Finite Group Databasebeta

← #7018166

Subgroups — #7018166

Order 512.

1577 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59862C211yesmaximal, characteristic, complemented
2#39409C211yesmaximal, characteristic, complemented
3#32605C211yesmaximal, characteristic, complemented
4#32550C211yesmaximal, characteristic, complemented
5#32487C211yesmaximal, characteristic, complemented
6#32300C211yesmaximal, characteristic, complemented
7#31855C211yesmaximal, characteristic, complemented
8#31209C211yesmaximal, characteristic, complemented
9#31008C211yesmaximal, characteristic, complemented
10#31008C211yesmaximal, characteristic, complemented
11#29466C211yesmaximal, characteristic, complemented
12#29025C211yesmaximal, characteristic, complemented
13#29016C211yesmaximal, characteristic, complemented
14#28885C211yesmaximal, characteristic, complemented
15#28276C211yesmaximal, characteristic, complemented
16#28017C211yesmaximal, characteristic, complemented
17#27557C211yesmaximal, characteristic, complemented
18#27539C211yesmaximal, characteristic, complemented
19#27367C211yesmaximal, characteristic, complemented
20#27179C211yesmaximal, characteristic, complemented
21#27179C211yesmaximal, characteristic, complemented
22#27075C211yesmaximal, characteristic, complemented
23#26587C211yesmaximal, characteristic, complemented
24#25309C211yesmaximal, characteristic, complemented
25#25168C211yesmaximal, characteristic
26#24500C211yesmaximal, characteristic, complemented
27#23700C211yesmaximal, characteristic, complemented
28#23108C211yesmaximal, characteristic, complemented
29#23054C211yesmaximal, characteristic, complemented
30#23007C211yesmaximal, characteristic, complemented
31#22040C211yesmaximal, characteristic, complemented
32C2×#539—21no—
33C2×#463C2211yescharacteristic
34C2×#463C2211yescharacteristic
35C2×#459C2211yescharacteristic
36C2×#447C2211yescharacteristic
37C2×#447C2211yescharacteristic
38C2×#446C2211yescharacteristic, complemented
39C2×#442C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic, complemented
41C2×#431C2211yescharacteristic
42#2854C2211yescharacteristic
43#2796—21no—
44#2751—21no—
45#2728—21no—
46#2707—21no—
47#2693—21no—
48#2691—21no—
49#2630—21no—
50#2595—21no—
51#2592C2211yescharacteristic
52#2580C2211yescharacteristic
53#2561—21no—
54#2538C2211yescharacteristic, complemented
55#2538C2211yescharacteristic, complemented
56#2516—21no—
57#2513C2211yescharacteristic
58#2513C2211yescharacteristic
59#2512C2211yescharacteristic, complemented
60#2506C2211yescharacteristic, complemented
61#2506C2211yescharacteristic, complemented
62#2503C2211yescharacteristic
63#2496C2211yescharacteristic
64#2483—21no—
65#2482—21no—
66#2481—21no—
67#2460—21no—
68#2448C2211yescharacteristic
69#2447C2211yescharacteristic
70#2445C2211yescharacteristic, complemented
71#2435C2211yescharacteristic
72#2428C2211yescharacteristic
73#2422C2211yescharacteristic
74#2422C2211yescharacteristic
75#2367C2211yescharacteristic
76#2366C2211yescharacteristic, complemented
77#2357C2211yescharacteristic
78D4×C4⋊C4C2211yescharacteristic, complemented
79#2344C2211yescharacteristic
80#2342—21no—
81D4×C22⋊C4C2211yescharacteristic
82C4×C22⋊Q8C2211yescharacteristic
83C4×C22⋊Q8C2211yescharacteristic
84C4×#121C2211yescharacteristic
85C2×#390C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2095C2211yescharacteristic, complemented
91#2088C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic
95#2073C2211yescharacteristic, complemented
96#2071C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2066C2211yescharacteristic, complemented
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic, complemented
110#2055C2211yescharacteristic, complemented
111#2055C2211yescharacteristic, complemented
112#2054C2211yescharacteristic
113#2054C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2014C2211yescharacteristic, complemented
121#2012C2211yescharacteristic
122#2012C2211yescharacteristic
123#2011C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1984C2211yescharacteristic, complemented
127#1972C2211yescharacteristic
128#1972C2211yescharacteristic
129#1972C2211yescharacteristic
130#1970C2211yescharacteristic
131#1970C2211yescharacteristic
132#1970C2211yescharacteristic
133#1970C2211yescharacteristic
134#1968C2211yescharacteristic, complemented
135#1961C2211yescharacteristic, complemented
136#1959C2211yescharacteristic
