Finite Group Databasebeta

← #7046395

Subgroups — #7046395

Order 512.

1492 conjugacy classes of subgroups.

The subgroup lattice has 1304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59399C211yesmaximal, characteristic, complemented
2#59208C211yesmaximal, characteristic, complemented
3#32487C211yesmaximal, characteristic, complemented
4#32349C211yesmaximal, characteristic, complemented
5#31949C211yesmaximal, characteristic, complemented
6#31710C211yesmaximal, characteristic, complemented
7#31561C211yesmaximal, characteristic, complemented
8#31020C211yesmaximal, characteristic
9#30641C211yesmaximal, characteristic, complemented
10#30420C211yesmaximal, characteristic, complemented
11#28926C211yesmaximal, characteristic, complemented
12#28120C211yesmaximal, characteristic, complemented
13#28021C211yesmaximal, characteristic, complemented
14#27632C211yesmaximal, characteristic, complemented
15#27567C211yesmaximal, characteristic, complemented
16#27520C211yesmaximal, characteristic, complemented
17#27514C211yesmaximal, characteristic, complemented
18#27357C211yesmaximal, characteristic, complemented
19#27076C211yesmaximal, characteristic, complemented
20#26944C211yesmaximal, characteristic, complemented
21#26568C211yesmaximal, characteristic, complemented
22#26214C211yesmaximal, characteristic, complemented
23#25326C211yesmaximal, characteristic, complemented
24#25231C211yesmaximal, characteristic, complemented
25#25164C211yesmaximal, characteristic, complemented
26#25014C211yesmaximal, characteristic, complemented
27#23765C211yesmaximal, characteristic, complemented
28#22924C211yesmaximal, characteristic, complemented
29#22775C211yesmaximal, characteristic, complemented
30#22359C211yesmaximal, characteristic, complemented
31#22046C211yesmaximal, characteristic, complemented
32C2×#488C2211yescharacteristic, complemented
33C2×#482C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#483C2211yescharacteristic, complemented
36C2×#468C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#440C2211yescharacteristic
41#2795—21no—
42#2783—21no—
43#2757—21no—
44#2749—21no—
45#2603—21no—
46#2602—21no—
47#2566—21no—
48#2566C2211yescharacteristic
49#2558—21no—
50#2554—21no—
51#2538C2211yescharacteristic
52#2534—21no—
53#2526—21no—
54#2526—21no—
55#2513C2211yescharacteristic
56#2512C2211yescharacteristic
57#2512C2211yescharacteristic, complemented
58#2506C2211yescharacteristic, complemented
59#2504C2211yescharacteristic
60#2497C2211yescharacteristic
61#2490C2211yescharacteristic
62#2483—21no—
63#2480—21no—
64#2442C2211yescharacteristic
65#2426C2211yescharacteristic
66#2426C2211yescharacteristic, complemented
67#2422C2211yescharacteristic, complemented
68#2420C2211yescharacteristic
69#2414C2211yescharacteristic
70#2408C2211yescharacteristic
71#2373—21no—
72#2367C2211yescharacteristic, complemented
73#2362C2211yescharacteristic, complemented
74#2361C2211yescharacteristic
75#2358—21no—
76#2357C2211yescharacteristic
77Q8×C4⋊C4C2211yescharacteristic, complemented
78D4×C4⋊C4C2211yescharacteristic
79#2346C2211yescharacteristic, complemented
80D4×C22⋊C4C2211yescharacteristic
81C4×C22⋊Q8C2211yescharacteristic
82C4×#123C2211yescharacteristic
83C4×#121C2211yescharacteristic
84C2×#390C2211yescharacteristic
85#2283C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2099C2211yescharacteristic, complemented
89#2097C2211yescharacteristic, complemented
90#2093C2211yescharacteristic
91#2092C2211yescharacteristic, complemented
92#2088C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic
97#2077C2211yescharacteristic, complemented
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic
100#2074C2211yescharacteristic, complemented
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic, complemented
110#2059C2211yescharacteristic, complemented
111#2059C2211yescharacteristic, complemented
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2054C2211yescharacteristic
115#2042C2211yescharacteristic, complemented
116#2036C2211yescharacteristic
117#2035C2211yescharacteristic
118#2035C2211yescharacteristic, complemented
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#2012C2211yescharacteristic
123#2000C2211yescharacteristic
124#1999C2211yescharacteristic
125#1999C2211yescharacteristic
