Finite Group Databasebeta

← #6506595

Subgroups — #6506595

Order 512.

1728 conjugacy classes of subgroups.

The subgroup lattice has 1377 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37455C211yesmaximal, characteristic
2#35253C211yesmaximal, characteristic, complemented
3#29345C211yesmaximal, characteristic, complemented
4#29345C211yesmaximal, characteristic, complemented
5#29341C211yesmaximal, characteristic, complemented
6#29340C211yesmaximal, characteristic, complemented
7#27984C211yesmaximal, characteristic, complemented
8#27984C211yesmaximal, characteristic, complemented
9#27726C211yesmaximal, characteristic, complemented
10#27724C211yesmaximal, characteristic, complemented
11#27714C211yesmaximal, characteristic, complemented
12#27712C211yesmaximal, characteristic, complemented
13#27706C211yesmaximal, characteristic, complemented
14#27704C211yesmaximal, characteristic, complemented
15#27702C211yesmaximal, characteristic, complemented
16#27700C211yesmaximal, characteristic, complemented
17#27284C211yesmaximal, characteristic, complemented
18#27280C211yesmaximal, characteristic, complemented
19#27274C211yesmaximal, characteristic, complemented
20#27270C211yesmaximal, characteristic, complemented
21#27267C211yesmaximal, characteristic, complemented
22#27263C211yesmaximal, characteristic, complemented
23#27261C211yesmaximal, characteristic, complemented
24#27257C211yesmaximal, characteristic, complemented
25#25915C211yesmaximal, characteristic, complemented
26#25914C211yesmaximal, characteristic, complemented
27#21769C211yesmaximal, characteristic, complemented
28#21763C211yesmaximal, characteristic, complemented
29#20910C211yesmaximal, characteristic, complemented
30#20908C211yesmaximal, characteristic, complemented
31#20527C211yesmaximal, characteristic, complemented
32C2×#544C2211yescharacteristic
33C2×#525C2211yescharacteristic
34C2×#525C2211yescharacteristic
35C22×#117C2211yescharacteristic
36C2×#491C2211yescharacteristic, complemented
37C2×#490C2211yescharacteristic, complemented
38C2×#487C2211yescharacteristic, complemented
39C2×#486C2211yescharacteristic, complemented
40C2×#417C2211yescharacteristic
41C2×#417C2211yescharacteristic
42C2×#416C2211yescharacteristic
43C2×#416C2211yescharacteristic
44C2×#407C2211yescharacteristic
45C22×C22⋊C8C2211yescharacteristic
46#2857—21no—
47#2851—21no—
48#2812—21no—
49#2812—21no—
50#2630—21no—
51#2630—21no—
52#2630—21no—
53#2630—21no—
54#2629—21no—
55#2628—21no—
56#2621C2211yescharacteristic
57#2620C2211yescharacteristic
58#2620C2211yescharacteristic
59#2619C2211yescharacteristic
60#2600—21no—
61#2600—21no—
62#2500C2211yescharacteristic
63#2500C2211yescharacteristic
64#2499C2211yescharacteristic
65#2499C2211yescharacteristic
66#2442C2211yescharacteristic
67#2442C2211yescharacteristic
68#2441C2211yescharacteristic
69#2441C2211yescharacteristic
70#2440C2211yescharacteristic
71#2440C2211yescharacteristic
72#2439C2211yescharacteristic
73#2439C2211yescharacteristic
74#2438—21no—
75#2438—21no—
76#2437—21no—
77#2437—21no—
78#2432C2211yescharacteristic
79#2432C2211yescharacteristic
80#2431C2211yescharacteristic
81#2431C2211yescharacteristic
82#2317C2211yescharacteristic
83#2317C2211yescharacteristic
84#2316C2211yescharacteristic
85#2280C2211yescharacteristic
86C2×#380C2211yescharacteristic
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2100C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2099C2211yescharacteristic, complemented
94#2099C2211yescharacteristic, complemented
95#2074C2211yescharacteristic, complemented
96#2074C2211yescharacteristic, complemented
97#2073C2211yescharacteristic, complemented
98#2073C2211yescharacteristic, complemented
99#2072C2211yescharacteristic, complemented
100#2072C2211yescharacteristic, complemented
101#2071C2211yescharacteristic, complemented
