Finite Group Databasebeta

← #7195323

Subgroups — #7195323

Order 512.

1766 conjugacy classes of subgroups.

The subgroup lattice has 1411 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59229C211yesmaximal, characteristic, complemented
2#59044C211yesmaximal, characteristic, complemented
3#32015C211yesmaximal, characteristic, complemented
4#32005C211yesmaximal, characteristic, complemented
5#31676C211yesmaximal, characteristic, complemented
6#31670C211yesmaximal, characteristic, complemented
7#31560C211yesmaximal, characteristic, complemented
8#31555C211yesmaximal, characteristic, complemented
9#31379C211yesmaximal, characteristic, complemented
10#31353C211yesmaximal, characteristic, complemented
11#27825C211yesmaximal, characteristic, complemented
12#27679C211yesmaximal, characteristic, complemented
13#26476C211yesmaximal, characteristic, complemented
14#26311C211yesmaximal, characteristic, complemented
15#25974C211yesmaximal, characteristic, complemented
16#25951C211yesmaximal, characteristic, complemented
17#25355C211yesmaximal, characteristic, complemented
18#24912C211yesmaximal, characteristic, complemented
19#24897C211yesmaximal, characteristic, complemented
20#24823C211yesmaximal, characteristic, complemented
21#24257C211yesmaximal, characteristic, complemented
22#24158C211yesmaximal, characteristic, complemented
23#24133C211yesmaximal, characteristic, complemented
24#24117C211yesmaximal, characteristic, complemented
25#23976C211yesmaximal, characteristic, complemented
26#23965C211yesmaximal, characteristic, complemented
27#23708C211yesmaximal, characteristic, complemented
28#23011C211yesmaximal, characteristic, complemented
29#22424C211yesmaximal, characteristic, complemented
30#22143C211yesmaximal, characteristic, complemented
31#21868C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#555C2211yescharacteristic, complemented
34C2×#546C2211yescharacteristic
35C2×#529C2211yescharacteristic
36C2×#475C2211yescharacteristic, complemented
37C2×#478C2211yescharacteristic, complemented
38C2×#476C2211yescharacteristic
39C2×#463C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#447C2211yescharacteristic
42C2×#442C2211yescharacteristic
43C2×#440C2211yescharacteristic, complemented
44C2×C4×D8C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×#432C2211yescharacteristic, complemented
47C2×#418C2211yescharacteristic
48C2×#416C2211yescharacteristic
49#2695—21no—
50#2686—21no—
51#2686—21no—
52#2685—21no—
53#2566C2211yescharacteristic
54#2562C2211yescharacteristic
55#2551C2211yescharacteristic, complemented
56#2547—21no—
57#2537C2211yescharacteristic
58#2537C2211yescharacteristic
59#2536C2211yescharacteristic
60#2491—21no—
61#2485C2211yescharacteristic
62#2485C2211yescharacteristic, complemented
63#2476—21no—
64#2474—21no—
65#2474—21no—
66#2464—21no—
67#2457—21no—
68#2439C2211yescharacteristic
69#2439C2211yescharacteristic, complemented
70#2424—21no—
71#2423C2211yescharacteristic
72#2420C2211yescharacteristic
73#2420C2211yescharacteristic
74#2420C2211yescharacteristic, complemented
75#2418—21no—
76#2416—21no—
77#2408C2211yescharacteristic
78#2407C2211yescharacteristic
79#2367C2211yescharacteristic
80#2354C2211yescharacteristic
81D4×C4⋊C4C2211yescharacteristic, complemented
82#2344—21no—
83#2342—21no—
84#2341C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86C4×#121C2211yescharacteristic
87C4×#121C2211yescharacteristic
88C4×#121C2211yescharacteristic, complemented
89#2285C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2100C2211yescharacteristic, complemented
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2088C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2077C2211yescharacteristic
100#2077C2211yescharacteristic, complemented
101#2076C2211yescharacteristic
102#2076C2211yescharacteristic, complemented
103#2075C2211yescharacteristic
104#2075C2211yescharacteristic, complemented
105#2075C2211yescharacteristic, complemented
106#2068C2211yescharacteristic, complemented
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic, complemented
