Finite Group Databasebeta

← #7013145

Subgroups — #7013145

Order 512.

1663 conjugacy classes of subgroups.

The subgroup lattice has 1381 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59628C211yesmaximal, characteristic, complemented
2#39020C211yesmaximal, characteristic, complemented
3#32208C211yesmaximal, characteristic, complemented
4#32128C211yesmaximal, characteristic, complemented
5#32024C211yesmaximal, characteristic, complemented
6#31665C211yesmaximal, characteristic, complemented
7#31216C211yesmaximal, characteristic, complemented
8#30922C211yesmaximal, characteristic, complemented
9#30535C211yesmaximal, characteristic, complemented
10#30509C211yesmaximal, characteristic
11#28913C211yesmaximal, characteristic, complemented
12#28890C211yesmaximal, characteristic, complemented
13#28579C211yesmaximal, characteristic, complemented
14#28107C211yesmaximal, characteristic, complemented
15#27804C211yesmaximal, characteristic, complemented
16#27787C211yesmaximal, characteristic, complemented
17#27222C211yesmaximal, characteristic, complemented
18#27129C211yesmaximal, characteristic, complemented
19#27112C211yesmaximal, characteristic, complemented
20#26722C211yesmaximal, characteristic, complemented
21#26706C211yesmaximal, characteristic, complemented
22#26593C211yesmaximal, characteristic, complemented
23#25452C211yesmaximal, characteristic, complemented
24#25402C211yesmaximal, characteristic, complemented
25#25088C211yesmaximal, characteristic, complemented
26#24654C211yesmaximal, characteristic, complemented
27#23697C211yesmaximal, characteristic, complemented
28#23226C211yesmaximal, characteristic, complemented
29#22904C211yesmaximal, characteristic, complemented
30#22870C211yesmaximal, characteristic, complemented
31#22187C211yesmaximal, characteristic, complemented
32C2×#559—21no—
33C2×#498C2211yescharacteristic, complemented
34C2×#489C2211yescharacteristic
35C2×#474C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#468C2211yescharacteristic, complemented
39C2×#465C2211yescharacteristic
40C2×#460C2211yescharacteristic, complemented
41C2×#463C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#447C2211yescharacteristic
44C2×C4×D8C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×#431C2211yescharacteristic, complemented
47C22×#102C2211yescharacteristic
48#2850C2211yescharacteristic
49#2778—21no—
50#2741—21no—
51#2736—21no—
52#2712—21no—
53#2709—21no—
54#2684—21no—
55#2653—21no—
56#2600—21no—
57#2563C2211yescharacteristic
58#2541C2211yescharacteristic
59#2536C2211yescharacteristic
60#2513C2211yescharacteristic
61#2494C2211yescharacteristic
62#2492C2211yescharacteristic
63#2491C2211yescharacteristic
64#2491C2211yescharacteristic
65#2491C2211yescharacteristic
66#2491C2211yescharacteristic, complemented
67#2491C2211yescharacteristic, complemented
68#2486C2211yescharacteristic
69#2459—21no—
70#2459—21no—
71#2459—21no—
72#2458—21no—
73#2458—21no—
74#2448C2211yescharacteristic
75#2445C2211yescharacteristic, complemented
76#2445C2211yescharacteristic, complemented
77#2435C2211yescharacteristic
78#2427C2211yescharacteristic
79#2418—21no—
80#2408C2211yescharacteristic
81#2367C2211yescharacteristic
82#2365C2211yescharacteristic, complemented
83#2365C2211yescharacteristic, complemented
84#2361C2211yescharacteristic
85#2361C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87#2312—21no—
88C4×#123C2211yescharacteristic
89C4×#121C2211yescharacteristic
90C4×#121C2211yescharacteristic, complemented
91C4×#121C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2087C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2076C2211yescharacteristic, complemented
97#2075C2211yescharacteristic
98#2073C2211yescharacteristic, complemented
99#2067C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic, complemented
104#2058C2211yescharacteristic, complemented
105#2055C2211yescharacteristic, complemented
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2042C2211yescharacteristic
110#2036C2211yescharacteristic, complemented
111#2035C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic, complemented
117#2033C2211yescharacteristic
118#2024C2211yescharacteristic, complemented
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#2023C2211yescharacteristic, complemented
123#2012C2211yescharacteristic
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2011C2211yescharacteristic
127#2011C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic, complemented
130#1999C2211yescharacteristic
131#1999C2211yescharacteristic
132#1987C2211yescharacteristic, complemented
133#1987C2211yescharacteristic, complemented
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic
136#1972C2211yescharacteristic
137#1970C2211yescharacteristic
138#1970C2211yescharacteristic
139#1968C2211yescharacteristic, complemented
140#1968C2211yescharacteristic, complemented
141#1961C2211yescharacteristic, complemented
142#1949C2211yescharacteristic, complemented
143#1949C2211yescharacteristic, complemented
144#1939C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic, complemented
148#1934C2211yescharacteristic
149#1933C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1927C2211yescharacteristic, complemented
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1926C2211yescharacteristic, complemented
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1925C2211yescharacteristic, complemented
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1921C2211yescharacteristic, complemented
164#1919C2211yescharacteristic, complemented
165#1919C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1895C2211yescharacteristic
