Subgroups — C₂×#2158 #33407

Order 256.

347 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#427	C₂	1	2	yes	maximal
3	#2158	C₂	1	8	yes	maximal, direct product factor
4	C₂×#367	C₂	1	2	yes	maximal, complemented
5	C₂×#366	C₂	1	2	yes	maximal, complemented
6	C₂³×C₈	C₂²	1	1	yes	characteristic
7	C₂×#117	—	2	2	no	—
8	C₂²×C₁₆	C₄	1	8	yes	complemented
9	C₂²×C₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₆	C₂²	1	4	yes	—
12	#427	—	2	4	no	—
13	#427	C₂²	1	8	yes	—
14	C₂×#107	C₂²	1	4	yes	—
15	C₂×#106	—	2	2	no	—
16	#367	C₂²	1	8	yes	complemented
17	#366	C₂²	1	8	yes	complemented
18	C₂³×C₄	D₄	1	1	yes	characteristic
19	C₂²×C₈	C₂×C₄	1	4	yes	—
20	C₂²×C₈	D₄	1	1	yes	characteristic
21	C₂²×C₈	D₄	1	2	yes	—
22	C₂²×C₈	Q₈	1	4	yes	—
23	C₂²×C₈	C₂³	1	1	yes	characteristic
24	C₂²×C₈	C₂³	1	2	yes	—
25	#117	—	2	8	no	—
26	#117	—	4	4	no	—
27	C₂×C₄⋊C₄	—	2	4	no	—
28	C₂×C₂²⋊C₄	—	4	2	no	—
29	C₂×C₄²	—	4	2	no	—
30	C₂×C₁₆	C₂×C₄	1	4	yes	—
31	C₂×C₁₆	C₂×C₄	1	4	yes	—
32	C₂×C₁₆	C₂×C₄	1	16	yes	complemented
33	C₂×C₁₆	C₂³	1	2	yes	—
34	C₂×C₁₆	C₂³	1	2	yes	—
35	#107	—	2	4	no	—
36	#107	C₂³	1	8	yes	—
37	#106	—	2	8	no	—
38	C₂⁴	D₈	1	1	yes	characteristic
39	C₂²×C₄	—	4	4	no	—
40	C₂²×C₄	C₄⋊C₄	1	4	yes	—
41	C₂²×C₄	D₈	1	2	yes	—
42	C₂²×C₄	D₈	1	1	yes	characteristic
43	C₂²×C₄	Q₁₆	1	4	yes	—
44	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄	C₂×D₄	1	2	yes	—
46	C₂×C₈	C₄⋊C₄	1	4	yes	—
47	C₂×C₈	C₄⋊C₄	1	8	yes	—
48	C₂×C₈	C₂²×C₄	1	2	yes	—
49	C₂×C₈	C₂²×C₄	1	4	yes	—
50	C₂×C₈	C₂×D₄	1	2	yes	—
51	C₂×C₈	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈	C₂×Q₈	1	2	yes	—
53	C₂×C₈	C₂×Q₈	1	4	yes	—
54	C₂×C₈	C₂⁴	1	1	yes	characteristic
55	C₄⋊C₄	—	2	8	no	—
56	C₄⋊C₄	—	4	4	no	—
57	C₂²⋊C₄	—	4	8	no	—
58	C₄²	—	4	8	no	—
59	C₁₆	C₂²×C₄	1	4	yes	—
60	C₁₆	C₂²×C₄	1	4	yes	—
61	C₂³	—	2	4	no	—
62	C₂³	#107	1	4	yes	—
63	C₂³	C₂×D₈	1	2	yes	—
64	C₂³	C₂×D₈	1	1	yes	characteristic
65	C₂×C₄	—	4	8	no	—
66	C₂×C₄	—	8	8	no	—
67	C₂×C₄	#107	1	8	yes	—
68	C₂×C₄	#107	1	4	yes	—
69	C₂×C₄	C₂×C₄⋊C₄	1	4	yes	—
70	C₂×C₄	C₂×C₄⋊C₄	1	2	yes	—
71	C₂×C₄	C₂×D₈	1	2	yes	—
72	C₂×C₄	C₂×D₈	1	1	yes	characteristic
73	C₂×C₄	C₂×Q₁₆	1	4	yes	—
74	C₂×C₄	C₂×Q₁₆	1	2	yes	—
75	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
76	C₈	C₂×C₄⋊C₄	1	2	yes	—
77	C₈	C₂×C₄⋊C₄	1	4	yes	—
78	C₈	C₂³×C₄	1	1	yes	characteristic
79	C₈	C₂²×Q₈	1	1	yes	characteristic
80	C₂²	—	2	4	no	—
81	C₂²	—	2	8	no	—
82	C₂²	C₂×#107	1	4	yes	—
83	C₂²	C₂×#107	1	2	yes	—
84	C₂²	#508	1	4	yes	—
85	C₂²	C₂²×D₈	1	1	yes	characteristic
86	C₄	—	8	8	no	—
87	C₄	C₂×#107	1	2	yes	—
88	C₄	C₂×#107	1	4	yes	—
89	C₄	C₂²×C₄⋊C₄	1	1	yes	characteristic
90	C₄	C₂²×Q₁₆	1	1	yes	characteristic
91	C₂	—	2	4	no	—
92	C₂	#2158	1	4	yes	direct product factor
93	C₂	C₂²×#107	1	1	yes	characteristic
94	C₂	C₂×#508	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₈
commutator	C₈	C₂³×C₄
Frattini, cosocle	C₂×C₈	C₂⁴
socle	C₂³	C₂×D₈
prime radical	C₂⁴	D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #2158	C₂	direct (N × H)
4. C₂×#367	C₂	semidirect
5. C₂×#366	C₂	semidirect
8. C₂²×C₁₆	C₄	semidirect
16. #367	C₂²	semidirect
17. #366	C₂²	semidirect
32. C₂×C₁₆	C₂×C₄	semidirect
92. C₂	#2158	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₆	2
C₂×#427	2
#2158	2
C₂×#367	2
C₂×#366	2

Subgroups — C2×#2158 #33407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2158 #33407