Finite Group Databasebeta

← #6459226

Subgroups — #6459226

Order 512.

1704 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34977C211yesmaximal, characteristic
2#34912C211yesmaximal, characteristic, complemented
3#27832C211yesmaximal, characteristic, complemented
4#27826C211yesmaximal, characteristic, complemented
5#27786C211yesmaximal, characteristic, complemented
6#27780C211yesmaximal, characteristic, complemented
7#27766C211yesmaximal, characteristic, complemented
8#27760C211yesmaximal, characteristic, complemented
9#27746C211yesmaximal, characteristic, complemented
10#27740C211yesmaximal, characteristic, complemented
11#27718C211yesmaximal, characteristic, complemented
12#27712C211yesmaximal, characteristic, complemented
13#27702C211yesmaximal, characteristic, complemented
14#27696C211yesmaximal, characteristic, complemented
15#27269C211yesmaximal, characteristic, complemented
16#27263C211yesmaximal, characteristic, complemented
17#27259C211yesmaximal, characteristic, complemented
18#27257C211yesmaximal, characteristic, complemented
19#23826C211yesmaximal, characteristic, complemented
20#23824C211yesmaximal, characteristic, complemented
21#23822C211yesmaximal, characteristic, complemented
22#23821C211yesmaximal, characteristic, complemented
23#21656C211yesmaximal, characteristic, complemented
24#21655C211yesmaximal, characteristic, complemented
25#21648C211yesmaximal, characteristic, complemented
26#21646C211yesmaximal, characteristic, complemented
27#21408C211yesmaximal, characteristic, complemented
28#21393C211yesmaximal, characteristic, complemented
29#20742C211yesmaximal, characteristic, complemented
30#20479C211yesmaximal, characteristic, complemented
31#20411C211yesmaximal, characteristic, complemented
32C2×#532C2211yescharacteristic
33C2×C4×#41C2211yescharacteristic
34C2×#490C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#486C2211yescharacteristic
38C2×#432C2211yescharacteristic
39C2×#416C2211yescharacteristic
40C2×#416C2211yescharacteristic
41C22×#97C2211yescharacteristic
42#2610—21no—
43#2610—21no—
44#2608—21no—
45#2607—21no—
46#2606—21no—
47#2605—21no—
48#2570C2211yescharacteristic
49#2570C2211yescharacteristic
50#2567C2211yescharacteristic
51#2563C2211yescharacteristic
52#2550C2211yescharacteristic
53#2550C2211yescharacteristic
54#2548C2211yescharacteristic
55#2541C2211yescharacteristic
56#2500C2211yescharacteristic
57#2500C2211yescharacteristic
58#2441C2211yescharacteristic
59#2441C2211yescharacteristic
60#2439C2211yescharacteristic
61#2439C2211yescharacteristic
62#2431C2211yescharacteristic
63#2431C2211yescharacteristic
64#2414—21no—
65#2414—21no—
66#2396—21no—
67#2396—21no—
68#2388—21no—
69#2388—21no—
70C4×C4⋊Q8C2211yescharacteristic
71C4×C4⋊Q8C2211yescharacteristic
72C4×#127C2211yescharacteristic
73C4×#127C2211yescharacteristic
74C4×#125C2211yescharacteristic
75C4×#125C2211yescharacteristic
76C4×#124C2211yescharacteristic
77C4×#124C2211yescharacteristic
78C4×#121—21no—
79C4×#121—21no—
80#2295—21no—
81#2295—21no—
82#2283C2211yescharacteristic
83C4×#117C2211yescharacteristic
84C4×#117C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2100C2211yescharacteristic
90#2100C2211yescharacteristic
91#2099C2211yescharacteristic
92#2099C2211yescharacteristic
93#2074C2211yescharacteristic
94#2073C2211yescharacteristic
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2072C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2042C2211yescharacteristic
102#2042C2211yescharacteristic
103#2042C2211yescharacteristic
104#2042C2211yescharacteristic
105#2041C2211yescharacteristic
106#2041C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2026C2211yescharacteristic
110#2025C2211yescharacteristic
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic
113#2024C2211yescharacteristic
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#1993C2211yescharacteristic
118#1993C2211yescharacteristic
119#1993C2211yescharacteristic
120#1992C2211yescharacteristic
121#1991C2211yescharacteristic
