Finite Group Databasebeta

← #7308838

Subgroups — #7308838

Order 512.

1542 conjugacy classes of subgroups.

The subgroup lattice has 1347 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45287C211yesmaximal, characteristic, complemented
2#42563C211yesmaximal, characteristic, complemented
3#32246C211yesmaximal, characteristic, complemented
4#32061C211yesmaximal, characteristic, complemented
5#31915C211yesmaximal, characteristic, complemented
6#31863C211yesmaximal, characteristic, complemented
7#31747C211yesmaximal, characteristic, complemented
8#31632C211yesmaximal, characteristic, complemented
9#31542C211yesmaximal, characteristic, complemented
10#31155C211yesmaximal, characteristic, complemented
11#31032C211yesmaximal, characteristic
12#31012C211yesmaximal, characteristic, complemented
13#30928C211yesmaximal, characteristic, complemented
14#30585C211yesmaximal, characteristic, complemented
15#29768C211yesmaximal, characteristic, complemented
16#29677C211yesmaximal, characteristic, complemented
17#29246C211yesmaximal, characteristic, complemented
18#27122C211yesmaximal, characteristic, complemented
19#26806C211yesmaximal, characteristic, complemented
20#26628C211yesmaximal, characteristic, complemented
21#26615C211yesmaximal, characteristic, complemented
22#26478C211yesmaximal, characteristic, complemented
23#26189C211yesmaximal, characteristic, complemented
24#25966C211yesmaximal, characteristic, complemented
25#25152C211yesmaximal, characteristic, complemented
26#25101C211yesmaximal, characteristic, complemented
27#24819C211yesmaximal, characteristic, complemented
28#24167C211yesmaximal, characteristic, complemented
29#24135C211yesmaximal, characteristic, complemented
30#23979C211yesmaximal, characteristic, complemented
31#23321C211yesmaximal, characteristic, complemented
32C2×#556C2211yescharacteristic
33C2×#542C2211yescharacteristic, complemented
34C2×#481C2211yescharacteristic
35C2×#483C2211yescharacteristic, complemented
36C2×#479C2211yescharacteristic, complemented
37C2×#477C2211yescharacteristic, complemented
38C2×#474C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#464C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#447C2211yescharacteristic
45C2×#441C2211yescharacteristic, complemented
46C2×C4×SD16C2211yescharacteristic
47C2×#418C2211yescharacteristic
48#2827—21no—
49#2781—21no—
50#2753—21no—
51#2735—21no—
52#2727—21no—
53#2723—21no—
54#2715—21no—
55#2685—21no—
56#2672—21no—
57#2648—21no—
58#2622—21no—
59#2620C2211yescharacteristic
60#2566C2211yescharacteristic
61#2553—21no—
62#2551C2211yescharacteristic, complemented
63#2536C2211yescharacteristic
64#2513C2211yescharacteristic
65#2500C2211yescharacteristic, complemented
66#2496C2211yescharacteristic
67#2491—21no—
68#2490C2211yescharacteristic
69#2489C2211yescharacteristic
70#2480—21no—
71#2469—21no—
72#2452C2211yescharacteristic, complemented
73#2448C2211yescharacteristic
74#2448C2211yescharacteristic, complemented
75#2439C2211yescharacteristic
76#2435C2211yescharacteristic
77#2429—21no—
78#2427C2211yescharacteristic
79#2426C2211yescharacteristic
80#2423C2211yescharacteristic
81#2416C2211yescharacteristic
82#2408C2211yescharacteristic
83#2395C2211yescharacteristic
84#2367C2211yescharacteristic
85#2363C2211yescharacteristic
86#2360C2211yescharacteristic, complemented
87#2351C2211yescharacteristic, complemented
88D4×C22⋊C4C2211yescharacteristic
89#2324C2211yescharacteristic
90#2316C2211yescharacteristic, complemented
91#2099C2211yescharacteristic, complemented
92#2092C2211yescharacteristic
93#2092C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2077C2211yescharacteristic
100#2074C2211yescharacteristic, complemented
101#2071C2211yescharacteristic
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic
104#2067C2211yescharacteristic
105#2066C2211yescharacteristic, complemented
106#2066C2211yescharacteristic, complemented
107#2066C2211yescharacteristic, complemented
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2065C2211yescharacteristic
111#2059C2211yescharacteristic, complemented
112#2055C2211yescharacteristic, complemented
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2034C2211yescharacteristic
121#2034C2211yescharacteristic
122#2033C2211yescharacteristic, complemented
