Finite Group Databasebeta

← #6915710

Subgroups — #6915710

Order 512.

1619 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39257C211yesmaximal, characteristic, complemented
2#37748C211yesmaximal, characteristic
3#32829C211yesmaximal, characteristic, complemented
4#32753C211yesmaximal, characteristic, complemented
5#31511C211yesmaximal, characteristic, complemented
6#31503C211yesmaximal, characteristic, complemented
7#30860C211yesmaximal, characteristic, complemented
8#30858C211yesmaximal, characteristic, complemented
9#30426C211yesmaximal, characteristic, complemented
10#30424C211yesmaximal, characteristic, complemented
11#30421C211yesmaximal, characteristic, complemented
12#30420C211yesmaximal, characteristic, complemented
13#30323C211yesmaximal, characteristic, complemented
14#30183C211yesmaximal, characteristic, complemented
15#30085C211yesmaximal, characteristic, complemented
16#30050C211yesmaximal, characteristic, complemented
17#29632C211yesmaximal, characteristic, complemented
18#28582C211yesmaximal, characteristic, complemented
19#28166C211yesmaximal, characteristic, complemented
20#27547C211yesmaximal, characteristic, complemented
21#27534C211yesmaximal, characteristic, complemented
22#27219C211yesmaximal, characteristic, complemented
23#27214C211yesmaximal, characteristic, complemented
24#26179C211yesmaximal, characteristic, complemented
25#26177C211yesmaximal, characteristic, complemented
26#25501C211yesmaximal, characteristic, complemented
27#25176C211yesmaximal, characteristic, complemented
28#25166C211yesmaximal, characteristic, complemented
29#24220C211yesmaximal, characteristic, complemented
30#23576C211yesmaximal, characteristic, complemented
31#22003C211yesmaximal, characteristic, complemented
32C2×#535C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#470C2211yescharacteristic, complemented
35C2×#468C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#468C2211yescharacteristic, complemented
38C2×#464C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#461C2211yescharacteristic
41C2×#461C2211yescharacteristic, complemented
42C2×#452C2211yescharacteristic
43C2×#452C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#440C2211yescharacteristic
47C2×#440C2211yescharacteristic, complemented
48#2855C2211yescharacteristic, complemented
49#2850C2211yescharacteristic
50#2793—21no—
51#2790—21no—
52#2776—21no—
53#2757—21no—
54#2688—21no—
55#2686—21no—
56#2684—21no—
57#2668—21no—
58#2647C2211yescharacteristic, complemented
59#2640C2211yescharacteristic
60#2628C2211yescharacteristic
61#2625C2211yescharacteristic
62#2606—21no—
63#2594—21no—
64#2573—21no—
65#2538C2211yescharacteristic
66#2536C2211yescharacteristic
67#2526—21no—
68#2495C2211yescharacteristic
69#2494C2211yescharacteristic, complemented
70#2447C2211yescharacteristic
71#2445C2211yescharacteristic
72#2444—21no—
73#2430—21no—
74#2429C2211yescharacteristic
75#2429C2211yescharacteristic, complemented
76#2428C2211yescharacteristic
77#2427C2211yescharacteristic
78#2418—21no—
79#2408C2211yescharacteristic
80#2407C2211yescharacteristic
81#2404—21no—
82#2356C2211yescharacteristic, complemented
83Q8×C4⋊C4C2211yescharacteristic, complemented
84#2339C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86#2328C2211yescharacteristic
87#2327C2211yescharacteristic, complemented
88#2323C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic, complemented
90#2290C2211yescharacteristic
91#2095C2211yescharacteristic, complemented
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2086C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2077C2211yescharacteristic
100#2076C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2074C2211yescharacteristic, complemented
104#2074C2211yescharacteristic, complemented
105#2074C2211yescharacteristic, complemented
106#2074C2211yescharacteristic, complemented
107#2073C2211yescharacteristic
108#2073C2211yescharacteristic
109#2071C2211yescharacteristic
110#2071C2211yescharacteristic, complemented
111#2068C2211yescharacteristic, complemented
112#2068C2211yescharacteristic, complemented
113#2068C2211yescharacteristic, complemented
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2066C2211yescharacteristic, complemented
117#2057C2211yescharacteristic, complemented
118#2057C2211yescharacteristic, complemented
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2041C2211yescharacteristic
123#2041C2211yescharacteristic
124#2041C2211yescharacteristic
125#2036C2211yescharacteristic
126#2036C2211yescharacteristic
127#2036C2211yescharacteristic
128#2036C2211yescharacteristic, complemented
129#2035C2211yescharacteristic
130#2034C2211yescharacteristic
131#2033C2211yescharacteristic
132#2033C2211yescharacteristic, complemented
133#2024C2211yescharacteristic, complemented
134#2024C2211yescharacteristic, complemented
135#2016C2211yescharacteristic, complemented
136#2015C2211yescharacteristic
137#2015C2211yescharacteristic
138#2015C2211yescharacteristic
139#2014C2211yescharacteristic
140#2014C2211yescharacteristic
141#2014C2211yescharacteristic
142#2013C2211yescharacteristic
143#2001C2211yescharacteristic, complemented
144#2000C2211yescharacteristic
145#2000C2211yescharacteristic
146#2000C2211yescharacteristic, complemented
147#1983C2211yescharacteristic
148#1982C2211yescharacteristic
149#1973C2211yescharacteristic
150#1971C2211yescharacteristic, complemented
151#1936C2211yescharacteristic
