Subgroups — C₂×#2961 #60188

Order 256.

947 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533	C₂	1	1	yes	maximal, characteristic
2	#2961	C₂	1	16	yes	maximal, direct product factor
3	C₂×#446	C₂	1	8	yes	maximal, complemented
4	C₂×#424	C₂	1	2	yes	maximal
5	C₂×#423	C₂	1	1	yes	maximal, characteristic
6	C₂×#405	C₂	1	2	yes	maximal
7	C₂²×#97	C₂	1	1	yes	maximal, characteristic
8	C₂²×M₁₆	C₂²	1	2	yes	—
9	C₂³×C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₈	C₂²	1	1	yes	characteristic
11	#533	C₄	1	8	yes	—
12	#533	C₂²	1	8	yes	—
13	C₂×C₄⋊Q₈	C₄	1	2	yes	—
14	C₂×#125	C₄	1	2	yes	—
15	C₂×C₂²⋊Q₈	C₄	1	4	yes	—
16	C₂×C₄×Q₈	C₂²	1	4	yes	—
17	C₂×#117	C₂²	1	2	yes	—
18	C₂²×C₄²	C₂²	1	1	yes	characteristic
19	#446	C₂²	1	64	yes	complemented
20	#424	C₂²	1	16	yes	—
21	#423	C₂²	1	8	yes	—
22	C₂×C₄⋊C₈	C₂²	1	4	yes	—
23	C₂×C₄⋊C₈	C₂²	1	8	yes	—
24	#405	C₂²	1	16	yes	—
25	C₂×#97	C₂²	1	4	yes	—
26	C₂×#97	C₂²	1	8	yes	—
27	C₂×#97	C₂²	1	4	yes	—
28	C₂×C₄×C₈	C₂²	1	4	yes	—
29	C₂²×Q₈	C₂×C₄	1	4	yes	—
30	C₂³×C₄	C₂×C₄	1	2	yes	—
31	C₂³×C₄	C₂³	1	1	yes	characteristic
32	C₂×M₁₆	—	2	8	no	—
33	C₂×M₁₆	C₂³	1	8	yes	—
34	C₂²×C₈	—	2	4	no	—
35	C₂²×C₈	Q₈	1	8	yes	complemented
36	C₂²×C₈	C₂³	1	4	yes	—
37	C₂²×C₈	C₂³	1	2	yes	—
38	C₂²×C₈	C₂³	1	4	yes	—
39	C₂²×C₈	C₂³	1	2	yes	—
40	C₂²×C₈	C₂³	1	4	yes	—
41	C₄⋊Q₈	C₂×C₄	1	16	yes	—
42	#125	C₂×C₄	1	16	yes	—
43	C₂²⋊Q₈	C₂×C₄	1	32	yes	—
44	C₄×Q₈	C₂×C₄	1	16	yes	—
45	C₄×Q₈	C₂³	1	16	yes	—
46	#117	C₂×C₄	1	8	yes	—
47	#117	C₂³	1	8	yes	—
48	C₂×C₄⋊C₄	C₂×C₄	1	4	yes	—
49	C₂×C₄⋊C₄	C₂×C₄	1	8	yes	—
50	C₂×C₄⋊C₄	C₂×C₄	1	4	yes	—
51	C₂×C₂²⋊C₄	C₂×C₄	1	4	yes	—
52	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²	C₂×C₄	1	4	yes	—
55	C₂×C₄²	C₂³	1	4	yes	—
56	C₂×C₄²	C₂³	1	4	yes	—
57	C₂×C₄²	C₂³	1	2	yes	—
58	C₄⋊C₈	C₂³	1	16	yes	—
59	C₄⋊C₈	C₂³	1	32	yes	—
60	#97	C₂³	1	16	yes	—
61	#97	C₂³	1	16	yes	—
62	C₄×C₈	C₂³	1	16	yes	—
63	C₂⁴	C₂²×C₄	1	1	yes	characteristic
64	C₂×Q₈	—	4	8	no	—
65	C₂×Q₈	C₂²×C₄	1	16	yes	—
66	C₂²×C₄	—	4	4	no	—
67	C₂²×C₄	C₂²×C₄	1	2	yes	—
68	C₂²×C₄	C₂²×C₄	1	2	yes	—
69	C₂²×C₄	C₂²×C₄	1	8	yes	—
70	C₂²×C₄	C₂²×C₄	1	8	yes	—
71	C₂²×C₄	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄	C₂²×C₄	1	2	yes	—
73	C₂²×C₄	C₂×Q₈	1	4	yes	—
74	C₂²×C₄	#41	1	4	yes	—
