Finite Group Databasebeta

← #7083246

Subgroups — #7083246

Order 512.

1523 conjugacy classes of subgroups.

The subgroup lattice has 1299 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59325C211yesmaximal, characteristic, complemented
2#39198C211yesmaximal, characteristic
3#32610C211yesmaximal, characteristic, complemented
4#32601C211yesmaximal, characteristic, complemented
5#32441C211yesmaximal, characteristic, complemented
6#32436C211yesmaximal, characteristic, complemented
7#32093C211yesmaximal, characteristic, complemented
8#32088C211yesmaximal, characteristic, complemented
9#30812C211yesmaximal, characteristic, complemented
10#30807C211yesmaximal, characteristic, complemented
11#28576C211yesmaximal, characteristic, complemented
12#28408C211yesmaximal, characteristic, complemented
13#28402C211yesmaximal, characteristic, complemented
14#28037C211yesmaximal, characteristic, complemented
15#28031C211yesmaximal, characteristic, complemented
16#27977C211yesmaximal, characteristic, complemented
17#27256C211yesmaximal, characteristic, complemented
18#27254C211yesmaximal, characteristic
19#26350C211yesmaximal, characteristic, complemented
20#26340C211yesmaximal, characteristic, complemented
21#26324C211yesmaximal, characteristic, complemented
22#26323C211yesmaximal, characteristic, complemented
23#26173C211yesmaximal, characteristic, complemented
24#26159C211yesmaximal, characteristic, complemented
25#25084C211yesmaximal, characteristic, complemented
26#25080C211yesmaximal, characteristic
27C2×#2092C211yesmaximal, characteristic, complemented
28#23237C211yesmaximal, characteristic, complemented
29#23024C211yesmaximal, characteristic, complemented
30#23022C211yesmaximal, characteristic, complemented
31#22043C211yesmaximal, characteristic, complemented
32C2×#488C2211yescharacteristic
33C2×#486C2211yescharacteristic
34C2×#475C2211yescharacteristic, complemented
35C2×#478C2211yescharacteristic, complemented
36C2×#467C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#464C2211yescharacteristic
39C2×#460C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×C4×Q16C2211yescharacteristic, complemented
42C2×C4×SD16C2211yescharacteristic, complemented
43C22×#107C2211yescharacteristic
44C22×#106C2211yescharacteristic
45C22×#102C2211yescharacteristic
46C22×#102C2211yescharacteristic
47#2850C2211yescharacteristic
48#2803—21no—
49#2803—21no—
50#2797—21no—
51#2774—21no—
52#2755—21no—
53#2710—21no—
54#2622—21no—
55#2592C2211yescharacteristic
56#2581C2211yescharacteristic, complemented
57#2568C2211yescharacteristic, complemented
58#2565C2211yescharacteristic, complemented
59#2550C2211yescharacteristic, complemented
60#2549—21no—
61#2548C2211yescharacteristic
62#2548C2211yescharacteristic
63#2544C2211yescharacteristic
64#2520—21no—
65#2513C2211yescharacteristic
66#2513C2211yescharacteristic
67#2509C2211yescharacteristic, complemented
68#2508—21no—
69#2508C2211yescharacteristic, complemented
70#2505—21no—
71#2505—21no—
72#2472—21no—
73#2448C2211yescharacteristic
74#2445C2211yescharacteristic
75#2442C2211yescharacteristic
76#2440C2211yescharacteristic
77#2435C2211yescharacteristic
78#2433C2211yescharacteristic
79#2418—21no—
80#2368—21no—
81#2361C2211yescharacteristic
82#2360C2211yescharacteristic
83#2360C2211yescharacteristic
84#2360C2211yescharacteristic
85#2355C2211yescharacteristic, complemented
86#2351C2211yescharacteristic, complemented
87#2321—21no—
88C4×C22⋊Q8C2211yescharacteristic
89C4×C22⋊Q8C2211yescharacteristic
90C2×#390C2211yescharacteristic
91C2×#382C2211yescharacteristic
92#2096C2211yescharacteristic, complemented
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic, complemented
102#2088C2211yescharacteristic, complemented
103#2087C2211yescharacteristic, complemented
104#2085C2211yescharacteristic, complemented
105#2074C2211yescharacteristic, complemented
106#2074C2211yescharacteristic, complemented
107#2074C2211yescharacteristic, complemented
108#2073C2211yescharacteristic
109#2073C2211yescharacteristic, complemented
110#2073C2211yescharacteristic, complemented
111#2071C2211yescharacteristic
112#2067C2211yescharacteristic
113#2067C2211yescharacteristic, complemented
114#2066C2211yescharacteristic, complemented
115#2065C2211yescharacteristic
116#2059C2211yescharacteristic, complemented
117#2058C2211yescharacteristic, complemented
118#2055C2211yescharacteristic
119#2055C2211yescharacteristic
