Subgroups — C₂×#362 #2147

Order 128.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×#108	C₂	1	1	yes	maximal, characteristic
4	#362	C₂	1	4	yes	maximal, direct product factor
5	C₂²×Q₈	—	2	1	no	—
6	C₂×Q₁₆	—	2	1	no	—
7	C₂×Q₁₆	—	2	1	no	—
8	C₂×Q₁₆	—	2	1	no	—
9	C₂×Q₁₆	C₄	1	2	yes	—
10	C₂×Q₁₆	C₄	1	2	yes	—
11	C₂×Q₁₆	C₂²	1	2	yes	—
12	C₂×M₁₆	—	2	1	no	—
13	C₂²×C₈	C₂²	1	1	yes	characteristic
14	M₃₂	—	2	1	no	—
15	M₃₂	C₂²	1	2	yes	—
16	C₂×C₁₆	—	2	1	no	—
17	#108	—	2	1	no	—
18	#108	C₂²	1	2	yes	—
19	C₂×Q₈	—	2	2	no	—
20	C₂×Q₈	—	2	2	no	—
21	C₂×Q₈	—	2	2	no	—
22	C₂×Q₈	—	4	1	no	—
23	C₂×Q₈	—	4	1	no	—
24	C₂×Q₈	—	4	1	no	—
25	C₂²×C₄	—	4	1	no	—
26	C₂²×C₄	D₄	1	1	yes	characteristic
27	Q₁₆	—	2	2	no	—
28	Q₁₆	—	2	2	no	—
29	Q₁₆	—	2	2	no	—
30	Q₁₆	C₂×C₄	1	4	yes	—
31	M₁₆	—	2	2	no	—
32	M₁₆	—	4	1	no	—
33	C₂×C₈	—	4	1	no	—
34	C₂×C₈	C₂×C₄	1	1	yes	characteristic
35	C₂×C₈	C₂×C₄	1	1	yes	characteristic
36	C₂×C₈	D₄	1	1	yes	characteristic
37	C₂×C₈	D₄	1	1	yes	characteristic
38	C₂×C₈	D₄	1	1	yes	characteristic
39	C₂×C₈	C₂³	1	1	yes	characteristic
40	C₁₆	—	2	2	no	—
41	C₂³	SD₁₆	1	1	yes	characteristic
42	Q₈	—	2	4	no	—
43	Q₈	—	4	2	no	—
44	Q₈	—	4	2	no	—
45	Q₈	—	4	2	no	—
46	C₂×C₄	—	4	2	no	—
47	C₂×C₄	—	4	2	no	—
48	C₂×C₄	—	4	2	no	—
49	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₄	D₈	1	1	yes	characteristic
52	C₂×C₄	D₈	1	1	yes	characteristic
53	C₂×C₄	SD₁₆	1	1	yes	characteristic
54	C₂×C₄	C₂×D₄	1	1	yes	characteristic
55	C₈	—	4	2	no	—
56	C₈	C₂²⋊C₄	1	1	yes	characteristic
57	C₈	C₂²⋊C₄	1	1	yes	characteristic
58	C₈	C₂²×C₄	1	1	yes	characteristic
59	C₈	C₂×D₄	1	1	yes	characteristic
60	C₂²	—	2	2	no	—
61	C₂²	#102	1	1	yes	characteristic
62	C₂²	#102	1	1	yes	characteristic
63	C₂²	C₂×SD₁₆	1	1	yes	characteristic
64	C₄	—	4	4	no	—
65	C₄	#102	1	1	yes	characteristic
66	C₄	#102	1	1	yes	characteristic
67	C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₄	C₂×D₈	1	1	yes	characteristic
69	C₂	—	2	1	no	—
70	C₂	—	2	1	no	—
71	C₂	#362	1	2	yes	direct product factor
72	C₂	C₂×#102	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#102
commutator	C₈	C₂²×C₄
Frattini, cosocle	C₂×C₈	C₂³
prime radical	C₂³	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×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
4. #362	C₂	direct (N × H)
71. C₂	#362	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×Q₁₆	2
C₂×M₃₂	2
C₂×#108	2
#362	2

Subgroups — C2×#362 #2147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#362 #2147