Finite Group Databasebeta

← #7044153

Subgroups — #7044153

Order 512.

1565 conjugacy classes of subgroups.

The subgroup lattice has 1339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45158C211yesmaximal, characteristic, complemented
2#45023C211yesmaximal, characteristic
3#32211C211yesmaximal, characteristic, complemented
4#32054C211yesmaximal, characteristic, complemented
5#31844C211yesmaximal, characteristic, complemented
6#31579C211yesmaximal, characteristic, complemented
7#31513C211yesmaximal, characteristic, complemented
8#31467C211yesmaximal, characteristic, complemented
9#31400C211yesmaximal, characteristic, complemented
10#30426C211yesmaximal, characteristic, complemented
11#28130C211yesmaximal, characteristic, complemented
12#27690C211yesmaximal, characteristic, complemented
13#27529C211yesmaximal, characteristic, complemented
14#27430C211yesmaximal, characteristic, complemented
15#27200C211yesmaximal, characteristic, complemented
16#27033C211yesmaximal, characteristic, complemented
17#26215C211yesmaximal, characteristic, complemented
18#25546C211yesmaximal, characteristic, complemented
19#25261C211yesmaximal, characteristic, complemented
20#25230C211yesmaximal, characteristic, complemented
21#25136C211yesmaximal, characteristic, complemented
22#24936C211yesmaximal, characteristic, complemented
23#24885C211yesmaximal, characteristic, complemented
24#24873C211yesmaximal, characteristic, complemented
25#24543C211yesmaximal, characteristic, complemented
26#24426C211yesmaximal, characteristic, complemented
27#23632C211yesmaximal, characteristic, complemented
28#22499C211yesmaximal, characteristic, complemented
29#22427C211yesmaximal, characteristic, complemented
30#22192C211yesmaximal, characteristic, complemented
31#22179C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#468C2211yescharacteristic
37C2×#467C2211yescharacteristic
38C2×#452C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×#436C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2779—21no—
46#2776—21no—
47#2772—21no—
48#2749—21no—
49#2711—21no—
50#2707—21no—
51#2685—21no—
52#2678—21no—
53#2608—21no—
54#2576—21no—
55#2571C2211yescharacteristic, complemented
56#2538C2211yescharacteristic, complemented
57#2530—21no—
58#2526—21no—
59#2503C2211yescharacteristic, complemented
60#2499C2211yescharacteristic, complemented
61#2497C2211yescharacteristic, complemented
62#2494C2211yescharacteristic, complemented
63#2490C2211yescharacteristic
64#2485C2211yescharacteristic
65#2480—21no—
66#2471—21no—
67#2454C2211yescharacteristic
68#2448C2211yescharacteristic
69#2426C2211yescharacteristic
70#2418—21no—
71#2417C2211yescharacteristic
72#2416C2211yescharacteristic
73#2415C2211yescharacteristic
74#2414—21no—
75#2408C2211yescharacteristic
76#2407C2211yescharacteristic
77#2392C2211yescharacteristic
78#2361C2211yescharacteristic
79#2356C2211yescharacteristic, complemented
80#2352C2211yescharacteristic
81#2352C2211yescharacteristic
82#2352C2211yescharacteristic, complemented
83#2341C2211yescharacteristic
84#2323C2211yescharacteristic
85#2323C2211yescharacteristic
86#2317C2211yescharacteristic
87#2309C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2095C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2088C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2077C2211yescharacteristic, complemented
97#2075C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2073C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2071C2211yescharacteristic
107#2071C2211yescharacteristic
108#2068C2211yescharacteristic, complemented
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2065C2211yescharacteristic
112#2059C2211yescharacteristic, complemented
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2055C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic, complemented
118#2035C2211yescharacteristic, complemented
119#2034C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2026C2211yescharacteristic, complemented
124#2015C2211yescharacteristic
125#2001C2211yescharacteristic, complemented
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1991C2211yescharacteristic, complemented
129#1989C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1968C2211yescharacteristic
132#1958C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1934C2211yescharacteristic
137#1933C2211yescharacteristic, complemented
138#1927C2211yescharacteristic, complemented
139#1927C2211yescharacteristic, complemented
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1923C2211yescharacteristic, complemented
145#1923C2211yescharacteristic, complemented
146#1921C2211yescharacteristic, complemented
147#1921C2211yescharacteristic, complemented
148#1920C2211yescharacteristic, complemented
149#1919C2211yescharacteristic, complemented
150#1916C2211yescharacteristic, complemented
151#1916C2211yescharacteristic, complemented
152#1895C2211yescharacteristic
153#1895C2211yescharacteristic
154#1894C2211yescharacteristic
155#1894C2211yescharacteristic
156#1894C2211yescharacteristic, complemented
157#1894C2211yescharacteristic, complemented
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1878C2211yescharacteristic, complemented
161#1878C2211yescharacteristic, complemented
162#1878C2211yescharacteristic, complemented
163#1877C2211yescharacteristic
164#1875C2211yescharacteristic
165#1874C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic, complemented
168#1872C2211yescharacteristic
169#1872C2211yescharacteristic, complemented
