Finite Group Databasebeta

← #7005590

Subgroups — #7005590

Order 512.

1625 conjugacy classes of subgroups.

The subgroup lattice has 1382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44887C211yesmaximal, characteristic
2#42920C211yesmaximal, characteristic, complemented
3#32126C211yesmaximal, characteristic, complemented
4#31997C211yesmaximal, characteristic, complemented
5#31717C211yesmaximal, characteristic, complemented
6#31630C211yesmaximal, characteristic, complemented
7#31395C211yesmaximal, characteristic, complemented
8#31351C211yesmaximal, characteristic, complemented
9#31260C211yesmaximal, characteristic, complemented
10#31028C211yesmaximal, characteristic, complemented
11#28979C211yesmaximal, characteristic, complemented
12#28555C211yesmaximal, characteristic, complemented
13#28155C211yesmaximal, characteristic, complemented
14#28065C211yesmaximal, characteristic, complemented
15#27720C211yesmaximal, characteristic, complemented
16#27520C211yesmaximal, characteristic, complemented
17#26408C211yesmaximal, characteristic, complemented
18#26303C211yesmaximal, characteristic, complemented
19#26211C211yesmaximal, characteristic, complemented
20#26157C211yesmaximal, characteristic, complemented
21#25552C211yesmaximal, characteristic, complemented
22#25249C211yesmaximal, characteristic, complemented
23#25213C211yesmaximal, characteristic, complemented
24#24921C211yesmaximal, characteristic, complemented
25#24563C211yesmaximal, characteristic, complemented
26#24394C211yesmaximal, characteristic, complemented
27#23643C211yesmaximal, characteristic, complemented
28#23040C211yesmaximal, characteristic, complemented
29#22847C211yesmaximal, characteristic, complemented
30#22489C211yesmaximal, characteristic, complemented
31#21770C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#485C2211yescharacteristic, complemented
35C2×#482C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#435C2211yescharacteristic, complemented
41C2×C8×D4C2211yescharacteristic, complemented
42C2×#428C2211yescharacteristic, complemented
43C2×#408C2211yescharacteristic
44C2×#408C2211yescharacteristic
45#2831—21no—
46#2797—21no—
47#2779—21no—
48#2730—21no—
49#2712—21no—
50#2702—21no—
51#2684—21no—
52#2673—21no—
53#2670—21no—
54#2662—21no—
55#2651—21no—
56#2616C2211yescharacteristic
57#2586—21no—
58#2547C2211yescharacteristic
59#2544—21no—
60#2538C2211yescharacteristic, complemented
61#2535C2211yescharacteristic
62#2500C2211yescharacteristic
63#2497C2211yescharacteristic
64#2496C2211yescharacteristic, complemented
65#2492C2211yescharacteristic, complemented
66#2491C2211yescharacteristic
67#2485C2211yescharacteristic, complemented
68#2474—21no—
69#2440C2211yescharacteristic, complemented
70#2439C2211yescharacteristic
71#2424—21no—
72#2423C2211yescharacteristic
73#2422C2211yescharacteristic
74#2417C2211yescharacteristic, complemented
75#2416C2211yescharacteristic
76#2415C2211yescharacteristic
77#2414C2211yescharacteristic
78#2411—21no—
79#2408C2211yescharacteristic
80#2388C2211yescharacteristic
81#2362C2211yescharacteristic, complemented
82#2361C2211yescharacteristic
83#2354C2211yescharacteristic
84#2354C2211yescharacteristic, complemented
85D4×C22⋊C4C2211yescharacteristic
86#2311C2211yescharacteristic
87#2311C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2093C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2086C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic, complemented
100#2077C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic, complemented
104#2076C2211yescharacteristic, complemented
105#2075C2211yescharacteristic
106#2075C2211yescharacteristic
107#2075C2211yescharacteristic, complemented
108#2072C2211yescharacteristic, complemented
109#2071C2211yescharacteristic
110#2067C2211yescharacteristic
111#2065C2211yescharacteristic
112#2057C2211yescharacteristic, complemented
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2036C2211yescharacteristic
116#2036C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2024C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1990C2211yescharacteristic, complemented
129#1990C2211yescharacteristic, complemented
130#1988C2211yescharacteristic, complemented
131#1987C2211yescharacteristic, complemented
132#1968C2211yescharacteristic
133#1954C2211yescharacteristic
134#1948C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1933C2211yescharacteristic, complemented
140#1927C2211yescharacteristic, complemented
141#1926C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1924C2211yescharacteristic
145#1923C2211yescharacteristic
146#1919C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1895C2211yescharacteristic
149#1895C2211yescharacteristic
150#1895C2211yescharacteristic
151#1894C2211yescharacteristic, complemented
152#1893C2211yescharacteristic
153#1893C2211yescharacteristic
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic
156#1893C2211yescharacteristic
157#1892C2211yescharacteristic, complemented
158#1892C2211yescharacteristic, complemented
159#1880C2211yescharacteristic
160#1877C2211yescharacteristic
161#1875C2211yescharacteristic
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic, complemented
168#1872C2211yescharacteristic, complemented
169#1870C2211yescharacteristic, complemented
170#1869C2211yescharacteristic
171#1869C2211yescharacteristic, complemented
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic, complemented
