Finite Group Databasebeta

← #7208347

Subgroups — #7208347

Order 512.

1496 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45624C211yesmaximal, characteristic
2#45622C211yesmaximal, characteristic
3#32937C211yesmaximal, characteristic, complemented
4#32937C211yesmaximal, characteristic, complemented
5#32711C211yesmaximal, characteristic, complemented
6#32710C211yesmaximal, characteristic, complemented
7#32044C211yesmaximal, characteristic, complemented
8#32039C211yesmaximal, characteristic, complemented
9#31565C211yesmaximal, characteristic, complemented
10#31562C211yesmaximal, characteristic, complemented
11#31516C211yesmaximal, characteristic, complemented
12#31505C211yesmaximal, characteristic, complemented
13#31501C211yesmaximal, characteristic, complemented
14#31497C211yesmaximal, characteristic, complemented
15#31412C211yesmaximal, characteristic, complemented
16#31405C211yesmaximal, characteristic, complemented
17#31388C211yesmaximal, characteristic, complemented
18#31383C211yesmaximal, characteristic, complemented
19#28489C211yesmaximal, characteristic, complemented
20#28238C211yesmaximal, characteristic, complemented
21#28234C211yesmaximal, characteristic, complemented
22#27842C211yesmaximal, characteristic, complemented
23#27836C211yesmaximal, characteristic, complemented
24#27670C211yesmaximal, characteristic, complemented
25#25427C211yesmaximal, characteristic, complemented
26#25415C211yesmaximal, characteristic, complemented
27#25049C211yesmaximal, characteristic, complemented
28#25039C211yesmaximal, characteristic, complemented
29#24793C211yesmaximal, characteristic, complemented
30#24791C211yesmaximal, characteristic, complemented
31#21441C211yesmaximal, characteristic
32C23×M16C2211yescharacteristic
33C2×#494C2211yescharacteristic, complemented
34C2×#470C2211yescharacteristic
35C2×#470C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#470C2211yescharacteristic
38C2×#470C2211yescharacteristic, complemented
39C2×#470C2211yescharacteristic, complemented
40C2×#467C2211yescharacteristic
41C2×#467C2211yescharacteristic
42C2×#441C2211yescharacteristic, complemented
43C2×C4×Q16C2211yescharacteristic, complemented
44C2×#436C2211yescharacteristic
45C2×#436C2211yescharacteristic
46C2×#435C2211yescharacteristic
47C2×#428C2211yescharacteristic, complemented
48#2848C2211yescharacteristic
49#2848C2211yescharacteristic
50#2848C2211yescharacteristic
51#2848C2211yescharacteristic
52#2834—21no—
53#2827—21no—
54#2807—21no—
55#2796—21no—
56#2790—21no—
57#2790—21no—
58#2790—21no—
59#2757—21no—
60#2746—21no—
61#2746—21no—
62#2735—21no—
63#2735—21no—
64#2697—21no—
65#2685—21no—
66#2542C2211yescharacteristic
67#2542C2211yescharacteristic
68#2538C2211yescharacteristic
69#2536C2211yescharacteristic
70#2536C2211yescharacteristic
71#2536C2211yescharacteristic
72#2496C2211yescharacteristic
73#2495C2211yescharacteristic
74#2494C2211yescharacteristic
75#2494C2211yescharacteristic
76#2486C2211yescharacteristic
77#2485C2211yescharacteristic
78#2429C2211yescharacteristic
79#2429C2211yescharacteristic
80#2429C2211yescharacteristic
81#2429C2211yescharacteristic
82#2423C2211yescharacteristic
83#2421C2211yescharacteristic
84#2421C2211yescharacteristic
85#2421C2211yescharacteristic
86#2417C2211yescharacteristic
87#2417C2211yescharacteristic
88#2415C2211yescharacteristic
89#2415C2211yescharacteristic
90#2383—21no—
91#2376—21no—
92C4×#120C2211yescharacteristic
93#2101C2211yescharacteristic, complemented
94#2101C2211yescharacteristic, complemented
95#2101C2211yescharacteristic, complemented
96#2100C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2086C2211yescharacteristic, complemented
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic
101#2076C2211yescharacteristic
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic
104#2075C2211yescharacteristic
105#2074C2211yescharacteristic, complemented
106#2074C2211yescharacteristic, complemented
107#2074C2211yescharacteristic, complemented
108#2072C2211yescharacteristic, complemented
109#2068C2211yescharacteristic, complemented
110#2068C2211yescharacteristic, complemented
111#2066C2211yescharacteristic, complemented