122#1990C2211yescharacteristic
123#1988C2211yescharacteristic
124#1988C2211yescharacteristic
125#1982C2211yescharacteristic
126#1982C2211yescharacteristic
127#1961C2211yescharacteristic
128#1961C2211yescharacteristic
129#1961C2211yescharacteristic
130#1959C2211yescharacteristic
131#1958C2211yescharacteristic
132#1957C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1935C2211yescharacteristic
140#1935C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1933C2211yescharacteristic
148#1933C2211yescharacteristic
149#1893C2211yescharacteristic
150#1893C2211yescharacteristic
151#1893C2211yescharacteristic
152#1893C2211yescharacteristic
153#1875C2211yescharacteristic
154#1875C2211yescharacteristic
155#1875C2211yescharacteristic
156#1875C2211yescharacteristic
157#1836C2211yescharacteristic
158#1836C2211yescharacteristic
159#1835C2211yescharacteristic
160#1834C2211yescharacteristic
161#1825C2211yescharacteristic
162#1825C2211yescharacteristic
163#1805C2211yescharacteristic
164#1805C2211yescharacteristic
165#1804C2211yescharacteristic
166#1804C2211yescharacteristic
167#1788C2211yescharacteristic
168#1788C2211yescharacteristic
169#1771C2211yescharacteristic
170#1771C2211yescharacteristic
171#1771C2211yescharacteristic
172#1771C2211yescharacteristic
173#1763C2211yescharacteristic
174#1763C2211yescharacteristic
175#1763C2211yescharacteristic
176#1763C2211yescharacteristic
177#1763C2211yescharacteristic
178#1763C2211yescharacteristic
179#1762C2211yescharacteristic
180#1762C2211yescharacteristic
181#1762C2211yescharacteristic
182#1762C2211yescharacteristic
183#1762C2211yescharacteristic
184#1762C2211yescharacteristic
185#1762C2211yescharacteristic
186#1762C2211yescharacteristic
187#1762C2211yescharacteristic
188#1762C2211yescharacteristic
189#1762C2211yescharacteristic
190#1762C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1752C2211yescharacteristic
194#1752C2211yescharacteristic
195C8×C22⋊C4C2211yescharacteristic
196C8×C22⋊C4C2211yescharacteristic
197#1745C2211yescharacteristic
198#1745C2211yescharacteristic
199#1735C2211yescharacteristic
200#1735C2211yescharacteristic
201C4×#97C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#532—24no—
208#532—24no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124—21no—
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#121—21no—
221C2×#121—21no—
222C2×#121—21no—
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C4×#41—24no—
226C4×#41—24no—
227C2×C4×Q8—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117—21no—
243C2×#117D411yescharacteristic
244C2×#117D411yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C42—21no—
249C22×C42C2311yescharacteristic
250#490—24no—
251#489—24no—
252#488—24no—
253#486—24no—
254#432—24no—
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257#416—24no—
258#416—24no—
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×#97—24no—
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308#400—21no—
309#400—21no—
310#399—21no—
311#399—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#395—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#393—21no—
331#393—21no—
332#393—21no—
333#393—21no—
334#392—21no—
335#392—21no—
336#392—21no—
337#392—21no—
338#392—21no—
339#392—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391—21no—
344#391—21no—
345#391—21no—
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#390—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
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#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#383—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#381—21no—
412#380—21no—
413#380—21no—
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4D411yescharacteristic
423C4×C4⋊C4D411yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4D411yescharacteristic
440C4×C22⋊C4D411yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443#376—21no—
444#376—21no—
445#376D411yescharacteristic
446#376D411yescharacteristic
447C43—21no—