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic, complemented
178#1854C2211yescharacteristic, complemented
179#1852C2211yescharacteristic, complemented
180#1851C2211yescharacteristic, complemented
181#1850C2211yescharacteristic, complemented
182#1836C2211yescharacteristic, complemented
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic
185#1825C2211yescharacteristic, complemented
186#1825C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1808C2211yescharacteristic, complemented
189#1805C2211yescharacteristic, complemented
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195C4×#107C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic, complemented
198C8×C22⋊C4C2211yescharacteristic, complemented
199#1736C2211yescharacteristic, complemented
200#1735C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#555—24no—
213#555—42no—
214#535—24no—
215#535—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127—21no—
219C2×#126—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121—21no—
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×#117—21no—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C22×C4⋊C4C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258#485—42no—
259#482—42no—
260#468—24no—
261#465—42no—
262#450—42no—
263#440—42no—
264#435—42no—
265C8×D4—42no—
266#428—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
300#408—42no—
301#408—42no—
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×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#400—21no—
318#400—21no—
319#399—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#395—21no—
337#395—21no—
338#395D411yescharacteristic
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394D411yescharacteristic
352#394D411yescharacteristic
353#394D411yescharacteristic
354#393—21no—
355#393—21no—
356#393—21no—
357#393D411yescharacteristic
358#392—21no—
359#392—21no—
360#392—21no—
361#392D411yescharacteristic
362#392D411yescharacteristic
363#392D411yescharacteristic
364#391—21no—
365#391—21no—
366#391—21no—
367#391—21no—
368#391—21no—
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#389—21no—
382#389—21no—
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
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#388—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#382C2311yescharacteristic
429#380—21no—
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
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—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8C2×D411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—21no—
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2×D411yescharacteristic
519C22×D4C2×D411yescharacteristic
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×M16—22no—
540C2×M16—22no—
541C2×M16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16—41no—
545C22×C8—22no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8—41no—
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C4⋊Q8—22no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566#127—44no—
567#126—82no—
568#124—44no—
569#124—44no—
570#124—44no—
571#124—82no—
572#124—82no—
573#123—82no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—82no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—44no—
593#121—41no—
594#121—41no—
595#121—82no—
596#121#4114yes—
597#120—44no—
598#120—44no—
599#120—82no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—82no—
613#117—22no—
614#117—22no—
615#117—22no—
616#117—22no—
617#117—44no—
618#117—41no—
619#117—41no—
620#117—41no—
621#117—41no—
622#117—41no—
623#117—41no—
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—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
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—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—82no—
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—21no—
721C2×C42—21no—
722C2×C42—21no—
723C2×C42—21no—
724C2×C42—21no—
725C2×C42—21no—
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—22no—
730#107—22no—
731#107—41no—
732#107—41no—
733#107—41no—
734#107—41no—
735#106—22no—
736#106—41no—
737#106—41no—
738#106—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742#103—22no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#102—22no—
749#102—22no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8—22no—
766C22⋊C8—22no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773#97—22no—
774C4×C8—41no—
775C4×C8—41no—
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#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—42no—
814C24—42no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24C22×D411yescharacteristic
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823C24C22×D411yescharacteristic
824#41—82no—
825#41—82no—
826#41—82no—
827#41—82no—
828C2×Q8—22no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—41no—
836C2×Q8—41no—
837C2×Q8—42no—
838C2×Q8—42no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×D4—22no—
844C2×D4—22no—
845C2×D4—24no—
846C2×D4—22no—
847C2×D4—22no—
848C2×D4—22no—
849C2×D4—22no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—41no—
862C2×D4—41no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—41no—
872C2×D4—41no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—81no—
880C2×D4—82no—
881C2×D4—82no—
882C2×D4—82no—
883C2×D4—82no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4C2×#4112yes—
