Finite Group Databasebeta

← #6819474

Subgroups — #6819474

Order 512.

1654 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39632C211yesmaximal, characteristic, complemented
2#39189C211yesmaximal, characteristic
3#33217C211yesmaximal, characteristic, complemented
4#32540C211yesmaximal, characteristic, complemented
5#32534C211yesmaximal, characteristic, complemented
6#32070C211yesmaximal, characteristic, complemented
7#32070C211yesmaximal, characteristic, complemented
8#32066C211yesmaximal, characteristic, complemented
9#32063C211yesmaximal, characteristic, complemented
10#31202C211yesmaximal, characteristic, complemented
11#31200C211yesmaximal, characteristic, complemented
12#29957C211yesmaximal, characteristic, complemented
13#29950C211yesmaximal, characteristic, complemented
14#28025C211yesmaximal, characteristic, complemented
15#28018C211yesmaximal, characteristic, complemented
16#27945C211yesmaximal, characteristic, complemented
17#27938C211yesmaximal, characteristic, complemented
18#27800C211yesmaximal, characteristic, complemented
19#27795C211yesmaximal, characteristic, complemented
20#24871C211yesmaximal, characteristic, complemented
21#24867C211yesmaximal, characteristic, complemented
22#24865C211yesmaximal, characteristic, complemented
23#24861C211yesmaximal, characteristic, complemented
24#24788C211yesmaximal, characteristic, complemented
25#24787C211yesmaximal, characteristic, complemented
26#24269C211yesmaximal, characteristic, complemented
27#24264C211yesmaximal, characteristic, complemented
28#22661C211yesmaximal, characteristic, complemented
29D4×#107C211yesmaximal, characteristic, complemented
30#21489C211yesmaximal, characteristic, complemented
31C2×#1973C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#501C2211yescharacteristic, complemented
34C2×#484C2211yescharacteristic, complemented
35C2×#481C2211yescharacteristic
36C2×#485C2211yescharacteristic, complemented
37C2×#480C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#465C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#435C2211yescharacteristic, complemented
44C2×C8×D4C2211yescharacteristic
45C2×#428C2211yescharacteristic, complemented
46C22×#107C2211yescharacteristic
47C22×#107C2211yescharacteristic, complemented
48C22×#103C2211yescharacteristic
49C22×#102C2211yescharacteristic
50C22×#97C2211yescharacteristic
51#2857C2211yescharacteristic
52#2851C2211yescharacteristic
53#2806—21no—
54#2804—21no—
55#2803—21no—
56#2800—21no—
57#2797—21no—
58#2788—21no—
59#2788—21no—
60#2714—21no—
61#2646—21no—
62#2622—21no—
63#2513C2211yescharacteristic
64#2512C2211yescharacteristic
65#2511C2211yescharacteristic, complemented
66#2511C2211yescharacteristic, complemented
67#2504C2211yescharacteristic
68#2502C2211yescharacteristic, complemented
69#2502C2211yescharacteristic, complemented
70#2500C2211yescharacteristic
71#2492C2211yescharacteristic, complemented
72#2492C2211yescharacteristic, complemented
73#2490C2211yescharacteristic
74#2490C2211yescharacteristic
75#2480—21no—
76#2450—21no—
77#2450—21no—
78#2424—21no—
79#2417C2211yescharacteristic, complemented
80#2417C2211yescharacteristic, complemented
81#2416C2211yescharacteristic
82#2414C2211yescharacteristic
83#2409C2211yescharacteristic
84#2409C2211yescharacteristic
85#2408C2211yescharacteristic
86#2408C2211yescharacteristic
87#2352C2211yescharacteristic
88D4×C4⋊C4C2211yescharacteristic
89D4×C4⋊C4C2211yescharacteristic
90D4×C4⋊C4C2211yescharacteristic
91#2325—21no—
92#2321—21no—
93C4×#121C2211yescharacteristic
94C2×#391C2211yescharacteristic
95C2×#390C2211yescharacteristic
96#2097C2211yescharacteristic, complemented
97#2097C2211yescharacteristic, complemented
98#2097C2211yescharacteristic, complemented
99#2095C2211yescharacteristic, complemented
100#2094C2211yescharacteristic
101#2093C2211yescharacteristic
102#2093C2211yescharacteristic
103#2093C2211yescharacteristic
104#2074C2211yescharacteristic, complemented
105#2072C2211yescharacteristic, complemented
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2068C2211yescharacteristic, complemented
109#2068C2211yescharacteristic, complemented
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic
114#2066C2211yescharacteristic, complemented
115#2066C2211yescharacteristic, complemented
116#2055C2211yescharacteristic
117#2055C2211yescharacteristic
118#2055C2211yescharacteristic
