Finite Group Databasebeta

← #6940535

Subgroups — #6940535

Order 512.

1558 conjugacy classes of subgroups.

The subgroup lattice has 1343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39070C211yesmaximal, characteristic, complemented
2#39070C211yesmaximal, characteristic, complemented
3#32859C211yesmaximal, characteristic, complemented
4#32817C211yesmaximal, characteristic, complemented
5#31915C211yesmaximal, characteristic, complemented
6#31899C211yesmaximal, characteristic, complemented
7#31831C211yesmaximal, characteristic, complemented
8#31815C211yesmaximal, characteristic, complemented
9#31219C211yesmaximal, characteristic, complemented
10#31217C211yesmaximal, characteristic, complemented
11#31170C211yesmaximal, characteristic, complemented
12#31160C211yesmaximal, characteristic, complemented
13#30134C211yesmaximal, characteristic, complemented
14#30133C211yesmaximal, characteristic, complemented
15#29839C211yesmaximal, characteristic, complemented
16#29838C211yesmaximal, characteristic, complemented
17#29786C211yesmaximal, characteristic, complemented
18#29542C211yesmaximal, characteristic, complemented
19#28256C211yesmaximal, characteristic, complemented
20#26415C211yesmaximal, characteristic, complemented
21#26413C211yesmaximal, characteristic, complemented
22#25974C211yesmaximal, characteristic, complemented
23#25966C211yesmaximal, characteristic, complemented
24#25105C211yesmaximal, characteristic, complemented
25#25105C211yesmaximal, characteristic, complemented
26#24516C211yesmaximal, characteristic, complemented
27#24516C211yesmaximal, characteristic, complemented
28#24355C211yesmaximal, characteristic
29#24355C211yesmaximal, characteristic
30#23540C211yesmaximal, characteristic
31#21980C211yesmaximal, characteristic, complemented
32C23×D8C2211yescharacteristic
33C2×#476C2211yescharacteristic, complemented
34C2×#474C2211yescharacteristic, complemented
35C2×#470C2211yescharacteristic
36C2×#464C2211yescharacteristic, complemented
37C2×#464C2211yescharacteristic, complemented
38C2×#463C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#463C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#433C2211yescharacteristic
45C2×#424C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C2×#418C2211yescharacteristic
48#2860C2211yescharacteristic, complemented
49#2860C2211yescharacteristic, complemented
50#2751—21no—
51#2751—21no—
52#2740—21no—
53#2740—21no—
54#2736—21no—
55#2736—21no—
56#2735—21no—
57#2735—21no—
58#2640C2211yescharacteristic, complemented
59#2640C2211yescharacteristic, complemented
60#2625C2211yescharacteristic
61#2625C2211yescharacteristic
62#2595—21no—
63#2595—21no—
64#2561—21no—
65#2561—21no—
66#2560—21no—
67#2560—21no—
68#2513C2211yescharacteristic, complemented
69#2513C2211yescharacteristic, complemented
70#2480—21no—
71#2480—21no—
72#2452C2211yescharacteristic, complemented
73#2452C2211yescharacteristic, complemented
74#2448C2211yescharacteristic, complemented
75#2448C2211yescharacteristic, complemented
76#2447C2211yescharacteristic, complemented
77#2447C2211yescharacteristic, complemented
78#2439C2211yescharacteristic
79#2439C2211yescharacteristic
80#2435C2211yescharacteristic
81#2435C2211yescharacteristic
82#2362C2211yescharacteristic
83#2362C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86#2319C2211yescharacteristic, complemented
87#2319C2211yescharacteristic, complemented
88#2309C2211yescharacteristic
89#2309C2211yescharacteristic
90C4×#124C2211yescharacteristic, complemented
91C4×#124C2211yescharacteristic, complemented
92#2298C2211yescharacteristic
93#2101C2211yescharacteristic, complemented
94#2101C2211yescharacteristic, complemented
95#2092C2211yescharacteristic, complemented
96#2092C2211yescharacteristic, complemented
97#2088C2211yescharacteristic, complemented
98#2088C2211yescharacteristic, complemented
99#2088C2211yescharacteristic, complemented
100#2087C2211yescharacteristic, complemented
101#2068C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2067C2211yescharacteristic, complemented
106#2067C2211yescharacteristic, complemented
107#2067C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2066C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2065C2211yescharacteristic, complemented
113#2065C2211yescharacteristic, complemented
114#2065C2211yescharacteristic, complemented
115#2065C2211yescharacteristic, complemented
116#2065C2211yescharacteristic, complemented
117#2056C2211yescharacteristic, complemented
