Finite Group Databasebeta

← #7083482

Subgroups — #7083482

Order 512.

1387 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44923C211yesmaximal, characteristic, complemented
2#42940C211yesmaximal, characteristic
3#32619C211yesmaximal, characteristic, complemented
4#32603C211yesmaximal, characteristic, complemented
5#32454C211yesmaximal, characteristic, complemented
6#32432C211yesmaximal, characteristic, complemented
7#32108C211yesmaximal, characteristic, complemented
8#32087C211yesmaximal, characteristic, complemented
9#30817C211yesmaximal, characteristic, complemented
10#30806C211yesmaximal, characteristic, complemented
11#28589C211yesmaximal, characteristic
12#28419C211yesmaximal, characteristic, complemented
13#28407C211yesmaximal, characteristic, complemented
14#28060C211yesmaximal, characteristic, complemented
15#28030C211yesmaximal, characteristic, complemented
16#27984C211yesmaximal, characteristic
17#27275C211yesmaximal, characteristic
18#27258C211yesmaximal, characteristic, complemented
19#26359C211yesmaximal, characteristic
20#26351C211yesmaximal, characteristic, complemented
21#26330C211yesmaximal, characteristic, complemented
22#26320C211yesmaximal, characteristic, complemented
23#26171C211yesmaximal, characteristic, complemented
24#26161C211yesmaximal, characteristic, complemented
25#25095C211yesmaximal, characteristic, complemented
26#25086C211yesmaximal, characteristic
27#23736C211yesmaximal, characteristic, complemented
28#23244C211yesmaximal, characteristic, complemented
29#23036C211yesmaximal, characteristic, complemented
30#23023C211yesmaximal, characteristic
31#22054C211yesmaximal, characteristic, complemented
32C2×#488C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#479C2211yescharacteristic
35C2×#476C2211yescharacteristic
36C2×#470C2211yescharacteristic
37C2×#465C2211yescharacteristic
38C2×#464C2211yescharacteristic
39C2×#462C2211yescharacteristic
40C2×#451C2211yescharacteristic
41C2×C4×Q16C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic
43C2×#428C2211yescharacteristic
44C2×#427C2211yescharacteristic
45C2×#419C2211yescharacteristic
46C22×#103C2211yescharacteristic
47#2831—21no—
48#2807—21no—
49#2805—21no—
50#2792—21no—
51#2761—21no—
52#2751—21no—
53#2750—21no—
54#2743—21no—
55#2720—21no—
56#2665—21no—
57#2650—21no—
58#2620C2211yescharacteristic
59#2592C2211yescharacteristic
60#2587—21no—
61#2585—21no—
62#2584—21no—
63#2581C2211yescharacteristic
64#2574—21no—
65#2568C2211yescharacteristic
66#2567C2211yescharacteristic
67#2565C2211yescharacteristic
68#2550C2211yescharacteristic
69#2547C2211yescharacteristic
70#2545C2211yescharacteristic
71#2511C2211yescharacteristic
72#2511C2211yescharacteristic
73#2509C2211yescharacteristic
74#2506C2211yescharacteristic
75#2465—21no—
76#2447C2211yescharacteristic
77#2446C2211yescharacteristic
78#2441C2211yescharacteristic
79#2440C2211yescharacteristic
80#2436C2211yescharacteristic
81#2434C2211yescharacteristic
82#2396C2211yescharacteristic
83#2363C2211yescharacteristic
84#2362C2211yescharacteristic
85#2362C2211yescharacteristic
86#2360C2211yescharacteristic
87Q8×C4⋊C4C2211yescharacteristic
88Q8×C4⋊C4C2211yescharacteristic
89#2323C2211yescharacteristic
90#2317C2211yescharacteristic
91#2310C2211yescharacteristic
92#2097C2211yescharacteristic
93#2097C2211yescharacteristic
94#2097C2211yescharacteristic
95#2097C2211yescharacteristic
96#2096C2211yescharacteristic
97#2096C2211yescharacteristic
98#2096C2211yescharacteristic
99#2095C2211yescharacteristic
100#2095C2211yescharacteristic
101#2093C2211yescharacteristic
102#2088C2211yescharacteristic
103#2087C2211yescharacteristic
