Finite Group Databasebeta

← #7584049

Subgroups — #7584049

Order 512.

1563 conjugacy classes of subgroups.

The subgroup lattice has 1313 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59488C211yesmaximal, characteristic, complemented
2#36462C211yesmaximal, characteristic, complemented
3#31523C211yesmaximal, characteristic, complemented
4#31503C211yesmaximal, characteristic, complemented
5#31160C211yesmaximal, characteristic, complemented
6#30468C211yesmaximal, characteristic
7#29503C211yesmaximal, characteristic, complemented
8#29444C211yesmaximal, characteristic, complemented
9#29005C211yesmaximal, characteristic, complemented
10#29004C211yesmaximal, characteristic, complemented
11#28973C211yesmaximal, characteristic, complemented
12#27481C211yesmaximal, characteristic, complemented
13#27243C211yesmaximal, characteristic, complemented
14#27211C211yesmaximal, characteristic, complemented
15#27202C211yesmaximal, characteristic, complemented
16#26905C211yesmaximal, characteristic, complemented
17#26813C211yesmaximal, characteristic, complemented
18#26781C211yesmaximal, characteristic, complemented
19#26708C211yesmaximal, characteristic, complemented
20#26572C211yesmaximal, characteristic, complemented
21#26268C211yesmaximal, characteristic, complemented
22#24909C211yesmaximal, characteristic, complemented
23#24684C211yesmaximal, characteristic, complemented
24#24493C211yesmaximal, characteristic, complemented
25#23290C211yesmaximal, characteristic, complemented
26#23195C211yesmaximal, characteristic, complemented
27#23067C211yesmaximal, characteristic, complemented
28#22880C211yesmaximal, characteristic, complemented
29#22868C211yesmaximal, characteristic, complemented
30#21507C211yesmaximal, characteristic, complemented
31#21122C211yesmaximal, characteristic, complemented
32C2×#496C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#478C2211yescharacteristic, complemented
35C2×#476C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#447C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×#442C2211yescharacteristic
40C2×#442C2211yescharacteristic
41C2×#440C2211yescharacteristic, complemented
42C2×C4×D8C2211yescharacteristic
43C2×#418C2211yescharacteristic
44#2860C2211yescharacteristic, complemented
45#2850—21no—
46#2746—21no—
47#2735—21no—
48#2609—21no—
49#2578—21no—
50#2576—21no—
51#2572—21no—
52#2566C2211yescharacteristic
53#2560—21no—
54#2559—21no—
55#2554—21no—
56#2518—21no—
57#2508C2211yescharacteristic, complemented
58#2494C2211yescharacteristic
59#2491C2211yescharacteristic
60#2489C2211yescharacteristic
61#2482—21no—
62#2480—21no—
63#2459—21no—
64#2454C2211yescharacteristic
65#2452C2211yescharacteristic, complemented
66#2447C2211yescharacteristic
67#2447C2211yescharacteristic
68#2445C2211yescharacteristic, complemented
69#2435C2211yescharacteristic
70#2428C2211yescharacteristic
71#2423C2211yescharacteristic
72#2420C2211yescharacteristic
73#2369C2211yescharacteristic, complemented
74#2367C2211yescharacteristic
75#2366C2211yescharacteristic, complemented
76#2363C2211yescharacteristic
77#2363C2211yescharacteristic
78#2357C2211yescharacteristic, complemented
79#2354C2211yescharacteristic
80#2347C2211yescharacteristic
81#2342—21no—
82D4×C22⋊C4C2211yescharacteristic
83D4×C22⋊C4C2211yescharacteristic
84C4×#126C2211yescharacteristic
85C4×#124C2211yescharacteristic
86C4×#123—21no—
87#2293C2211yescharacteristic
88C42×D4C2211yescharacteristic, complemented
89#2094C2211yescharacteristic, complemented
90#2092C2211yescharacteristic
91#2088C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2077C2211yescharacteristic
96#2074C2211yescharacteristic, complemented
97#2073C2211yescharacteristic, complemented
98#2071C2211yescharacteristic, complemented
99#2067C2211yescharacteristic, complemented
100#2066C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic
103#2059C2211yescharacteristic, complemented
104#2055C2211yescharacteristic, complemented
105#2054C2211yescharacteristic
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2041C2211yescharacteristic, complemented
112#2034C2211yescharacteristic
113#2033C2211yescharacteristic
114#2025C2211yescharacteristic, complemented
115#2024C2211yescharacteristic, complemented
116#2023C2211yescharacteristic
117#2012C2211yescharacteristic
