Finite Group Databasebeta

← #6608266

Subgroups — #6608266

Order 512.

1883 conjugacy classes of subgroups.

The subgroup lattice has 1416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36366C211yesmaximal, characteristic, complemented
2#36264C211yesmaximal, characteristic, complemented
3#33265C211yesmaximal, characteristic, complemented
4#33251C211yesmaximal, characteristic, complemented
5#33143C211yesmaximal, characteristic, complemented
6#29556C211yesmaximal, characteristic, complemented
7#29552C211yesmaximal, characteristic, complemented
8#29493C211yesmaximal, characteristic, complemented
9#29492C211yesmaximal, characteristic, complemented
10#28902C211yesmaximal, characteristic, complemented
11#28898C211yesmaximal, characteristic, complemented
12#28025C211yesmaximal, characteristic, complemented
13#27282C211yesmaximal, characteristic, complemented
14#27279C211yesmaximal, characteristic, complemented
15#26827C211yesmaximal, characteristic, complemented
16#26826C211yesmaximal, characteristic, complemented
17#26488C211yesmaximal, characteristic, complemented
18#26264C211yesmaximal, characteristic, complemented
19#26258C211yesmaximal, characteristic, complemented
20#26077C211yesmaximal, characteristic, complemented
21#25794C211yesmaximal, characteristic
22#24504C211yesmaximal, characteristic, complemented
23#24500C211yesmaximal, characteristic, complemented
24#23037C211yesmaximal, characteristic, complemented
25#22880C211yesmaximal, characteristic, complemented
26#22878C211yesmaximal, characteristic, complemented
27#22442C211yesmaximal, characteristic, complemented
28C4×#493C211yesmaximal, characteristic, complemented
29#21286C211yesmaximal, characteristic, complemented
30#21236C211yesmaximal, characteristic, complemented
31#20472C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#551—21no—
34C2×#501C2211yescharacteristic, complemented
35C2×#496C2211yescharacteristic
36C2×#493C2211yescharacteristic
37C2×#490C2211yescharacteristic
38C2×#489C2211yescharacteristic, complemented
39C2×#469C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#442C2211yescharacteristic
43C2×C4×D8C2211yescharacteristic
44C2×C4×D8C2211yescharacteristic
45C2×C4×D8C2211yescharacteristic, complemented
46C2×C4×D8C2211yescharacteristic, complemented
47C2×#431C2211yescharacteristic
48C2×#428C2211yescharacteristic
49C2×#417C2211yescharacteristic
50C2×#418C2211yescharacteristic
51C2×C4×M16C2211yescharacteristic
52#2863C2211yescharacteristic, complemented
53#2861C2211yescharacteristic, complemented
54#2860C2211yescharacteristic
55#2858C2211yescharacteristic
56#2854C2211yescharacteristic
57#2854C2211yescharacteristic
58#2610—21no—
59#2603—21no—
60#2598—21no—
61#2554—21no—
62#2526—21no—
63#2516—21no—
64#2512C2211yescharacteristic
65#2511C2211yescharacteristic, complemented
66#2472—21no—
67#2471—21no—
68#2471—21no—
69#2461—21no—
70#2457—21no—
71#2454C2211yescharacteristic, complemented
72#2452C2211yescharacteristic
73#2447C2211yescharacteristic, complemented
74#2445C2211yescharacteristic
75#2445C2211yescharacteristic
76#2445C2211yescharacteristic, complemented
77#2441C2211yescharacteristic
78#2440C2211yescharacteristic
79#2433C2211yescharacteristic
80#2431C2211yescharacteristic
81#2411—21no—
82#2363C2211yescharacteristic
83#2361C2211yescharacteristic
84#2359—21no—
85#2358—21no—
86#2353—21no—
87#2339C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89C4×#127C2211yescharacteristic
90C4×#127C2211yescharacteristic, complemented
91#2297C2211yescharacteristic
92#2293C2211yescharacteristic
93#2293C2211yescharacteristic, complemented
94C2×#390C2211yescharacteristic
95C4×#117C2211yescharacteristic
96#2084C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2072C2211yescharacteristic, complemented
