Finite Group Databasebeta

← #7525803

Subgroups — #7525803

Order 512.

1864 conjugacy classes of subgroups.

The subgroup lattice has 1389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59273C211yesmaximal, characteristic, complemented
2#36578C211yesmaximal, characteristic, complemented
3#31960C211yesmaximal, characteristic, complemented
4#31928C211yesmaximal, characteristic, complemented
5#31656C211yesmaximal, characteristic, complemented
6#31563C211yesmaximal, characteristic, complemented
7#28998C211yesmaximal, characteristic, complemented
8#28891C211yesmaximal, characteristic, complemented
9#28104C211yesmaximal, characteristic, complemented
10#27856C211yesmaximal, characteristic, complemented
11#27711C211yesmaximal, characteristic, complemented
12#27578C211yesmaximal, characteristic, complemented
13#27559C211yesmaximal, characteristic, complemented
14#27231C211yesmaximal, characteristic, complemented
15#27197C211yesmaximal, characteristic, complemented
16#26659C211yesmaximal, characteristic, complemented
17#25963C211yesmaximal, characteristic, complemented
18#24939C211yesmaximal, characteristic, complemented
19#24916C211yesmaximal, characteristic, complemented
20#24827C211yesmaximal, characteristic, complemented
21#24542C211yesmaximal, characteristic, complemented
22#24531C211yesmaximal, characteristic, complemented
23#24500C211yesmaximal, characteristic, complemented
24#23858C211yesmaximal, characteristic
25#22902C211yesmaximal, characteristic, complemented
26#22863C211yesmaximal, characteristic, complemented
27#22781C211yesmaximal, characteristic, complemented
28#22437C211yesmaximal, characteristic, complemented
29#22421C211yesmaximal, characteristic, complemented
30C2×#1880C211yesmaximal, characteristic, complemented
31#20734C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#551—21no—
34C2×#548C2211yescharacteristic
35C22×C4×Q8C2211yescharacteristic
36C2×#477C2211yescharacteristic, complemented
37C2×#449C2211yescharacteristic
38C2×#449C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#435C2211yescharacteristic
43C2×#431C2211yescharacteristic
44C2×#417C2211yescharacteristic, complemented
45C22×#103C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2854—21no—
48#2854C2211yescharacteristic
49#2723—21no—
50#2706—21no—
51#2542C2211yescharacteristic
52#2512C2211yescharacteristic
53#2512C2211yescharacteristic
54#2504—21no—
55#2504C2211yescharacteristic
56#2501C2211yescharacteristic
57#2491C2211yescharacteristic
58#2487—21no—
59#2487C2211yescharacteristic
60#2482—21no—
61#2479—21no—
62#2461—21no—
63#2448—21no—
64#2448—21no—
65#2448C2211yescharacteristic, complemented
66#2448C2211yescharacteristic, complemented
67#2440C2211yescharacteristic
68#2437—21no—
69#2422C2211yescharacteristic
70#2421—21no—
71#2421—21no—
72#2421C2211yescharacteristic, complemented
73#2421C2211yescharacteristic, complemented
74#2418—21no—
75#2408C2211yescharacteristic
76#2361C2211yescharacteristic
77#2354C2211yescharacteristic
78#2351C2211yescharacteristic, complemented
79#2351C2211yescharacteristic, complemented
80D4×C4⋊C4C2211yescharacteristic
81#2341C2211yescharacteristic, complemented
82#2341C2211yescharacteristic, complemented
83Q8×C22⋊C4C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85C4×#123—21no—
86C4×#123C2211yescharacteristic
87C2×#390C2211yescharacteristic
88#2285C2211yescharacteristic
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2100C2211yescharacteristic, complemented
92#2099C2211yescharacteristic, complemented
93#2095C2211yescharacteristic, complemented
94#2093C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2076C2211yescharacteristic, complemented
98#2076C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2071C2211yescharacteristic, complemented
102#2071C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2054C2211yescharacteristic
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2024C2211yescharacteristic, complemented
116#2023C2211yescharacteristic, complemented
117#2012C2211yescharacteristic
118#2012C2211yescharacteristic
119#2000C2211yescharacteristic
120#2000C2211yescharacteristic
121#1993C2211yescharacteristic, complemented
122#1983C2211yescharacteristic, complemented
123#1973C2211yescharacteristic
124#1973C2211yescharacteristic
125#1970C2211yescharacteristic
126#1970C2211yescharacteristic
127#1959C2211yescharacteristic, complemented
128#1940C2211yescharacteristic, complemented
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic, complemented
132#1936C2211yescharacteristic, complemented
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1925C2211yescharacteristic, complemented
136#1925C2211yescharacteristic, complemented
137#1924C2211yescharacteristic, complemented
138#1923C2211yescharacteristic, complemented
139#1921C2211yescharacteristic, complemented
140#1921C2211yescharacteristic, complemented