104#2084C2211yescharacteristic
105#2074C2211yescharacteristic
106#2073C2211yescharacteristic
107#2072C2211yescharacteristic
108#2072C2211yescharacteristic
109#2072C2211yescharacteristic
110#2072C2211yescharacteristic
111#2071C2211yescharacteristic
112#2068C2211yescharacteristic
113#2067C2211yescharacteristic
114#2066C2211yescharacteristic
115#2066C2211yescharacteristic
116#2059C2211yescharacteristic
117#2057C2211yescharacteristic
118#2056C2211yescharacteristic
119#2056C2211yescharacteristic
120#2043C2211yescharacteristic
121#2043C2211yescharacteristic
122#2043C2211yescharacteristic
123#2042C2211yescharacteristic
124#2042C2211yescharacteristic
125#2042C2211yescharacteristic
126#2042C2211yescharacteristic
127#2026C2211yescharacteristic
128#2024C2211yescharacteristic
129#2016C2211yescharacteristic
130#2015C2211yescharacteristic
131#2015C2211yescharacteristic
132#1985C2211yescharacteristic
133#1984C2211yescharacteristic
134#1983C2211yescharacteristic
135#1981C2211yescharacteristic
136#1971C2211yescharacteristic
137#1971C2211yescharacteristic
138#1969C2211yescharacteristic
139#1968C2211yescharacteristic
140#1959C2211yescharacteristic
141#1959C2211yescharacteristic
142#1958C2211yescharacteristic
143#1956C2211yescharacteristic
144#1948C2211yescharacteristic
145#1947C2211yescharacteristic
146#1941C2211yescharacteristic
147#1941C2211yescharacteristic
148#1935C2211yescharacteristic
149#1935C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1933C2211yescharacteristic
153#1933C2211yescharacteristic
154#1928C2211yescharacteristic
155#1928C2211yescharacteristic
156#1928C2211yescharacteristic
157#1927C2211yescharacteristic
158#1927C2211yescharacteristic
159#1927C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1926C2211yescharacteristic
163#1925C2211yescharacteristic
164#1920C2211yescharacteristic
165#1919C2211yescharacteristic
166#1917C2211yescharacteristic
167#1916C2211yescharacteristic
168#1916C2211yescharacteristic
169#1916C2211yescharacteristic
170#1895C2211yescharacteristic
171#1892C2211yescharacteristic
172#1880C2211yescharacteristic
173#1878C2211yescharacteristic
174#1878C2211yescharacteristic
175#1878C2211yescharacteristic
176#1878C2211yescharacteristic
177#1878C2211yescharacteristic
178#1875C2211yescharacteristic
179#1874C2211yescharacteristic
180#1873C2211yescharacteristic
181#1873C2211yescharacteristic
182#1872C2211yescharacteristic
183#1865C2211yescharacteristic
184#1864C2211yescharacteristic
185#1863C2211yescharacteristic
186#1863C2211yescharacteristic
187#1863C2211yescharacteristic
188#1862C2211yescharacteristic
189#1854C2211yescharacteristic
190#1851C2211yescharacteristic
191#1850C2211yescharacteristic
192#1836C2211yescharacteristic
193#1834C2211yescharacteristic
194#1787C2211yescharacteristic
195#1776C2211yescharacteristic
196C4×#106C2211yescharacteristic
197#1770C2211yescharacteristic
198C8×C4⋊C4C2211yescharacteristic
199#1753C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201#1750C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×Q16C2311yescharacteristic
206C22×Q16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#125—21no—
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×C22⋊Q8C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×C4×Q8—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233#488—42no—
234#487—42no—
235#479—42no—
236#476—42no—
237#470—24no—
238#465—24no—
239#464—42no—
240#462—42no—
241#451—24no—
242C4×Q16—42no—
243C4×SD16—42no—
244#428—42no—
245#427—42no—
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262#419—42no—
263C2×#103—42no—
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400D411yescharacteristic
