Subgroups — #1304×C₁₉₇ #38738238

Order 25216.

396 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#379×C₁₉₇	C₂	1	3	yes	maximal
2	C₂⁵×C₁₉₇	C₂²	1	1	yes	characteristic
3	C₂×C₂²⋊C₄×C₁₉₇	—	2	6	no	—
4	C₂×C₂²⋊C₄×C₁₉₇	C₄	1	6	yes	complemented
5	C₂⁴×C₁₉₇	—	4	6	no	—
6	C₂⁴×C₁₉₇	C₂×C₄	1	3	yes	—
7	C₂⁴×C₁₉₇	D₄	1	3	yes	—
8	C₂⁴×C₁₉₇	Q₈	1	1	yes	characteristic
9	C₂²×C₄×C₁₉₇	—	2	6	no	—
10	C₂²⋊C₄×C₁₉₇	—	4	12	no	—
11	C₂²⋊C₄×C₁₉₇	—	4	6	no	—
12	C₂³×C₁₉₇	—	2	6	no	—
13	C₂³×C₁₉₇	—	2	12	no	—
14	C₂³×C₁₉₇	—	4	6	no	—
15	C₂³×C₁₉₇	—	4	3	no	—
16	C₂³×C₁₉₇	—	4	3	no	—
17	C₂³×C₁₉₇	—	4	16	no	—
18	C₂³×C₁₉₇	C₄²	1	1	yes	characteristic
19	C₂³×C₁₉₇	C₂²⋊C₄	1	3	yes	—
20	C₂³×C₁₉₇	C₄⋊C₄	1	3	yes	—
21	C₂×C₄×C₁₉₇	—	4	12	no	—
22	C₂×C₄×C₁₉₇	—	4	6	no	—
23	C₂²×C₁₉₇	—	2	6	no	—
24	C₂²×C₁₉₇	—	2	3	no	—
25	C₂²×C₁₉₇	—	2	3	no	—
26	C₂²×C₁₉₇	—	2	6	no	—
27	C₂²×C₁₉₇	—	4	12	no	—
28	C₂²×C₁₉₇	—	4	12	no	—
29	C₂²×C₁₉₇	—	4	4	no	—
30	C₂²×C₁₉₇	#95	1	1	yes	characteristic
31	C₂²×C₁₉₇	#99	1	6	yes	—
32	C₄×C₁₉₇	—	8	6	no	—
33	C₂×C₁₉₇	—	2	6	no	—
34	C₂×C₁₉₇	—	4	1	no	—
35	C₂×C₁₉₇	—	4	3	no	—
36	C₂×C₁₉₇	#342	1	3	yes	—
37	C₁₉₇	#1304	1	1	yes	characteristic, direct product factor, Sylow
38	#1304	C₁₉₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	#379	C₂×C₁₉₇	1	3	yes	—
40	C₂⁵	C₂²×C₁₉₇	1	1	yes	characteristic
41	C₂×C₂²⋊C₄	—	2	6	no	—
42	C₂×C₂²⋊C₄	C₄×C₁₉₇	1	6	yes	complemented
43	C₂⁴	—	4	6	no	—
44	C₂⁴	C₂×C₄×C₁₉₇	1	3	yes	—
45	C₂⁴	D₄×C₁₉₇	1	3	yes	—
46	C₂⁴	Q₈×C₁₉₇	1	1	yes	characteristic
47	C₂²×C₄	—	2	6	no	—
48	C₂²⋊C₄	—	4	12	no	—
49	C₂²⋊C₄	—	4	6	no	—
50	C₂³	—	2	6	no	—
51	C₂³	—	2	12	no	—
52	C₂³	—	4	6	no	—
53	C₂³	—	4	3	no	—
54	C₂³	—	4	3	no	—
55	C₂³	—	4	16	no	—
56	C₂³	C₄²×C₁₉₇	1	1	yes	characteristic
57	C₂³	C₂²⋊C₄×C₁₉₇	1	3	yes	—
58	C₂³	C₄⋊C₄×C₁₉₇	1	3	yes	—
59	C₂×C₄	—	4	12	no	—
60	C₂×C₄	—	4	6	no	—
61	C₂²	—	2	6	no	—
62	C₂²	—	2	3	no	—
63	C₂²	—	2	3	no	—
64	C₂²	—	2	6	no	—
65	C₂²	—	4	12	no	—
66	C₂²	—	4	12	no	—
67	C₂²	—	4	4	no	—
68	C₂²	#95×C₁₉₇	1	1	yes	characteristic
69	C₂²	#99×C₁₉₇	1	6	yes	—
70	C₄	—	8	6	no	—
71	C₂	—	2	6	no	—
72	C₂	—	4	1	no	—
73	C₂	—	4	3	no	—
74	C₂	#342×C₁₉₇	1	3	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉₇	#95
commutator	C₂³	C₄²×C₁₉₇
Frattini, cosocle	C₂⁵	C₂²×C₁₉₇
prime radical	C₂⁵×C₁₉₇	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉₇ ◁ C₂⁵×C₁₉₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₂×C₂²⋊C₄×C₁₉₇	C₄	semidirect
37. C₁₉₇	#1304	direct (N × H)
38. #1304	C₁₉₇	direct (N × H)
42. C₂×C₂²⋊C₄	C₄×C₁₉₇	semidirect

Maximal subgroups

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

subgroup	index
#379×C₁₉₇	2
#1304	197

Subgroups — #1304×C197 #38738238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1304×C₁₉₇ #38738238