120#2042C2211yescharacteristic
121#2042C2211yescharacteristic
122#2042C2211yescharacteristic
123#2042C2211yescharacteristic, complemented
124#2041C2211yescharacteristic
125#2041C2211yescharacteristic
126#2041C2211yescharacteristic
127#2025C2211yescharacteristic
128#2023C2211yescharacteristic
129#2015C2211yescharacteristic
130#2015C2211yescharacteristic, complemented
131#2014C2211yescharacteristic
132#1984C2211yescharacteristic, complemented
133#1984C2211yescharacteristic, complemented
134#1983C2211yescharacteristic
135#1982C2211yescharacteristic
136#1969C2211yescharacteristic, complemented
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1968C2211yescharacteristic, complemented
140#1958C2211yescharacteristic
141#1958C2211yescharacteristic, complemented
142#1958C2211yescharacteristic, complemented
143#1957C2211yescharacteristic
144#1949C2211yescharacteristic, complemented
145#1948C2211yescharacteristic, complemented
146#1942C2211yescharacteristic, complemented
147#1941C2211yescharacteristic, complemented
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1928C2211yescharacteristic, complemented
155#1928C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1926C2211yescharacteristic
159#1926C2211yescharacteristic
160#1926C2211yescharacteristic
161#1926C2211yescharacteristic, complemented
162#1925C2211yescharacteristic
163#1925C2211yescharacteristic, complemented
164#1921C2211yescharacteristic, complemented
165#1919C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1916C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1893C2211yescharacteristic
171#1892C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1874C2211yescharacteristic
179#1874C2211yescharacteristic
180#1872C2211yescharacteristic
181#1872C2211yescharacteristic
182#1872C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1865C2211yescharacteristic, complemented
185#1864C2211yescharacteristic, complemented
186#1863C2211yescharacteristic, complemented
187#1863C2211yescharacteristic, complemented
188#1862C2211yescharacteristic, complemented
189#1853C2211yescharacteristic
190#1850C2211yescharacteristic
191#1850C2211yescharacteristic
192#1835C2211yescharacteristic, complemented
193#1835C2211yescharacteristic, complemented
194#1786C2211yescharacteristic
195C4×#107C2211yescharacteristic, complemented
196C4×#106C2211yescharacteristic, complemented
197C8×C4⋊C4C2211yescharacteristic, complemented
198C8×C4⋊C4C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124—21no—
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8D411yescharacteristic
221C2×C22⋊Q8C2311yescharacteristic
222C2×C22⋊Q8C2311yescharacteristic
223C2×#121C2311yescharacteristic
224C2×#120—21no—
225C2×#120—21no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4C2311yescharacteristic
233C22×C4⋊C4C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C42C2311yescharacteristic
239#488—42no—
240#486—42no—
241#478—42no—
242#475—42no—
243#467—24no—
244#465—24no—
245#464—42no—
246#460—42no—
247#450—24no—
248C4×Q16—42no—
249C4×SD16—42no—
250C2×#107—42no—
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106—42no—
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#102—42no—
280C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#400—21no—
317#399—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#395—21no—
331#395—21no—
332#395—21no—
333#394—21no—
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#393—21no—
344#392—21no—
345#392—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391D411yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390—21no—
357#390—21no—
358#390—21no—
359#390—21no—
360#390—21no—
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389D411yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
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#388—21no—
398#388—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#387—21no—
410#387—21no—
411#387D411yescharacteristic
412#387D411yescharacteristic
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#385D411yescharacteristic
427#385D411yescharacteristic
428#384C2311yescharacteristic
429#382—21no—
430#382—21no—
431#382—21no—
432#382—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#380—21no—
440#380D411yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C2×#95—21no—
462C2×#95—21no—
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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8C2×D411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4—41no—