110#2065C2211yescharacteristic
111#2065C2211yescharacteristic
112#2054C2211yescharacteristic
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2034C2211yescharacteristic, complemented
119#2034C2211yescharacteristic, complemented
120#2033C2211yescharacteristic
121#2024C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic, complemented
127#1999C2211yescharacteristic
128#1999C2211yescharacteristic
129#1999C2211yescharacteristic
130#1993C2211yescharacteristic, complemented
131#1992C2211yescharacteristic, complemented
132#1992C2211yescharacteristic, complemented
133#1990C2211yescharacteristic, complemented
134#1989C2211yescharacteristic, complemented
135#1983C2211yescharacteristic
136#1959C2211yescharacteristic
137#1959C2211yescharacteristic
138#1955C2211yescharacteristic
139#1955C2211yescharacteristic
140#1954C2211yescharacteristic, complemented
141#1948C2211yescharacteristic, complemented
142#1947C2211yescharacteristic, complemented
143#1940C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1934C2211yescharacteristic
147#1933C2211yescharacteristic, complemented
148#1924C2211yescharacteristic, complemented
149#1923C2211yescharacteristic
150#1895C2211yescharacteristic
151#1894C2211yescharacteristic
152#1893C2211yescharacteristic
153#1893C2211yescharacteristic, complemented
154#1880C2211yescharacteristic, complemented
155#1879C2211yescharacteristic
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1877C2211yescharacteristic, complemented
160#1875C2211yescharacteristic
161#1875C2211yescharacteristic
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic
165#1873C2211yescharacteristic
166#1873C2211yescharacteristic, complemented
167#1873C2211yescharacteristic, complemented
168#1870C2211yescharacteristic
169#1869C2211yescharacteristic, complemented
170#1865C2211yescharacteristic, complemented
171#1865C2211yescharacteristic, complemented
172#1864C2211yescharacteristic
173#1863C2211yescharacteristic, complemented
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic, complemented
178#1854C2211yescharacteristic, complemented
179#1854C2211yescharacteristic, complemented
180#1851C2211yescharacteristic
181#1850C2211yescharacteristic, complemented
182#1825C2211yescharacteristic
183#1825C2211yescharacteristic, complemented
184#1809C2211yescharacteristic
185#1807C2211yescharacteristic, complemented
186#1805C2211yescharacteristic, complemented
187#1805C2211yescharacteristic, complemented
188#1804C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic, complemented
194#1797C2211yescharacteristic, complemented
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1786C2211yescharacteristic
198#1786C2211yescharacteristic
199#1776C2211yescharacteristic, complemented
200#1771C2211yescharacteristic, complemented
201#1762C2211yescharacteristic
202#1762C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#555—42no—
211#555—42no—
212#555—42no—
213#555—42no—
214#546—24no—
215#546—42no—
216C2×C4⋊Q8—21no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×C4⋊Q8C2311yescharacteristic
219#529—24no—
220#529—42no—
221C2×#126—21no—
222C2×#125C2311yescharacteristic
223C2×#124—21no—
224C2×#124—21no—
225C2×#124—21no—
226C2×#124—21no—
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121D411yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×#120—21no—
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×#117—21no—
261C2×#117—21no—
262C2×#117—21no—
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C2×#117C2311yescharacteristic
267C22×C4⋊C4—21no—
268C22×C22⋊C4—21no—
269C22×C22⋊C4—21no—
270C22×C42C2311yescharacteristic
271#478—42no—
272#476—42no—
273#475—42no—
274#463—24no—
275#449—42no—
276#447—42no—
277#442—42no—
278#440—42no—
279C4×D8—42no—
280#435—42no—
281#432—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#107C2311yescharacteristic
285C2×#107C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×#106C2311yescharacteristic
288C2×#106C2311yescharacteristic
289C2×#106C2311yescharacteristic
290C2×#106C2311yescharacteristic