118#2056C2211yescharacteristic, complemented
119#2055C2211yescharacteristic, complemented
120#2055C2211yescharacteristic, complemented
121#2055C2211yescharacteristic, complemented
122#2055C2211yescharacteristic, complemented
123#2055C2211yescharacteristic, complemented
124#2055C2211yescharacteristic, complemented
125#2054C2211yescharacteristic
126#2054C2211yescharacteristic
127#2054C2211yescharacteristic
128#2054C2211yescharacteristic
129#2054C2211yescharacteristic
130#2054C2211yescharacteristic
131#2054C2211yescharacteristic
132#2054C2211yescharacteristic
133#2054C2211yescharacteristic
134#2054C2211yescharacteristic
135#2054C2211yescharacteristic
136#2054C2211yescharacteristic
137#2042C2211yescharacteristic, complemented
138#2042C2211yescharacteristic, complemented
139#2024C2211yescharacteristic, complemented
140#2024C2211yescharacteristic, complemented
141#2023C2211yescharacteristic, complemented
142#2023C2211yescharacteristic, complemented
143#2015C2211yescharacteristic, complemented
144#2015C2211yescharacteristic, complemented
145#2012C2211yescharacteristic
146#2012C2211yescharacteristic
147#2012C2211yescharacteristic
148#2012C2211yescharacteristic
149#1988C2211yescharacteristic, complemented
150#1987C2211yescharacteristic, complemented
151#1983C2211yescharacteristic, complemented
152#1983C2211yescharacteristic, complemented
153#1973C2211yescharacteristic, complemented
154#1973C2211yescharacteristic, complemented
155#1968C2211yescharacteristic, complemented
156#1968C2211yescharacteristic, complemented
157#1940C2211yescharacteristic, complemented
158#1940C2211yescharacteristic, complemented
159#1939C2211yescharacteristic, complemented
160#1939C2211yescharacteristic, complemented
161#1936C2211yescharacteristic, complemented
162#1936C2211yescharacteristic, complemented
163#1934C2211yescharacteristic, complemented
164#1934C2211yescharacteristic, complemented
165#1926C2211yescharacteristic, complemented
166#1926C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1918C2211yescharacteristic, complemented
169#1892C2211yescharacteristic
170#1892C2211yescharacteristic
171#1880C2211yescharacteristic, complemented
172#1880C2211yescharacteristic, complemented
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1873C2211yescharacteristic
178#1873C2211yescharacteristic
179#1865C2211yescharacteristic, complemented
180#1864C2211yescharacteristic, complemented
181#1864C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic, complemented
184#1862C2211yescharacteristic, complemented
185#1854C2211yescharacteristic
186#1854C2211yescharacteristic
187#1851C2211yescharacteristic
188#1851C2211yescharacteristic
189#1850C2211yescharacteristic
190#1850C2211yescharacteristic
191#1843C2211yescharacteristic, complemented
192#1842C2211yescharacteristic, complemented
193#1832C2211yescharacteristic, complemented
194#1831C2211yescharacteristic, complemented
195#1809C2211yescharacteristic
196#1805C2211yescharacteristic, complemented
197#1805C2211yescharacteristic, complemented
198#1804C2211yescharacteristic, complemented
199#1804C2211yescharacteristic, complemented
200#1786C2211yescharacteristic
201#1786C2211yescharacteristic
202#1735C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×D8—42no—
211C22×D8—42no—
212C22×D8—42no—
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#126—21no—
222C2×#126—21no—
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117C2311yescharacteristic
238C2×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C22×C22⋊C4—21no—
241C22×C22⋊C4—21no—
242#476—42no—
243#474—42no—
244#470—42no—
245#464—42no—
246#464—42no—
247#463—42no—
248#463—42no—
249#463—42no—
250#463—42no—
251#450—42no—
252#450—42no—
253#433—42no—
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261#424—42no—
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276#418—42no—
277#418—42no—
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×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×C4×C8C2311yescharacteristic
312#400—21no—
313#400—21no—
314#399—21no—
315#399—21no—
316#398—21no—
317#398—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#396—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#393—21no—
345#393—21no—
346#393—21no—
347#393—21no—
348#393—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#391—21no—
353#391—21no—
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#390—21no—
361#390—21no—
362#390—21no—
363#390—21no—
364#390C2311yescharacteristic
