Finite Group Databasebeta

← #7035419

Subgroups — #7035419

Order 512.

1501 conjugacy classes of subgroups.

The subgroup lattice has 1257 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59321C211yesmaximal, characteristic, complemented
2#38962C211yesmaximal, characteristic
3#32658C211yesmaximal, characteristic, complemented
4#32649C211yesmaximal, characteristic, complemented
5#32371C211yesmaximal, characteristic, complemented
6#32368C211yesmaximal, characteristic, complemented
7#31539C211yesmaximal, characteristic, complemented
8#31539C211yesmaximal, characteristic, complemented
9#30975C211yesmaximal, characteristic, complemented
10#30951C211yesmaximal, characteristic, complemented
11#29158C211yesmaximal, characteristic, complemented
12#28966C211yesmaximal, characteristic, complemented
13#28951C211yesmaximal, characteristic, complemented
14#28549C211yesmaximal, characteristic, complemented
15#28537C211yesmaximal, characteristic, complemented
16#27953C211yesmaximal, characteristic, complemented
17#26387C211yesmaximal, characteristic, complemented
18#26373C211yesmaximal, characteristic, complemented
19#26346C211yesmaximal, characteristic, complemented
20#26340C211yesmaximal, characteristic, complemented
21#26068C211yesmaximal, characteristic, complemented
22#26062C211yesmaximal, characteristic, complemented
23#25960C211yesmaximal, characteristic
24#25952C211yesmaximal, characteristic
25#25073C211yesmaximal, characteristic, complemented
26#25065C211yesmaximal, characteristic, complemented
27C2×#2094C211yesmaximal, characteristic
28#23238C211yesmaximal, characteristic, complemented
29#22874C211yesmaximal, characteristic
30#22854C211yesmaximal, characteristic
31#22049C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic, complemented
33C2×#499C2211yescharacteristic, complemented
34C2×#479C2211yescharacteristic, complemented
35C2×#475C2211yescharacteristic, complemented
36C2×#478C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C22×#106C2211yescharacteristic
42C22×#106C2211yescharacteristic
43C22×#102C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2851C2211yescharacteristic
46#2791—21no—
47#2791—21no—
48#2784—21no—
49#2780—21no—
50#2748—21no—
51#2692—21no—
52#2626—21no—
53#2582C2211yescharacteristic, complemented
54#2580C2211yescharacteristic
55#2566C2211yescharacteristic
56#2565C2211yescharacteristic, complemented
57#2565C2211yescharacteristic, complemented
58#2563C2211yescharacteristic
59#2552—21no—
60#2552C2211yescharacteristic, complemented
61#2538C2211yescharacteristic
62#2511—21no—
63#2506C2211yescharacteristic, complemented
64#2506C2211yescharacteristic, complemented
65#2502—21no—
66#2473—21no—
67#2473—21no—
68#2454C2211yescharacteristic
69#2454C2211yescharacteristic
70#2454C2211yescharacteristic
71#2452C2211yescharacteristic
72#2442C2211yescharacteristic
73#2442C2211yescharacteristic
74#2442C2211yescharacteristic
75#2440C2211yescharacteristic
76#2437—21no—
77#2437—21no—
78#2360C2211yescharacteristic
79#2360C2211yescharacteristic
80#2355C2211yescharacteristic, complemented
81Q8×C4⋊C4C2211yescharacteristic, complemented
82#2345—21no—
83D4×C22⋊C4C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85#2315—21no—
86C4×C22⋊Q8C2211yescharacteristic
87C4×C22⋊Q8C2211yescharacteristic
88C2×#390C2211yescharacteristic
89C2×#384C2211yescharacteristic
90#2101C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2097C2211yescharacteristic, complemented
93#2096C2211yescharacteristic, complemented
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic
96#2094C2211yescharacteristic
97#2094C2211yescharacteristic
98#2094C2211yescharacteristic
99#2094C2211yescharacteristic
100#2094C2211yescharacteristic
101#2094C2211yescharacteristic
102#2092C2211yescharacteristic
103#2092C2211yescharacteristic
104#2088C2211yescharacteristic, complemented
105#2088C2211yescharacteristic, complemented
106#2085C2211yescharacteristic, complemented
107#2085C2211yescharacteristic, complemented
108#2085C2211yescharacteristic, complemented
109#2084C2211yescharacteristic, complemented
110#2084C2211yescharacteristic, complemented
111#2084C2211yescharacteristic, complemented
112#2083C2211yescharacteristic, complemented
113#2083C2211yescharacteristic, complemented
114#2067C2211yescharacteristic
115#2067C2211yescharacteristic
