Finite Group Databasebeta

← #7339250

Subgroups — #7339250

Order 512.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59094C211yesmaximal, characteristic
2#45627C211yesmaximal, characteristic, complemented
3#32099C211yesmaximal, characteristic, complemented
4#31992C211yesmaximal, characteristic, complemented
5#31788C211yesmaximal, characteristic, complemented
6#31496C211yesmaximal, characteristic, complemented
7#31324C211yesmaximal, characteristic, complemented
8#31311C211yesmaximal, characteristic, complemented
9#31302C211yesmaximal, characteristic, complemented
10#31298C211yesmaximal, characteristic, complemented
11#31129C211yesmaximal, characteristic, complemented
12#30966C211yesmaximal, characteristic, complemented
13#30832C211yesmaximal, characteristic, complemented
14#30796C211yesmaximal, characteristic, complemented
15#29956C211yesmaximal, characteristic, complemented
16#29691C211yesmaximal, characteristic, complemented
17#29109C211yesmaximal, characteristic, complemented
18#28952C211yesmaximal, characteristic, complemented
19#28079C211yesmaximal, characteristic, complemented
20#27774C211yesmaximal, characteristic, complemented
21#27527C211yesmaximal, characteristic, complemented
22#27267C211yesmaximal, characteristic, complemented
23#27116C211yesmaximal, characteristic, complemented
24#27036C211yesmaximal, characteristic, complemented
25#26776C211yesmaximal, characteristic, complemented
26#26478C211yesmaximal, characteristic, complemented
27#25959C211yesmaximal, characteristic, complemented
28#25897C211yesmaximal, characteristic
29#25677C211yesmaximal, characteristic, complemented
30#24037C211yesmaximal, characteristic
31#22371C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#533C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#491C2211yescharacteristic, complemented
36C2×#489C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#477C2211yescharacteristic, complemented
39C2×#477C2211yescharacteristic, complemented
40C2×#474C2211yescharacteristic
41C2×#416C2211yescharacteristic
42#2857C2211yescharacteristic
43#2851C2211yescharacteristic
44#2838—21no—
45#2789—21no—
46#2745—21no—
47#2729—21no—
48#2723—21no—
49#2716—21no—
50#2711—21no—
51#2707—21no—
52#2707—21no—
53#2563C2211yescharacteristic
54#2551C2211yescharacteristic, complemented
55#2550C2211yescharacteristic, complemented
56#2545C2211yescharacteristic
57#2508C2211yescharacteristic, complemented
58#2506C2211yescharacteristic, complemented
59#2497C2211yescharacteristic
60#2496C2211yescharacteristic, complemented
61#2494C2211yescharacteristic
62#2494C2211yescharacteristic, complemented
63#2491C2211yescharacteristic
64#2485C2211yescharacteristic
65#2472—21no—
66#2458—21no—
67#2452C2211yescharacteristic
68#2448C2211yescharacteristic
69#2441C2211yescharacteristic, complemented
70#2439C2211yescharacteristic, complemented
71#2437—21no—
72#2435C2211yescharacteristic
73#2432C2211yescharacteristic
74#2426—21no—
75#2426C2211yescharacteristic
76#2417C2211yescharacteristic
77#2411—21no—
78#2382—21no—
79#2367C2211yescharacteristic
80#2360C2211yescharacteristic
81#2342—21no—
82#2341C2211yescharacteristic
83C4×#123C2211yescharacteristic
84C2×#390C2211yescharacteristic
85#2093C2211yescharacteristic
86#2092C2211yescharacteristic
87#2092C2211yescharacteristic
88#2092C2211yescharacteristic
89#2088C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2077C2211yescharacteristic, complemented
93#2076C2211yescharacteristic, complemented
94#2072C2211yescharacteristic, complemented
95#2071C2211yescharacteristic
96#2071C2211yescharacteristic
97#2068C2211yescharacteristic, complemented
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2066C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2057C2211yescharacteristic, complemented
106#2057C2211yescharacteristic, complemented
107#2057C2211yescharacteristic, complemented
108#2043C2211yescharacteristic, complemented
109#2043C2211yescharacteristic, complemented
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2036C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2036C2211yescharacteristic, complemented
