Finite Group Databasebeta

← #7528951

Subgroups — #7528951

Order 512.

1719 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45050C211yesmaximal, characteristic, complemented
2#35741C211yesmaximal, characteristic, complemented
3#31290C211yesmaximal, characteristic, complemented
4#31286C211yesmaximal, characteristic, complemented
5#31000C211yesmaximal, characteristic, complemented
6#30984C211yesmaximal, characteristic, complemented
7#29015C211yesmaximal, characteristic, complemented
8#29011C211yesmaximal, characteristic, complemented
9#28276C211yesmaximal, characteristic, complemented
10#27903C211yesmaximal, characteristic, complemented
11#27747C211yesmaximal, characteristic, complemented
12#27211C211yesmaximal, characteristic, complemented
13#27190C211yesmaximal, characteristic, complemented
14#27056C211yesmaximal, characteristic, complemented
15#27039C211yesmaximal, characteristic, complemented
16#26771C211yesmaximal, characteristic, complemented
17#26755C211yesmaximal, characteristic, complemented
18#26669C211yesmaximal, characteristic, complemented
19#26668C211yesmaximal, characteristic, complemented
20#26102C211yesmaximal, characteristic, complemented
21#24999C211yesmaximal, characteristic, complemented
22#24744C211yesmaximal, characteristic, complemented
23#24662C211yesmaximal, characteristic, complemented
24#24184C211yesmaximal, characteristic, complemented
25#23099C211yesmaximal, characteristic, complemented
26#23093C211yesmaximal, characteristic, complemented
27#23057C211yesmaximal, characteristic, complemented
28#22772C211yesmaximal, characteristic, complemented
29#22545C211yesmaximal, characteristic, complemented
30#21458C211yesmaximal, characteristic, complemented
31#20744C211yesmaximal, characteristic, complemented
32C2×#550C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#459C2211yescharacteristic
35C2×#459C2211yescharacteristic
36C2×#459C2211yescharacteristic, complemented
37C2×#447C2211yescharacteristic
38C2×#446C2211yescharacteristic, complemented
39C2×#442C2211yescharacteristic
40C2×C4×D8C2211yescharacteristic
41C2×#433C2211yescharacteristic
42#2747—21no—
43#2739—21no—
44#2707—21no—
45#2702—21no—
46#2635—21no—
47#2619C2211yescharacteristic
48#2601—21no—
49#2580C2211yescharacteristic
50#2552C2211yescharacteristic, complemented
51#2541C2211yescharacteristic
52#2539—21no—
53#2538C2211yescharacteristic, complemented
54#2509C2211yescharacteristic, complemented
55#2507C2211yescharacteristic, complemented
56#2498—21no—
57#2497C2211yescharacteristic
58#2496C2211yescharacteristic
59#2475—21no—
60#2464—21no—
61#2464—21no—
62#2445C2211yescharacteristic
63#2445C2211yescharacteristic
64#2438—21no—
65#2433C2211yescharacteristic
66#2433C2211yescharacteristic
67#2424—21no—
68#2424—21no—
69#2422C2211yescharacteristic
70#2420C2211yescharacteristic
71#2404—21no—
72#2396C2211yescharacteristic
73#2388—21no—
74#2366C2211yescharacteristic
75#2366C2211yescharacteristic
76#2363C2211yescharacteristic
77#2363C2211yescharacteristic
78#2357C2211yescharacteristic
79#2355C2211yescharacteristic, complemented
80#2354C2211yescharacteristic, complemented
81#2354C2211yescharacteristic, complemented
82#2349C2211yescharacteristic, complemented
83#2324C2211yescharacteristic
84#2314C2211yescharacteristic
85#2101C2211yescharacteristic, complemented
86#2100C2211yescharacteristic, complemented
87#2094C2211yescharacteristic
88#2093C2211yescharacteristic
89#2073C2211yescharacteristic
90#2071C2211yescharacteristic
91#2071C2211yescharacteristic, complemented
92#2071C2211yescharacteristic, complemented
93#2067C2211yescharacteristic
94#2067C2211yescharacteristic
95#2067C2211yescharacteristic, complemented
96#2065C2211yescharacteristic
97#2065C2211yescharacteristic