112#2066C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2043C2211yescharacteristic, complemented
115#2043C2211yescharacteristic, complemented
116#2043C2211yescharacteristic, complemented
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic
123#2036C2211yescharacteristic
124#2036C2211yescharacteristic
125#2036C2211yescharacteristic, complemented
126#2036C2211yescharacteristic, complemented
127#2036C2211yescharacteristic, complemented
128#2035C2211yescharacteristic
129#2035C2211yescharacteristic
130#2035C2211yescharacteristic
131#2035C2211yescharacteristic
132#2035C2211yescharacteristic, complemented
133#2001C2211yescharacteristic
134#2001C2211yescharacteristic
135#2001C2211yescharacteristic
136#2001C2211yescharacteristic
137#2001C2211yescharacteristic
138#2001C2211yescharacteristic
139#2001C2211yescharacteristic, complemented
140#2001C2211yescharacteristic, complemented
141#1981C2211yescharacteristic, complemented
142#1981C2211yescharacteristic, complemented
143#1971C2211yescharacteristic, complemented
144#1969C2211yescharacteristic, complemented
145#1943C2211yescharacteristic, complemented
146#1942C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1941C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1919C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1894C2211yescharacteristic
154#1894C2211yescharacteristic
155#1894C2211yescharacteristic
156#1894C2211yescharacteristic
157#1894C2211yescharacteristic
158#1894C2211yescharacteristic
159#1894C2211yescharacteristic
160#1894C2211yescharacteristic
161#1892C2211yescharacteristic
162#1892C2211yescharacteristic
163#1892C2211yescharacteristic
164#1892C2211yescharacteristic
165#1878C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1878C2211yescharacteristic, complemented
168#1878C2211yescharacteristic, complemented
169#1873C2211yescharacteristic, complemented
170#1873C2211yescharacteristic, complemented
171#1872C2211yescharacteristic, complemented
172#1872C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1870C2211yescharacteristic
175#1869C2211yescharacteristic
176#1865C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1863C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1851C2211yescharacteristic
181#1851C2211yescharacteristic
182#1850C2211yescharacteristic
183#1847C2211yescharacteristic, complemented
184#1846C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1824C2211yescharacteristic, complemented
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic, complemented
192#1807C2211yescharacteristic
193#1807C2211yescharacteristic
194#1805C2211yescharacteristic, complemented
195#1805C2211yescharacteristic, complemented
196#1805C2211yescharacteristic, complemented
197#1803C2211yescharacteristic, complemented
198#1779C2211yescharacteristic
199C4×#106C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C24×C4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×M16—42no—
209C22×M16—42no—
210C22×M16—42no—
211C22×M16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×#126—21no—
221C2×#123—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#120D411yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248#494—42no—
249#470—42no—
250#470—42no—
251#470—42no—
252#470—42no—
253#470—42no—
254#470—42no—
255#467—42no—
256#467—42no—
257#441—42no—
258C4×Q16—42no—
259#436—42no—
260#436—42no—
261#435—42no—
262#428—42no—
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#401—21no—
315#401—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#399—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#398—21no—
333#398—21no—
334#398—21no—
335#398—21no—
336#398—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#396—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#390—21no—
367#390—21no—
368#390—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
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#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#386—21no—
413#386—21no—
414#386D411yescharacteristic
415#386D411yescharacteristic
416#386D411yescharacteristic
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#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385D411yescharacteristic