137#1959C2211yescharacteristic
138#1949C2211yescharacteristic, complemented
139#1948C2211yescharacteristic, complemented
140#1948C2211yescharacteristic, complemented
141#1943C2211yescharacteristic, complemented
142#1943C2211yescharacteristic, complemented
143#1941C2211yescharacteristic, complemented
144#1939C2211yescharacteristic, complemented
145#1936C2211yescharacteristic
146#1935C2211yescharacteristic, complemented
147#1935C2211yescharacteristic, complemented
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1928C2211yescharacteristic, complemented
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic, complemented
160#1925C2211yescharacteristic, complemented
161#1924C2211yescharacteristic
162#1924C2211yescharacteristic
163#1924C2211yescharacteristic
164#1924C2211yescharacteristic
165#1921C2211yescharacteristic, complemented
166#1921C2211yescharacteristic, complemented
167#1919C2211yescharacteristic, complemented
168#1916C2211yescharacteristic, complemented
169#1916C2211yescharacteristic, complemented
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1877C2211yescharacteristic, complemented
178#1874C2211yescharacteristic
179#1874C2211yescharacteristic
180#1865C2211yescharacteristic, complemented
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1864C2211yescharacteristic, complemented
185#1864C2211yescharacteristic, complemented
186#1852C2211yescharacteristic
187#1852C2211yescharacteristic
188#1847C2211yescharacteristic, complemented
189#1804C2211yescharacteristic, complemented
190#1802C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193C4×#106C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic, complemented
199#1762C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic, complemented
202C4×C22⋊C8C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210#539—48no—
211C2×#127C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#125—21no—
215C2×#125—21no—
216C2×#124C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#123—21no—
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8D411yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117—21no—
240C22×C4⋊C4—21no—
241C22×C4⋊C4C2311yescharacteristic
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245C22×C42C2311yescharacteristic
246#463—24no—
247#463—42no—
248#459—24no—
249#447—24no—
250#447—42no—
251#446—42no—
252#442—42no—
253C4×SD16—42no—
254#431—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×#97C2311yescharacteristic
306C2×#97C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308C2×C4×C8C2311yescharacteristic
309C2×C4×C8C2311yescharacteristic
310C2×C4×C8C2311yescharacteristic
311#400—21no—
312#400—21no—
313#400—21no—
314#400—21no—
315#400—21no—
316#399—21no—
317#399—21no—
318#398—21no—
319#398—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#394—21no—
343#394—21no—
344#393—21no—
345#393—21no—
346#392—21no—
347#391D411yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#390—21no—
352#390—21no—
353#390—21no—
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#389D411yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387D411yescharacteristic
403#387D411yescharacteristic
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385D411yescharacteristic
422#385D411yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#381—21no—
429#381—21no—
430#381—21no—
431#381—21no—
432#381—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380D411yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441#379—21no—
442#379—21no—
443C4×C4⋊C4—21no—
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
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⋊C4—21no—
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
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
488C25—21no—
489C22×Q8C2×D411yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×D4—22no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2411yescharacteristic
516C2×SD16—22no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×D8—22no—
523C2×D8—22no—
524C2×D8—22no—
525C2×D8—41no—
526C2×D8—41no—
527C2×D8—41no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8#4114yes—
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542#127—22no—
543#127—41no—
544#126—44no—
545#126—44no—
546#125—44no—
547#125—44no—
548#124—22no—
549#124—41no—
550#124—41no—
551#124—41no—
552#123—44no—
553#123—44no—
554#123—44no—
555#123—44no—
556C22⋊Q8—24no—
557C22⋊Q8—41no—
558C22⋊Q8—41no—
