Finite Group Databasebeta

← #7033678

Subgroups — #7033678

Order 512.

1665 conjugacy classes of subgroups.

The subgroup lattice has 1416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44887C211yesmaximal, characteristic, complemented
2#42447C211yesmaximal, characteristic, complemented
3#32206C211yesmaximal, characteristic, complemented
4#31769C211yesmaximal, characteristic, complemented
5#31680C211yesmaximal, characteristic, complemented
6#31550C211yesmaximal, characteristic, complemented
7#31423C211yesmaximal, characteristic, complemented
8#31406C211yesmaximal, characteristic, complemented
9#31349C211yesmaximal, characteristic, complemented
10#30416C211yesmaximal, characteristic, complemented
11#28999C211yesmaximal, characteristic, complemented
12#28861C211yesmaximal, characteristic, complemented
13#28557C211yesmaximal, characteristic, complemented
14#27712C211yesmaximal, characteristic, complemented
15#27539C211yesmaximal, characteristic, complemented
16#27222C211yesmaximal, characteristic, complemented
17#26352C211yesmaximal, characteristic, complemented
18#26198C211yesmaximal, characteristic, complemented
19#25538C211yesmaximal, characteristic, complemented
20#25350C211yesmaximal, characteristic, complemented
21#25218C211yesmaximal, characteristic, complemented
22#24978C211yesmaximal, characteristic, complemented
23#24964C211yesmaximal, characteristic, complemented
24#24792C211yesmaximal, characteristic, complemented
25#24565C211yesmaximal, characteristic, complemented
26#24390C211yesmaximal, characteristic, complemented
27#23643C211yesmaximal, characteristic, complemented
28#23132C211yesmaximal, characteristic, complemented
29#22849C211yesmaximal, characteristic, complemented
30#22503C211yesmaximal, characteristic, complemented
31#21770C211yesmaximal, characteristic, complemented
32C2×#555C2211yescharacteristic
33C2×#535C2211yescharacteristic
34C2×#482C2211yescharacteristic, complemented
35C2×#474C2211yescharacteristic
36C2×#469C2211yescharacteristic
37C2×#469C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#436C2211yescharacteristic, complemented
41C2×#435C2211yescharacteristic, complemented
42C2×#428C2211yescharacteristic, complemented
43C2×#408C2211yescharacteristic
44C2×#408C2211yescharacteristic
45#2824—21no—
46#2804—21no—
47#2775—21no—
48#2714—21no—
49#2712—21no—
50#2710—21no—
51#2684—21no—
52#2673—21no—
53#2670—21no—
54#2636—21no—
55#2631—21no—
56#2615C2211yescharacteristic
57#2563C2211yescharacteristic, complemented
58#2544—21no—
59#2535C2211yescharacteristic
60#2535C2211yescharacteristic
61#2500C2211yescharacteristic
62#2496C2211yescharacteristic
63#2495C2211yescharacteristic, complemented
64#2491C2211yescharacteristic
65#2491C2211yescharacteristic
66#2487C2211yescharacteristic
67#2474—21no—
68#2456—21no—
69#2439C2211yescharacteristic
70#2439C2211yescharacteristic, complemented
71#2424—21no—
72#2422C2211yescharacteristic
73#2422C2211yescharacteristic, complemented
74#2416C2211yescharacteristic
75#2416C2211yescharacteristic, complemented
76#2414C2211yescharacteristic
77#2414C2211yescharacteristic, complemented
78#2411—21no—
79#2408C2211yescharacteristic
80#2388C2211yescharacteristic
81#2361C2211yescharacteristic
82#2361C2211yescharacteristic, complemented
83#2354C2211yescharacteristic
84D4×C4⋊C4C2211yescharacteristic, complemented
85D4×C22⋊C4C2211yescharacteristic
86#2311C2211yescharacteristic
87#2311C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic
101#2076C2211yescharacteristic, complemented
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic, complemented
104#2075C2211yescharacteristic, complemented
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic, complemented
107#2071C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic, complemented
111#2065C2211yescharacteristic
112#2057C2211yescharacteristic, complemented
113#2057C2211yescharacteristic, complemented
114#2054C2211yescharacteristic
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic, complemented
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic, complemented
125#1999C2211yescharacteristic
126#1999C2211yescharacteristic
127#1999C2211yescharacteristic
128#1993C2211yescharacteristic, complemented
129#1990C2211yescharacteristic, complemented
130#1987C2211yescharacteristic, complemented
131#1970C2211yescharacteristic
132#1955C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1949C2211yescharacteristic, complemented
135#1941C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic, complemented
140#1926C2211yescharacteristic
141#1925C2211yescharacteristic
142#1924C2211yescharacteristic
143#1923C2211yescharacteristic
144#1921C2211yescharacteristic, complemented
145#1921C2211yescharacteristic, complemented
146#1921C2211yescharacteristic, complemented
147#1918C2211yescharacteristic, complemented