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4C2×D411yescharacteristic
518C23×C4C2×D411yescharacteristic
519C23×C4C2411yescharacteristic
520C2×Q16—22no—
521C2×Q16—22no—
522C2×Q16—41no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C22×C8—22no—
533C22×C8—22no—
534C22×C8—22no—
535C22×C8—22no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—41no—
547C4⋊Q8—41no—
548#127—41no—
549#127—41no—
550#127—41no—
551#127—41no—
552#125—41no—
553#125—41no—
554#124—41no—
555#124—41no—
556#124—41no—
557#124—41no—
558#124—41no—
559#124—41no—
560#124—82no—
561#123—82no—
562C22⋊Q8—22no—
563C22⋊Q8—24no—
564C22⋊Q8—22no—
565C22⋊Q8—22no—
566C22⋊Q8—44no—
567C22⋊Q8#4114yes—
568#121—22no—
569#121—22no—
570#120—44no—
571#120—82no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×Q8—41no—
576C4×Q8—41no—
577C4×Q8—41no—
578C4×Q8—41no—
579C4×Q8—41no—
580C4×Q8—41no—
581C4×Q8—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—82no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4C2×D411yescharacteristic
621C2×C4⋊C4C2×D411yescharacteristic
622C2×C4⋊C4C2×D411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—82no—
666C2×C22⋊C4—82no—
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—41no—
681C2×C42—41no—
682C2×C42C2×D411yescharacteristic
683C2×C42C2×D411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690#107—22no—
691#107—22no—
692#107—22no—
693#107—41no—
694#107—41no—
695#106—22no—
696#106—22no—
697#106—22no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702C4⋊C8—22no—
703C4⋊C8—22no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706#103—22no—
707#103—22no—
708#103—22no—
709#103—22no—
710#103—41no—
711#103—41no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102—41no—
732#102—41no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738C22⋊C8—22no—
739C22⋊C8—22no—
740C4×C8—22no—
741C4×C8—22no—
742C4×C8—41no—
743C4×C8—41no—
744C4×C8—41no—
745C4×C8—41no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793C24—21no—
794C24—21no—
795C24—21no—
796C24—42no—
797C24—42no—
798C24—42no—
799C24—81no—
800C24—81no—
801C24—81no—
802C24—81no—
803C24C22×D411yescharacteristic
804C2×Q8—22no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—41no—
817C2×Q8—41no—
818C2×Q8—42no—
819C2×Q8—81no—
820C2×Q8—81no—
821C2×Q8C2×#4112yes—
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—44no—
841C2×D4—44no—
842C2×D4—42no—
843C2×D4—42no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—82no—
849C2×D4—82no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4—81no—
853C2×D4—81no—
854C2×D4—81no—
855C2×D4—81no—
856C2×D4—81no—
857C2×D4—81no—
858C2×D4—81no—
859C2×D4—81no—
860C2×D4—81no—
861C2×D4—81no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—22no—
869C22×C4—22no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—41no—
882C22×C4—41no—
883C22×C4—41no—
884C22×C4—41no—
885C22×C4—42no—
886C22×C4—42no—
887C22×C4—42no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4—81no—
896C22×C4—81no—
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C22×D411yescharacteristic
906C22×C4C22×D411yescharacteristic
907C22×C4C22×D411yescharacteristic
908C22×C4C22×D411yescharacteristic
909C22×C4C22×D411yescharacteristic
910C22×C4C2×#4112yes—
911C22×C42−1+412yes—
912C22×C4C2511yescharacteristic
913Q16—44no—
914SD16—44no—
915SD16—82no—
916SD16—82no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—21no—
935C2×C8—21no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—44no—
940C2×C8—44no—
941C2×C8H(5,𝔽2)12yes—
942C2×C8H(5,𝔽2)12yes—
943C4⋊C4—24no—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—22no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—41no—
969C4⋊C4—41no—
970C4⋊C4—41no—
971C4⋊C4—41no—
972C4⋊C4—41no—
973C4⋊C4—41no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—42no—
977C4⋊C4—42no—
978C4⋊C4—42no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C4⋊C4—81no—
995C4⋊C4—81no—
996C4⋊C4C2×#4112yes—
997C22⋊C4—24no—
998C22⋊C4—22no—
999C22⋊C4—22no—
1000C22⋊C4—22no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C22⋊C4#13514yes—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—41no—
1045C42—41no—
1046C42—42no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C42—81no—
1051C42—81no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—84no—
1081C23—84no—
1082C23—84no—
1083C23—162no—
1084C23—162no—
1085C23—162no—
