Subgroups — C₂×#27163007 #38762471

Order 25408.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15691787	C₂	1	2	yes	maximal
2	#27163007	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄²×C₃₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#15691787	C₄	1	8	yes	complemented
5	C₂×#15691787	C₂²	1	4	yes	—
6	C₂²×C₄×C₃₉₇	C₄	1	2	yes	—
7	C₂²×C₄×C₃₉₇	C₂²	1	1	yes	characteristic
8	C₄²×C₃₉₇	C₄	1	2	yes	—
9	C₄²×C₃₉₇	C₂²	1	2	yes	—
10	#15691787	C₂×C₄	1	8	yes	complemented
11	C₂³×C₃₉₇	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₃₉₇	—	2	4	no	—
13	C₂×C₄×C₃₉₇	C₂×C₄	1	4	yes	—
14	C₂×C₄×C₃₉₇	C₂×C₄	1	4	yes	—
15	C₂×C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₃₉₇	C₂³	1	1	yes	characteristic
17	C₂²×C₃₉₇	C₄²	1	2	yes	—
18	C₂²×C₃₉₇	M₁₆	1	4	yes	—
19	C₂²×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
20	C₄×C₃₉₇	—	2	4	no	—
21	C₄×C₃₉₇	C₄²	1	2	yes	—
22	C₄×C₃₉₇	C₂²×C₄	1	2	yes	—
23	C₂×C₃₉₇	#97	1	4	yes	complemented
24	C₂×C₃₉₇	C₂×C₄²	1	1	yes	characteristic
25	C₂×C₃₉₇	C₂×M₁₆	1	2	yes	—
26	C₃₉₇	C₂×#97	1	1	yes	characteristic, complemented, Sylow
27	C₂×#97	—	397	1	no	maximal, Sylow
28	C₂²×C₈	—	397	2	no	—
29	C₂×C₄²	D₃₉₇	1	1	yes	characteristic
30	#97	—	397	4	no	—
31	C₂²×C₄	Dic₃₉₇	1	2	yes	—
32	C₂²×C₄	C₂×D₃₉₇	1	1	yes	characteristic
33	C₂×C₈	—	397	8	no	—
34	C₂×C₈	—	397	4	no	—
35	C₄²	Dic₃₉₇	1	2	yes	—
36	C₄²	C₂×D₃₉₇	1	2	yes	—
37	C₂³	C₂×Dic₃₉₇	1	1	yes	characteristic
38	C₂×C₄	—	2	4	no	—
39	C₂×C₄	C₄×D₃₉₇	1	4	yes	—
40	C₂×C₄	C₂×Dic₃₉₇	1	4	yes	—
41	C₂×C₄	C₂×Dic₃₉₇	1	1	yes	characteristic
42	C₂×C₄	C₂²×D₃₉₇	1	1	yes	characteristic
43	C₈	—	397	8	no	—
44	C₂²	C₄×Dic₃₉₇	1	2	yes	—
45	C₂²	#20263715	1	4	yes	—
46	C₂²	C₂²×Dic₃₉₇	1	1	yes	characteristic
47	C₄	—	2	4	no	—
48	C₄	C₄×Dic₃₉₇	1	2	yes	—
49	C₄	C₂×C₄×D₃₉₇	1	2	yes	—
50	C₂	#27163007	1	4	yes	direct product factor
51	C₂	C₂×C₄×Dic₃₉₇	1	1	yes	characteristic
52	C₂	C₂×#20263715	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₃₉₇
commutator	C₂×C₃₉₇	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₃₉₇
Fitting	C₂×C₄²×C₃₉₇	C₂
socle, prime radical	C₂³×C₃₉₇	C₂×C₄
cosocle	C₂×C₄×C₃₉₇	C₂³
hypercenter	C₂×C₄²	D₃₉₇
hypocenter	C₃₉₇	C₂×#97
LCS	G ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #27163007	C₂	direct (N × H)
4. C₂×#15691787	C₄	semidirect
10. #15691787	C₂×C₄	semidirect
23. C₂×C₃₉₇	#97	semidirect
26. C₃₉₇	C₂×#97	semidirect
50. C₂	#27163007	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×#15691787	2
#27163007	2
C₂×C₄²×C₃₉₇	2
C₂×#97	397

Subgroups — C2×#27163007 #38762471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27163007 #38762471