Finite Group Databasebeta

← #6825359

Subgroups — #6825359

Order 512.

1637 conjugacy classes of subgroups.

The subgroup lattice has 1379 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42844C211yesmaximal, characteristic, complemented
2#42566C211yesmaximal, characteristic
3#33271C211yesmaximal, characteristic, complemented
4#32617C211yesmaximal, characteristic, complemented
5#32615C211yesmaximal, characteristic, complemented
6#31855C211yesmaximal, characteristic, complemented
7#31853C211yesmaximal, characteristic, complemented
8#31316C211yesmaximal, characteristic, complemented
9#31310C211yesmaximal, characteristic, complemented
10#31043C211yesmaximal, characteristic, complemented
11#31040C211yesmaximal, characteristic, complemented
12#30139C211yesmaximal, characteristic, complemented
13#30138C211yesmaximal, characteristic, complemented
14#28738C211yesmaximal, characteristic, complemented
15#28266C211yesmaximal, characteristic, complemented
16#27926C211yesmaximal, characteristic, complemented
17#27836C211yesmaximal, characteristic, complemented
18#26644C211yesmaximal, characteristic, complemented
19#26641C211yesmaximal, characteristic, complemented
20#25774C211yesmaximal, characteristic, complemented
21#25410C211yesmaximal, characteristic, complemented
22#25410C211yesmaximal, characteristic, complemented
23#25031C211yesmaximal, characteristic, complemented
24#24917C211yesmaximal, characteristic, complemented
25#24914C211yesmaximal, characteristic, complemented
26#24776C211yesmaximal, characteristic, complemented
27#24264C211yesmaximal, characteristic, complemented
28#23022C211yesmaximal, characteristic, complemented
29C22⋊C4×SD16C211yesmaximal, characteristic, complemented
30#21695C211yesmaximal, characteristic, complemented
31#21635C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#492C2211yescharacteristic
34C2×#492C2211yescharacteristic
35C2×#484C2211yescharacteristic, complemented
36C2×#480C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#465C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#465C2211yescharacteristic, complemented
41C2×#448C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×C8×Q8C2211yescharacteristic, complemented
44C2×#440C2211yescharacteristic
45C2×#440C2211yescharacteristic, complemented
46C2×C4×SD16C2211yescharacteristic
47C2×C4×SD16C2211yescharacteristic
48C2×C4×SD16C2211yescharacteristic, complemented
49C2×C8×D4C2211yescharacteristic
50C22×#106C2211yescharacteristic, complemented
51#2833—21no—
52#2826—21no—
53#2788—21no—
54#2774—21no—
55#2750—21no—
56#2749—21no—
57#2745—21no—
58#2688—21no—
59#2684—21no—
60#2668—21no—
61#2665—21no—
62#2652—21no—
63#2645C2211yescharacteristic, complemented
64#2644C2211yescharacteristic
65#2631—21no—
66#2622—21no—
67#2581C2211yescharacteristic, complemented
68#2580C2211yescharacteristic
69#2576—21no—
70#2568C2211yescharacteristic, complemented
71#2548C2211yescharacteristic
72#2504C2211yescharacteristic
73#2503C2211yescharacteristic, complemented
74#2495C2211yescharacteristic
75#2494C2211yescharacteristic
76#2434C2211yescharacteristic
77#2433C2211yescharacteristic
78#2429C2211yescharacteristic, complemented
79#2429C2211yescharacteristic, complemented
80#2428C2211yescharacteristic
81#2428C2211yescharacteristic
82#2424—21no—
83#2421C2211yescharacteristic
84#2420C2211yescharacteristic
85#2417C2211yescharacteristic
86#2416C2211yescharacteristic
87#2409C2211yescharacteristic
88#2408C2211yescharacteristic
89#2398C2211yescharacteristic
90#2361C2211yescharacteristic
91#2360C2211yescharacteristic, complemented
92Q8×C22⋊C4C2211yescharacteristic
93D4×C22⋊C4C2211yescharacteristic
94#2328C2211yescharacteristic
95#2327C2211yescharacteristic, complemented
96#2101C2211yescharacteristic, complemented
97#2101C2211yescharacteristic, complemented
98#2097C2211yescharacteristic, complemented
99#2097C2211yescharacteristic, complemented
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic
102#2076C2211yescharacteristic
103#2075C2211yescharacteristic
104#2074C2211yescharacteristic, complemented
105#2073C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2068C2211yescharacteristic, complemented
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic, complemented
111#2065C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2055C2211yescharacteristic, complemented
117#2055C2211yescharacteristic, complemented
118#2043C2211yescharacteristic, complemented