123#2035C2211yescharacteristic
124#2035C2211yescharacteristic
125#2035C2211yescharacteristic, complemented
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2025C2211yescharacteristic
129#2025C2211yescharacteristic
130#2024C2211yescharacteristic, complemented
131#2023C2211yescharacteristic
132#2023C2211yescharacteristic
133#1993C2211yescharacteristic, complemented
134#1983C2211yescharacteristic
135#1983C2211yescharacteristic
136#1983C2211yescharacteristic
137#1960C2211yescharacteristic, complemented
138#1959C2211yescharacteristic
139#1958C2211yescharacteristic
140#1955C2211yescharacteristic
141#1947C2211yescharacteristic, complemented
142#1944C2211yescharacteristic, complemented
143#1942C2211yescharacteristic, complemented
144#1940C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1935C2211yescharacteristic, complemented
151#1935C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1928C2211yescharacteristic, complemented
154#1927C2211yescharacteristic, complemented
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic, complemented
159#1923C2211yescharacteristic
160#1923C2211yescharacteristic, complemented
161#1921C2211yescharacteristic, complemented
162#1921C2211yescharacteristic, complemented
163#1921C2211yescharacteristic, complemented
164#1920C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1893C2211yescharacteristic
168#1892C2211yescharacteristic, complemented
169#1873C2211yescharacteristic, complemented
170#1869C2211yescharacteristic
171#1865C2211yescharacteristic, complemented
172#1865C2211yescharacteristic, complemented
173#1865C2211yescharacteristic, complemented
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1862C2211yescharacteristic
179#1854C2211yescharacteristic, complemented
180#1853C2211yescharacteristic
181#1852C2211yescharacteristic
182#1850C2211yescharacteristic, complemented
183#1824C2211yescharacteristic
184#1824C2211yescharacteristic
185#1808C2211yescharacteristic, complemented
186#1805C2211yescharacteristic, complemented
187#1803C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1797C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1776C2211yescharacteristic, complemented
198#1770C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200C4×#103C2211yescharacteristic, complemented
201#1752C2211yescharacteristic, complemented
202#1749C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#546—42no—
207#546—42no—
208#533—42no—
209#533—42no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#126—21no—
216C2×#125—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123D411yescharacteristic
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#120—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117C2311yescharacteristic
242C22×C4⋊C4C2311yescharacteristic
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246C22×C42C2311yescharacteristic
247#501—42no—
248#491—42no—
249#489—42no—
250#482—42no—
251#477—42no—
252#477—42no—
253#474—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271#416—42no—
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#401—21no—
317#401—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#399—21no—
323#399—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#393—21no—
352#393—21no—
353#393—21no—
354#393—21no—
355#393—21no—
356#391—21no—
357#391—21no—
358#391—21no—
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
391#388—21no—
392#388—21no—
393#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#388D411yescharacteristic
403#388D411yescharacteristic
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#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387D411yescharacteristic
417#387D411yescharacteristic
418#386—21no—
419#386D411yescharacteristic
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385D411yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#382—21no—
431#382—21no—
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#381D411yescharacteristic
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
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×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—41no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8—21no—
