Finite Group Databasebeta

← #7105485

Subgroups — #7105485

Order 512.

1590 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59315C211yesmaximal, characteristic, complemented
2#39503C211yesmaximal, characteristic, complemented
3#32247C211yesmaximal, characteristic, complemented
4#32236C211yesmaximal, characteristic, complemented
5#31933C211yesmaximal, characteristic, complemented
6#31933C211yesmaximal, characteristic, complemented
7#31739C211yesmaximal, characteristic, complemented
8#31738C211yesmaximal, characteristic, complemented
9#31399C211yesmaximal, characteristic, complemented
10#31389C211yesmaximal, characteristic, complemented
11#29162C211yesmaximal, characteristic, complemented
12#28999C211yesmaximal, characteristic, complemented
13#28975C211yesmaximal, characteristic, complemented
14#28110C211yesmaximal, characteristic, complemented
15#28100C211yesmaximal, characteristic, complemented
16#27962C211yesmaximal, characteristic, complemented
17#27704C211yesmaximal, characteristic, complemented
18#27702C211yesmaximal, characteristic, complemented
19#27581C211yesmaximal, characteristic, complemented
20#27560C211yesmaximal, characteristic, complemented
21#26228C211yesmaximal, characteristic, complemented
22#26203C211yesmaximal, characteristic, complemented
23#24963C211yesmaximal, characteristic, complemented
24#24957C211yesmaximal, characteristic, complemented
25#23976C211yesmaximal, characteristic, complemented
26#23973C211yesmaximal, characteristic, complemented
27#23628C211yesmaximal, characteristic, complemented
28#23118C211yesmaximal, characteristic, complemented
29#22501C211yesmaximal, characteristic, complemented
30#22492C211yesmaximal, characteristic, complemented
31#22040C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#553C2211yescharacteristic
34C2×#447C2211yescharacteristic
35C2×#436C2211yescharacteristic
36C2×#435C2211yescharacteristic
37C2×#418C2211yescharacteristic
38C2×#418C2211yescharacteristic
39#2857C2211yescharacteristic
40#2808—21no—
41#2803—21no—
42#2803—21no—
43#2733—21no—
44#2717—21no—
45#2671—21no—
46#2617—21no—
47#2550C2211yescharacteristic, complemented
48#2535C2211yescharacteristic, complemented
49#2521—21no—
50#2513C2211yescharacteristic
51#2513C2211yescharacteristic
52#2500C2211yescharacteristic
53#2500C2211yescharacteristic
54#2491C2211yescharacteristic
55#2491C2211yescharacteristic
56#2485C2211yescharacteristic
57#2485C2211yescharacteristic
58#2478—21no—
59#2472—21no—
60#2472—21no—
61#2461—21no—
62#2441C2211yescharacteristic, complemented
63#2440C2211yescharacteristic, complemented
64#2427—21no—
65#2425—21no—
66#2422C2211yescharacteristic, complemented
67#2422C2211yescharacteristic, complemented
68#2414C2211yescharacteristic
69#2414C2211yescharacteristic
70#2408C2211yescharacteristic
71#2408C2211yescharacteristic
72#2359—21no—
73#2352C2211yescharacteristic
74#2352C2211yescharacteristic
75#2352C2211yescharacteristic, complemented
76#2349C2211yescharacteristic, complemented
77#2312—21no—
78C4×#121C2211yescharacteristic
79C4×#121C2211yescharacteristic
80C2×#390C2211yescharacteristic
81#2285C2211yescharacteristic
82#2101C2211yescharacteristic, complemented
83#2101C2211yescharacteristic, complemented
84#2101C2211yescharacteristic, complemented
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2094C2211yescharacteristic, complemented
90#2085C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2076C2211yescharacteristic, complemented
93#2076C2211yescharacteristic, complemented
94#2075C2211yescharacteristic, complemented
95#2075C2211yescharacteristic, complemented
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2057C2211yescharacteristic, complemented
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#2023C2211yescharacteristic, complemented
118#1999C2211yescharacteristic
119#1999C2211yescharacteristic
120#1999C2211yescharacteristic
121#1999C2211yescharacteristic
122#1993C2211yescharacteristic, complemented
123#1991C2211yescharacteristic, complemented
124#1990C2211yescharacteristic, complemented
125#1990C2211yescharacteristic, complemented
126#1989C2211yescharacteristic, complemented