118#2011C2211yescharacteristic
119#2000C2211yescharacteristic
120#2000C2211yescharacteristic
121#1991C2211yescharacteristic, complemented
122#1990C2211yescharacteristic, complemented
123#1983C2211yescharacteristic
124#1983C2211yescharacteristic
125#1982C2211yescharacteristic, complemented
126#1973C2211yescharacteristic, complemented
127#1972C2211yescharacteristic
128#1972C2211yescharacteristic
129#1970C2211yescharacteristic
130#1968C2211yescharacteristic, complemented
131#1968C2211yescharacteristic, complemented
132#1949C2211yescharacteristic, complemented
133#1947C2211yescharacteristic, complemented
134#1943C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1939C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic, complemented
141#1935C2211yescharacteristic, complemented
142#1934C2211yescharacteristic
143#1928C2211yescharacteristic, complemented
144#1927C2211yescharacteristic, complemented
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic, complemented
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic
154#1920C2211yescharacteristic, complemented
155#1920C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1919C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1916C2211yescharacteristic, complemented
163#1895C2211yescharacteristic
164#1895C2211yescharacteristic
165#1894C2211yescharacteristic
166#1880C2211yescharacteristic, complemented
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1877C2211yescharacteristic, complemented
177#1877C2211yescharacteristic, complemented
178#1865C2211yescharacteristic, complemented
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic, complemented
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1862C2211yescharacteristic, complemented
184#1854C2211yescharacteristic
185#1854C2211yescharacteristic
186#1851C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic, complemented
189#1786C2211yescharacteristic
190#1776C2211yescharacteristic, complemented
191#1776C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1770C2211yescharacteristic, complemented
194#1767C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1745C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#127C2311yescharacteristic
213C2×#126—21no—
214C2×#126D411yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#123—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8C2311yescharacteristic
222C2×#121—21no—
223C2×#121C2311yescharacteristic
224C2×#121C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×#117—21no—
236C2×#117—21no—
237C2×#117C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C42—21no—
241#496—24no—
242#485—42no—
243#478—42no—
244#476—24no—
245#463—24no—
246#447—24no—
247#447—24no—
248#442—24no—
249#442—42no—
250#440—42no—
251C4×D8—42no—
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267#418—42no—
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306#401—21no—
307#400—21no—
308#400—21no—
309#399—21no—
310#399—21no—
311#398—21no—
312#398—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#393—21no—
332#393—21no—
333#392—21no—
334#391—21no—
335#391—21no—
336#391C2311yescharacteristic
337#391C2311yescharacteristic
338#391C2311yescharacteristic
339#390—21no—
340#390—21no—
341#390—21no—
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#389—21no—
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388D411yescharacteristic
386#388D411yescharacteristic
387#388D411yescharacteristic
388#387—21no—
389#387—21no—
390#387—21no—
391#387D411yescharacteristic
392#387D411yescharacteristic
393#387D411yescharacteristic
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#384C2311yescharacteristic
413#383—21no—
414#383D411yescharacteristic
415#382—21no—
416#382—21no—
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#381—21no—
420#381—21no—
421#381—21no—
422#381—21no—
423#380—21no—
424#380—21no—
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#379—21no—
429#379—21no—
430#379—21no—
431#379—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C43C2311yescharacteristic
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#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8—21no—
492C22×Q8C2411yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2411yescharacteristic
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—22no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×D8—22no—
