Subgroups — C₂×#13050235 #14581350

Order 2624.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10620297	C₂	1	2	yes	maximal
2	#13050235	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×D₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×D₄₁	C₂²	1	1	yes	characteristic
5	C₂×#66493	—	2	2	no	—
6	#10620297	—	2	2	no	—
7	#10620297	C₂²	1	4	yes	—
8	C₂×C₈×C₄₁	C₄	1	1	yes	characteristic
9	C₂×#66491	C₄	1	1	yes	characteristic
10	C₈×D₄₁	C₄	1	2	yes	—
11	C₈×D₄₁	C₂²	1	2	yes	—
12	C₂²×D₄₁	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₄₁	D₄	1	1	yes	characteristic
15	C₄×D₄₁	C₂×C₄	1	1	yes	characteristic
16	C₄×D₄₁	D₄	1	1	yes	characteristic
17	C₄×D₄₁	Q₈	1	1	yes	characteristic
18	C₄×D₄₁	C₂³	1	1	yes	characteristic
19	#66493	—	2	4	no	—
20	C₈×C₄₁	C₂×C₄	1	2	yes	—
21	#66491	C₂×C₄	1	2	yes	—
22	C₂²×C₄₁	C₄⋊C₄	1	1	yes	characteristic
23	C₂×D₄₁	—	2	2	no	—
24	C₂×D₄₁	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₄₁	C₂×Q₈	1	1	yes	characteristic
26	C₄×C₄₁	C₄⋊C₄	1	1	yes	characteristic
27	C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
28	Dic₄₁	C₄⋊C₄	1	1	yes	characteristic
29	Dic₄₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄₁	#108	1	2	yes	complemented
31	C₂×C₄₁	C₂×C₄⋊C₄	1	1	yes	characteristic
32	D₄₁	—	2	1	no	—
33	D₄₁	—	2	1	no	—
34	C₂×#108	—	41	1	no	maximal, Sylow
35	C₄₁	C₂×#108	1	1	yes	characteristic, complemented, Sylow
36	C₂×M₁₆	—	41	2	no	—
37	C₂²×C₈	—	41	1	no	—
38	#108	—	41	4	no	—
39	C₂²×C₄	—	41	1	no	—
40	M₁₆	—	41	4	no	—
41	M₁₆	—	82	2	no	—
42	C₂×C₈	—	41	1	no	—
43	C₂×C₈	—	41	2	no	—
44	C₂×C₈	—	41	2	no	—
45	C₂×C₈	—	82	2	no	—
46	C₂×C₈	#4223	1	1	yes	characteristic
47	C₂³	—	41	1	no	—
48	C₂×C₄	—	41	1	no	—
49	C₂×C₄	—	41	1	no	—
50	C₂×C₄	—	41	1	no	—
51	C₂×C₄	—	41	1	no	—
52	C₂×C₄	—	41	1	no	—
53	C₂×C₄	C₂×#4223	1	1	yes	characteristic
54	C₈	—	41	2	no	—
55	C₈	—	82	4	no	—
56	C₈	C₂×#4223	1	2	yes	—
57	C₂²	—	41	1	no	—
58	C₂²	—	41	1	no	—
59	C₂²	—	82	2	no	—
60	C₂²	C₄⋊#4223	1	1	yes	characteristic
61	C₄	—	41	1	no	—
62	C₄	—	41	1	no	—
63	C₄	C₄⋊#4223	1	1	yes	characteristic
64	C₄	C₂²×#4223	1	1	yes	characteristic
65	C₂	—	82	1	no	—
66	C₂	—	82	1	no	—
67	C₂	#13050235	1	2	yes	direct product factor
68	C₂	C₂×C₄⋊#4223	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#4223
commutator	C₄×C₄₁	C₂²×C₄
Frattini	C₄	C₂²×#4223
Fitting	C₂×C₈×C₄₁	C₄
socle	C₂²×C₄₁	C₄⋊C₄
prime radical	C₂²×D₄₁	Q₈
cosocle	C₄×D₄₁	C₂³
hypercenter	C₂×C₈	#4223
hypocenter	C₄₁	C₂×#108
LCS	G ▷ C₄×C₄₁ ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #13050235	C₂	direct (N × H)
30. C₂×C₄₁	#108	semidirect
35. C₄₁	C₂×#108	semidirect
67. C₂	#13050235	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×#10620297	2
#13050235	2
C₂×C₈×D₄₁	2
C₂×#108	41

Subgroups — C2×#13050235 #14581350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13050235 #14581350