102#2071C2211yescharacteristic, complemented
103#2043C2211yescharacteristic, complemented
104#2043C2211yescharacteristic, complemented
105#2042C2211yescharacteristic, complemented
106#2042C2211yescharacteristic, complemented
107#2042C2211yescharacteristic, complemented
108#2042C2211yescharacteristic, complemented
109#2041C2211yescharacteristic, complemented
110#2041C2211yescharacteristic, complemented
111#2026C2211yescharacteristic, complemented
112#2026C2211yescharacteristic, complemented
113#2025C2211yescharacteristic, complemented
114#2025C2211yescharacteristic, complemented
115#2024C2211yescharacteristic, complemented
116#2024C2211yescharacteristic, complemented
117#2023C2211yescharacteristic, complemented
118#2023C2211yescharacteristic, complemented
119#1993C2211yescharacteristic, complemented
120#1993C2211yescharacteristic, complemented
121#1991C2211yescharacteristic, complemented
122#1991C2211yescharacteristic, complemented
123#1959C2211yescharacteristic, complemented
124#1959C2211yescharacteristic, complemented
125#1958C2211yescharacteristic, complemented
126#1958C2211yescharacteristic, complemented
127#1936C2211yescharacteristic, complemented
128#1936C2211yescharacteristic, complemented
129#1936C2211yescharacteristic, complemented
130#1936C2211yescharacteristic, complemented
131#1935C2211yescharacteristic, complemented
132#1935C2211yescharacteristic, complemented
133#1935C2211yescharacteristic, complemented
134#1935C2211yescharacteristic, complemented
135#1934C2211yescharacteristic, complemented
136#1934C2211yescharacteristic, complemented
137#1934C2211yescharacteristic, complemented
138#1934C2211yescharacteristic, complemented
139#1933C2211yescharacteristic, complemented
140#1933C2211yescharacteristic, complemented
141#1933C2211yescharacteristic, complemented
142#1933C2211yescharacteristic, complemented
143#1895C2211yescharacteristic
144#1895C2211yescharacteristic
145#1894C2211yescharacteristic
146#1894C2211yescharacteristic
147#1893C2211yescharacteristic
148#1893C2211yescharacteristic
149#1892C2211yescharacteristic
150#1892C2211yescharacteristic
151#1875C2211yescharacteristic
152#1875C2211yescharacteristic
153#1875C2211yescharacteristic
154#1875C2211yescharacteristic
155#1875C2211yescharacteristic
156#1875C2211yescharacteristic
157#1874C2211yescharacteristic
158#1874C2211yescharacteristic
159#1874C2211yescharacteristic
160#1874C2211yescharacteristic
161#1874C2211yescharacteristic
162#1874C2211yescharacteristic
163#1873C2211yescharacteristic
164#1873C2211yescharacteristic
165#1873C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic
168#1873C2211yescharacteristic
169#1872C2211yescharacteristic
170#1872C2211yescharacteristic
171#1872C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic
175#1836C2211yescharacteristic, complemented
176#1836C2211yescharacteristic, complemented
177#1834C2211yescharacteristic, complemented
178#1834C2211yescharacteristic, complemented
179#1825C2211yescharacteristic
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1788C2211yescharacteristic
184#1788C2211yescharacteristic
185#1788C2211yescharacteristic
186#1788C2211yescharacteristic
187#1753C2211yescharacteristic
188#1753C2211yescharacteristic
189#1753C2211yescharacteristic
190#1753C2211yescharacteristic
191#1752C2211yescharacteristic
192#1752C2211yescharacteristic
193C8×C22⋊C4C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195#1750C2211yescharacteristic
196#1750C2211yescharacteristic
197#1750C2211yescharacteristic
198#1750C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C24×C4C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#544—42no—
211#544—42no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8C2311yescharacteristic
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#127C2311yescharacteristic
