Finite Group Databasebeta

← #6800679

Subgroups — #6800679

Order 512.

1573 conjugacy classes of subgroups.

The subgroup lattice has 1327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39591C211yesmaximal, characteristic, complemented
2#35556C211yesmaximal, characteristic
3#33156C211yesmaximal, characteristic, complemented
4#32647C211yesmaximal, characteristic, complemented
5#32642C211yesmaximal, characteristic, complemented
6#32638C211yesmaximal, characteristic, complemented
7#32635C211yesmaximal, characteristic, complemented
8#32624C211yesmaximal, characteristic, complemented
9#32617C211yesmaximal, characteristic, complemented
10#32617C211yesmaximal, characteristic, complemented
11#32601C211yesmaximal, characteristic, complemented
12#29961C211yesmaximal, characteristic, complemented
13#29956C211yesmaximal, characteristic, complemented
14#29116C211yesmaximal, characteristic, complemented
15#29114C211yesmaximal, characteristic, complemented
16#28650C211yesmaximal, characteristic, complemented
17#28644C211yesmaximal, characteristic, complemented
18#28130C211yesmaximal, characteristic, complemented
19#28122C211yesmaximal, characteristic, complemented
20#26329C211yesmaximal, characteristic, complemented
21#26321C211yesmaximal, characteristic, complemented
22#25944C211yesmaximal, characteristic, complemented
23#25937C211yesmaximal, characteristic, complemented
24#25867C211yesmaximal, characteristic
25#25307C211yesmaximal, characteristic, complemented
26#25303C211yesmaximal, characteristic, complemented
27#24220C211yesmaximal, characteristic
28#22511C211yesmaximal, characteristic, complemented
29#22057C211yesmaximal, characteristic, complemented
30#22049C211yesmaximal, characteristic, complemented
31#21591C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic, complemented
33C2×#535C2211yescharacteristic
34C2×#533C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#464C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#452C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#446C2211yescharacteristic, complemented
43C2×#446C2211yescharacteristic, complemented
44#2851C2211yescharacteristic
45#2734—21no—
46#2729—21no—
47#2720—21no—
48#2713—21no—
49#2629C2211yescharacteristic
50#2628C2211yescharacteristic
51#2592C2211yescharacteristic
52#2592C2211yescharacteristic
53#2592C2211yescharacteristic
54#2592C2211yescharacteristic
55#2584C2211yescharacteristic, complemented
56#2584C2211yescharacteristic, complemented
57#2582C2211yescharacteristic, complemented
58#2581C2211yescharacteristic, complemented
59#2581C2211yescharacteristic, complemented
60#2567C2211yescharacteristic, complemented
61#2556—21no—
62#2548C2211yescharacteristic
63#2548C2211yescharacteristic
64#2548C2211yescharacteristic
65#2548C2211yescharacteristic
66#2506—21no—
67#2491—21no—
68#2491—21no—
69#2490—21no—
70#2490—21no—
71#2472—21no—
72#2472—21no—
73#2472—21no—
74#2472—21no—
75#2465—21no—
76#2462—21no—
77#2355C2211yescharacteristic, complemented
78#2323C2211yescharacteristic
79#2323C2211yescharacteristic
80#2311C2211yescharacteristic
81#2309C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83#2297C2211yescharacteristic
84C2×#390C2211yescharacteristic
85#2274C2211yescharacteristic
86#2097C2211yescharacteristic, complemented
87#2092C2211yescharacteristic
88#2092C2211yescharacteristic
89#2092C2211yescharacteristic, complemented
90#2074C2211yescharacteristic, complemented
91#2073C2211yescharacteristic
92#2073C2211yescharacteristic
93#2073C2211yescharacteristic, complemented
94#2068C2211yescharacteristic, complemented
95#2067C2211yescharacteristic
96#2067C2211yescharacteristic
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic, complemented
99#2067C2211yescharacteristic, complemented
100#2066C2211yescharacteristic, complemented
101#2066C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic, complemented
106#2056C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic, complemented
110#2042C2211yescharacteristic
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic
116#2026C2211yescharacteristic, complemented
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic, complemented
120#2024C2211yescharacteristic, complemented
121#2023C2211yescharacteristic
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2014C2211yescharacteristic
126#1989C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1985C2211yescharacteristic, complemented
129#1985C2211yescharacteristic, complemented
130#1985C2211yescharacteristic, complemented