116#2066C2211yescharacteristic, complemented
117#2066C2211yescharacteristic, complemented
118#2065C2211yescharacteristic
119#2065C2211yescharacteristic
120#2059C2211yescharacteristic, complemented
121#2059C2211yescharacteristic, complemented
122#2059C2211yescharacteristic, complemented
123#2059C2211yescharacteristic, complemented
124#2059C2211yescharacteristic, complemented
125#2058C2211yescharacteristic, complemented
126#2058C2211yescharacteristic, complemented
127#2026C2211yescharacteristic, complemented
128#2025C2211yescharacteristic
129#2025C2211yescharacteristic
130#1992C2211yescharacteristic, complemented
131#1992C2211yescharacteristic, complemented
132#1985C2211yescharacteristic, complemented
133#1984C2211yescharacteristic, complemented
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1968C2211yescharacteristic
138#1949C2211yescharacteristic, complemented
139#1948C2211yescharacteristic, complemented
140#1944C2211yescharacteristic, complemented
141#1943C2211yescharacteristic, complemented
142#1941C2211yescharacteristic, complemented
143#1941C2211yescharacteristic, complemented
144#1936C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1934C2211yescharacteristic
148#1926C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1920C2211yescharacteristic, complemented
153#1920C2211yescharacteristic, complemented
154#1919C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1917C2211yescharacteristic, complemented
159#1916C2211yescharacteristic, complemented
160#1892C2211yescharacteristic
161#1892C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1872C2211yescharacteristic
169#1865C2211yescharacteristic, complemented
170#1865C2211yescharacteristic, complemented
171#1865C2211yescharacteristic, complemented
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic
181#1852C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1850C2211yescharacteristic
185#1850C2211yescharacteristic
186#1847C2211yescharacteristic, complemented
187#1847C2211yescharacteristic, complemented
188#1847C2211yescharacteristic, complemented
189#1846C2211yescharacteristic, complemented
190#1808C2211yescharacteristic
191#1807C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1786C2211yescharacteristic
195#1771C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1752C2211yescharacteristic
200C8×C22⋊C4C2211yescharacteristic
201#1749C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125—21no—
210C2×#125—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8D411yescharacteristic
219C2×C22⋊Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C22×C4⋊C4—21no—
229C22×C4⋊C4—21no—
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C22⋊C4—21no—
234C22×C22⋊C4—21no—
235C22×C22⋊C4—21no—
236C22×C22⋊C4—21no—
237C22×C42C2311yescharacteristic
238#501—42no—
239#499—42no—
240#479—42no—
241#478—42no—
242#478—42no—
243#475—42no—
244#450Q818yescomplemented
245#440—42no—
246C4×SD16—42no—
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106—42no—
256C2×#106—42no—
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102—42no—
282C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302C2×#97C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#399—21no—
311#399—21no—
312#399—21no—
313#399—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#395—21no—
337#393—21no—
338#393—21no—
339#393—21no—
340#393—21no—
341#391—21no—
342#391—21no—
343#391D411yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#390—21no—
348#390—21no—
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389D411yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387D411yescharacteristic
391#387D411yescharacteristic
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385D411yescharacteristic
414#385D411yescharacteristic
415#384—21no—
416#384—21no—
417#384—21no—
418#384—21no—
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#380—21no—
429#380—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380D411yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4—21no—
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C25—21no—
492C22×Q8—21no—
493C22×Q8C2×D411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C2×Q814yes—
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4C2×D411yescharacteristic
512C23×C4C2×D411yescharacteristic