169#1895C2211yescharacteristic
170#1895C2211yescharacteristic, complemented
171#1894C2211yescharacteristic, complemented
172#1893C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1877C2211yescharacteristic, complemented
179#1872C2211yescharacteristic
180#1870C2211yescharacteristic
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic, complemented
185#1852C2211yescharacteristic
186#1851C2211yescharacteristic, complemented
187#1850C2211yescharacteristic
188#1823C2211yescharacteristic
189#1809C2211yescharacteristic, complemented
190#1807C2211yescharacteristic
191#1804C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194C4×#106C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic
202#1728C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C22×M16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#559—48no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127—21no—
218C2×#127C2311yescharacteristic
219C2×#124—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×#123—21no—
228C2×#123—21no—
229C2×#123D411yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#120—21no—
239C2×C4×Q8—21no—
240C2×C4×Q8—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4—21no—
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C22×C4⋊C4C2311yescharacteristic
253C22×C22⋊C4—21no—
254C22×C42C2311yescharacteristic
255#498—42no—
256#489—24no—
257#474—42no—
258#469—24no—
259#469—42no—
260#468—42no—
261#465—42no—
262#463—42no—
263#460—42no—
264#447—24no—
265#447—42no—
266C4×D8—42no—
267#435—42no—
268#431—42no—
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#102—42no—
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#401—21no—
324#400—21no—
325#399—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
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#393—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#393—21no—
354#393—21no—
355#393—21no—
356#392—21no—
357#392—21no—
358#392—21no—
359#391—21no—
360#391—21no—
361#391—21no—
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#390—21no—
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#388—21no—
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#388—21no—
405#388D411yescharacteristic
406#388D411yescharacteristic
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387D411yescharacteristic
413#387D411yescharacteristic
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#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386D411yescharacteristic
427#385—21no—
428#385—21no—
429#385—21no—
430#385D411yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#381—21no—
434#381D411yescharacteristic
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#379—21no—
445#379—21no—
446#379—21no—
447#379—21no—
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C25—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8—21no—
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×D411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C2×SD16—22no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×M16—22no—
547C2×M16—41no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C22×C8—22no—
553C22×C8—41no—
554C22×C8—41no—
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C4⋊Q8—22no—
564C4⋊Q8—22no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569#127—41no—
570#127—41no—
571#127—44no—
572#124—22no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—44no—
577#124—44no—
578#124—44no—
579#124—44no—
580#124—82no—
581#123—24no—
582#123—44no—
583#123—44no—
584#123—44no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589#121—22no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#120—82no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—44no—
605C4×Q8—44no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—44no—
617C4×D4—44no—
618C4×D4—44no—
619C4×D4—44no—
620C4×D4—82no—
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—41no—
635C2×C4⋊C4—41no—
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×C22⋊C4—21no—
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⋊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—44no—
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×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—41no—
716C2×C42—41no—
717C2×C42C2×D411yescharacteristic
718C2×C42C2×D411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724#107—22no—
725#107—41no—
726#107—41no—
727#107—41no—
728#106—22no—
729#106—22no—
730#106—22no—
731#106—41no—
732#106—41no—
733#106—41no—
734C4⋊C8—22no—
735C4⋊C8—22no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—41no—
743#103—41no—
744#103—41no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
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—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102#4114yes—
767C22⋊C8—22no—
768C22⋊C8—22no—
769C22⋊C8—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772#97—22no—
773#97—41no—
774C4×C8—22no—
775C4×C8—41no—
776C4×C8—41no—
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#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814C24—21no—
815C24—21no—
816C24—21no—
817C24—21no—
818C24—42no—
819C24—42no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—42no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×D4—22no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—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—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—44no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—82no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4C2×#4112yes—
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—22no—