127#1988C2211yescharacteristic, complemented
128#1970C2211yescharacteristic
129#1970C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1925C2211yescharacteristic
137#1925C2211yescharacteristic
138#1923C2211yescharacteristic, complemented
139#1923C2211yescharacteristic, complemented
140#1921C2211yescharacteristic, complemented
141#1921C2211yescharacteristic, complemented
142#1919C2211yescharacteristic, complemented
143#1919C2211yescharacteristic, complemented
144#1918C2211yescharacteristic, complemented
145#1918C2211yescharacteristic, complemented
146#1917C2211yescharacteristic, complemented
147#1916C2211yescharacteristic, complemented
148#1895C2211yescharacteristic
149#1895C2211yescharacteristic
150#1895C2211yescharacteristic
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic, complemented
153#1893C2211yescharacteristic
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic, complemented
156#1879C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic, complemented
165#1875C2211yescharacteristic, complemented
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic
168#1874C2211yescharacteristic
169#1870C2211yescharacteristic
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic, complemented
172#1869C2211yescharacteristic, complemented
173#1862C2211yescharacteristic, complemented
174#1862C2211yescharacteristic, complemented
175#1854C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1852C2211yescharacteristic
178#1834C2211yescharacteristic, complemented
179#1834C2211yescharacteristic, complemented
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1825C2211yescharacteristic
184#1825C2211yescharacteristic, complemented
185#1825C2211yescharacteristic, complemented
186#1825C2211yescharacteristic, complemented
187#1823C2211yescharacteristic, complemented
188#1809C2211yescharacteristic
189#1809C2211yescharacteristic
190#1804C2211yescharacteristic, complemented
191#1804C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193#1762C2211yescharacteristic, complemented
194C4×#102C2211yescharacteristic, complemented
195#1753C2211yescharacteristic, complemented
196C8×C22⋊C4C2211yescharacteristic, complemented
197C4×C22⋊C8C2211yescharacteristic
198#1736C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202#1728C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#555—24no—
211#555—42no—
212#553—24no—
213#553—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×#124—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121D411yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#120—21no—
238C2×#120—21no—
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117—21no—
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C2×#117C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C22×C4⋊C4C2311yescharacteristic
254C22×C4⋊C4C2311yescharacteristic
255C22×C22⋊C4—21no—
256C22×C22⋊C4—21no—
257C22×C42C2311yescharacteristic
258#447—24no—
259#436—42no—
260#435—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269#418—42no—
270#418—42no—
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#399—21no—
304#398—21no—
305#398—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#396—21no—
316#395—21no—
317#395—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#393—21no—
333#393—21no—
334#392—21no—
335#392—21no—
336#392—21no—
337#392—21no—
338#392—21no—
339#391—21no—
340#391—21no—
341#390—21no—
342#390—21no—
343#390—21no—
344#390—21no—
345#390D411yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#389—21no—
356#389—21no—
357#389—21no—
358#389D411yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388D411yescharacteristic
385#388D411yescharacteristic
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386D411yescharacteristic
399#386D411yescharacteristic
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#380—21no—
413#380—21no—
414#380—21no—
415#380—21no—
416#380D411yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#379—21no—
427#379—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C2×#95—21no—
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4C2×D411yescharacteristic
505C22×D4C2×D411yescharacteristic