141#1918C2211yescharacteristic, complemented
142#1918C2211yescharacteristic, complemented
143#1917C2211yescharacteristic, complemented
144#1916C2211yescharacteristic, complemented
145#1895C2211yescharacteristic
146#1895C2211yescharacteristic
147#1894C2211yescharacteristic, complemented
148#1893C2211yescharacteristic
149#1893C2211yescharacteristic
150#1880C2211yescharacteristic
151#1880C2211yescharacteristic
152#1880C2211yescharacteristic
153#1880C2211yescharacteristic
154#1880C2211yescharacteristic
155#1880C2211yescharacteristic
156#1880C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1874C2211yescharacteristic
167#1872C2211yescharacteristic, complemented
168#1869C2211yescharacteristic
169#1863C2211yescharacteristic, complemented
170#1863C2211yescharacteristic, complemented
171#1852C2211yescharacteristic
172#1852C2211yescharacteristic, complemented
173#1851C2211yescharacteristic, complemented
174#1850C2211yescharacteristic
175#1836C2211yescharacteristic, complemented
176#1824C2211yescharacteristic
177#1824C2211yescharacteristic
178#1824C2211yescharacteristic, complemented
179#1808C2211yescharacteristic
180#1808C2211yescharacteristic
181#1804C2211yescharacteristic
182#1804C2211yescharacteristic
183#1803C2211yescharacteristic, complemented
184#1803C2211yescharacteristic, complemented
185#1803C2211yescharacteristic, complemented
186#1803C2211yescharacteristic, complemented
187#1803C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1788C2211yescharacteristic, complemented
190#1787C2211yescharacteristic
191#1787C2211yescharacteristic
192#1786C2211yescharacteristic
193#1771C2211yescharacteristic, complemented
194#1763C2211yescharacteristic, complemented
195C4×#103C2211yescharacteristic, complemented
196C4×#103C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1752C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16—24no—
207C22×SD16—24no—
208C22×SD16—42no—
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×M16C2311yescharacteristic
216C23×C8C2311yescharacteristic
217C23×C8C2311yescharacteristic
218#551—48no—
219#548—24no—
220#548—42no—
221C2×C4⋊Q8C2311yescharacteristic
222C2×#126—21no—
223C2×#126—21no—
224C2×#124—21no—
225C2×#124—21no—
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#123D411yescharacteristic
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#120—21no—
242C2×C4×Q8—21no—
243C2×C4×Q8—21no—
244C2×C4×Q8—24no—
245C2×C4×Q8—42no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×Q8C2311yescharacteristic
249C2×C4×Q8C2311yescharacteristic
250C2×C4×Q8C2311yescharacteristic
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4—21no—
255C2×C4×D4—21no—
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×#117—21no—
260C2×#117—21no—
261C22×C4⋊C4—21no—
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C22⋊C4—21no—
266C22×C22⋊C4—21no—
267C22×C22⋊C4—21no—
268C22×C42—21no—
269C22×C42C2311yescharacteristic
270#477—42no—
271#449—24no—
272#449—42no—
273#447—42no—
274#440—24no—
275#440—42no—
276#435—42no—
277#431—42no—
278C2×#107C2311yescharacteristic
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289#417—42no—
290C2×#103—42no—
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#102—42no—
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×#97C2311yescharacteristic
326C2×#97C2311yescharacteristic
327C2×#97C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
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#399—21no—
338#399—21no—
339#399—21no—
340#398—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#396—21no—
351#396—21no—
352#395—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#393—21no—
357#392—21no—
358#391—21no—
359#391—21no—
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#390—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388D411yescharacteristic
406#388D411yescharacteristic
407#387—21no—
408#387—21no—
409#387D411yescharacteristic
410#387D411yescharacteristic
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386D411yescharacteristic
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385D411yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#382—21no—
431#382—21no—
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381D411yescharacteristic
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#379—21no—
448#379—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497C25—21no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—22no—
507C22×Q8—22no—
508C22×Q8—22no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8#4114yes—
512C22×Q8C2411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×D4—22no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×D411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—416no—
552C2×SD16#4114yes—
553C2×D8—22no—
554C2×D8—41no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×M16—41no—
560C2×M16—41no—