119#2055C2211yescharacteristic
120#2036C2211yescharacteristic, complemented
121#2036C2211yescharacteristic, complemented
122#2036C2211yescharacteristic, complemented
123#2035C2211yescharacteristic, complemented
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2026C2211yescharacteristic, complemented
129#2026C2211yescharacteristic, complemented
130#2023C2211yescharacteristic
131#2023C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#1993C2211yescharacteristic, complemented
137#1992C2211yescharacteristic, complemented
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1973C2211yescharacteristic
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic
143#1973C2211yescharacteristic
144#1973C2211yescharacteristic
145#1973C2211yescharacteristic
146#1973C2211yescharacteristic
147#1973C2211yescharacteristic
148#1968C2211yescharacteristic
149#1968C2211yescharacteristic
150#1955C2211yescharacteristic, complemented
151#1949C2211yescharacteristic, complemented
152#1947C2211yescharacteristic, complemented
153#1947C2211yescharacteristic, complemented
154#1947C2211yescharacteristic, complemented
155#1944C2211yescharacteristic, complemented
156#1944C2211yescharacteristic, complemented
157#1943C2211yescharacteristic, complemented
158#1943C2211yescharacteristic, complemented
159#1940C2211yescharacteristic, complemented
160#1928C2211yescharacteristic, complemented
161#1928C2211yescharacteristic, complemented
162#1928C2211yescharacteristic, complemented
163#1927C2211yescharacteristic, complemented
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1925C2211yescharacteristic
167#1925C2211yescharacteristic
168#1924C2211yescharacteristic, complemented
169#1924C2211yescharacteristic, complemented
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1873C2211yescharacteristic, complemented
173#1872C2211yescharacteristic, complemented
174#1869C2211yescharacteristic
175#1869C2211yescharacteristic
176#1854C2211yescharacteristic, complemented
177#1853C2211yescharacteristic
178#1852C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic, complemented
182#1852C2211yescharacteristic, complemented
183#1852C2211yescharacteristic, complemented
184#1847C2211yescharacteristic, complemented
185#1847C2211yescharacteristic, complemented
186#1845C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1808C2211yescharacteristic
189#1808C2211yescharacteristic
190#1808C2211yescharacteristic, complemented
191#1807C2211yescharacteristic
192#1807C2211yescharacteristic
193#1797C2211yescharacteristic
194#1787C2211yescharacteristic
195#1787C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1776C2211yescharacteristic, complemented
199C4×#107C2211yescharacteristic, complemented
200#1771C2211yescharacteristic, complemented
201#1753C2211yescharacteristic, complemented
202#1752C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16—24no—
206C22×SD16—42no—
207C22×SD16—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C23×C8C2311yescharacteristic
215C23×C8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#126—21no—
218C2×#125C2311yescharacteristic
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×#121—21no—
225C2×#121D411yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246C22×C42C2311yescharacteristic
247#501—42no—
248#485—42no—
249#484—42no—
250#481—42no—
251#480—42no—
252#468—42no—
253#468—42no—
254#465—42no—
255#465—42no—
256#435—24no—
257#435—42no—
258C8×D4—24no—
259#428—42no—
260C2×#107—42no—
261C2×#107—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×#103—42no—
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×#102—42no—
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×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×#97—42no—
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#398—21no—
338#398—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#395—21no—
351#395—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#393—21no—
361#393—21no—
362#393—21no—
363#393—21no—
364#392—21no—
365#392—21no—
366#392—21no—
367#391—21no—
368#391—21no—
369#391—21no—
370#391—21no—
371#391—21no—
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
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#390D411yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389D411yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388D411yescharacteristic
415#388D411yescharacteristic