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4C2×D411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4C2×D411yescharacteristic
518C23×C4C2×D411yescharacteristic
519C23×C4C2411yescharacteristic
520C23×C4C2411yescharacteristic
521C22×C8—41no—
522C22×C8—41no—
523C22×C8—41no—
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C4⋊Q8—22no—
533C4⋊Q8—22no—
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—82no—
541#126—82no—
542#125—41no—
543#125—41no—
544#125—44no—
545#125—44no—
546#124—22no—
547#124—22no—
548#124—41no—
549#124—41no—
550#124—41no—
551#124—41no—
552#124—82no—
553#123—42no—
554#123—44no—
555C22⋊Q8—22no—
556C22⋊Q8—22no—
557C22⋊Q8—44no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—82no—
563C22⋊Q8—82no—
564#121—22no—
565#121—41no—
566#121—44no—
567#120—44no—
568C4×Q8—22no—
569C4×Q8—22no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—44no—
575C4×D4—22no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579#117—44no—
580#117—41no—
581#117—41no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
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—44no—
664C2×C22⋊C4—44no—
665C2×C22⋊C4—82no—
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—41no—
683C2×C42—41no—
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#107—22no—
692#107—22no—
693#107—22no—
694#107—41no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#106—22no—
700#106—41no—
701#106—41no—
702#106—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708#103—22no—
709#103—22no—
710#103—22no—
711#103—22no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#102—22no—
725#102—22no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740C22⋊C8—41no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743C22⋊C8—41no—
744C22⋊C8—41no—
745C22⋊C8—41no—
746C22⋊C8—41no—
747#97—41no—
748#97—41no—
749#97—41no—
750#97—41no—
751C4×C8—41no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794C24—21no—
795C24—21no—
796C24—42no—
797C24—42no—
798C24—42no—
799C24—42no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24C22×D411yescharacteristic
804C24C22×D411yescharacteristic
805#41—44no—
806#41—82no—
807#41—82no—
808#41—82no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—42no—
821C2×Q8—42no—
822C2×Q8—42no—
823C2×Q8—81no—
824C2×Q8—81no—
825C2×Q8—81no—
826C2×Q8—81no—
827C2×Q8—81no—
828C2×Q8—81no—
829C2×Q8H(5,𝔽2)12yes—
830C2×D4—22no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—41no—
843C2×D4—41no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—81no—
850C2×D4—82no—
851C2×D4—82no—
852C2×D4—82no—
853C2×D4—82no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D42−1+412yes—
858C22×C4—22no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—22no—
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—41no—
887C22×C4—41no—
888C22×C4—41no—
889C22×C4—41no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4—42no—
893C22×C4—42no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4—81no—
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C22×D411yescharacteristic
911C22×C4C2511yescharacteristic
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—82no—
937C4⋊C4—24no—
938C4⋊C4—22no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4H(5,𝔽2)12yes—
996C22⋊C4—24no—
997C22⋊C4—22no—
998C22⋊C4—22no—
999C22⋊C4—41no—
1000C22⋊C4—41no—
1001C22⋊C4—41no—
1002C22⋊C4—41no—
1003C22⋊C4—41no—
1004C22⋊C4—41no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—41no—
1047C42—41no—
1048C42—42no—
1049C42—42no—
1050C42—42no—
1051C42—81no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—22no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—84no—
1084C23—84no—
1085C23—84no—
1086C23—84no—
1087C23—162no—
1088C23—162no—
1089C23—162no—
1090C23#57812yes—
1091C23C23×D411yescharacteristic
1092Q8—22no—
1093Q8—22no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—84no—
1101Q8—162no—
1102Q8—162no—
1103D4—22no—
1104D4—22no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—82no—
1112D4—84no—
1113D4—84no—
