Finite Group Databasebeta

← #7039736

Subgroups — #7039736

Order 512.

1426 conjugacy classes of subgroups.

The subgroup lattice has 1293 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44925C211yesmaximal, characteristic, complemented
2#42894C211yesmaximal, characteristic, complemented
3#32256C211yesmaximal, characteristic, complemented
4#32011C211yesmaximal, characteristic, complemented
5#31335C211yesmaximal, characteristic, complemented
6#31318C211yesmaximal, characteristic, complemented
7#31268C211yesmaximal, characteristic, complemented
8#30956C211yesmaximal, characteristic, complemented
9#30579C211yesmaximal, characteristic, complemented
10#30414C211yesmaximal, characteristic, complemented
11#29485C211yesmaximal, characteristic, complemented
12#28713C211yesmaximal, characteristic, complemented
13#28557C211yesmaximal, characteristic, complemented
14#28072C211yesmaximal, characteristic, complemented
15#27868C211yesmaximal, characteristic, complemented
16#27804C211yesmaximal, characteristic, complemented
17#27486C211yesmaximal, characteristic, complemented
18#27473C211yesmaximal, characteristic, complemented
19#27445C211yesmaximal, characteristic, complemented
20#27326C211yesmaximal, characteristic, complemented
21#27249C211yesmaximal, characteristic, complemented
22#26733C211yesmaximal, characteristic, complemented
23#25353C211yesmaximal, characteristic, complemented
24#25139C211yesmaximal, characteristic, complemented
25#24951C211yesmaximal, characteristic, complemented
26#24883C211yesmaximal, characteristic, complemented
27#23773C211yesmaximal, characteristic, complemented
28#23125C211yesmaximal, characteristic, complemented
29#22947C211yesmaximal, characteristic, complemented
30#22579C211yesmaximal, characteristic, complemented
31#22200C211yesmaximal, characteristic, complemented
32C2×#498C2211yescharacteristic
33C2×#484C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#449C2211yescharacteristic
38C2×#436C2211yescharacteristic
39C2×#435C2211yescharacteristic
40C2×#417C2211yescharacteristic
41#2829—21no—
42#2808—21no—
43#2800—21no—
44#2786—21no—
45#2784—21no—
46#2783—21no—
47#2733—21no—
48#2715—21no—
49#2686—21no—
50#2662—21no—
51#2648—21no—
52#2624C2211yescharacteristic
53#2609—21no—
54#2589—21no—
55#2563C2211yescharacteristic
56#2562C2211yescharacteristic
57#2550C2211yescharacteristic
58#2547C2211yescharacteristic
59#2538C2211yescharacteristic
60#2535C2211yescharacteristic
61#2512C2211yescharacteristic
62#2497C2211yescharacteristic
63#2491C2211yescharacteristic
64#2491C2211yescharacteristic
65#2490C2211yescharacteristic
66#2485C2211yescharacteristic
67#2476—21no—
68#2459—21no—
69#2451C2211yescharacteristic
70#2416C2211yescharacteristic
71#2416C2211yescharacteristic
72#2414—21no—
73#2414C2211yescharacteristic
74#2407C2211yescharacteristic
75#2407C2211yescharacteristic
76#2392C2211yescharacteristic
77#2362C2211yescharacteristic
78#2354C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80#2345C2211yescharacteristic
81#2344C2211yescharacteristic
82#2341C2211yescharacteristic
83#2324C2211yescharacteristic
84#2323C2211yescharacteristic
85#2314C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2097C2211yescharacteristic
89#2093C2211yescharacteristic
90#2093C2211yescharacteristic
91#2088C2211yescharacteristic
92#2085C2211yescharacteristic
93#2083C2211yescharacteristic
94#2083C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2075C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2073C2211yescharacteristic
104#2072C2211yescharacteristic
105#2067C2211yescharacteristic
106#2059C2211yescharacteristic
107#2057C2211yescharacteristic
108#2055C2211yescharacteristic
109#2054C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2034C2211yescharacteristic
114#2034C2211yescharacteristic
115#2034C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2025C2211yescharacteristic
121#2024C2211yescharacteristic
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2000C2211yescharacteristic
125#1999C2211yescharacteristic
126#1992C2211yescharacteristic
127#1988C2211yescharacteristic
128#1987C2211yescharacteristic
129#1972C2211yescharacteristic
130#1970C2211yescharacteristic
131#1947C2211yescharacteristic
132#1943C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1933C2211yescharacteristic
138#1927C2211yescharacteristic
139#1927C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1924C2211yescharacteristic
148#1923C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1919C2211yescharacteristic
