Subgroups — C₂×#27165798 #38787098

Order 25664.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20264375	C₂	1	2	yes	maximal
2	#27165798	C₂	1	4	yes	maximal, direct product factor
3	C₂²×Dic₈₀₂	C₂	1	1	yes	maximal, characteristic
4	#20264375	—	2	2	no	—
5	#20264375	C₂²	1	4	yes	—
6	C₂×#15692006	—	2	2	no	—
7	C₂×Dic₈₀₂	—	2	2	no	—
8	C₂×Dic₈₀₂	—	2	2	no	—
9	C₂×Dic₈₀₂	C₄	1	2	yes	—
10	C₂×Dic₈₀₂	C₂²	1	2	yes	—
11	C₂²×Dic₄₀₁	C₄	1	1	yes	characteristic
12	C₂²×Dic₄₀₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₄₀₁	C₄	1	1	yes	characteristic
14	#15692006	—	2	4	no	—
15	Dic₈₀₂	—	2	4	no	—
16	Dic₈₀₂	—	2	4	no	—
17	C₂×Dic₄₀₁	—	2	1	no	—
18	C₂×Dic₄₀₁	—	2	1	no	—
19	C₂×Dic₄₀₁	C₂×C₄	1	2	yes	—
20	C₂×Dic₄₀₁	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₄₀₁	D₄	1	2	yes	—
22	C₂×Dic₄₀₁	D₄	1	2	yes	—
23	C₂×Dic₄₀₁	C₂³	1	1	yes	characteristic
24	C₂³×C₄₀₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×C₄₀₁	—	2	1	no	—
26	C₂×C₄×C₄₀₁	—	2	1	no	—
27	C₂×C₄×C₄₀₁	C₂×C₄	1	2	yes	—
28	C₂²×C₄₀₁	—	2	2	no	—
29	C₂²×C₄₀₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₄₀₁	C₂²⋊C₄	1	1	yes	characteristic
31	C₂²×C₄₀₁	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₄₀₁	—	2	2	no	—
33	Dic₄₀₁	—	2	2	no	—
34	Dic₄₀₁	C₂²⋊C₄	1	2	yes	—
35	Dic₄₀₁	C₂×D₄	1	2	yes	—
36	C₂×C₄₀₁	—	2	1	no	—
37	C₂×C₄₀₁	—	2	1	no	—
38	C₂×C₄₀₁	#101	1	2	yes	complemented
39	C₂×C₄₀₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₄₀₁	C₂×#101	1	1	yes	characteristic, complemented, Sylow
41	C₂×#101	—	401	1	no	maximal, Sylow
42	C₂²×Q₈	—	401	1	no	—
43	C₂×M₁₆	—	401	2	no	—
44	#101	—	401	4	no	—
45	C₂×Q₈	—	802	2	no	—
46	C₂×Q₈	—	802	2	no	—
47	C₂×Q₈	—	401	2	no	—
48	C₂×Q₈	—	401	2	no	—
49	C₂²×C₄	—	401	1	no	—
50	C₂²×C₄	—	401	1	no	—
51	C₂²×C₄	#13107944	1	1	yes	characteristic
52	M₁₆	—	802	2	no	—
53	M₁₆	—	401	4	no	—
54	C₂×C₈	—	802	2	no	—
55	C₂³	C₂×#13107944	1	1	yes	characteristic
56	Q₈	—	802	4	no	—
57	Q₈	—	802	4	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	802	1	no	—
61	C₂×C₄	—	802	1	no	—
62	C₂×C₄	—	401	2	no	—
63	C₂×C₄	—	401	2	no	—
64	C₂×C₄	—	401	2	no	—
65	C₂×C₄	—	401	1	no	—
66	C₂×C₄	—	401	1	no	—
67	C₂×C₄	C₂×#13107944	1	2	yes	—
68	C₈	—	802	4	no	—
69	C₂²	—	2	2	no	—
70	C₂²	C₂²⋊#13107944	1	1	yes	characteristic
71	C₂²	C₂²⋊#13107944	1	1	yes	characteristic
72	C₂²	C₂²×#13107944	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	802	2	no	—
75	C₄	—	401	2	no	—
76	C₄	—	401	2	no	—
77	C₂	—	2	1	no	—
78	C₂	—	2	1	no	—
79	C₂	#27165798	1	2	yes	direct product factor
80	C₂	C₂×C₂²⋊#13107944	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#13107944
commutator	C₂²×C₄₀₁	C₂²×C₄
Frattini	C₂²	C₂²×#13107944
Fitting	C₂²×C₄×C₄₀₁	C₄
socle	C₂²×C₄₀₁	C₂²⋊C₄
prime radical	C₂³×C₄₀₁	C₂×C₄
cosocle	C₂×Dic₄₀₁	C₂³
hypercenter	C₂²×C₄	#13107944
hypocenter	C₄₀₁	C₂×#101
LCS	G ▷ C₂²×C₄₀₁ ▷ C₂×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. #27165798	C₂	direct (N × H)
38. C₂×C₄₀₁	#101	semidirect
40. C₄₀₁	C₂×#101	semidirect
79. C₂	#27165798	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#20264375	2
#27165798	2
C₂²×Dic₈₀₂	2
C₂×#101	401

Subgroups — C2×#27165798 #38787098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27165798 #38787098