Finite Group Databasebeta

← #6605950

Subgroups — #6605950

Order 512.

1692 conjugacy classes of subgroups.

The subgroup lattice has 1353 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38098C211yesmaximal, characteristic, complemented
2#38090C211yesmaximal, characteristic
3#33283C211yesmaximal, characteristic, complemented
4#33054C211yesmaximal, characteristic, complemented
5#33048C211yesmaximal, characteristic, complemented
6#29363C211yesmaximal, characteristic, complemented
7#29345C211yesmaximal, characteristic, complemented
8#29328C211yesmaximal, characteristic, complemented
9#29136C211yesmaximal, characteristic, complemented
10#29116C211yesmaximal, characteristic, complemented
11#29107C211yesmaximal, characteristic, complemented
12#27813C211yesmaximal, characteristic, complemented
13#27783C211yesmaximal, characteristic, complemented
14#27751C211yesmaximal, characteristic, complemented
15#27744C211yesmaximal, characteristic, complemented
16#27726C211yesmaximal, characteristic, complemented
17#27722C211yesmaximal, characteristic, complemented
18#27720C211yesmaximal, characteristic, complemented
19#27700C211yesmaximal, characteristic, complemented
20#27282C211yesmaximal, characteristic, complemented
21#27280C211yesmaximal, characteristic, complemented
22#27279C211yesmaximal, characteristic, complemented
23#27254C211yesmaximal, characteristic, complemented
24#22503C211yesmaximal, characteristic, complemented
25#22492C211yesmaximal, characteristic, complemented
26#22427C211yesmaximal, characteristic, complemented
27#22419C211yesmaximal, characteristic, complemented
28#21652C211yesmaximal, characteristic, complemented
29#21093C211yesmaximal, characteristic, complemented
30#21091C211yesmaximal, characteristic, complemented
31#20490C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#489C2211yescharacteristic, complemented
36C2×#486C2211yescharacteristic
37C2×#436C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#417C2211yescharacteristic
40C2×#417C2211yescharacteristic
41C2×#418C2211yescharacteristic
42C22×#102C2211yescharacteristic
43C2×#405C2211yescharacteristic
44C2×C4×M16C2211yescharacteristic, complemented
45#2857C2211yescharacteristic, complemented
46#2856C2211yescharacteristic
47#2807—21no—
48#2792—21no—
49#2774—21no—
50#2729—21no—
51#2676—21no—
52#2676—21no—
53#2668—21no—
54#2668—21no—
55#2647C2211yescharacteristic, complemented
56#2640C2211yescharacteristic
57#2628C2211yescharacteristic
58#2620C2211yescharacteristic
59#2570C2211yescharacteristic, complemented
60#2564—21no—
61#2551C2211yescharacteristic, complemented
62#2544C2211yescharacteristic
63#2542C2211yescharacteristic
64#2505—21no—
65#2500C2211yescharacteristic
66#2499C2211yescharacteristic
67#2472—21no—
68#2472—21no—
69#2471—21no—
70#2471—21no—
71#2449—21no—
72#2442C2211yescharacteristic, complemented
73#2441C2211yescharacteristic
74#2440—21no—
75#2440C2211yescharacteristic
76#2440C2211yescharacteristic, complemented
77#2433C2211yescharacteristic
78#2431C2211yescharacteristic
79#2352C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic
81#2330C2211yescharacteristic, complemented
82#2328C2211yescharacteristic
83#2317C2211yescharacteristic
84#2309C2211yescharacteristic
85#2297C2211yescharacteristic
86C2×#389C2211yescharacteristic, complemented
87#2290C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2100C2211yescharacteristic, complemented
91#2099C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2099C2211yescharacteristic, complemented
94#2073C2211yescharacteristic
95#2073C2211yescharacteristic
96#2072C2211yescharacteristic, complemented
97#2072C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2042C2211yescharacteristic, complemented
101#2042C2211yescharacteristic, complemented
102#2041C2211yescharacteristic
103#2041C2211yescharacteristic
104#2041C2211yescharacteristic
105#2041C2211yescharacteristic
106#2026C2211yescharacteristic, complemented
107#2025C2211yescharacteristic
108#2024C2211yescharacteristic, complemented
109#2023C2211yescharacteristic
110#2023C2211yescharacteristic
111#2023C2211yescharacteristic
112#1993C2211yescharacteristic, complemented
113#1991C2211yescharacteristic, complemented
114#1990C2211yescharacteristic, complemented
115#1990C2211yescharacteristic, complemented
116#1990C2211yescharacteristic, complemented