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#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
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#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388D411yescharacteristic
417#388D411yescharacteristic
418#388D411yescharacteristic
419#388D411yescharacteristic
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387D411yescharacteristic
425#387D411yescharacteristic
426#387D411yescharacteristic
427#387D411yescharacteristic
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#381—21no—
439#381—21no—
440#381—21no—
441#381—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447#379—21no—
448#379—21no—
449#379—21no—
450#379—21no—
451#379—21no—
452#379—21no—
453#379—21no—
454#379—21no—
455#379—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468#376C2311yescharacteristic
469C43C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C25—21no—
498C22×Q8—21no—
499C22×Q8—21no—
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2411yescharacteristic
525C2×Q16—41no—
526C2×Q16—41no—
527C2×Q16—41no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C2×D8—41no—
550C2×D8—41no—
551C2×D8—41no—
552C2×D8—416no—
553C2×M16—22no—
554C2×M16—41no—
555C2×M16—41no—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C4⋊Q8—41no—
568C4⋊Q8—41no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571#126—82no—
572#126—82no—
573#124—22no—
574#124—22no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—41no—
579#124—41no—
580#124—41no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—82no—
586C22⋊Q8—82no—
587C4×Q8—41no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599#117—22no—
600#117—22no—
601#117—41no—
602#117—41no—
603#117—41no—
604#117—41no—
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—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
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—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—82no—
688C2×C22⋊C4—82no—
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42C2×D411yescharacteristic
702C2×C42C2×D411yescharacteristic
703C2×C42C2×D411yescharacteristic
704C2×C42C2×D411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711#107—41no—
712#107—41no—
713#107—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718C4⋊C8—41no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721C4⋊C8—41no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764#97—41no—
765C4×C8—41no—
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#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#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—42no—
813C24—42no—
814C24—42no—
815C24—42no—
816C24—81no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24—81no—
826C24C22×D411yescharacteristic
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8—81no—
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—21no—
867C2×D4—44no—
868C2×D4—44no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—82no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—82no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4H(5,𝔽2)12yes—
882C2×D4H(5,𝔽2)12yes—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—81no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4C22×D411yescharacteristic
912C22×C4C22×D411yescharacteristic
913C22×C4C22×D411yescharacteristic
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4H(5,𝔽2)12yes—
925C22×C42−1+412yes—
926C22×C4C2511yescharacteristic
927Q16—82no—
928SD16—82no—
929SD16—82no—
930SD16—82no—
931SD16—82no—
932D8—44no—
933D8—44no—
934D8—44no—
935D8—44no—
936M16—82no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—44no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C22⋊C4—22no—
1005C22⋊C4—22no—
1006C22⋊C4—41no—
1007C22⋊C4—41no—
1008C22⋊C4—41no—
1009C22⋊C4—41no—
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—42no—
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—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—41no—
1073C42—41no—
1074C42—41no—
1075C42—41no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—22no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—84no—
1117C23—84no—
1118C23—84no—
1119C23—84no—
1120C23—162no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23—162no—
1125C23—162no—
1126C23—162no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23#53712yes—
1131C23C23×D411yescharacteristic
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—162no—
1141Q8—162no—
1142D4—22no—
1143D4—22no—
1144D4—22no—
