Finite Group Databasebeta

← #6840550

Subgroups — #6840550

Order 512.

1521 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40176C211yesmaximal, characteristic
2#39660C211yesmaximal, characteristic, complemented
3#33250C211yesmaximal, characteristic, complemented
4#32430C211yesmaximal, characteristic, complemented
5#31936C211yesmaximal, characteristic, complemented
6#30962C211yesmaximal, characteristic, complemented
7#30877C211yesmaximal, characteristic, complemented
8#30799C211yesmaximal, characteristic, complemented
9#30762C211yesmaximal, characteristic, complemented
10#30527C211yesmaximal, characteristic
11#30464C211yesmaximal, characteristic, complemented
12#30061C211yesmaximal, characteristic, complemented
13#30039C211yesmaximal, characteristic, complemented
14#29101C211yesmaximal, characteristic, complemented
15#28977C211yesmaximal, characteristic, complemented
16#28936C211yesmaximal, characteristic, complemented
17#28929C211yesmaximal, characteristic, complemented
18#28898C211yesmaximal, characteristic, complemented
19#28428C211yesmaximal, characteristic, complemented
20#28332C211yesmaximal, characteristic
21#27778C211yesmaximal, characteristic, complemented
22#27262C211yesmaximal, characteristic, complemented
23#27245C211yesmaximal, characteristic, complemented
24#27207C211yesmaximal, characteristic, complemented
25#27088C211yesmaximal, characteristic, complemented
26#26946C211yesmaximal, characteristic, complemented
27#26845C211yesmaximal, characteristic, complemented
28#23107C211yesmaximal, characteristic, complemented
29#22854C211yesmaximal, characteristic, complemented
30#21665C211yesmaximal, characteristic, complemented
31#21646C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic, complemented
33C2×#497C2211yescharacteristic
34C2×#491C2211yescharacteristic, complemented
35C2×#489C2211yescharacteristic
36C2×#489C2211yescharacteristic, complemented
37C2×#486C2211yescharacteristic
38C2×#481C2211yescharacteristic
39C2×#474C2211yescharacteristic
40C2×#465C2211yescharacteristic
41C2×#464C2211yescharacteristic
42C2×#464C2211yescharacteristic, complemented
43C2×#450C2211yescharacteristic
44C2×#450C2211yescharacteristic
45C2×#440C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2862C2211yescharacteristic, complemented
48#2861C2211yescharacteristic
49#2797—21no—
50#2774—21no—
51#2763—21no—
52#2756—21no—
53#2755—21no—
54#2729—21no—
55#2685—21no—
56#2685—21no—
57#2666—21no—
58#2630—21no—
59#2567C2211yescharacteristic, complemented
60#2551C2211yescharacteristic, complemented
61#2548C2211yescharacteristic
62#2544C2211yescharacteristic
63#2512C2211yescharacteristic
64#2511C2211yescharacteristic, complemented
65#2502C2211yescharacteristic
66#2492C2211yescharacteristic
67#2492C2211yescharacteristic
68#2490C2211yescharacteristic
69#2467—21no—
70#2465—21no—
71#2454C2211yescharacteristic
72#2451—21no—
73#2451C2211yescharacteristic, complemented
74#2446C2211yescharacteristic, complemented
75#2445C2211yescharacteristic
76#2440C2211yescharacteristic
77#2435C2211yescharacteristic
78#2433C2211yescharacteristic
79#2429C2211yescharacteristic
80#2427C2211yescharacteristic
81#2423C2211yescharacteristic
82#2418—21no—
83#2367C2211yescharacteristic
84#2360C2211yescharacteristic
85#2355C2211yescharacteristic, complemented
86D4×C22⋊C4C2211yescharacteristic
87#2334—21no—
88#2321—21no—
89C4×C4⋊Q8C2211yescharacteristic, complemented
90C4×#127C2211yescharacteristic
91C4×#126C2211yescharacteristic
92#2095C2211yescharacteristic, complemented
93#2094C2211yescharacteristic
94#2094C2211yescharacteristic
95#2093C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2083C2211yescharacteristic, complemented
98#2076C2211yescharacteristic
99#2072C2211yescharacteristic, complemented
100#2072C2211yescharacteristic, complemented
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2058C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2042C2211yescharacteristic, complemented
