Finite Group Databasebeta

← #6825372

Subgroups — #6825372

Order 512.

1582 conjugacy classes of subgroups.

The subgroup lattice has 1359 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42869C211yesmaximal, characteristic, complemented
2#42627C211yesmaximal, characteristic, complemented
3#33271C211yesmaximal, characteristic, complemented
4#32626C211yesmaximal, characteristic, complemented
5#32620C211yesmaximal, characteristic, complemented
6#31865C211yesmaximal, characteristic, complemented
7#31859C211yesmaximal, characteristic, complemented
8#31308C211yesmaximal, characteristic, complemented
9#31302C211yesmaximal, characteristic, complemented
10#31039C211yesmaximal, characteristic, complemented
11#31036C211yesmaximal, characteristic
12#30143C211yesmaximal, characteristic, complemented
13#30142C211yesmaximal, characteristic, complemented
14#28739C211yesmaximal, characteristic, complemented
15#28266C211yesmaximal, characteristic, complemented
16#27925C211yesmaximal, characteristic, complemented
17#27835C211yesmaximal, characteristic, complemented
18#26638C211yesmaximal, characteristic, complemented
19#26635C211yesmaximal, characteristic, complemented
20#25776C211yesmaximal, characteristic, complemented
21#25411C211yesmaximal, characteristic, complemented
22#25411C211yesmaximal, characteristic, complemented
23#25031C211yesmaximal, characteristic, complemented
24#24922C211yesmaximal, characteristic, complemented
25#24909C211yesmaximal, characteristic, complemented
26#24777C211yesmaximal, characteristic, complemented
27#24264C211yesmaximal, characteristic, complemented
28#23023C211yesmaximal, characteristic, complemented
29C22⋊C4×SD16C211yesmaximal, characteristic, complemented
30#21694C211yesmaximal, characteristic, complemented
31#21635C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#495C2211yescharacteristic
34C2×#495C2211yescharacteristic
35C2×#485C2211yescharacteristic, complemented
36C2×#482C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#465C2211yescharacteristic, complemented
41C2×#451C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×C8×Q8C2211yescharacteristic, complemented
44C2×#442C2211yescharacteristic
45C2×#441C2211yescharacteristic, complemented
46C2×C4×SD16C2211yescharacteristic
47C2×C4×SD16C2211yescharacteristic
48C2×C4×SD16C2211yescharacteristic, complemented
49C2×C8×D4C2211yescharacteristic
50C2×#427C2211yescharacteristic, complemented
51#2832—21no—
52#2824—21no—
53#2797—21no—
54#2784—21no—
55#2779—21no—
56#2778—21no—
57#2751—21no—
58#2745—21no—
59#2736—21no—
60#2685—21no—
61#2650—21no—
62#2649—21no—
63#2648—21no—
64#2645C2211yescharacteristic, complemented
65#2644C2211yescharacteristic
66#2622—21no—
67#2595—21no—
68#2592C2211yescharacteristic
69#2592C2211yescharacteristic, complemented
70#2581C2211yescharacteristic, complemented
71#2580C2211yescharacteristic
72#2500C2211yescharacteristic
73#2499C2211yescharacteristic, complemented
74#2497C2211yescharacteristic
75#2496C2211yescharacteristic
76#2480—21no—
77#2436C2211yescharacteristic
78#2435C2211yescharacteristic
79#2427C2211yescharacteristic
80#2427C2211yescharacteristic, complemented
81#2426C2211yescharacteristic
82#2426C2211yescharacteristic, complemented
83#2421C2211yescharacteristic
84#2420C2211yescharacteristic
85#2415C2211yescharacteristic
86#2414C2211yescharacteristic
87#2409C2211yescharacteristic
88#2408C2211yescharacteristic
89#2398C2211yescharacteristic
90#2363C2211yescharacteristic
91#2362C2211yescharacteristic, complemented
92Q8×C22⋊C4C2211yescharacteristic
93D4×C22⋊C4C2211yescharacteristic
94#2326C2211yescharacteristic
95#2326C2211yescharacteristic, complemented
96#2100C2211yescharacteristic, complemented
97#2099C2211yescharacteristic, complemented
98#2097C2211yescharacteristic, complemented
99#2095C2211yescharacteristic, complemented
100#2093C2211yescharacteristic
101#2092C2211yescharacteristic
102#2077C2211yescharacteristic
103#2077C2211yescharacteristic
104#2074C2211yescharacteristic, complemented
105#2073C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2068C2211yescharacteristic, complemented
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic, complemented
112#2056C2211yescharacteristic, complemented
113#2056C2211yescharacteristic, complemented
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2054C2211yescharacteristic
117#2054C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic, complemented
121#2042C2211yescharacteristic, complemented
122#2036C2211yescharacteristic
