Finite Group Databasebeta

← #6730860

Subgroups — #6730860

Order 512.

1588 conjugacy classes of subgroups.

The subgroup lattice has 1349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42585C211yesmaximal, characteristic, complemented
2#36033C211yesmaximal, characteristic, complemented
3#33014C211yesmaximal, characteristic, complemented
4#32613C211yesmaximal, characteristic, complemented
5#32580C211yesmaximal, characteristic, complemented
6#32189C211yesmaximal, characteristic, complemented
7#31302C211yesmaximal, characteristic, complemented
8#30899C211yesmaximal, characteristic, complemented
9#30535C211yesmaximal, characteristic, complemented
10#30535C211yesmaximal, characteristic, complemented
11#30468C211yesmaximal, characteristic
12#30333C211yesmaximal, characteristic, complemented
13#30120C211yesmaximal, characteristic, complemented
14#27514C211yesmaximal, characteristic, complemented
15#27450C211yesmaximal, characteristic, complemented
16#27206C211yesmaximal, characteristic, complemented
17#27060C211yesmaximal, characteristic, complemented
18#26950C211yesmaximal, characteristic, complemented
19#26907C211yesmaximal, characteristic, complemented
20#26826C211yesmaximal, characteristic, complemented
21#26808C211yesmaximal, characteristic, complemented
22#26748C211yesmaximal, characteristic, complemented
23#26708C211yesmaximal, characteristic, complemented
24#26608C211yesmaximal, characteristic, complemented
25#26258C211yesmaximal, characteristic, complemented
26#25662C211yesmaximal, characteristic, complemented
27#25644C211yesmaximal, characteristic, complemented
28#23232C211yesmaximal, characteristic, complemented
29#23109C211yesmaximal, characteristic, complemented
30#22326C211yesmaximal, characteristic, complemented
31#21458C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#496C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#489C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#475C2211yescharacteristic, complemented
39C2×#460C2211yescharacteristic, complemented
40C2×#463C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#442C2211yescharacteristic
44C2×C4×D8C2211yescharacteristic
45#2832—21no—
46#2718—21no—
47#2712—21no—
48#2692—21no—
49#2672—21no—
50#2662—21no—
51#2638—21no—
52#2624C2211yescharacteristic
53#2621C2211yescharacteristic
54#2620—21no—
55#2580C2211yescharacteristic
56#2567C2211yescharacteristic, complemented
57#2561—21no—
58#2548C2211yescharacteristic, complemented
59#2547C2211yescharacteristic
60#2512C2211yescharacteristic, complemented
61#2497C2211yescharacteristic
62#2491C2211yescharacteristic
63#2491C2211yescharacteristic
64#2482—21no—
65#2480—21no—
66#2480—21no—
67#2474—21no—
68#2468—21no—
69#2468—21no—
70#2452C2211yescharacteristic, complemented
71#2452C2211yescharacteristic, complemented
72#2447C2211yescharacteristic
73#2447C2211yescharacteristic
74#2445C2211yescharacteristic, complemented
75#2435C2211yescharacteristic
76#2435C2211yescharacteristic
77#2428C2211yescharacteristic
78#2396C2211yescharacteristic
79#2395—21no—
80#2369C2211yescharacteristic, complemented
81#2367C2211yescharacteristic
82#2367C2211yescharacteristic
83#2362C2211yescharacteristic
84#2362C2211yescharacteristic
85#2357C2211yescharacteristic
86#2354C2211yescharacteristic, complemented
87#2324C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2093C2211yescharacteristic
90#2092C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2073C2211yescharacteristic, complemented
94#2072C2211yescharacteristic, complemented
95#2068C2211yescharacteristic, complemented
96#2067C2211yescharacteristic
97#2067C2211yescharacteristic, complemented
98#2057C2211yescharacteristic, complemented
99#2055C2211yescharacteristic, complemented
100#2054C2211yescharacteristic
101#2054C2211yescharacteristic
102#2054C2211yescharacteristic
103#2043C2211yescharacteristic, complemented
104#2043C2211yescharacteristic, complemented
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2041C2211yescharacteristic, complemented
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2035C2211yescharacteristic
112#2035C2211yescharacteristic
113#2024C2211yescharacteristic, complemented
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2013C2211yescharacteristic, complemented
117#2013C2211yescharacteristic, complemented
118#2012C2211yescharacteristic
119#2012C2211yescharacteristic
120#2012C2211yescharacteristic
121#2012C2211yescharacteristic
122#2012C2211yescharacteristic
123#2011C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1988C2211yescharacteristic, complemented
129#1985C2211yescharacteristic, complemented
130#1985C2211yescharacteristic, complemented
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1983C2211yescharacteristic
134#1973C2211yescharacteristic, complemented
135#1973C2211yescharacteristic, complemented
136#1973C2211yescharacteristic, complemented
137#1972C2211yescharacteristic
138#1972C2211yescharacteristic
139#1968C2211yescharacteristic, complemented
140#1959C2211yescharacteristic
141#1948C2211yescharacteristic, complemented
142#1944C2211yescharacteristic, complemented
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic, complemented
146#1935C2211yescharacteristic, complemented
