Finite Group Databasebeta

← #6911159

Subgroups — #6911159

Order 512.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39427C211yesmaximal, characteristic, complemented
2#38947C211yesmaximal, characteristic
3#32811C211yesmaximal, characteristic, complemented
4#32781C211yesmaximal, characteristic, complemented
5#32066C211yesmaximal, characteristic, complemented
6#32060C211yesmaximal, characteristic, complemented
7#31544C211yesmaximal, characteristic, complemented
8#31532C211yesmaximal, characteristic, complemented
9#30897C211yesmaximal, characteristic, complemented
10#30881C211yesmaximal, characteristic, complemented
11#30540C211yesmaximal, characteristic, complemented
12#30520C211yesmaximal, characteristic, complemented
13#30257C211yesmaximal, characteristic, complemented
14#30065C211yesmaximal, characteristic, complemented
15#30046C211yesmaximal, characteristic, complemented
16#29961C211yesmaximal, characteristic, complemented
17#29676C211yesmaximal, characteristic, complemented
18#29261C211yesmaximal, characteristic, complemented
19#28320C211yesmaximal, characteristic, complemented
20#25914C211yesmaximal, characteristic, complemented
21#25562C211yesmaximal, characteristic, complemented
22#25546C211yesmaximal, characteristic, complemented
23#25220C211yesmaximal, characteristic, complemented
24#25201C211yesmaximal, characteristic, complemented
25#25105C211yesmaximal, characteristic, complemented
26#25084C211yesmaximal, characteristic, complemented
27#24442C211yesmaximal, characteristic
28#24426C211yesmaximal, characteristic
29#23944C211yesmaximal, characteristic, complemented
30#23456C211yesmaximal, characteristic, complemented
31#22005C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#544C2211yescharacteristic
35C2×#541C2211yescharacteristic, complemented
36C2×#491C2211yescharacteristic, complemented
37C2×#487C2211yescharacteristic, complemented
38C2×#485C2211yescharacteristic
39C2×#485C2211yescharacteristic
40C2×#470C2211yescharacteristic
41C2×#470C2211yescharacteristic
42C2×#467C2211yescharacteristic
43C2×#467C2211yescharacteristic
44C2×#464C2211yescharacteristic
45C2×#464C2211yescharacteristic
46C2×#452C2211yescharacteristic
47C2×#452C2211yescharacteristic
48C2×#450C2211yescharacteristic
49C2×#450C2211yescharacteristic
50C2×#418C2211yescharacteristic
51C22×#102C2211yescharacteristic
52#2862C2211yescharacteristic, complemented
53#2861C2211yescharacteristic
54#2723—21no—
55#2719—21no—
56#2716—21no—
57#2707—21no—
58#2707—21no—
59#2697—21no—
60#2697—21no—
61#2690—21no—
62#2628C2211yescharacteristic, complemented
63#2621C2211yescharacteristic
64#2621C2211yescharacteristic
65#2620C2211yescharacteristic
66#2566C2211yescharacteristic
67#2560—21no—
68#2550—21no—
69#2545C2211yescharacteristic
70#2519—21no—
71#2504C2211yescharacteristic
72#2499C2211yescharacteristic
73#2492C2211yescharacteristic, complemented
74#2489—21no—
75#2489C2211yescharacteristic, complemented
76#2480—21no—
77#2480—21no—
78#2476—21no—
79#2476—21no—
80#2453C2211yescharacteristic, complemented
81#2451C2211yescharacteristic, complemented
82#2435C2211yescharacteristic
83#2432C2211yescharacteristic
84#2417C2211yescharacteristic
85#2415C2211yescharacteristic
86#2362C2211yescharacteristic
87#2360C2211yescharacteristic
88#2311C2211yescharacteristic
89#2309C2211yescharacteristic
90C4×#125C2211yescharacteristic, complemented
91C4×#124C2211yescharacteristic
92#2293C2211yescharacteristic
93#2097C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2097C2211yescharacteristic, complemented
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2084C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2074C2211yescharacteristic, complemented
102#2074C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic, complemented
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2056C2211yescharacteristic, complemented
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic, complemented
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2026C2211yescharacteristic, complemented
123#2026C2211yescharacteristic, complemented
124#2026C2211yescharacteristic, complemented
125#2025C2211yescharacteristic
126#2025C2211yescharacteristic
127#2025C2211yescharacteristic
128#2025C2211yescharacteristic
129#2024C2211yescharacteristic, complemented
130#2024C2211yescharacteristic, complemented
131#2023C2211yescharacteristic
132#2023C2211yescharacteristic
133#2023C2211yescharacteristic
134#2023C2211yescharacteristic
135#2016C2211yescharacteristic, complemented
136#2016C2211yescharacteristic, complemented
137#2016C2211yescharacteristic, complemented
138#2016C2211yescharacteristic, complemented
