Finite Group Databasebeta

← #6931448

Subgroups — #6931448

Order 512.

1715 conjugacy classes of subgroups.

The subgroup lattice has 1454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38034C211yesmaximal, characteristic, complemented
2#37554C211yesmaximal, characteristic, complemented
3#32765C211yesmaximal, characteristic, complemented
4#32752C211yesmaximal, characteristic, complemented
5#32622C211yesmaximal, characteristic, complemented
6#32597C211yesmaximal, characteristic, complemented
7#32554C211yesmaximal, characteristic, complemented
8#32550C211yesmaximal, characteristic, complemented
9#31401C211yesmaximal, characteristic, complemented
10#31387C211yesmaximal, characteristic, complemented
11#30416C211yesmaximal, characteristic, complemented
12#30400C211yesmaximal, characteristic, complemented
13#30335C211yesmaximal, characteristic, complemented
14#30195C211yesmaximal, characteristic, complemented
15#30179C211yesmaximal, characteristic, complemented
16#29912C211yesmaximal, characteristic, complemented
17#29721C211yesmaximal, characteristic, complemented
18#29116C211yesmaximal, characteristic, complemented
19#28584C211yesmaximal, characteristic, complemented
20#28567C211yesmaximal, characteristic, complemented
21#28557C211yesmaximal, characteristic, complemented
22#26229C211yesmaximal, characteristic, complemented
23#26225C211yesmaximal, characteristic, complemented
24#25502C211yesmaximal, characteristic, complemented
25#25133C211yesmaximal, characteristic, complemented
26#25117C211yesmaximal, characteristic, complemented
27#24444C211yesmaximal, characteristic, complemented
28#24444C211yesmaximal, characteristic, complemented
29#23932C211yesmaximal, characteristic, complemented
30#23631C211yesmaximal, characteristic, complemented
31#22472C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#532C2211yescharacteristic, complemented
34C2×#529C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#449C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#447C2211yescharacteristic
43C2×#436C2211yescharacteristic, complemented
44C2×#435C2211yescharacteristic, complemented
45C2×#417C2211yescharacteristic
46C2×#417C2211yescharacteristic
47#2854C2211yescharacteristic
48#2820—21no—
49#2819—21no—
50#2703—21no—
51#2697—21no—
52#2681—21no—
53#2678—21no—
54#2656—21no—
55#2639—21no—
56#2636—21no—
57#2636—21no—
58#2628C2211yescharacteristic
59#2628C2211yescharacteristic, complemented
60#2625C2211yescharacteristic
61#2620C2211yescharacteristic
62#2619C2211yescharacteristic
63#2619C2211yescharacteristic, complemented
64#2592C2211yescharacteristic
65#2580C2211yescharacteristic, complemented
66#2580C2211yescharacteristic, complemented
67#2558—21no—
68#2554—21no—
69#2538C2211yescharacteristic
70#2535C2211yescharacteristic
71#2535C2211yescharacteristic
72#2480—21no—
73#2472—21no—
74#2430—21no—
75#2430—21no—
76#2416C2211yescharacteristic
77#2416C2211yescharacteristic
78#2416C2211yescharacteristic, complemented
79#2416C2211yescharacteristic, complemented
80#2415C2211yescharacteristic
81#2414C2211yescharacteristic
82#2408C2211yescharacteristic
83#2407C2211yescharacteristic
84#2354C2211yescharacteristic
85#2324C2211yescharacteristic
86#2309C2211yescharacteristic
87#2297C2211yescharacteristic
88C2×#382C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2100C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2076C2211yescharacteristic
103#2074C2211yescharacteristic, complemented
104#2074C2211yescharacteristic, complemented
105#2074C2211yescharacteristic, complemented
106#2074C2211yescharacteristic, complemented
