Finite Group Databasebeta

← #6990410

Subgroups — #6990410

Order 512.

1561 conjugacy classes of subgroups.

The subgroup lattice has 1373 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38277C211yesmaximal, characteristic, complemented
2#37305C211yesmaximal, characteristic
3#32833C211yesmaximal, characteristic, complemented
4#32823C211yesmaximal, characteristic, complemented
5#31315C211yesmaximal, characteristic, complemented
6#31314C211yesmaximal, characteristic, complemented
7#31313C211yesmaximal, characteristic, complemented
8#31298C211yesmaximal, characteristic, complemented
9#31012C211yesmaximal, characteristic, complemented
10#31007C211yesmaximal, characteristic, complemented
11#31004C211yesmaximal, characteristic, complemented
12#30989C211yesmaximal, characteristic, complemented
13#30225C211yesmaximal, characteristic, complemented
14#30222C211yesmaximal, characteristic, complemented
15#29803C211yesmaximal, characteristic, complemented
16#29801C211yesmaximal, characteristic, complemented
17#29696C211yesmaximal, characteristic, complemented
18#29567C211yesmaximal, characteristic, complemented
19#29561C211yesmaximal, characteristic, complemented
20#28424C211yesmaximal, characteristic, complemented
21#28420C211yesmaximal, characteristic, complemented
22#27760C211yesmaximal, characteristic, complemented
23#27754C211yesmaximal, characteristic, complemented
24#25865C211yesmaximal, characteristic, complemented
25#25285C211yesmaximal, characteristic, complemented
26#25277C211yesmaximal, characteristic, complemented
27#24747C211yesmaximal, characteristic, complemented
28#24734C211yesmaximal, characteristic, complemented
29#24220C211yesmaximal, characteristic, complemented
30#23581C211yesmaximal, characteristic, complemented
31#22638C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#486C2211yescharacteristic
36C2×#477C2211yescharacteristic, complemented
37C2×#474C2211yescharacteristic, complemented
38C2×#464C2211yescharacteristic
39C2×#464C2211yescharacteristic
40C2×#464C2211yescharacteristic, complemented
41C2×#464C2211yescharacteristic, complemented
42C2×#460C2211yescharacteristic
43C2×#460C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×#441C2211yescharacteristic, complemented
47C2×C4×SD16C2211yescharacteristic, complemented
48#2864C2211yescharacteristic, complemented
49#2858C2211yescharacteristic
50#2858C2211yescharacteristic
51#2776—21no—
52#2773—21no—
53#2762—21no—
54#2754—21no—
55#2714—21no—
56#2714—21no—
57#2678—21no—
58#2678—21no—
59#2676—21no—
60#2676—21no—
61#2670—21no—
62#2670—21no—
63#2657C2211yescharacteristic
64#2647C2211yescharacteristic, complemented
65#2640C2211yescharacteristic
66#2628C2211yescharacteristic
67#2596—21no—
68#2570C2211yescharacteristic, complemented
69#2568C2211yescharacteristic, complemented
70#2548C2211yescharacteristic
71#2545C2211yescharacteristic
72#2544C2211yescharacteristic
73#2541C2211yescharacteristic
74#2533—21no—
75#2532—21no—
76#2520—21no—
77#2495C2211yescharacteristic
78#2494C2211yescharacteristic
79#2435C2211yescharacteristic
80#2433C2211yescharacteristic
81#2432C2211yescharacteristic
82#2431C2211yescharacteristic
83#2423C2211yescharacteristic
84#2421C2211yescharacteristic
85#2369C2211yescharacteristic, complemented
86#2351C2211yescharacteristic, complemented
87#2323C2211yescharacteristic
88#2320C2211yescharacteristic, complemented
89#2298C2211yescharacteristic
90#2295C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2092C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic, complemented
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic, complemented
97#2072C2211yescharacteristic, complemented
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic, complemented
107#2058C2211yescharacteristic, complemented
108#2057C2211yescharacteristic, complemented
109#2057C2211yescharacteristic, complemented
110#2043C2211yescharacteristic, complemented
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic, complemented
118#2042C2211yescharacteristic, complemented
119#2042C2211yescharacteristic, complemented
120#2042C2211yescharacteristic, complemented
121#2042C2211yescharacteristic, complemented
122#2042C2211yescharacteristic, complemented
123#2042C2211yescharacteristic, complemented
124#2041C2211yescharacteristic
125#2041C2211yescharacteristic
126#2041C2211yescharacteristic
127#2041C2211yescharacteristic
128#2041C2211yescharacteristic
129#2041C2211yescharacteristic
130#2041C2211yescharacteristic, complemented
131#2036C2211yescharacteristic
