Finite Group Databasebeta

← #7086220

Subgroups — #7086220

Order 512.

1505 conjugacy classes of subgroups.

The subgroup lattice has 1301 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59556C211yesmaximal, characteristic, complemented
2#59488C211yesmaximal, characteristic, complemented
3#32058C211yesmaximal, characteristic, complemented
4#31985C211yesmaximal, characteristic, complemented
5#31653C211yesmaximal, characteristic, complemented
6#31501C211yesmaximal, characteristic, complemented
7#31210C211yesmaximal, characteristic, complemented
8#30916C211yesmaximal, characteristic, complemented
9#30759C211yesmaximal, characteristic, complemented
10#30464C211yesmaximal, characteristic, complemented
11#29537C211yesmaximal, characteristic, complemented
12#29096C211yesmaximal, characteristic, complemented
13#28163C211yesmaximal, characteristic, complemented
14#27374C211yesmaximal, characteristic, complemented
15#27112C211yesmaximal, characteristic, complemented
16#27093C211yesmaximal, characteristic, complemented
17#26980C211yesmaximal, characteristic, complemented
18#26918C211yesmaximal, characteristic, complemented
19#26679C211yesmaximal, characteristic, complemented
20#26181C211yesmaximal, characteristic, complemented
21#25164C211yesmaximal, characteristic
22#25152C211yesmaximal, characteristic
23#25088C211yesmaximal, characteristic
24#24819C211yesmaximal, characteristic, complemented
25#24640C211yesmaximal, characteristic, complemented
26#24527C211yesmaximal, characteristic, complemented
27#23687C211yesmaximal, characteristic, complemented
28#23192C211yesmaximal, characteristic, complemented
29#22854C211yesmaximal, characteristic, complemented
30#22351C211yesmaximal, characteristic, complemented
31#22155C211yesmaximal, characteristic, complemented
32C2×#497C2211yescharacteristic
33C2×#479C2211yescharacteristic, complemented
34C2×#465C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#441C2211yescharacteristic, complemented
43C2×#440C2211yescharacteristic
44C2×#440C2211yescharacteristic
45C2×C4×SD16C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2772—21no—
48#2761—21no—
49#2746—21no—
50#2735—21no—
51#2609—21no—
52#2587—21no—
53#2578—21no—
54#2576—21no—
55#2573—21no—
56#2566C2211yescharacteristic
57#2545C2211yescharacteristic, complemented
58#2529—21no—
59#2526—21no—
60#2513C2211yescharacteristic, complemented
61#2508C2211yescharacteristic, complemented
62#2503C2211yescharacteristic
63#2494C2211yescharacteristic
64#2489C2211yescharacteristic
65#2482—21no—
66#2480—21no—
67#2466—21no—
68#2454C2211yescharacteristic
69#2447C2211yescharacteristic
70#2447C2211yescharacteristic
71#2447C2211yescharacteristic, complemented
72#2435C2211yescharacteristic
73#2429C2211yescharacteristic
74#2426C2211yescharacteristic
75#2426C2211yescharacteristic
76#2423C2211yescharacteristic
77#2367C2211yescharacteristic
78#2365C2211yescharacteristic, complemented
79#2361C2211yescharacteristic
80#2360C2211yescharacteristic
81#2357—21no—
82#2354C2211yescharacteristic
83#2351C2211yescharacteristic, complemented
84#2342—21no—
85D4×C22⋊C4C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87C4×#126C2211yescharacteristic
88C4×#124C2211yescharacteristic
89C4×#124C2211yescharacteristic, complemented
90#2295C2211yescharacteristic, complemented
91#2293C2211yescharacteristic
92#2099C2211yescharacteristic, complemented
93#2097C2211yescharacteristic, complemented
94#2087C2211yescharacteristic, complemented
95#2086C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2074C2211yescharacteristic, complemented
99#2074C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2056C2211yescharacteristic, complemented
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic, complemented
113#2054C2211yescharacteristic
114#2043C2211yescharacteristic, complemented
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2035C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2026C2211yescharacteristic, complemented
122#2025C2211yescharacteristic, complemented
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic, complemented
125#2015C2211yescharacteristic, complemented
126#2013C2211yescharacteristic
127#2012C2211yescharacteristic
128#2012C2211yescharacteristic
129#2012C2211yescharacteristic
130#2001C2211yescharacteristic
131#2001C2211yescharacteristic
132#1991C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1983C2211yescharacteristic, complemented
135#1981C2211yescharacteristic, complemented
136#1973C2211yescharacteristic
137#1972C2211yescharacteristic
138#1970C2211yescharacteristic
139#1969C2211yescharacteristic, complemented
140#1959C2211yescharacteristic, complemented
141#1949C2211yescharacteristic, complemented
142#1940C2211yescharacteristic, complemented
143#1939C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic, complemented
147#1936C2211yescharacteristic, complemented
148#1935C2211yescharacteristic, complemented
149#1935C2211yescharacteristic, complemented
150#1928C2211yescharacteristic, complemented
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic, complemented
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic
156#1923C2211yescharacteristic
157#1921C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1892C2211yescharacteristic