126#1989C2211yescharacteristic, complemented
127#1972C2211yescharacteristic
128#1972C2211yescharacteristic
129#1972C2211yescharacteristic
130#1970C2211yescharacteristic
131#1954C2211yescharacteristic
132#1949C2211yescharacteristic, complemented
133#1949C2211yescharacteristic, complemented
134#1948C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1941C2211yescharacteristic, complemented
137#1939C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic, complemented
148#1926C2211yescharacteristic, complemented
149#1925C2211yescharacteristic, complemented
150#1924C2211yescharacteristic
151#1924C2211yescharacteristic, complemented
152#1924C2211yescharacteristic, complemented
153#1923C2211yescharacteristic
154#1921C2211yescharacteristic, complemented
155#1919C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1917C2211yescharacteristic, complemented
159#1916C2211yescharacteristic, complemented
160#1895C2211yescharacteristic
161#1895C2211yescharacteristic, complemented
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1875C2211yescharacteristic
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1854C2211yescharacteristic, complemented
179#1853C2211yescharacteristic
180#1853C2211yescharacteristic, complemented
181#1851C2211yescharacteristic, complemented
182#1844C2211yescharacteristic, complemented
183#1836C2211yescharacteristic, complemented
184#1823C2211yescharacteristic
185#1805C2211yescharacteristic, complemented
186#1804C2211yescharacteristic, complemented
187#1804C2211yescharacteristic, complemented
188#1803C2211yescharacteristic, complemented
189#1802C2211yescharacteristic
190#1797C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195#1771C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1763C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200#1753C2211yescharacteristic, complemented
201#1749C2211yescharacteristic
202#1736C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C2×#126—21no—
210C2×#126—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×#123—21no—
215C2×#123D411yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×Q8C2311yescharacteristic
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4—21no—
227C2×C4×D4—21no—
228C2×C4×D4—21no—
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C4⋊C4C2311yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238C22×C22⋊C4—21no—
239C22×C42C2311yescharacteristic
240#488—42no—
241#483—42no—
242#483—42no—
243#482—24no—
244#468—42no—
245#463—42no—
246#450—42no—
247#447—24no—
248#440—24no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302#400—21no—
303#400—21no—
304#400—21no—
305#398—21no—
306#398—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#392—21no—
333#392—21no—
334#391C2311yescharacteristic
335#390—21no—
336#390—21no—
337#390—21no—
338#390—21no—
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#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
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#388D411yescharacteristic
385#388D411yescharacteristic
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#386—21no—
397#386—21no—
398#386—21no—
399#386D411yescharacteristic
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#385D411yescharacteristic
410#384—21no—
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#384C2311yescharacteristic
414#383—21no—
415#382—21no—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#381—21no—
420#381—21no—
421#381—21no—
422#381D411yescharacteristic
423#380—21no—
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#379—21no—
431#379—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
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×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450C4×C22⋊C4C2311yescharacteristic
451#376—21no—
452#376—21no—
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
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
487C25—21no—
488C22×Q8C2411yescharacteristic
489C22×D4—22no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4C2×D411yescharacteristic
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C22×D4C2411yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4C2×D411yescharacteristic
510C23×C4C2×D411yescharacteristic
511C23×C4C2411yescharacteristic
512C23×C4C2411yescharacteristic
513C2×SD16—22no—
514C2×SD16—22no—
515C2×SD16—22no—
