Finite Group Databasebeta

← #6605993

Subgroups — #6605993

Order 512.

1606 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38098C211yesmaximal, characteristic, complemented
2#38095C211yesmaximal, characteristic
3#33283C211yesmaximal, characteristic, complemented
4#33057C211yesmaximal, characteristic, complemented
5#33045C211yesmaximal, characteristic, complemented
6#29363C211yesmaximal, characteristic, complemented
7#29343C211yesmaximal, characteristic, complemented
8#29336C211yesmaximal, characteristic, complemented
9#29137C211yesmaximal, characteristic, complemented
10#29118C211yesmaximal, characteristic, complemented
11#29113C211yesmaximal, characteristic, complemented
12#27823C211yesmaximal, characteristic, complemented
13#27783C211yesmaximal, characteristic, complemented
14#27753C211yesmaximal, characteristic, complemented
15#27742C211yesmaximal, characteristic, complemented
16#27718C211yesmaximal, characteristic, complemented
17#27708C211yesmaximal, characteristic, complemented
18#27706C211yesmaximal, characteristic, complemented
19#27704C211yesmaximal, characteristic, complemented
20#27276C211yesmaximal, characteristic, complemented
21#27275C211yesmaximal, characteristic, complemented
22#27270C211yesmaximal, characteristic, complemented
23#27266C211yesmaximal, characteristic, complemented
24#22503C211yesmaximal, characteristic, complemented
25#22492C211yesmaximal, characteristic, complemented
26#22429C211yesmaximal, characteristic, complemented
27#22421C211yesmaximal, characteristic, complemented
28#21643C211yesmaximal, characteristic, complemented
29#21093C211yesmaximal, characteristic, complemented
30#21090C211yesmaximal, characteristic, complemented
31#20487C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#488C2211yescharacteristic
36C2×#486C2211yescharacteristic
37C2×#436C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#417C2211yescharacteristic
40C2×#417C2211yescharacteristic
41C2×#419C2211yescharacteristic
42C22×#103C2211yescharacteristic
43C2×#405C2211yescharacteristic
44C2×C4×M16C2211yescharacteristic
45#2857C2211yescharacteristic
46#2850C2211yescharacteristic
47#2807—21no—
48#2792—21no—
49#2774—21no—
50#2729—21no—
51#2712—21no—
52#2712—21no—
53#2688—21no—
54#2688—21no—
55#2647C2211yescharacteristic
56#2640C2211yescharacteristic
57#2628C2211yescharacteristic
58#2619C2211yescharacteristic
59#2570C2211yescharacteristic
60#2568C2211yescharacteristic
61#2564—21no—
62#2551C2211yescharacteristic
63#2544C2211yescharacteristic
64#2505—21no—
65#2500C2211yescharacteristic
66#2499C2211yescharacteristic
67#2477—21no—
68#2477—21no—
69#2459—21no—
70#2459—21no—
71#2449—21no—
72#2442C2211yescharacteristic
73#2441C2211yescharacteristic
74#2440—21no—
75#2440C2211yescharacteristic
76#2440C2211yescharacteristic
77#2436C2211yescharacteristic
78#2431C2211yescharacteristic
79#2352C2211yescharacteristic
80D4×C4⋊C4C2211yescharacteristic
81#2330C2211yescharacteristic
82#2326C2211yescharacteristic
83#2317C2211yescharacteristic
84#2310C2211yescharacteristic
85#2297C2211yescharacteristic
86C2×#389C2211yescharacteristic
87#2290C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2101C2211yescharacteristic
92#2100C2211yescharacteristic
93#2099C2211yescharacteristic
94#2074C2211yescharacteristic
95#2074C2211yescharacteristic
96#2072C2211yescharacteristic
97#2072C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2042C2211yescharacteristic
101#2042C2211yescharacteristic
102#2042C2211yescharacteristic
103#2042C2211yescharacteristic
104#2041C2211yescharacteristic
105#2041C2211yescharacteristic
106#2026C2211yescharacteristic
107#2025C2211yescharacteristic
108#2024C2211yescharacteristic
109#2024C2211yescharacteristic
110#2024C2211yescharacteristic
111#2023C2211yescharacteristic
112#1993C2211yescharacteristic
113#1993C2211yescharacteristic
114#1993C2211yescharacteristic
115#1992C2211yescharacteristic
116#1990C2211yescharacteristic
117#1988C2211yescharacteristic
118#1987C2211yescharacteristic
119#1983C2211yescharacteristic
120#1983C2211yescharacteristic
121#1961C2211yescharacteristic
122#1959C2211yescharacteristic
123#1959C2211yescharacteristic
124#1959C2211yescharacteristic
125#1958C2211yescharacteristic
126#1936C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1935C2211yescharacteristic
137#1935C2211yescharacteristic
138#1935C2211yescharacteristic
139#1935C2211yescharacteristic
140#1935C2211yescharacteristic
141#1935C2211yescharacteristic
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1933C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1933C2211yescharacteristic
153#1933C2211yescharacteristic
154#1895C2211yescharacteristic