98#2065C2211yescharacteristic, complemented
99#2065C2211yescharacteristic, complemented
100#2065C2211yescharacteristic, complemented
101#2041C2211yescharacteristic
102#2041C2211yescharacteristic
103#2041C2211yescharacteristic
104#2041C2211yescharacteristic
105#2041C2211yescharacteristic
106#2041C2211yescharacteristic
107#2034C2211yescharacteristic
108#2034C2211yescharacteristic
109#2034C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2033C2211yescharacteristic
113#2011C2211yescharacteristic
114#2011C2211yescharacteristic
115#1999C2211yescharacteristic
116#1999C2211yescharacteristic
117#1984C2211yescharacteristic, complemented
118#1982C2211yescharacteristic
119#1982C2211yescharacteristic
120#1982C2211yescharacteristic, complemented
121#1972C2211yescharacteristic
122#1972C2211yescharacteristic, complemented
123#1970C2211yescharacteristic
124#1970C2211yescharacteristic, complemented
125#1961C2211yescharacteristic
126#1961C2211yescharacteristic, complemented
127#1957C2211yescharacteristic
128#1957C2211yescharacteristic
129#1957C2211yescharacteristic
130#1957C2211yescharacteristic, complemented
131#1949C2211yescharacteristic, complemented
132#1948C2211yescharacteristic, complemented
133#1947C2211yescharacteristic, complemented
134#1943C2211yescharacteristic, complemented
135#1941C2211yescharacteristic, complemented
136#1940C2211yescharacteristic, complemented
137#1936C2211yescharacteristic, complemented
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic, complemented
141#1934C2211yescharacteristic, complemented
142#1934C2211yescharacteristic, complemented
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic, complemented
145#1926C2211yescharacteristic, complemented
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic, complemented
148#1925C2211yescharacteristic, complemented
149#1924C2211yescharacteristic
150#1923C2211yescharacteristic
151#1923C2211yescharacteristic
152#1923C2211yescharacteristic
153#1921C2211yescharacteristic, complemented
154#1921C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1917C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic, complemented
166#1879C2211yescharacteristic, complemented
167#1879C2211yescharacteristic, complemented
168#1879C2211yescharacteristic, complemented
169#1875C2211yescharacteristic
170#1864C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic, complemented
173#1862C2211yescharacteristic, complemented
174#1854C2211yescharacteristic
175#1847C2211yescharacteristic, complemented
176#1835C2211yescharacteristic, complemented
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1804C2211yescharacteristic
180#1804C2211yescharacteristic
181#1804C2211yescharacteristic, complemented
182#1804C2211yescharacteristic, complemented
183#1802C2211yescharacteristic
184#1802C2211yescharacteristic
185#1802C2211yescharacteristic, complemented
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1770C2211yescharacteristic, complemented
190C8×C4⋊C4C2211yescharacteristic, complemented
191C8×C4⋊C4C2211yescharacteristic, complemented
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C22×#41—21no—
204C23×D4C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209#550—24no—
210#550—42no—
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#127C2311yescharacteristic
216C2×#126—21no—
217C2×#125—21no—
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×C22⋊Q8—21no—
222C2×#121—21no—
223C2×#121—21no—
224C2×#121—21no—
225C2×#121—21no—
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120—21no—
232C2×#120—21no—
233C2×#120—21no—
234#518—24no—
235#518—42no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—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×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×#117—21no—