114#2036C2211yescharacteristic
115#2034C2211yescharacteristic
116#2024C2211yescharacteristic, complemented
117#2023C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#2023C2211yescharacteristic, complemented
121#2015C2211yescharacteristic
122#2015C2211yescharacteristic, complemented
123#2014C2211yescharacteristic
124#2014C2211yescharacteristic
125#2014C2211yescharacteristic
126#2014C2211yescharacteristic
127#2013C2211yescharacteristic
128#2013C2211yescharacteristic, complemented
129#2001C2211yescharacteristic
130#2001C2211yescharacteristic
131#2000C2211yescharacteristic
132#1990C2211yescharacteristic, complemented
133#1982C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic, complemented
137#1971C2211yescharacteristic, complemented
138#1971C2211yescharacteristic, complemented
139#1969C2211yescharacteristic, complemented
140#1969C2211yescharacteristic, complemented
141#1968C2211yescharacteristic
142#1968C2211yescharacteristic
143#1968C2211yescharacteristic
144#1959C2211yescharacteristic
145#1957C2211yescharacteristic
146#1957C2211yescharacteristic
147#1948C2211yescharacteristic, complemented
148#1936C2211yescharacteristic
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic
152#1936C2211yescharacteristic, complemented
153#1936C2211yescharacteristic, complemented
154#1935C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1926C2211yescharacteristic
160#1925C2211yescharacteristic
161#1925C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1923C2211yescharacteristic
165#1921C2211yescharacteristic, complemented
166#1919C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1892C2211yescharacteristic
171#1892C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1877C2211yescharacteristic, complemented
181#1877C2211yescharacteristic, complemented
182#1872C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1862C2211yescharacteristic
185#1852C2211yescharacteristic
186#1839C2211yescharacteristic, complemented
187#1834C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1786C2211yescharacteristic
190#1771C2211yescharacteristic, complemented
191#1771C2211yescharacteristic, complemented
192#1770C2211yescharacteristic, complemented
193#1763C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic, complemented
197#1762C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199#1752C2211yescharacteristic
200#1752C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202C4×#97C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#126—21no—
221C2×#126D411yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#124C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#123—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233C2×#120—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C22×C4⋊C4C2311yescharacteristic
244C22×C22⋊C4—21no—
245#501—42no—
246#497—42no—
247#491—42no—
248#489—42no—
249#489—42no—
250#486—24no—
251#481—42no—
252#474—42no—
253#465—42no—
254#464—24no—
255#464—42no—
256#450—24no—
257#450—42no—
258#440—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#102—42no—
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×#97C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#399—21no—
321#399—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#395—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#393—21no—
352#393—21no—
353#392—21no—
354#392—21no—
355#391—21no—
356#391—21no—
357#391—21no—
358#391—21no—
359#391—21no—
360#391—21no—
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#389—21no—
385#389—21no—
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388D411yescharacteristic
409#388D411yescharacteristic
410#388D411yescharacteristic
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387D411yescharacteristic
421#387D411yescharacteristic
422#387D411yescharacteristic
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#383D411yescharacteristic
440#382—21no—
441#382—21no—
442#382—21no—
443#380—21no—
