Finite Group Databasebeta

← #7087204

Subgroups — #7087204

Order 512.

1593 conjugacy classes of subgroups.

The subgroup lattice has 1371 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59575C211yesmaximal, characteristic, complemented
2#40049C211yesmaximal, characteristic, complemented
3#32532C211yesmaximal, characteristic, complemented
4#32165C211yesmaximal, characteristic, complemented
5#32097C211yesmaximal, characteristic, complemented
6#32065C211yesmaximal, characteristic, complemented
7#30899C211yesmaximal, characteristic, complemented
8#30613C211yesmaximal, characteristic, complemented
9#30464C211yesmaximal, characteristic, complemented
10#30460C211yesmaximal, characteristic
11#29561C211yesmaximal, characteristic, complemented
12#28959C211yesmaximal, characteristic, complemented
13#28915C211yesmaximal, characteristic, complemented
14#28621C211yesmaximal, characteristic, complemented
15#28479C211yesmaximal, characteristic, complemented
16#28365C211yesmaximal, characteristic, complemented
17#27072C211yesmaximal, characteristic, complemented
18#26638C211yesmaximal, characteristic, complemented
19#26603C211yesmaximal, characteristic, complemented
20#26565C211yesmaximal, characteristic, complemented
21#26269C211yesmaximal, characteristic, complemented
22#26188C211yesmaximal, characteristic, complemented
23#25429C211yesmaximal, characteristic, complemented
24#25373C211yesmaximal, characteristic, complemented
25#25172C211yesmaximal, characteristic, complemented
26#25101C211yesmaximal, characteristic, complemented
27#23804C211yesmaximal, characteristic, complemented
28#23290C211yesmaximal, characteristic, complemented
29#23001C211yesmaximal, characteristic, complemented
30#22864C211yesmaximal, characteristic, complemented
31#22156C211yesmaximal, characteristic, complemented
32C2×#497C2211yescharacteristic
33C2×#496C2211yescharacteristic
34C2×#495C2211yescharacteristic, complemented
35C2×#489C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#468C2211yescharacteristic
38C2×#468C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#463C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#461C2211yescharacteristic, complemented
43C2×#459C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#447C2211yescharacteristic
47C2×#442C2211yescharacteristic
48C2×#442C2211yescharacteristic, complemented
49C2×#441C2211yescharacteristic, complemented
50C2×#440C2211yescharacteristic
51C2×#440C2211yescharacteristic, complemented
52C2×#418C2211yescharacteristic
53#2858C2211yescharacteristic
54#2779—21no—
55#2749—21no—
56#2747—21no—
57#2730—21no—
58#2685—21no—
59#2684—21no—
60#2648—21no—
61#2595—21no—
62#2577—21no—
63#2547C2211yescharacteristic, complemented
64#2544C2211yescharacteristic
65#2544C2211yescharacteristic
66#2531—21no—
67#2530—21no—
68#2513C2211yescharacteristic
69#2511C2211yescharacteristic, complemented
70#2509C2211yescharacteristic, complemented
71#2499C2211yescharacteristic
72#2492C2211yescharacteristic
73#2481—21no—
74#2472—21no—
75#2459—21no—
76#2452C2211yescharacteristic
77#2448C2211yescharacteristic
78#2446C2211yescharacteristic, complemented
79#2435C2211yescharacteristic
80#2433C2211yescharacteristic
81#2429C2211yescharacteristic
82#2427C2211yescharacteristic
83#2427C2211yescharacteristic
84#2426C2211yescharacteristic
85#2420C2211yescharacteristic
86#2367C2211yescharacteristic, complemented
87#2366C2211yescharacteristic
88#2363C2211yescharacteristic
89#2362C2211yescharacteristic
90D4×C4⋊C4C2211yescharacteristic, complemented
91#2345—21no—
92D4×C22⋊C4C2211yescharacteristic
93#2321—21no—
94C4×#126C2211yescharacteristic
95C4×#124C2211yescharacteristic
96C4×#124C2211yescharacteristic, complemented
97#2295C2211yescharacteristic, complemented
98#2097C2211yescharacteristic, complemented
99#2097C2211yescharacteristic, complemented
100#2093C2211yescharacteristic
101#2092C2211yescharacteristic
102#2092C2211yescharacteristic, complemented
103#2087C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2068C2211yescharacteristic, complemented
106#2067C2211yescharacteristic
107#2065C2211yescharacteristic
108#2057C2211yescharacteristic, complemented
109#2056C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic, complemented
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic, complemented
115#2043C2211yescharacteristic, complemented