123#2025C2211yescharacteristic, complemented
124#2024C2211yescharacteristic, complemented
125#2023C2211yescharacteristic
126#2023C2211yescharacteristic
127#2023C2211yescharacteristic
128#2015C2211yescharacteristic
129#2015C2211yescharacteristic, complemented
130#2012C2211yescharacteristic
131#2012C2211yescharacteristic
132#2001C2211yescharacteristic
133#2001C2211yescharacteristic, complemented
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic
136#2000C2211yescharacteristic, complemented
137#1999C2211yescharacteristic
138#1999C2211yescharacteristic
139#1993C2211yescharacteristic, complemented
140#1991C2211yescharacteristic, complemented
141#1987C2211yescharacteristic, complemented
142#1983C2211yescharacteristic
143#1983C2211yescharacteristic, complemented
144#1973C2211yescharacteristic
145#1972C2211yescharacteristic
146#1970C2211yescharacteristic
147#1959C2211yescharacteristic
148#1955C2211yescharacteristic
149#1947C2211yescharacteristic, complemented
150#1940C2211yescharacteristic, complemented
151#1939C2211yescharacteristic, complemented
152#1936C2211yescharacteristic
153#1936C2211yescharacteristic, complemented
154#1933C2211yescharacteristic, complemented
155#1927C2211yescharacteristic, complemented
156#1926C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic, complemented
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic, complemented
162#1921C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1894C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic, complemented
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1878C2211yescharacteristic, complemented
176#1875C2211yescharacteristic
177#1875C2211yescharacteristic
178#1874C2211yescharacteristic
179#1873C2211yescharacteristic
180#1873C2211yescharacteristic, complemented
181#1870C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1862C2211yescharacteristic
187#1862C2211yescharacteristic, complemented
188#1854C2211yescharacteristic
189#1854C2211yescharacteristic, complemented
190#1852C2211yescharacteristic, complemented
191#1851C2211yescharacteristic
192#1851C2211yescharacteristic
193#1825C2211yescharacteristic
194#1809C2211yescharacteristic
195#1805C2211yescharacteristic, complemented
196#1804C2211yescharacteristic
197#1803C2211yescharacteristic, complemented
198#1802C2211yescharacteristic, complemented
199#1798C2211yescharacteristic, complemented
200#1798C2211yescharacteristic, complemented
201#1786C2211yescharacteristic
202#1776C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211#556—42no—
212#556—42no—
213#542—42no—
214#542—42no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#126—21no—
222C2×#125C2311yescharacteristic
223C2×#124—21no—
224C2×#124—21no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×C4×Q8—21no—
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255#483—42no—
256#481—42no—
257#479—42no—
258#477—42no—
259#474—42no—
260#468—42no—
261#464—42no—
262#463—42no—
263#463—42no—
264#450—42no—
265#447—42no—
266#441—42no—
267C4×SD16—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285#418—42no—
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#400—21no—
325#400—21no—
326#400D411yescharacteristic
327#399—21no—
328#399—21no—
329#399—21no—
330#399D411yescharacteristic
331#398—21no—
332#398—21no—
333#398D411yescharacteristic
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397D411yescharacteristic
343#397D411yescharacteristic
344#397D411yescharacteristic
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#395—21no—
354#395—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394D411yescharacteristic
368#394D411yescharacteristic
369#393—21no—
370#393—21no—
371#392—21no—
372#391—21no—
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#390—21no—
377#390—21no—
378#390—21no—
379#390—21no—
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
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#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#382—21no—
440#382—21no—
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#380—21no—
444#380—21no—
445#380—21no—
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#379—21no—
451#379—21no—
452#379—21no—
453#379—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8—21no—
498C22×Q8—21no—