147#1933C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1928C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic, complemented
154#1926C2211yescharacteristic, complemented
155#1925C2211yescharacteristic
156#1925C2211yescharacteristic, complemented
157#1924C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic
160#1924C2211yescharacteristic
161#1921C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1880C2211yescharacteristic, complemented
169#1880C2211yescharacteristic, complemented
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1877C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1877C2211yescharacteristic, complemented
180#1875C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1865C2211yescharacteristic, complemented
183#1864C2211yescharacteristic
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1854C2211yescharacteristic
190#1825C2211yescharacteristic
191#1818C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1776C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1771C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic
202#1750C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212#556—42no—
213#556—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×#121—21no—
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237#518—42no—
238#518—42no—
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117—21no—
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256#496—42no—
257#489—24no—
258#489—42no—
259#482—42no—
260#475—42no—
261#463—24no—
262#460—42no—
263#447—24no—
264#447—42no—
265#442—42no—
266C4×D8—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321#400—21no—
322#400D411yescharacteristic
323#399—21no—
324#399—21no—
325#399D411yescharacteristic
326#398—21no—
327#398—21no—
328#398D411yescharacteristic
329#398D411yescharacteristic
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396D411yescharacteristic
345#396D411yescharacteristic
346#395—21no—
347#395—21no—
348#395D411yescharacteristic
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#393—21no—
363#393—21no—
364#393—21no—
365#393—21no—
366#393—21no—
367#393D411yescharacteristic
368#392—21no—
369#391—21no—
370#391—21no—
371#391—21no—
372#391C2311yescharacteristic
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#390—21no—
377#390—21no—
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#389—21no—
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
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#387—21no—
417#387—21no—
418#387—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#384—21no—
432#384C2311yescharacteristic
433#382C2311yescharacteristic
434#381—21no—
435#381—21no—
436#381—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2411yescharacteristic
521C2×SD16—22no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—22no—
554C4⋊Q8—41no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559#127—41no—
560#127—41no—
561#126—44no—
562#126—44no—
563#126—82no—
564#124—22no—
565#124—22no—
566#124—22no—
567#124—22no—
568#124—41no—
569#124—41no—
570#124—41no—
571#124—41no—
572#124—82no—
573#124—82no—
574#124—82no—
575#123—82no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—44no—
581C22⋊Q8—82no—
582C22⋊Q8—82no—
583#121—22no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—82no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—44no—
607C4×D4—44no—
608#117—22no—
609#117—41no—
610#117—41no—
611#117—41no—
612#117—44no—
613#117—82no—
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⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4—44no—
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721#107—41no—
722#107—41no—
723#107—41no—
724#107—41no—
725#106—22no—
726#106—22no—
727#106—41no—
728#106—41no—
729C4⋊C8—22no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733#103—22no—
734#103—22no—
735#103—22no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—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—
762#102—41no—
763#102—41no—
764#102#4114yes—
765C22⋊C8—22no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769#97—22no—
770#97—41no—
771#97—41no—
772#97—41no—
773#97—41no—
774C4×C8—41no—
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#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—42no—
816C24—42no—
817C24—42no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24C22×D411yescharacteristic
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
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—41no—
836C2×Q8—41no—
837C2×Q8—41no—
838C2×Q8—42no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—44no—
872C2×D4—44no—
873C2×D4—44no—
874C2×D4—44no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4C2×#4112yes—
886C2×D4H(5,𝔽2)12yes—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—24no—
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—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C2511yescharacteristic
937SD16—82no—
938SD16—82no—
939SD16—82no—
940SD16—82no—
941D8—44no—
942D8—44no—
943D8—82no—
944D8—82no—
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—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8C2×#4112yes—
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—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4C2×#4112yes—
1017C4⋊C4H(5,𝔽2)12yes—
1018C22⋊C4—24no—
1019C22⋊C4—41no—