524C2×D8—22no—
525C2×D8—22no—
526C2×D8—22no—
527C2×D8—22no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8#4114yes—
535C2×M16—41no—
536C2×M16—41no—
537C2×M16—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C4⋊Q8—22no—
547C4⋊Q8—41no—
548#127—22no—
549#127—41no—
550#126—42no—
551#126—82no—
552#125—41no—
553#125—41no—
554#124—22no—
555#124—22no—
556#124—41no—
557#124—41no—
558#124—82no—
559#123—44no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562C22⋊Q8—82no—
563#121—22no—
564#121—22no—
565#121—41no—
566#121—41no—
567#121—82no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—22no—
574C4×D4—22no—
575C4×D4—22no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—82no—
587#117—22no—
588#117—41no—
589#117—82no—
590#117—82no—
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⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
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—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—44no—
668C2×C22⋊C4—82no—
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—82no—
685C2×C42C2×D411yescharacteristic
686C2×C42C2×D411yescharacteristic
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#107—22no—
696#107—22no—
697#107—41no—
698#107—41no—
699#106—22no—
700#106—22no—
701#106—22no—
702#106—22no—
703#106—41no—
704#106—41no—
705C4⋊C8—22no—
706C4⋊C8—22no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710#103—22no—
711#103—22no—
712#103—41no—
713#103—41no—
714#103—41no—
715#103—41no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—41no—
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#4114yes—
738C22⋊C8—22no—
739C22⋊C8—22no—
740C22⋊C8—41no—
741#97—22no—
742#97—22no—
743#97—41no—
744#97—41no—
745#97—41no—
746C4×C8—41no—
747C4×C8—41no—
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
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—42no—
794C24—42no—
795C24—42no—
796C24—81no—
797C24—81no—
798C24—81no—
799C24—81no—
800C24C22×D411yescharacteristic
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—42no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—21no—
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—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—44no—
838C2×D4—42no—
839C2×D4—81no—
840C2×D4—81no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—82no—
844C2×D4—82no—
845C2×D4—82no—
846C2×D4—81no—
847C2×D4—81no—
848C2×D4—81no—
849C2×D4—81no—
850C2×D4C2×#4112yes—
851C2×D4C2×#4112yes—
852C2×D4C2×#4112yes—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4—81no—
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
909SD16—44no—
910SD16—82no—
911D8—44no—
912D8—44no—
913D8—44no—
914D8—82no—
915M16—82no—
916C2×C8—21no—
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×C8C2×#4112yes—
939C2×C8C2×#4112yes—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
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—41no—
963C4⋊C4—41no—
964C4⋊C4—41no—
965C4⋊C4—41no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4C2×#4112yes—
983C4⋊C4H(5,𝔽2)12yes—
984C22⋊C4—22no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
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—42no—
1010C22⋊C4—42no—
1011C22⋊C4—42no—
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—81no—
1032C22⋊C4—81no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—41no—
1046C42—41no—
1047C42—41no—
1048C42—41no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42—81no—
1053C42—81no—
1054C42—81no—
1055C42—81no—
1056C42—81no—
1057C42—81no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
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—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—84no—
1094C23—84no—
1095C23—84no—
1096C23—162no—
1097C23—162no—
1098C23—162no—
1099C23—162no—
1100C23C23×D411yescharacteristic
1101Q8—41no—
1102Q8—41no—
1103Q8—41no—
1104Q8—41no—
1105Q8—162no—
1106D4—22no—
1107D4—22no—
1108D4—22no—
1109D4—22no—
1110D4—22no—
1111D4—22no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—84no—
1123D4—84no—
1124D4—162no—
1125D4—162no—
1126D4—162no—
1127C2×C4—21no—
1128C2×C4—21no—
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—21no—
1140C2×C4—21no—
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—22no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