75	C₂²×C₄	C₂⁴	1	2	yes	—
76	C₂²×C₄	C₂⁴	1	1	yes	characteristic
77	M₁₆	—	2	16	no	—
78	C₂×C₈	—	2	4	no	—
79	C₂×C₈	—	2	8	no	—
80	C₂×C₈	—	2	8	no	—
81	C₂×C₈	C₂×Q₈	1	8	yes	—
82	C₂×C₈	C₂×Q₈	1	16	yes	complemented
83	C₂×C₈	C₂⁴	1	8	yes	—
84	C₂×C₈	C₂⁴	1	4	yes	—
85	C₂×C₈	C₂⁴	1	4	yes	—
86	C₄⋊C₄	C₂²×C₄	1	16	yes	—
87	C₄⋊C₄	C₂²×C₄	1	32	yes	—
88	C₄⋊C₄	C₂²×C₄	1	16	yes	—
89	C₂²⋊C₄	C₂²×C₄	1	16	yes	—
90	C₄²	C₂²×C₄	1	4	yes	—
91	C₄²	C₂²×C₄	1	4	yes	—
92	C₄²	C₂²×C₄	1	4	yes	—
93	C₄²	C₂²×C₄	1	8	yes	—
94	C₄²	C₂⁴	1	8	yes	—
95	C₄²	C₂⁴	1	4	yes	—
96	C₂³	—	2	4	no	—
97	C₂³	C₄×Q₈	1	4	yes	—
98	C₂³	C₂³×C₄	1	2	yes	—
99	C₂³	C₂³×C₄	1	1	yes	characteristic
100	Q₈	—	4	16	no	—
101	C₂×C₄	—	2	4	no	—
102	C₂×C₄	—	2	4	no	—
103	C₂×C₄	—	2	16	no	—
104	C₂×C₄	—	4	8	no	—
105	C₂×C₄	C₄×Q₈	1	8	yes	—
106	C₂×C₄	C₄×Q₈	1	4	yes	—
107	C₂×C₄	C₂³×C₄	1	4	yes	—
108	C₂×C₄	C₂³×C₄	1	4	yes	—
109	C₂×C₄	C₂³×C₄	1	16	yes	—
110	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
111	C₂×C₄	C₂³×C₄	1	2	yes	—
112	C₂×C₄	C₂²×Q₈	1	2	yes	—
113	C₂×C₄	C₂²×Q₈	1	4	yes	—
114	C₂×C₄	C₂×#41	1	2	yes	—
115	C₂×C₄	C₂×#41	1	4	yes	—
116	C₂×C₄	C₂⁵	1	1	yes	characteristic
117	C₈	—	2	4	no	—
118	C₈	—	2	8	no	—
119	C₈	C₂²×Q₈	1	8	yes	—
120	C₂²	—	2	8	no	—
121	C₂²	—	2	4	no	—
122	C₂²	C₂×C₄×Q₈	1	4	yes	—
123	C₂²	C₂×C₄×Q₈	1	2	yes	—
124	C₂²	#568	1	4	yes	—
125	C₂²	C₂⁴×C₄	1	1	yes	characteristic
126	C₄	—	2	4	no	—
127	C₄	—	2	4	no	—
128	C₄	—	2	16	no	—
129	C₄	C₂×C₄×Q₈	1	2	yes	—
130	C₄	C₂×C₄×Q₈	1	4	yes	—
131	C₄	C₂³×Q₈	1	1	yes	characteristic
132	C₄	C₂²×#41	1	1	yes	characteristic
133	C₂	—	2	4	no	—
134	C₂	#2961	1	4	yes	direct product factor
135	C₂	C₂²×C₄×Q₈	1	1	yes	characteristic
136	C₂	C₂×#568	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂⁴
commutator	C₂²	C₂⁴×C₄
Frattini, cosocle	C₂×C₄	C₂⁵
socle	C₂³	C₂³×C₄
prime radical	C₂⁴	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #2961	C₂	direct (N × H)
3. C₂×#446	C₂	semidirect
19. #446	C₂²	semidirect
35. C₂²×C₈	Q₈	semidirect
82. C₂×C₈	C₂×Q₈	semidirect
134. C₂	#2961	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×#533	2
#2961	2
C₂×#446	2
C₂×#424	2
C₂×#423	2
C₂×#405	2
C₂²×#97	2

Subgroups — C2×#2961 #60188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2961 #60188