Subgroups — C₂×#27212302 #41002886

Order 26944.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20269755	C₂	1	2	yes	maximal
2	#27212302	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₈×C₄₂₁	C₂	1	1	yes	maximal, characteristic
4	#20269755	—	2	2	no	—
5	#20269755	C₂²	1	4	yes	—
6	C₂×#16809890	—	2	2	no	—
7	C₂²×C₄×C₄₂₁	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₄₂₁	C₄	1	2	yes	—
9	C₂×C₈×C₄₂₁	C₄	1	2	yes	—
10	C₂×C₈×C₄₂₁	C₂²	1	2	yes	—
11	#16809890	—	2	4	no	—
12	C₂³×C₄₂₁	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₄₂₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₄₂₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₄₂₁	D₄	1	1	yes	characteristic
16	C₂×C₄×C₄₂₁	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₂₁	Q₈	1	1	yes	characteristic
18	C₂×C₄×C₄₂₁	C₂³	1	1	yes	characteristic
19	C₈×C₄₂₁	C₂×C₄	1	4	yes	—
20	C₂²×C₄₂₁	—	2	2	no	—
21	C₂²×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
23	C₂²×C₄₂₁	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
25	C₄×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
26	C₄×C₄₂₁	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₄₂₁	C₂×D₄	1	1	yes	characteristic
28	C₂×C₄₂₁	—	2	1	no	—
29	C₂×C₄₂₁	—	2	1	no	—
30	C₂×C₄₂₁	#108	1	2	yes	complemented
31	C₂×C₄₂₁	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₄₂₁	C₂×#108	1	1	yes	characteristic, complemented, Sylow
33	C₂×#108	—	421	1	no	maximal, Sylow
34	C₂×M₁₆	—	421	2	no	—
35	C₂²×C₈	D₄₂₁	1	1	yes	characteristic
36	#108	—	421	4	no	—
37	C₂²×C₄	C₂×D₄₂₁	1	1	yes	characteristic
38	M₁₆	—	842	2	no	—
39	M₁₆	—	421	4	no	—
40	C₂×C₈	—	842	2	no	—
41	C₂×C₈	Dic₄₂₁	1	2	yes	—
42	C₂×C₈	Dic₄₂₁	1	2	yes	—
43	C₂×C₈	C₂×D₄₂₁	1	2	yes	—
44	C₂³	Dic₈₄₂	1	1	yes	characteristic
45	C₂×C₄	C₂×Dic₄₂₁	1	1	yes	characteristic
46	C₂×C₄	C₂×Dic₄₂₁	1	1	yes	characteristic
47	C₂×C₄	D₁₆₈₄	1	1	yes	characteristic
48	C₂×C₄	D₁₆₈₄	1	1	yes	characteristic
49	C₂×C₄	Dic₈₄₂	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₄₂₁	1	1	yes	characteristic
51	C₈	—	842	4	no	—
52	C₈	C₂×Dic₄₂₁	1	4	yes	—
53	C₂²	—	2	2	no	—
54	C₂²	C₄⋊Dic₄₂₁	1	1	yes	characteristic
55	C₂²	C₄⋊Dic₄₂₁	1	1	yes	characteristic
56	C₂²	C₂×Dic₈₄₂	1	1	yes	characteristic
57	C₄	C₄⋊Dic₄₂₁	1	1	yes	characteristic
58	C₄	C₄⋊Dic₄₂₁	1	1	yes	characteristic
59	C₄	C₂²×Dic₄₂₁	1	1	yes	characteristic
60	C₄	C₂×D₁₆₈₄	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	—	2	1	no	—
63	C₂	#27212302	1	2	yes	direct product factor
64	C₂	C₂×C₄⋊Dic₄₂₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₆₈₄
commutator	C₄×C₄₂₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₂₁
Fitting	C₂²×C₈×C₄₂₁	C₂
socle	C₂²×C₄₂₁	C₄⋊C₄
prime radical	C₂³×C₄₂₁	Q₈
cosocle	C₂×C₄×C₄₂₁	C₂³
hypercenter	C₂²×C₈	D₄₂₁
hypocenter	C₄₂₁	C₂×#108
LCS	G ▷ C₄×C₄₂₁ ▷ C₂×C₄₂₁ ▷ C₄₂₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #27212302	C₂	direct (N × H)
30. C₂×C₄₂₁	#108	semidirect
32. C₄₂₁	C₂×#108	semidirect
63. C₂	#27212302	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×#20269755	2
#27212302	2
C₂²×C₈×C₄₂₁	2
C₂×#108	421

Subgroups — C2×#27212302 #41002886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27212302 #41002886