Subgroups — C₂×#479 #3075

Order 128.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#125	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
3	#479	C₂	1	8	yes	maximal, direct product factor
4	C₂×#107	C₂	1	1	yes	maximal, characteristic
5	C₂×#106	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
7	C₂×#103	C₂	1	1	yes	maximal, characteristic
8	C₂×#103	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₈	C₂²	1	1	yes	characteristic
10	C₂²×C₈	C₂²	1	1	yes	characteristic
11	C₂²×C₈	C₂²	1	1	yes	characteristic
12	#125	—	2	2	no	—
13	#125	C₂²	1	4	yes	—
14	C₄×Q₈	—	2	2	no	—
15	C₄×Q₈	C₂²	1	4	yes	—
16	C₂×C₄⋊C₄	—	2	1	no	—
17	C₂×C₄⋊C₄	—	2	1	no	—
18	C₂×C₄⋊C₄	—	2	1	no	—
19	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₄²	—	2	1	no	—
23	C₂×C₄²	C₂²	1	1	yes	characteristic
24	#107	C₂²	1	4	yes	—
25	#106	C₂²	1	4	yes	—
26	C₄⋊C₈	C₂²	1	4	yes	—
27	#103	C₂²	1	4	yes	—
28	#103	C₂²	1	4	yes	—
29	C₂×Q₈	—	2	1	no	—
30	C₂×Q₈	—	2	2	no	—
31	C₂×Q₈	Q₈	1	4	yes	—
32	C₂×Q₈	C₂³	1	2	yes	—
33	C₂²×C₄	—	2	1	no	—
34	C₂²×C₄	—	2	1	no	—
35	C₂²×C₄	—	2	1	no	—
36	C₂²×C₄	—	2	1	no	—
37	C₂²×C₄	D₄	1	1	yes	characteristic
38	C₂²×C₄	D₄	1	1	yes	characteristic
39	C₂²×C₄	C₂³	1	1	yes	characteristic
40	C₂×C₈	—	2	2	no	—
41	C₂×C₈	—	2	2	no	—
42	C₂×C₈	C₂³	1	2	yes	—
43	C₂×C₈	C₂³	1	2	yes	—
44	C₄⋊C₄	—	2	4	no	—
45	C₄⋊C₄	—	2	4	no	—
46	C₄⋊C₄	—	2	4	no	—
47	C₄⋊C₄	—	2	1	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	2	1	no	—
50	C₄⋊C₄	C₂³	1	2	yes	—
51	C₄⋊C₄	C₂³	1	2	yes	—
52	C₄⋊C₄	C₂³	1	2	yes	—
53	C₄²	—	2	4	no	—
54	C₄²	D₄	1	2	yes	—
55	C₄²	C₂³	1	2	yes	—
56	C₂³	C₂×D₄	1	1	yes	characteristic
57	Q₈	—	2	4	no	—
58	Q₈	—	2	2	no	—
59	Q₈	C₂×Q₈	1	4	yes	—
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	2	2	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	4	2	no	—
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	—	4	2	no	—
70	C₂×C₄	C₂×D₄	1	2	yes	—
71	C₂×C₄	C₂×D₄	1	2	yes	—
72	C₂×C₄	C₂×D₄	1	1	yes	characteristic
73	C₂×C₄	C₂×Q₈	1	2	yes	—
74	C₂×C₄	#41	1	2	yes	—
75	C₂×C₄	C₂⁴	1	1	yes	characteristic
76	C₈	—	2	2	no	—
77	C₈	—	2	2	no	—
78	C₂²	C₂²⋊Q₈	1	2	yes	—
79	C₂²	#135	1	2	yes	—
80	C₂²	#137	1	2	yes	—
81	C₂²	C₂²×D₄	1	1	yes	characteristic
82	C₄	—	2	4	no	—
83	C₄	—	2	2	no	—
84	C₄	—	2	2	no	—
85	C₄	—	4	2	no	—
86	C₄	—	4	2	no	—
87	C₄	—	4	2	no	—
88	C₄	C₂²⋊Q₈	1	2	yes	—
89	C₄	C₂²×Q₈	1	1	yes	characteristic
90	C₄	C₂×#41	1	1	yes	characteristic
91	C₂	#479	1	4	yes	direct product factor
92	C₂	C₂×C₂²⋊Q₈	1	1	yes	characteristic
93	C₂	C₂×#135	1	1	yes	characteristic
94	C₂	C₂×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #479	C₂	direct (N × H)
91. C₂	#479	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×#125	2
C₂×C₄×Q₈	2
#479	2
C₂×#107	2
C₂×#106	2
C₂×C₄⋊C₈	2
C₂×#103	2

Subgroups — C2×#479 #3075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#479 #3075