117#1988C2211yescharacteristic, complemented
118#1987C2211yescharacteristic, complemented
119#1983C2211yescharacteristic
120#1983C2211yescharacteristic
121#1959C2211yescharacteristic
122#1958C2211yescharacteristic
123#1958C2211yescharacteristic, complemented
124#1957C2211yescharacteristic
125#1957C2211yescharacteristic
126#1936C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic, complemented
134#1936C2211yescharacteristic, complemented
135#1935C2211yescharacteristic, complemented
136#1935C2211yescharacteristic, complemented
137#1935C2211yescharacteristic, complemented
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic, complemented
148#1934C2211yescharacteristic, complemented
149#1933C2211yescharacteristic, complemented
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1933C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic, complemented
158#1895C2211yescharacteristic, complemented
159#1894C2211yescharacteristic
160#1893C2211yescharacteristic
161#1892C2211yescharacteristic
162#1875C2211yescharacteristic
163#1874C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic, complemented
167#1874C2211yescharacteristic, complemented
168#1873C2211yescharacteristic
169#1872C2211yescharacteristic
170#1836C2211yescharacteristic, complemented
171#1836C2211yescharacteristic, complemented
172#1834C2211yescharacteristic, complemented
173#1825C2211yescharacteristic
174#1825C2211yescharacteristic
175#1825C2211yescharacteristic, complemented
176#1825C2211yescharacteristic, complemented
177#1804C2211yescharacteristic
178#1804C2211yescharacteristic, complemented
179#1802C2211yescharacteristic
180#1802C2211yescharacteristic, complemented
181#1788C2211yescharacteristic
182#1788C2211yescharacteristic
183#1786C2211yescharacteristic
184#1786C2211yescharacteristic
185#1771C2211yescharacteristic, complemented
186C8×C4⋊C4C2211yescharacteristic, complemented
187#1768C2211yescharacteristic, complemented
188#1762C2211yescharacteristic
189#1762C2211yescharacteristic, complemented
190C4×#102C2211yescharacteristic
191C4×#102C2211yescharacteristic, complemented
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic, complemented
194#1753C2211yescharacteristic, complemented
195C8×C22⋊C4C2211yescharacteristic
196#1750C2211yescharacteristic
197C4×C22⋊C8C2211yescharacteristic, complemented
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic
202#1726C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#555—24no—
210#555—24no—
211#546—24no—
212#546—24no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124—21no—
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×#120—21no—
240C2×#120—21no—
241C2×C4×D4—21no—
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117—21no—
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4—21no—
251C22×C4⋊C4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C42C2311yescharacteristic
256#490—24no—
257#489—42no—
258#486—42no—
259#436—24no—
260#435—24no—
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263#418—24no—
264#417—24no—
265#417—42no—
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#102—42no—
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303#405—42no—
304C4×M16—42no—
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#399—21no—
323#399—21no—
324#399—21no—
325#399—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#392—21no—
354#392—21no—
355#392—21no—
356#392—21no—
357#391—21no—
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#388D411yescharacteristic
394#388D411yescharacteristic
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387D411yescharacteristic
404#387D411yescharacteristic
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386D411yescharacteristic
417#386D411yescharacteristic
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385D411yescharacteristic
426#385D411yescharacteristic
427#384—21no—
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#382—21no—
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453#376C2311yescharacteristic
454C2×#95—21no—
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
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#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2×D411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2×D411yescharacteristic