119#2043C2211yescharacteristic, complemented
120#2041C2211yescharacteristic
121#2041C2211yescharacteristic
122#2036C2211yescharacteristic
123#2035C2211yescharacteristic
124#2034C2211yescharacteristic
125#2033C2211yescharacteristic
126#2014C2211yescharacteristic
127#2014C2211yescharacteristic
128#2013C2211yescharacteristic
129#2013C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic, complemented
135#2000C2211yescharacteristic, complemented
136#1985C2211yescharacteristic, complemented
137#1982C2211yescharacteristic
138#1981C2211yescharacteristic, complemented
139#1973C2211yescharacteristic
140#1973C2211yescharacteristic, complemented
141#1968C2211yescharacteristic
142#1968C2211yescharacteristic
143#1968C2211yescharacteristic
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1968C2211yescharacteristic, complemented
148#1968C2211yescharacteristic, complemented
149#1961C2211yescharacteristic
150#1960C2211yescharacteristic, 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#1927C2211yescharacteristic, complemented
163#1926C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1924C2211yescharacteristic, complemented
167#1924C2211yescharacteristic, complemented
168#1921C2211yescharacteristic, complemented
169#1918C2211yescharacteristic, complemented
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic, complemented
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic, complemented
178#1874C2211yescharacteristic
179#1874C2211yescharacteristic, complemented
180#1872C2211yescharacteristic, complemented
181#1872C2211yescharacteristic, complemented
182#1865C2211yescharacteristic, complemented
183#1864C2211yescharacteristic
184#1863C2211yescharacteristic, complemented
185#1862C2211yescharacteristic, complemented
186#1846C2211yescharacteristic, complemented
187#1846C2211yescharacteristic, 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×SD16—24no—
206C22×SD16—42no—
207C22×SD16—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C23×C8C2311yescharacteristic
218C23×C8C2311yescharacteristic
219C2×C4⋊Q8C2311yescharacteristic
220C2×C4⋊Q8C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#124—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121—21no—
230C2×#121—21no—
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×#120—21no—
237C2×#120—21no—
238C2×C4×Q8C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×D4—21no—
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250#492—24no—
251#492—42no—
252#484—42no—
253#480—42no—
254#465—24no—
255#465—42no—
256#465—42no—
257#465—42no—
258#450—42no—
259#448—42no—
260C8×Q8—42no—
261#440—42no—
262#440—42no—
263C4×SD16—42no—
264C4×SD16—42no—
265C4×SD16—42no—
266C8×D4—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106—42no—
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324C2×C4×C8C2311yescharacteristic
325C2×C4×C8C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327#401—21no—
328#401—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400D411yescharacteristic
340#400D411yescharacteristic
341#399—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397D411yescharacteristic
355#397D411yescharacteristic
356#396—21no—
357#396—21no—
358#396—21no—
359#396—21no—
360#396—21no—
361#395—21no—
362#395—21no—
363#395—21no—
364#395—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394—21no—
372#394D411yescharacteristic
373#394D411yescharacteristic
374#393—21no—
375#393—21no—
376#393D411yescharacteristic
377#393D411yescharacteristic
378#392—21no—
379#392—21no—
380#392—21no—
381#392—21no—
382#392—21no—
383#391—21no—
384#391—21no—
385#391—21no—
386#391C2311yescharacteristic
387#391C2311yescharacteristic
388#391C2311yescharacteristic
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#391C2311yescharacteristic
394#390—21no—
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#389—21no—
404#389—21no—
405#389—21no—
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387—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#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#383—21no—
452#382—21no—
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#381—21no—
458#381—21no—
459#381—21no—
460#380—21no—
461#380—21no—
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464#380C2311yescharacteristic
465#380C2311yescharacteristic
466#379—21no—
467#379—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—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4C2×D411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
