Subgroups — C₂×#27163153 #38763491

Order 25408.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15691794	C₂	1	2	yes	maximal, complemented
2	#27163153	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₄×D₃₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#15691794	—	2	4	no	—
5	C₂×#15691794	C₂²	1	4	yes	complemented
6	C₂³×D₃₉₇	C₄	1	1	yes	characteristic
7	C₂²×Dic₃₉₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₃₉₇	—	2	4	no	—
9	C₂×C₄×D₃₉₇	C₄	1	2	yes	—
10	C₂×C₄×D₃₉₇	C₂²	1	2	yes	—
11	C₂²×C₄×C₃₉₇	C₄	1	1	yes	characteristic
12	#15691794	—	2	4	no	—
13	C₂²×D₃₉₇	—	2	2	no	—
14	C₂²×D₃₉₇	—	2	2	no	—
15	C₂²×D₃₉₇	C₈	1	4	yes	complemented
16	C₂²×D₃₉₇	C₂×C₄	1	2	yes	—
17	C₂×Dic₃₉₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₃₉₇	D₄	1	4	yes	—
19	C₂×Dic₃₉₇	C₂³	1	1	yes	characteristic
20	C₄×D₃₉₇	—	2	4	no	—
21	C₄×D₃₉₇	—	2	4	no	—
22	C₂³×C₃₉₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₃₉₇	—	2	2	no	—
24	C₂×C₄×C₃₉₇	C₂×C₄	1	2	yes	—
25	C₂²×C₃₉₇	C₂²⋊C₄	1	2	yes	—
26	C₂²×C₃₉₇	C₂×C₈	1	2	yes	—
27	C₂²×C₃₉₇	M₁₆	1	2	yes	—
28	C₂²×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×D₃₉₇	—	2	8	no	—
30	C₂×D₃₉₇	—	2	2	no	—
31	C₂×D₃₉₇	—	2	2	no	—
32	C₂×D₃₉₇	C₂×C₈	1	4	yes	complemented
33	C₄×C₃₉₇	—	2	2	no	—
34	Dic₃₉₇	C₂²⋊C₄	1	2	yes	—
35	Dic₃₉₇	C₂×D₄	1	2	yes	—
36	C₂×C₃₉₇	C₂²⋊C₈	1	4	yes	complemented
37	C₂×C₃₉₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₃₉₇	C₂²×C₈	1	1	yes	characteristic
39	C₂×C₃₉₇	C₂×M₁₆	1	1	yes	characteristic
40	D₃₉₇	—	2	4	no	—
41	C₃₉₇	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₂²⋊C₈	—	397	1	no	maximal, Sylow
43	C₂³×C₄	—	397	1	no	—
44	C₂²×C₈	—	397	2	no	—
45	C₂²⋊C₈	—	397	4	no	—
46	C₂⁴	—	397	1	no	—
47	C₂²×C₄	—	794	4	no	—
48	C₂²×C₄	—	397	2	no	—
49	C₂²×C₄	—	397	2	no	—
50	C₂²×C₄	—	397	1	no	—
51	C₂²×C₄	#13097544	1	1	yes	characteristic
52	C₂×C₈	—	794	4	no	—
53	C₂×C₈	—	397	4	no	—
54	C₂³	—	794	2	no	—
55	C₂³	—	794	2	no	—
56	C₂³	—	397	4	no	—
57	C₂³	—	397	2	no	—
58	C₂³	C₂×#13097544	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	794	4	no	—
61	C₂×C₄	—	794	4	no	—
62	C₂×C₄	—	397	4	no	—
63	C₂×C₄	—	397	1	no	—
64	C₂×C₄	—	397	1	no	—
65	C₂×C₄	C₂×#13097544	1	2	yes	—
66	C₈	—	794	4	no	—
67	C₂²	—	794	8	no	—
68	C₂²	—	794	2	no	—
69	C₂²	—	794	2	no	—
70	C₂²	—	397	4	no	—
71	C₂²	C₂²⋊#13097544	1	2	yes	—
72	C₂²	D₃₉₇⋊C₈	1	2	yes	—
73	C₂²	#20263741	1	2	yes	—
74	C₂²	C₂²×#13097544	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	397	2	no	—
77	C₄	—	397	2	no	—
78	C₂	—	794	4	no	—
79	C₂	#27163153	1	4	yes	direct product factor
80	C₂	C₂×C₂²⋊#13097544	1	1	yes	characteristic
81	C₂	C₂×D₃₉₇⋊C₈	1	1	yes	characteristic
82	C₂	C₂×#20263741	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#13097544
commutator	C₂×C₃₉₇	C₂²×C₈
Frattini	C₂²	C₂²×#13097544
Fitting	C₂²×C₄×C₃₉₇	C₄
socle	C₂³×C₃₉₇	C₂×C₄
prime radical	C₂³×D₃₉₇	C₄
cosocle	C₂×Dic₃₉₇	C₂³
hypercenter	C₂²×C₄	#13097544
hypocenter	C₃₉₇	C₂×C₂²⋊C₈
LCS	G ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#15691794	C₂	semidirect
2. #27163153	C₂	direct (N × H)
5. C₂×#15691794	C₂²	semidirect
15. C₂²×D₃₉₇	C₈	semidirect
32. C₂×D₃₉₇	C₂×C₈	semidirect
36. C₂×C₃₉₇	C₂²⋊C₈	semidirect
41. C₃₉₇	C₂×C₂²⋊C₈	semidirect
79. C₂	#27163153	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#15691794	2
#27163153	2
C₂²×C₄×D₃₉₇	2
C₂×C₂²⋊C₈	397

Subgroups — C2×#27163153 #38763491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27163153 #38763491