506C22×D4C2×D411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4C2×D411yescharacteristic
516C23×C4C2×D411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×D8—22no—
521C2×D8—22no—
522C2×D8—41no—
523C2×D8—41no—
524C2×D8—41no—
525C2×D8—41no—
526C2×M16—22no—
527C2×M16—22no—
528C2×M16—41no—
529C2×M16—41no—
530C2×M16—41no—
531C2×M16—41no—
532C2×M16—41no—
533C2×M16—41no—
534C2×M16—41no—
535C22×C8—41no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—22no—
547C4⋊Q8—41no—
548C4⋊Q8—41no—
549C4⋊Q8—41no—
550#126—44no—
551#125—22no—
552#125—41no—
553#124—44no—
554#124—44no—
555#124—82no—
556#124—82no—
557#123—44no—
558#123—44no—
559#123—82no—
560C22⋊Q8—82no—
561C22⋊Q8—82no—
562#121—22no—
563#121—22no—
564#121—22no—
565#121—42no—
566#121—41no—
567#121—41no—
568#121—44no—
569#121—44no—
570#121—41no—
571#121—41no—
572#121—41no—
573#121—41no—
574#121—41no—
575#121—41no—
576#121—41no—
577#121—41no—
578#121#4114yes—
579#120—82no—
580#120—82no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—44no—
594C4×D4—82no—
595#117—22no—
596#117—22no—
597#117—22no—
598#117—22no—
599#117—22no—
600#117—44no—
601#117—41no—
602#117—41no—
603#117—41no—
604#117—41no—
605#117—41no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—41no—
627C2×C4⋊C4—41no—
628C2×C4⋊C4—41no—
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
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—44no—
690C2×C22⋊C4—82no—
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—41no—
710C2×C42—41no—
711C2×C42C2×D411yescharacteristic
712C2×C42C2×D411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#106—41no—
722#106—41no—
723C4⋊C8—41no—
724C4⋊C8—41no—
725#102—22no—
726#102—22no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752C22⋊C8—41no—
753#97—41no—
754C4×C8—41no—
755C4×C8—41no—
756C4×C8—41no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790C24—21no—
791C24—21no—
792C24—21no—
793C24—42no—
794C24—42no—
795C24—42no—
796C24—81no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24C22×D411yescharacteristic
801C24C22×D411yescharacteristic
802C24C22×D411yescharacteristic
803C2×Q8—42no—
804C2×Q8—42no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×D4—22no—
810C2×D4—22no—
811C2×D4—24no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—44no—
830C2×D4—44no—
831C2×D4—41no—
832C2×D4—41no—
833C2×D4—41no—
834C2×D4—41no—
835C2×D4—41no—
836C2×D4—41no—
837C2×D4—41no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—82no—
843C2×D4—82no—
844C2×D4—81no—
845C2×D4—81no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4C2×#4112yes—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—22no—
882C22×C4—22no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—41no—
896C22×C4—41no—
897C22×C4—41no—
898C22×C4—41no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4C22×D411yescharacteristic
915C22×C4C22×D411yescharacteristic
916C22×C4C22×D411yescharacteristic
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C2×#4112yes—
926C22×C4H(5,𝔽2)12yes—
927C22×C4C2511yescharacteristic
928D8—82no—
929D8—82no—
930M16—82no—
931M16—82no—
932M16—82no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—82no—
958C4⋊C4—22no—
959C4⋊C4—22no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—81no—
997C4⋊C4—81no—
998C4⋊C4—81no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4C2×#4112yes—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—24no—
1011C22⋊C4—22no—
1012C22⋊C4—22no—
1013C22⋊C4—22no—
1014C22⋊C4—22no—
1015C22⋊C4—22no—
1016C22⋊C4—22no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C42—21no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—41no—
1069C42—41no—
1070C42—42no—
1071C42—42no—
1072C42—42no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—84no—
1120C23—84no—
1121C23—84no—
1122C23—162no—
1123C23—162no—
1124C23—162no—
1125C23—162no—
1126C23#54612yes—
1127C23C23×D411yescharacteristic
1128Q8—162no—
1129Q8—162no—
1130D4—22no—
1131D4—22no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—84no—
1143D4—82no—
1144D4—82no—
1145D4—84no—
1146D4—82no—
1147D4—84no—
1148D4—162no—
1149D4—162no—
1150D4—162no—
1151D4—162no—