1145D4—22no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—84no—
1159D4—84no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
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—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4#53712yes—
1243C2×C4C2×H(5,𝔽2)11yescharacteristic
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4C2×2−1+411yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C22—22no—
1258C22—22no—
1259C22—22no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—168no—
1293C22—168no—
1294C22C2×#53711yescharacteristic
1295C22#348811yescharacteristic
1296C22#348811yescharacteristic
1297C22#358411yescharacteristic
1298C22#358411yescharacteristic
1299C22#358511yescharacteristic
1300C22#358511yescharacteristic
1301C4—22no—
1302C4—41no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4#353211yescharacteristic
1327C4#353511yescharacteristic
1328C4#353511yescharacteristic
1329C4#354511yescharacteristic
1330C2—42no—
1331C2—82no—
1332C2—82no—
1333C2—161no—
1334C2—161no—
1335C2#4198311yescharacteristic
1336C2#6092611yescharacteristic
1337C2#6092611yescharacteristic
1338C2#6201111yescharacteristic
1339C2#6204711yescharacteristic
1340C2#6206011yescharacteristic
1341C2#6208811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39070C2semidirect
2. #39070C2semidirect
3. #32859C2semidirect
4. #32817C2semidirect
5. #31915C2semidirect
6. #31899C2semidirect
7. #31831C2semidirect
8. #31815C2semidirect
9. #31219C2semidirect
10. #31217C2semidirect
11. #31170C2semidirect
12. #31160C2semidirect
13. #30134C2semidirect
14. #30133C2semidirect
15. #29839C2semidirect
16. #29838C2semidirect
17. #29786C2semidirect
18. #29542C2semidirect
19. #28256C2semidirect
20. #26415C2semidirect
21. #26413C2semidirect
22. #25974C2semidirect
23. #25966C2semidirect
24. #25105C2semidirect
25. #25105C2semidirect
26. #24516C2semidirect
27. #24516C2semidirect
31. #21980C2semidirect
33. C2×#476C22semidirect
34. C2×#474C22semidirect
36. C2×#464C22semidirect
37. C2×#464C22semidirect
48. #2860C22semidirect
49. #2860C22semidirect
58. #2640C22semidirect
59. #2640C22semidirect
68. #2513C22semidirect
69. #2513C22semidirect
72. #2452C22semidirect
73. #2452C22semidirect
74. #2448C22semidirect
75. #2448C22semidirect
76. #2447C22semidirect
77. #2447C22semidirect
86. #2319C22semidirect
87. #2319C22semidirect
90. C4×#124C22semidirect
91. C4×#124C22semidirect
93. #2101C22semidirect
94. #2101C22semidirect
95. #2092C22semidirect
96. #2092C22semidirect
97. #2088C22semidirect
98. #2088C22semidirect
99. #2088C22semidirect
100. #2087C22semidirect
101. #2068C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
104. #2067C22semidirect
105. #2067C22semidirect
106. #2067C22semidirect
107. #2067C22semidirect
108. #2066C22semidirect
109. #2066C22semidirect
110. #2066C22semidirect
111. #2065C22semidirect
112. #2065C22semidirect
113. #2065C22semidirect
114. #2065C22semidirect
115. #2065C22semidirect
116. #2065C22semidirect
117. #2056C22semidirect
118. #2056C22semidirect
119. #2055C22semidirect
120. #2055C22semidirect
121. #2055C22semidirect
122. #2055C22semidirect
123. #2055C22semidirect
124. #2055C22semidirect
137. #2042C22semidirect
138. #2042C22semidirect
139. #2024C22semidirect
140. #2024C22semidirect
141. #2023C22semidirect
142. #2023C22semidirect
143. #2015C22semidirect
144. #2015C22semidirect
149. #1988C22semidirect
150. #1987C22semidirect
151. #1983C22semidirect
152. #1983C22semidirect
153. #1973C22semidirect
154. #1973C22semidirect
155. #1968C22semidirect
156. #1968C22semidirect
157. #1940C22semidirect
158. #1940C22semidirect
159. #1939C22semidirect
160. #1939C22semidirect
161. #1936C22semidirect
162. #1936C22semidirect
163. #1934C22semidirect
164. #1934C22semidirect
165. #1926C22semidirect
166. #1926C22semidirect
167. #1920C22semidirect
168. #1918C22semidirect
171. #1880C22semidirect
172. #1880C22semidirect
179. #1865C22semidirect
180. #1864C22semidirect
181. #1864C22semidirect
182. #1863C22semidirect
183. #1862C22semidirect
184. #1862C22semidirect
191. #1843C22semidirect
192. #1842C22semidirect
193. #1832C22semidirect
194. #1831C22semidirect
196. #1805C22semidirect
197. #1805C22semidirect
198. #1804C22semidirect
199. #1804C22semidirect

Maximal subgroups

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

subgroupindex
#390702
#328592
#328172
#319152
#318992
#318312
#318152
#312192
#312172
#311702
#311602
#301342
#301332
#298392
#298382
#297862
#295422
#282562
#264152
#264132
#259742
#259662
#251052
#245162
#243552
#235402
#219802