430#385D411yescharacteristic
431#385D411yescharacteristic
432#384—21no—
433#384—21no—
434#384C2311yescharacteristic
435#383—21no—
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#381—21no—
440#380—21no—
441#380—21no—
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#379—21no—
457#379—21no—
458#379—21no—
459#379—21no—
460#379D411yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×D4C2×D411yescharacteristic
502C22×D4C2×D411yescharacteristic
503C22×D4C2×D411yescharacteristic
504C23×C4—21no—
505C23×C4—41no—
506C23×C4—41no—
507C23×C4—41no—
508C23×C4—41no—
509C23×C4—41no—
510C23×C4—41no—
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C23×C4C2411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×Q16—22no—
519C2×Q16—22no—
520C2×Q16—22no—
521C2×Q16—22no—
522C2×Q16—22no—
523C2×Q16—22no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×Q16—41no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×M16—22no—
531C2×M16—22no—
532C2×M16—22no—
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—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—416no—
546C22×C8—22no—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564#126—44no—
565#123—44no—
566C22⋊Q8—41no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—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—41no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598#120—42no—
599C4×Q8—41no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613#117—41no—
614#117—41no—
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—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
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—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720#107—22no—
721#107—22no—
722#107—41no—
723#107—41no—
724#107—41no—
725#107—41no—
726#106—22no—
727#106—22no—
728#106—22no—
729#106—22no—
730#106—41no—
731#106—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768#97—22no—
769C4×C8—22no—
770C4×C8—22no—
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#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#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—22no—
816C24—41no—
817C24—41no—
818C24—41no—
819C24—41no—
820C24—41no—
821C24—41no—
822C24C22×D411yescharacteristic
823C24C22×D411yescharacteristic
824C24C22×D411yescharacteristic
825C24C22×D411yescharacteristic
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
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—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×D4—22no—
851C2×D4—22no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—41no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
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—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—41no—
900C22×C4—41no—
901C22×C4—41no—
902C22×C4—41no—
903C22×C4—41no—
904C22×C4—41no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—42no—
913C22×C4—81no—
914C22×C4—81no—
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×C4C2511yescharacteristic
926Q16—44no—
927Q16—44no—
928Q16—82no—
929Q16—82no—
930M16—44no—
931M16—44no—
932M16—44no—
933M16—44no—
934M16—44no—
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—21no—
956C2×C8—44no—
957C2×C8—44no—
958C2×C8H(5,𝔽2)12yes—
959C2×C8H(5,𝔽2)12yes—
960C2×C8H(5,𝔽2)12yes—
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—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—81no—
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—81no—
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—
1023C22⋊C4—22no—
1024C22⋊C4—22no—
1025C22⋊C4—22no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
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—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—42no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
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—21no—
1104C23—21no—
1105C23—21no—
1106C23—44no—
1107C23—82no—
1108C23—82no—
1109C23—82no—
1110C23—82no—
1111C23—82no—
1112C23—82no—
1113C23#57812yes—
1114C23C23×D411yescharacteristic
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131D4—82no—
1132D4—82no—
1133D4—82no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