513C23×C4C2411yescharacteristic
514C2×SD16—41no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16C2×Q814yes—
519C2×SD16C2×Q814yes—
520C22×C8—22no—
521C22×C8—22no—
522C22×C8—22no—
523C22×C8—22no—
524C22×C8—41no—
525C22×C8—41no—
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536#125—41no—
537#125—41no—
538#125—41no—
539#125—41no—
540#125—41no—
541#125—41no—
542#125—41no—
543#125—41no—
544#125—82no—
545#125—82no—
546C22⋊Q8—22no—
547C22⋊Q8—42no—
548C22⋊Q8—82no—
549C22⋊Q8—82no—
550C22⋊Q8—82no—
551C22⋊Q8C2×Q814yes—
552C4×Q8—41no—
553C4×Q8—41no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×Q8—41no—
557C4×Q8—41no—
558C4×Q8—41no—
559C4×Q8—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
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—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—44no—
614C2×C4⋊C4—82no—
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⋊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×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
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—44no—
662C2×C22⋊C4—82no—
663C2×C22⋊C4—82no—
664C2×C22⋊C4—82no—
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—41no—
676C2×C42—41no—
677C2×C42C2×D411yescharacteristic
678C2×C42C2×D411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685#107—22no—
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—22no—
694#106—22no—
695#106—22no—
696#106—22no—
697#106—22no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707C4⋊C8—22no—
708C4⋊C8—22no—
709C4⋊C8—41no—
710C4⋊C8—41no—
711#103—22no—
712#103—22no—
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—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102C2×Q814yes—
730#102C2×Q814yes—
731C22⋊C8—22no—
732C22⋊C8C2×Q814yes—
733#97—22no—
734#97—41no—
735#97—41no—
736#97—41no—
737C4×C8—22no—
738C4×C8—41no—
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#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782C24—21no—
783C24—21no—
784C24—24no—
785C24—42no—
786C24—42no—
787C24—81no—
788C24—81no—
789C24—81no—
790C24—81no—
791C24C22×D411yescharacteristic
792C2×Q8—22no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—41no—
799C2×Q8—41no—
800C2×Q8—81no—
801C2×Q8—81no—
802C2×Q8—81no—
803C2×Q8C22×Q812yes—
804C2×D4—24no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—44no—
816C2×D4—44no—
817C2×D4—82no—
818C2×D4—82no—
819C2×D4—81no—
820C2×D4—81no—
821C2×D4C22×Q812yes—
822C2×D4C22×Q812yes—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
828C22×C4—22no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—22no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
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—41no—
845C22×C4—41no—
846C22×C4—41no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4—81no—
864C22×C4—81no—
865C22×C4—81no—
866C22×C4—81no—
867C22×C4—81no—
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×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×Q812yes—
882C22×C42−1+412yes—
883C22×C4C2511yescharacteristic
884SD16—44no—
885SD16—44no—
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×C8—44no—
908C2×C8C22×Q812yes—
909C2×C8C22×Q812yes—
910C2×C8H(5,𝔽2)12yes—
911C2×C8H(5,𝔽2)12yes—
912C4⋊C4—24no—
913C4⋊C4—22no—
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—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
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⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4C22×Q812yes—
986C22⋊C4—24no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—21no—
1018C42—21no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—41no—
1027C42—41no—
1028C42—42no—
1029C42—42no—
1030C42—81no—
1031C42—81no—
1032C42—81no—
1033C42—81no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—22no—
1039C23—22no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—48no—
1053C23—84no—
1054C23—84no—
1055C23—162no—
1056C23—162no—
1057C23—162no—
1058C23—162no—
1059C23D4×Q812yes—
1060C23#57512yes—
1061C23#57712yes—
1062C23C23×D411yescharacteristic
1063Q8—22no—
1064Q8—22no—
1065Q8—41no—
1066Q8—41no—
1067Q8—82no—
1068Q8—162no—
1069D4—22no—
1070D4—22no—
1071D4—22no—
1072D4—22no—
1073D4—41no—
1074D4—41no—
1075D4—41no—
1076D4—41no—
1077D4—84no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—22no—
