Subgroups — #38763526

Order 25408.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20263741	C₂	1	2	yes	maximal
2	C₄⋊#15691794	C₂	1	4	yes	maximal, complemented
3	C₄²×D₃₉₇	C₂	1	1	yes	maximal, characteristic
4	#20263741	—	2	4	no	—
5	C₂×#15691794	C₂²	1	4	yes	—
6	C₂×C₄×D₃₉₇	C₄	1	2	yes	—
7	C₂×C₄×D₃₉₇	C₂²	1	1	yes	characteristic
8	C₄×Dic₃₉₇	C₄	1	1	yes	characteristic
9	C₄×Dic₃₉₇	C₂²	1	2	yes	—
10	C₄²×C₃₉₇	C₄	1	1	yes	characteristic
11	#15691794	—	2	4	no	—
12	C₂²×D₃₉₇	C₂×C₄	1	1	yes	characteristic
13	C₂×Dic₃₉₇	C₂×C₄	1	2	yes	—
14	C₂×Dic₃₉₇	C₂³	1	1	yes	characteristic
15	C₄×D₃₉₇	—	2	4	no	—
16	C₄×D₃₉₇	D₄	1	2	yes	—
17	C₄×D₃₉₇	Q₈	1	2	yes	—
18	C₂×C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₃₉₇	C₂×C₄	1	2	yes	—
20	C₂²×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
21	C₂×D₃₉₇	—	2	2	no	—
22	C₂×D₃₉₇	C₄⋊C₄	1	2	yes	—
23	C₄×C₃₉₇	C₄⋊C₄	1	2	yes	—
24	C₄×C₃₉₇	M₁₆	1	4	yes	complemented
25	Dic₃₉₇	—	2	2	no	—
26	Dic₃₉₇	C₂×D₄	1	1	yes	characteristic
27	Dic₃₉₇	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₃₉₇	C₂×C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₃₉₇	C₂×M₁₆	1	2	yes	—
30	D₃₉₇	—	2	2	no	—
31	C₃₉₇	#423	1	1	yes	characteristic, complemented, Sylow
32	#423	—	397	1	no	maximal, Sylow
33	C₂×M₁₆	—	397	2	no	—
34	C₂×C₄²	—	397	1	no	—
35	C₄⋊C₈	—	397	4	no	—
36	C₂²×C₄	—	397	2	no	—
37	C₂²×C₄	—	397	1	no	—
38	M₁₆	—	794	4	no	—
39	C₂×C₈	—	397	4	no	—
40	C₄²	—	397	1	no	—
41	C₄²	—	397	2	no	—
42	C₄²	#13097544	1	1	yes	characteristic
43	C₂³	—	397	1	no	—
44	C₂×C₄	—	794	4	no	—
45	C₂×C₄	—	397	2	no	—
46	C₂×C₄	—	397	1	no	—
47	C₂×C₄	—	397	2	no	—
48	C₂×C₄	—	397	2	no	—
49	C₂×C₄	C₂×#13097544	1	1	yes	characteristic
50	C₂×C₄	C₂×#13097544	1	2	yes	—
51	C₈	—	794	4	no	—
52	C₂²	—	794	2	no	—
53	C₂²	—	397	2	no	—
54	C₂²	C₂²×#13097544	1	1	yes	characteristic
55	C₄	—	794	2	no	—
56	C₄	—	397	1	no	—
57	C₄	—	397	1	no	—
58	C₄	C₄⋊#13097544	1	2	yes	—
59	C₄	#20263741	1	4	yes	complemented
60	C₂	—	794	2	no	—
61	C₂	C₂×C₄⋊#13097544	1	1	yes	characteristic
62	C₂	C₂×#20263741	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#13097544
commutator, socle	C₂²×C₃₉₇	C₂²×C₄
Fitting	C₄²×C₃₉₇	C₄
prime radical	C₂²×D₃₉₇	C₂×C₄
cosocle	C₂×Dic₃₉₇	C₂³
hypercenter	C₄²	#13097544
hypocenter	C₃₉₇	#423
LCS	G ▷ C₂²×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₄⋊#15691794	C₂	semidirect
24. C₄×C₃₉₇	M₁₆	semidirect
31. C₃₉₇	#423	semidirect
59. C₄	#20263741	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20263741	2
C₄⋊#15691794	2
C₄²×D₃₉₇	2
#423	397