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—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
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×SD16—41no—
563C2×SD16—41no—
564C2×SD16—416no—
565C2×SD16#4114yes—
566C22×C8—22no—
567C22×C8—22no—
568C22×C8—22no—
569C22×C8—22no—
570C22×C8—22no—
571C22×C8—22no—
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C4⋊Q8—22no—
581C4⋊Q8—41no—
582C4⋊Q8—41no—
583C4⋊Q8—41no—
584#127—22no—
585#127—41no—
586#127—41no—
587#127—41no—
588#124—82no—
589C22⋊Q8—22no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597#121—22no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—82no—
606#121—82no—
607#121—82no—
608#120—82no—
609#120—82no—
610#120—82no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×Q8—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—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—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—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4—41no—
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
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—82no—
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×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719#107—22no—
720#107—22no—
721#107—41no—
722#107—41no—
723#106—22no—
724#106—22no—
725#106—22no—
726#106—22no—
727#106—22no—
728#106—41no—
729#106—41no—
730C4⋊C8—41no—
731C4⋊C8—41no—
732C4⋊C8—41no—
733C4⋊C8—41no—
734#103—22no—
735#103—22no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#102—22no—
750#102—22no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764C22⋊C8—22no—
765C22⋊C8—22no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769C22⋊C8—41no—
770#97—22no—
771#97—41no—
772#97—41no—
773C4×C8—22no—
774C4×C8—22no—
775C4×C8—22no—
776C4×C8—22no—
777C4×C8—22no—
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#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
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
827#95C2×D411yescharacteristic
828C24—21no—
829C24—21no—
830C24—21no—
831C24—42no—
832C24—42no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24—81no—
837C24—81no—
838C24C22×D411yescharacteristic
839C24C22×D411yescharacteristic
840C2×Q8—22no—
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—21no—
858C2×Q8—41no—
859C2×Q8—41no—
860C2×Q8—42no—
861C2×Q8—44no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8—82no—
865C2×Q8—82no—
866C2×Q8—82no—
867C2×Q8C2×#4112yes—
868C2×D4—22no—
869C2×D4—22no—
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—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—41no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—42no—
891C2×D4—44no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—82no—
910C2×D4—82no—
911C2×D4—82no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4C2×#4112yes—
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—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
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×C4—81no—
962C22×C4—81no—
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×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C2511yescharacteristic
976SD16—28no—
977SD16—44no—
978SD16—44no—
979SD16—44no—
980SD16—44no—
981SD16—44no—
982SD16—44no—
983SD16—82no—
984SD16—82no—
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—44no—
1006C2×C8—44no—
1007C2×C8C2×#4112yes—
1008C2×C8H(5,𝔽2)12yes—
1009C2×C8H(5,𝔽2)12yes—
1010C2×C8H(5,𝔽2)12yes—
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—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—41no—
1034C4⋊C4—41no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—81no—
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—
1055C4⋊C4—81no—
1056C22⋊C4—22no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
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—
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—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—42no—
1108C42—81no—
1109C42—81no—
1110C42—81no—
1111C42—81no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—22no—
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—41no—
1144C23—41no—
1145C23—84no—
1146C23—84no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23—162no—
1152C23#57712yes—
1153C23#57712yes—
1154C23C23×D411yescharacteristic
1155Q8—22no—
1156Q8—22no—
1157Q8—44no—
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—44no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—41no—