516C2×SD16—41no—
517C2×SD16—41no—
518C2×SD16—41no—
519C2×D8—22no—
520C2×D8—22no—
521C2×D8—41no—
522C2×D8—41no—
523C2×D8—41no—
524C2×D8—41no—
525C2×M16—41no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536#126—44no—
537#126—82no—
538#125—41no—
539#125—41no—
540#125—82no—
541#124—22no—
542#124—41no—
543#123—42no—
544#123—82no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547C22⋊Q8—41no—
548C22⋊Q8—41no—
549#121—22no—
550#121—22no—
551#121—41no—
552#121—41no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557#120—44no—
558C4×Q8—22no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—41no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×D4—22no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—82no—
573C4×D4—82no—
574C4×D4—82no—
575#117—22no—
576#117—41no—
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—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
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—82no—
662C2×C22⋊C4—82no—
663C2×C22⋊C4—82no—
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—41no—
683C2×C42—41no—
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#107—22no—
692#107—22no—
693#107—41no—
694#107—41no—
695#106—22no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703C4⋊C8—41no—
704C4⋊C8—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708#103—22no—
709#103—22no—
710#103—22no—
711#103—22no—
712#103—22no—
713#103—41no—
714#102—22no—
715#102—22no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
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#102—41no—
730#102—41no—
731#102#4114yes—
732C22⋊C8—22no—
733C22⋊C8—22no—
734C22⋊C8—41no—
735C22⋊C8—41no—
736C22⋊C8—41no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739#97—22no—
740#97—41no—
741#97—41no—
742C4×C8—41no—
743C4×C8—41no—
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—21no—
785C24—42no—
786C24—42no—
787C24—42no—
788C24—42no—
789C24—81no—
790C24—81no—
791C24—81no—
792C24C22×D411yescharacteristic
793C24C22×D411yescharacteristic
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—21no—
799C2×Q8H(5,𝔽2)12yes—
800C2×D4—22no—
801C2×D4—22no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
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—21no—
816C2×D4—21no—
817C2×D4—21no—
818C2×D4—21no—
819C2×D4—41no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—81no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—82no—
831C2×D4—82no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4C2×#4112yes—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—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—41no—
867C22×C4—41no—
868C22×C4—41no—
869C22×C4—41no—
870C22×C4—41no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C2511yescharacteristic
899SD16—44no—
900SD16—82no—
901D8—82no—
902D8—82no—
903M16—82no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
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×C8C2×#4112yes—
928C4⋊C4—22no—
929C4⋊C4—22no—
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—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
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—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
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⋊C4C2×#4112yes—
980C22⋊C4—22no—
981C22⋊C4—41no—
982C22⋊C4—41no—
983C22⋊C4—41no—
984C22⋊C4—41no—
985C22⋊C4—41no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—42no—
989C22⋊C4—42no—
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—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—
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—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—41no—
1039C42—41no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—42no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—22no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—84no—
1085C23—84no—
1086C23—84no—
1087C23—84no—
1088C23—162no—
1089C23—162no—
1090C23—162no—
1091C23#57712yes—
1092C23C23×D411yescharacteristic
1093Q8—22no—
1094Q8—22no—
1095Q8—41no—
1096Q8—41no—
1097D4—22no—
1098D4—22no—
1099D4—44no—
1100D4—41no—
1101D4—41no—
1102D4—41no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—84no—
1111D4—84no—
1112D4—84no—
1113D4—162no—
1114D4—162no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—22no—