1114D4—162no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—22no—
1134C2×C4—22no—
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—44no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—82no—
1202C2×C4—84no—
1203C2×C4—162no—
1204C2×C4—162no—
1205C2×C4#57512yes—
1206C2×C4C2×H(5,𝔽2)11yescharacteristic
1207C2×C4C2×H(5,𝔽2)11yescharacteristic
1208C2×C4C2×2−1+411yescharacteristic
1209C2×C4#58511yescharacteristic
1210C2×C4#58511yescharacteristic
1211C2×C4#58511yescharacteristic
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—42no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—41no—
1233C22—42no—
1234C22—41no—
1235C22—41no—
1236C22—42no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—168no—
1249C22#348411yescharacteristic
1250C22#348911yescharacteristic
1251C22#350011yescharacteristic
1252C22C2×#57511yescharacteristic
1253C22C2×#57811yescharacteristic
1254C22#358511yescharacteristic
1255C22#358511yescharacteristic
1256C4—22no—
1257C4—41no—
1258C4—41no—
1259C4—42no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—42no—
1269C4—41no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4#353511yescharacteristic
1283C4#355111yescharacteristic
1284C4#356011yescharacteristic
1285C4#356111yescharacteristic
1286C2—42no—
1287C2—81no—
1288C2—82no—
1289C2—161no—
1290C2#4795611yescharacteristic
1291C2#6160311yescharacteristic
1292C2#6165311yescharacteristic
1293C2#6211511yescharacteristic
1294C2#6216511yescharacteristic
1295C2#6258011yescharacteristic
1296C2#6260411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
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
2. #45627C2semidirect
3. #32099C2semidirect
4. #31992C2semidirect
5. #31788C2semidirect
6. #31496C2semidirect
7. #31324C2semidirect
8. #31311C2semidirect
9. #31302C2semidirect
10. #31298C2semidirect
11. #31129C2semidirect
12. #30966C2semidirect
13. #30832C2semidirect
14. #30796C2semidirect
15. #29956C2semidirect
16. #29691C2semidirect
17. #29109C2semidirect
18. #28952C2semidirect
19. #28079C2semidirect
20. #27774C2semidirect
21. #27527C2semidirect
22. #27267C2semidirect
23. #27116C2semidirect
24. #27036C2semidirect
25. #26776C2semidirect
26. #26478C2semidirect
27. #25959C2semidirect
29. #25677C2semidirect
31. #22371C2semidirect
34. C2×#501C22semidirect
35. C2×#491C22semidirect
38. C2×#477C22semidirect
39. C2×#477C22semidirect
54. #2551C22semidirect
55. #2550C22semidirect
57. #2508C22semidirect
58. #2506C22semidirect
60. #2496C22semidirect
62. #2494C22semidirect
69. #2441C22semidirect
70. #2439C22semidirect
89. #2088C22semidirect
90. #2088C22semidirect
91. #2085C22semidirect
92. #2077C22semidirect
93. #2076C22semidirect
94. #2072C22semidirect
97. #2068C22semidirect
101. #2066C22semidirect
105. #2057C22semidirect
106. #2057C22semidirect
107. #2057C22semidirect
108. #2043C22semidirect
109. #2043C22semidirect
122. #2036C22semidirect
125. #2035C22semidirect
130. #2024C22semidirect
133. #1993C22semidirect
137. #1960C22semidirect
141. #1947C22semidirect
142. #1944C22semidirect
143. #1942C22semidirect
144. #1940C22semidirect
150. #1935C22semidirect
151. #1935C22semidirect
153. #1928C22semidirect
154. #1927C22semidirect
158. #1924C22semidirect
160. #1923C22semidirect
161. #1921C22semidirect
162. #1921C22semidirect
163. #1921C22semidirect
164. #1920C22semidirect
165. #1917C22semidirect
166. #1917C22semidirect
168. #1892C22semidirect
169. #1873C22semidirect
171. #1865C22semidirect
172. #1865C22semidirect
173. #1865C22semidirect
175. #1863C22semidirect
176. #1863C22semidirect
177. #1863C22semidirect
179. #1854C22semidirect
182. #1850C22semidirect
185. #1808C22semidirect
186. #1805C22semidirect
187. #1803C22semidirect
188. #1803C22semidirect
197. #1776C22semidirect
198. #1770C22semidirect
200. C4×#103C22semidirect
201. #1752C22semidirect

Maximal subgroups

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

subgroupindex
#590942
#456272
#320992
#319922
#317882
#314962
#313242
#313112
#313022
#312982
#311292
#309662
#308322
#307962
#299562
#296912
#291092
#289522
#280792
#277742
#275272
#272672
#271162
#270362
#267762
#264782
#259592
#258972
#256772
#240372
#223712