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222#525—24no—
223#525—24no—
224#525—24no—
225#525—24no—
226C2×#123—21no—
227C2×#123—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×#120—21no—
242C2×C4×D4—21no—
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×#117—21no—
247C2×#117—21no—
248C2×#117—42no—
249C2×#117—42no—
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C2×#117C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264C22×C42—21no—
265#491—42no—
266#490—42no—
267#487—42no—
268#486—42no—
269#417—42no—
270#417—42no—
271#416—42no—
272#416—42no—
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305#407—24no—
306C2×C22⋊C8—24no—
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#400—21no—
324#400—21no—
325#399—21no—
326#399—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#396—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#395—21no—
348#395—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#393—21no—
364#393—21no—
365#392—21no—
366#392—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#391—21no—
372#391—21no—
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—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#385—21no—
421#385—21no—
422#385—21no—
423#384—21no—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#382—21no—
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#381D411yescharacteristic
434#381D411yescharacteristic
435#380—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380D411yescharacteristic
442#380D411yescharacteristic
443#380D411yescharacteristic
444#380D411yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#379D411yescharacteristic
450#379D411yescharacteristic
451C4×C22⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C2×#95—21no—
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#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25C2×D411yescharacteristic
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C22×Q8—21no—
510C22×Q8—21no—
511C22×Q8C2411yescharacteristic
512C22×Q8C2411yescharacteristic
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4C2411yescharacteristic
522C22×D4C2411yescharacteristic
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—41no—
530C23×C4—41no—
531C23×C4—41no—
532C23×C4—41no—
533C23×C4C2×D411yescharacteristic
534C23×C4C2×D411yescharacteristic
535C23×C4C2×D411yescharacteristic
536C23×C4#4114yes—
537C23×C4#4114yes—
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C23×C4C2411yescharacteristic
541C2×M16—22no—
542C2×M16—22no—
543C2×M16—41no—
544C2×M16—41no—
545C2×M16—41no—
546C2×M16—41no—
547C22×C8—22no—
548C22×C8—22no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8—41no—
552C22×C8—41no—
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C4⋊Q8—22no—
562C4⋊Q8—22no—
563C4⋊Q8—41no—
564C4⋊Q8—41no—
565C4⋊Q8—44no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568#127—41no—
569#127—41no—
570#125—22no—
571#125—22no—
572#125—41no—
573#125—41no—
574#125—44no—
575#124—41no—
576#124—41no—
577#124—41no—
578#124—41no—
579#123—44no—
580#123—44no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—44no—
590C22⋊Q8—44no—
591C22⋊Q8—82no—
592C22⋊Q8—82no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#120—44no—
602#120—44no—
603C4×D4—44no—
604C4×D4—44no—
605C4×D4—44no—
606C4×D4—44no—
607#117—22no—
608#117—22no—
609#117—22no—
610#117—22no—
611#117—22no—
612#117—22no—
613#117—22no—
614#117—22no—
615#117—41no—
616#117—41no—
617#117—41no—
618#117—41no—
619#117—44no—
620#117—44no—
621#117—41no—
622#117—41no—
623#117—41no—
624#117—41no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C4⋊C4—41no—
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—44no—
712C2×C22⋊C4—82no—
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—44no—
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#103—22no—