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2065C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2057C2211yescharacteristic, complemented
106#2055C2211yescharacteristic, complemented
107#2054C2211yescharacteristic
108#2054C2211yescharacteristic
109#2054C2211yescharacteristic, complemented
110#2042C2211yescharacteristic, complemented
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic, complemented
114#2025C2211yescharacteristic
115#2023C2211yescharacteristic, complemented
116#2014C2211yescharacteristic
117#2012C2211yescharacteristic
118#2011C2211yescharacteristic
119#2011C2211yescharacteristic
120#1973C2211yescharacteristic
121#1973C2211yescharacteristic
122#1973C2211yescharacteristic
123#1973C2211yescharacteristic, complemented
124#1972C2211yescharacteristic
125#1972C2211yescharacteristic
126#1972C2211yescharacteristic
127#1972C2211yescharacteristic
128#1972C2211yescharacteristic, complemented
129#1972C2211yescharacteristic, complemented
130#1970C2211yescharacteristic
131#1970C2211yescharacteristic
132#1970C2211yescharacteristic
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic, complemented
135#1970C2211yescharacteristic, complemented
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic
140#1968C2211yescharacteristic, complemented
141#1957C2211yescharacteristic
142#1957C2211yescharacteristic, complemented
143#1944C2211yescharacteristic, complemented
144#1943C2211yescharacteristic, complemented
145#1941C2211yescharacteristic, complemented
146#1941C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic, complemented
150#1936C2211yescharacteristic, complemented
151#1936C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic
156#1934C2211yescharacteristic, complemented
157#1934C2211yescharacteristic, complemented
158#1934C2211yescharacteristic, complemented
159#1933C2211yescharacteristic, complemented
160#1933C2211yescharacteristic, complemented
161#1933C2211yescharacteristic, complemented
162#1928C2211yescharacteristic, complemented
163#1926C2211yescharacteristic, complemented
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic, complemented
166#1895C2211yescharacteristic
167#1895C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic, complemented
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic, complemented
176#1875C2211yescharacteristic
177#1874C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic, complemented
180#1862C2211yescharacteristic, complemented
181#1862C2211yescharacteristic, complemented
182#1854C2211yescharacteristic
183#1852C2211yescharacteristic
184#1845C2211yescharacteristic, complemented
185#1809C2211yescharacteristic
186#1788C2211yescharacteristic
187#1786C2211yescharacteristic
188#1776C2211yescharacteristic, complemented
189#1771C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191#1771C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic, complemented
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199#1744C2211yescharacteristic, complemented
200#1744C2211yescharacteristic, complemented
201C4×#97C2211yescharacteristic, complemented
202C42×C8C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C22×M16C2311yescharacteristic
219#551—48no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#126—21no—
225C2×#126—21no—
226C2×#125C2311yescharacteristic
227C2×#124—21no—
228C2×#124—21no—
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#120—21no—
240C2×#120—21no—
241C2×C4×D4—21no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117—21no—
254C2×#117D411yescharacteristic
255C2×#117D411yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C22⋊C4—21no—
259C22×C22⋊C4—21no—
260C22×C22⋊C4—21no—
261C22×C42C2311yescharacteristic
262#501—42no—
263#496—42no—
264#493—24no—
265#490—42no—
266#489—42no—
267#469—24no—
268#449—24no—
269#447—24no—
270#442—24no—
271C4×D8—42no—
272C4×D8—42no—
273C4×D8—42no—