444#380—21no—
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#379—21no—
448#379—21no—
449#379—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C43C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—21no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×Q8C2411yescharacteristic
500C22×D4—22no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C2411yescharacteristic
520C2×Q16—22no—
521C2×Q16—22no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×Q16—41no—
525C2×Q16—41no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C22×C8—22no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C4⋊Q8—22no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559C4⋊Q8—41no—
560C4⋊Q8—41no—
561C4⋊Q8—41no—
562C4⋊Q8—41no—
563C4⋊Q8—82no—
564#127—22no—
565#127—41no—
566#127—41no—
567#127—41no—
568#126—24no—
569#126—82no—
570#125—41no—
571#125—41no—
572#124—22no—
573#124—41no—
574#124—41no—
575#124—41no—
576#124—41no—
577#124—41no—
578#123—82no—
579C22⋊Q8—22no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584C22⋊Q8—41no—
585C22⋊Q8—82no—
586#121—41no—
587#121—41no—
588#120—44no—
589#120—82no—
590C4×Q8—22no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—82no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—82no—
604C4×D4—82no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—82no—
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42C2×D411yescharacteristic
697C2×C42C2×D411yescharacteristic
698C2×C42C2×D411yescharacteristic
699C2×C42C2×D411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706#107—22no—
707#107—41no—
708#107—41no—
709#107—41no—
710#106—22no—
711#106—41no—
712#106—41no—
713#106—41no—
714C4⋊C8—22no—
715C4⋊C8—22no—
716C4⋊C8—41no—
717#103—22no—
718#103—22no—
719#103—22no—
720#103—22no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102#4114yes—
749C22⋊C8—22no—
750C22⋊C8—22no—
751C22⋊C8—41no—
752#97—22no—
753#97—22no—
754#97—22no—
755#97—41no—
756#97—41no—
757#97—41no—
758C4×C8—22no—
759C4×C8—41no—
760C4×C8—41no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805C24—21no—
806C24—21no—
807C24—21no—
808C24—42no—
809C24—42no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24C22×D411yescharacteristic
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—42no—
835C2×Q8—42no—
836C2×Q8—42no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8—81no—
842C2×Q8—81no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—44no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—82no—
878C2×D4—82no—
879C2×D4—82no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4C2×#4112yes—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C2511yescharacteristic
928Q16—82no—
929Q16—82no—
930SD16—44no—
931SD16—82no—
932SD16—82no—
933SD16—82no—
934SD16—82no—
935SD16—82no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—82no—
958C2×C8C2×#4112yes—
959C2×C8H(5,𝔽2)12yes—
960C2×C8H(5,𝔽2)12yes—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4C2×#4112yes—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—22no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4#13714yes—
1052C42—22no—
1053C42—22no—
1054C42—21no—
1055C42—21no—
1056C42—21no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—41no—
1067C42—41no—
1068C42—42no—
1069C42—81no—
1070C42—81no—
1071C42—81no—
1072C42—81no—
1073C42—81no—
1074C42—81no—
1075C23—21no—
1076C23—21no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—22no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—84no—
1103C23—84no—
1104C23—162no—
1105C23—162no—
1106C23—162no—
1107C23—162no—
1108C23—162no—
1109C23C2×#13712yes—
1110C23C23×D411yescharacteristic
1111Q8—41no—
1112Q8—41no—
1113Q8—41no—
1114Q8—41no—
1115Q8—41no—
1116Q8—41no—
1117Q8—41no—
1118Q8—41no—
1119Q8—41no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—84no—
1124Q8—162no—
1125Q8—162no—
1126D4—22no—
1127D4—22no—
1128D4—41no—
1129D4—41no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—84no—
1139D4—84no—
1140D4—84no—