107#2073C2211yescharacteristic
108#2073C2211yescharacteristic
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2073C2211yescharacteristic
112#2073C2211yescharacteristic
113#2071C2211yescharacteristic, complemented
114#2071C2211yescharacteristic, complemented
115#2068C2211yescharacteristic, complemented
116#2066C2211yescharacteristic, complemented
117#2058C2211yescharacteristic, complemented
118#2054C2211yescharacteristic
119#2054C2211yescharacteristic
120#2054C2211yescharacteristic
121#2054C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic
124#2041C2211yescharacteristic, complemented
125#2035C2211yescharacteristic
126#2035C2211yescharacteristic
127#2034C2211yescharacteristic
128#2034C2211yescharacteristic
129#2033C2211yescharacteristic
130#2033C2211yescharacteristic
131#2024C2211yescharacteristic, complemented
132#2023C2211yescharacteristic
133#2023C2211yescharacteristic
134#2014C2211yescharacteristic, complemented
135#2012C2211yescharacteristic
136#2012C2211yescharacteristic
137#2011C2211yescharacteristic
138#2011C2211yescharacteristic
139#2000C2211yescharacteristic
140#2000C2211yescharacteristic
141#2000C2211yescharacteristic, complemented
142#2000C2211yescharacteristic, complemented
143#1999C2211yescharacteristic
144#1999C2211yescharacteristic
145#1985C2211yescharacteristic, complemented
146#1984C2211yescharacteristic, complemented
147#1973C2211yescharacteristic, complemented
148#1968C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic, complemented
155#1926C2211yescharacteristic, complemented
156#1925C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1895C2211yescharacteristic
160#1895C2211yescharacteristic, complemented
161#1895C2211yescharacteristic, complemented
162#1895C2211yescharacteristic, complemented
163#1894C2211yescharacteristic, complemented
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic, complemented
166#1892C2211yescharacteristic, complemented
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1877C2211yescharacteristic, complemented
174#1877C2211yescharacteristic, complemented
175#1875C2211yescharacteristic
176#1875C2211yescharacteristic
177#1875C2211yescharacteristic, complemented
178#1875C2211yescharacteristic, complemented
179#1874C2211yescharacteristic
180#1874C2211yescharacteristic
181#1870C2211yescharacteristic
182#1870C2211yescharacteristic
183#1870C2211yescharacteristic
184#1869C2211yescharacteristic
185#1864C2211yescharacteristic
186#1864C2211yescharacteristic
187#1864C2211yescharacteristic, complemented
188#1864C2211yescharacteristic, complemented
189#1853C2211yescharacteristic, complemented
190#1852C2211yescharacteristic, complemented
191#1825C2211yescharacteristic
192#1825C2211yescharacteristic
193#1818C2211yescharacteristic, complemented
194#1817C2211yescharacteristic, complemented
195#1798C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1750C2211yescharacteristic
199#1736C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201#1729C2211yescharacteristic, complemented
202#1728C2211yescharacteristic, complemented
203C22×#41—21no—
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×M16C2311yescharacteristic
213C22×M16C2311yescharacteristic
214C22×M16C2311yescharacteristic
215C23×C8C2311yescharacteristic
216#546—42no—
217#546—42no—
218#532—42no—
219#532—42no—
220C2×C4⋊Q8C2311yescharacteristic
221C2×#127C2311yescharacteristic
222#529—42no—
223#529—42no—
224C2×#126D411yescharacteristic
225C2×#126D411yescharacteristic
226C2×#125D411yescharacteristic
227C2×#124—21no—
228C2×#124D411yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×#123—21no—
232C2×#123D411yescharacteristic