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic, complemented
119#2042C2211yescharacteristic, complemented
120#2041C2211yescharacteristic
121#2035C2211yescharacteristic
122#2033C2211yescharacteristic
123#2024C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2015C2211yescharacteristic, complemented
126#2015C2211yescharacteristic, complemented
127#2014C2211yescharacteristic
128#2014C2211yescharacteristic
129#2014C2211yescharacteristic
130#2013C2211yescharacteristic
131#2012C2211yescharacteristic
132#2012C2211yescharacteristic
133#2012C2211yescharacteristic
134#2001C2211yescharacteristic
135#2001C2211yescharacteristic
136#2000C2211yescharacteristic
137#1999C2211yescharacteristic
138#1993C2211yescharacteristic, complemented
139#1983C2211yescharacteristic
140#1983C2211yescharacteristic, complemented
141#1973C2211yescharacteristic
142#1973C2211yescharacteristic
143#1973C2211yescharacteristic, complemented
144#1971C2211yescharacteristic, complemented
145#1969C2211yescharacteristic, complemented
146#1968C2211yescharacteristic
147#1968C2211yescharacteristic
148#1961C2211yescharacteristic
149#1957C2211yescharacteristic
150#1949C2211yescharacteristic, complemented
151#1948C2211yescharacteristic, complemented
152#1943C2211yescharacteristic, complemented
153#1942C2211yescharacteristic, complemented
154#1939C2211yescharacteristic, complemented
155#1936C2211yescharacteristic
156#1936C2211yescharacteristic
157#1936C2211yescharacteristic
158#1936C2211yescharacteristic, complemented
159#1935C2211yescharacteristic, complemented
160#1928C2211yescharacteristic, complemented
161#1928C2211yescharacteristic, complemented
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic, complemented
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic
167#1924C2211yescharacteristic
168#1919C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1916C2211yescharacteristic, complemented
172#1894C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic, complemented
176#1880C2211yescharacteristic, complemented
177#1879C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1879C2211yescharacteristic, complemented
181#1878C2211yescharacteristic, complemented
182#1877C2211yescharacteristic
183#1877C2211yescharacteristic
184#1877C2211yescharacteristic, complemented
185#1873C2211yescharacteristic
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic, complemented
188#1863C2211yescharacteristic, complemented
189#1862C2211yescharacteristic
190#1862C2211yescharacteristic, complemented
191#1862C2211yescharacteristic, complemented
192#1854C2211yescharacteristic
193#1851C2211yescharacteristic
194#1805C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1767C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1745C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×M16C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#126D411yescharacteristic
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×C22⋊Q8C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4—21no—
249C22×C22⋊C4—21no—
250#497—42no—
251#496—42no—
252#495—42no—
253#489—42no—
254#482—42no—
255#468—42no—
256#468—42no—
257#464—24no—
258#463—42no—
259#463—42no—
260#461—42no—
261#459—24no—
262#450—24no—
263#450—42no—
264#447—42no—
265#442—42no—
266#442—42no—
267#441—42no—
268#440—42no—
269#440—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283#418—42no—
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×#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×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×#97C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#399—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#397—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#394—21no—
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#393—21no—
359#393—21no—
360#392—21no—
361#392—21no—
362#391—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#389—21no—
386#389—21no—
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388D411yescharacteristic
411#388D411yescharacteristic
412#388D411yescharacteristic
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387D411yescharacteristic
424#387D411yescharacteristic
425#387D411yescharacteristic
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#384C2311yescharacteristic
443#383D411yescharacteristic
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#381—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380—21no—