155#1895C2211yescharacteristic
156#1895C2211yescharacteristic
157#1895C2211yescharacteristic
158#1894C2211yescharacteristic
159#1894C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic
168#1872C2211yescharacteristic
169#1872C2211yescharacteristic
170#1836C2211yescharacteristic
171#1835C2211yescharacteristic
172#1834C2211yescharacteristic
173#1825C2211yescharacteristic
174#1825C2211yescharacteristic
175#1825C2211yescharacteristic
176#1825C2211yescharacteristic
177#1805C2211yescharacteristic
178#1804C2211yescharacteristic
179#1803C2211yescharacteristic
180#1802C2211yescharacteristic
181#1788C2211yescharacteristic
182#1788C2211yescharacteristic
183#1787C2211yescharacteristic
184#1787C2211yescharacteristic
185#1771C2211yescharacteristic
186#1770C2211yescharacteristic
187#1768C2211yescharacteristic
188#1763C2211yescharacteristic
189#1762C2211yescharacteristic
190C4×#103C2211yescharacteristic
191C4×#102C2211yescharacteristic
192#1753C2211yescharacteristic
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic
195#1752C2211yescharacteristic
196#1750C2211yescharacteristic
197#1749C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#555—24no—
210#555—24no—
211#548—24no—
212#548—24no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#124—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×#121—21no—
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C22×C4⋊C4—21no—
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C42C2311yescharacteristic
250#489—42no—
251#488—24no—
252#486—42no—
253#436—24no—
254#435—24no—
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257#419—24no—
258#417—24no—
259#417—42no—
260C2×#103—42no—
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297#405—42no—
298C4×M16—42no—
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#400—21no—
318#399—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#396—21no—
331#395—21no—
332#395—21no—
333#395—21no—
334#395—21no—
335#395—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#393—21no—
343#393—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#392—21no—
348#392—21no—
349#392—21no—
350#392—21no—
351#391—21no—
352#391—21no—
353#391—21no—
354#391—21no—
355#391—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388D411yescharacteristic
392#388D411yescharacteristic
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387D411yescharacteristic
402#387D411yescharacteristic
403#386—21no—
404#386—21no—
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#386D411yescharacteristic
415#386D411yescharacteristic
416#385—21no—
417#385—21no—
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#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#381—21no—
438#381—21no—
439#380—21no—
440#380—21no—
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
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
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—41no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8—41no—
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C4⋊Q8—22no—
551C4⋊Q8—22no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556C4⋊Q8—82no—
557#127—41no—
558#127—41no—
559#125—22no—
560#125—41no—
561#124—22no—
562#124—22no—
563#124—22no—
564#124—41no—
565#124—41no—
566#124—41no—
567#124—44no—
568#124—44no—
569#124—44no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—44no—
573C22⋊Q8—82no—
574C22⋊Q8—82no—
575C22⋊Q8—82no—
576#121—22no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—22no—
582#121—44no—
583#121—44no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589C4×D4—82no—
590C4×D4#4114yes—
591C4×D4#4114yes—
592#117—22no—
593#117—22no—
594#117—22no—
595#117—22no—
596#117—22no—
597#117—41no—
598#117—41no—
599#117—41no—
600#117—44no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
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—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—82no—
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—41no—
694C2×C42—41no—
695C2×C42C2×D411yescharacteristic
696C2×C42C2×D411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C4⋊C8—22no—
703C4⋊C8—22no—
704#103—22no—
705#103—22no—
706#103—22no—
707#103—22no—
708#103—22no—
709#103—22no—
710#103—22no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103#4114yes—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—22no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736C22⋊C8—22no—
737C22⋊C8—22no—
738C22⋊C8—22no—
739C22⋊C8—22no—
740#97—22no—
741#97—22no—
742#97—41no—
743#97—41no—
744#97—41no—
745#97—41no—
746#97—41no—
747C4×C8—22no—
748C4×C8—22no—
749C4×C8—22no—
750C4×C8—22no—
751C4×C8—41no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