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—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—44no—
1122C2×C4—44no—
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—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—162no—
1164C2×C4—162no—
1165C2×C4—162no—
1166C2×C4—162no—
1167C2×C4—162no—
1168C2×C4—162no—
1169C2×C4—162no—
1170C2×C4D4×Q812yes—
1171C2×C4#57712yes—
1172C2×C4C23×Q811yescharacteristic
1173C2×C4C2×H(5,𝔽2)11yescharacteristic
1174C2×C4C2×H(5,𝔽2)11yescharacteristic
1175C2×C4C2×2−1+411yescharacteristic
1176C2×C4#58511yescharacteristic
1177C2×C4#58511yescharacteristic
1178C8—22no—
1179C8—22no—
1180C8—22no—
1181C8—22no—
1182C8—41no—
1183C8—41no—
1184C8—41no—
1185C8—41no—
1186C22—22no—
1187C22—22no—
1188C22—22no—
1189C22—22no—
1190C22—22no—
1191C22—22no—
1192C22—42no—
1193C22—42no—
1194C22—42no—
1195C22—42no—
1196C22—42no—
1197C22—42no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—168no—
1207C22#338814yes—
1208C22C2×D4×Q811yescharacteristic
1209C22#348511yescharacteristic
1210C22#349811yescharacteristic
1211C22C2×#57511yescharacteristic
1212C22C2×#57711yescharacteristic
1213C22C2×#57711yescharacteristic
1214C22#358511yescharacteristic
1215C4—22no—
1216C4—22no—
1217C4—41no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—42no—
1225C4—41no—
1226C4—41no—
1227C4—42no—
1228C4—41no—
1229C4—41no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4#350111yescharacteristic
1243C4#350111yescharacteristic
1244C4#353511yescharacteristic
1245C4#353511yescharacteristic
1246C2—24no—
1247C2—82no—
1248C2—82no—
1249C2#4349411yescharacteristic
1250C2C2×#338811yescharacteristic
1251C2#6138211yescharacteristic
1252C2#6172911yescharacteristic
1253C2#6174611yescharacteristic
1254C2#6243011yescharacteristic
1255C2#6244911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
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. #59321C2semidirect
3. #32658C2semidirect
4. #32649C2semidirect
5. #32371C2semidirect
6. #32368C2semidirect
7. #31539C2semidirect
8. #31539C2semidirect
9. #30975C2semidirect
10. #30951C2semidirect
11. #29158C2semidirect
12. #28966C2semidirect
13. #28951C2semidirect
14. #28549C2semidirect
15. #28537C2semidirect
16. #27953C2semidirect
17. #26387C2semidirect
18. #26373C2semidirect
19. #26346C2semidirect
20. #26340C2semidirect
21. #26068C2semidirect
22. #26062C2semidirect
25. #25073C2semidirect
26. #25065C2semidirect
28. #23238C2semidirect
32. C2×#501C22semidirect
33. C2×#499C22semidirect
34. C2×#479C22semidirect
35. C2×#475C22semidirect
53. #2582C22semidirect
56. #2565C22semidirect
57. #2565C22semidirect
60. #2552C22semidirect
63. #2506C22semidirect
64. #2506C22semidirect
80. #2355C22semidirect
81. Q8×C4⋊C4C22semidirect
90. #2101C22semidirect
91. #2097C22semidirect
92. #2097C22semidirect
93. #2096C22semidirect
104. #2088C22semidirect
105. #2088C22semidirect
106. #2085C22semidirect
107. #2085C22semidirect
108. #2085C22semidirect
109. #2084C22semidirect
110. #2084C22semidirect
111. #2084C22semidirect
112. #2083C22semidirect
113. #2083C22semidirect
116. #2066C22semidirect
117. #2066C22semidirect
120. #2059C22semidirect
121. #2059C22semidirect
122. #2059C22semidirect
123. #2059C22semidirect
124. #2059C22semidirect
125. #2058C22semidirect
126. #2058C22semidirect
127. #2026C22semidirect
130. #1992C22semidirect
131. #1992C22semidirect
132. #1985C22semidirect
133. #1984C22semidirect
138. #1949C22semidirect
139. #1948C22semidirect
140. #1944C22semidirect
141. #1943C22semidirect
142. #1941C22semidirect
143. #1941C22semidirect
152. #1920C22semidirect
153. #1920C22semidirect
154. #1919C22semidirect
155. #1918C22semidirect
156. #1917C22semidirect
157. #1917C22semidirect
158. #1917C22semidirect
159. #1916C22semidirect
169. #1865C22semidirect
170. #1865C22semidirect
171. #1865C22semidirect
175. #1863C22semidirect
186. #1847C22semidirect
187. #1847C22semidirect
188. #1847C22semidirect
189. #1846C22semidirect
195. #1771C22semidirect
196. #1770C22semidirect
244. #450Q8semidirect

Maximal subgroups

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

subgroupindex
#593212
#389622
#326582
#326492
#323712
#323682
#315392
#309752
#309512
#291582
#289662
#289512
#285492
#285372
#279532
#263872
#263732
#263462
#263402
#260682
#260622
#259602
#259522
#250732
#250652
C2×#20942
#232382
#228742
#228542
#220492