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455#379—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C4⋊C4C2311yescharacteristic
464C4×C22⋊C4—21no—
465C4×C22⋊C4—21no—
466C4×C22⋊C4—21no—
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4—21no—
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#376—21no—
474C43C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4C2411yescharacteristic
528C2×Q16—22no—
529C2×Q16—22no—
530C2×Q16—41no—
531C2×Q16—41no—
532C2×Q16—41no—
533C2×Q16—41no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C4⋊Q8—41no—
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578C4⋊Q8—41no—
579#127—22no—
580#127—41no—
581#127—41no—
582#127—41no—
583#126—42no—
584#124—22no—
585#124—22no—
586#124—22no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124—41no—
591#124—41no—
592#124—41no—
593#124—41no—
594#124—82no—
595#124—82no—
596C22⋊Q8—22no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—82no—
603#121—22no—
604#121—41no—
605#121—41no—
606#121—41no—
607#120—44no—
608#120—82no—
609C4×Q8—22no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×D4—22no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—82no—
628#117—41no—
629#117—41no—
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—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—44no—
649C2×C4⋊C4C2×D411yescharacteristic
650C2×C4⋊C4C2×D411yescharacteristic
651C2×C4⋊C4C2×D411yescharacteristic
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
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—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—82no—
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—21no—
719C2×C42C2×D411yescharacteristic
720C2×C42C2×D411yescharacteristic
721C2×C42C2×D411yescharacteristic
722C2×C42C2×D411yescharacteristic
723C2×C42C2411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—22no—
730#107—41no—
731#107—41no—
732#107—41no—
733#107—41no—
734#106—22no—
735#106—41no—
736#106—41no—
737C4⋊C8—22no—
738C4⋊C8—22no—
739C4⋊C8—22no—
740C4⋊C8—41no—
741C4⋊C8—41no—
742#103—22no—
743#103—22no—
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#103—41no—
754#103—41no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102#4114yes—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—41no—
777#97—22no—
778#97—22no—
779#97—22no—
780#97—41no—
781#97—41no—
782C4×C8—41no—
783C4×C8—41no—
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
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—42no—
832C24—42no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24C22×D411yescharacteristic
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
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—42no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
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—21no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—44no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—82no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4C2×#4112yes—
908C2×D4H(5,𝔽2)12yes—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C2511yescharacteristic
959Q16—44no—
960Q16—82no—
961SD16—44no—
962SD16—44no—
963SD16—82no—
964SD16—82no—
965SD16—82no—
966SD16—82no—
967SD16—82no—
968D8—44no—
969D8—44no—
970D8—82no—
971M16—82no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8C2×#4112yes—
994C2×C8H(5,𝔽2)12yes—
995C2×C8H(5,𝔽2)12yes—
996C4⋊C4—22no—
997C4⋊C4—22no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—41no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4C2×#4112yes—
1038C22⋊C4—22no—
1039C22⋊C4—41no—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
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—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
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—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—21no—
1095C42—21no—
1096C42—21no—
1097C42—41no—
1098C42—41no—
1099C42—41no—
1100C42—41no—
1101C42—42no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42—81no—
1106C42—81no—
1107C42—81no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—22no—
1113C23—22no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
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—84no—
1144C23—84no—
1145C23—162no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23C23×D411yescharacteristic
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—162no—