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386D411yescharacteristic
432#386D411yescharacteristic
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#382C2311yescharacteristic
452#382C2311yescharacteristic
453#380—21no—
454#380—21no—
455#380—21no—
456#380D411yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#379—21no—
466#379—21no—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C22⋊C4—21no—
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475C2×#95—21no—
476C2×#95—21no—
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—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—22no—
516C22×D4—22no—
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×C4—21no—
532C23×C4C2×D411yescharacteristic
533C23×C4C2×D411yescharacteristic
534C23×C4C2411yescharacteristic
535C23×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
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—416no—
550C2×M16—22no—
551C2×M16—22no—
552C2×M16—22no—
553C22×C8—22no—
554C22×C8—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—22no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8#4114yes—
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572#126—82no—
573#125—41no—
574#125—41no—
575C22⋊Q8—41no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—82no—
584#121—24no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—41no—
593#121—82no—
594#120—44no—
595#120—82no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—82no—
603C4×D4—82no—
604C4×D4—82no—
605#117—41no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—82no—
692C2×C22⋊C4—82no—
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—41no—
709C2×C42—41no—
710C2×C42C2×D411yescharacteristic
711C2×C42C2×D411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#107—22no—
717#107—22no—
718#107—22no—
719#107—22no—
720#107—22no—
721#107—41no—
722#107—41no—
723#107—41no—
724#107—41no—
725#107—41no—
726#107—41no—
727#107—41no—
728#107—41no—
729#107—41no—
730#106—22no—
731#106—22no—
732#106—22no—
733#106—41no—
734#106—41no—
735#106—41no—
736C4⋊C8—22no—
737C4⋊C8—22no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740#103—22no—
741#103—22no—
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#102—22no—
753#102—22no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764C22⋊C8—22no—
765C22⋊C8—22no—
766C22⋊C8—22no—
767C22⋊C8—22no—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772#97—22no—
773#97—22no—
774#97—22no—
775#97—41no—
776#97—41no—
777C4×C8—22no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
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#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—81no—
826C24—81no—
827C24—81no—
828C24—81no—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C24C22×D411yescharacteristic
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—42no—
845C2×Q8—44no—
846C2×Q8—44no—
847C2×Q8—42no—
848C2×Q8—81no—
849C2×Q8—81no—
850C2×Q8—81no—
851C2×Q8—81no—
852C2×Q8—82no—
853C2×Q8—82no—
854C2×D4—22no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—22no—
858C2×D4—22no—
859C2×D4—22no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—82no—
880C2×D4—82no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4#13714yes—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—22no—
899C22×C4—22no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C2×#4112yes—
960C22×C42−1+412yes—
961C22×C4C2511yescharacteristic
962SD16—44no—
963SD16—44no—
964SD16—44no—
965SD16—44no—
966M16—44no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—28no—
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—44no—
988C2×C8—44no—
989C2×C8C2×#4112yes—
990C2×C8C2×#4112yes—
991C2×C8H(5,𝔽2)12yes—
992C2×C8H(5,𝔽2)12yes—
993C2×C8H(5,𝔽2)12yes—
994C4⋊C4—22no—
995C4⋊C4—22no—
996C4⋊C4—22no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—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—41no—
1022C4⋊C4—41no—
1023C4⋊C4—42no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C22⋊C4—22no—
1048C22⋊C4—22no—
1049C22⋊C4—22no—
1050C22⋊C4—22no—
1051C22⋊C4—22no—
1052C22⋊C4—22no—
1053C22⋊C4—41no—
1054C22⋊C4—41no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—41no—
1099C42—41no—
1100C42—81no—
1101C42—81no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—84no—
1137C23—84no—
1138C23—84no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23—162no—
1143C23#54712yes—