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—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C2×#4112yes—
957C22×C4H(5,𝔽2)12yes—
958C22×C4C2511yescharacteristic
959SD16—44no—
960SD16—82no—
961M16—44no—
962M16—82no—
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—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—82no—
987C2×C8—82no—
988C2×C8—82no—
989C2×C8H(5,𝔽2)12yes—
990C4⋊C4—22no—
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—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4C2×#4112yes—
1040C22⋊C4—22no—
1041C22⋊C4—24no—
1042C22⋊C4—22no—
1043C22⋊C4—22no—
1044C22⋊C4—22no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—41no—
1052C22⋊C4—41no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—42no—
1098C42—42no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—22no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—84no—
1148C23—84no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23—162no—
1154C23#54612yes—
1155C23C23×D411yescharacteristic
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—82no—
1161Q8—162no—
1162Q8—162no—
1163D4—22no—
1164D4—22no—
1165D4—44no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—82no—
1173D4—82no—
1174D4—82no—
1175D4—82no—
1176D4—84no—
1177D4—82no—
1178D4—84no—
1179D4—162no—
1180D4—162no—
1181D4—162no—
1182D4—162no—
1183D4—162no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—84no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4—162no—
1273C2×C4#54612yes—
1274C2×C4#57612yes—
1275C2×C4#57712yes—
1276C2×C4C22×#4111yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×H(5,𝔽2)11yescharacteristic
1279C2×C4#58511yescharacteristic
1280C2×C4#58511yescharacteristic
1281C2×C4#58511yescharacteristic
1282C8—22no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—42no—
1301C22—42no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—41no—
1314C22—41no—
1315C22—41no—
1316C22—41no—
1317C22—42no—
1318C22—41no—
1319C22—41no—
1320C22—41no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—168no—
1333C22C2×#54611yescharacteristic
1334C22#348511yescharacteristic
1335C22#349611yescharacteristic
1336C22C2×#57611yescharacteristic
1337C22C2×#57711yescharacteristic
1338C22#358411yescharacteristic
1339C22#358611yescharacteristic
1340C4—22no—
1341C4—22no—
1342C4—22no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—42no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4#351311yescharacteristic
1365C4#352111yescharacteristic
1366C4#355811yescharacteristic
1367C4#356011yescharacteristic
1368C2—42no—
1369C2—81no—
1370C2—81no—
1371C2—81no—
1372C2—82no—
1373C2—161no—
1374C2#4302111yescharacteristic
1375C2#6117211yescharacteristic
1376C2#6119911yescharacteristic
1377C2#6177211yescharacteristic
1378C2#6180311yescharacteristic
1379C2#6230911yescharacteristic
1380C2#6234211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#44887C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42920C2semidirect
3. #32126C2semidirect
4. #31997C2semidirect
5. #31717C2semidirect
6. #31630C2semidirect
7. #31395C2semidirect
8. #31351C2semidirect
9. #31260C2semidirect
10. #31028C2semidirect
11. #28979C2semidirect
12. #28555C2semidirect
13. #28155C2semidirect
14. #28065C2semidirect
15. #27720C2semidirect
16. #27520C2semidirect
17. #26408C2semidirect
18. #26303C2semidirect
19. #26211C2semidirect
20. #26157C2semidirect
21. #25552C2semidirect
22. #25249C2semidirect
23. #25213C2semidirect
24. #24921C2semidirect
25. #24563C2semidirect
26. #24394C2semidirect
27. #23643C2semidirect
28. #23040C2semidirect
29. #22847C2semidirect
30. #22489C2semidirect
31. #21770C2semidirect
34. C2×#485C22semidirect
40. C2×#435C22semidirect
41. C2×C8×D4C22semidirect
42. C2×#428C22semidirect
60. #2538C22semidirect
64. #2496C22semidirect
65. #2492C22semidirect
67. #2485C22semidirect
69. #2440C22semidirect
74. #2417C22semidirect
81. #2362C22semidirect
84. #2354C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
92. #2088C22semidirect
93. #2086C22semidirect
94. #2085C22semidirect
95. #2083C22semidirect
99. #2077C22semidirect
100. #2077C22semidirect
101. #2077C22semidirect
103. #2076C22semidirect
104. #2076C22semidirect
107. #2075C22semidirect
108. #2072C22semidirect
112. #2057C22semidirect
121. #2024C22semidirect
128. #1990C22semidirect
129. #1990C22semidirect
130. #1988C22semidirect
131. #1987C22semidirect
134. #1948C22semidirect
135. #1943C22semidirect
139. #1933C22semidirect
140. #1927C22semidirect
146. #1919C22semidirect
147. #1918C22semidirect
151. #1894C22semidirect
157. #1892C22semidirect
158. #1892C22semidirect
167. #1873C22semidirect
168. #1872C22semidirect
169. #1870C22semidirect
171. #1869C22semidirect
174. #1863C22semidirect
177. #1854C22semidirect
178. #1854C22semidirect
179. #1852C22semidirect
180. #1851C22semidirect
181. #1850C22semidirect
182. #1836C22semidirect
185. #1825C22semidirect
186. #1825C22semidirect
187. #1809C22semidirect
188. #1808C22semidirect
189. #1805C22semidirect
195. C4×#107C22semidirect
197. #1753C22semidirect
198. C8×C22⋊C4C22semidirect
199. #1736C22semidirect
200. #1735C22semidirect
201. #1735C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#448872
#429202
#321262
#319972
#317172
#316302
#313952
#313512
#312602
#310282
#289792
#285552
#281552
#280652
#277202
#275202
#264082
#263032
#262112
#261572
#255522
#252492
#252132
#249212
#245632
#243942
#236432
#230402
#228472
#224892
#217702