Subgroups — C₂×#13050231 #14581338

Order 2624.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66493	C₂	1	2	yes	maximal
2	#13050231	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×Dic₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₁	C₄	1	1	yes	characteristic
5	C₂²×Dic₄₁	C₄	1	1	yes	characteristic
6	C₂²×Dic₄₁	C₂²	1	1	yes	characteristic
7	C₂×#66493	—	2	4	no	—
8	C₂×#66493	C₂²	1	4	yes	—
9	C₄×Dic₄₁	C₄	1	2	yes	—
10	C₄×Dic₄₁	C₂²	1	2	yes	—
11	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄×C₄₁	—	2	2	no	—
13	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
14	C₂×Dic₄₁	C₈	1	4	yes	complemented
15	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
16	C₂×Dic₄₁	C₂×C₄	1	2	yes	—
17	C₂×Dic₄₁	D₄	1	2	yes	—
18	C₂×Dic₄₁	Q₈	1	2	yes	—
19	C₂×Dic₄₁	C₂³	1	1	yes	characteristic
20	#66493	—	2	4	no	—
21	C₂²×C₄₁	C₄⋊C₄	1	2	yes	—
22	C₂²×C₄₁	C₂×C₈	1	2	yes	—
23	C₂²×C₄₁	M₁₆	1	2	yes	—
24	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
25	C₄×C₄₁	—	2	2	no	—
26	Dic₄₁	C₄⋊C₄	1	2	yes	—
27	Dic₄₁	C₂×C₈	1	4	yes	complemented
28	Dic₄₁	C₂×D₄	1	1	yes	characteristic
29	Dic₄₁	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₄₁	C₄⋊C₈	1	4	yes	complemented
31	C₂×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄₁	C₂²×C₈	1	1	yes	characteristic
33	C₂×C₄₁	C₂×M₁₆	1	1	yes	characteristic
34	C₂×C₄⋊C₈	—	41	1	no	maximal, Sylow
35	C₄₁	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
36	C₂²×C₈	—	41	2	no	—
37	C₂×C₄²	—	41	1	no	—
38	C₄⋊C₈	—	41	4	no	—
39	C₂²×C₄	—	41	1	no	—
40	C₂²×C₄	—	41	1	no	—
41	C₂²×C₄	#4223	1	1	yes	characteristic
42	C₂×C₈	—	41	4	no	—
43	C₂×C₈	—	82	4	no	—
44	C₄²	—	41	2	no	—
45	C₄²	—	41	2	no	—
46	C₂³	C₂×#4223	1	1	yes	characteristic
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	41	4	no	—
49	C₂×C₄	—	41	2	no	—
50	C₂×C₄	—	41	2	no	—
51	C₂×C₄	—	41	1	no	—
52	C₂×C₄	—	41	1	no	—
53	C₂×C₄	—	41	2	no	—
54	C₂×C₄	C₂×#4223	1	2	yes	—
55	C₈	—	82	4	no	—
56	C₂²	#10620296	1	2	yes	—
57	C₂²	C₄⋊#4223	1	2	yes	—
58	C₂²	#10620301	1	2	yes	—
59	C₂²	C₂²×#4223	1	1	yes	characteristic
60	C₄	—	2	2	no	—
61	C₄	—	41	1	no	—
62	C₄	—	41	2	no	—
63	C₄	—	41	1	no	—
64	C₄	—	41	4	no	—
65	C₂	#13050231	1	4	yes	direct product factor
66	C₂	C₂×C₄⋊#4223	1	1	yes	characteristic
67	C₂	C₂×#10620296	1	1	yes	characteristic
68	C₂	C₂×#10620301	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#4223
commutator	C₂×C₄₁	C₂²×C₈
Frattini	C₂²	C₂²×#4223
Fitting	C₂²×C₄×C₄₁	C₄
socle, prime radical	C₂³×C₄₁	C₂×C₄
cosocle	C₂×Dic₄₁	C₂³
hypercenter	C₂²×C₄	#4223
hypocenter	C₄₁	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. #13050231	C₂	direct (N × H)
14. C₂×Dic₄₁	C₈	semidirect
27. Dic₄₁	C₂×C₈	semidirect
30. C₂×C₄₁	C₄⋊C₈	semidirect
35. C₄₁	C₂×C₄⋊C₈	semidirect
65. C₂	#13050231	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×#66493	2
#13050231	2
C₂×C₄×Dic₄₁	2
C₂×C₄⋊C₈	41

Subgroups — C2×#13050231 #14581338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13050231 #14581338