139#2015C2211yescharacteristic
140#2015C2211yescharacteristic
141#2015C2211yescharacteristic
142#2015C2211yescharacteristic
143#2013C2211yescharacteristic
144#2013C2211yescharacteristic
145#2001C2211yescharacteristic, complemented
146#2001C2211yescharacteristic, complemented
147#2000C2211yescharacteristic
148#2000C2211yescharacteristic
149#1993C2211yescharacteristic, complemented
150#1991C2211yescharacteristic, complemented
151#1983C2211yescharacteristic
152#1983C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic
155#1968C2211yescharacteristic
156#1968C2211yescharacteristic
157#1949C2211yescharacteristic, complemented
158#1949C2211yescharacteristic, complemented
159#1928C2211yescharacteristic, complemented
160#1927C2211yescharacteristic, complemented
161#1926C2211yescharacteristic
162#1925C2211yescharacteristic
163#1924C2211yescharacteristic, complemented
164#1923C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1878C2211yescharacteristic, complemented
170#1878C2211yescharacteristic, complemented
171#1878C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1873C2211yescharacteristic
176#1873C2211yescharacteristic
177#1872C2211yescharacteristic
178#1872C2211yescharacteristic
179#1872C2211yescharacteristic, complemented
180#1872C2211yescharacteristic, complemented
181#1870C2211yescharacteristic
182#1869C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1864C2211yescharacteristic
185#1863C2211yescharacteristic, complemented
186#1862C2211yescharacteristic
187#1853C2211yescharacteristic, complemented
188#1852C2211yescharacteristic, complemented
189#1851C2211yescharacteristic
190#1850C2211yescharacteristic
191#1839C2211yescharacteristic, complemented
192#1831C2211yescharacteristic, complemented
193#1818C2211yescharacteristic, complemented
194#1803C2211yescharacteristic, complemented
195#1803C2211yescharacteristic, complemented
196#1798C2211yescharacteristic, complemented
197#1788C2211yescharacteristic
198#1788C2211yescharacteristic
199#1750C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×Q16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C23×C8C2311yescharacteristic
215#552—42no—
216#552—42no—
217#546—42no—
218#546—42no—
219#544—42no—
220#544—42no—
221#541—42no—
222#541—42no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×#126—21no—
229C2×#126—21no—
230C2×#126—21no—
231C2×#125—21no—
232C2×#125—21no—
233C2×#125—21no—
234C2×#125—21no—
235C2×#125C2311yescharacteristic
236C2×#125C2311yescharacteristic
237C2×#125C2311yescharacteristic
238C2×#124C2311yescharacteristic
239C2×#124C2311yescharacteristic
240C2×#124C2311yescharacteristic
241C2×#123—21no—
242C2×#123—21no—
243C2×C22⋊Q8—21no—
244C2×C22⋊Q8—21no—
245C2×C22⋊Q8C2311yescharacteristic
246C2×C22⋊Q8C2311yescharacteristic
247C2×C22⋊Q8C2311yescharacteristic
248C2×C22⋊Q8C2311yescharacteristic
249C2×C22⋊Q8C2311yescharacteristic
250C2×C22⋊Q8C2311yescharacteristic
251C2×C22⋊Q8C2311yescharacteristic
252C2×#121—21no—
253C2×#121C2311yescharacteristic
254C2×#120—21no—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117—21no—
261C2×#117C2311yescharacteristic
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C4⋊C4C2311yescharacteristic
267C22×C22⋊C4—21no—
268#491—42no—
269#487—42no—
270#485—42no—
271#485—42no—
272#470—42no—
273#470—42no—
274#467—42no—
275#467—42no—
276#464—42no—
277#464—42no—
278#452—42no—
279#452—42no—
280#450—42no—
281#450—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294#418—42no—
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#103C2311yescharacteristic
309C2×#103C2311yescharacteristic
310C2×#103C2311yescharacteristic
311C2×#103C2311yescharacteristic
312C2×#103C2311yescharacteristic
313C2×#103C2311yescharacteristic
314C2×#103C2311yescharacteristic
315C2×#102—42no—
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×#102C2311yescharacteristic
326C2×#102C2311yescharacteristic
327C2×#102C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×#97C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#399—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#397—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#396—21no—
362#396—21no—
363#396—21no—
364#396—21no—
365#395—21no—
366#395—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394—21no—
373#394—21no—
374#393—21no—
375#393—21no—
376#391—21no—
377#391—21no—
378#391—21no—
379#391—21no—
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#390—21no—
391#390—21no—
392#390D411yescharacteristic
393#390D411yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#389—21no—
401#389—21no—
402#389—21no—
403#389D411yescharacteristic