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—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—44no—
1164C2×C4—44no—
1165C2×C4—44no—
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—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—162no—
1231C2×C4#57512yes—
1232C2×C4C2×H(5,𝔽2)11yescharacteristic
1233C2×C4C2×H(5,𝔽2)11yescharacteristic
1234C2×C4C2×H(5,𝔽2)11yescharacteristic
1235C2×C4#58511yescharacteristic
1236C2×C4#58511yescharacteristic
1237C2×C4#58511yescharacteristic
1238C8—41no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8#56014yes—
1246C22—22no—
1247C22—22no—
1248C22—22no—
1249C22—41no—
1250C22—41no—
1251C22—41no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
1256C22—41no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—88no—
1275C22#349611yescharacteristic
1276C22#349611yescharacteristic
1277C22#349611yescharacteristic
1278C22C2×#57511yescharacteristic
1279C22C2×#57811yescharacteristic
1280C22#358611yescharacteristic
1281C22#358611yescharacteristic
1282C4—22no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4C2×#56011yescharacteristic
1309C4#353911yescharacteristic
1310C4#353911yescharacteristic
1311C4#354011yescharacteristic
1312C2—42no—
1313C2—81no—
1314C2—81no—
1315C2—81no—
1316C2#4547811yescharacteristic
1317C2#6226411yescharacteristic
1318C2#6229111yescharacteristic
1319C2#6230211yescharacteristic
1320C2#6230611yescharacteristic
1321C2#6231711yescharacteristic
1322C2#6231711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#120D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#120 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #32937C2semidirect
4. #32937C2semidirect
5. #32711C2semidirect
6. #32710C2semidirect
7. #32044C2semidirect
8. #32039C2semidirect
9. #31565C2semidirect
10. #31562C2semidirect
11. #31516C2semidirect
12. #31505C2semidirect
13. #31501C2semidirect
14. #31497C2semidirect
15. #31412C2semidirect
16. #31405C2semidirect
17. #31388C2semidirect
18. #31383C2semidirect
19. #28489C2semidirect
20. #28238C2semidirect
21. #28234C2semidirect
22. #27842C2semidirect
23. #27836C2semidirect
24. #27670C2semidirect
25. #25427C2semidirect
26. #25415C2semidirect
27. #25049C2semidirect
28. #25039C2semidirect
29. #24793C2semidirect
30. #24791C2semidirect
33. C2×#494C22semidirect
38. C2×#470C22semidirect
39. C2×#470C22semidirect
42. C2×#441C22semidirect
43. C2×C4×Q16C22semidirect
47. C2×#428C22semidirect
93. #2101C22semidirect
94. #2101C22semidirect
95. #2101C22semidirect
96. #2100C22semidirect
97. #2088C22semidirect
98. #2086C22semidirect
105. #2074C22semidirect
106. #2074C22semidirect
107. #2074C22semidirect
108. #2072C22semidirect
109. #2068C22semidirect
110. #2068C22semidirect
111. #2066C22semidirect
112. #2066C22semidirect
113. #2043C22semidirect
114. #2043C22semidirect
115. #2043C22semidirect
116. #2043C22semidirect
125. #2036C22semidirect
126. #2036C22semidirect
127. #2036C22semidirect
132. #2035C22semidirect
139. #2001C22semidirect
140. #2001C22semidirect
141. #1981C22semidirect
142. #1981C22semidirect
143. #1971C22semidirect
144. #1969C22semidirect
145. #1943C22semidirect
146. #1942C22semidirect
147. #1941C22semidirect
148. #1941C22semidirect
149. #1921C22semidirect
150. #1919C22semidirect
151. #1918C22semidirect
152. #1918C22semidirect
165. #1878C22semidirect
166. #1878C22semidirect
167. #1878C22semidirect
168. #1878C22semidirect
169. #1873C22semidirect
170. #1873C22semidirect
171. #1872C22semidirect
172. #1872C22semidirect
176. #1865C22semidirect
177. #1863C22semidirect
178. #1863C22semidirect
179. #1863C22semidirect
183. #1847C22semidirect
184. #1846C22semidirect
185. #1825C22semidirect
186. #1824C22semidirect
191. #1809C22semidirect
194. #1805C22semidirect
195. #1805C22semidirect
196. #1805C22semidirect
197. #1803C22semidirect
199. C4×#106C22semidirect

Maximal subgroups

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

subgroupindex
#456242
#456222
#329372
#327112
#327102
#320442
#320392
#315652
#315622
#315162
#315052
#315012
#314972
#314122
#314052
#313882
#313832
#284892
#282382
#282342
#278422
#278362
#276702
#254272
#254152
#250492
#250392
#247932
#247912
#214412