132#2036C2211yescharacteristic
133#2035C2211yescharacteristic
134#2034C2211yescharacteristic
135#2033C2211yescharacteristic
136#2033C2211yescharacteristic
137#2024C2211yescharacteristic, complemented
138#2016C2211yescharacteristic, complemented
139#2015C2211yescharacteristic
140#2015C2211yescharacteristic
141#2015C2211yescharacteristic, complemented
142#2014C2211yescharacteristic
143#2014C2211yescharacteristic
144#2014C2211yescharacteristic, complemented
145#2001C2211yescharacteristic
146#2000C2211yescharacteristic
147#1983C2211yescharacteristic
148#1983C2211yescharacteristic
149#1983C2211yescharacteristic, complemented
150#1983C2211yescharacteristic, complemented
151#1982C2211yescharacteristic
152#1982C2211yescharacteristic
153#1973C2211yescharacteristic
154#1973C2211yescharacteristic
155#1973C2211yescharacteristic, complemented
156#1969C2211yescharacteristic, complemented
157#1961C2211yescharacteristic
158#1961C2211yescharacteristic
159#1961C2211yescharacteristic
160#1961C2211yescharacteristic, complemented
161#1960C2211yescharacteristic, complemented
162#1960C2211yescharacteristic, complemented
163#1959C2211yescharacteristic
164#1958C2211yescharacteristic
165#1958C2211yescharacteristic
166#1957C2211yescharacteristic, complemented
167#1940C2211yescharacteristic, complemented
168#1939C2211yescharacteristic, complemented
169#1936C2211yescharacteristic
170#1936C2211yescharacteristic, complemented
171#1935C2211yescharacteristic, complemented
172#1934C2211yescharacteristic
173#1928C2211yescharacteristic, complemented
174#1925C2211yescharacteristic
175#1925C2211yescharacteristic
176#1925C2211yescharacteristic, complemented
177#1924C2211yescharacteristic
178#1924C2211yescharacteristic
179#1924C2211yescharacteristic
180#1923C2211yescharacteristic
181#1880C2211yescharacteristic
182#1880C2211yescharacteristic
183#1880C2211yescharacteristic, complemented
184#1878C2211yescharacteristic, complemented
185#1832C2211yescharacteristic, complemented
186#1831C2211yescharacteristic, complemented
187#1805C2211yescharacteristic, complemented
188#1804C2211yescharacteristic, complemented
189#1798C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1771C2211yescharacteristic, complemented
197#1770C2211yescharacteristic, complemented
198#1762C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1746C2211yescharacteristic, complemented
202#1745C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211#542—42no—
212#542—42no—
213#535—42no—
214#535—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#126—21no—
224C2×#124—21no—
225C2×#124—21no—
226C2×#124—21no—
227C2×#124C2311yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#124C2311yescharacteristic
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#123—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121C2311yescharacteristic
243C2×#120—21no—
244C2×#120—21no—
245C2×#120—21no—
246C2×#120—21no—
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117C2311yescharacteristic
253#489—42no—
254#486—42no—
255#477—42no—
256#474—42no—
257#464—42no—
258#464—42no—
259#464—42no—
260#464—42no—
261#460—42no—
262#460—42no—
263#452—42no—
264#450—42no—
265#441—42no—
266C4×SD16—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
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×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
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×#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×#102C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#401—21no—
334#400—21no—
335#400—21no—
336#400—21no—
337#400—21no—
338#400—21no—
339#400—21no—
340#400—21no—
341#400—21no—
342#399—21no—
343#399—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#396—21no—
354#396—21no—
355#395—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#393—21no—
365#393—21no—
366#393—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#391—21no—
378#391—21no—
379#391—21no—
380#391—21no—
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#391C2311yescharacteristic
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390—21no—
392#390—21no—
393#390—21no—
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#389—21no—
401#389—21no—
402#389—21no—
403#389—21no—
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#389C2311yescharacteristic
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
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#388D411yescharacteristic
422#388D411yescharacteristic
423#388D411yescharacteristic
424#388D411yescharacteristic
425#387—21no—