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#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798C24—21no—
799C24—21no—
800C24C22×D411yescharacteristic
801C24C22×D411yescharacteristic
802#41—44no—
803#41—44no—
804#41—82no—
805#41—82no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—42no—
818C2×Q8—42no—
819C2×Q8—44no—
820C2×Q8—44no—
821C2×Q8—42no—
822C2×Q8—42no—
823C2×Q8—81no—
824C2×Q8—81no—
825C2×Q8—81no—
826C2×Q8—81no—
827C2×Q8—81no—
828C2×Q8—81no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—82no—
832C2×Q8—82no—
833C2×Q8C2×#4112yes—
834C2×D4—21no—
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—41no—
847C2×D4—41no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4—81no—
866C2×D4#12414yes—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—41no—
890C22×C4—41no—
891C22×C4—41no—
892C22×C4—41no—
893C22×C4—41no—
894C22×C4—41no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C2×#4112yes—
926C22×C4C2×#4112yes—
927C22×C4C2×#4112yes—
928C22×C4C2×#4112yes—
929C22×C4C2511yescharacteristic
930M16—44no—
931M16—44no—
932M16—44no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—44no—
956C2×C8C2×#4112yes—
957C2×C8H(5,𝔽2)12yes—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—41no—
982C4⋊C4—41no—
983C4⋊C4—41no—
984C4⋊C4—41no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4#12414yes—
1014C4⋊C4C2×#4112yes—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4#12414yes—
1048C22⋊C4#12414yes—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—41no—
1058C42—41no—
1059C42—42no—
1060C42—42no—
1061C42—42no—
1062C42—42no—
1063C42—81no—
1064C42—81no—
1065C42C2×#4112yes—
1066C42C2×#4112yes—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—21no—
1074C23—21no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23C2×#12412yes—
1094C23C2×#12412yes—
1095C23C23×D411yescharacteristic
1096Q8—22no—
1097Q8—22no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—84no—
1105Q8—162no—
1106Q8—162no—
1107Q8—162no—
1108D4—44no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—84no—
1118D4—84no—
1119D4—162no—
1120D4—162no—
1121D4—162no—
1122D4—162no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—84no—
1206C2×C4—84no—
1207C2×C4—82no—
1208C2×C4—82no—
1209C2×C4—84no—
1210C2×C4—84no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4C2×#12412yes—
1214C2×C4C2×#12412yes—
1215C2×C4C2×#12412yes—
1216C2×C4C2×#12412yes—
1217C2×C4C22×#4111yescharacteristic
1218C2×C4C22×#4111yescharacteristic
1219C2×C4C22×#4111yescharacteristic
1220C2×C4C2×H(5,𝔽2)11yescharacteristic
1221C2×C4#58511yescharacteristic
1222C2×C4#58511yescharacteristic
1223C8—22no—
1224C8—22no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—22no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—41no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22C22×#12411yescharacteristic
1260C22D4×#4111yescharacteristic
1261C22#349611yescharacteristic
1262C22#358511yescharacteristic
1263C22#358511yescharacteristic
1264C22#358611yescharacteristic
1265C22#358611yescharacteristic
1266C4—22no—
1267C4—22no—
1268C4—22no—
1269C4—22no—
1270C4—41no—
1271C4—42no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—42no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4#347511yescharacteristic
1293C4#348111yescharacteristic
1294C4#351311yescharacteristic
1295C4#352111yescharacteristic
1296C2—42no—
1297C2—42no—
1298C2—161no—
1299C2—161no—
1300C2#3623811yescharacteristic
1301C2#6062111yescharacteristic
1302C2#6062511yescharacteristic
1303C2#6150811yescharacteristic
1304C2#6151611yescharacteristic
1305C2#6228611yescharacteristic
1306C2#6228711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#38095C2
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. #33057C2semidirect
5. #33045C2semidirect
6. #29363C2semidirect
7. #29343C2semidirect
8. #29336C2semidirect
9. #29137C2semidirect
10. #29118C2semidirect
11. #29113C2semidirect
12. #27823C2semidirect
13. #27783C2semidirect
14. #27753C2semidirect
15. #27742C2semidirect
16. #27718C2semidirect
17. #27708C2semidirect
18. #27706C2semidirect
19. #27704C2semidirect
20. #27276C2semidirect
21. #27275C2semidirect
22. #27270C2semidirect
23. #27266C2semidirect
24. #22503C2semidirect
25. #22492C2semidirect
26. #22429C2semidirect
27. #22421C2semidirect
28. #21643C2semidirect
29. #21093C2semidirect
30. #21090C2semidirect
31. #20487C2semidirect

Maximal subgroups

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

subgroupindex
#380982
#380952
#332832
#330572
#330452
#293632
#293432
#293362
#291372
#291182
#291132
#278232
#277832
#277532
#277422
#277182
#277082
#277062
#277042
#272762
#272752
#272702
#272662
#225032
#224922
#224292
#224212
#216432
#210932
#210902
#204872