123#2036C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#2015C2211yescharacteristic
127#2015C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2001C2211yescharacteristic, complemented
131#2001C2211yescharacteristic, complemented
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#1999C2211yescharacteristic
135#1999C2211yescharacteristic
136#1985C2211yescharacteristic, complemented
137#1983C2211yescharacteristic
138#1983C2211yescharacteristic, complemented
139#1972C2211yescharacteristic
140#1971C2211yescharacteristic, complemented
141#1968C2211yescharacteristic
142#1968C2211yescharacteristic
143#1968C2211yescharacteristic
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1968C2211yescharacteristic, complemented
148#1968C2211yescharacteristic, complemented
149#1959C2211yescharacteristic
150#1959C2211yescharacteristic, complemented
151#1955C2211yescharacteristic
152#1941C2211yescharacteristic, complemented
153#1941C2211yescharacteristic, complemented
154#1941C2211yescharacteristic, complemented
155#1941C2211yescharacteristic, complemented
156#1936C2211yescharacteristic
157#1936C2211yescharacteristic
158#1936C2211yescharacteristic
159#1935C2211yescharacteristic, complemented
160#1935C2211yescharacteristic, complemented
161#1935C2211yescharacteristic, complemented
162#1928C2211yescharacteristic, complemented
163#1925C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic, complemented
167#1924C2211yescharacteristic, complemented
168#1920C2211yescharacteristic, complemented
169#1919C2211yescharacteristic, complemented
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1875C2211yescharacteristic
179#1875C2211yescharacteristic, complemented
180#1873C2211yescharacteristic, complemented
181#1873C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1863C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic, complemented
186#1846C2211yescharacteristic, complemented
187#1844C2211yescharacteristic, complemented
188#1832C2211yescharacteristic, complemented
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic
191#1805C2211yescharacteristic, complemented
192#1804C2211yescharacteristic
193#1787C2211yescharacteristic
194#1787C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197C4×#106C2211yescharacteristic, complemented
198C8×C22⋊C4C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic, complemented
202#1726C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16—24no—
208C22×SD16—42no—
209C22×SD16—42no—
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C2×#126—21no—
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C22×C22⋊C4—21no—
244#495—24no—
245#495—42no—
246#485—42no—
247#482—42no—
248#465—24no—
249#465—42no—
250#465—42no—
251#465—42no—
252#451—42no—
253#447—42no—
254C8×Q8—42no—
255#442—42no—
256#441—42no—
257C4×SD16—42no—
258C4×SD16—42no—
259C4×SD16—42no—
260C8×D4—42no—
261#427—42no—
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321#401—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400D411yescharacteristic
330#400D411yescharacteristic
331#399—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397D411yescharacteristic
346#397D411yescharacteristic
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#395—21no—
352#395—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394D411yescharacteristic
366#394D411yescharacteristic
367#393—21no—
368#393—21no—
369#393—21no—
370#393—21no—
371#393—21no—
372#393—21no—
373#393D411yescharacteristic
374#393D411yescharacteristic
375#392—21no—
376#392—21no—
377#391—21no—
378#391—21no—
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#391C2311yescharacteristic
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#389—21no—
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
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#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#387—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#386—21no—
440#386—21no—
441#386—21no—
442#386—21no—
443#386—21no—
444#385—21no—
445#385—21no—
446#385—21no—
447#385—21no—
448#385—21no—
449#385—21no—
450#385—21no—
451#384C2311yescharacteristic
452#384C2311yescharacteristic
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#381—21no—
456#380—21no—
457#380—21no—
458#380—21no—
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#379—21no—
464#379—21no—
465#379—21no—
466#379—21no—
467C4×C4⋊C4—21no—
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C22⋊C4—21no—
471C4×C22⋊C4—21no—
472C4×C22⋊C4C2311yescharacteristic
473C4×C22⋊C4C2311yescharacteristic
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