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—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4C22×D411yescharacteristic
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×C4C22×D411yescharacteristic
957C22×C4C2511yescharacteristic
958SD16—82no—
959SD16—82no—
960D8—44no—
961D8—82no—
962D8—82no—
963D8—82no—
964M16—82no—
965M16—82no—
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—21no—
987C2×C8—21no—
988C2×C8—82no—
989C2×C8C2×#4112yes—
990C2×C8H(5,𝔽2)12yes—
991C4⋊C4—22no—
992C4⋊C4—22no—
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—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—42no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4C2×#4112yes—
1030C4⋊C4H(5,𝔽2)12yes—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—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⋊C4AGL(1,ℤ/8)14yes—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—41no—
1096C42—41no—
1097C42—42no—
1098C42—42no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—22no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—84no—
1147C23—84no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23C2×AGL(1,ℤ/8)12yes—
1154C23C23×D411yescharacteristic
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—84no—
1160Q8—84no—
1161Q8—162no—
1162D4—22no—
1163D4—22no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—82no—
1179D4—84no—
1180D4—84no—
1181D4—84no—
1182D4—84no—
1183D4—84no—
1184D4—84no—
1185D4—162no—
1186D4—162no—
1187D4—162no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—22no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—22no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—44no—
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—82no—
1268C2×C4—162no—
1269C2×C4—162no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4—162no—
1273C2×C4C2×AGL(1,ℤ/8)12yes—
1274C2×C4C2×AGL(1,ℤ/8)12yes—
1275C2×C4C22×#4111yescharacteristic
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4#58511yescharacteristic
1279C2×C4#58511yescharacteristic
1280C2×C4#58511yescharacteristic
1281C8—22no—
1282C8—22no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—42no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—42no—
1304C22—41no—
1305C22—42no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—168no—
1332C22D4×#4111yescharacteristic
1333C22#348811yescharacteristic
1334C22#349611yescharacteristic
1335C22C22×AGL(1,ℤ/8)11yescharacteristic
1336C22#358411yescharacteristic
1337C22#358411yescharacteristic
1338C22#358511yescharacteristic
1339C4—22no—
1340C4—22no—
1341C4—41no—
1342C4—41no—
1343C4—42no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—42no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4#350611yescharacteristic
1364C4#351411yescharacteristic
1365C4#355811yescharacteristic
1366C4#356611yescharacteristic
1367C2—42no—
1368C2—81no—
1369C2—82no—
1370C2—161no—
1371C2—161no—
1372C2—161no—
1373C2#4303511yescharacteristic
1374C2#6143711yescharacteristic
1375C2#6154711yescharacteristic
1376C2#6198911yescharacteristic
1377C2#6204911yescharacteristic
1378C2#6227311yescharacteristic
1379C2#6229911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30509C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59628C2semidirect
2. #39020C2semidirect
3. #32208C2semidirect
4. #32128C2semidirect
5. #32024C2semidirect
6. #31665C2semidirect
7. #31216C2semidirect
8. #30922C2semidirect
9. #30535C2semidirect
11. #28913C2semidirect
12. #28890C2semidirect
13. #28579C2semidirect
14. #28107C2semidirect
15. #27804C2semidirect
16. #27787C2semidirect
17. #27222C2semidirect
18. #27129C2semidirect
19. #27112C2semidirect
20. #26722C2semidirect
21. #26706C2semidirect
22. #26593C2semidirect
23. #25452C2semidirect
24. #25402C2semidirect
25. #25088C2semidirect
26. #24654C2semidirect
27. #23697C2semidirect
28. #23226C2semidirect
29. #22904C2semidirect
30. #22870C2semidirect
31. #22187C2semidirect
33. C2×#498C22semidirect
38. C2×#468C22semidirect
40. C2×#460C22semidirect
46. C2×#431C22semidirect
66. #2491C22semidirect
67. #2491C22semidirect
75. #2445C22semidirect
76. #2445C22semidirect
82. #2365C22semidirect
83. #2365C22semidirect
90. C4×#121C22semidirect
91. C4×#121C22semidirect
92. #2101C22semidirect
93. #2087C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
96. #2076C22semidirect
98. #2073C22semidirect
99. #2067C22semidirect
103. #2065C22semidirect
104. #2058C22semidirect
105. #2055C22semidirect
110. #2036C22semidirect
116. #2034C22semidirect
118. #2024C22semidirect
121. #2023C22semidirect
122. #2023C22semidirect
129. #2000C22semidirect
132. #1987C22semidirect
133. #1987C22semidirect
139. #1968C22semidirect
140. #1968C22semidirect
141. #1961C22semidirect
142. #1949C22semidirect
143. #1949C22semidirect
144. #1939C22semidirect
147. #1936C22semidirect
149. #1933C22semidirect
150. #1927C22semidirect
151. #1927C22semidirect
156. #1926C22semidirect
157. #1926C22semidirect
160. #1925C22semidirect
163. #1921C22semidirect
164. #1919C22semidirect
165. #1919C22semidirect
166. #1917C22semidirect
167. #1916C22semidirect
170. #1895C22semidirect
171. #1894C22semidirect
178. #1877C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
184. #1862C22semidirect
186. #1851C22semidirect
189. #1809C22semidirect
191. #1804C22semidirect
193. #1776C22semidirect
194. C4×#106C22semidirect
195. #1771C22semidirect
196. #1763C22semidirect
199. C4×#102C22semidirect
200. #1753C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#596282
#390202
#322082
#321282
#320242
#316652
#312162
#309222
#305352
#305092
#289132
#288902
#285792
#281072
#278042
#277872
#272222
#271292
#271122
#267222
#267062
#265932
#254522
#254022
#250882
#246542
#236972
#232262
#229042
#228702
#221872