233C2×#123D411yescharacteristic
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8D411yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121—21no—
243C2×#121—21no—
244C2×#121D411yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#121C2311yescharacteristic
251C2×#121C2311yescharacteristic
252C2×#121C2311yescharacteristic
253C2×#121C2311yescharacteristic
254C2×#120—21no—
255C2×#120—21no—
256C2×C4×Q8C2311yescharacteristic
257C2×C4×D4—21no—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C2×#117C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269C22×C4⋊C4C2311yescharacteristic
270C22×C22⋊C4—21no—
271C22×C42C2311yescharacteristic
272#469—42no—
273#469—42no—
274#469—42no—
275#466—42no—
276#449—42no—
277#449—42no—
278#447—42no—
279#447—42no—
280#436—42no—
281#435—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290#417—42no—
291#417—42no—
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×C4×C8C2311yescharacteristic
330#400—21no—
331#400—21no—
332#400—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#399—21no—
337#398—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#396—21no—
345#396—21no—
346#396—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#395—21no—
353#395—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#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#393—21no—
369#393—21no—
370#393—21no—
371#393—21no—
372#393—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#392—21no—
379#392—21no—
380#392—21no—
381#392—21no—
382#391C2311yescharacteristic
383#391C2311yescharacteristic
384#391C2311yescharacteristic
385#390—21no—
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#389—21no—
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
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#388—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#386—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#384C2311yescharacteristic
437#382—21no—
438#382—21no—
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#379—21no—
452#379—21no—
453#379—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C2×#95—21no—
459C2×#95—21no—
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#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C2×#41—22no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—41no—
501C2×#41—44no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—82no—
505C2×#41—82no—
506C22×Q8—21no—
507C22×Q8C2×D411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
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×D4—21no—
522C22×D4—21no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4C2×D411yescharacteristic
529C22×D4C2×D411yescharacteristic
530C22×D4C2×D411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4C2×D411yescharacteristic
542C23×C4C2×D411yescharacteristic
543C23×C4C2411yescharacteristic
544C23×C4C2411yescharacteristic
545C23×C4C2411yescharacteristic
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C2×D8—41no—
564C2×M16—22no—
565C2×M16—22no—
566C2×M16—41no—
567C2×M16—41no—
568C2×M16—41no—
569C2×M16—41no—
570C2×M16—41no—
571C2×M16—41no—
572C2×M16—41no—
573C22×C8—41no—
574C22×C8—41no—
575C22×C8—41no—
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C4⋊Q8—41no—
585C4⋊Q8—41no—
586#127—41no—
587#127—41no—
588#126—42no—
589#126—42no—
590#125—42no—
591#124—42no—
592#124—41no—
593#124—41no—
594#124—44no—
595#123—42no—
596#123—42no—
597#123—44no—
598#123—82no—
599C22⋊Q8—42no—
600C22⋊Q8—41no—
601C22⋊Q8—41no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—82no—
605#121—22no—
606#121—22no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—22no—