404#389D411yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388D411yescharacteristic
423#388D411yescharacteristic
424#388D411yescharacteristic
425#388D411yescharacteristic
426#387—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#384C2311yescharacteristic
445#382—21no—
446#382—21no—
447#382—21no—
448#382C2311yescharacteristic
449#382C2311yescharacteristic
450#382C2311yescharacteristic
451#380—21no—
452#380—21no—
453#380—21no—
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#379—21no—
457#379—21no—
458#379—21no—
459#379—21no—
460C4×C4⋊C4—21no—
461C4×C4⋊C4—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C43C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500#336C2311yescharacteristic
501#336C2311yescharacteristic
502C25—21no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2×D411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×Q16—41no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×Q16—41no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×M16—22no—
558C2×M16—41no—
559C2×M16—41no—
560C22×C8—22no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C4⋊Q8—22no—
572C4⋊Q8—41no—
573C4⋊Q8—41no—
574C4⋊Q8—41no—
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—44no—
580#126—44no—
581#126—44no—
582#126—44no—
583#125—22no—
584#125—22no—
585#125—22no—
586#125—41no—
587#125—41no—
588#125—41no—
589#125—44no—
590#125—44no—
591#125—44no—
592#125—44no—
593#124—22no—
594#124—41no—
595#124—41no—
596#124—41no—
597#124—41no—
598#124—41no—
599#123—44no—
600#123—44no—
601C22⋊Q8—22no—
602C22⋊Q8—22no—
603C22⋊Q8—22no—
604C22⋊Q8—22no—
605C22⋊Q8—22no—
606C22⋊Q8—22no—
607C22⋊Q8—22no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—41no—
612C22⋊Q8—41no—
613C22⋊Q8—41no—
614C22⋊Q8—41no—
615C22⋊Q8—44no—
616C22⋊Q8—44no—
617#121—44no—
618#121—41no—
619#121—41no—
620#120—44no—
621C4×Q8—22no—
622C4×Q8—22no—
623C4×Q8—41no—
624C4×Q8—41no—
625C4×Q8—41no—
626C4×Q8—41no—
627C4×D4—22no—
628C4×D4—22no—
629C4×D4—41no—
630C4×D4—41no—
631#117—22no—
632#117—22no—
633#117—22no—
634#117—41no—
635#117—41no—
636#117—41no—
637#117—41no—
638#117—44no—
639#117—41no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—21no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4—41no—
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
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—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—44no—
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42C2×D411yescharacteristic
741C2×C42C2×D411yescharacteristic
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749#107—41no—
750#107—41no—
751#107—41no—
752#107—41no—
753#106—41no—
754#106—41no—
755#106—41no—
756#106—41no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#103—41no—
776#103—41no—
777#103—41no—
778#103—41no—
779#103—41no—
780#103—41no—
781#102—22no—
782#102—22no—
783#102—22no—
784#102—22no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793C22⋊C8—22no—
794C22⋊C8—22no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797C22⋊C8—41no—
798C22⋊C8—41no—
799#97—41no—
800C4×C8—41no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839#95C2×D411yescharacteristic
840#95C2×D411yescharacteristic
841C24—21no—
842C24—21no—
843C24—42no—
844C24—42no—
845C24—81no—
846C24—81no—
847C24—81no—
848C24—81no—
849C24—81no—
850C24C22×D411yescharacteristic
851C24C22×D411yescharacteristic
852#41—82no—
853#41—82no—
854#41—82no—
855#41—82no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—21no—
876C2×Q8—21no—
877C2×Q8—21no—
878C2×Q8—21no—
879C2×Q8—21no—
880C2×Q8—42no—
881C2×Q8—42no—
882C2×Q8—81no—
883C2×Q8—81no—
884C2×Q8—81no—
885C2×Q8—81no—
886C2×D4—22no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—41no—
901C2×D4—41no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—82no—
908C2×D4—82no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D42−1+412yes—
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—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4H(5,𝔽2)12yes—
963C22×C4H(5,𝔽2)12yes—
964C22×C4C2511yescharacteristic
965Q16—82no—
966Q16—82no—
967Q16—82no—
968Q16—82no—
969SD16—82no—
970SD16—82no—
971SD16—82no—
972SD16—82no—
973M16—82no—
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—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—82no—
999C4⋊C4—24no—
1000C4⋊C4—24no—
1001C4⋊C4—22no—
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—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—41no—
1025C4⋊C4—41no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4H(5,𝔽2)12yes—
1055C4⋊C4H(5,𝔽2)12yes—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
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—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—41no—
