×H(5,𝔽2)11yescharacteristic
1326C2×C4C2×H(5,𝔽2)11yescharacteristic
1327C2×C4C2×H(5,𝔽2)11yescharacteristic
1328C2×C4C2×H(5,𝔽2)11yescharacteristic
1329C2×C4#58511yescharacteristic
1330C2×C4#58511yescharacteristic
1331C8—41no—
1332C8—41no—
1333C8—41no—
1334C8—41no—
1335C8—41no—
1336C8—41no—
1337C8—41no—
1338C8—41no—
1339C22—22no—
1340C22—22no—
1341C22—22no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—41no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—168no—
1375C22#348411yescharacteristic
1376C22#348811yescharacteristic
1377C22#348811yescharacteristic
1378C22C22×#13711yescharacteristic
1379C22C2×#57711yescharacteristic
1380C22#358411yescharacteristic
1381C22#358511yescharacteristic
1382C4—22no—
1383C4—22no—
1384C4—22no—
1385C4—41no—
1386C4—41no—
1387C4—42no—
1388C4—41no—
1389C4—42no—
1390C4—41no—
1391C4—41no—
1392C4—42no—
1393C4—41no—
1394C4—41no—
1395C4—41no—
1396C4—41no—
1397C4—42no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4#352911yescharacteristic
1408C4#354911yescharacteristic
1409C4#355811yescharacteristic
1410C4#355811yescharacteristic
1411C2—42no—
1412C2—81no—
1413C2—161no—
1414C2—161no—
1415C2—161no—
1416C2#4622511yescharacteristic
1417C2#6159311yescharacteristic
1418C2#6169011yescharacteristic
1419C2#6196511yescharacteristic
1420C2#6199111yescharacteristic
1421C2#6203311yescharacteristic
1422C2#6207011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#46054C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36562C2semidirect
3. #33031C2semidirect
4. #33029C2semidirect
5. #32811C2semidirect
6. #32807C2semidirect
7. #32647C2semidirect
8. #32636C2semidirect
9. #30937C2semidirect
10. #30924C2semidirect
11. #30920C2semidirect
12. #30917C2semidirect
13. #30510C2semidirect
14. #30504C2semidirect
15. #30474C2semidirect
16. #30464C2semidirect
17. #30459C2semidirect
18. #30456C2semidirect
19. #26742C2semidirect
20. #26741C2semidirect
21. #26727C2semidirect
22. #26726C2semidirect
23. #25640C2semidirect
24. #25630C2semidirect
25. #25102C2semidirect
26. #25096C2semidirect
27. #25084C2semidirect
28. #25080C2semidirect
29. #23981C2semidirect
30. #23969C2semidirect
31. #23349C2semidirect
32. C2×#557C22semidirect
36. C2×#479C22semidirect
37. C2×#477C22semidirect
46. C2×#452C22semidirect
47. C2×#452C22semidirect
48. C2×#452C22semidirect
52. C2×#417C22semidirect
54. #2862C22semidirect
66. #2567C22semidirect
85. #2429C22semidirect
86. #2429C22semidirect
92. #2360C22semidirect
93. #2360C22semidirect
96. C42×Q8C22semidirect
97. #2068C22semidirect
99. #2067C22semidirect
101. #2056C22semidirect
102. #2056C22semidirect
107. #2055C22semidirect
108. #2055C22semidirect
115. #2036C22semidirect
116. #2035C22semidirect
117. #2026C22semidirect
118. #2026C22semidirect
119. #2024C22semidirect
120. #2024C22semidirect
121. #2024C22semidirect
124. #2023C22semidirect
125. #2016C22semidirect
126. #2016C22semidirect
135. #2013C22semidirect
136. #2013C22semidirect
145. #1989C22semidirect
146. #1987C22semidirect
147. #1985C22semidirect
148. #1984C22semidirect
151. #1981C22semidirect
152. #1981C22semidirect
154. #1936C22semidirect
156. #1933C22semidirect
157. #1928C22semidirect
158. #1927C22semidirect
163. #1925C22semidirect
164. #1925C22semidirect
166. #1924C22semidirect
168. #1923C22semidirect
169. #1921C22semidirect
170. #1921C22semidirect
171. #1919C22semidirect
172. #1918C22semidirect
173. #1894C22semidirect
181. #1880C22semidirect
182. #1880C22semidirect
183. #1880C22semidirect
184. #1878C22semidirect
185. #1878C22semidirect
186. #1878C22semidirect
193. #1851C22semidirect
194. #1851C22semidirect
197. #1831C22semidirect
198. #1831C22semidirect
200. #1823C22semidirect
201. #1763C22semidirect
202. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#460542
#365622
#330312
#330292
#328112
#328072
#326472
#326362
#309372
#309242
#309202
#309172
#305102
#305042
#304742
#304642
#304592
#304562
#267422
#267412
#267272
#267262
#256402
#256302
#251022
#250962
#250842
#250802
#239812
#239692
#233492