611#121—22no—
612#121—44no—
613#121—41no—
614#121—42no—
615#121—44no—
616#121—41no—
617#121—41no—
618#121—41no—
619#121—41no—
620#121—41no—
621#121—41no—
622#121—41no—
623#121—41no—
624#121—41no—
625#121—41no—
626#121—82no—
627#121—82no—
628#121—82no—
629#121—82no—
630#120—44no—
631#120—82no—
632C4×Q8—41no—
633C4×Q8—41no—
634C4×D4—22no—
635C4×D4—22no—
636C4×D4—22no—
637C4×D4—22no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—41no—
644C4×D4—41no—
645C4×D4—41no—
646C4×D4—44no—
647#117—41no—
648#117—41no—
649#117—41no—
650#117—41no—
651#117—41no—
652#117—41no—
653#117—41no—
654#117—41no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4—41no—
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2×D411yescharacteristic
680C2×C4⋊C4C2×D411yescharacteristic
681C2×C4⋊C4C2×D411yescharacteristic
682C2×C4⋊C4C2×D411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2411yescharacteristic
692C2×C4⋊C4C2411yescharacteristic
693C2×C4⋊C4C2411yescharacteristic
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—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—21no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—21no—
731C2×C22⋊C4—21no—
732C2×C22⋊C4—21no—
733C2×C22⋊C4—21no—
734C2×C22⋊C4—21no—
735C2×C22⋊C4—21no—
736C2×C22⋊C4—21no—
737C2×C22⋊C4—21no—
738C2×C22⋊C4—21no—
739C2×C22⋊C4—44no—
740C2×C22⋊C4C2×D411yescharacteristic
741C2×C22⋊C4C2×D411yescharacteristic
742C2×C22⋊C4C2×D411yescharacteristic
743C2×C22⋊C4C2×D411yescharacteristic
744C2×C22⋊C4C2×D411yescharacteristic
745C2×C22⋊C4C2×D411yescharacteristic
746C2×C22⋊C4C2×D411yescharacteristic
747C2×C22⋊C4C2×D411yescharacteristic
748C2×C22⋊C4C2×D411yescharacteristic
749C2×C22⋊C4C2×D411yescharacteristic
750C2×C42—22no—
751C2×C42—22no—
752C2×C42—21no—
753C2×C42—21no—
754C2×C42—21no—
755C2×C42C2×D411yescharacteristic
756C2×C42C2×D411yescharacteristic
757C2×C42C2411yescharacteristic
758C2×C42C2411yescharacteristic
759C2×C42C2411yescharacteristic
760C2×C42C2411yescharacteristic
761#107—41no—
762#107—41no—
763#106—41no—
764#106—41no—
765#106—41no—
766#106—41no—
767C4⋊C8—41no—
768C4⋊C8—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795#102—41no—
796#102—41no—
797C22⋊C8—22no—
798C22⋊C8—22no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801C22⋊C8—41no—
802C22⋊C8—41no—
803C22⋊C8—41no—
804C22⋊C8—41no—
805#97—41no—
806C4×C8—41no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95—21no—
832#95—21no—
833#95—21no—
834#95—21no—
835#95—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—21no—
840C24—42no—
841C24—42no—
842C24—81no—
843C24—81no—
844C24—81no—
845C24—81no—
846C24—81no—
847C24C22×D411yescharacteristic
848C24C22×D411yescharacteristic
849C24C22×D411yescharacteristic
850#41—44no—
851#41—44no—
852#41—82no—
853#41—82no—
854#41—816no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—41no—
862C2×Q8—41no—
863C2×Q8—41no—
864C2×Q8—42no—
865C2×Q8—81no—
866C2×Q8—81no—
867C2×D4—22no—
868C2×D4—22no—
869C2×D4—21no—
870C2×D4—21no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—41no—
893C2×D4—41no—
894C2×D4—41no—
895C2×D4—41no—
896C2×D4—41no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—81no—
917C2×D4—81no—
918C2×D4—82no—
919C2×D4—82no—
920C2×D4—82no—
921C2×D4—82no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4H(5,𝔽2)12yes—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—22no—
948C22×C4—22no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—41no—
974C22×C4—41no—
975C22×C4—41no—
976C22×C4—41no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—42no—
983C22×C4—42no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4H(5,𝔽2)12yes—