448C43C2311yescharacteristic
449C43C2311yescharacteristic
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—22no—
494C2×#41—41no—
495C2×#41—41no—
496C2×#41—44no—
497C2×#41—82no—
498C2×#41—82no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4C2411yescharacteristic
513C22×D4C2411yescharacteristic
514C22×D4C2411yescharacteristic
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4—21no—
520C23×C4C2×D411yescharacteristic
521C23×C4C2×D411yescharacteristic
522C23×C4C2411yescharacteristic
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—22no—
526C22×C8—22no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—22no—
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—22no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543#127—22no—
544#127—22no—
545#127—22no—
546#127—22no—
547#127—41no—
548#127—41no—
549#125—22no—
550#125—22no—
551#125—41no—
552#125—41no—
553#124—22no—
554#124—22no—
555#124—41no—
556#124—41no—
557#124—44no—
558#121—22no—
559#121—22no—
560#121—22no—
561#121—22no—
562#121—44no—
563#121—44no—
564#121—44no—
565C4×Q8—22no—
566C4×Q8—22no—
567C4×Q8—22no—
568C4×Q8—22no—
569C4×Q8—44no—
570C4×Q8—44no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—44no—
580C4×D4—44no—
581C4×D4—44no—
582C4×D4—82no—
583C4×D4—82no—
584C4×D4—82no—
585C4×D4—82no—
586#117—22no—
587#117—22no—
588#117—22no—
589#117—22no—
590#117—42no—
591#117—42no—
592#117—41no—
593#117—41no—
594#117—44no—
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—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⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
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×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⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—44no—
679C2×C42C2×D411yescharacteristic
680C2×C42C2×D411yescharacteristic
681C2×C42C2×D411yescharacteristic
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42#4114yes—
690C2×C42#4114yes—
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697C4⋊C8—22no—
698C4⋊C8—22no—
699#103—22no—
700#103—22no—
701#103—22no—
702#103—22no—
703#103—22no—
704#103—41no—
705#103—41no—
706#103#4114yescomplemented
707#102—22no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102#4114yescomplemented
731C22⋊C8—22no—
732C22⋊C8—22no—
733#97—22no—
734#97—22no—
735#97—22no—
736#97—22no—
737#97—22no—
738#97—22no—
739#97—22no—
740#97—22no—
741#97—41no—
742#97—41no—
743C4×C8—22no—
744C4×C8—22no—
745C4×C8—41no—
746C4×C8—41no—
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#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787C24—21no—
788C24—21no—
789C24—21no—
790C24C22×D411yescharacteristic
791#41—28no—
792#41—44no—
793#41—44no—
794#41—44no—
795#41—816no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—42no—
802C2×Q8—42no—
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—42no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×Q8C2×#4112yes—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4C2×#4112yes—
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—21no—
872C22×C4—21no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—42no—
889C22×C4—42no—
890C22×C4—42no—
891C22×C4—42no—
892C22×C4#12414yes—
893C22×C4#12414yes—
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×C4C2×#4112yes—
908C22×C4C2×#4112yes—
909C22×C4C2511yescharacteristic
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—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—44no—
933C2×C8—44no—
934C2×C8C2×#4112yes—
935C2×C8C2×#4112yes—
936C4⋊C4—22no—
937C4⋊C4—22no—
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—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—41no—
961C4⋊C4—41no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
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⋊C4C2×#4112yes—
988C4⋊C4C2×#4112yes—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—41no—
992C22⋊C4—41no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
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—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—
