Subgroups — #38763400

Order 25408.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊#13097544	C₂	1	2	yes	maximal
2	C₂×#20263708	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13097544	—	2	2	no	—
4	C₂²⋊#13097544	—	2	2	no	—
5	C₂²⋊#13097544	C₄	1	4	yes	complemented
6	C₂³×D₃₉₇	C₂²	1	1	yes	characteristic
7	C₂²×Dic₃₉₇	C₄	1	1	yes	characteristic, complemented
8	#20263708	—	2	2	no	—
9	C₂²×C₄×C₃₉₇	C₄	1	1	yes	characteristic, complemented
10	C₂×#13097544	—	2	4	no	—
11	C₂×#13097544	—	4	2	no	—
12	C₂×#13097544	—	4	2	no	—
13	C₂²×D₃₉₇	—	4	1	no	—
14	C₂²×D₃₉₇	—	4	1	no	—
15	C₂²×D₃₉₇	C₂×C₄	1	2	yes	—
16	C₂²×D₃₉₇	D₄	1	2	yes	—
17	C₂²×D₃₉₇	D₄	1	1	yes	characteristic
18	C₂²×D₃₉₇	Q₈	1	1	yes	characteristic
19	C₂×Dic₃₉₇	—	2	1	no	—
20	C₂×Dic₃₉₇	—	4	1	no	—
21	C₂³×C₃₉₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₃₉₇	—	2	1	no	—
23	C₂×C₄×C₃₉₇	—	4	1	no	—
24	C₂²×C₃₉₇	—	2	1	no	—
25	C₂²×C₃₉₇	—	2	1	no	—
26	C₂²×C₃₉₇	C₄²	1	1	yes	characteristic
27	C₂²×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²×C₃₉₇	C₄⋊C₄	1	1	yes	characteristic
29	C₂×D₃₉₇	—	2	2	no	—
30	C₂×D₃₉₇	—	2	2	no	—
31	C₂×D₃₉₇	—	4	2	no	—
32	C₂×D₃₉₇	—	4	1	no	—
33	C₂×D₃₉₇	—	4	1	no	—
34	C₂×D₃₉₇	C₂²⋊C₄	1	2	yes	—
35	C₂×D₃₉₇	C₄⋊C₄	1	2	yes	—
36	#13097544	—	4	4	no	—
37	C₄×C₃₉₇	—	4	1	no	—
38	Dic₃₉₇	—	4	1	no	—
39	C₂×C₃₉₇	—	2	1	no	—
40	C₂×C₃₉₇	—	2	1	no	—
41	C₂×C₃₉₇	#95	1	1	yes	characteristic
42	C₂×C₃₉₇	#99	1	1	yes	characteristic
43	C₂×C₃₉₇	#99	1	1	yes	characteristic
44	D₃₉₇	—	2	2	no	—
45	D₃₉₇	—	2	2	no	—
46	C₃₉₇	#342	1	1	yes	characteristic, complemented, Sylow
47	#342	—	397	1	no	maximal, Sylow
48	C₂×C₂²⋊C₄	—	397	1	no	—
49	C₂×C₂²⋊C₄	—	397	2	no	—
50	C₂⁴	—	397	1	no	—
51	C₂²×C₄	—	794	2	no	—
52	C₂²×C₄	—	397	1	no	—
53	C₂²×C₄	#13097544	1	1	yes	characteristic, complemented
54	C₂²⋊C₄	—	794	2	no	—
55	C₂²⋊C₄	—	794	2	no	—
56	C₂²⋊C₄	—	397	4	no	—
57	C₂³	—	1588	1	no	—
58	C₂³	—	1588	1	no	—
59	C₂³	—	397	2	no	—
60	C₂³	—	397	2	no	—
61	C₂³	—	397	1	no	—
62	C₂³	—	397	1	no	—
63	C₂³	C₂×#13097544	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	4	1	no	—
66	C₂×C₄	—	794	4	no	—
67	C₂×C₄	—	794	1	no	—
68	C₂×C₄	—	1588	2	no	—
69	C₂×C₄	—	1588	2	no	—
70	C₂×C₄	—	1588	1	no	—
71	C₂²	—	2	1	no	—
72	C₂²	—	2	1	no	—
73	C₂²	—	794	2	no	—
74	C₂²	—	794	2	no	—
75	C₂²	—	1588	2	no	—
76	C₂²	—	1588	1	no	—
77	C₂²	—	1588	1	no	—
78	C₂²	—	397	2	no	—
79	C₂²	—	397	2	no	—
80	C₂²	C₄×#13097544	1	1	yes	characteristic
81	C₂²	C₂²⋊#13097544	1	1	yes	characteristic
82	C₂²	C₄⋊#13097544	1	1	yes	characteristic
83	C₄	—	4	1	no	—
84	C₄	—	1588	4	no	—
85	C₄	—	1588	1	no	—
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	—	794	2	no	—
89	C₂	—	794	2	no	—
90	C₂	(C₂×#13097544)⋊C₄	1	1	yes	characteristic
91	C₂	#27163154	1	1	yes	characteristic
92	C₂	#27163155	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#13097544
commutator	C₂²×C₃₉₇	C₄²
Frattini	C₂³	C₂×#13097544
Fitting	C₂²×C₄×C₃₉₇	C₄
socle	C₂²×C₃₉₇	C₂²⋊C₄
prime radical, cosocle	C₂³×D₃₉₇	C₂²
hypercenter	C₂²×C₄	#13097544
hypocenter	C₃₉₇	#342
LCS	G ▷ C₂²×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
5. C₂²⋊#13097544	C₄	semidirect
7. C₂²×Dic₃₉₇	C₄	semidirect
9. C₂²×C₄×C₃₉₇	C₄	semidirect
46. C₃₉₇	#342	semidirect
53. C₂²×C₄	#13097544	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂²⋊#13097544	2
C₂×#20263708	2
#342	397