148#1895C2211yescharacteristic
149#1895C2211yescharacteristic
150#1895C2211yescharacteristic
151#1895C2211yescharacteristic
152#1895C2211yescharacteristic, complemented
153#1893C2211yescharacteristic
154#1893C2211yescharacteristic
155#1893C2211yescharacteristic
156#1893C2211yescharacteristic, complemented
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1875C2211yescharacteristic
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic, complemented
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1874C2211yescharacteristic
168#1874C2211yescharacteristic
169#1874C2211yescharacteristic, complemented
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic, complemented
172#1869C2211yescharacteristic, complemented
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic, complemented
177#1852C2211yescharacteristic, complemented
178#1851C2211yescharacteristic, complemented
179#1850C2211yescharacteristic, complemented
180#1836C2211yescharacteristic, complemented
181#1825C2211yescharacteristic
182#1825C2211yescharacteristic
183#1825C2211yescharacteristic, complemented
184#1825C2211yescharacteristic, complemented
185#1823C2211yescharacteristic, complemented
186#1809C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1808C2211yescharacteristic, complemented
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic, complemented
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197#1753C2211yescharacteristic, complemented
198#1752C2211yescharacteristic, complemented
199#1736C2211yescharacteristic, complemented
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#555—24no—
213#555—42no—
214#535—24no—
215#535—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127—21no—
219C2×#126—21no—
220C2×#124—21no—
221C2×#124—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124—21no—
225C2×#123—21no—
226C2×#123—21no—
227C2×#121—21no—
228C2×#121—21no—
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×#120—21no—
242C2×#120—21no—
243C2×C4×D4—21no—
244C2×C4×D4—21no—
245C2×C4×D4—21no—
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C22⋊C4—21no—
261#482—42no—
262#474—42no—
263#469—42no—
264#469—42no—
265#466—24no—
266#447—42no—
267#436—42no—
268#435—42no—
269#428—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303#408—42no—
304#408—42no—
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319#400—21no—
320#400—21no—
321#400—21no—
322#399—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#395D411yescharacteristic
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#394—21no—
345#394D411yescharacteristic
346#394D411yescharacteristic
347#394D411yescharacteristic
348#393—21no—
349#393—21no—
350#393—21no—
351#393—21no—
352#393—21no—
353#393—21no—
354#393—21no—
355#393D411yescharacteristic
356#392—21no—
357#392—21no—
358#392—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#392—21no—
363#392—21no—
364#392D411yescharacteristic
365#392D411yescharacteristic
366#392D411yescharacteristic
367#391—21no—
368#391—21no—
369#391—21no—
370#391—21no—
371#390—21no—
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#389—21no—
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#388—21no—
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#387—21no—
402#387—21no—
403#387—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—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#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#383—21no—
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#380C2311yescharacteristic
433#380C2311yescharacteristic
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#379—21no—
447#379—21no—
448C4×C4⋊C4—21no—
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4C2311yescharacteristic
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
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#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
493C25—21no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8C2×D411yescharacteristic
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4C2×D411yescharacteristic
521C22×D4C2×D411yescharacteristic
522C22×D4C2×D411yescharacteristic
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×C4C2411yescharacteristic
536C23×C4C2411yescharacteristic
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
539C2×D8—22no—
540C2×D8—22no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×M16—22no—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16—41no—
549C2×M16—41no—
550C2×M16—41no—
551C2×M16—41no—
552C2×M16—41no—
553C2×M16—41no—
554C22×C8—22no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—41no—
558C22×C8—41no—
559C22×C8—41no—
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C4⋊Q8—22no—
569C4⋊Q8—41no—
570C4⋊Q8—41no—
571C4⋊Q8—41no—
572#127—44no—
573#126—82no—
574#124—44no—
575#124—44no—
576#124—44no—
577#124—82no—
578#124—82no—