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×D4—22no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2×D411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C22×D4C2411yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2411yescharacteristic
521C23×C4C2411yescharacteristic
522C2×Q16—22no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×D8—22no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—22no—
552C4⋊Q8—22no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555C4⋊Q8—82no—
556#126—44no—
557#126—44no—
558#126—44no—
559#126—82no—
560#125—41no—
561#125—41no—
562#124—22no—
563#124—22no—
564#124—41no—
565#124—41no—
566#124—41no—
567#124—41no—
568#124—44no—
569#124—44no—
570#123—44no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—41no—
575C22⋊Q8—44no—
576C22⋊Q8—41no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—82no—
581#121—22no—
582#121—22no—
583#121—41no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—82no—
590#120—82no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—22no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×Q8—41no—
598C4×Q8—41no—
599C4×Q8—44no—
600C4×D4—22no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608#117—22no—
609#117—41no—
610#117—41no—
611#117—41no—
612#117—41no—
613#117—41no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—22no—
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⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
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—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—82no—
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725#107—22no—
726#107—22no—
727#107—41no—
728#107—41no—
729#107—41no—
730#106—22no—
731#106—22no—
732#106—41no—
733#106—41no—
734#106—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#103—41no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777#97—41no—
778#97—41no—
779C4×C8—41no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—21no—
817C24—21no—
818C24—42no—
819C24—42no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24—81no—
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—42no—
839C2×Q8—42no—
840C2×Q8—42no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×Q8—81no—
844C2×Q8H(5,𝔽2)12yes—
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—41no—
863C2×D4—41no—
864C2×D4—41no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—44no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—82no—
873C2×D4—82no—
874C2×D4—82no—
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×D42−1+412yes—
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—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—42no—
911C22×C4—42no—
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×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
935Q16—44no—
936SD16—44no—
937SD16—82no—
938SD16—82no—
939D8—82no—
940D8—82no—
941M16—82no—
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—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C4⋊C4—24no—
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—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—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
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⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4H(5,𝔽2)12yes—
1019C4⋊C4H(5,𝔽2)12yes—
1020C22⋊C4—24no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
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—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
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—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—22no—
1103C23—21no—
1104C23—21no—
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—84no—
1126C23—84no—
1127C23—162no—
1128C23—162no—
1129C23—162no—
1130C23—162no—
1131C23—162no—
1132C23C23×D411yescharacteristic
1133Q8—22no—
1134Q8—22no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—41no—
1139Q8—41no—
1140Q8—41no—
1141Q8—84no—
1142Q8—162no—
1143D4—22no—
1144D4—22no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—41no—
1152D4—41no—
1153D4—41no—
1154D4—41no—
1155D4—82no—
1156D4—84no—
1157D4—162no—
1158D4—162no—
1159D4—162no—
1160D4—162no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
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—22no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