476#376C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8—21no—
501C22×Q8—22no—
502C22×Q8—41no—
503C22×Q8—41no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8C2×D411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×Q8C2411yescharacteristic
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×Q16—22no—
533C2×Q16—22no—
534C2×Q16—41no—
535C2×Q16—41no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×SD16—22no—
539C2×SD16—22no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—416no—
553C2×SD16#4114yes—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C22×C8—22no—
561C22×C8—22no—
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8—22no—
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574#126—82no—
575#124—22no—
576#124—22no—
577#124—41no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583C22⋊Q8—22no—
584C22⋊Q8—41no—
585C22⋊Q8—41no—
586C22⋊Q8—41no—
587C22⋊Q8—41no—
588C22⋊Q8—41no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591#121—22no—
592#121—41no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#120—82no—
600C4×Q8—41no—
601C4×Q8—41no—
602C4×Q8—41no—
603C4×Q8—41no—
604C4×Q8—41no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616#117—41no—
617#117—41no—
618#117—41no—
619#117—41no—
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⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—82no—
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#106—22no—
722#106—22no—
723#106—22no—
724#106—22no—
725#106—22no—
726#106—22no—
727#106—22no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732#103—22no—
733#103—22no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#102—22no—
748#102—22no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—41no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768#97—22no—
769#97—41no—
770#97—41no—
771C4×C8—22no—
772C4×C8—22no—
773C4×C8—22no—
774C4×C8—22no—
775C4×C8—22no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#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#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822C24—21no—
823C24—21no—
824C24—21no—
825C24—42no—
826C24—42no—
827C24—81no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24C22×D411yescharacteristic
833C24C22×D411yescharacteristic
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—21no—
838C2×Q8—21no—
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—41no—
852C2×Q8—41no—
853C2×Q8—41no—
854C2×Q8—42no—
855C2×Q8—44no—
856C2×Q8—81no—
857C2×Q8—81no—
858C2×Q8—82no—
859C2×Q8—82no—
860C2×Q8—82no—
861C2×Q8C2×#4112yes—
862C2×D4—22no—
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—41no—
881C2×D4—41no—
882C2×D4—42no—
883C2×D4—44no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—82no—
889C2×D4—82no—
890C2×D4—82no—
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—81no—
901C2×D4C2×#4112yes—
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—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—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C2511yescharacteristic
952Q16—44no—
953Q16—82no—
954SD16—28no—
955SD16—44no—
956SD16—44no—
957SD16—44no—
958SD16—44no—
959D8—44no—
960D8—82no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
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—44no—
982C2×C8—44no—
983C2×C8C2×#4112yes—
984C2×C8H(5,𝔽2)12yes—
985C2×C8H(5,𝔽2)12yes—
986C2×C8H(5,𝔽2)12yes—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
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—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—42no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—41no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
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—
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—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42—81no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—21no—
1107C23—22no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—84no—
1133C23—84no—
1134C23—162no—
1135C23—162no—
1136C23—162no—
1137C23—162no—
1138C23—162no—
1139C23#57712yes—
1140C23C23×D411yescharacteristic
1141Q8—22no—
1142Q8—22no—
1143Q8—44no—
1144Q8—41no—
1145Q8—41no—
1146Q8—41no—
1147Q8—41no—
1148Q8—41no—
1149Q8—41no—
1150Q8—41no—
1151Q8—41no—
1152Q8—41no—
1153Q8—41no—
1154Q8—84no—
1155D4—22no—
1156D4—22no—
1157D4—44no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—84no—
1169D4—162no—
1170D4—162no—
1171D4—162no—
1172D4—162no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—22no—