579#123—82no—
580#123—82no—
581#121—22no—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—41no—
590#121—41no—
591#121—41no—
592#121—44no—
593#121—41no—
594#121—41no—
595#121—41no—
596#121—41no—
597#121—41no—
598#121—41no—
599#121—41no—
600#121—41no—
601#121—82no—
602#121—82no—
603#121#4114yes—
604#120—44no—
605#120—44no—
606#120—82no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—41no—
611C4×D4—41no—
612C4×D4—41no—
613C4×D4—41no—
614C4×D4—41no—
615C4×D4—41no—
616C4×D4—41no—
617C4×D4—41no—
618C4×D4—41no—
619C4×D4—82no—
620C4×D4—82no—
621C4×D4—82no—
622#117—22no—
623#117—22no—
624#117—22no—
625#117—22no—
626#117—44no—
627#117—41no—
628#117—41no—
629#117—41no—
630#117—41no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4—41no—
652C2×C4⋊C4C2×D411yescharacteristic
653C2×C4⋊C4C2×D411yescharacteristic
654C2×C4⋊C4C2×D411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C4⋊C4C2411yescharacteristic
659C2×C4⋊C4C2411yescharacteristic
660C2×C4⋊C4C2411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
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—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—82no—
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C42—21no—
725C2×C42—21no—
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42C2411yescharacteristic
732C2×C42C2411yescharacteristic
733C2×C42C2411yescharacteristic
734#107—22no—
735#107—22no—
736#107—41no—
737#107—41no—
738#107—41no—
739#107—41no—
740#106—22no—
741#106—41no—
742#106—41no—
743#106—41no—
744C4⋊C8—22no—
745C4⋊C8—41no—
746C4⋊C8—41no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763#102—41no—
764#102—41no—
765#102—41no—
766#102—41no—
767C22⋊C8—22no—
768C22⋊C8—22no—
769C22⋊C8—22no—
770C22⋊C8—22no—
771C22⋊C8—41no—
772C22⋊C8—41no—
773C22⋊C8—41no—
774C22⋊C8—41no—
775C22⋊C8—41no—
776C22⋊C8—41no—
777C22⋊C8—41no—
778#97—41no—
779#97—41no—
780C4×C8—41no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814C24—21no—
815C24—21no—
816C24—21no—
817C24—42no—
818C24—42no—
819C24—81no—
820C24—81no—
821C24—81no—
822C24—81no—
823C24—81no—
824C24C22×D411yescharacteristic
825C24C22×D411yescharacteristic
826C24C22×D411yescharacteristic
827C24C22×D411yescharacteristic
828#41—82no—
829#41—82no—
830#41—82no—
831#41—82no—
832C2×Q8—22no—
833C2×Q8—41no—
834C2×Q8—41no—
835C2×Q8—42no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×D4—22no—
842C2×D4—22no—
843C2×D4—24no—
844C2×D4—22no—
845C2×D4—22no—
846C2×D4—22no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—21no—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—41no—
865C2×D4—41no—
866C2×D4—41no—
867C2×D4—41no—
868C2×D4—41no—
869C2×D4—41no—
870C2×D4—41no—
871C2×D4—41no—
872C2×D4—41no—
873C2×D4—41no—
874C2×D4—41no—
875C2×D4—41no—
876C2×D4—41no—
877C2×D4—42no—
878C2×D4—42no—
879C2×D4—42no—
880C2×D4—42no—
881C2×D4—42no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—81no—
886C2×D4—82no—
887C2×D4—82no—
888C2×D4—82no—
889C2×D4—82no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
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×D4C2×#4112yes—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
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—21no—
938C22×C4—21no—
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—42no—
950C22×C4—42no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4—81no—
963C22×C4—81no—
964C22×C4—81no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C2×#4112yes—
978C22×C4H(5,𝔽2)12yes—
979C22×C4C2511yescharacteristic
980D8—82no—
981D8—82no—
982M16—44no—
983M16—82no—
984M16—82no—
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—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—82no—
1009C2×C8—82no—
1010C2×C8H(5,𝔽2)12yes—
1011C4⋊C4—22no—
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—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—81no—
1044C4⋊C4—81no—
1045C4⋊C4—81no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4C2×#4112yes—
1055C22⋊C4—22no—
1056C22⋊C4—24no—
1057C22⋊C4—22no—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—41no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
1066C22⋊C4—41no—
1067C22⋊C4—41no—
1068C22⋊C4—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—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
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—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—42no—
1117C42—42no—
1118C42—42no—
1119C42—42no—
1120C42—42no—
1121C42—42no—
1122C42—81no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—21no—
1130C23—21no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—22no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
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—84no—
1172C23—84no—
1173C23—162no—
1174C23—162no—
1175C23—162no—
1176C23—162no—
1177C23—162no—
1178C23#54612yes—
1179C23C23×D411yescharacteristic