165#1892C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1878C2211yescharacteristic, complemented
175#1878C2211yescharacteristic, complemented
176#1878C2211yescharacteristic, complemented
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1872C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1865C2211yescharacteristic, complemented
183#1864C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic
186#1862C2211yescharacteristic, complemented
187#1852C2211yescharacteristic
188#1850C2211yescharacteristic
189#1850C2211yescharacteristic
190#1831C2211yescharacteristic, complemented
191#1823C2211yescharacteristic
192#1805C2211yescharacteristic, complemented
193#1804C2211yescharacteristic
194#1804C2211yescharacteristic
195#1804C2211yescharacteristic, complemented
196#1803C2211yescharacteristic, complemented
197#1776C2211yescharacteristic, complemented
198#1771C2211yescharacteristic, complemented
199#1767C2211yescharacteristic, complemented
200#1763C2211yescharacteristic, complemented
201#1762C2211yescharacteristic
202#1752C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×#126D411yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×D4—21no—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×#117—21no—
237C2×#117—21no—
238C22×C4⋊C4C2311yescharacteristic
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241#497—24no—
242#479—42no—
243#465—42no—
244#464—42no—
245#463—24no—
246#463—42no—
247#463—42no—
248#450—24no—
249#450—42no—
250#447—42no—
251#441—42no—
252#440—42no—
253#440—42no—
254C4×SD16—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308#401—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#399—21no—
314#399—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#390—21no—
348#390—21no—
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388D411yescharacteristic
393#388D411yescharacteristic
394#388D411yescharacteristic
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387D411yescharacteristic
404#387D411yescharacteristic
405#387D411yescharacteristic
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#384C2311yescharacteristic
421#383D411yescharacteristic
422#382—21no—
423#382—21no—
424#382—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#381—21no—
429#381—21no—
430#381—21no—
431#381—21no—
432#381—21no—
433#380—21no—
434#380—21no—
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#379—21no—
438#379—21no—
439#379—21no—
440#379—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461#376—21no—
462C43C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
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×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—41no—
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C2411yescharacteristic
515C2×Q16—22no—
516C2×Q16—22no—
517C2×Q16—41no—
518C2×Q16—41no—
519C2×Q16—41no—
520C2×Q16—41no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—41no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16#4114yes—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—22no—
554C4⋊Q8—41no—
555#126—42no—
556#125—41no—
557#125—41no—
558#124—22no—
559#124—22no—
560#124—22no—
561#124—41no—
562#124—41no—
563#124—41no—
564#124—41no—
565#124—41no—
566C22⋊Q8—22no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572#121—22no—
573#121—41no—
574C4×Q8—22no—
575C4×Q8—22no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×Q8—41no—
583C4×Q8—41no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—44no—
595#117—82no—
596#117—82no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
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—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
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—44no—
676C2×C22⋊C4—82no—
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C22⋊C4C2×D411yescharacteristic
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42—21no—
692C2×C42C2×D411yescharacteristic
693C2×C42C2×D411yescharacteristic
694C2×C42C2×D411yescharacteristic
695C2×C42C2×D411yescharacteristic
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701C2×C42C2411yescharacteristic
702#107—22no—
703#107—41no—
704#107—41no—
705#107—41no—
706#106—22no—
707#106—22no—
708#106—41no—
709C4⋊C8—22no—
710C4⋊C8—41no—
711C4⋊C8—41no—
712C4⋊C8—41no—
713C4⋊C8—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716#103—22no—
717#103—22no—
718#103—41no—
719#103—41no—
720#103—41no—
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—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745#102—41no—
746C22⋊C8—22no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749#97—22no—
750#97—41no—
751#97—41no—
752#97—41no—
753C4×C8—41no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
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#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800C24—21no—
801C24—21no—
802C24—21no—
803C24—42no—
804C24—42no—
805C24—42no—
806C24—81no—
807C24—81no—
808C24—81no—
809C24—81no—
810C24C22×D411yescharacteristic
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
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×Q8C2×#4112yes—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—44no—
849C2×D4—42no—
850C2×D4—81no—
851C2×D4—82no—
852C2×D4—82no—
853C2×D4—82no—
854C2×D4—81no—
855C2×D4C2×#4112yes—
856C2×D4H(5,𝔽2)12yes—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C2511yescharacteristic