1007C22×C4H(5,𝔽2)12yes—
1008C22×C4C2511yescharacteristic
1009SD16—82no—
1010SD16—82no—
1011D8—82no—
1012D8—82no—
1013D8—82no—
1014D8—82no—
1015M16—82no—
1016M16—82no—
1017M16—82no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—21no—
1041C2×C8—21no—
1042C2×C8—82no—
1043C4⋊C4—22no—
1044C4⋊C4—22no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—21no—
1061C4⋊C4—21no—
1062C4⋊C4—21no—
1063C4⋊C4—21no—
1064C4⋊C4—21no—
1065C4⋊C4—21no—
1066C4⋊C4—21no—
1067C4⋊C4—41no—
1068C4⋊C4—41no—
1069C4⋊C4—41no—
1070C4⋊C4—41no—
1071C4⋊C4—41no—
1072C4⋊C4—41no—
1073C4⋊C4—41no—
1074C4⋊C4—41no—
1075C4⋊C4—42no—
1076C4⋊C4—42no—
1077C4⋊C4—42no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4—81no—
1085C4⋊C4—81no—
1086C4⋊C4—81no—
1087C4⋊C4—81no—
1088C4⋊C4—81no—
1089C22⋊C4—22no—
1090C22⋊C4—22no—
1091C22⋊C4—22no—
1092C22⋊C4—22no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
1097C22⋊C4—41no—
1098C22⋊C4—41no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C22⋊C4—81no—
1135C22⋊C4—81no—
1136C22⋊C4—81no—
1137C22⋊C4—81no—
1138C22⋊C4—81no—
1139C22⋊C4—81no—
1140C22⋊C4—81no—
1141C22⋊C4—81no—
1142C22⋊C4—81no—
1143C22⋊C4—81no—
1144C42—22no—
1145C42—22no—
1146C42—21no—
1147C42—21no—
1148C42—21no—
1149C42—21no—
1150C42—21no—
1151C42—21no—
1152C42—21no—
1153C42—21no—
1154C42—81no—
1155C42—81no—
1156C42—81no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—21no—
1171C23—21no—
1172C23—21no—
1173C23—22no—
1174C23—21no—
1175C23—21no—
1176C23—21no—
1177C23—21no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—41no—
1197C23—41no—
1198C23—41no—
1199C23—41no—
1200C23—41no—
1201C23—41no—
1202C23—41no—
1203C23—41no—
1204C23—41no—
1205C23—84no—
1206C23—84no—
1207C23—162no—
1208C23—162no—
1209C23—162no—
1210C23—162no—
1211C23—162no—
1212C23#53412yes—
1213C23C23×D411yescharacteristic
1214Q8—41no—
1215Q8—41no—
1216Q8—41no—
1217Q8—41no—
1218Q8—82no—
1219Q8—84no—
1220D4—22no—
1221D4—22no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—41no—
1231D4—41no—
1232D4—41no—
1233D4—41no—
1234D4—41no—
1235D4—41no—
1236D4—82no—
1237D4—82no—
1238D4—82no—
1239D4—84no—
1240D4—84no—
1241D4—84no—
1242D4—84no—
1243D4—84no—
1244D4—84no—
1245D4—162no—
1246D4—162no—
1247D4—162no—
1248D4—162no—
1249D4—162no—
1250D4—162no—
1251D4—162no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—22no—
1255C2×C4—22no—
1256C2×C4—22no—
1257C2×C4—22no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—44no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—41no—
1327C2×C4—41no—
1328C2×C4—41no—
1329C2×C4—41no—
1330C2×C4—41no—
1331C2×C4—41no—
1332C2×C4—41no—
1333C2×C4—84no—
1334C2×C4—82no—
1335C2×C4—84no—
1336C2×C4—84no—
1337C2×C4—162no—
1338C2×C4—162no—
1339C2×C4—162no—
1340C2×C4#53412yes—
1341C2×C4C2×H(5,𝔽2)11yescharacteristic
1342C2×C4C2×H(5,𝔽2)11yescharacteristic
1343C2×C4C2×H(5,𝔽2)11yescharacteristic
1344C2×C4#58511yescharacteristic
1345C2×C4#58511yescharacteristic
1346C2×C4#58511yescharacteristic
1347C8—41no—
1348C8—41no—
1349C8—41no—
1350C8—41no—
1351C8—41no—
1352C8—41no—
1353C8—41no—
1354C8—41no—
1355C22—22no—
1356C22—22no—
1357C22—22no—
1358C22—41no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—41no—
1363C22—41no—
1364C22—41no—
1365C22—41no—
1366C22—41no—
1367C22—41no—
1368C22—42no—
1369C22—41no—
1370C22—41no—
1371C22—41no—
1372C22—41no—
1373C22—42no—
1374C22—41no—
1375C22—41no—
1376C22—41no—
1377C22—41no—
1378C22—42no—
1379C22—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—81no—
1391C22—81no—
1392C22—81no—
1393C22—81no—
1394C22—81no—
1395C22—81no—
1396C22—81no—
1397C22—81no—
1398C22—81no—
1399C22—81no—
1400C22—81no—
1401C22—81no—