152#1919C2211yescharacteristic
153#1918C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1917C2211yescharacteristic
157#1916C2211yescharacteristic
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1892C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1879C2211yescharacteristic
167#1877C2211yescharacteristic
168#1875C2211yescharacteristic
169#1874C2211yescharacteristic
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic
172#1870C2211yescharacteristic
173#1869C2211yescharacteristic
174#1865C2211yescharacteristic
175#1864C2211yescharacteristic
176#1863C2211yescharacteristic
177#1862C2211yescharacteristic
178#1854C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1825C2211yescharacteristic
183#1823C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1808C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1776C2211yescharacteristic
193C4×#107C2211yescharacteristic
194C4×#107C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197C4×#103C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1750C2211yescharacteristic
201#1736C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#124—21no—
215C2×#124—21no—
216C2×#124—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121—21no—
220C2×#121—21no—
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117—21no—
234C2×#117—21no—
235C2×#117C2311yescharacteristic
236C2×#117C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C4⋊C4C2311yescharacteristic
239#498—42no—
240#484—24no—
241#479—42no—
242#469—42no—
243#468—24no—
244#449—42no—
245#436—42no—
246#435—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263#417—24no—
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296#400—21no—
297#400—21no—
298#399—21no—
299#398—21no—
300#398—21no—
301#398D411yescharacteristic
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397D411yescharacteristic
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396D411yescharacteristic
317#396D411yescharacteristic
318#395—21no—
319#395—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394D411yescharacteristic
333#394D411yescharacteristic
334#394D411yescharacteristic
335#393—21no—
336#393—21no—
337#393—21no—
338#393—21no—
339#392—21no—
340#392—21no—
341#392—21no—
342#392—21no—
343#392D411yescharacteristic
344#391—21no—
345#391—21no—
346#391—21no—
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#390—21no—
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390—21no—
355#390—21no—
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
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#387—21no—
393#387—21no—
394#387—21no—
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#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#382—21no—
418#382C2311yescharacteristic
419#381—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C2×#41—22no—
488C2×#41—41no—
489C2×#41—41no—
490C2×#41—41no—
491C2×#41—41no—
492C2×#41—41no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4C2×D411yescharacteristic
503C22×D4C2×D411yescharacteristic
504C22×D4C2×D411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C23×C4C2411yescharacteristic
514C2×SD16—22no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×D8—22no—
518C2×D8—41no—
519C2×D8—41no—
520C2×M16—22no—
521C2×M16—22no—
522C2×M16—22no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—41no—
528C2×M16—41no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8—41no—
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544#126—82no—
545#125—41no—
546#125—41no—
547#124—82no—
548#124—82no—
549#124—82no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—41no—
553C22⋊Q8—41no—
554#121—22no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—41no—
559#121—41no—
560#121—41no—
561#121—41no—
562#121—41no—
563#121—41no—
564#121—82no—
565#121—82no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—82no—
579#117—41no—
580#117—41no—
581#117—41no—
582#117—41no—
583#117—82no—
584#117—82no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
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—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692#107—22no—
693#107—22no—
694#107—22no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#107—41no—
701#106—22no—
702#106—22no—
703#106—41no—
704#106—41no—
705#106—41no—
706C4⋊C8—22no—
707C4⋊C8—41no—
708#103—22no—
709#103—22no—
710#103—22no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103#4114yes—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728C22⋊C8—22no—
729C22⋊C8—22no—
730C22⋊C8—22no—