170#1870C2211yescharacteristic, complemented
171#1870C2211yescharacteristic, complemented
172#1869C2211yescharacteristic
173#1869C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1865C2211yescharacteristic, complemented
176#1863C2211yescharacteristic, complemented
177#1862C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic, complemented
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic, complemented
182#1851C2211yescharacteristic, complemented
183#1851C2211yescharacteristic, complemented
184#1825C2211yescharacteristic
185#1824C2211yescharacteristic, complemented
186#1824C2211yescharacteristic, complemented
187#1809C2211yescharacteristic, complemented
188#1807C2211yescharacteristic
189#1805C2211yescharacteristic, complemented
190#1805C2211yescharacteristic, complemented
191#1804C2211yescharacteristic
192#1803C2211yescharacteristic, complemented
193#1798C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1786C2211yescharacteristic
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#552—24no—
213#552—42no—
214#546—24no—
215#546—42no—
216C2×#126—21no—
217C2×#125—21no—
218C2×#125C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×C22⋊Q8C2311yescharacteristic
227C2×#121—21no—
228C2×#121—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×#120—21no—
233C2×#120—21no—
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117—21no—
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C22⋊C4—21no—
251#485—42no—
252#482—42no—
253#468—42no—
254#467—24no—
255#452—42no—
256#450—42no—
257#436—42no—
258#436—42no—
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272#418—42no—
273#417—42no—
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#401—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#399—21no—
318#399—21no—
319#398—21no—
320#398D411yescharacteristic
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397D411yescharacteristic
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396D411yescharacteristic
337#396D411yescharacteristic
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#392—21no—
349#392—21no—
350#392D411yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#390—21no—
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390—21no—
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#383—21no—
424#382—21no—
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#381—21no—
430#381—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444#379—21no—
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376—21no—
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
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×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4C2×D411yescharacteristic
514C22×D4C2×D411yescharacteristic
515C22×D4C2×D411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C23×C4C2411yescharacteristic
526C2×Q16—22no—
527C2×Q16—41no—
528C2×Q16—41no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×M16—22no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C22×C8—22no—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555#126—44no—
556#125—22no—
557#125—41no—
558#125—44no—
559#124—22no—
560#124—41no—
561#123—44no—
562#123—44no—
563C22⋊Q8—22no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—22no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—41no—
570C22⋊Q8—41no—
571C22⋊Q8—41no—
572C22⋊Q8#4114yes—
573#121—22no—
574#121—22no—
575#121—44no—
576#121—41no—
577#121—41no—
578#121—41no—
579#121—41no—
580#121—82no—
581#120—44no—
582#120—82no—
583C4×Q8—22no—
584C4×Q8—41no—
585C4×Q8—41no—
586C4×Q8—41no—
587C4×Q8—41no—
588C4×Q8—41no—
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—82no—
598#117—22no—
599#117—22no—
600#117—41no—
601#117—41no—
602#117—44no—
603#117—41no—
604#117—41no—
605#117—41no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—22no—
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—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716#107—22no—
717#107—41no—
718#107—41no—
719#107—41no—
720#107—41no—
721#106—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729#103—22no—
730#103—22no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#102—22no—
742#102—22no—
743#102—22no—
744#102—22no—
745#102—22no—
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—
755C22⋊C8—22no—
756C22⋊C8—22no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760C22⋊C8—41no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C4×C8—41no—
764C4×C8—41no—
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#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#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805C24—21no—
806C24—21no—
807C24—42no—
808C24—42no—
809C24—81no—
810C24—81no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24C22×D411yescharacteristic
815C24C22×D411yescharacteristic
816C24C22×D411yescharacteristic
817#41—44no—
818#41—82no—
819#41—82no—
820#41—82no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8C2×#4112yes—
833C2×D4—22no—
834C2×D4—22no—
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—44no—
847C2×D4—44no—
848C2×D4—41no—
849C2×D4—41no—
850C2×D4—41no—
851C2×D4—41no—
852C2×D4—41no—
853C2×D4—41no—
854C2×D4—41no—
855C2×D4—42no—
856C2×D4—42no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—81no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4H(5,𝔽2)12yes—
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—21no—
882C22×C4—21no—
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—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C2×#4112yes—