1141D4—162no—
1142D4—162no—
1143D4—162no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4C2×#13712yes—
1228C2×C4C2×#13712yes—
1229C2×C4#57712yes—
1230C2×C4C22×#4111yescharacteristic
1231C2×C4C2×H(5,𝔽2)11yescharacteristic
1232C2×C4C2×H(5,𝔽2)11yescharacteristic
1233C2×C4#58511yescharacteristic
1234C2×C4#58511yescharacteristic
1235C2×C4#58511yescharacteristic
1236C8—22no—
1237C8—22no—
1238C8—22no—
1239C8—41no—
1240C8—41no—
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C22—22no—
1245C22—22no—
1246C22—22no—
1247C22—41no—
1248C22—41no—
1249C22—41no—
1250C22—41no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22—81no—
1271C22—81no—
1272C22—168no—
1273C22D4×#4111yescharacteristic
1274C22#349811yescharacteristic
1275C22#350011yescharacteristic
1276C22C22×#13711yescharacteristic
1277C22C2×#57711yescharacteristic
1278C22#358511yescharacteristic
1279C22#358511yescharacteristic
1280C4—22no—
1281C4—22no—
1282C4—22no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—42no—
1287C4—41no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4#346011yescharacteristic
1307C4#351411yescharacteristic
1308C4#354511yescharacteristic
1309C4#356011yescharacteristic
1310C2—42no—
1311C2—82no—
1312C2—161no—
1313C2—161no—
1314C2#3944311yescharacteristic
1315C2#6145311yescharacteristic
1316C2#6152211yescharacteristic
1317C2#6242211yescharacteristic
1318C2#6244311yescharacteristic
1319C2#6258211yescharacteristic
1320C2#6260811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #39660C2semidirect
3. #33250C2semidirect
4. #32430C2semidirect
5. #31936C2semidirect
6. #30962C2semidirect
7. #30877C2semidirect
8. #30799C2semidirect
9. #30762C2semidirect
11. #30464C2semidirect
12. #30061C2semidirect
13. #30039C2semidirect
14. #29101C2semidirect
15. #28977C2semidirect
16. #28936C2semidirect
17. #28929C2semidirect
18. #28898C2semidirect
19. #28428C2semidirect
21. #27778C2semidirect
22. #27262C2semidirect
23. #27245C2semidirect
24. #27207C2semidirect
25. #27088C2semidirect
26. #26946C2semidirect
27. #26845C2semidirect
28. #23107C2semidirect
29. #22854C2semidirect
30. #21665C2semidirect
31. #21646C2semidirect
32. C2×#501C22semidirect
34. C2×#491C22semidirect
36. C2×#489C22semidirect
42. C2×#464C22semidirect
47. #2862C22semidirect
59. #2567C22semidirect
60. #2551C22semidirect
64. #2511C22semidirect
73. #2451C22semidirect
74. #2446C22semidirect
85. #2355C22semidirect
89. C4×C4⋊Q8C22semidirect
92. #2095C22semidirect
95. #2093C22semidirect
96. #2088C22semidirect
97. #2083C22semidirect
99. #2072C22semidirect
100. #2072C22semidirect
102. #2068C22semidirect
103. #2067C22semidirect
104. #2059C22semidirect
105. #2059C22semidirect
106. #2058C22semidirect
113. #2042C22semidirect
116. #2024C22semidirect
120. #2023C22semidirect
122. #2015C22semidirect
128. #2013C22semidirect
132. #1990C22semidirect
136. #1973C22semidirect
137. #1971C22semidirect
138. #1971C22semidirect
139. #1969C22semidirect
140. #1969C22semidirect
147. #1948C22semidirect
152. #1936C22semidirect
153. #1936C22semidirect
154. #1935C22semidirect
155. #1933C22semidirect
156. #1927C22semidirect
157. #1927C22semidirect
158. #1927C22semidirect
165. #1921C22semidirect
166. #1919C22semidirect
167. #1917C22semidirect
168. #1917C22semidirect
169. #1916C22semidirect
174. #1880C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
180. #1877C22semidirect
181. #1877C22semidirect
183. #1865C22semidirect
186. #1839C22semidirect
187. #1834C22semidirect
188. #1803C22semidirect
190. #1771C22semidirect
191. #1771C22semidirect
192. #1770C22semidirect
193. #1763C22semidirect
196. #1762C22semidirect
197. #1762C22semidirect
198. C4×#103C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#401762
#396602
#332502
#324302
#319362
#309622
#308772
#307992
#307622
#305272
#304642
#300612
#300392
#291012
#289772
#289362
#289292
#288982
#284282
#283322
#277782
#272622
#272452
#272072
#270882
#269462
#268452
#231072
#228542
#216652
#216462