731C22⋊C8—41no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736#97—41no—
737#97—41no—
738C4×C8—22no—
739C4×C8—41no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
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#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779C24—21no—
780C24—21no—
781C24C22×D411yescharacteristic
782C24C22×D411yescharacteristic
783C24C22×D411yescharacteristic
784#41—44no—
785#41—82no—
786#41—82no—
787#41—82no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—42no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8C2×#4112yes—
800C2×D4—22no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—41no—
814C2×D4—41no—
815C2×D4—41no—
816C2×D4—41no—
817C2×D4—41no—
818C2×D4—41no—
819C2×D4—41no—
820C2×D4—41no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
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—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C2511yescharacteristic
895SD16—82no—
896D8—82no—
897M16—82no—
898M16—82no—
899M16—82no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—82no—
923C2×C8C2×#4112yes—
924C2×C8H(5,𝔽2)12yes—
925C4⋊C4—22no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
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—41no—
952C4⋊C4—41no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4C2×#4112yes—
979C22⋊C4—22no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
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—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—42no—
1036C42—42no—
1037C42—81no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—41no—
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—
1080C23C23×D411yescharacteristic
1081Q8—22no—
1082Q8—22no—
1083Q8—41no—
1084Q8—41no—
1085Q8—162no—
1086Q8—162no—
1087D4—44no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—82no—
1097D4—82no—
1098D4—84no—
1099D4—162no—
1100D4—162no—
1101D4—162no—
1102D4—162no—
1103D4—162no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—21no—
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—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
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—84no—
1191C2×C4—84no—
1192C2×C4—84no—
1193C2×C4—162no—
1194C2×C4#57612yes—
1195C2×C4C22×#4111yescharacteristic
1196C2×C4C2×H(5,𝔽2)11yescharacteristic
1197C2×C4#58511yescharacteristic
1198C2×C4#58511yescharacteristic
1199C2×C4#58511yescharacteristic
1200C2×C4#58511yescharacteristic
1201C8—22no—
1202C8—22no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C8—41no—
1208C8—41no—
1209C22—41no—
1210C22—41no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22D4×#4111yescharacteristic
1245C22#348511yescharacteristic
1246C22#349611yescharacteristic
1247C22C2×#57611yescharacteristic
1248C22#358511yescharacteristic
1249C22#358611yescharacteristic
1250C22#358611yescharacteristic
1251C4—22no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—42no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—42no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4#349311yescharacteristic
1277C4#351411yescharacteristic
1278C4#354511yescharacteristic
1279C4#356611yescharacteristic
1280C2—81no—
1281C2—81no—
1282C2—81no—
1283C2—161no—
1284C2—161no—
1285C2#4350411yescharacteristic
1286C2#6151111yescharacteristic
1287C2#6155511yescharacteristic
1288C2#6177511yescharacteristic
1289C2#6180711yescharacteristic
1290C2#6228511yescharacteristic
1291C2#6231111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44925C2semidirect
2. #42894C2semidirect
3. #32256C2semidirect
4. #32011C2semidirect
5. #31335C2semidirect
6. #31318C2semidirect
7. #31268C2semidirect
8. #30956C2semidirect
9. #30579C2semidirect
10. #30414C2semidirect
11. #29485C2semidirect
12. #28713C2semidirect
13. #28557C2semidirect
14. #28072C2semidirect
15. #27868C2semidirect
16. #27804C2semidirect
17. #27486C2semidirect
18. #27473C2semidirect
19. #27445C2semidirect
20. #27326C2semidirect
21. #27249C2semidirect
22. #26733C2semidirect
23. #25353C2semidirect
24. #25139C2semidirect
25. #24951C2semidirect
26. #24883C2semidirect
27. #23773C2semidirect
28. #23125C2semidirect
29. #22947C2semidirect
30. #22579C2semidirect
31. #22200C2semidirect

Maximal subgroups

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

subgroupindex
#449252
#428942
#322562
#320112
#313352
#313182
#312682
#309562
#305792
#304142
#294852
#287132
#285572
#280722
#278682
#278042
#274862
#274732
#274452
#273262
#272492
#267332
#253532
#251392
#249512
#248832
#237732
#231252
#229472
#225792
#222002