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—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—84no—
1206C2×C4—84no—
1207C2×C4—84no—
1208C2×C4—84no—
1209C2×C4—84no—
1210C2×C4—162no—
1211C2×C4—162no—
1212C2×C4—162no—
1213C2×C4#57512yes—
1214C2×C4C22×#4111yescharacteristic
1215C2×C4C22×#4111yescharacteristic
1216C2×C4C2×H(5,𝔽2)11yescharacteristic
1217C2×C4#58511yescharacteristic
1218C2×C4#58511yescharacteristic
1219C2×C4#58511yescharacteristic
1220C8—22no—
1221C8—22no—
1222C8—41no—
1223C8—41no—
1224C8—41no—
1225C8—41no—
1226C8—41no—
1227C8—41no—
1228C22—42no—
1229C22—41no—
1230C22—41no—
1231C22—42no—
1232C22—41no—
1233C22—42no—
1234C22—41no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—41no—
1240C22—42no—
1241C22—41no—
1242C22—42no—
1243C22—41no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—168no—
1264C22D4×#4111yescharacteristic
1265C22D4×#4111yescharacteristic
1266C22#348811yescharacteristic
1267C22C2×#57511yescharacteristic
1268C22#358511yescharacteristic
1269C22#358511yescharacteristic
1270C22#358511yescharacteristic
1271C4—22no—
1272C4—41no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—42no—
1283C4—41no—
1284C4—41no—
1285C4—42no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4#348111yescharacteristic
1297C4#349111yescharacteristic
1298C4#351011yescharacteristic
1299C4#356211yescharacteristic
1300C2—81no—
1301C2—82no—
1302C2—82no—
1303C2—82no—
1304C2—161no—
1305C2#5917711yescharacteristic
1306C2#6145611yescharacteristic
1307C2#6146411yescharacteristic
1308C2#6150511yescharacteristic
1309C2#6150611yescharacteristic
1310C2#6197511yescharacteristic
1311C2#6208311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30468C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#126 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59488C2semidirect
2. #36462C2semidirect
3. #31523C2semidirect
4. #31503C2semidirect
5. #31160C2semidirect
7. #29503C2semidirect
8. #29444C2semidirect
9. #29005C2semidirect
10. #29004C2semidirect
11. #28973C2semidirect
12. #27481C2semidirect
13. #27243C2semidirect
14. #27211C2semidirect
15. #27202C2semidirect
16. #26905C2semidirect
17. #26813C2semidirect
18. #26781C2semidirect
19. #26708C2semidirect
20. #26572C2semidirect
21. #26268C2semidirect
22. #24909C2semidirect
23. #24684C2semidirect
24. #24493C2semidirect
25. #23290C2semidirect
26. #23195C2semidirect
27. #23067C2semidirect
28. #22880C2semidirect
29. #22868C2semidirect
30. #21507C2semidirect
31. #21122C2semidirect
34. C2×#478C22semidirect
41. C2×#440C22semidirect
44. #2860C22semidirect
57. #2508C22semidirect
65. #2452C22semidirect
68. #2445C22semidirect
73. #2369C22semidirect
75. #2366C22semidirect
78. #2357C22semidirect
88. C42×D4C22semidirect
89. #2094C22semidirect
91. #2088C22semidirect
92. #2086C22semidirect
93. #2085C22semidirect
96. #2074C22semidirect
97. #2073C22semidirect
98. #2071C22semidirect
99. #2067C22semidirect
100. #2066C22semidirect
103. #2059C22semidirect
104. #2055C22semidirect
111. #2041C22semidirect
114. #2025C22semidirect
115. #2024C22semidirect
121. #1991C22semidirect
122. #1990C22semidirect
125. #1982C22semidirect
126. #1973C22semidirect
130. #1968C22semidirect
131. #1968C22semidirect
132. #1949C22semidirect
133. #1947C22semidirect
134. #1943C22semidirect
135. #1943C22semidirect
136. #1939C22semidirect
140. #1936C22semidirect
141. #1935C22semidirect
143. #1928C22semidirect
144. #1927C22semidirect
147. #1926C22semidirect
154. #1920C22semidirect
155. #1920C22semidirect
156. #1920C22semidirect
157. #1919C22semidirect
158. #1919C22semidirect
159. #1919C22semidirect
160. #1917C22semidirect
161. #1917C22semidirect
162. #1916C22semidirect
166. #1880C22semidirect
176. #1877C22semidirect
177. #1877C22semidirect
178. #1865C22semidirect
180. #1864C22semidirect
183. #1862C22semidirect
188. #1804C22semidirect
190. #1776C22semidirect
191. #1776C22semidirect
192. #1771C22semidirect
193. #1770C22semidirect
194. #1767C22semidirect
195. #1763C22semidirect
198. #1762C22semidirect
202. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#594882
#364622
#315232
#315032
#311602
#304682
#295032
#294442
#290052
#290042
#289732
#274812
#272432
#272112
#272022
#269052
#268132
#267812
#267082
#265722
#262682
#249092
#246842
#244932
#232902
#231952
#230672
#228802
#228682
#215072
#211222