1402C22—81no—
1403C22—81no—
1404C22—168no—
1405C22C2×#53411yescharacteristic
1406C22#348811yescharacteristic
1407C22#350011yescharacteristic
1408C22#358411yescharacteristic
1409C22#358511yescharacteristic
1410C22#358511yescharacteristic
1411C22#358511yescharacteristic
1412C4—22no—
1413C4—41no—
1414C4—41no—
1415C4—41no—
1416C4—41no—
1417C4—41no—
1418C4—41no—
1419C4—41no—
1420C4—41no—
1421C4—41no—
1422C4—41no—
1423C4—81no—
1424C4—81no—
1425C4—81no—
1426C4—81no—
1427C4—81no—
1428C4—81no—
1429C4—81no—
1430C4—81no—
1431C4—81no—
1432C4—81no—
1433C4—81no—
1434C4—81no—
1435C4#353411yescharacteristic
1436C4#353411yescharacteristic
1437C4#356011yescharacteristic
1438C4#356011yescharacteristic
1439C2—42no—
1440C2—81no—
1441C2—81no—
1442C2—82no—
1443C2—161no—
1444C2—161no—
1445C2—161no—
1446C2#4193611yescharacteristic
1447C2#6075311yescharacteristic
1448C2#6076711yescharacteristic
1449C2#6204711yescharacteristic
1450C2#6208811yescharacteristic
1451C2#6257311yescharacteristic
1452C2#6261311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38034C2semidirect
2. #37554C2semidirect
3. #32765C2semidirect
4. #32752C2semidirect
5. #32622C2semidirect
6. #32597C2semidirect
7. #32554C2semidirect
8. #32550C2semidirect
9. #31401C2semidirect
10. #31387C2semidirect
11. #30416C2semidirect
12. #30400C2semidirect
13. #30335C2semidirect
14. #30195C2semidirect
15. #30179C2semidirect
16. #29912C2semidirect
17. #29721C2semidirect
18. #29116C2semidirect
19. #28584C2semidirect
20. #28567C2semidirect
21. #28557C2semidirect
22. #26229C2semidirect
23. #26225C2semidirect
24. #25502C2semidirect
25. #25133C2semidirect
26. #25117C2semidirect
27. #24444C2semidirect
28. #24444C2semidirect
29. #23932C2semidirect
30. #23631C2semidirect
31. #22472C2semidirect
33. C2×#532C22semidirect
43. C2×#436C22semidirect
44. C2×#435C22semidirect
59. #2628C22semidirect
63. #2619C22semidirect
65. #2580C22semidirect
66. #2580C22semidirect
78. #2416C22semidirect
79. #2416C22semidirect
88. C2×#382C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2100C22semidirect
92. #2099C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2085C22semidirect
98. #2085C22semidirect
100. #2077C22semidirect
101. #2077C22semidirect
103. #2074C22semidirect
104. #2074C22semidirect
105. #2074C22semidirect
106. #2074C22semidirect
113. #2071C22semidirect
114. #2071C22semidirect
115. #2068C22semidirect
116. #2066C22semidirect
117. #2058C22semidirect
124. #2041C22semidirect
131. #2024C22semidirect
134. #2014C22semidirect
141. #2000C22semidirect
142. #2000C22semidirect
145. #1985C22semidirect
146. #1984C22semidirect
147. #1973C22semidirect
148. #1968C22semidirect
151. #1936C22semidirect
154. #1934C22semidirect
155. #1926C22semidirect
156. #1925C22semidirect
157. #1919C22semidirect
158. #1918C22semidirect
160. #1895C22semidirect
161. #1895C22semidirect
162. #1895C22semidirect
163. #1894C22semidirect
165. #1893C22semidirect
166. #1892C22semidirect
173. #1877C22semidirect
174. #1877C22semidirect
177. #1875C22semidirect
178. #1875C22semidirect
187. #1864C22semidirect
188. #1864C22semidirect
189. #1853C22semidirect
190. #1852C22semidirect
193. #1818C22semidirect
194. #1817C22semidirect
199. #1736C22semidirect
200. #1736C22semidirect
201. #1729C22semidirect
202. #1728C22semidirect

Maximal subgroups

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

subgroupindex
#380342
#375542
#327652
#327522
#326222
#325972
#325542
#325502
#314012
#313872
#304162
#304002
#303352
#301952
#301792
#299122
#297212
#291162
#285842
#285672
#285572
#262292
#262252
#255022
#251332
#251172
#244442
#239322
#236312
#224722