152#1935C2211yescharacteristic, complemented
153#1928C2211yescharacteristic, complemented
154#1926C2211yescharacteristic
155#1924C2211yescharacteristic
156#1924C2211yescharacteristic
157#1919C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1917C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1895C2211yescharacteristic
162#1895C2211yescharacteristic
163#1895C2211yescharacteristic, complemented
164#1894C2211yescharacteristic, complemented
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic, complemented
171#1880C2211yescharacteristic, complemented
172#1878C2211yescharacteristic, complemented
173#1878C2211yescharacteristic, complemented
174#1878C2211yescharacteristic, complemented
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic, complemented
177#1870C2211yescharacteristic
178#1870C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic, complemented
186#1862C2211yescharacteristic, complemented
187#1851C2211yescharacteristic, complemented
188#1851C2211yescharacteristic, complemented
189#1840C2211yescharacteristic, complemented
190#1832C2211yescharacteristic, complemented
191#1818C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic, complemented
194#1798C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic, complemented
201#1749C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×Q16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C22×M16C2311yescharacteristic
216#535—42no—
217#535—42no—
218#532—42no—
219#532—42no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×C4⋊Q8C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#124—21no—
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×#120—21no—
242C2×#120—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C42C2311yescharacteristic
256#470—42no—
257#468—42no—
258#468—42no—
259#468—42no—
260#464—42no—
261#461—42no—
262#461—42no—
263#460—42no—
264#452—42no—
265#452—42no—
266#450—42no—
267#450—42no—
268#440—42no—
269#440—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322#401—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#399—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#395—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#393—21no—
357#393—21no—
358#393—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#390—21no—
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#388—21no—
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#388D411yescharacteristic
400#388D411yescharacteristic
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387D411yescharacteristic
413#387D411yescharacteristic
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386D411yescharacteristic
429#386D411yescharacteristic
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385D411yescharacteristic
435#385D411yescharacteristic
436#384—21no—
437#384C2311yescharacteristic
438#383—21no—
439#383—21no—
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#381—21no—
444#381—21no—
445#381—21no—
446#380—21no—
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463#376—21no—
464#376C2311yescharacteristic
465C2×#95—21no—
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#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—44no—
504C2×#41—82no—
505C2×#41—82no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—22no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×D411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C2×Q16—22no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×M16—41no—
563C2×M16—41no—
564C2×M16—41no—
565C2×M16—41no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C4⋊Q8—22no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579C4⋊Q8—41no—
580#127—22no—
581#127—22no—
582#127—22no—
583#127—41no—
584#124—22no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—44no—
589#123—82no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600#121—22no—
601#121—22no—
602#121—41no—
603#121—41no—
604#121—44no—
605#121—44no—
606#121—44no—
607#121—41no—
608#121—41no—
609#121—82no—
610#120—44no—
611#120—44no—
612#120—82no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×D4—22no—
622C4×D4—22no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—44no—
632#117—41no—
633#117—41no—
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—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
659C2×C4⋊C4C2×D411yescharacteristic
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
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—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—41no—
719C2×C42—41no—
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727#107—41no—
728#107—41no—
729#107—41no—
730#107—41no—
731#107—41no—
732#107—41no—
733#106—41no—
734#106—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—22no—
740#103—22no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
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—
770#102—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—
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#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—21no—
828C24—42no—
829C24—42no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837#41—82no—
838#41—82no—
839#41—82no—
840#41—82no—
841#41—816no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—42no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8H(5,𝔽2)12yes—
863C2×D4—24no—
864C2×D4—24no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—82no—