930C22×C4H(5,𝔽2)12yes—
931C22×C4C2511yescharacteristic
932Q16—82no—
933SD16—82no—
934SD16—82no—
935M16—82no—
936M16—82no—
937M16—82no—
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—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—82no—
963C4⋊C4—24no—
964C4⋊C4—22no—
965C4⋊C4—22no—
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—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4C2×#4112yes—
1017C22⋊C4—24no—
1018C22⋊C4—22no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
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—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—42no—
1072C42—42no—
1073C42—42no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—22no—
1100C23—21no—
1101C23—21no—
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—84no—
1116C23—84no—
1117C23—162no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23—162no—
1122C23#54612yes—
1123C23C23×D411yescharacteristic
1124Q8—22no—
1125Q8—22no—
1126Q8—41no—
1127Q8—41no—
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132D4—22no—
1133D4—22no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—84no—
1141D4—82no—
1142D4—82no—
1143D4—82no—
1144D4—84no—
1145D4—84no—
1146D4—162no—
1147D4—162no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
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—22no—
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—41no—
1187C2×C4—41no—
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—84no—
1235C2×C4—84no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4#54612yes—
1240C2×C4C22×#4111yescharacteristic
1241C2×C4C2×H(5,𝔽2)11yescharacteristic
1242C2×C4C2×H(5,𝔽2)11yescharacteristic
1243C2×C4#58511yescharacteristic
1244C2×C4#58511yescharacteristic
1245C2×C4#58511yescharacteristic
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—42no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—42no—
1270C22—41no—
1271C22—41no—
1272C22—41no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—42no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—168no—
1290C22C2×#54611yescharacteristic
1291C22#348511yescharacteristic
1292C22#348811yescharacteristic
1293C22#358411yescharacteristic
1294C22#358411yescharacteristic
1295C22#358511yescharacteristic
1296C22#358611yescharacteristic
1297C4—22no—
1298C4—41no—
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—42no—
1303C4—41no—
1304C4—41no—
1305C4—42no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—81no—
1311C4—81no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4#351311yescharacteristic
1323C4#352111yescharacteristic
1324C4#353411yescharacteristic
1325C4#356011yescharacteristic
1326C2—42no—
1327C2—81no—
1328C2—81no—
1329C2—82no—
1330C2—161no—
1331C2#4353011yescharacteristic
1332C2#6119011yescharacteristic
1333C2#6119611yescharacteristic
1334C2#6178011yescharacteristic
1335C2#6179011yescharacteristic
1336C2#6202811yescharacteristic
1337C2#6204811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45023C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45158C2semidirect
3. #32211C2semidirect
4. #32054C2semidirect
5. #31844C2semidirect
6. #31579C2semidirect
7. #31513C2semidirect
8. #31467C2semidirect
9. #31400C2semidirect
10. #30426C2semidirect
11. #28130C2semidirect
12. #27690C2semidirect
13. #27529C2semidirect
14. #27430C2semidirect
15. #27200C2semidirect
16. #27033C2semidirect
17. #26215C2semidirect
18. #25546C2semidirect
19. #25261C2semidirect
20. #25230C2semidirect
21. #25136C2semidirect
22. #24936C2semidirect
23. #24885C2semidirect
24. #24873C2semidirect
25. #24543C2semidirect
26. #24426C2semidirect
27. #23632C2semidirect
28. #22499C2semidirect
29. #22427C2semidirect
30. #22192C2semidirect
31. #22179C2semidirect
55. #2571C22semidirect
56. #2538C22semidirect
59. #2503C22semidirect
60. #2499C22semidirect
61. #2497C22semidirect
62. #2494C22semidirect
79. #2356C22semidirect
82. #2352C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2099C22semidirect
91. #2097C22semidirect
92. #2095C22semidirect
94. #2088C22semidirect
95. #2085C22semidirect
96. #2077C22semidirect
97. #2075C22semidirect
98. #2075C22semidirect
108. #2068C22semidirect
112. #2059C22semidirect
117. #2036C22semidirect
118. #2035C22semidirect
123. #2026C22semidirect
125. #2001C22semidirect
128. #1991C22semidirect
129. #1989C22semidirect
133. #1949C22semidirect
134. #1947C22semidirect
135. #1942C22semidirect
137. #1933C22semidirect
138. #1927C22semidirect
139. #1927C22semidirect
144. #1923C22semidirect
145. #1923C22semidirect
146. #1921C22semidirect
147. #1921C22semidirect
148. #1920C22semidirect
149. #1919C22semidirect
150. #1916C22semidirect
151. #1916C22semidirect
156. #1894C22semidirect
157. #1894C22semidirect
160. #1878C22semidirect
161. #1878C22semidirect
162. #1878C22semidirect
167. #1873C22semidirect
169. #1872C22semidirect
170. #1870C22semidirect
171. #1870C22semidirect
174. #1865C22semidirect
175. #1865C22semidirect
176. #1863C22semidirect
179. #1853C22semidirect
181. #1852C22semidirect
182. #1851C22semidirect
183. #1851C22semidirect
185. #1824C22semidirect
186. #1824C22semidirect
187. #1809C22semidirect
189. #1805C22semidirect
190. #1805C22semidirect
192. #1803C22semidirect
197. C4×#103C22semidirect
200. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#451582
#450232
#322112
#320542
#318442
#315792
#315132
#314672
#314002
#304262
#281302
#276902
#275292
#274302
#272002
#270332
#262152
#255462
#252612
#252302
#251362
#249362
#248852
#248732
#245432
#244262
#236322
#224992
#224272
#221922
#221792