1020C42—22no—
1021C42—22no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—41no—
1031C42—41no—
1032C42—41no—
1033C42—41no—
1034C42—41no—
1035C42—41no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—42no—
1045C42—81no—
1046C42—81no—
1047C42#12414yes—
1048C42#12414yes—
1049C42C2×#4112yes—
1050C42C2×#4112yes—
1051C42C2×#4112yes—
1052C42C2×#4112yes—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—22no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
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—
1080C23C2×#12412yes—
1081C23C23×D411yescharacteristic
1082Q8—22no—
1083Q8—22no—
1084Q8—41no—
1085Q8—41no—
1086Q8—84no—
1087Q8—84no—
1088Q8—84no—
1089D4—22no—
1090D4—22no—
1091D4—48no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—41no—
1098D4—41no—
1099D4—41no—
1100D4—41no—
1101D4—41no—
1102D4—84no—
1103D4—84no—
1104D4—84no—
1105D4—84no—
1106D4—84no—
1107D4—84no—
1108D4—84no—
1109D4—84no—
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—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
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—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—44no—
1150C2×C4—44no—
1151C2×C4—48no—
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—84no—
1189C2×C4—84no—
1190C2×C4—84no—
1191C2×C4—84no—
1192C2×C4C2×#12412yes—
1193C2×C4C2×#12412yes—
1194C2×C4C2×#12412yes—
1195C2×C4C2×#12412yes—
1196C2×C4C2×#12412yes—
1197C2×C4#57512yes—
1198C2×C4#57512yes—
1199C2×C4C22×#4111yescharacteristic
1200C2×C4C22×#4111yescharacteristic
1201C2×C4C22×#4111yescharacteristic
1202C2×C4C22×#4111yescharacteristic
1203C2×C4#58511yescharacteristic
1204C2×C4#58511yescharacteristic
1205C8—22no—
1206C8—22no—
1207C8—41no—
1208C8—41no—
1209C8—41no—
1210C8—41no—
1211C8—41no—
1212C8—41no—
1213C22—22no—
1214C22—22no—
1215C22—22no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—42no—
1221C22—42no—
1222C22—42no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22C22×#12411yescharacteristic
1242C22D4×#4111yescharacteristic
1243C22D4×#4111yescharacteristic
1244C22C2×#57511yescharacteristic
1245C22C2×#57511yescharacteristic
1246C22#358511yescharacteristic
1247C22#358511yescharacteristic
1248C4—22no—
1249C4—22no—
1250C4—22no—
1251C4—22no—
1252C4—22no—
1253C4—22no—
1254C4—22no—
1255C4—41no—
1256C4—42no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—42no—
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#344411yescharacteristic
1275C4#345511yescharacteristic
1276C4#347511yescharacteristic
1277C4#347511yescharacteristic
1278C2—42no—
1279C2—82no—
1280C2—161no—
1281C2—161no—
1282C2#3481311yescharacteristic
1283C2#6061811yescharacteristic
1284C2#6061911yescharacteristic
1285C2#6145411yescharacteristic
1286C2#6145611yescharacteristic
1287C2#6145911yescharacteristic
1288C2#6146211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#34977C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34912C2semidirect
3. #27832C2semidirect
4. #27826C2semidirect
5. #27786C2semidirect
6. #27780C2semidirect
7. #27766C2semidirect
8. #27760C2semidirect
9. #27746C2semidirect
10. #27740C2semidirect
11. #27718C2semidirect
12. #27712C2semidirect
13. #27702C2semidirect
14. #27696C2semidirect
15. #27269C2semidirect
16. #27263C2semidirect
17. #27259C2semidirect
18. #27257C2semidirect
19. #23826C2semidirect
20. #23824C2semidirect
21. #23822C2semidirect
22. #23821C2semidirect
23. #21656C2semidirect
24. #21655C2semidirect
25. #21648C2semidirect
26. #21646C2semidirect
27. #21408C2semidirect
28. #21393C2semidirect
29. #20742C2semidirect
30. #20479C2semidirect
31. #20411C2semidirect
706. #103#41semidirect
730. #102#41semidirect

Maximal subgroups

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

subgroupindex
#349772
#349122
#278322
#278262
#277862
#277802
#277662
#277602
#277462
#277402
#277182
#277122
#277022
#276962
#272692
#272632
#272592
#272572
#238262
#238242
#238222
#238212
#216562
#216552
#216482
#216462
#214082
#213932
#207422
#204792
#204112