905C2×D4—82no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4H(5,𝔽2)12yes—
914C2×D4H(5,𝔽2)12yes—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—41no—
944C22×C4—41no—
945C22×C4—41no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C2511yescharacteristic
974Q16—82no—
975Q16—82no—
976SD16—44no—
977SD16—44no—
978SD16—82no—
979SD16—82no—
980SD16—82no—
981SD16—82no—
982M16—82no—
983M16—82no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—41no—
1029C4⋊C4—41no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C22⋊C4—41no—
1056C22⋊C4—41no—
1057C22⋊C4—41no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C42—21no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—41no—
1106C42—41no—
1107C42—42no—
1108C42—42no—
1109C42—42no—
1110C42—81no—
1111C42—81no—
1112C42—81no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—22no—
1124C23—21no—
1125C23—22no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—84no—
1149C23—84no—
1150C23—162no—
1151C23—162no—
1152C23—162no—
1153C23—162no—
1154C23—162no—
1155C23C23×D411yescharacteristic
1156Q8—22no—
1157Q8—22no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—41no—
1167Q8—41no—
1168Q8—84no—
1169D4—22no—
1170D4—22no—
1171D4—22no—
1172D4—22no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—84no—
1182D4—84no—
1183D4—82no—
1184D4—84no—
1185D4—84no—
1186D4—84no—
1187D4—84no—
1188D4—162no—
1189D4—162no—
1190D4—162no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—44no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—82no—
1276C2×C4—84no—
1277C2×C4—84no—
1278C2×C4—84no—
1279C2×C4—162no—
1280C2×C4—162no—
1281C2×C4C2×H(5,𝔽2)11yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4C2×H(5,𝔽2)11yescharacteristic
1284C2×C4#58511yescharacteristic
1285C2×C4#58511yescharacteristic
1286C2×C4#58511yescharacteristic
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8—41no—
1294C8—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—42no—
1306C22—42no—
1307C22—41no—
1308C22—42no—
1309C22—42no—
1310C22—41no—
1311C22—41no—
1312C22—42no—
1313C22—42no—
1314C22—41no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—168no—
1331C22#344911yescharacteristic
1332C22#348411yescharacteristic
1333C22#348811yescharacteristic
1334C22#358511yescharacteristic
1335C22#358511yescharacteristic
1336C22#358611yescharacteristic
1337C22#358611yescharacteristic
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—42no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4#353411yescharacteristic
1364C4#353411yescharacteristic
1365C4#356011yescharacteristic
1366C4#356011yescharacteristic
1367C2—81no—
1368C2—81no—
1369C2—82no—
1370C2—82no—
1371C2—161no—
1372C2#4060611yescharacteristic
1373C2#6097311yescharacteristic
1374C2#6100411yescharacteristic
1375C2#6164311yescharacteristic
1376C2#6164911yescharacteristic
1377C2#6208511yescharacteristic
1378C2#6209211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37748C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39257C2semidirect
3. #32829C2semidirect
4. #32753C2semidirect
5. #31511C2semidirect
6. #31503C2semidirect
7. #30860C2semidirect
8. #30858C2semidirect
9. #30426C2semidirect
10. #30424C2semidirect
11. #30421C2semidirect
12. #30420C2semidirect
13. #30323C2semidirect
14. #30183C2semidirect
15. #30085C2semidirect
16. #30050C2semidirect
17. #29632C2semidirect
18. #28582C2semidirect
19. #28166C2semidirect
20. #27547C2semidirect
21. #27534C2semidirect
22. #27219C2semidirect
23. #27214C2semidirect
24. #26179C2semidirect
25. #26177C2semidirect
26. #25501C2semidirect
27. #25176C2semidirect
28. #25166C2semidirect
29. #24220C2semidirect
30. #23576C2semidirect
31. #22003C2semidirect
34. C2×#470C22semidirect
37. C2×#468C22semidirect
41. C2×#461C22semidirect
47. C2×#440C22semidirect
48. #2855C22semidirect
58. #2647C22semidirect
69. #2494C22semidirect
75. #2429C22semidirect
82. #2356C22semidirect
83. Q8×C4⋊C4C22semidirect
87. #2327C22semidirect
89. C4×C22⋊Q8C22semidirect
91. #2095C22semidirect
94. #2092C22semidirect
95. #2087C22semidirect
96. #2086C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
103. #2074C22semidirect
104. #2074C22semidirect
105. #2074C22semidirect
106. #2074C22semidirect
110. #2071C22semidirect
111. #2068C22semidirect
112. #2068C22semidirect
113. #2068C22semidirect
116. #2066C22semidirect
117. #2057C22semidirect
118. #2057C22semidirect
128. #2036C22semidirect
132. #2033C22semidirect
133. #2024C22semidirect
134. #2024C22semidirect
135. #2016C22semidirect
143. #2001C22semidirect
146. #2000C22semidirect
150. #1971C22semidirect
152. #1935C22semidirect
153. #1928C22semidirect
157. #1919C22semidirect
158. #1918C22semidirect
159. #1917C22semidirect
160. #1917C22semidirect
163. #1895C22semidirect
164. #1894C22semidirect
170. #1880C22semidirect
171. #1880C22semidirect
172. #1878C22semidirect
173. #1878C22semidirect
174. #1878C22semidirect
176. #1877C22semidirect
180. #1864C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
185. #1862C22semidirect
186. #1862C22semidirect
187. #1851C22semidirect
188. #1851C22semidirect
189. #1840C22semidirect
190. #1832C22semidirect
193. #1804C22semidirect
200. #1762C22semidirect
201. #1749C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#392572
#377482
#328292
#327532
#315112
#315032
#308602
#308582
#304262
#304242
#304212
#304202
#303232
#301832
#300852
#300502
#296322
#285822
#281662
#275472
#275342
#272192
#272142
#261792
#261772
#255012
#251762
#251662
#242202
#235762
#220032