131#1985C2211yescharacteristic, complemented
132#1984C2211yescharacteristic, complemented
133#1984C2211yescharacteristic, complemented
134#1983C2211yescharacteristic
135#1982C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1973C2211yescharacteristic, complemented
139#1969C2211yescharacteristic, complemented
140#1959C2211yescharacteristic
141#1957C2211yescharacteristic
142#1947C2211yescharacteristic, complemented
143#1947C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1936C2211yescharacteristic
148#1936C2211yescharacteristic, complemented
149#1936C2211yescharacteristic, complemented
150#1935C2211yescharacteristic, complemented
151#1935C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic, complemented
156#1928C2211yescharacteristic, complemented
157#1928C2211yescharacteristic, complemented
158#1927C2211yescharacteristic, complemented
159#1927C2211yescharacteristic, complemented
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic, complemented
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic
164#1925C2211yescharacteristic
165#1925C2211yescharacteristic, complemented
166#1921C2211yescharacteristic, complemented
167#1921C2211yescharacteristic, complemented
168#1921C2211yescharacteristic, complemented
169#1919C2211yescharacteristic, complemented
170#1918C2211yescharacteristic, complemented
171#1918C2211yescharacteristic, complemented
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic, complemented
177#1880C2211yescharacteristic, complemented
178#1878C2211yescharacteristic, complemented
179#1878C2211yescharacteristic, complemented
180#1872C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1825C2211yescharacteristic
185#1825C2211yescharacteristic
186#1825C2211yescharacteristic
187#1798C2211yescharacteristic
188#1798C2211yescharacteristic
189#1797C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1776C2211yescharacteristic, complemented
197C4×#106C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199C4×#103C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1749C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209#557—42no—
210#557—42no—
211#535—42no—
212#535—42no—
213#533—42no—
214#533—42no—
215C2×C4⋊Q8—21no—
216C2×C4⋊Q8D411yescharacteristic
217C2×C4⋊Q8D411yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#125—21no—
222C2×#125—21no—
223C2×#125D411yescharacteristic
224C2×#125D411yescharacteristic
225C2×#125C2311yescharacteristic
226C2×#125C2311yescharacteristic
227C2×#124—21no—
228C2×#124—21no—
229C2×#124—21no—
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×C22⋊Q8D411yescharacteristic
234C2×C22⋊Q8D411yescharacteristic
235C2×C22⋊Q8D411yescharacteristic
236C2×C22⋊Q8D411yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8C2311yescharacteristic
244C2×C4×Q8C2311yescharacteristic
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C42C2311yescharacteristic
257#490—42no—
258#488—42no—
259#485—24no—
260#464—42no—
261#460—42no—
262#452—24no—
263#450—24no—
264#446—42no—
265#446—42no—
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#400—21no—
323#400—21no—
324#400—21no—
325#399—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#396—21no—
337#396—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#395—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#393—21no—
354#393—21no—
355#393—21no—
356#393—21no—
357#393—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#390—21no—
369#390—21no—
370#390—21no—
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#390C2311yescharacteristic
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389—21no—
389#389—21no—
390#389—21no—
391#389—21no—
392#389—21no—
393#389—21no—
394#389—21no—
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#384—21no—
435#384C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#379—21no—
444#379—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461#340C2311yescharacteristic
462#340C2311yescharacteristic
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—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8C2×D411yescharacteristic
502C22×Q8C2×D411yescharacteristic
503C22×Q8C2×D411yescharacteristic
504C22×Q8C2×D411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×Q8C2411yescharacteristic
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—22no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4C2×D411yescharacteristic
525C23×C4C2×D411yescharacteristic
526C23×C4C2411yescharacteristic
527C2×Q16—22no—
528C2×Q16—41no—