251C2×#117—21no—
252C2×#117C2311yescharacteristic
253C2×#117C2311yescharacteristic
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256#459—24no—
257#459—24no—
258#459—42no—
259#447—24no—
260#446—42no—
261#442—42no—
262C4×D8—24no—
263#433—42no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×C4⋊C8C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
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×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319C2×C4×C8C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322#400—21no—
323#400—21no—
324#400—21no—
325#400—21no—
326#400D411yescharacteristic
327#399—21no—
328#399D411yescharacteristic
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398D411yescharacteristic
334#398D411yescharacteristic
335#397—21no—
336#397—21no—
337#397—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396D411yescharacteristic
342#396D411yescharacteristic
343#395D411yescharacteristic
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#393—21no—
353#393D411yescharacteristic
354#392—21no—
355#392—21no—
356#392—21no—
357#392—21no—
358#392—21no—
359#392—21no—
360#392—21no—
361#392—21no—
362#391—21no—
363#390—21no—
364#390—21no—
365#390—21no—
366#390—21no—
367#390—21no—
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#389—21no—
380#389—21no—
381#389—21no—
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
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#387—21no—
404#387—21no—
405#387—21no—
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#386—21no—
420#386—21no—
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#384C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#381—21no—
435#381—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C2×#95—21no—
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C2×#41—44no—
492C2×#41—82no—
493C2×#41—82no—
494C22×Q8C2×D411yescharacteristic
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—41no—
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530C2×D8—22no—
531C2×D8—22no—
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8—41no—
540C2×D8—41no—
541C2×D8#4114yescomplemented
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550#127—22no—
551#127—22no—
552#127—22no—
553#127—22no—
554#127—22no—
555#127—22no—
556#127—41no—
557#127—41no—
558#127—41no—
559#127—41no—
560#126—82no—
561#125—82no—
562#123—82no—
563#123—82no—
564#123—82no—
565C22⋊Q8—82no—
566#121—22no—
567#121—44no—
568#121—44no—
569#121—41no—
570#121—41no—
571#121—41no—
572#121—41no—
573#121—41no—
574#121—44no—
575#121—82no—
576#121—82no—
577#120—82no—
578#120—82no—
579#120—82no—
580#120—82no—
581C4×Q8—22no—
582C4×Q8—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—22no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—44no—
601C4×D4—44no—
602C4×D4—82no—
603C4×D4—82no—
604C4×D4#4114yes—
605#117—22no—
606#117—22no—
607#117—22no—
608#117—41no—
609#117—82no—
610#117—82no—
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—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
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—44no—
689C2×C22⋊C4—44no—
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710#107—22no—
711#107—41no—
712#107—41no—
713#107—41no—
714#106—41no—
715#106—41no—
716#106—41no—
717#106—41no—
718C4⋊C8—22no—
719C4⋊C8—22no—
720C4⋊C8—22no—
721C4⋊C8—22no—
722C4⋊C8—41no—
723C4⋊C8—41no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
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—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756C22⋊C8—22no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760#97—22no—
761#97—41no—
762#97—41no—
763C4×C8—22no—
764C4×C8—41no—
765C4×C8—41no—
766C4×C8—41no—
767C4×C8—41no—