291C2×C4⋊C8C2311yescharacteristic
292C2×C4⋊C8C2311yescharacteristic
293C2×C4⋊C8C2311yescharacteristic
294C2×C4⋊C8C2311yescharacteristic
295C2×C4⋊C8C2311yescharacteristic
296C2×C4⋊C8C2311yescharacteristic
297#418—42no—
298#416—42no—
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×#102C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×#97C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×#97C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339#400—21no—
340#399—21no—
341#398—21no—
342#398—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#397—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#393—21no—
368#393—21no—
369#392—21no—
370#392—21no—
371#391—21no—
372#391—21no—
373#391C2311yescharacteristic
374#390—21no—
375#390—21no—
376#390—21no—
377#390D411yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#389—21no—
384#389D411yescharacteristic
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#388D411yescharacteristic
405#388D411yescharacteristic
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#386D411yescharacteristic
420#386D411yescharacteristic
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#381—21no—
434#381—21no—
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442#380D411yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455C4×C4⋊C4—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4—21no—
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
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#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8—21no—
508C22×Q8C2411yescharacteristic
509C22×D4—21no—
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2×D411yescharacteristic
524C22×D4C2×D411yescharacteristic
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
540C23×C4C2411yescharacteristic
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—41no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—22no—
547C2×D8—22no—
548C2×D8—41no—
549C2×D8—41no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C22×C8—41no—
554C22×C8—41no—
555C22×C8—41no—
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C4⋊Q8—22no—
565C4⋊Q8—22no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568C4⋊Q8—82no—
569#126—44no—
570#125—22no—
571#125—22no—
572#124—22no—
573#124—44no—
574#124—44no—
575#124—44no—
576#124—44no—
577#124#4114yes—
578#123—44no—
579#123—44no—
580C22⋊Q8—22no—
581C22⋊Q8—22no—
582C22⋊Q8—41no—
583C22⋊Q8—41no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—44no—
592#121—42no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—44no—
599#121—44no—
600#121—82no—
601#121—82no—
602#120—44no—
603#120—82no—
604C4×Q8—22no—
605C4×Q8—41no—
606C4×Q8—41no—
607C4×Q8—41no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C4×D4—22no—
612C4×D4—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—41no—
625C4×D4—41no—
626C4×D4—44no—
627C4×D4—82no—
628C4×D4—82no—
629#117—22no—
630#117—22no—
631#117—44no—
632#117—44no—
633#117—44no—
634#117—41no—
635#117—41no—
636#117—41no—
637#117—41no—
638#117—41no—
639#117—41no—
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—21no—
660C2×C4⋊C4—44no—
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2×D411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
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—21no—
718C2×C22⋊C4—44no—
719C2×C22⋊C4—44no—
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×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C42—22no—
731C2×C42—22no—
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×C42C2×D411yescharacteristic
741C2×C42C2×D411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746#107—41no—
747#107—41no—
748#107—41no—
749#107—41no—
750#106—22no—
751#106—41no—
752#106—41no—
753#106—41no—
754#106—41no—
755C4⋊C8—22no—
756C4⋊C8—22no—
757C4⋊C8—41no—
758C4⋊C8—41no—
759C4⋊C8—41no—
760C4⋊C8—41no—
761#103—22no—
762#103—22no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#103—41no—
768#102—22no—
769#102—22no—
770#102—22no—
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—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796C22⋊C8—41no—