908Q16—44no—
909Q16—82no—
910SD16—44no—
911SD16—44no—
912SD16—44no—
913SD16—82no—
914SD16—82no—
915D8—82no—
916D8—82no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—82no—
941C2×C8C2×#4112yes—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—41no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4H(5,𝔽2)12yes—
991C22⋊C4—22no—
992C22⋊C4—22no—
993C22⋊C4—22no—
994C22⋊C4—41no—
995C22⋊C4—41no—
996C22⋊C4—41no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4—81no—
1032C22⋊C4—81no—
1033C22⋊C4—81no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—41no—
1047C42—41no—
1048C42—41no—
1049C42—41no—
1050C42—42no—
1051C42—42no—
1052C42—42no—
1053C42—42no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C42—81no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—22no—
1066C23—22no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—84no—
1087C23—84no—
1088C23—84no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23—162no—
1093C23#57512yes—
1094C23C23×D411yescharacteristic
1095Q8—22no—
1096Q8—22no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—41no—
1106Q8—41no—
1107D4—22no—
1108D4—22no—
1109D4—22no—
1110D4—22no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—84no—
1120D4—84no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—22no—
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—22no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
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—84no—
1204C2×C4—84no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4—162no—
1208C2×C4—162no—
1209C2×C4C22×#4111yescharacteristic
1210C2×C4C2×H(5,𝔽2)11yescharacteristic
1211C2×C4C2×H(5,𝔽2)11yescharacteristic
1212C2×C4#58511yescharacteristic
1213C2×C4#58511yescharacteristic
1214C2×C4#58511yescharacteristic
1215C8—22no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—168no—
1252C22D4×#4111yescharacteristic
1253C22#348811yescharacteristic
1254C22#348811yescharacteristic
1255C22C2×#57511yescharacteristic
1256C22#358411yescharacteristic
1257C22#358511yescharacteristic
1258C22#358611yescharacteristic
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—41no—
1264C4—41no—
1265C4—42no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—42no—
1272C4—41no—
1273C4—41no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4#350511yescharacteristic
1286C4#351311yescharacteristic
1287C4#354211yescharacteristic
1288C4#356611yescharacteristic
1289C2—42no—
1290C2—82no—
1291C2—82no—
1292C2—161no—
1293C2#4416511yescharacteristic
1294C2#6145511yescharacteristic
1295C2#6154711yescharacteristic
1296C2#6197111yescharacteristic
1297C2#6199011yescharacteristic
1298C2#6202311yescharacteristic
1299C2#6208511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#447C22
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
1. #59556C2semidirect
2. #59488C2semidirect
3. #32058C2semidirect
4. #31985C2semidirect
5. #31653C2semidirect
6. #31501C2semidirect
7. #31210C2semidirect
8. #30916C2semidirect
9. #30759C2semidirect
10. #30464C2semidirect
11. #29537C2semidirect
12. #29096C2semidirect
13. #28163C2semidirect
14. #27374C2semidirect
15. #27112C2semidirect
16. #27093C2semidirect
17. #26980C2semidirect
18. #26918C2semidirect
19. #26679C2semidirect
20. #26181C2semidirect
24. #24819C2semidirect
25. #24640C2semidirect
26. #24527C2semidirect
27. #23687C2semidirect
28. #23192C2semidirect
29. #22854C2semidirect
30. #22351C2semidirect
31. #22155C2semidirect
33. C2×#479C22semidirect
42. C2×#441C22semidirect
57. #2545C22semidirect
60. #2513C22semidirect
61. #2508C22semidirect
71. #2447C22semidirect
78. #2365C22semidirect
83. #2351C22semidirect
89. C4×#124C22semidirect
90. #2295C22semidirect
92. #2099C22semidirect
93. #2097C22semidirect
94. #2087C22semidirect
95. #2086C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
98. #2074C22semidirect
99. #2074C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
104. #2068C22semidirect
108. #2056C22semidirect
112. #2055C22semidirect
114. #2043C22semidirect
121. #2026C22semidirect
122. #2025C22semidirect
124. #2015C22semidirect
125. #2015C22semidirect
132. #1991C22semidirect
134. #1983C22semidirect
135. #1981C22semidirect
139. #1969C22semidirect
140. #1959C22semidirect
141. #1949C22semidirect
142. #1940C22semidirect
143. #1939C22semidirect
146. #1936C22semidirect
147. #1936C22semidirect
148. #1935C22semidirect
149. #1935C22semidirect
150. #1928C22semidirect
153. #1925C22semidirect
157. #1921C22semidirect
158. #1919C22semidirect
159. #1919C22semidirect
160. #1918C22semidirect
161. #1917C22semidirect
162. #1917C22semidirect
163. #1917C22semidirect
170. #1880C22semidirect
174. #1878C22semidirect
175. #1878C22semidirect
176. #1878C22semidirect
181. #1865C22semidirect
182. #1865C22semidirect
186. #1862C22semidirect
190. #1831C22semidirect
192. #1805C22semidirect
195. #1804C22semidirect
196. #1803C22semidirect
197. #1776C22semidirect
198. #1771C22semidirect
199. #1767C22semidirect
200. #1763C22semidirect

Maximal subgroups

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

subgroupindex
#595562
#594882
#320582
#319852
#316532
#315012
#312102
#309162
#307592
#304642
#295372
#290962
#281632
#273742
#271122
#270932
#269802
#269182
#266792
#261812
#251642
#251522
#250882
#248192
#246402
#245272
#236872
#231922
#228542
#223512
#221552