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#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#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24C22×D411yescharacteristic
816#41—816no—
817C2×Q8—22no—
818C2×Q8—22no—
819C2×Q8—41no—
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—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—42no—
853C2×D4—42no—
854C2×D4—42no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—44no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—42no—
869C2×D4—42no—
870C2×D4—42no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4C2×#4112yes—
894C2×D4C2×#4112yes—
895C2×D4C2×#4112yes—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—24no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—42no—
920C22×C4—42no—
921C22×C4—42no—
922C22×C4—42no—
923C22×C4—42no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4—81no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C2511yescharacteristic
954D8—44no—
955D8—44no—
956D8—82no—
957D8—82no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8C2×#4112yes—
982C4⋊C4—22no—
983C4⋊C4—22no—
984C4⋊C4—22no—
985C4⋊C4—22no—
986C4⋊C4—22no—
987C4⋊C4—22no—
988C4⋊C4—22no—
989C4⋊C4—22no—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—41no—
1014C4⋊C4—42no—
1015C4⋊C4—42no—
1016C4⋊C4—42no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4C2×#4112yes—
1032C22⋊C4—24no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—41no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—42no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—21no—
1081C42—21no—
1082C42—21no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—42no—
1087C42—42no—
1088C42—81no—
1089C42—81no—
1090C42—81no—
1091C42—81no—
1092C42—81no—
1093C42—81no—
1094C42C2×#4112yes—
1095C42H(5,𝔽2)12yes—
1096C23—21no—
1097C23—21no—
1098C23—22no—
1099C23—22no—
1100C23—21no—
1101C23—22no—
1102C23—21no—
1103C23—21no—
1104C23—21no—
1105C23—21no—
1106C23—48no—
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—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—162no—
1140C23—162no—
1141C23—162no—
1142C23—162no—
1143C23—162no—
1144C23—162no—
1145C23C23×D411yescharacteristic
1146Q8—44no—
1147D4—22no—
1148D4—22no—
1149D4—22no—
1150D4—22no—
1151D4—22no—
1152D4—22no—
1153D4—48no—
1154D4—41no—
1155D4—41no—
1156D4—41no—
1157D4—41no—
1158D4—41no—
1159D4—41no—
1160D4—41no—
1161D4—41no—
1162D4—41no—
1163D4—41no—
1164D4—41no—
1165D4—41no—
1166D4—41no—
1167D4—41no—
1168D4—84no—
1169D4—84no—
1170D4—84no—
1171D4—84no—
1172D4—84no—
1173D4—162no—
1174D4—162no—
1175D4—162no—
1176D4—162no—
1177D4—162no—
1178D4—162no—
1179D4—162no—
1180D4—162no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—22no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
1206C2×C4—21no—
1207C2×C4—21no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
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—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—84no—
1253C2×C4—84no—
1254C2×C4—84no—
1255C2×C4—84no—
1256C2×C4—84no—
1257C2×C4—162no—
1258C2×C4—162no—
1259C2×C4—162no—
1260C2×C4—162no—
1261C2×C4#54612yes—
1262C2×C4#54612yes—
1263C2×C4#57612yes—
1264C2×C4#57612yes—
1265C2×C4#57712yes—
1266C2×C4C22×#4111yescharacteristic
1267C2×C4C22×#4111yescharacteristic
1268C2×C4C2×H(5,𝔽2)11yescharacteristic
1269C2×C4#58511yescharacteristic
1270C2×C4#58511yescharacteristic
1271C2×C4#58511yescharacteristic
1272C8—22no—
1273C8—41no—
1274C8—41no—
1275C8—41no—
1276C8—41no—
1277C8—41no—
1278C8—41no—
1279C8—41no—
1280C22—42no—
1281C22—41no—
1282C22—42no—
1283C22—42no—
1284C22—41no—
1285C22—42no—
1286C22—42no—
1287C22—41no—
1288C22—41no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—41no—
1293C22—41no—
1294C22—42no—
1295C22—41no—