529C2×Q16—41no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8—42no—
550C4⋊Q8—42no—
551C4⋊Q8—44no—
552#127—22no—
553#127—22no—
554#127—41no—
555#127—41no—
556#125—22no—
557#125—22no—
558#125—41no—
559#125—41no—
560#125—42no—
561#125—42no—
562#125—44no—
563#125—44no—
564#124—22no—
565#124—22no—
566#124—41no—
567#124—41no—
568#124—82no—
569#124—82no—
570#124—82no—
571#124—82no—
572C22⋊Q8—22no—
573C22⋊Q8—42no—
574C22⋊Q8—42no—
575C22⋊Q8—42no—
576C22⋊Q8—42no—
577C22⋊Q8#4114yes—
578#121—44no—
579#121—44no—
580#120—44no—
581#120—44no—
582C4×Q8—22no—
583C4×Q8—22no—
584C4×Q8—22no—
585C4×Q8—22no—
586C4×Q8—22no—
587C4×Q8—22no—
588C4×Q8—41no—
589C4×Q8—41no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—44no—
597#117—22no—
598#117—22no—
599#117—22no—
600#117—22no—
601#117—41no—
602#117—41no—
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—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
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—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—82no—
687C2×C22⋊C4—82no—
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—41no—
704C2×C42—41no—
705C2×C42C2×D411yescharacteristic
706C2×C42C2×D411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713#107—22no—
714#107—41no—
715#107—41no—
716#107—41no—
717#107—41no—
718#106—22no—
719#106—41no—
720#106—41no—
721C4⋊C8—22no—
722C4⋊C8—22no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727#103—22no—
728#103—22no—
729#103—22no—
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#102—22no—
739#102—22no—
740#102—22no—
741#102—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—
759C22⋊C8—22no—
760C22⋊C8—22no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763#97—22no—
764#97—41no—
765#97—41no—
766#97—41no—
767C4×C8—22no—
768C4×C8—41no—
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#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—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—42no—
810C24—42no—
811C24—42no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24C22×D411yescharacteristic
817#41—82no—
818#41—82no—
819#41—82no—
820#41—82no—
821C2×Q8—22no—
822C2×Q8—22no—
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—41no—
835C2×Q8—41no—
836C2×Q8—41no—
837C2×Q8—41no—
838C2×Q8—41no—
839C2×Q8—41no—
840C2×Q8—41no—
841C2×Q8—41no—
842C2×Q8—41no—
843C2×Q8—41no—
844C2×Q8—42no—
845C2×Q8—81no—
846C2×Q8—81no—
847C2×Q8C2×#4112yes—
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—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—82no—
877C2×D4—82no—
878C2×D4—82no—
879C2×D4—82no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
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—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—41no—
906C22×C4—41no—
907C22×C4—41no—
908C22×C4—41no—
909C22×C4—41no—
910C22×C4—41no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—81no—
916C22×C4—81no—
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×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C2×#4112yes—
931C22×C42−1+412yes—
932C22×C4C2511yescharacteristic
933Q16—82no—
934SD16—82no—
935SD16—82no—
936SD16—82no—
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—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C4⋊C4—22no—
962C4⋊C4—22no—
963C4⋊C4—22no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—24no—
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—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—41no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—42no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4C2×#4112yes—
1020C22⋊C4—24no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
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—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C42—21no—
1058C42—21no—
1059C42—21no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—41no—
1068C42—41no—
1069C42—42no—
1070C42—42no—
1071C42—42no—
1072C42—42no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42H(5,𝔽2)12yes—
1081C42H(5,𝔽2)12yes—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
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—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—84no—
1110C23—84no—
1111C23—84no—
1112C23—162no—
1113C23—162no—
1114C23—162no—
1115C23—162no—
1116C23#54812yes—
1117C23C23×D411yescharacteristic
1118Q8—22no—
1119Q8—22no—
1120Q8—41no—
1121Q8—41no—
1122Q8—41no—
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—82no—
1127Q8—82no—
1128Q8—82no—
1129Q8—82no—
1130Q8—84no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—84no—