426#387—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#387—21no—
436#387—21no—
437#387—21no—
438#387—21no—
439#387D411yescharacteristic
440#387D411yescharacteristic
441#387D411yescharacteristic
442#387D411yescharacteristic
443#386—21no—
444#386—21no—
445#386—21no—
446#386—21no—
447#385—21no—
448#385—21no—
449#384C2311yescharacteristic
450#383—21no—
451#383—21no—
452#382—21no—
453#382—21no—
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#379—21no—
462#379—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4C2311yescharacteristic
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472C4×C22⋊C4C2311yescharacteristic
473#376—21no—
474#376C2311yescharacteristic
475C43C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×Q8C2411yescharacteristic
508C22×D4—21no—
509C22×D4—21no—
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—21no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2411yescharacteristic
534C2×Q16—22no—
535C2×Q16—22no—
536C2×Q16—41no—
537C2×Q16—41no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C4⋊Q8—22no—
561C4⋊Q8—22no—
562C4⋊Q8—41no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566#127—22no—
567#127—22no—
568#127—41no—
569#127—41no—
570#127—41no—
571#127—41no—
572#127—41no—
573#127—41no—
574#127—41no—
575#127—41no—
576#126—44no—
577#124—22no—
578#124—22no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#124—41no—
584#124—41no—
585#124—41no—
586#124—41no—
587#124—41no—
588#124—41no—
589#124—41no—
590#124—41no—
591#124—44no—
592#124—82no—
593#124—82no—
594#123—44no—
595C22⋊Q8—22no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599C22⋊Q8—44no—
600#121—41no—
601#121—41no—
602#121—44no—
603#121—44no—
604#121—82no—
605#121—82no—
606#120—44no—
607#120—44no—
608#120—82no—
609#120—82no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—22no—
613C4×Q8—22no—
614C4×Q8—22no—
615C4×Q8—22no—
616C4×Q8—41no—
617C4×Q8—41no—
618C4×D4—22no—
619C4×D4—22no—
620#117—22no—
621#117—22no—
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⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2×D411yescharacteristic
648C2×C4⋊C4C2×D411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42C2×D411yescharacteristic
705C2×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714#107—41no—
715#107—41no—
716#107—41no—
717#107—41no—
718#106—41no—
719#106—41no—
720C4⋊C8—22no—
721C4⋊C8—22no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
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#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
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—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770C22⋊C8—41no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774#97—22no—
775#97—41no—
776#97—41no—
777#97—41no—
778C4×C8—22no—
779C4×C8—41no—
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#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
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—42no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24—81no—
836C24C22×D411yescharacteristic
837#41—82no—
838#41—82no—
839#41—82no—
840#41—82no—
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—42no—
859C2×Q8—42no—
860C2×Q8—81no—
861C2×Q8—81no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8H(5,𝔽2)12yes—
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—42no—
890C2×D4—42no—
891C2×D4—42no—
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—81no—
910C2×D4—81no—
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×D4—81no—
924C2×D4—82no—
925C2×D4—82no—
926C2×D4—82no—
927C2×D4—82no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
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—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C2511yescharacteristic
970Q16—44no—
971Q16—82no—
972SD16—44no—
973SD16—82no—
974SD16—82no—
975SD16—82no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C4⋊C4—22no—
1001C4⋊C4—22no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—41no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C22⋊C4—22no—
1046C22⋊C4—22no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—41no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—21no—
1094C42—41no—
1095C42—41no—
1096C42—41no—
1097C42—41no—
1098C42—42no—
1099C42—42no—
1100C42—42no—
1101C42—42no—
1102C42—81no—
1103C42—81no—
1104C42—81no—
1105C42H(5,𝔽2)12yes—
1106C42H(5,𝔽2)12yes—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
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—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—84no—
