Subgroups — C₂×#4318 #66974

Order 352.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₁₁	C₂	1	1	yes	maximal, characteristic
2	#4318	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₁⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂³×C₁₁	C₄	1	1	yes	characteristic
5	C₂×C₄×C₁₁	C₄	1	2	yes	—
6	C₂×C₄×C₁₁	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₁	C₂²	1	2	yes	—
8	C₂×C₄×C₁₁	C₂²	1	1	yes	characteristic
9	C₁₁⋊C₈	C₂²	1	4	yes	complemented
10	C₂²×C₁₁	—	2	2	no	—
11	C₂²×C₁₁	C₂×C₄	1	2	yes	—
12	C₂²×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₄×C₁₁	C₂×C₄	1	2	yes	—
14	C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₄×C₁₁	C₂³	1	1	yes	characteristic
16	C₂×M₁₆	—	11	1	no	maximal, Sylow
17	C₂×C₁₁	—	2	2	no	—
18	C₂×C₁₁	M₁₆	1	2	yes	complemented
19	C₂×C₁₁	C₂²×C₄	1	1	yes	characteristic
20	C₂²×C₄	D₁₁	1	1	yes	characteristic
21	M₁₆	—	11	4	no	—
22	C₂×C₈	—	11	2	no	—
23	C₁₁	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
24	C₂³	Dic₁₁	1	1	yes	characteristic
25	C₂×C₄	Dic₁₁	1	1	yes	characteristic
26	C₂×C₄	Dic₁₁	1	2	yes	—
27	C₂×C₄	C₂×D₁₁	1	2	yes	—
28	C₂×C₄	C₂×D₁₁	1	1	yes	characteristic
29	C₈	—	11	4	no	—
30	C₂²	—	2	2	no	—
31	C₂²	C₂×Dic₁₁	1	2	yes	—
32	C₂²	C₂×Dic₁₁	1	1	yes	characteristic
33	C₄	C₂×Dic₁₁	1	2	yes	—
34	C₄	C₂×Dic₁₁	1	1	yes	characteristic
35	C₄	C₂²×D₁₁	1	1	yes	characteristic
36	C₂	—	2	2	no	—
37	C₂	#4318	1	2	yes	direct product factor
38	C₂	C₂²×Dic₁₁	1	1	yes	characteristic

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.