1144D4—84no—
1145D4—162no—
1146D4—162no—
1147D4—162no—
1148D4—162no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
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—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
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—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—84no—
1229C2×C4—82no—
1230C2×C4—82no—
1231C2×C4—162no—
1232C2×C4#53412yes—
1233C2×C4#53412yes—
1234C2×C4#54812yes—
1235C2×C4C22×#4111yescharacteristic
1236C2×C4C2×H(5,𝔽2)11yescharacteristic
1237C2×C4C2×H(5,𝔽2)11yescharacteristic
1238C2×C4C2×2−1+411yescharacteristic
1239C2×C4#58511yescharacteristic
1240C2×C4#58511yescharacteristic
1241C8—41no—
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C22—22no—
1250C22—22no—
1251C22—22no—
1252C22—41no—
1253C22—41no—
1254C22—41no—
1255C22—41no—
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—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—168no—
1278C22C2×#53411yescharacteristic
1279C22C2×#54811yescharacteristic
1280C22#348711yescharacteristic
1281C22#358411yescharacteristic
1282C22#358511yescharacteristic
1283C22#358511yescharacteristic
1284C22#358611yescharacteristic
1285C4—22no—
1286C4—22no—
1287C4—22no—
1288C4—41no—
1289C4—41no—
1290C4—41no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—41no—
1298C4—42no—
1299C4—42no—
1300C4—81no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4#351411yescharacteristic
1312C4#351411yescharacteristic
1313C4#356111yescharacteristic
1314C4#356111yescharacteristic
1315C2—42no—
1316C2—161no—
1317C2—161no—
1318C2—161no—
1319C2#3912311yescharacteristic
1320C2#6076711yescharacteristic
1321C2#6077211yescharacteristic
1322C2#6133411yescharacteristic
1323C2#6134911yescharacteristic
1324C2#6192511yescharacteristic
1325C2#6194511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#535C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#533 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39591C2semidirect
3. #33156C2semidirect
4. #32647C2semidirect
5. #32642C2semidirect
6. #32638C2semidirect
7. #32635C2semidirect
8. #32624C2semidirect
9. #32617C2semidirect
10. #32617C2semidirect
11. #32601C2semidirect
12. #29961C2semidirect
13. #29956C2semidirect
14. #29116C2semidirect
15. #29114C2semidirect
16. #28650C2semidirect
17. #28644C2semidirect
18. #28130C2semidirect
19. #28122C2semidirect
20. #26329C2semidirect
21. #26321C2semidirect
22. #25944C2semidirect
23. #25937C2semidirect
25. #25307C2semidirect
26. #25303C2semidirect
28. #22511C2semidirect
29. #22057C2semidirect
30. #22049C2semidirect
31. #21591C2semidirect
32. C2×#557C22semidirect
42. C2×#446C22semidirect
43. C2×#446C22semidirect
55. #2584C22semidirect
56. #2584C22semidirect
57. #2582C22semidirect
58. #2581C22semidirect
59. #2581C22semidirect
60. #2567C22semidirect
77. #2355C22semidirect
86. #2097C22semidirect
89. #2092C22semidirect
90. #2074C22semidirect
93. #2073C22semidirect
94. #2068C22semidirect
98. #2067C22semidirect
99. #2067C22semidirect
100. #2066C22semidirect
101. #2066C22semidirect
105. #2065C22semidirect
106. #2056C22semidirect
109. #2055C22semidirect
116. #2026C22semidirect
119. #2025C22semidirect
120. #2024C22semidirect
123. #2023C22semidirect
126. #1989C22semidirect
127. #1989C22semidirect
128. #1985C22semidirect
129. #1985C22semidirect
130. #1985C22semidirect
131. #1985C22semidirect
132. #1984C22semidirect
133. #1984C22semidirect
138. #1973C22semidirect
139. #1969C22semidirect
142. #1947C22semidirect
143. #1947C22semidirect
148. #1936C22semidirect
149. #1936C22semidirect
150. #1935C22semidirect
151. #1935C22semidirect
152. #1935C22semidirect
155. #1934C22semidirect
156. #1928C22semidirect
157. #1928C22semidirect
158. #1927C22semidirect
159. #1927C22semidirect
161. #1926C22semidirect
165. #1925C22semidirect
166. #1921C22semidirect
167. #1921C22semidirect
168. #1921C22semidirect
169. #1919C22semidirect
170. #1918C22semidirect
171. #1918C22semidirect
176. #1880C22semidirect
177. #1880C22semidirect
178. #1878C22semidirect
179. #1878C22semidirect
196. #1776C22semidirect
197. C4×#106C22semidirect
198. #1763C22semidirect
199. C4×#103C22semidirect

Maximal subgroups

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

subgroupindex
#395912
#355562
#331562
#326472
#326422
#326382
#326352
#326242
#326172
#326012
#299612
#299562
#291162
#291142
#286502
#286442
#281302
#281222
#263292
#263212
#259442
#259372
#258672
#253072
#253032
#242202
#225112
#220572
#220492
#215912