797#97—22no—
798#97—22no—
799#97—41no—
800C4×C8—41no—
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#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833C24—21no—
834C24—21no—
835C24—21no—
836C24—42no—
837C24—42no—
838C24—42no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24C22×D411yescharacteristic
844C24C22×D411yescharacteristic
845C24C22×D411yescharacteristic
846#41—44no—
847#41—82no—
848#41—82no—
849#41—82no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—42no—
856C2×Q8—42no—
857C2×Q8—81no—
858C2×Q8—81no—
859C2×Q8—81no—
860C2×Q8—81no—
861C2×Q8C2×#4112yes—
862C2×D4—24no—
863C2×D4—22no—
864C2×D4—22no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
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—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—41no—
884C2×D4—41no—
885C2×D4—41no—
886C2×D4—41no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—42no—
890C2×D4—44no—
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—81no—
900C2×D4—82no—
901C2×D4—82no—
902C2×D4—82no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4C2×#4112yes—
915C2×D4H(5,𝔽2)12yes—
916C2×D42−1+412yes—
917C22×C4—21no—
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—21no—
936C22×C4—21no—
937C22×C4—22no—
938C22×C4—22no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—41no—
951C22×C4—41no—
952C22×C4—41no—
953C22×C4—41no—
954C22×C4—42no—
955C22×C4—42no—
956C22×C4—42no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C22×D411yescharacteristic
984C22×C4C22×D411yescharacteristic
985C22×C4C22×D411yescharacteristic
986C22×C4C2511yescharacteristic
987SD16—44no—
988D8—44no—
989D8—44no—
990M16—82no—
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—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—82no—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
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—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—41no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4H(5,𝔽2)12yes—
1065C22⋊C4—24no—
1066C22⋊C4—24no—
1067C22⋊C4—24no—
1068C22⋊C4—22no—
1069C22⋊C4—22no—
1070C22⋊C4—22no—
1071C22⋊C4—41no—
1072C22⋊C4—41no—
1073C22⋊C4—41no—
1074C22⋊C4—41no—
1075C22⋊C4—41no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
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—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C42—22no—
1116C42—22no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—42no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42—81no—
1130C42—81no—
1131C42C2×#4112yes—
1132C42H(5,𝔽2)12yes—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—22no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—22no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—22no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—41no—
1158C23—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—84no—
1176C23—84no—
1177C23—84no—
1178C23—162no—
1179C23—162no—
1180C23—162no—
1181C23—162no—
1182C23C23×D411yescharacteristic
1183Q8—22no—
1184Q8—22no—
1185Q8—41no—
1186Q8—41no—
1187Q8—162no—
1188Q8—162no—
1189D4—22no—
1190D4—22no—
1191D4—22no—
1192D4—22no—
1193D4—22no—
1194D4—22no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—82no—
1202D4—82no—
1203D4—84no—
1204D4—82no—
1205D4—84no—
1206D4—84no—
1207D4—84no—
1208D4—84no—
1209D4—162no—
1210D4—162no—
1211D4—162no—
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—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—22no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—22no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
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—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—82no—
1294C2×C4—82no—
1295C2×C4—84no—
1296C2×C4—84no—
1297C2×C4—84no—
1298C2×C4—84no—
1299C2×C4—84no—
1300C2×C4—162no—
1301C2×C4—162no—
1302C2×C4#54612yes—
1303C2×C4#54612yes—
1304C2×C4#57512yes—
1305C2×C4C22×#4111yescharacteristic
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4C2×2−1+411yescharacteristic
1310C2×C4#58511yescharacteristic