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—41no—
1201C2×C4—41no—
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—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4—162no—
1247C2×C4—162no—
1248C2×C4C2×H(5,𝔽2)11yescharacteristic
1249C2×C4C2×H(5,𝔽2)11yescharacteristic
1250C2×C4C2×H(5,𝔽2)11yescharacteristic
1251C2×C4C2×2−1+411yescharacteristic
1252C2×C4#58511yescharacteristic
1253C2×C4#58511yescharacteristic
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C8—41no—
1261C8—41no—
1262C22—41no—
1263C22—41no—
1264C22—42no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—42no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—42no—
1277C22—41no—
1278C22—41no—
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—168no—
1298C22#348411yescharacteristic
1299C22#348811yescharacteristic
1300C22#348911yescharacteristic
1301C22#358411yescharacteristic
1302C22#358511yescharacteristic
1303C22#358511yescharacteristic
1304C22#358611yescharacteristic
1305C4—41no—
1306C4—41no—
1307C4—42no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—42no—
1313C4—41no—
1314C4—41no—
1315C4—41no—
1316C4—42no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4#353311yescharacteristic
1331C4#353611yescharacteristic
1332C4#354111yescharacteristic
1333C4#354611yescharacteristic
1334C2—81no—
1335C2—81no—
1336C2—82no—
1337C2—161no—
1338C2—161no—
1339C2#4784511yescharacteristic
1340C2#6165311yescharacteristic
1341C2#6168111yescharacteristic
1342C2#6201111yescharacteristic
1343C2#6209211yescharacteristic
1344C2#6217511yescharacteristic
1345C2#6222711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#31032C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45287C2semidirect
2. #42563C2semidirect
3. #32246C2semidirect
4. #32061C2semidirect
5. #31915C2semidirect
6. #31863C2semidirect
7. #31747C2semidirect
8. #31632C2semidirect
9. #31542C2semidirect
10. #31155C2semidirect
12. #31012C2semidirect
13. #30928C2semidirect
14. #30585C2semidirect
15. #29768C2semidirect
16. #29677C2semidirect
17. #29246C2semidirect
18. #27122C2semidirect
19. #26806C2semidirect
20. #26628C2semidirect
21. #26615C2semidirect
22. #26478C2semidirect
23. #26189C2semidirect
24. #25966C2semidirect
25. #25152C2semidirect
26. #25101C2semidirect
27. #24819C2semidirect
28. #24167C2semidirect
29. #24135C2semidirect
30. #23979C2semidirect
31. #23321C2semidirect
33. C2×#542C22semidirect
35. C2×#483C22semidirect
36. C2×#479C22semidirect
37. C2×#477C22semidirect
45. C2×#441C22semidirect
62. #2551C22semidirect
65. #2500C22semidirect
72. #2452C22semidirect
74. #2448C22semidirect
86. #2360C22semidirect
87. #2351C22semidirect
90. #2316C22semidirect
91. #2099C22semidirect
93. #2092C22semidirect
94. #2088C22semidirect
95. #2087C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
98. #2084C22semidirect
100. #2074C22semidirect
105. #2066C22semidirect
106. #2066C22semidirect
107. #2066C22semidirect
111. #2059C22semidirect
112. #2055C22semidirect
119. #2036C22semidirect
122. #2033C22semidirect
123. #2025C22semidirect
124. #2024C22semidirect
129. #2015C22semidirect
133. #2001C22semidirect
136. #2000C22semidirect
139. #1993C22semidirect
140. #1991C22semidirect
141. #1987C22semidirect
143. #1983C22semidirect
149. #1947C22semidirect
150. #1940C22semidirect
151. #1939C22semidirect
153. #1936C22semidirect
154. #1933C22semidirect
155. #1927C22semidirect
156. #1926C22semidirect
159. #1924C22semidirect
161. #1923C22semidirect
162. #1921C22semidirect
163. #1920C22semidirect
164. #1918C22semidirect
165. #1917C22semidirect
166. #1917C22semidirect
172. #1880C22semidirect
175. #1878C22semidirect
180. #1873C22semidirect
184. #1863C22semidirect
185. #1863C22semidirect
187. #1862C22semidirect
189. #1854C22semidirect
190. #1852C22semidirect
195. #1805C22semidirect
197. #1803C22semidirect
198. #1802C22semidirect
199. #1798C22semidirect
200. #1798C22semidirect
202. #1776C22semidirect

Maximal subgroups

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

subgroupindex
#452872
#425632
#322462
#320612
#319152
#318632
#317472
#316322
#315422
#311552
#310322
#310122
#309282
#305852
#297682
#296772
#292462
#271222
#268062
#266282
#266152
#264782
#261892
#259662
#251522
#251012
#248192
#241672
#241352
#239792
#233212