1164D4—22no—
1165D4—22no—
1166D4—22no—
1167D4—22no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—84no—
1181D4—84no—
1182D4—162no—
1183D4—162no—
1184D4—162no—
1185D4—162no—
1186D4—162no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—22no—
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—21no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—84no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4—162no—
1269C2×C4—162no—
1270C2×C4—162no—
1271C2×C4#57512yes—
1272C2×C4C22×#4111yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4C2×H(5,𝔽2)11yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4#58511yescharacteristic
1277C2×C4#58511yescharacteristic
1278C8—22no—
1279C8—22no—
1280C8—22no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C22—42no—
1287C22—41no—
1288C22—41no—
1289C22—42no—
1290C22—42no—
1291C22—41no—
1292C22—41no—
1293C22—42no—
1294C22—41no—
1295C22—42no—
1296C22—42no—
1297C22—41no—
1298C22—41no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—168no—
1322C22D4×#4111yescharacteristic
1323C22#348811yescharacteristic
1324C22#349811yescharacteristic
1325C22C2×#57511yescharacteristic
1326C22#358511yescharacteristic
1327C22#358511yescharacteristic
1328C22#358611yescharacteristic
1329C4—22no—
1330C4—41no—
1331C4—42no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4#350611yescharacteristic
1355C4#351911yescharacteristic
1356C4#353311yescharacteristic
1357C4#353411yescharacteristic
1358C2—81no—
1359C2—82no—
1360C2—82no—
1361C2—161no—
1362C2—161no—
1363C2#4418411yescharacteristic
1364C2#6145411yescharacteristic
1365C2#6151311yescharacteristic
1366C2#6197311yescharacteristic
1367C2#6207911yescharacteristic
1368C2#6244511yescharacteristic
1369C2#6245511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30460C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59575C2semidirect
2. #40049C2semidirect
3. #32532C2semidirect
4. #32165C2semidirect
5. #32097C2semidirect
6. #32065C2semidirect
7. #30899C2semidirect
8. #30613C2semidirect
9. #30464C2semidirect
11. #29561C2semidirect
12. #28959C2semidirect
13. #28915C2semidirect
14. #28621C2semidirect
15. #28479C2semidirect
16. #28365C2semidirect
17. #27072C2semidirect
18. #26638C2semidirect
19. #26603C2semidirect
20. #26565C2semidirect
21. #26269C2semidirect
22. #26188C2semidirect
23. #25429C2semidirect
24. #25373C2semidirect
25. #25172C2semidirect
26. #25101C2semidirect
27. #23804C2semidirect
28. #23290C2semidirect
29. #23001C2semidirect
30. #22864C2semidirect
31. #22156C2semidirect
34. C2×#495C22semidirect
35. C2×#489C22semidirect
42. C2×#461C22semidirect
48. C2×#442C22semidirect
49. C2×#441C22semidirect
51. C2×#440C22semidirect
63. #2547C22semidirect
69. #2511C22semidirect
70. #2509C22semidirect
78. #2446C22semidirect
86. #2367C22semidirect
90. D4×C4⋊C4C22semidirect
96. C4×#124C22semidirect
97. #2295C22semidirect
98. #2097C22semidirect
99. #2097C22semidirect
102. #2092C22semidirect
103. #2087C22semidirect
104. #2072C22semidirect
105. #2068C22semidirect
108. #2057C22semidirect
109. #2056C22semidirect
112. #2055C22semidirect
114. #2054C22semidirect
115. #2043C22semidirect
118. #2042C22semidirect
119. #2042C22semidirect
123. #2024C22semidirect
125. #2015C22semidirect
126. #2015C22semidirect
138. #1993C22semidirect
140. #1983C22semidirect
143. #1973C22semidirect
144. #1971C22semidirect
145. #1969C22semidirect
150. #1949C22semidirect
151. #1948C22semidirect
152. #1943C22semidirect
153. #1942C22semidirect
154. #1939C22semidirect
158. #1936C22semidirect
159. #1935C22semidirect
160. #1928C22semidirect
161. #1928C22semidirect
164. #1925C22semidirect
168. #1919C22semidirect
169. #1917C22semidirect
170. #1917C22semidirect
171. #1916C22semidirect
175. #1880C22semidirect
176. #1880C22semidirect
180. #1879C22semidirect
181. #1878C22semidirect
184. #1877C22semidirect
187. #1864C22semidirect
188. #1863C22semidirect
190. #1862C22semidirect
191. #1862C22semidirect
194. #1805C22semidirect
195. #1771C22semidirect
196. #1770C22semidirect
197. #1767C22semidirect
199. C4×#102C22semidirect
202. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#595752
#400492
#325322
#321652
#320972
#320652
#308992
#306132
#304642
#304602
#295612
#289592
#289152
#286212
#284792
#283652
#270722
#266382
#266032
#265652
#262692
#261882
#254292
#253732
#251722
#251012
#238042
#232902
#230012
#228642
#221562