737#103—22no—
738#103—22no—
739#103—22no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
751#103—41no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—22no—
772C22⋊C8—22no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776#97—41no—
777#97—41no—
778#97—41no—
779#97—41no—
780C4×C8—41no—
781C4×C8—41no—
782C4×C8—41no—
783C4×C8—41no—
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—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818#95C2×D411yescharacteristic
819#95C2×D411yescharacteristic
820C24—21no—
821C24—21no—
822C24—41no—
823C24—41no—
824C24—41no—
825C24—41no—
826C24—41no—
827C24—41no—
828C24#12414yes—
829C24C22×D411yescharacteristic
830C24C22×D411yescharacteristic
831C24C22×D411yescharacteristic
832#41—44no—
833#41—44no—
834#41—44no—
835#41—44no—
836#41—82no—
837#41—82no—
838#41—82no—
839#41—82no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—42no—
853C2×Q8—42no—
854C2×Q8—81no—
855C2×Q8—81no—
856C2×Q8—81no—
857C2×Q8—81no—
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—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
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—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—41no—
925C22×C4—41no—
926C22×C4—41no—
927C22×C4—41no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—42no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4#12414yes—
949C22×C4#12414yes—
950C22×C4#12414yes—
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C2×#4112yes—
963C22×C4C2×#4112yes—
964C22×C4C2×#4112yes—
965C22×C4C2×#4112yes—
966C22×C4C2×#4112yes—
967C22×C4C2×#4112yes—
968C22×C4C2511yescharacteristic
969M16—82no—
970M16—82no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—82no—
996C2×C8—82no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
1018C4⋊C4—21no—
1019C4⋊C4—41no—
1020C4⋊C4—41no—
1021C4⋊C4—41no—
1022C4⋊C4—41no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—42no—
1027C4⋊C4—42no—
1028C4⋊C4—42no—
1029C4⋊C4—42no—
1030C4⋊C4—42no—
1031C4⋊C4—42no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—81no—
1038C4⋊C4—81no—
1039C4⋊C4—81no—
1040C4⋊C4—81no—
1041C4⋊C4—81no—
1042C4⋊C4—81no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4H(5,𝔽2)12yes—
1056C4⋊C4H(5,𝔽2)12yes—
1057C22⋊C4—24no—
1058C22⋊C4—41no—
1059C22⋊C4—41no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—41no—
1069C22⋊C4—41no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C42—24no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42—42no—
1112C42—42no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—44no—
1132C23—44no—
1133C23—44no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—82no—
1149C23—82no—
1150C23—82no—
1151C23—82no—
1152C23C2×#12412yes—
1153C23C2×#12412yes—
1154C23C2×#12412yes—
1155C23C23×D411yescharacteristic
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—162no—
1165Q8—162no—
1166D4—41no—
1167D4—41no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—84no—
1175D4—84no—
1176D4—84no—
1177D4—84no—
1178D4—84no—
1179D4—84no—
1180D4—162no—
1181D4—162no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—22no—
1199C2×C4—22no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—44no—
1227C2×C4—44no—
1228C2×C4—44no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—84no—
1270C2×C4—84no—
1271C2×C4—84no—
1272C2×C4—84no—
1273C2×C4—162no—
1274C2×C4—162no—
1275C2×C4C2×#12412yes—
1276C2×C4C2×#12412yes—
1277C2×C4C2×#12412yes—
1278C2×C4C22×#4111yescharacteristic
1279C2×C4C22×#4111yescharacteristic
1280C2×C4C2×H(5,𝔽2)11yescharacteristic
1281C2×C4C2×H(5,𝔽2)11yescharacteristic
1282C2×C4#58511yescharacteristic
1283C2×C4#58511yescharacteristic
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C8—41no—
1289C8—41no—
1290C8—41no—
1291C8—41no—
1292C22—22no—
1293C22—22no—
1294C22—22no—
1295C22—22no—
1296C22—22no—