316#399—21no—
317#399D411yescharacteristic
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398D411yescharacteristic
325#398D411yescharacteristic
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396D411yescharacteristic
337#396D411yescharacteristic
338#395—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#395—21no—
345#395D411yescharacteristic
346#394—21no—
347#394—21no—
348#393—21no—
349#393—21no—
350#393—21no—
351#393D411yescharacteristic
352#391—21no—
353#391—21no—
354#391—21no—
355#391—21no—
356#391C2311yescharacteristic
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#390—21no—
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
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#388—21no—
404#388—21no—
405#388—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#384—21no—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#382—21no—
440#382C2311yescharacteristic
441#382C2311yescharacteristic
442#381—21no—
443#381—21no—
444#381—21no—
445#380—21no—
446#380—21no—
447#380C2311yescharacteristic
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4—21no—
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
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
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—22no—
496C22×Q8—22no—
497C22×Q8—41no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8C2×D411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C2411yescharacteristic
512C2×Q16—22no—
513C2×Q16—22no—
514C2×Q16—22no—
515C2×Q16—22no—
516C2×Q16—41no—
517C2×Q16—41no—
518C2×Q16—41no—
519C2×Q16—41no—
520C2×Q16—41no—
521C2×SD16—22no—
522C2×SD16—22no—
523C2×SD16—41no—
524C2×M16—22no—
525C2×M16—22no—
526C2×M16—41no—
527C22×C8—22no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8—41no—
544#125—41no—
545#125—41no—
546#125—82no—
547#124—41no—
548#124—41no—
549#124—41no—
550#124—41no—
551#124—41no—
552#124—41no—
553C22⋊Q8—22no—
554C22⋊Q8—22no—
555C22⋊Q8—22no—
556C22⋊Q8—82no—
557C22⋊Q8#4114yes—
558#121—22no—
559#121—22no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×Q8—41no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—82no—
571C4×D4—41no—
572C4×D4—41no—
573#117—41no—
574#117—41no—
575#117—41no—
576#117—41no—
577#117—41no—
578#117—41no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
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—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
624C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672C2×C42C2411yescharacteristic
673C2×C42C2411yescharacteristic
674C2×C42C2411yescharacteristic
675C2×C42C2411yescharacteristic
676#107—22no—
677#107—41no—
678#107—41no—
679#107—41no—
680#107—41no—
681#106—22no—
682#106—22no—
683#106—22no—
684#106—22no—
685#106—22no—
686#106—41no—
687#106—41no—
688C4⋊C8—22no—
689C4⋊C8—22no—
690C4⋊C8—41no—
691C4⋊C8—41no—
692#103—22no—
693#103—22no—
694#103—22no—
695#103—22no—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—22no—
700#103—22no—
701#103—22no—
702#103—41no—
703#103—41no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
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—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724C22⋊C8—22no—
725C22⋊C8—22no—
726#97—41no—
727#97—41no—
728C4×C8—22no—
729C4×C8—22no—
730C4×C8—41no—
731C4×C8—41no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
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#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787C24—21no—
788C24C22×D411yescharacteristic
789C2×Q8—22no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
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—41no—
814C2×Q8—41no—
815C2×Q8—44no—
