Subgroups — C₂×#2245 #33700

Order 256.

291 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#499	C₂	1	1	yes	maximal, characteristic
2	C₂×#494	C₂	1	1	yes	maximal, characteristic
3	#2245	C₂	1	8	yes	maximal, direct product factor
4	C₂×#358	C₂	1	4	yes	maximal
5	C₂×#346	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₁₆	—	2	1	no	—
7	C₂²×Q₁₆	C₂²	1	2	yes	—
8	C₂×C₄⋊Q₈	—	2	1	no	—
9	C₂×#125	—	2	1	no	—
10	C₂²×C₁₆	C₂²	1	2	yes	—
11	#499	—	2	2	no	—
12	#499	C₂²	1	4	yes	—
13	#494	—	2	2	no	—
14	#494	C₂²	1	4	yes	—
15	C₂×#107	C₂²	1	2	yes	—
16	C₂×#106	—	2	1	no	—
17	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
18	#358	C₂²	1	16	yes	—
19	#346	C₂²	1	4	yes	—
20	C₂²×Q₈	—	2	2	no	—
21	C₂×Q₁₆	—	2	4	no	—
22	C₂×Q₁₆	—	2	2	no	—
23	C₂×Q₁₆	—	2	8	no	—
24	C₂×Q₁₆	—	4	4	no	—
25	C₂×Q₁₆	C₂³	1	4	yes	—
26	C₂²×C₈	D₄	1	1	yes	characteristic
27	C₂²×C₈	C₂³	1	1	yes	characteristic
28	C₄⋊Q₈	—	2	4	no	—
29	C₄⋊Q₈	—	4	2	no	—
30	#125	—	2	4	no	—
31	#125	—	4	2	no	—
32	C₂×C₄⋊C₄	—	2	2	no	—
33	C₂×C₄⋊C₄	—	4	2	no	—
34	C₂×C₄⋊C₄	—	4	2	no	—
35	C₂×C₄²	D₄	1	1	yes	characteristic
36	C₂×C₁₆	—	2	4	no	—
37	C₂×C₁₆	C₂³	1	4	yes	—
38	#107	—	2	2	no	—
39	#107	C₂³	1	4	yes	—
40	#106	—	2	4	no	—
41	C₄×C₈	D₄	1	2	yes	—
42	C₄×C₈	C₂³	1	2	yes	—
43	C₂×Q₈	—	2	4	no	—
44	C₂×Q₈	—	4	2	no	—
45	C₂×Q₈	—	4	4	no	—
46	C₂×Q₈	—	4	4	no	—
47	C₂²×C₄	—	4	2	no	—
48	C₂²×C₄	—	4	2	no	—
49	C₂²×C₄	D₈	1	2	yes	—
50	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
51	Q₁₆	—	2	8	no	—
52	Q₁₆	—	4	4	no	—
53	Q₁₆	—	4	8	no	—
54	C₂×C₈	SD₁₆	1	4	yes	—
55	C₂×C₈	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈	C₂×D₄	1	2	yes	—
57	C₂×C₈	#41	1	4	yes	—
58	C₂×C₈	C₂⁴	1	1	yes	characteristic
59	C₄⋊C₄	—	2	4	no	—
60	C₄⋊C₄	—	4	2	no	—
61	C₄⋊C₄	—	4	8	no	—
62	C₄⋊C₄	—	4	8	no	—
63	C₄²	D₈	1	2	yes	—
64	C₄²	C₂×D₄	1	2	yes	—
65	C₁₆	—	2	4	no	—
66	C₂³	C₂×D₈	1	1	yes	characteristic
67	Q₈	—	4	4	no	—
68	Q₈	—	4	4	no	—
69	Q₈	—	8	4	no	—
70	C₂×C₄	—	2	4	no	—
71	C₂×C₄	—	4	4	no	—
72	C₂×C₄	—	4	4	no	—
73	C₂×C₄	—	8	4	no	—
74	C₂×C₄	—	8	4	no	—
75	C₂×C₄	#124	1	2	yes	—
76	C₂×C₄	C₂×D₈	1	4	yes	—
77	C₂×C₄	C₂×D₈	1	1	yes	characteristic
78	C₂×C₄	C₂×SD₁₆	1	2	yes	—
79	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
80	C₈	#124	1	2	yes	—
81	C₈	C₂×SD₁₆	1	4	yes	—
82	C₈	C₂×#41	1	2	yes	—
83	C₂²	#486	1	2	yes	—
84	C₂²	#510	1	4	yes	—
85	C₂²	C₂²×D₈	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	—	8	4	no	—
88	C₄	—	8	4	no	—
89	C₄	#486	1	2	yes	—
90	C₄	C₂×#124	1	1	yes	characteristic
91	C₄	C₂²×SD₁₆	1	1	yes	characteristic
92	C₂	#2245	1	4	yes	direct product factor
93	C₂	C₂×#486	1	1	yes	characteristic
94	C₂	C₂×#510	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×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
3. #2245	C₂	direct (N × H)
92. C₂	#2245	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×#499	2
C₂×#494	2
#2245	2
C₂×#358	2
C₂×#346	2

Subgroups — C2×#2245 #33700

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2245 #33700