1086C23—162no—
1087C23#54812yes—
1088C23C2×#13512yes—
1089C23#57712yes—
1090C23C23×D411yescharacteristic
1091Q8—22no—
1092Q8—22no—
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—82no—
1100Q8—162no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—84no—
1114D4—84no—
1115D4—162no—
1116D4—162no—
1117D4—162no—
1118D4—162no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
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—82no—
1199C2×C4—82no—
1200C2×C4—162no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4—162no—
1204C2×C4#54812yes—
1205C2×C4C2×#13512yes—
1206C2×C4C2×#13512yes—
1207C2×C4C22×#4111yescharacteristic
1208C2×C4C2×H(5,𝔽2)11yescharacteristic
1209C2×C4C2×H(5,𝔽2)11yescharacteristic
1210C2×C4C2×2−1+411yescharacteristic
1211C2×C4#58511yescharacteristic
1212C2×C4#58511yescharacteristic
1213C8—22no—
1214C8—22no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—22no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—168no—
1249C22#336514yes—
1250C22C2×#54811yescharacteristic
1251C22#348511yescharacteristic
1252C22#349811yescharacteristic
1253C22C22×#13511yescharacteristic
1254C22C2×#57711yescharacteristic
1255C22#358411yescharacteristic
1256C22#358511yescharacteristic
1257C4—22no—
1258C4—22no—
1259C4—22no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—42no—
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—42no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4—81no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4#351311yescharacteristic
1284C4#351311yescharacteristic
1285C4#354111yescharacteristic
1286C4#354111yescharacteristic
1287C2—24no—
1288C2—161no—
1289C2—161no—
1290C2—161no—
1291C2#4410311yescharacteristic
1292C2C2×#336511yescharacteristic
1293C2#6134911yescharacteristic
1294C2#6170211yescharacteristic
1295C2#6177011yescharacteristic
1296C2#6241911yescharacteristic
1297C2#6245711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59325C2semidirect
3. #32610C2semidirect
4. #32601C2semidirect
5. #32441C2semidirect
6. #32436C2semidirect
7. #32093C2semidirect
8. #32088C2semidirect
9. #30812C2semidirect
10. #30807C2semidirect
11. #28576C2semidirect
12. #28408C2semidirect
13. #28402C2semidirect
14. #28037C2semidirect
15. #28031C2semidirect
16. #27977C2semidirect
17. #27256C2semidirect
19. #26350C2semidirect
20. #26340C2semidirect
21. #26324C2semidirect
22. #26323C2semidirect
23. #26173C2semidirect
24. #26159C2semidirect
25. #25084C2semidirect
27. C2×#2092C2semidirect
28. #23237C2semidirect
29. #23024C2semidirect
30. #23022C2semidirect
31. #22043C2semidirect
34. C2×#475C22semidirect
35. C2×#478C22semidirect
41. C2×C4×Q16C22semidirect
42. C2×C4×SD16C22semidirect
56. #2581C22semidirect
57. #2568C22semidirect
58. #2565C22semidirect
59. #2550C22semidirect
67. #2509C22semidirect
69. #2508C22semidirect
85. #2355C22semidirect
86. #2351C22semidirect
92. #2096C22semidirect
101. #2092C22semidirect
102. #2088C22semidirect
103. #2087C22semidirect
104. #2085C22semidirect
105. #2074C22semidirect
106. #2074C22semidirect
107. #2074C22semidirect
109. #2073C22semidirect
110. #2073C22semidirect
113. #2067C22semidirect
114. #2066C22semidirect
116. #2059C22semidirect
117. #2058C22semidirect
123. #2042C22semidirect
130. #2015C22semidirect
132. #1984C22semidirect
133. #1984C22semidirect
136. #1969C22semidirect
139. #1968C22semidirect
141. #1958C22semidirect
142. #1958C22semidirect
144. #1949C22semidirect
145. #1948C22semidirect
146. #1942C22semidirect
147. #1941C22semidirect
154. #1928C22semidirect
155. #1928C22semidirect
156. #1927C22semidirect
157. #1927C22semidirect
161. #1926C22semidirect
163. #1925C22semidirect
164. #1921C22semidirect
165. #1919C22semidirect
166. #1916C22semidirect
167. #1916C22semidirect
168. #1916C22semidirect
169. #1916C22semidirect
176. #1880C22semidirect
177. #1878C22semidirect
183. #1865C22semidirect
184. #1865C22semidirect
185. #1864C22semidirect
186. #1863C22semidirect
187. #1863C22semidirect
188. #1862C22semidirect
192. #1835C22semidirect
193. #1835C22semidirect
195. C4×#107C22semidirect
196. C4×#106C22semidirect
197. C8×C4⋊C4C22semidirect
198. C8×C4⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#593252
#391982
#326102
#326012
#324412
#324362
#320932
#320882
#308122
#308072
#285762
#284082
#284022
#280372
#280312
#279772
#272562
#272542
#263502
#263402
#263242
#263232
#261732
#261592
#250842
#250802
C2×#20922
#232372
#230242
#230222
#220432