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C22—41no—
1320C22—42no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—42no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—42no—
1331C22—42no—
1332C22—42no—
1333C22—42no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—42no—
1341C22—41no—
1342C22—42no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—42no—
1347C22—41no—
1348C22—41no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—168no—
1362C22C2×#54611yescharacteristic
1363C22#348411yescharacteristic
1364C22#348911yescharacteristic
1365C22C2×#57511yescharacteristic
1366C22#358411yescharacteristic
1367C22#358511yescharacteristic
1368C22#358511yescharacteristic
1369C4—22no—
1370C4—22no—
1371C4—22no—
1372C4—41no—
1373C4—41no—
1374C4—41no—
1375C4—41no—
1376C4—42no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—42no—
1382C4—81no—
1383C4—81no—
1384C4—81no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4#351311yescharacteristic
1394C4#352011yescharacteristic
1395C4#353611yescharacteristic
1396C4#354611yescharacteristic
1397C2—81no—
1398C2—81no—
1399C2—81no—
1400C2—82no—
1401C2—82no—
1402C2—82no—
1403C2#4535311yescharacteristic
1404C2#6116611yescharacteristic
1405C2#6119511yescharacteristic
1406C2#6157911yescharacteristic
1407C2#6167811yescharacteristic
1408C2#6214111yescharacteristic
1409C2#6223111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#121 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59229C2semidirect
2. #59044C2semidirect
3. #32015C2semidirect
4. #32005C2semidirect
5. #31676C2semidirect
6. #31670C2semidirect
7. #31560C2semidirect
8. #31555C2semidirect
9. #31379C2semidirect
10. #31353C2semidirect
11. #27825C2semidirect
12. #27679C2semidirect
13. #26476C2semidirect
14. #26311C2semidirect
15. #25974C2semidirect
16. #25951C2semidirect
17. #25355C2semidirect
18. #24912C2semidirect
19. #24897C2semidirect
20. #24823C2semidirect
21. #24257C2semidirect
22. #24158C2semidirect
23. #24133C2semidirect
24. #24117C2semidirect
25. #23976C2semidirect
26. #23965C2semidirect
27. #23708C2semidirect
28. #23011C2semidirect
29. #22424C2semidirect
30. #22143C2semidirect
31. #21868C2semidirect
33. C2×#555C22semidirect
36. C2×#475C22semidirect
37. C2×#478C22semidirect
43. C2×#440C22semidirect
46. C2×#432C22semidirect
55. #2551C22semidirect
62. #2485C22semidirect
69. #2439C22semidirect
74. #2420C22semidirect
81. D4×C4⋊C4C22semidirect
88. C4×#121C22semidirect
89. #2285C22semidirect
90. #2101C22semidirect
91. #2101C22semidirect
92. #2101C22semidirect
93. #2100C22semidirect
96. #2088C22semidirect
97. #2085C22semidirect
98. #2084C22semidirect
100. #2077C22semidirect
102. #2076C22semidirect
104. #2075C22semidirect
105. #2075C22semidirect
106. #2068C22semidirect
109. #2067C22semidirect
113. #2036C22semidirect
118. #2034C22semidirect
119. #2034C22semidirect
121. #2024C22semidirect
126. #2000C22semidirect
130. #1993C22semidirect
131. #1992C22semidirect
132. #1992C22semidirect
133. #1990C22semidirect
134. #1989C22semidirect
140. #1954C22semidirect
141. #1948C22semidirect
142. #1947C22semidirect
143. #1940C22semidirect
147. #1933C22semidirect
148. #1924C22semidirect
153. #1893C22semidirect
154. #1880C22semidirect
159. #1877C22semidirect
166. #1873C22semidirect
167. #1873C22semidirect
169. #1869C22semidirect
170. #1865C22semidirect
171. #1865C22semidirect
173. #1863C22semidirect
177. #1854C22semidirect
178. #1854C22semidirect
179. #1854C22semidirect
181. #1850C22semidirect
183. #1825C22semidirect
185. #1807C22semidirect
186. #1805C22semidirect
187. #1805C22semidirect
190. #1804C22semidirect
193. #1802C22semidirect
194. #1797C22semidirect
199. #1776C22semidirect
200. #1771C22semidirect
202. #1762C22semidirect

Maximal subgroups

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

subgroupindex
#592292
#590442
#320152
#320052
#316762
#316702
#315602
#315552
#313792
#313532
#278252
#276792
#264762
#263112
#259742
#259512
#253552
#249122
#248972
#248232
#242572
#241582
#241332
#241172
#239762
#239652
#237082
#230112
#224242
#221432
#218682