Subgroups — C₂×#1358 #11919

Order 256.

195 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#494	C₂	1	1	yes	maximal, characteristic
2	C₂×#364	C₂	1	2	yes	maximal
3	#1358	C₂	1	4	yes	maximal, direct product factor
4	C₂²×Q₁₆	—	2	2	no	—
5	C₂×C₄⋊Q₈	C₄	1	2	yes	—
6	C₂×M₃₂	—	2	2	no	—
7	#494	—	2	2	no	—
8	#494	C₄	1	2	yes	—
9	#494	C₂²	1	2	yes	—
10	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
11	#364	—	2	2	no	—
12	#364	C₂²	1	4	yes	—
13	C₂²×Q₈	—	2	2	no	—
14	C₂×Q₁₆	—	2	4	no	—
15	C₂×Q₁₆	—	2	4	no	—
16	C₂×Q₁₆	—	4	2	no	—
17	C₂×Q₁₆	—	4	2	no	—
18	C₂×Q₁₆	—	4	2	no	—
19	C₂×Q₁₆	—	4	2	no	—
20	C₂²×C₈	D₄	1	2	yes	—
21	C₄⋊Q₈	—	2	2	no	—
22	C₄⋊Q₈	—	4	2	no	—
23	C₄⋊Q₈	C₂×C₄	1	4	yes	—
24	C₂×C₄⋊C₄	—	4	2	no	—
25	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
26	M₃₂	—	2	4	no	—
27	M₃₂	—	4	2	no	—
28	C₂×C₁₆	—	4	2	no	—
29	C₄×C₈	C₂×C₄	1	1	yes	characteristic
30	C₄×C₈	D₄	1	2	yes	—
31	C₄×C₈	C₂³	1	1	yes	characteristic
32	C₂×Q₈	—	2	4	no	—
33	C₂×Q₈	—	4	2	no	—
34	C₂×Q₈	—	4	4	no	—
35	C₂×Q₈	—	4	4	no	—
36	C₂²×C₄	—	2	1	no	—
37	C₂²×C₄	—	4	2	no	—
38	C₂²×C₄	C₂²⋊C₄	1	1	yes	characteristic
39	Q₁₆	—	4	4	no	—
40	Q₁₆	—	4	4	no	—
41	Q₁₆	—	4	4	no	—
42	Q₁₆	—	4	4	no	—
43	C₂×C₈	C₂²⋊C₄	1	2	yes	—
44	C₂×C₈	D₈	1	2	yes	—
45	C₂×C₈	D₈	1	2	yes	—
46	C₂×C₈	SD₁₆	1	2	yes	—
47	C₂×C₈	SD₁₆	1	2	yes	—
48	C₂×C₈	C₂×D₄	1	2	yes	—
49	C₄⋊C₄	—	4	4	no	—
50	C₄⋊C₄	—	4	4	no	—
51	C₄²	—	2	1	no	—
52	C₄²	C₂²⋊C₄	1	1	yes	characteristic
53	C₄²	C₂²×C₄	1	1	yes	characteristic
54	C₁₆	—	4	4	no	—
55	C₂³	#100	1	1	yes	characteristic
56	Q₈	—	4	8	no	—
57	Q₈	—	8	4	no	—
58	C₂×C₄	—	2	4	no	—
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	4	4	no	—
62	C₂×C₄	—	8	2	no	—
63	C₂×C₄	—	8	2	no	—
64	C₂×C₄	#100	1	1	yes	characteristic
65	C₂×C₄	#102	1	2	yes	—
66	C₂×C₄	#102	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₈	#102	1	2	yes	—
69	C₈	#102	1	2	yes	—
70	C₈	C₂×D₈	1	2	yes	—
71	C₈	C₂×SD₁₆	1	2	yes	—
72	C₂²	—	2	2	no	—
73	C₂²	#331	1	1	yes	characteristic
74	C₂²	#331	1	1	yes	characteristic
75	C₂²	C₂×#100	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	2	2	no	—
78	C₄	—	8	4	no	—
79	C₄	#331	1	2	yes	—
80	C₄	C₂×#102	1	2	yes	—
81	C₂	—	2	1	no	—
82	C₂	—	2	1	no	—
83	C₂	#1358	1	2	yes	direct product factor
84	C₂	C₂×#331	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#331
commutator	C₄²	C₂²×C₄
Frattini, cosocle	C₄×C₈	C₂³
prime radical	C₂³	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ G
LECS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #1358	C₂	direct (N × H)
83. C₂	#1358	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×#494	2
C₂×#364	2
#1358	2

Subgroups — C2×#1358 #11919

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1358 #11919