1108C42—41no—
1109C42—41no—
1110C42—41no—
1111C42—42no—
1112C42—42no—
1113C42—42no—
1114C42—42no—
1115C42—42no—
1116C42—42no—
1117C42—81no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—22no—
1131C23—21no—
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—84no—
1146C23—84no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23#53512yes—
1153C23C23×D411yescharacteristic
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—162no—
1171Q8—162no—
1172D4—22no—
1173D4—22no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—84no—
1181D4—82no—
1182D4—84no—
1183D4—162no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
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—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
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—84no—
1271C2×C4—162no—
1272C2×C4—162no—
1273C2×C4#53512yes—
1274C2×C4C2×H(5,𝔽2)11yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4C2×2−1+411yescharacteristic
1279C2×C4#58511yescharacteristic
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—42no—
1298C22—41no—
1299C22—41no—
1300C22—42no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—42no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—168no—
1317C22C2×#53511yescharacteristic
1318C22#348411yescharacteristic
1319C22#348911yescharacteristic
1320C22#358411yescharacteristic
1321C22#358411yescharacteristic
1322C22#358611yescharacteristic
1323C22#358611yescharacteristic
1324C4—22no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—42no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—42no—
1337C4—41no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4#353611yescharacteristic
1351C4#353611yescharacteristic
1352C4#355811yescharacteristic
1353C4#355811yescharacteristic
1354C2—42no—
1355C2—81no—
1356C2—82no—
1357C2—161no—
1358C2#4059311yescharacteristic
1359C2#6081611yescharacteristic
1360C2#6083511yescharacteristic
1361C2#6166311yescharacteristic
1362C2#6167611yescharacteristic
1363C2#6217211yescharacteristic
1364C2#6219611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39427C2semidirect
3. #32811C2semidirect
4. #32781C2semidirect
5. #32066C2semidirect
6. #32060C2semidirect
7. #31544C2semidirect
8. #31532C2semidirect
9. #30897C2semidirect
10. #30881C2semidirect
11. #30540C2semidirect
12. #30520C2semidirect
13. #30257C2semidirect
14. #30065C2semidirect
15. #30046C2semidirect
16. #29961C2semidirect
17. #29676C2semidirect
18. #29261C2semidirect
19. #28320C2semidirect
20. #25914C2semidirect
21. #25562C2semidirect
22. #25546C2semidirect
23. #25220C2semidirect
24. #25201C2semidirect
25. #25105C2semidirect
26. #25084C2semidirect
29. #23944C2semidirect
30. #23456C2semidirect
31. #22005C2semidirect
35. C2×#541C22semidirect
36. C2×#491C22semidirect
37. C2×#487C22semidirect
52. #2862C22semidirect
62. #2628C22semidirect
73. #2492C22semidirect
75. #2489C22semidirect
80. #2453C22semidirect
81. #2451C22semidirect
90. C4×#125C22semidirect
93. #2097C22semidirect
94. #2097C22semidirect
95. #2097C22semidirect
96. #2097C22semidirect
99. #2084C22semidirect
100. #2083C22semidirect
101. #2074C22semidirect
102. #2074C22semidirect
103. #2068C22semidirect
105. #2066C22semidirect
107. #2059C22semidirect
108. #2059C22semidirect
109. #2056C22semidirect
110. #2056C22semidirect
117. #2036C22semidirect
118. #2035C22semidirect
121. #2026C22semidirect
122. #2026C22semidirect
123. #2026C22semidirect
124. #2026C22semidirect
129. #2024C22semidirect
130. #2024C22semidirect
135. #2016C22semidirect
136. #2016C22semidirect
137. #2016C22semidirect
138. #2016C22semidirect
145. #2001C22semidirect
146. #2001C22semidirect
149. #1993C22semidirect
150. #1991C22semidirect
157. #1949C22semidirect
158. #1949C22semidirect
159. #1928C22semidirect
160. #1927C22semidirect
163. #1924C22semidirect
164. #1923C22semidirect
165. #1917C22semidirect
166. #1916C22semidirect
169. #1878C22semidirect
170. #1878C22semidirect
171. #1878C22semidirect
172. #1878C22semidirect
179. #1872C22semidirect
180. #1872C22semidirect
183. #1865C22semidirect
185. #1863C22semidirect
187. #1853C22semidirect
188. #1852C22semidirect
191. #1839C22semidirect
192. #1831C22semidirect
193. #1818C22semidirect
194. #1803C22semidirect
195. #1803C22semidirect
196. #1798C22semidirect

Maximal subgroups

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

subgroupindex
#394272
#389472
#328112
#327812
#320662
#320602
#315442
#315322
#308972
#308812
#305402
#305202
#302572
#300652
#300462
#299612
#296762
#292612
#283202
#259142
#255622
#255462
#252202
#252012
#251052
#250842
#244422
#244262
#239442
#234562
#220052