274C4×D8—42no—
275#431—24no—
276#428—42no—
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290#418—42no—
291#417—42no—
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×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C4×M16—24no—
325C2×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339#400—21no—
340#400—21no—
341#399—21no—
342#399—21no—
343#398—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#395—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#393—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#390—21no—
369#390—21no—
370#390—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#389—21no—
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388—21no—
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—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#384C2311yescharacteristic
450#384C2311yescharacteristic
451#383—21no—
452#381—21no—
453#381—21no—
454#380—21no—
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#379—21no—
458C4×C4⋊C4D411yescharacteristic
459C4×C4⋊C4D411yescharacteristic
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⋊C4D411yescharacteristic
470C4×C22⋊C4D411yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#376D411yescharacteristic
474#376D411yescharacteristic
475C2×#95—21no—
476C43C2311yescharacteristic
477C43C2311yescharacteristic
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#340C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499#336C2311yescharacteristic
500C25—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C22×Q8—21no—
508C22×Q8C2411yescharacteristic
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
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×C4—21no—
537C23×C4—21no—
538C23×C4C2×D411yescharacteristic
539C23×C4C2×D411yescharacteristic
540C23×C4C2411yescharacteristic
541AGL(1,ℤ/8)—416no—
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×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—22no—
563C2×D8—41no—
564C2×D8—41no—
565C2×D8—41no—
566C2×D8—41no—
567C2×D8—41no—
568C2×D8#4114yes—
569C2×M16—22no—
570C2×M16—22no—
571C2×M16—22no—
572C2×M16—22no—
573C2×M16—41no—
574C2×M16#4114yes—
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C4⋊Q8—41no—
584C4⋊Q8—41no—
585#127—22no—
586#127—22no—
587#127—41no—
588#127—41no—
589#127—41no—
590#127—41no—
591#126—44no—
592#126—44no—
593#125—41no—
594#125—41no—
595#124—44no—
596#124—41no—
597#124—41no—
598#124—82no—
599#123—44no—
600#123—44no—
601#123—44no—
602#123—44no—
603#123—82no—
604C22⋊Q8—44no—
605C22⋊Q8—44no—
606#121—22no—
607#121—22no—
608#121—22no—
609#121—22no—
610#120—44no—
611#120—44no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—41no—
615C4×D4—41no—
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—44no—
625C4×D4—44no—
626C4×D4—44no—
627C4×D4—82no—
628C4×D4—82no—
629#117—24no—
630#117—42no—
631#117—44no—
632#117—41no—
633#117—41no—
634#117—82no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4C2×D411yescharacteristic
656C2×C4⋊C4C2×D411yescharacteristic
657C2×C4⋊C4C2×D411yescharacteristic
658C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
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—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—44no—
717C2×C22⋊C4—44no—
718C2×C22⋊C4—82no—
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42C2×D411yescharacteristic
729C2×C42C2×D411yescharacteristic
730C2×C42C2×D411yescharacteristic
731C2×C42C2×D411yescharacteristic
732C2×C42C2×D411yescharacteristic
733C2×C42C2×D411yescharacteristic
734C2×C42C2×D411yescharacteristic
735C2×C42C2×D411yescharacteristic
736C2×C42C2×D411yescharacteristic
737C2×C42C2×D411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744#107—22no—
745#107—22no—
746#107—41no—
747#107—41no—
748#107—41no—
749#107—41no—
750#106—22no—
751#106—22no—
752#106—22no—
753#106—41no—