530C23×C4C2×D411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—22no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C22×C8—22no—
543C22×C8—22no—
544C22×C8—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—22no—
554C4⋊Q8—22no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—82no—
560#127—22no—
561#127—41no—
562#127—41no—
563#127—41no—
564#125—22no—
565#125—41no—
566#124—22no—
567#124—22no—
568#124—41no—
569#124—41no—
570#124—44no—
571#124—44no—
572#123—44no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8—82no—
576C22⋊Q8—82no—
577C22⋊Q8—82no—
578C22⋊Q8—82no—
579C22⋊Q8—82no—
580#121—22no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—44no—
587#121—44no—
588#121—82no—
589#121—82no—
590#120—44no—
591#120—82no—
592#120—82no—
593C4×D4—22no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—82no—
598C4×D4#4114yes—
599C4×D4#4114yes—
600#117—22no—
601#117—22no—
602#117—22no—
603#117—22no—
604#117—22no—
605#117—41no—
606#117—41no—
607#117—41no—
608#117—44no—
609C2×C4⋊C4—22no—
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—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—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—82no—
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
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—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—44no—
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×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—41no—
708C2×C42—41no—
709C2×C42C2×D411yescharacteristic
710C2×C42C2×D411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C4⋊C8—22no—
717C4⋊C8—22no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102#4114yes—
750C22⋊C8—22no—
751C22⋊C8—22no—
752C22⋊C8—22no—
753C22⋊C8—22no—
754#97—22no—
755#97—22no—
756#97—22no—
757#97—22no—
758#97—41no—
759C4×C8—22no—
760C4×C8—22no—
761C4×C8—41no—
762C4×C8—41no—
763C4×C8—41no—
764C4×C8—41no—
765C4×C8—41no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
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#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804C24—21no—
805C24—21no—
806C24—21no—
807C24—42no—
808C24—42no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816#41—44no—
817#41—44no—
818#41—82no—
819#41—82no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—42no—
827C2×Q8—42no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—82no—
868C2×D4—82no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4#12414yes—
886C2×D4C2×#4112yes—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—22no—
897C22×C4—22no—
898C22×C4—21no—
899C22×C4—21no—
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—41no—
911C22×C4—41no—
912C22×C4—41no—
913C22×C4—41no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C2×#4112yes—
945C22×C4C2×#4112yes—
946C22×C4C2×#4112yes—
947C22×C4C2×#4112yes—
948C22×C4C2511yescharacteristic
949M16—44no—
950M16—44no—
951M16—44no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—44no—
975C2×C8C2×#4112yes—
976C2×C8H(5,𝔽2)12yes—
977C4⋊C4—22no—
978C4⋊C4—22no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—41no—
1003C4⋊C4—41no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—42no—
1010C4⋊C4—42no—
1011C4⋊C4—42no—
1012C4⋊C4—42no—
1013C4⋊C4—42no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
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#12414yes—
1034C4⋊C4C2×#4112yes—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4#12414yes—
1073C22⋊C4#12414yes—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—41no—
1083C42—41no—
1084C42—42no—
1085C42—42no—
1086C42—42no—
1087C42—81no—
1088C42—81no—
1089C42C2×#4112yes—
1090C42C2×#4112yes—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—22no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—84no—
1125C23—84no—
1126C23—162no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23—162no—
1131C23C2×#12412yes—
1132C23C2×#12412yes—
1133C23C23×D411yescharacteristic
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—162no—
1139Q8—162no—
1140Q8—162no—
1141D4—22no—
1142D4—22no—
1143D4—44no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—84no—
1155D4—84no—
1156D4—162no—
1157D4—162no—
1158D4—162no—
1159D4—162no—
1160D4—162no—
1161D4—162no—
1162D4—162no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
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—22no—