816C2×Q8—44no—
817C2×Q8—42no—
818C2×Q8—81no—
819C2×Q8—81no—
820C2×Q8—81no—
821C2×Q8—81no—
822C2×Q8—81no—
823C2×Q8—82no—
824C2×Q8—82no—
825C2×Q8C2×#4112yes—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—42no—
833C2×D4—81no—
834C2×D4—81no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—42no—
855C22×C4—42no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C2×#4112yes—
877C22×C42−1+412yes—
878C22×C4C2511yescharacteristic
879Q16—44no—
880Q16—82no—
881Q16—82no—
882SD16—44no—
883M16—44no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—44no—
907C2×C8H(5,𝔽2)12yes—
908C2×C8H(5,𝔽2)12yes—
909C4⋊C4—24no—
910C4⋊C4—22no—
911C4⋊C4—22no—
912C4⋊C4—22no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4C2×#4112yes—
975C22⋊C4—24no—
976C22⋊C4—22no—
977C22⋊C4—22no—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—42no—
1011C42—42no—
1012C42—81no—
1013C42—81no—
1014C42—81no—
1015C42—81no—
1016C42—81no—
1017C42—81no—
1018C42—81no—
1019C42—81no—
1020C42—81no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23#54812yes—
1035C23C23×D411yescharacteristic
1036Q8—22no—
1037Q8—22no—
1038Q8—44no—
1039Q8—41no—
1040Q8—41no—
1041Q8—41no—
1042Q8—41no—
1043Q8—41no—
1044Q8—41no—
1045Q8—41no—
1046Q8—41no—
1047Q8—41no—
1048Q8—41no—
1049Q8—41no—
1050Q8—41no—
1051Q8—41no—
1052Q8—41no—
1053Q8—84no—
1054Q8—162no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—162no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—84no—
1146C2×C4—162no—
1147C2×C4—162no—
1148C2×C4#54812yes—
1149C2×C4#57712yes—
1150C2×C4#57812yes—
1151C2×C4C22×#4111yescharacteristic
1152C2×C4C2×H(5,𝔽2)11yescharacteristic
1153C2×C4C2×H(5,𝔽2)11yescharacteristic
1154C2×C4C2×2−1+411yescharacteristic
1155C2×C4#58511yescharacteristic
1156C2×C4#58511yescharacteristic
1157C8—22no—
1158C8—22no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—41no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22C2×#54811yescharacteristic
1180C22#348511yescharacteristic
1181C22#349811yescharacteristic
1182C22C2×#57711yescharacteristic
1183C22C2×#57811yescharacteristic
1184C22#358411yescharacteristic
1185C22#358611yescharacteristic
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—42no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—42no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4#351311yescharacteristic
1215C4#351311yescharacteristic
1216C4#354111yescharacteristic
1217C4#354111yescharacteristic
1218C2—42no—
1219C2—161no—
1220C2#4410311yescharacteristic
1221C2#6133011yescharacteristic
1222C2#6134411yescharacteristic
1223C2#6174511yescharacteristic
1224C2#6178711yescharacteristic
1225C2#6243811yescharacteristic
1226C2#6246011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
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. #44923C2semidirect
3. #32619C2semidirect
4. #32603C2semidirect
5. #32454C2semidirect
6. #32432C2semidirect
7. #32108C2semidirect
8. #32087C2semidirect
9. #30817C2semidirect
10. #30806C2semidirect
12. #28419C2semidirect
13. #28407C2semidirect
14. #28060C2semidirect
15. #28030C2semidirect
18. #27258C2semidirect
20. #26351C2semidirect
21. #26330C2semidirect
22. #26320C2semidirect
23. #26171C2semidirect
24. #26161C2semidirect
25. #25095C2semidirect
27. #23736C2semidirect
28. #23244C2semidirect
29. #23036C2semidirect
31. #22054C2semidirect

Maximal subgroups

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

subgroupindex
#449232
#429402
#326192
#326032
#324542
#324322
#321082
#320872
#308172
#308062
#285892
#284192
#284072
#280602
#280302
#279842
#272752
#272582
#263592
#263512
#263302
#263202
#261712
#261612
#250952
#250862
#237362
#232442
#230362
#230232
#220542