754#106—41no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757#103—22no—
758#103—22no—
759#103—41no—
760#103—41no—
761#103—41no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—22no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787C22⋊C8—22no—
788C22⋊C8#4114yes—
789#97—22no—
790#97—22no—
791#97—22no—
792#97—22no—
793#97—22no—
794#97—41no—
795C4×C8—22no—
796C4×C8—22no—
797C4×C8—22no—
798C4×C8—22no—
799C4×C8—22no—
800C4×C8—22no—
801C4×C8—22no—
802C4×C8—41no—
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#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—42no—
841C24—42no—
842C24—42no—
843C24—42no—
844C24—81no—
845C24—81no—
846C24—81no—
847C24C22×D411yescharacteristic
848#41—44no—
849#41—44no—
850#41—82no—
851#41—82no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—42no—
859C2×Q8—81no—
860C2×Q8—81no—
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—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—82no—
910C2×D4—82no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4C2×#4112yes—
924C2×D4C2×#4112yes—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—22no—
930C22×C4—22no—
931C22×C4—22no—
932C22×C4—22no—
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—41no—
945C22×C4—41no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—42no—
953C22×C4—42no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C2×#4112yes—
984C22×C4C2×#4112yes—
985C22×C4C2511yescharacteristic
986SD16—44no—
987SD16—44no—
988SD16—82no—
989D8—28no—
990D8—44no—
991D8—44no—
992D8—44no—
993D8—44no—
994D8—82no—
995M16—28no—
996M16—44no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8C2×#4112yes—
1015C2×C8C2×#4112yes—
1016C2×C8C2×#4112yes—
1017C2×C8C2×#4112yes—
1018C2×C8C2×#4112yes—
1019C2×C8H(5,𝔽2)12yes—
1020C2×C8H(5,𝔽2)12yes—
1021C4⋊C4—22no—
1022C4⋊C4—22no—
1023C4⋊C4—22no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—41no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C22⋊C4—22no—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—41no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C42—22no—
1115C42—22no—
1116C42—22no—
1117C42—22no—
1118C42—22no—
1119C42—22no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—21no—
1124C42—21no—
1125C42—21no—
1126C42—21no—
1127C42—21no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—41no—
1133C42—41no—
1134C42—41no—
1135C42—42no—
1136C42—81no—
1137C42—81no—
1138C42AGL(1,ℤ/8)14yescomplemented
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—22no—
1146C23—22no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—84no—
1181C23—84no—
1182C23—84no—
1183C23—84no—
1184C23—162no—
1185C23—162no—
1186C23—162no—
1187C23#53212yes—
1188C23C23×D411yescharacteristic
1189Q8—41no—
1190Q8—41no—
1191Q8—41no—
1192Q8—41no—
1193Q8—162no—
1194D4—22no—
1195D4—22no—
1196D4—22no—
1197D4—22no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—41no—
1209D4—41no—
1210D4—41no—
1211D4—41no—
1212D4—41no—
1213D4—41no—
1214D4—84no—
1215D4—84no—
1216D4—84no—
1217D4—84no—
1218D4—84no—
1219D4—84no—
1220D4—84no—
1221D4—162no—
1222D4—162no—
1223D4—162no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—22no—
1238C2×C4—22no—
1239C2×C4—22no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—44no—
1262C2×C4—44no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—84no—
1297C2×C4—84no—
1298C2×C4—84no—
1299C2×C4—162no—
1300C2×C4—162no—
1301C2×C4—162no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4#53212yes—
1305C2×C4C2×AGL(1,ℤ/8)12yes—
1306C2×C4C2×AGL(1,ℤ/8)12yes—
1307C2×C4C2×AGL(1,ℤ/8)12yes—
1308C2×C4#57512yes—
1309C2×C4#57612yes—
1310C2×C4C22×#4111yescharacteristic
1311C2×C4C22×#4111yescharacteristic
1312C2×C4C22×#4111yescharacteristic
1313C2×C4C2×H(5,𝔽2)11yescharacteristic
1314C2×C4C2×H(5,𝔽2)11yescharacteristic
1315C2×C4#58511yescharacteristic
1316C8—22no—