559C22⋊Q8—44no—
560C22⋊Q8—44no—
561#121—22no—
562#121—44no—
563#121—41no—
564#121—41no—
565#121—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—41no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—44no—
583C4×D4—44no—
584#117—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—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—44no—
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
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—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—44no—
673C2×C22⋊C4—82no—
674C2×C22⋊C4—82no—
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C22⋊C4C2×D411yescharacteristic
677C2×C22⋊C4C2×D411yescharacteristic
678C2×C22⋊C4C2×D411yescharacteristic
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—41no—
686C2×C42—41no—
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705C4⋊C8—22no—
706C4⋊C8—22no—
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—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—41no—
738#102—41no—
739C22⋊C8—22no—
740C22⋊C8—22no—
741C22⋊C8—41no—
742C22⋊C8—41no—
743#97—22no—
744#97—41no—
745#97—41no—
746#97—41no—
747C4×C8—22no—
748C4×C8—41no—
749C4×C8—41no—
750C4×C8—41no—
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#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
789#95C2×D411yescharacteristic
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—42no—
795C24—42no—
796C24—42no—
797C24—42no—
798C24—81no—
799C24—81no—
800C24—81no—
801C24C22×D411yescharacteristic
802C2×Q8—22no—
803C2×Q8—21no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—41no—
810C2×Q8—41no—
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—21no—
832C2×D4—21no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—42no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—81no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4—81no—
845C2×D4—82no—
846C2×D4—82no—
847C2×D4—82no—
848C2×D4—82no—
849C2×D4—81no—
850C2×D4—81no—
851C2×D4—81no—
852C2×D4C2×#4112yes—
853C2×D4C2×#4112yes—
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—21no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—41no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—42no—
883C22×C4—42no—
884C22×C4—42no—
885C22×C4—42no—
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×C4—81no—
896C22×C4—81no—
897C22×C4—81no—
898C22×C4AGL(1,ℤ/8)14yes—
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×C4C22×D411yescharacteristic
911C22×C4C22×D411yescharacteristic
912C22×C4C2511yescharacteristic
913SD16—44no—
914SD16—82no—
915D8—44no—
916D8—82no—
917D8—82no—
918D8—82no—
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—21no—
940C2×C8—21no—
941C2×C8C2×#4112yes—
942C2×C8H(5,𝔽2)12yes—
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—22no—
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—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—42no—
980C4⋊C4—42no—
981C4⋊C4—42no—
982C4⋊C4—42no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—42no—
986C4⋊C4—42no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4—81no—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—41no—
997C22⋊C4—41no—
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—42no—
1013C22⋊C4—42no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
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—
1033C22⋊C4—81no—
1034C22⋊C4—81no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—21no—
1047C42—21no—
1048C42—21no—
1049C42—21no—
1050C42—21no—
1051C42—21no—
1052C42—21no—
1053C42—21no—
1054C42—41no—
1055C42—41no—
1056C42—42no—
1057C42—42no—
1058C42—81no—
1059C42—81no—
1060C42—81no—
1061C42—81no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—22no—
1069C23—22no—
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—41no—
1094C23—41no—
1095C23—41no—
1096C23—84no—
1097C23—84no—
1098C23—84no—
1099C23—84no—
1100C23—162no—
1101C23—162no—
1102C23—162no—
1103C23C2×AGL(1,ℤ/8)12yes—
1104C23C23×D411yescharacteristic
1105Q8—41no—
1106Q8—41no—
1107Q8—41no—
1108Q8—41no—
1109Q8—82no—
1110D4—22no—
1111D4—22no—
1112D4—22no—
1113D4—22no—
1114D4—41no—
1115D4—41no—
1116D4—41no—
1117D4—41no—
1118D4—41no—
1119D4—41no—
1120D4—41no—
1121D4—41no—
1122D4—41no—
1123D4—41no—
1124D4—41no—
1125D4—41no—
1126D4—84no—
1127D4—84no—
1128D4—84no—
1129D4—162no—
1130D4—162no—
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—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—44no—