1020C22⋊C4—41no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—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—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—42no—
1082C42—42no—
1083C42—42no—
1084C42—42no—
1085C42—42no—
1086C42—81no—
1087C42—81no—
1088C42—81no—
1089C42—81no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—22no—
1095C23—21no—
1096C23—22no—
1097C23—21no—
1098C23—21no—
1099C23—48no—
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—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—162no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23—162no—
1131C23—162no—
1132C23C23×D411yescharacteristic
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—82no—
1142Q8—162no—
1143Q8—162no—
1144D4—22no—
1145D4—22no—
1146D4—22no—
1147D4—22no—
1148D4—48no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—162no—
1162D4—162no—
1163D4—162no—
1164D4—162no—
1165C2×C4—21no—
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—22no—
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—22no—
1204C2×C4—21no—
1205C2×C4—21no—
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—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—84no—
1245C2×C4—84no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4—162no—
1249C2×C4—162no—
1250C2×C4C22×#4111yescharacteristic
1251C2×C4C2×H(5,𝔽2)11yescharacteristic
1252C2×C4C2×H(5,𝔽2)11yescharacteristic
1253C2×C4#58511yescharacteristic
1254C2×C4#58511yescharacteristic
1255C2×C4#58511yescharacteristic
1256C8—22no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C8—41no—
1263C8—41no—
1264C22—41no—
1265C22—42no—
1266C22—41no—
1267C22—42no—
1268C22—41no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—41no—
1273C22—42no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
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—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—168no—
1300C22D4×#4111yescharacteristic
1301C22#348411yescharacteristic
1302C22#348711yescharacteristic
1303C22#358511yescharacteristic
1304C22#358511yescharacteristic
1305C22#358511yescharacteristic
1306C22#358611yescharacteristic
1307C4—41no—
1308C4—41no—
1309C4—42no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—42no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4#346011yescharacteristic
1333C4#351311yescharacteristic
1334C4#353311yescharacteristic
1335C4#354011yescharacteristic
1336C2—81no—
1337C2—82no—
1338C2—82no—
1339C2—161no—
1340C2—161no—
1341C2#3780311yescharacteristic
1342C2#6150611yescharacteristic
1343C2#6151811yescharacteristic
1344C2#6164711yescharacteristic
1345C2#6167311yescharacteristic
1346C2#6194211yescharacteristic
1347C2#6194411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30468C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42585C2semidirect
2. #36033C2semidirect
3. #33014C2semidirect
4. #32613C2semidirect
5. #32580C2semidirect
6. #32189C2semidirect
7. #31302C2semidirect
8. #30899C2semidirect
9. #30535C2semidirect
10. #30535C2semidirect
12. #30333C2semidirect
13. #30120C2semidirect
14. #27514C2semidirect
15. #27450C2semidirect
16. #27206C2semidirect
17. #27060C2semidirect
18. #26950C2semidirect
19. #26907C2semidirect
20. #26826C2semidirect
21. #26808C2semidirect
22. #26748C2semidirect
23. #26708C2semidirect
24. #26608C2semidirect
25. #26258C2semidirect
26. #25662C2semidirect
27. #25644C2semidirect
28. #23232C2semidirect
29. #23109C2semidirect
30. #22326C2semidirect
31. #21458C2semidirect
38. C2×#475C22semidirect
39. C2×#460C22semidirect
56. #2567C22semidirect
58. #2548C22semidirect
60. #2512C22semidirect
70. #2452C22semidirect
71. #2452C22semidirect
74. #2445C22semidirect
80. #2369C22semidirect
86. #2354C22semidirect
88. #2101C22semidirect
90. #2092C22semidirect
91. #2086C22semidirect
92. #2085C22semidirect
93. #2073C22semidirect
94. #2072C22semidirect
95. #2068C22semidirect
97. #2067C22semidirect
98. #2057C22semidirect
99. #2055C22semidirect
103. #2043C22semidirect
104. #2043C22semidirect
108. #2041C22semidirect
113. #2024C22semidirect
116. #2013C22semidirect
117. #2013C22semidirect
128. #1988C22semidirect
129. #1985C22semidirect
130. #1985C22semidirect
134. #1973C22semidirect
135. #1973C22semidirect
136. #1973C22semidirect
139. #1968C22semidirect
141. #1948C22semidirect
142. #1944C22semidirect
145. #1936C22semidirect
146. #1935C22semidirect
147. #1933C22semidirect
148. #1928C22semidirect
149. #1928C22semidirect
150. #1927C22semidirect
153. #1926C22semidirect
154. #1926C22semidirect
156. #1925C22semidirect
161. #1921C22semidirect
162. #1920C22semidirect
163. #1920C22semidirect
164. #1917C22semidirect
165. #1917C22semidirect
166. #1917C22semidirect
167. #1917C22semidirect
168. #1880C22semidirect
169. #1880C22semidirect
177. #1877C22semidirect
178. #1877C22semidirect
179. #1877C22semidirect
181. #1865C22semidirect
182. #1865C22semidirect
194. #1776C22semidirect
195. #1771C22semidirect
196. #1771C22semidirect
197. #1763C22semidirect
198. #1763C22semidirect
200. #1762C22semidirect

Maximal subgroups

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

subgroupindex
#425852
#360332
#330142
#326132
#325802
#321892
#313022
#308992
#305352
#304682
#303332
#301202
#275142
#274502
#272062
#270602
#269502
#269072
#268262
#268082
#267482
#267082
#266082
#262582
#256622
#256442
#232322
#231092
#223262
#214582