1317C8—22no—
1318C8—22no—
1319C8—22no—
1320C8—41no—
1321C8—41no—
1322C8—41no—
1323C8#55114yescomplemented
1324C22—22no—
1325C22—22no—
1326C22—22no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—42no—
1335C22—42no—
1336C22—42no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—168no—
1367C22C2×#53211yescharacteristic
1368C22D4×#4111yescharacteristic
1369C22#349811yescharacteristic
1370C22C22×AGL(1,ℤ/8)11yescharacteristic
1371C22C2×#57511yescharacteristic
1372C22C2×#57611yescharacteristic
1373C22#358411yescharacteristic
1374C4—22no—
1375C4—22no—
1376C4—22no—
1377C4—22no—
1378C4—22no—
1379C4—22no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4C2×#55111yescharacteristic
1399C4#348111yescharacteristic
1400C4#349411yescharacteristic
1401C4#351411yescharacteristic
1402C2—42no—
1403C2—82no—
1404C2—82no—
1405C2—161no—
1406C2—161no—
1407C2—161no—
1408C2#3626411yescharacteristic
1409C2#6070011yescharacteristic
1410C2#6070711yescharacteristic
1411C2#6143711yescharacteristic
1412C2#6144411yescharacteristic
1413C2#6242311yescharacteristic
1414C2#6242911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25794C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36366C2semidirect
2. #36264C2semidirect
3. #33265C2semidirect
4. #33251C2semidirect
5. #33143C2semidirect
6. #29556C2semidirect
7. #29552C2semidirect
8. #29493C2semidirect
9. #29492C2semidirect
10. #28902C2semidirect
11. #28898C2semidirect
12. #28025C2semidirect
13. #27282C2semidirect
14. #27279C2semidirect
15. #26827C2semidirect
16. #26826C2semidirect
17. #26488C2semidirect
18. #26264C2semidirect
19. #26258C2semidirect
20. #26077C2semidirect
22. #24504C2semidirect
23. #24500C2semidirect
24. #23037C2semidirect
25. #22880C2semidirect
26. #22878C2semidirect
27. #22442C2semidirect
28. C4×#493C2semidirect
29. #21286C2semidirect
30. #21236C2semidirect
31. #20472C2semidirect
34. C2×#501C22semidirect
38. C2×#489C22semidirect
45. C2×C4×D8C22semidirect
46. C2×C4×D8C22semidirect
52. #2863C22semidirect
53. #2861C22semidirect
65. #2511C22semidirect
71. #2454C22semidirect
73. #2447C22semidirect
76. #2445C22semidirect
90. C4×#127C22semidirect
93. #2293C22semidirect
96. #2084C22semidirect
97. #2083C22semidirect
98. #2072C22semidirect
100. #2068C22semidirect
103. #2065C22semidirect
104. #2059C22semidirect
105. #2057C22semidirect
106. #2055C22semidirect
109. #2054C22semidirect
110. #2042C22semidirect
113. #2041C22semidirect
115. #2023C22semidirect
123. #1973C22semidirect
128. #1972C22semidirect
129. #1972C22semidirect
134. #1970C22semidirect
135. #1970C22semidirect
140. #1968C22semidirect
142. #1957C22semidirect
143. #1944C22semidirect
144. #1943C22semidirect
145. #1941C22semidirect
146. #1941C22semidirect
147. #1941C22semidirect
149. #1936C22semidirect
150. #1936C22semidirect
151. #1936C22semidirect
156. #1934C22semidirect
157. #1934C22semidirect
158. #1934C22semidirect
159. #1933C22semidirect
160. #1933C22semidirect
161. #1933C22semidirect
162. #1928C22semidirect
163. #1926C22semidirect
165. #1925C22semidirect
172. #1879C22semidirect
175. #1877C22semidirect
179. #1864C22semidirect
180. #1862C22semidirect
181. #1862C22semidirect
184. #1845C22semidirect
188. #1776C22semidirect
189. #1771C22semidirect
190. #1771C22semidirect
191. #1771C22semidirect
192. #1771C22semidirect
194. #1762C22semidirect
199. #1744C22semidirect
200. #1744C22semidirect
201. C4×#97C22semidirect
202. C42×C8C22semidirect
1138. C42AGL(1,ℤ/8)semidirect
1323. C8#551semidirect

Maximal subgroups

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

subgroupindex
#363662
#362642
#332652
#332512
#331432
#295562
#295522
#294932
#294922
#289022
#288982
#280252
#272822
#272792
#268272
#268262
#264882
#262642
#262582
#260772
#257942
#245042
#245002
#230372
#228802
#228782
#224422
C4×#4932
#212862
#212362
#204722