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—22no—
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—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—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—82no—
1198C2×C4—82no—
1199C2×C4—162no—
1200C2×C4—162no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4—162no—
1204C2×C4#57512yes—
1205C2×C4C22×#4111yescharacteristic
1206C2×C4C2×H(5,𝔽2)11yescharacteristic
1207C2×C4#58511yescharacteristic
1208C2×C4#58511yescharacteristic
1209C2×C4#58511yescharacteristic
1210C2×C4#58511yescharacteristic
1211C8—22no—
1212C8—41no—
1213C8—41no—
1214C8—41no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—42no—
1228C22—41no—
1229C22—41no—
1230C22—42no—
1231C22—41no—
1232C22—41no—
1233C22—42no—
1234C22—41no—
1235C22—41no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—168no—
1255C22D4×#4111yescharacteristic
1256C22#348511yescharacteristic
1257C22#348811yescharacteristic
1258C22C2×#57511yescharacteristic
1259C22C2×#57711yescharacteristic
1260C22#358511yescharacteristic
1261C22#358511yescharacteristic
1262C4—22no—
1263C4—41no—
1264C4—41no—
1265C4—42no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—42no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—81no—
1277C4—81no—
1278C4—81no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4#349411yescharacteristic
1288C4#352111yescharacteristic
1289C4#356011yescharacteristic
1290C4#356611yescharacteristic
1291C2—42no—
1292C2—81no—
1293C2—82no—
1294C2—161no—
1295C2—161no—
1296C2#4353511yescharacteristic
1297C2#6146811yescharacteristic
1298C2#6152211yescharacteristic
1299C2#6173611yescharacteristic
1300C2#6178311yescharacteristic
1301C2#6197511yescharacteristic
1302C2#6200911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#31020C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59399C2semidirect
2. #59208C2semidirect
3. #32487C2semidirect
4. #32349C2semidirect
5. #31949C2semidirect
6. #31710C2semidirect
7. #31561C2semidirect
9. #30641C2semidirect
10. #30420C2semidirect
11. #28926C2semidirect
12. #28120C2semidirect
13. #28021C2semidirect
14. #27632C2semidirect
15. #27567C2semidirect
16. #27520C2semidirect
17. #27514C2semidirect
18. #27357C2semidirect
19. #27076C2semidirect
20. #26944C2semidirect
21. #26568C2semidirect
22. #26214C2semidirect
23. #25326C2semidirect
24. #25231C2semidirect
25. #25164C2semidirect
26. #25014C2semidirect
27. #23765C2semidirect
28. #22924C2semidirect
29. #22775C2semidirect
30. #22359C2semidirect
31. #22046C2semidirect
32. C2×#488C22semidirect
35. C2×#483C22semidirect
57. #2512C22semidirect
58. #2506C22semidirect
66. #2426C22semidirect
67. #2422C22semidirect
72. #2367C22semidirect
73. #2362C22semidirect
77. Q8×C4⋊C4C22semidirect
79. #2346C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
88. #2099C22semidirect
89. #2097C22semidirect
91. #2092C22semidirect
92. #2088C22semidirect
93. #2085C22semidirect
94. #2085C22semidirect
97. #2077C22semidirect
100. #2074C22semidirect
103. #2071C22semidirect
109. #2065C22semidirect
110. #2059C22semidirect
111. #2059C22semidirect
115. #2042C22semidirect
118. #2035C22semidirect
126. #1989C22semidirect
132. #1949C22semidirect
133. #1949C22semidirect
134. #1948C22semidirect
135. #1944C22semidirect
136. #1941C22semidirect
137. #1939C22semidirect
147. #1926C22semidirect
148. #1926C22semidirect
149. #1925C22semidirect
151. #1924C22semidirect
152. #1924C22semidirect
154. #1921C22semidirect
155. #1919C22semidirect
156. #1918C22semidirect
157. #1918C22semidirect
158. #1917C22semidirect
159. #1916C22semidirect
161. #1895C22semidirect
172. #1874C22semidirect
174. #1865C22semidirect
178. #1854C22semidirect
180. #1853C22semidirect
181. #1851C22semidirect
182. #1844C22semidirect
183. #1836C22semidirect
185. #1805C22semidirect
186. #1804C22semidirect
187. #1804C22semidirect
188. #1803C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. #1771C22semidirect
196. #1763C22semidirect
197. #1763C22semidirect
198. C4×#103C22semidirect
200. #1753C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#593992
#592082
#324872
#323492
#319492
#317102
#315612
#310202
#306412
#304202
#289262
#281202
#280212
#276322
#275672
#275202
#275142
#273572
#270762
#269442
#265682
#262142
#253262
#252312
#251642
#250142
#237652
#229242
#227752
#223592
#220462