1296C22—81no—
1297C22—81no—
1298C22—81no—
1299C22—81no—
1300C22—81no—
1301C22—81no—
1302C22—81no—
1303C22—81no—
1304C22—81no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—81no—
1320C22—81no—
1321C22—81no—
1322C22—168no—
1323C22C2×#54611yescharacteristic
1324C22D4×#4111yescharacteristic
1325C22#348711yescharacteristic
1326C22C2×#57611yescharacteristic
1327C22C2×#57611yescharacteristic
1328C22C2×#57711yescharacteristic
1329C22#358511yescharacteristic
1330C4—22no—
1331C4—22no—
1332C4—22no—
1333C4—22no—
1334C4—22no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—41no—
1343C4—42no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4—81no—
1354C4#347511yescharacteristic
1355C4#349311yescharacteristic
1356C4#350511yescharacteristic
1357C4#353911yescharacteristic
1358C2—81no—
1359C2—82no—
1360C2—82no—
1361C2—82no—
1362C2—161no—
1363C2—161no—
1364C2#5901911yescharacteristic
1365C2#6118311yescharacteristic
1366C2#6121511yescharacteristic
1367C2#6149611yescharacteristic
1368C2#6151911yescharacteristic
1369C2#6192111yescharacteristic
1370C2#6193211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45050C2semidirect
2. #35741C2semidirect
3. #31290C2semidirect
4. #31286C2semidirect
5. #31000C2semidirect
6. #30984C2semidirect
7. #29015C2semidirect
8. #29011C2semidirect
9. #28276C2semidirect
10. #27903C2semidirect
11. #27747C2semidirect
12. #27211C2semidirect
13. #27190C2semidirect
14. #27056C2semidirect
15. #27039C2semidirect
16. #26771C2semidirect
17. #26755C2semidirect
18. #26669C2semidirect
19. #26668C2semidirect
20. #26102C2semidirect
21. #24999C2semidirect
22. #24744C2semidirect
23. #24662C2semidirect
24. #24184C2semidirect
25. #23099C2semidirect
26. #23093C2semidirect
27. #23057C2semidirect
28. #22772C2semidirect
29. #22545C2semidirect
30. #21458C2semidirect
31. #20744C2semidirect
36. C2×#459C22semidirect
38. C2×#446C22semidirect
50. #2552C22semidirect
53. #2538C22semidirect
54. #2509C22semidirect
55. #2507C22semidirect
79. #2355C22semidirect
80. #2354C22semidirect
81. #2354C22semidirect
82. #2349C22semidirect
85. #2101C22semidirect
86. #2100C22semidirect
91. #2071C22semidirect
92. #2071C22semidirect
95. #2067C22semidirect
98. #2065C22semidirect
99. #2065C22semidirect
100. #2065C22semidirect
117. #1984C22semidirect
120. #1982C22semidirect
122. #1972C22semidirect
124. #1970C22semidirect
126. #1961C22semidirect
130. #1957C22semidirect
131. #1949C22semidirect
132. #1948C22semidirect
133. #1947C22semidirect
134. #1943C22semidirect
135. #1941C22semidirect
136. #1940C22semidirect
137. #1936C22semidirect
140. #1934C22semidirect
141. #1934C22semidirect
142. #1934C22semidirect
144. #1926C22semidirect
145. #1926C22semidirect
147. #1925C22semidirect
148. #1925C22semidirect
153. #1921C22semidirect
154. #1921C22semidirect
155. #1921C22semidirect
156. #1920C22semidirect
157. #1919C22semidirect
158. #1918C22semidirect
159. #1917C22semidirect
160. #1916C22semidirect
165. #1879C22semidirect
166. #1879C22semidirect
167. #1879C22semidirect
168. #1879C22semidirect
172. #1862C22semidirect
173. #1862C22semidirect
175. #1847C22semidirect
176. #1835C22semidirect
181. #1804C22semidirect
182. #1804C22semidirect
185. #1802C22semidirect
189. #1770C22semidirect
190. C8×C4⋊C4C22semidirect
191. C8×C4⋊C4C22semidirect
195. #1762C22semidirect
199. C4×#102C22semidirect
200. C4×#102C22semidirect
201. C4×#102C22semidirect
541. C2×D8#41semidirect

Maximal subgroups

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

subgroupindex
#450502
#357412
#312902
#312862
#310002
#309842
#290152
#290112
#282762
#279032
#277472
#272112
#271902
#270562
#270392
#267712
#267552
#266692
#266682
#261022
#249992
#247442
#246622
#241842
#230992
#230932
#230572
#227722
#225452
#214582
#207442