1143C23—162no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23C23×D411yescharacteristic
1150Q8—22no—
1151Q8—22no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—162no—
1163Q8—162no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—41no—
1179D4—41no—
1180D4—84no—
1181D4—84no—
1182D4—162no—
1183D4—162no—
1184D4—162no—
1185D4—162no—
1186D4—162no—
1187D4—162no—
1188D4—162no—
1189D4—162no—
1190D4—162no—
1191D4—162no—
1192D4—162no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—22no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
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—84no—
1271C2×C4—162no—
1272C2×C4#53512yes—
1273C2×C4#53512yes—
1274C2×C4C2×H(5,𝔽2)11yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4#58511yescharacteristic
1278C2×C4#58511yescharacteristic
1279C2×C4#58511yescharacteristic
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C22—41no—
1289C22—41no—
1290C22—41no—
1291C22—41no—
1292C22—41no—
1293C22—41no—
1294C22—41no—
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—81no—
1310C22—81no—
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—168no—
1324C22C2×#53511yescharacteristic
1325C22#348811yescharacteristic
1326C22#350011yescharacteristic
1327C22#358411yescharacteristic
1328C22#358511yescharacteristic
1329C22#358511yescharacteristic
1330C22#358611yescharacteristic
1331C4—22no—
1332C4—22no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—42no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4#354211yescharacteristic
1357C4#354211yescharacteristic
1358C4#355111yescharacteristic
1359C4#355111yescharacteristic
1360C2—81no—
1361C2—161no—
1362C2—161no—
1363C2—161no—
1364C2—161no—
1365C2#4296211yescharacteristic
1366C2#6082711yescharacteristic
1367C2#6083511yescharacteristic
1368C2#6202611yescharacteristic
1369C2#6208511yescharacteristic
1370C2#6256811yescharacteristic
1371C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37305C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38277C2semidirect
3. #32833C2semidirect
4. #32823C2semidirect
5. #31315C2semidirect
6. #31314C2semidirect
7. #31313C2semidirect
8. #31298C2semidirect
9. #31012C2semidirect
10. #31007C2semidirect
11. #31004C2semidirect
12. #30989C2semidirect
13. #30225C2semidirect
14. #30222C2semidirect
15. #29803C2semidirect
16. #29801C2semidirect
17. #29696C2semidirect
18. #29567C2semidirect
19. #29561C2semidirect
20. #28424C2semidirect
21. #28420C2semidirect
22. #27760C2semidirect
23. #27754C2semidirect
24. #25865C2semidirect
25. #25285C2semidirect
26. #25277C2semidirect
27. #24747C2semidirect
28. #24734C2semidirect
29. #24220C2semidirect
30. #23581C2semidirect
31. #22638C2semidirect
36. C2×#477C22semidirect
37. C2×#474C22semidirect
40. C2×#464C22semidirect
41. C2×#464C22semidirect
46. C2×#441C22semidirect
47. C2×C4×SD16C22semidirect
48. #2864C22semidirect
64. #2647C22semidirect
68. #2570C22semidirect
69. #2568C22semidirect
85. #2369C22semidirect
86. #2351C22semidirect
88. #2320C22semidirect
90. #2295C22semidirect
91. #2097C22semidirect
94. #2092C22semidirect
96. #2073C22semidirect
97. #2072C22semidirect
99. #2068C22semidirect
102. #2067C22semidirect
103. #2066C22semidirect
106. #2065C22semidirect
107. #2058C22semidirect
108. #2057C22semidirect
109. #2057C22semidirect
110. #2043C22semidirect
117. #2042C22semidirect
118. #2042C22semidirect
119. #2042C22semidirect
120. #2042C22semidirect
121. #2042C22semidirect
122. #2042C22semidirect
123. #2042C22semidirect
130. #2041C22semidirect
137. #2024C22semidirect
138. #2016C22semidirect
141. #2015C22semidirect
144. #2014C22semidirect
149. #1983C22semidirect
150. #1983C22semidirect
155. #1973C22semidirect
156. #1969C22semidirect
160. #1961C22semidirect
161. #1960C22semidirect
162. #1960C22semidirect
166. #1957C22semidirect
167. #1940C22semidirect
168. #1939C22semidirect
170. #1936C22semidirect
171. #1935C22semidirect
173. #1928C22semidirect
176. #1925C22semidirect
183. #1880C22semidirect
184. #1878C22semidirect
185. #1832C22semidirect
186. #1831C22semidirect
187. #1805C22semidirect
188. #1804C22semidirect
196. #1771C22semidirect
197. #1770C22semidirect
198. #1762C22semidirect
199. C4×#103C22semidirect
201. #1746C22semidirect
202. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#382772
#373052
#328332
#328232
#313152
#313142
#313132
#312982
#310122
#310072
#310042
#309892
#302252
#302222
#298032
#298012
#296962
#295672
#295612
#284242
#284202
#277602
#277542
#258652
#252852
#252772
#247472
#247342
#242202
#235812
#226382