1297C22—22no—
1298C22—22no—
1299C22—22no—
1300C22—22no—
1301C22—41no—
1302C22—41no—
1303C22—41no—
1304C22—41no—
1305C22—41no—
1306C22—41no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—88no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22C22×#12411yescharacteristic
1329C22#348411yescharacteristic
1330C22#348511yescharacteristic
1331C22#358411yescharacteristic
1332C22#358411yescharacteristic
1333C22#358511yescharacteristic
1334C22#358611yescharacteristic
1335C4—22no—
1336C4—22no—
1337C4—22no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—41no—
1344C4—42no—
1345C4—41no—
1346C4—41no—
1347C4—42no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4—81no—
1355C4—81no—
1356C4—81no—
1357C4—81no—
1358C4—81no—
1359C4—81no—
1360C4#350511yescharacteristic
1361C4#350511yescharacteristic
1362C4#350511yescharacteristic
1363C4#350511yescharacteristic
1364C2—42no—
1365C2—42no—
1366C2—42no—
1367C2—161no—
1368C2—161no—
1369C2#3537711yescharacteristic
1370C2#6061211yescharacteristic
1371C2#6062111yescharacteristic
1372C2#6162511yescharacteristic
1373C2#6162711yescharacteristic
1374C2#6176111yescharacteristic
1375C2#6176311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37455C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2280 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35253C2semidirect
3. #29345C2semidirect
4. #29345C2semidirect
5. #29341C2semidirect
6. #29340C2semidirect
7. #27984C2semidirect
8. #27984C2semidirect
9. #27726C2semidirect
10. #27724C2semidirect
11. #27714C2semidirect
12. #27712C2semidirect
13. #27706C2semidirect
14. #27704C2semidirect
15. #27702C2semidirect
16. #27700C2semidirect
17. #27284C2semidirect
18. #27280C2semidirect
19. #27274C2semidirect
20. #27270C2semidirect
21. #27267C2semidirect
22. #27263C2semidirect
23. #27261C2semidirect
24. #27257C2semidirect
25. #25915C2semidirect
26. #25914C2semidirect
27. #21769C2semidirect
28. #21763C2semidirect
29. #20910C2semidirect
30. #20908C2semidirect
31. #20527C2semidirect
36. C2×#491C22semidirect
37. C2×#490C22semidirect
38. C2×#487C22semidirect
39. C2×#486C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2100C22semidirect
92. #2100C22semidirect
93. #2099C22semidirect
94. #2099C22semidirect
95. #2074C22semidirect
96. #2074C22semidirect
97. #2073C22semidirect
98. #2073C22semidirect
99. #2072C22semidirect
100. #2072C22semidirect
101. #2071C22semidirect
102. #2071C22semidirect
103. #2043C22semidirect
104. #2043C22semidirect
105. #2042C22semidirect
106. #2042C22semidirect
107. #2042C22semidirect
108. #2042C22semidirect
109. #2041C22semidirect
110. #2041C22semidirect
111. #2026C22semidirect
112. #2026C22semidirect
113. #2025C22semidirect
114. #2025C22semidirect
115. #2024C22semidirect
116. #2024C22semidirect
117. #2023C22semidirect
118. #2023C22semidirect
119. #1993C22semidirect
120. #1993C22semidirect
121. #1991C22semidirect
122. #1991C22semidirect
123. #1959C22semidirect
124. #1959C22semidirect
125. #1958C22semidirect
126. #1958C22semidirect
127. #1936C22semidirect
128. #1936C22semidirect
129. #1936C22semidirect
130. #1936C22semidirect
131. #1935C22semidirect
132. #1935C22semidirect
133. #1935C22semidirect
134. #1935C22semidirect
135. #1934C22semidirect
136. #1934C22semidirect
137. #1934C22semidirect
138. #1934C22semidirect
139. #1933C22semidirect
140. #1933C22semidirect
141. #1933C22semidirect
142. #1933C22semidirect
175. #1836C22semidirect
176. #1836C22semidirect
177. #1834C22semidirect
178. #1834C22semidirect

Maximal subgroups

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

subgroupindex
#374552
#352532
#293452
#293412
#293402
#279842
#277262
#277242
#277142
#277122
#277062
#277042
#277022
#277002
#272842
#272802
#272742
#272702
#272672
#272632
#272612
#272572
#259152
#259142
#217692
#217632
#209102
#209082
#205272