561C2×M16—41no—
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8—41no—
566C22×C8—41no—
567C22×C8—41no—
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C4⋊Q8—41no—
577C4⋊Q8—41no—
578#126—44no—
579#126—44no—
580#124—22no—
581#124—41no—
582#124—44no—
583#124—44no—
584#123—24no—
585#123—44no—
586#123—44no—
587#123—44no—
588#123—82no—
589C22⋊Q8—22no—
590C22⋊Q8—44no—
591C22⋊Q8—41no—
592C22⋊Q8—44no—
593C22⋊Q8—44no—
594C22⋊Q8—82no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—41no—
599#121—44no—
600#121—41no—
601#121—41no—
602#120—44no—
603C4×Q8—22no—
604C4×Q8—22no—
605C4×Q8—22no—
606C4×Q8—22no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—41no—
611C4×Q8—41no—
612C4×Q8—41no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×Q8—44no—
618C4×Q8—44no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—44no—
626C4×D4—44no—
627C4×D4—44no—
628#117—44no—
629#117—44no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
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—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—44no—
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2×D411yescharacteristic
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—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—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—44no—
718C2×C22⋊C4—44no—
719C2×C22⋊C4—82no—
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—44no—
741C2×C42C2×D411yescharacteristic
742C2×C42C2×D411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748#107—22no—
749#107—41no—
750#107—41no—
751#107—41no—
752#107—41no—
753#107—41no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756C4⋊C8—41no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759#103—22no—
760#103—22no—
761#103—22no—
762#103—22no—
763#103—22no—
764#103—22no—
765#103—41no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#102—22no—
772#102—22no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787C22⋊C8—22no—
788C22⋊C8—22no—
789C22⋊C8—22no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792#97—22no—
793#97—41no—
794#97—41no—
795C4×C8—41no—
796C4×C8—41no—
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#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95C2×D411yescharacteristic
821#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830C24—21no—
831C24—21no—
832C24—21no—
833C24—42no—
834C24—42no—
835C24—42no—
836C24—42no—
837C24—81no—
838C24—81no—
839C24—81no—
840C24C22×D411yescharacteristic
841C24C22×D411yescharacteristic
842#41—44no—
843#41—82no—
844#41—82no—
845#41—82no—
846C2×Q8—24no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—28no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—42no—
857C2×Q8—42no—
858C2×Q8—44no—
859C2×Q8—44no—
860C2×Q8—44no—
861C2×Q8—42no—
862C2×Q8—81no—
863C2×Q8—81no—
864C2×Q8C2×#4112yes—
865C2×Q8C2×#4112yes—
866C2×Q8C2×#4112yes—
867C2×Q8H(5,𝔽2)12yes—
868C2×D4—22no—
869C2×D4—22no—
870C2×D4—22no—
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—44no—
889C2×D4—44no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4C2×#4112yes—
908C22×C4—22no—
909C22×C4—22no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—24no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—41no—
936C22×C4—41no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4AGL(1,ℤ/8)14yes—
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C2×#4112yes—
971C22×C4H(5,𝔽2)12yes—
972C22×C4C2511yescharacteristic
973SD16—28no—
974SD16—44no—
975SD16—44no—
976SD16—44no—
977D8—82no—
978D8—82no—
979M16—82no—
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—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—44no—
1004C2×C8—82no—
1005C2×C8C2×#4112yes—
1006C4⋊C4—22no—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
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—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—41no—
1032C4⋊C4—41no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—22no—
1063C22⋊C4—22no—
1064C22⋊C4—22no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
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—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
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—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C42—22no—
1106C42—22no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—42no—
1123C42—42no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—22no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—41no—
1159C23—84no—
1160C23—84no—
1161C23—84no—
1162C23—84no—
1163C23—162no—
1164C23—162no—
1165C23—162no—
1166C23#54612yes—
1167C23C2×AGL(1,ℤ/8)12yes—
1168C23#57812yes—
1169C23C23×D411yescharacteristic
1170Q8—22no—
1171Q8—22no—
1172Q8—22no—
1173Q8—22no—
1174Q8—22no—
1175Q8—48no—
1176Q8—41no—
1177Q8—41no—
1178Q8—162no—
1179Q8#55114yescomplemented
1180D4—22no—
1181D4—22no—
1182D4—44no—
1183D4—41no—