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—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—82no—
1210C2×C4—84no—
1211C2×C4—84no—
1212C2×C4—162no—
1213C2×C4—162no—
1214C2×C4—162no—
1215C2×C4—162no—
1216C2×C4—162no—
1217C2×C4C2×AGL(1,ℤ/8)12yes—
1218C2×C4C2×AGL(1,ℤ/8)12yes—
1219C2×C4C22×#4111yescharacteristic
1220C2×C4C2×H(5,𝔽2)11yescharacteristic
1221C2×C4#58511yescharacteristic
1222C2×C4#58511yescharacteristic
1223C2×C4#58511yescharacteristic
1224C2×C4#58511yescharacteristic
1225C8—22no—
1226C8—22no—
1227C8—41no—
1228C8—41no—
1229C8—41no—
1230C8—41no—
1231C8—41no—
1232C8—41no—
1233C22—22no—
1234C22—22no—
1235C22—22no—
1236C22—41no—
1237C22—41no—
1238C22—41no—
1239C22—41no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
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—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—168no—
1269C22D4×#4111yescharacteristic
1270C22#348711yescharacteristic
1271C22#349611yescharacteristic
1272C22C22×AGL(1,ℤ/8)11yescharacteristic
1273C22#358411yescharacteristic
1274C22#358411yescharacteristic
1275C22#358511yescharacteristic
1276C4—22no—
1277C4—22no—
1278C4—41no—
1279C4—41no—
1280C4—41no—
1281C4—41no—
1282C4—41no—
1283C4—41no—
1284C4—41no—
1285C4—41no—
1286C4—41no—
1287C4—41no—
1288C4—41no—
1289C4—81no—
1290C4—81no—
1291C4—81no—
1292C4—81no—
1293C4—81no—
1294C4—81no—
1295C4—81no—
1296C4—81no—
1297C4—81no—
1298C4—81no—
1299C4—81no—
1300C4—81no—
1301C4#350511yescharacteristic
1302C4#352111yescharacteristic
1303C4#356011yescharacteristic
1304C4#356611yescharacteristic
1305C2—42no—
1306C2—82no—
1307C2—82no—
1308C2—161no—
1309C2—161no—
1310C2#4304511yescharacteristic
1311C2#6143711yescharacteristic
1312C2#6153611yescharacteristic
1313C2#6189111yescharacteristic
1314C2#6193011yescharacteristic
1315C2#6225311yescharacteristic
1316C2#6232011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25168C2
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. #59862C2semidirect
2. #39409C2semidirect
3. #32605C2semidirect
4. #32550C2semidirect
5. #32487C2semidirect
6. #32300C2semidirect
7. #31855C2semidirect
8. #31209C2semidirect
9. #31008C2semidirect
10. #31008C2semidirect
11. #29466C2semidirect
12. #29025C2semidirect
13. #29016C2semidirect
14. #28885C2semidirect
15. #28276C2semidirect
16. #28017C2semidirect
17. #27557C2semidirect
18. #27539C2semidirect
19. #27367C2semidirect
20. #27179C2semidirect
21. #27179C2semidirect
22. #27075C2semidirect
23. #26587C2semidirect
24. #25309C2semidirect
26. #24500C2semidirect
27. #23700C2semidirect
28. #23108C2semidirect
29. #23054C2semidirect
30. #23007C2semidirect
31. #22040C2semidirect
38. C2×#446C22semidirect
40. C2×C4×SD16C22semidirect
54. #2538C22semidirect
55. #2538C22semidirect
59. #2512C22semidirect
60. #2506C22semidirect
61. #2506C22semidirect
70. #2445C22semidirect
76. #2366C22semidirect
78. D4×C4⋊C4C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2100C22semidirect
89. #2100C22semidirect
90. #2095C22semidirect
91. #2088C22semidirect
92. #2085C22semidirect
95. #2073C22semidirect
99. #2068C22semidirect
102. #2067C22semidirect
103. #2067C22semidirect
104. #2066C22semidirect
109. #2065C22semidirect
110. #2055C22semidirect
111. #2055C22semidirect
120. #2014C22semidirect
126. #1984C22semidirect
134. #1968C22semidirect
135. #1961C22semidirect
138. #1949C22semidirect
139. #1948C22semidirect
140. #1948C22semidirect
141. #1943C22semidirect
142. #1943C22semidirect
143. #1941C22semidirect
144. #1939C22semidirect
146. #1935C22semidirect
147. #1935C22semidirect
152. #1934C22semidirect
153. #1933C22semidirect
154. #1928C22semidirect
156. #1926C22semidirect
159. #1925C22semidirect
160. #1925C22semidirect
165. #1921C22semidirect
166. #1921C22semidirect
167. #1919C22semidirect
168. #1916C22semidirect
169. #1916C22semidirect
170. #1880C22semidirect
177. #1877C22semidirect
180. #1865C22semidirect
184. #1864C22semidirect
185. #1864C22semidirect
188. #1847C22semidirect
189. #1804C22semidirect
193. C4×#106C22semidirect
194. #1771C22semidirect
195. #1771C22semidirect
196. #1770C22semidirect
198. #1762C22semidirect
199. #1762C22semidirect
200. C4×#103C22semidirect
201. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#598622
#394092
#326052
#325502
#324872
#323002
#318552
#312092
#310082
#294662
#290252
#290162
#288852
#282762
#280172
#275572
#275392
#273672
#271792
#270752
#265872
#253092
#251682
#245002
#237002
#231082
#230542
#230072
#220402