Subgroups — C₂×#27212435 #41003849

Order 26944.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#13132997	C₂	1	2	yes	maximal
2	#27212435	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×D₄₂₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13132997	—	2	2	no	—
5	C₄⋊#13132997	—	2	2	no	—
6	C₄⋊#13132997	C₂²	1	4	yes	—
7	C₂×C₄×D₄₂₁	C₂²	1	1	yes	characteristic
8	C₂×#16809890	C₄	1	1	yes	characteristic, complemented
9	C₈×D₄₂₁	C₄	1	2	yes	complemented
10	C₈×D₄₂₁	C₂²	1	2	yes	—
11	C₂×C₈×C₄₂₁	C₄	1	1	yes	characteristic, complemented
12	C₂×#13132997	—	2	4	no	—
13	C₂×#13132997	—	4	4	no	—
14	C₂²×D₄₂₁	D₄	1	1	yes	characteristic
15	C₂×Dic₄₂₁	Q₈	1	1	yes	characteristic
16	C₄×D₄₂₁	C₂×C₄	1	1	yes	characteristic
17	C₄×D₄₂₁	D₄	1	1	yes	characteristic
18	C₄×D₄₂₁	Q₈	1	1	yes	characteristic
19	C₄×D₄₂₁	C₂³	1	1	yes	characteristic
20	#16809890	C₂×C₄	1	2	yes	complemented
21	C₂×C₄×C₄₂₁	C₂×C₄	1	1	yes	characteristic
22	C₈×C₄₂₁	C₂×C₄	1	2	yes	complemented
23	C₂²×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
24	C₂×D₄₂₁	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₄₂₁	D₈	1	2	yes	—
26	C₂×D₄₂₁	Q₁₆	1	2	yes	—
27	C₂×D₄₂₁	C₂×D₄	1	1	yes	characteristic
28	#13132997	—	4	4	no	—
29	C₄×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₄₂₁	C₂²×C₄	1	1	yes	characteristic
31	Dic₄₂₁	C₄⋊C₄	1	1	yes	characteristic
32	Dic₄₂₁	C₂×Q₈	1	1	yes	characteristic
33	C₂×C₄₂₁	#107	1	2	yes	complemented
34	C₂×C₄₂₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	D₄₂₁	#107	1	2	yes	complemented
36	D₄₂₁	C₂×D₈	1	1	yes	characteristic
37	D₄₂₁	C₂×Q₁₆	1	1	yes	characteristic
38	C₄₂₁	C₂×#107	1	1	yes	characteristic, complemented, Sylow
39	C₂×#107	—	421	1	no	maximal, Sylow
40	C₂²×C₈	—	421	1	no	—
41	C₂×C₄⋊C₄	—	421	2	no	—
42	#107	—	421	4	no	—
43	C₂²×C₄	—	842	2	no	—
44	C₂²×C₄	—	421	1	no	—
45	C₂×C₈	—	421	1	no	—
46	C₂×C₈	—	421	2	no	—
47	C₂×C₈	—	421	2	no	—
48	C₂×C₈	#13132997	1	1	yes	characteristic, complemented
49	C₄⋊C₄	—	842	2	no	—
50	C₄⋊C₄	—	421	4	no	—
51	C₂³	—	421	1	no	—
52	C₂×C₄	—	842	4	no	—
53	C₂×C₄	—	1684	4	no	—
54	C₂×C₄	—	421	1	no	—
55	C₂×C₄	—	421	1	no	—
56	C₂×C₄	—	421	1	no	—
57	C₂×C₄	—	421	1	no	—
58	C₂×C₄	—	421	1	no	—
59	C₂×C₄	C₂×#13132997	1	1	yes	characteristic
60	C₈	—	421	2	no	—
61	C₈	C₂×#13132997	1	2	yes	complemented
62	C₂²	—	421	2	no	—
63	C₂²	—	421	2	no	—
64	C₂²	—	421	1	no	—
65	C₂²	—	421	1	no	—
66	C₂²	C₄⋊#13132997	1	1	yes	characteristic
67	C₄	—	1684	4	no	—
68	C₄	—	421	1	no	—
69	C₄	—	421	1	no	—
70	C₄	C₄⋊#13132997	1	1	yes	characteristic
71	C₄	C₂²×#13132997	1	1	yes	characteristic
72	C₂	—	421	1	no	—
73	C₂	—	421	2	no	—
74	C₂	—	421	1	no	—
75	C₂	#27212435	1	2	yes	direct product factor
76	C₂	C₂×C₄⋊#13132997	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#13132997
commutator	C₄×C₄₂₁	C₂²×C₄
Frattini	C₄	C₂²×#13132997
Fitting	C₂×C₈×C₄₂₁	C₄
socle	C₂²×C₄₂₁	C₄⋊C₄
prime radical	C₂²×D₄₂₁	D₄
cosocle	C₄×D₄₂₁	C₂³
hypercenter	C₂×C₈	#13132997
hypocenter	C₄₂₁	C₂×#107
LCS	G ▷ C₄×C₄₂₁ ▷ C₂×C₄₂₁ ▷ C₄₂₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #27212435	C₂	direct (N × H)
8. C₂×#16809890	C₄	semidirect
9. C₈×D₄₂₁	C₄	semidirect
11. C₂×C₈×C₄₂₁	C₄	semidirect
20. #16809890	C₂×C₄	semidirect
22. C₈×C₄₂₁	C₂×C₄	semidirect
33. C₂×C₄₂₁	#107	semidirect
35. D₄₂₁	#107	semidirect
38. C₄₂₁	C₂×#107	semidirect
48. C₂×C₈	#13132997	semidirect
61. C₈	C₂×#13132997	semidirect
75. C₂	#27212435	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×C₄⋊#13132997	2
#27212435	2
C₂×C₈×D₄₂₁	2
C₂×#107	421

Subgroups — C2×#27212435 #41003849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27212435 #41003849