1144C23C2×#13712yes—
1145C23C2×#13712yes—
1146C23#57612yes—
1147C23C23×D411yescharacteristic
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—84no—
1157Q8—162no—
1158D4—28no—
1159D4—44no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—84no—
1169D4—82no—
1170D4—162no—
1171D4—162no—
1172D4—162no—
1173D4—162no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
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—82no—
1260C2×C4—82no—
1261C2×C4—84no—
1262C2×C4—162no—
1263C2×C4—162no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4#54712yes—
1268C2×C4C2×#13712yes—
1269C2×C4C22×#4111yescharacteristic
1270C2×C4C2×H(5,𝔽2)11yescharacteristic
1271C2×C4C2×H(5,𝔽2)11yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4C2×2−1+411yescharacteristic
1274C2×C4#58511yescharacteristic
1275C8—22no—
1276C8—22no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8#53814yes—
1283C22—22no—
1284C22—22no—
1285C22—22no—
1286C22—22no—
1287C22—22no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—168no—
1318C22#334614yes—
1319C22C2×#54711yescharacteristic
1320C22#349611yescharacteristic
1321C22#349811yescharacteristic
1322C22C22×#13711yescharacteristic
1323C22C2×#57611yescharacteristic
1324C22#358511yescharacteristic
1325C22#358611yescharacteristic
1326C4—22no—
1327C4—22no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4C2×#53811yescharacteristic
1352C4#350611yescharacteristic
1353C4#353611yescharacteristic
1354C4#356111yescharacteristic
1355C2—24no—
1356C2—42no—
1357C2—81no—
1358C2—161no—
1359C2—161no—
1360C2#3937511yescharacteristic
1361C2C2×#334611yescharacteristic
1362C2#6129111yescharacteristic
1363C2#6229611yescharacteristic
1364C2#6231111yescharacteristic
1365C2#6244811yescharacteristic
1366C2#6245911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#39189C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39632C2semidirect
3. #33217C2semidirect
4. #32540C2semidirect
5. #32534C2semidirect
6. #32070C2semidirect
7. #32070C2semidirect
8. #32066C2semidirect
9. #32063C2semidirect
10. #31202C2semidirect
11. #31200C2semidirect
12. #29957C2semidirect
13. #29950C2semidirect
14. #28025C2semidirect
15. #28018C2semidirect
16. #27945C2semidirect
17. #27938C2semidirect
18. #27800C2semidirect
19. #27795C2semidirect
20. #24871C2semidirect
21. #24867C2semidirect
22. #24865C2semidirect
23. #24861C2semidirect
24. #24788C2semidirect
25. #24787C2semidirect
26. #24269C2semidirect
27. #24264C2semidirect
28. #22661C2semidirect
29. D4×#107C2semidirect
30. #21489C2semidirect
31. C2×#1973C2semidirect
33. C2×#501C22semidirect
34. C2×#484C22semidirect
36. C2×#485C22semidirect
43. C2×#435C22semidirect
45. C2×#428C22semidirect
47. C22×#107C22semidirect
65. #2511C22semidirect
66. #2511C22semidirect
68. #2502C22semidirect
69. #2502C22semidirect
71. #2492C22semidirect
72. #2492C22semidirect
79. #2417C22semidirect
80. #2417C22semidirect
96. #2097C22semidirect
97. #2097C22semidirect
98. #2097C22semidirect
99. #2095C22semidirect
104. #2074C22semidirect
105. #2072C22semidirect
108. #2068C22semidirect
109. #2068C22semidirect
114. #2066C22semidirect
115. #2066C22semidirect
120. #2036C22semidirect
121. #2036C22semidirect
122. #2036C22semidirect
123. #2035C22semidirect
128. #2026C22semidirect
129. #2026C22semidirect
136. #1993C22semidirect
137. #1992C22semidirect
150. #1955C22semidirect
151. #1949C22semidirect
152. #1947C22semidirect
153. #1947C22semidirect
154. #1947C22semidirect
155. #1944C22semidirect
156. #1944C22semidirect
157. #1943C22semidirect
158. #1943C22semidirect
159. #1940C22semidirect
160. #1928C22semidirect
161. #1928C22semidirect
162. #1928C22semidirect
163. #1927C22semidirect
168. #1924C22semidirect
169. #1924C22semidirect
172. #1873C22semidirect
173. #1872C22semidirect
176. #1854C22semidirect
181. #1852C22semidirect
182. #1852C22semidirect
183. #1852C22semidirect
184. #1847C22semidirect
185. #1847C22semidirect
186. #1845C22semidirect
187. #1809C22semidirect
190. #1808C22semidirect
198. #1776C22semidirect
199. C4×#107C22semidirect
200. #1771C22semidirect
201. #1753C22semidirect
202. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#396322
#391892
#332172
#325402
#325342
#320702
#320662
#320632
#312022
#312002
#299572
#299502
#280252
#280182
#279452
#279382
#278002
#277952
#248712
#248672
#248652
#248612
#247882
#247872
#242692
#242642
#226612
D4×#1072
#214892
C2×#19732