1184D4—41no—
1185D4—41no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—84no—
1194D4—84no—
1195D4—84no—
1196D4—84no—
1197D4—162no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—22no—
1204C2×C4—21no—
1205C2×C4—28no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—22no—
1211C2×C4—22no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
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—22no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—48no—
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—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—84no—
1281C2×C4—82no—
1282C2×C4—84no—
1283C2×C4—84no—
1284C2×C4—162no—
1285C2×C4—162no—
1286C2×C4—162no—
1287C2×C4#54612yes—
1288C2×C4C2×AGL(1,ℤ/8)12yes—
1289C2×C4C2×AGL(1,ℤ/8)12yes—
1290C2×C4C22×#4111yescharacteristic
1291C2×C4C22×#4111yescharacteristic
1292C2×C4C2×H(5,𝔽2)11yescharacteristic
1293C2×C4C2×H(5,𝔽2)11yescharacteristic
1294C2×C4#58511yescharacteristic
1295C2×C4#58511yescharacteristic
1296C8—22no—
1297C8—41no—
1298C8—41no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—22no—
1308C22—22no—
1309C22—22no—
1310C22—41no—
1311C22—41no—
1312C22—41no—
1313C22—42no—
1314C22—41no—
1315C22—41no—
1316C22—42no—
1317C22—41no—
1318C22—42no—
1319C22—41no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—168no—
1339C22#330814yes—
1340C22C2×#54611yescharacteristic
1341C22D4×#4111yescharacteristic
1342C22#348811yescharacteristic
1343C22C22×AGL(1,ℤ/8)11yescharacteristic
1344C22C2×#57811yescharacteristic
1345C22#358411yescharacteristic
1346C22#358511yescharacteristic
1347C4—22no—
1348C4—24no—
1349C4—22no—
1350C4—22no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—42no—
1359C4—41no—
1360C4—41no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4C2×#55111yescharacteristic
1373C4#349111yescharacteristic
1374C4#351311yescharacteristic
1375C4#353411yescharacteristic
1376C2—24no—
1377C2—81no—
1378C2—82no—
1379C2—161no—
1380C2—161no—
1381C2#5901111yescharacteristic
1382C2C2×#330811yescharacteristic
1383C2#6118911yescharacteristic
1384C2#6143911yescharacteristic
1385C2#6152411yescharacteristic
1386C2#6196311yescharacteristic
1387C2#6206511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23858C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59273C2semidirect
2. #36578C2semidirect
3. #31960C2semidirect
4. #31928C2semidirect
5. #31656C2semidirect
6. #31563C2semidirect
7. #28998C2semidirect
8. #28891C2semidirect
9. #28104C2semidirect
10. #27856C2semidirect
11. #27711C2semidirect
12. #27578C2semidirect
13. #27559C2semidirect
14. #27231C2semidirect
15. #27197C2semidirect
16. #26659C2semidirect
17. #25963C2semidirect
18. #24939C2semidirect
19. #24916C2semidirect
20. #24827C2semidirect
21. #24542C2semidirect
22. #24531C2semidirect
23. #24500C2semidirect
25. #22902C2semidirect
26. #22863C2semidirect
27. #22781C2semidirect
28. #22437C2semidirect
29. #22421C2semidirect
30. C2×#1880C2semidirect
31. #20734C2semidirect
36. C2×#477C22semidirect
44. C2×#417C22semidirect
65. #2448C22semidirect
66. #2448C22semidirect
72. #2421C22semidirect
73. #2421C22semidirect
78. #2351C22semidirect
79. #2351C22semidirect
81. #2341C22semidirect
82. #2341C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2100C22semidirect
92. #2099C22semidirect
93. #2095C22semidirect
94. #2093C22semidirect
95. #2083C22semidirect
96. #2083C22semidirect
97. #2076C22semidirect
98. #2076C22semidirect
101. #2071C22semidirect
102. #2071C22semidirect
103. #2068C22semidirect
104. #2068C22semidirect
115. #2024C22semidirect
116. #2023C22semidirect
121. #1993C22semidirect
122. #1983C22semidirect
127. #1959C22semidirect
128. #1940C22semidirect
131. #1936C22semidirect
132. #1936C22semidirect
135. #1925C22semidirect
136. #1925C22semidirect
137. #1924C22semidirect
138. #1923C22semidirect
139. #1921C22semidirect
140. #1921C22semidirect
141. #1918C22semidirect
142. #1918C22semidirect
143. #1917C22semidirect
144. #1916C22semidirect
147. #1894C22semidirect
167. #1872C22semidirect
169. #1863C22semidirect
170. #1863C22semidirect
172. #1852C22semidirect
173. #1851C22semidirect
175. #1836C22semidirect
178. #1824C22semidirect
183. #1803C22semidirect
184. #1803C22semidirect
185. #1803C22semidirect
186. #1803C22semidirect
187. #1803C22semidirect
188. #1803C22semidirect
189. #1788C22semidirect
193. #1771C22semidirect
194. #1763C22semidirect
195. C4×#103C22semidirect
196. C4×#103C22semidirect
197. C4×#103C22semidirect
198. C4×#103C22semidirect
199. #1753C22semidirect
1179. Q8#551semidirect

Maximal subgroups

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

subgroupindex
#592732
#365782
#319602
#319282
#316562
#315632
#289982
#288912
#281042
#278562
#277112
#275782
#275592
#272312
#271972
#266592
#259632
#249392
#249162
#248272
#245422
#245312
#245002
#238582
#229022
#228632
#227812
#224372
#224212
C2×#18802
#207342