1152D4—162no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—82no—
1235C2×C4—82no—
1236C2×C4—84no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4#54612yes—
1242C2×C4#57512yes—
1243C2×C4#57612yes—
1244C2×C4C22×#4111yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C2×C4#58511yescharacteristic
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C22—22no—
1259C22—22no—
1260C22—22no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—42no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—42no—
1279C22—42no—
1280C22—41no—
1281C22—41no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—81no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—168no—
1301C22C2×#54611yescharacteristic
1302C22#348511yescharacteristic
1303C22#350011yescharacteristic
1304C22C2×#57511yescharacteristic
1305C22C2×#57611yescharacteristic
1306C22#358411yescharacteristic
1307C22#358511yescharacteristic
1308C4—22no—
1309C4—22no—
1310C4—22no—
1311C4—41no—
1312C4—41no—
1313C4—42no—
1314C4—41no—
1315C4—41no—
1316C4—41no—
1317C4—41no—
1318C4—41no—
1319C4—41no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4—81no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4#352111yescharacteristic
1333C4#352111yescharacteristic
1334C4#353311yescharacteristic
1335C4#353311yescharacteristic
1336C2—42no—
1337C2—81no—
1338C2—81no—
1339C2—82no—
1340C2—161no—
1341C2—161no—
1342C2#4445011yescharacteristic
1343C2#6116611yescharacteristic
1344C2#6121111yescharacteristic
1345C2#6174111yescharacteristic
1346C2#6175211yescharacteristic
1347C2#6254611yescharacteristic
1348C2#6261411yescharacteristic
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. #59315C2semidirect
2. #39503C2semidirect
3. #32247C2semidirect
4. #32236C2semidirect
5. #31933C2semidirect
6. #31933C2semidirect
7. #31739C2semidirect
8. #31738C2semidirect
9. #31399C2semidirect
10. #31389C2semidirect
11. #29162C2semidirect
12. #28999C2semidirect
13. #28975C2semidirect
14. #28110C2semidirect
15. #28100C2semidirect
16. #27962C2semidirect
17. #27704C2semidirect
18. #27702C2semidirect
19. #27581C2semidirect
20. #27560C2semidirect
21. #26228C2semidirect
22. #26203C2semidirect
23. #24963C2semidirect
24. #24957C2semidirect
25. #23976C2semidirect
26. #23973C2semidirect
27. #23628C2semidirect
28. #23118C2semidirect
29. #22501C2semidirect
30. #22492C2semidirect
31. #22040C2semidirect
47. #2550C22semidirect
48. #2535C22semidirect
62. #2441C22semidirect
63. #2440C22semidirect
66. #2422C22semidirect
67. #2422C22semidirect
75. #2352C22semidirect
76. #2349C22semidirect
82. #2101C22semidirect
83. #2101C22semidirect
84. #2101C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2100C22semidirect
89. #2094C22semidirect
90. #2085C22semidirect
91. #2085C22semidirect
92. #2076C22semidirect
93. #2076C22semidirect
94. #2075C22semidirect
95. #2075C22semidirect
108. #2057C22semidirect
117. #2023C22semidirect
122. #1993C22semidirect
123. #1991C22semidirect
124. #1990C22semidirect
125. #1990C22semidirect
126. #1989C22semidirect
127. #1988C22semidirect
138. #1923C22semidirect
139. #1923C22semidirect
140. #1921C22semidirect
141. #1921C22semidirect
142. #1919C22semidirect
143. #1919C22semidirect
144. #1918C22semidirect
145. #1918C22semidirect
146. #1917C22semidirect
147. #1916C22semidirect
152. #1895C22semidirect
155. #1893C22semidirect
164. #1875C22semidirect
165. #1875C22semidirect
171. #1870C22semidirect
172. #1869C22semidirect
173. #1862C22semidirect
174. #1862C22semidirect
175. #1854C22semidirect
176. #1854C22semidirect
178. #1834C22semidirect
179. #1834C22semidirect
184. #1825C22semidirect
185. #1825C22semidirect
186. #1825C22semidirect
187. #1823C22semidirect
190. #1804C22semidirect
191. #1804C22semidirect
193. #1762C22semidirect
194. C4×#102C22semidirect
195. #1753C22semidirect
196. C8×C22⋊C4C22semidirect
200. #1736C22semidirect
201. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#593152
#395032
#322472
#322362
#319332
#317392
#317382
#313992
#313892
#291622
#289992
#289752
#281102
#281002
#279622
#277042
#277022
#275812
#275602
#262282
#262032
#249632
#249572
#239762
#239732
#236282
#231182
#225012
#224922
#220402