1180Q8—82no—
1181Q8—162no—
1182Q8—162no—
1183D4—22no—
1184D4—22no—
1185D4—44no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—82no—
1197D4—82no—
1198D4—82no—
1199D4—84no—
1200D4—82no—
1201D4—82no—
1202D4—84no—
1203D4—84no—
1204D4—162no—
1205D4—162no—
1206D4—162no—
1207D4—162no—
1208D4—162no—
1209D4—162no—
1210D4—162no—
1211D4—162no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—22no—
1219C2×C4—22no—
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—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
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—41no—
1294C2×C4—41no—
1295C2×C4—84no—
1296C2×C4—162no—
1297C2×C4—162no—
1298C2×C4—162no—
1299C2×C4—162no—
1300C2×C4—162no—
1301C2×C4#54612yes—
1302C2×C4#57612yes—
1303C2×C4C22×#4111yescharacteristic
1304C2×C4C2×H(5,𝔽2)11yescharacteristic
1305C2×C4C2×H(5,𝔽2)11yescharacteristic
1306C2×C4#58511yescharacteristic
1307C2×C4#58511yescharacteristic
1308C2×C4#58511yescharacteristic
1309C8—22no—
1310C8—41no—
1311C8—41no—
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C22—22no—
1318C22—22no—
1319C22—22no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—42no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—42no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—41no—
1342C22—41no—
1343C22—41no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—42no—
1348C22—81no—
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—81no—
1362C22—81no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—168no—
1367C22C2×#54611yescharacteristic
1368C22#348511yescharacteristic
1369C22#349611yescharacteristic
1370C22C2×#57611yescharacteristic
1371C22#358511yescharacteristic
1372C22#358511yescharacteristic
1373C22#358611yescharacteristic
1374C4—22no—
1375C4—22no—
1376C4—41no—
1377C4—42no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4#351411yescharacteristic
1398C4#352111yescharacteristic
1399C4#353411yescharacteristic
1400C4#356011yescharacteristic
1401C2—42no—
1402C2—81no—
1403C2—81no—
1404C2—81no—
1405C2—82no—
1406C2—161no—
1407C2—161no—
1408C2#4348911yescharacteristic
1409C2#6119111yescharacteristic
1410C2#6121811yescharacteristic
1411C2#6178211yescharacteristic
1412C2#6180211yescharacteristic
1413C2#6229411yescharacteristic
1414C2#6234911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #44887C2semidirect
2. #42447C2semidirect
3. #32206C2semidirect
4. #31769C2semidirect
5. #31680C2semidirect
6. #31550C2semidirect
7. #31423C2semidirect
8. #31406C2semidirect
9. #31349C2semidirect
10. #30416C2semidirect
11. #28999C2semidirect
12. #28861C2semidirect
13. #28557C2semidirect
14. #27712C2semidirect
15. #27539C2semidirect
16. #27222C2semidirect
17. #26352C2semidirect
18. #26198C2semidirect
19. #25538C2semidirect
20. #25350C2semidirect
21. #25218C2semidirect
22. #24978C2semidirect
23. #24964C2semidirect
24. #24792C2semidirect
25. #24565C2semidirect
26. #24390C2semidirect
27. #23643C2semidirect
28. #23132C2semidirect
29. #22849C2semidirect
30. #22503C2semidirect
31. #21770C2semidirect
34. C2×#482C22semidirect
40. C2×#436C22semidirect
41. C2×#435C22semidirect
42. C2×#428C22semidirect
57. #2563C22semidirect
63. #2495C22semidirect
70. #2439C22semidirect
73. #2422C22semidirect
75. #2416C22semidirect
77. #2414C22semidirect
82. #2361C22semidirect
84. D4×C4⋊C4C22semidirect
88. #2101C22semidirect
89. #2099C22semidirect
90. #2099C22semidirect
92. #2088C22semidirect
93. #2084C22semidirect
97. #2077C22semidirect
98. #2077C22semidirect
101. #2076C22semidirect
103. #2075C22semidirect
104. #2075C22semidirect
106. #2073C22semidirect
110. #2067C22semidirect
112. #2057C22semidirect
113. #2057C22semidirect
116. #2034C22semidirect
124. #2023C22semidirect
128. #1993C22semidirect
129. #1990C22semidirect
130. #1987C22semidirect
133. #1949C22semidirect
134. #1949C22semidirect
135. #1941C22semidirect
139. #1936C22semidirect
144. #1921C22semidirect
145. #1921C22semidirect
146. #1921C22semidirect
147. #1918C22semidirect
152. #1895C22semidirect
156. #1893C22semidirect
164. #1875C22semidirect
169. #1874C22semidirect
171. #1870C22semidirect
172. #1869C22semidirect
176. #1854C22semidirect
177. #1852C22semidirect
178. #1851C22semidirect
179. #1850C22semidirect
180. #1836C22semidirect
183. #1825C22semidirect
184. #1825C22semidirect
185. #1823C22semidirect
186. #1809C22semidirect
187. #1809C22semidirect
188. #1808C22semidirect
190. #1802C22semidirect
195. #1762C22semidirect
197. #1753C22semidirect
198. #1752C22semidirect
199. #1736C22semidirect
200. #1736C22semidirect
201. #1735C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#448872
#424472
#322062
#317692
#316802
#315502
#314232
#314062
#313492
#304162
#289992
#288612
#285572
#277122
#275392
#272222
#263522
#261982
#255382
#253502
#252182
#249782
#249642
#247922
#245652
#243902
#236432
#231322
#228492
#225032
#217702