Subgroups — C₂×#1844 #20794

Order 256.

679 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#106	C₂	1	4	yes	maximal
2	C₂²×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#384	C₂	1	2	yes	maximal
4	#1844	C₂	1	8	yes	maximal, direct product factor
5	C₂³×C₈	C₂²	1	2	yes	—
6	C₂²×C₄⋊C₄	—	2	4	no	—
7	C₂²×C₄⋊C₄	C₂²	1	4	yes	—
8	C₂²×C₄²	C₂²	1	1	yes	characteristic
9	C₂×#106	—	2	16	no	—
10	C₂×#106	C₂²	1	16	yes	—
11	C₂×C₄×C₈	C₄	1	8	yes	complemented
12	C₂×C₄×C₈	C₂²	1	4	yes	—
13	#384	—	2	4	no	—
14	#384	C₂²	1	8	yes	—
15	C₂³×C₄	—	2	4	no	—
16	C₂³×C₄	D₄	1	2	yes	—
17	C₂³×C₄	C₂³	1	1	yes	characteristic
18	C₂²×C₈	C₂×C₄	1	8	yes	—
19	C₂²×C₈	D₄	1	8	yes	—
20	C₂²×C₈	Q₈	1	8	yes	—
21	C₂²×C₈	C₂³	1	4	yes	—
22	C₂×C₄⋊C₄	—	2	16	no	—
23	C₂×C₄⋊C₄	—	2	16	no	—
24	C₂×C₄⋊C₄	—	2	4	no	—
25	C₂×C₄⋊C₄	—	4	16	no	—
26	C₂×C₄⋊C₄	C₂³	1	8	yes	—
27	C₂×C₄²	C₂×C₄	1	4	yes	—
28	C₂×C₄²	D₄	1	2	yes	—
29	C₂×C₄²	Q₈	1	4	yes	—
30	C₂×C₄²	C₂³	1	2	yes	—
31	#106	—	2	32	no	—
32	C₄×C₈	C₂×C₄	1	16	yes	complemented
33	C₂⁴	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₄	—	2	8	no	—
35	C₂²×C₄	—	4	8	no	—
36	C₂²×C₄	—	4	16	no	—
37	C₂²×C₄	C₄⋊C₄	1	8	yes	—
38	C₂²×C₄	SD₁₆	1	16	yes	—
39	C₂²×C₄	C₂²×C₄	1	2	yes	—
40	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄	C₂×D₄	1	4	yes	—
42	C₂²×C₄	C₂×D₄	1	4	yes	—
43	C₂²×C₄	C₂×Q₈	1	4	yes	—
44	C₂²×C₄	C₂×Q₈	1	2	yes	—
45	C₂²×C₄	C₂⁴	1	1	yes	characteristic
46	C₂×C₈	C₄⋊C₄	1	32	yes	complemented
47	C₂×C₈	C₂²×C₄	1	8	yes	—
48	C₂×C₈	C₂×D₄	1	8	yes	—
49	C₂×C₈	C₂×Q₈	1	8	yes	—
50	C₄⋊C₄	—	2	16	no	—
51	C₄⋊C₄	—	4	8	no	—
52	C₄⋊C₄	—	4	32	no	—
53	C₄²	C₄⋊C₄	1	8	yes	—
54	C₄²	C₂²×C₄	1	4	yes	—
55	C₄²	C₂×Q₈	1	4	yes	—
56	C₂³	C₂×C₄⋊C₄	1	2	yes	—
57	C₂³	#127	1	2	yes	—
58	C₂³	C₄⋊Q₈	1	2	yes	—
59	C₂³	C₂×SD₁₆	1	8	yes	—
60	C₂³	C₂²×D₄	1	1	yes	characteristic
61	C₂×C₄	—	4	8	no	—
62	C₂×C₄	—	4	16	no	—
63	C₂×C₄	—	8	16	no	—
64	C₂×C₄	#106	1	32	yes	complemented
65	C₂×C₄	C₂×C₄⋊C₄	1	8	yes	—
66	C₂×C₄	C₂×C₄⋊C₄	1	2	yes	—
67	C₂×C₄	C₂×C₄⋊C₄	1	8	yes	—
68	C₂×C₄	#127	1	2	yes	—
69	C₂×C₄	C₄⋊Q₈	1	8	yes	—
70	C₂×C₄	C₄⋊Q₈	1	2	yes	—
71	C₂×C₄	C₂×SD₁₆	1	16	yes	—
72	C₂×C₄	C₂³×C₄	1	1	yes	characteristic
73	C₂×C₄	C₂²×D₄	1	2	yes	—
74	C₂×C₄	C₂²×Q₈	1	2	yes	—
75	C₂×C₄	C₂²×Q₈	1	1	yes	characteristic
76	C₈	C₂×C₄⋊C₄	1	16	yes	complemented
77	C₂²	#384	1	4	yes	—
78	C₂²	C₂×#106	1	8	yes	—
79	C₂²	#492	1	8	yes	—
80	C₂²	#498	1	8	yes	—
81	C₂²	C₂²×C₄⋊C₄	1	1	yes	characteristic
82	C₂²	C₂×#127	1	1	yes	characteristic
83	C₂²	C₂×C₄⋊Q₈	1	1	yes	characteristic
84	C₂²	C₂²×SD₁₆	1	4	yes	—
85	C₄	—	8	8	no	—
86	C₄	#384	1	4	yes	—
87	C₄	C₂×#106	1	16	yes	complemented
88	C₄	C₂²×C₄⋊C₄	1	2	yes	—
89	C₄	C₂×C₄⋊Q₈	1	2	yes	—
90	C₂	#1844	1	8	yes	direct product factor
91	C₂	C₂×#384	1	1	yes	characteristic
92	C₂	C₂²×#106	1	2	yes	—
93	C₂	C₂×#492	1	2	yes	—
94	C₂	C₂×#498	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴	C₂×D₄
commutator	C₂×C₄	C₂³×C₄
Frattini, cosocle	C₂²×C₄	C₂⁴
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
4. #1844	C₂	direct (N × H)
11. C₂×C₄×C₈	C₄	semidirect
32. C₄×C₈	C₂×C₄	semidirect
46. C₂×C₈	C₄⋊C₄	semidirect
64. C₂×C₄	#106	semidirect
76. C₈	C₂×C₄⋊C₄	semidirect
87. C₄	C₂×#106	semidirect
90. C₂	#1844	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×#106	2
C₂²×C₄×C₈	2
C₂×#384	2
#1844	2

Subgroups — C2×#1844 #20794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1844 #20794