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—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—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—84no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4—162no—
1260C2×C4C22×#4111yescharacteristic
1261C2×C4C2×H(5,𝔽2)11yescharacteristic
1262C2×C4C2×H(5,𝔽2)11yescharacteristic
1263C2×C4C2×H(5,𝔽2)11yescharacteristic
1264C2×C4#58511yescharacteristic
1265C2×C4#58511yescharacteristic
1266C8—22no—
1267C8—41no—
1268C8—41no—
1269C8—41no—
1270C8—41no—
1271C8—41no—
1272C8—41no—
1273C8#53814yes—
1274C22—22no—
1275C22—22no—
1276C22—22no—
1277C22—41no—
1278C22—41no—
1279C22—41no—
1280C22—41no—
1281C22—41no—
1282C22—42no—
1283C22—41no—
1284C22—42no—
1285C22—41no—
1286C22—41no—
1287C22—41no—
1288C22—41no—
1289C22—41no—
1290C22—42no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—168no—
1310C22D4×#4111yescharacteristic
1311C22#349611yescharacteristic
1312C22#349811yescharacteristic
1313C22C2×#57711yescharacteristic
1314C22#358411yescharacteristic
1315C22#358411yescharacteristic
1316C22#358411yescharacteristic
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—41no—
1321C4—41no—
1322C4—41no—
1323C4—41no—
1324C4—41no—
1325C4—41no—
1326C4—41no—
1327C4—41no—
1328C4—41no—
1329C4—42no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C4—81no—
1334C4—81no—
1335C4—81no—
1336C4—81no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4C2×#53811yescharacteristic
1343C4#351311yescharacteristic
1344C4#354611yescharacteristic
1345C4#356211yescharacteristic
1346C2—42no—
1347C2—81no—
1348C2—82no—
1349C2—161no—
1350C2—161no—
1351C2#3939611yescharacteristic
1352C2#6147211yescharacteristic
1353C2#6148611yescharacteristic
1354C2#6226511yescharacteristic
1355C2#6227311yescharacteristic
1356C2#6243311yescharacteristic
1357C2#6243511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#31036C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2398 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42869C2semidirect
2. #42627C2semidirect
3. #33271C2semidirect
4. #32626C2semidirect
5. #32620C2semidirect
6. #31865C2semidirect
7. #31859C2semidirect
8. #31308C2semidirect
9. #31302C2semidirect
10. #31039C2semidirect
12. #30143C2semidirect
13. #30142C2semidirect
14. #28739C2semidirect
15. #28266C2semidirect
16. #27925C2semidirect
17. #27835C2semidirect
18. #26638C2semidirect
19. #26635C2semidirect
20. #25776C2semidirect
21. #25411C2semidirect
22. #25411C2semidirect
23. #25031C2semidirect
24. #24922C2semidirect
25. #24909C2semidirect
26. #24777C2semidirect
27. #24264C2semidirect
28. #23023C2semidirect
29. C22⋊C4×SD16C2semidirect
30. #21694C2semidirect
31. #21635C2semidirect
35. C2×#485C22semidirect
40. C2×#465C22semidirect
43. C2×C8×Q8C22semidirect
45. C2×#441C22semidirect
48. C2×C4×SD16C22semidirect
50. C2×#427C22semidirect
64. #2645C22semidirect
69. #2592C22semidirect
70. #2581C22semidirect
73. #2499C22semidirect
80. #2427C22semidirect
82. #2426C22semidirect
91. #2362C22semidirect
95. #2326C22semidirect
96. #2100C22semidirect
97. #2099C22semidirect
98. #2097C22semidirect
99. #2095C22semidirect
104. #2074C22semidirect
105. #2073C22semidirect
106. #2068C22semidirect
107. #2068C22semidirect
108. #2068C22semidirect
111. #2067C22semidirect
112. #2056C22semidirect
113. #2056C22semidirect
120. #2042C22semidirect
121. #2042C22semidirect
130. #2001C22semidirect
131. #2001C22semidirect
136. #1985C22semidirect
138. #1983C22semidirect
140. #1971C22semidirect
147. #1968C22semidirect
148. #1968C22semidirect
150. #1959C22semidirect
152. #1941C22semidirect
153. #1941C22semidirect
154. #1941C22semidirect
155. #1941C22semidirect
159. #1935C22semidirect
160. #1935C22semidirect
161. #1935C22semidirect
162. #1928C22semidirect
166. #1924C22semidirect
167. #1924C22semidirect
168. #1920C22semidirect
169. #1919C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
179. #1875C22semidirect
180. #1873C22semidirect
181. #1873C22semidirect
182. #1863C22semidirect
183. #1863C22semidirect
185. #1862C22semidirect
186. #1846C22semidirect
187. #1844C22semidirect
188. #1832C22semidirect
191. #1805C22semidirect
197. C4×#106C22semidirect
200. C8×C22⋊C4C22semidirect
201. C8×C22⋊C4C22semidirect
202. #1726C22semidirect

Maximal subgroups

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

subgroupindex
#428692
#426272
#332712
#326262
#326202
#318652
#318592
#313082
#313022
#310392
#310362
#301432
#301422
#287392
#282662
#279252
#278352
#266382
#266352
#257762
#254112
#250312
#249222
#249092
#247772
#242642
#230232
C22⋊C4×SD162
#216942
#216352