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—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
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—82no—
1241C2×C4—82no—
1242C2×C4—84no—
1243C2×C4—84no—
1244C2×C4—84no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4C2×#12412yes—
1249C2×C4C2×#12412yes—
1250C2×C4C2×#12412yes—
1251C2×C4C2×#12412yes—
1252C2×C4#57612yes—
1253C2×C4#57712yes—
1254C2×C4C22×#4111yescharacteristic
1255C2×C4C22×#4111yescharacteristic
1256C2×C4C22×#4111yescharacteristic
1257C2×C4C2×H(5,𝔽2)11yescharacteristic
1258C2×C4#58511yescharacteristic
1259C2×C4#58511yescharacteristic
1260C8—22no—
1261C8—22no—
1262C8—41no—
1263C8—41no—
1264C8—41no—
1265C8—41no—
1266C8—41no—
1267C8—41no—
1268C22—22no—
1269C22—22no—
1270C22—22no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—168no—
1304C22C22×#12411yescharacteristic
1305C22D4×#4111yescharacteristic
1306C22#349611yescharacteristic
1307C22C2×#57611yescharacteristic
1308C22C2×#57711yescharacteristic
1309C22#358511yescharacteristic
1310C22#358611yescharacteristic
1311C4—22no—
1312C4—22no—
1313C4—22no—
1314C4—22no—
1315C4—22no—
1316C4—22no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—42no—
1323C4—41no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4#347511yescharacteristic
1337C4#348111yescharacteristic
1338C4#351311yescharacteristic
1339C4#352111yescharacteristic
1340C2—42no—
1341C2—42no—
1342C2—82no—
1343C2—161no—
1344C2—161no—
1345C2#3623811yescharacteristic
1346C2#6062111yescharacteristic
1347C2#6062211yescharacteristic
1348C2#6155311yescharacteristic
1349C2#6155411yescharacteristic
1350C2#6230711yescharacteristic
1351C2#6231511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38090C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38098C2semidirect
3. #33283C2semidirect
4. #33054C2semidirect
5. #33048C2semidirect
6. #29363C2semidirect
7. #29345C2semidirect
8. #29328C2semidirect
9. #29136C2semidirect
10. #29116C2semidirect
11. #29107C2semidirect
12. #27813C2semidirect
13. #27783C2semidirect
14. #27751C2semidirect
15. #27744C2semidirect
16. #27726C2semidirect
17. #27722C2semidirect
18. #27720C2semidirect
19. #27700C2semidirect
20. #27282C2semidirect
21. #27280C2semidirect
22. #27279C2semidirect
23. #27254C2semidirect
24. #22503C2semidirect
25. #22492C2semidirect
26. #22427C2semidirect
27. #22419C2semidirect
28. #21652C2semidirect
29. #21093C2semidirect
30. #21091C2semidirect
31. #20490C2semidirect
35. C2×#489C22semidirect
44. C2×C4×M16C22semidirect
45. #2857C22semidirect
55. #2647C22semidirect
59. #2570C22semidirect
61. #2551C22semidirect
72. #2442C22semidirect
76. #2440C22semidirect
81. #2330C22semidirect
86. C2×#389C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2100C22semidirect
91. #2099C22semidirect
92. #2099C22semidirect
93. #2099C22semidirect
96. #2072C22semidirect
97. #2072C22semidirect
100. #2042C22semidirect
101. #2042C22semidirect
106. #2026C22semidirect
108. #2024C22semidirect
112. #1993C22semidirect
113. #1991C22semidirect
114. #1990C22semidirect
115. #1990C22semidirect
116. #1990C22semidirect
117. #1988C22semidirect
118. #1987C22semidirect
123. #1958C22semidirect
133. #1936C22semidirect
134. #1936C22semidirect
135. #1935C22semidirect
136. #1935C22semidirect
137. #1935C22semidirect
147. #1934C22semidirect
148. #1934C22semidirect
149. #1933C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1933C22semidirect
153. #1933C22semidirect
157. #1895C22semidirect
158. #1895C22semidirect
166. #1874C22semidirect
167. #1874C22semidirect
170. #1836C22semidirect
171. #1836C22semidirect
172. #1834C22semidirect
175. #1825C22semidirect
176. #1825C22semidirect
178. #1804C22semidirect
180. #1802C22semidirect
185. #1771C22semidirect
186. C8×C4⋊C4C22semidirect
187. #1768C22semidirect
189. #1762C22semidirect
191. C4×#102C22semidirect
193. #1753C22semidirect
194. #1753C22semidirect
197. C4×C22⋊C8C22semidirect
199. #1736C22semidirect
200. #1736C22semidirect
202. #1726C22semidirect

Maximal subgroups

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

subgroupindex
#380982
#380902
#332832
#330542
#330482
#293632
#293452
#293282
#291362
#291162
#291072
#278132
#277832
#277512
#277442
#277262
#277222
#277202
#277002
#272822
#272802
#272792
#272542
#225032
#224922
#224272
#224192
#216522
#210932
#210912
#204902