1181D4—41no—
1182D4—84no—
1183D4—84no—
1184D4—162no—
1185D4—162no—
1186D4—162no—
1187D4—162no—
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—22no—
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—21no—
1226C2×C4—21no—
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—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—84no—
1274C2×C4—162no—
1275C2×C4—162no—
1276C2×C4—162no—
1277C2×C4—162no—
1278C2×C4—162no—
1279C2×C4#57712yes—
1280C2×C4C22×#4111yescharacteristic
1281C2×C4C2×H(5,𝔽2)11yescharacteristic
1282C2×C4C2×H(5,𝔽2)11yescharacteristic
1283C2×C4C2×H(5,𝔽2)11yescharacteristic
1284C2×C4#58511yescharacteristic
1285C2×C4#58511yescharacteristic
1286C8—22no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C8—41no—
1293C8#53814yes—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—41no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—42no—
1309C22—42no—
1310C22—42no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
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—168no—
1330C22D4×#4111yescharacteristic
1331C22#349611yescharacteristic
1332C22#349811yescharacteristic
1333C22C2×#57711yescharacteristic
1334C22C2×#57711yescharacteristic
1335C22C2×#57711yescharacteristic
1336C22#358411yescharacteristic
1337C4—22no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—41no—
1345C4—41no—
1346C4—41no—
1347C4—41no—
1348C4—41no—
1349C4—42no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4—81no—
1361C4—81no—
1362C4C2×#53811yescharacteristic
1363C4#351311yescharacteristic
1364C4#354611yescharacteristic
1365C4#356211yescharacteristic
1366C2—42no—
1367C2—42no—
1368C2—82no—
1369C2—161no—
1370C2—161no—
1371C2#3939611yescharacteristic
1372C2#6147211yescharacteristic
1373C2#6148111yescharacteristic
1374C2#6226511yescharacteristic
1375C2#6226811yescharacteristic
1376C2#6243011yescharacteristic
1377C2#6243511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42566C2
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. #42844C2semidirect
3. #33271C2semidirect
4. #32617C2semidirect
5. #32615C2semidirect
6. #31855C2semidirect
7. #31853C2semidirect
8. #31316C2semidirect
9. #31310C2semidirect
10. #31043C2semidirect
11. #31040C2semidirect
12. #30139C2semidirect
13. #30138C2semidirect
14. #28738C2semidirect
15. #28266C2semidirect
16. #27926C2semidirect
17. #27836C2semidirect
18. #26644C2semidirect
19. #26641C2semidirect
20. #25774C2semidirect
21. #25410C2semidirect
22. #25410C2semidirect
23. #25031C2semidirect
24. #24917C2semidirect
25. #24914C2semidirect
26. #24776C2semidirect
27. #24264C2semidirect
28. #23022C2semidirect
29. C22⋊C4×SD16C2semidirect
30. #21695C2semidirect
31. #21635C2semidirect
35. C2×#484C22semidirect
40. C2×#465C22semidirect
43. C2×C8×Q8C22semidirect
45. C2×#440C22semidirect
48. C2×C4×SD16C22semidirect
50. C22×#106C22semidirect
63. #2645C22semidirect
67. #2581C22semidirect
70. #2568C22semidirect
73. #2503C22semidirect
78. #2429C22semidirect
79. #2429C22semidirect
91. #2360C22semidirect
95. #2327C22semidirect
96. #2101C22semidirect
97. #2101C22semidirect
98. #2097C22semidirect
99. #2097C22semidirect
104. #2074C22semidirect
105. #2073C22semidirect
106. #2068C22semidirect
107. #2068C22semidirect
110. #2066C22semidirect
111. #2065C22semidirect
116. #2055C22semidirect
117. #2055C22semidirect
118. #2043C22semidirect
119. #2043C22semidirect
134. #2000C22semidirect
135. #2000C22semidirect
136. #1985C22semidirect
138. #1981C22semidirect
140. #1973C22semidirect
147. #1968C22semidirect
148. #1968C22semidirect
150. #1960C22semidirect
152. #1941C22semidirect
153. #1941C22semidirect
154. #1941C22semidirect
155. #1941C22semidirect
159. #1935C22semidirect
160. #1935C22semidirect
161. #1935C22semidirect
162. #1927C22semidirect
166. #1924C22semidirect
167. #1924C22semidirect
168. #1921C22semidirect
169. #1918C22semidirect
173. #1880C22semidirect
177. #1877C22semidirect
179. #1874C22semidirect
180. #1872C22semidirect
181. #1872C22semidirect
182. #1865C22semidirect
184. #1863C22semidirect
185. #1862C22semidirect
186. #1846C22semidirect
187. #1846C22semidirect
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
#428442
#425662
#332712
#326172
#326152
#318552
#318532
#313162
#313102
#310432
#310402
#301392
#301382
#287382
#282662
#279262
#278362
#266442
#266412
#257742
#254102
#250312
#249172
#249142
#247762
#242642
#230222
C22⋊C4×SD162
#216952
#216352