Subgroups — C₂²⋊#15667734 #26015084

Order 11296.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15667734	C₂	1	2	yes	maximal, complemented
2	C₂²×#13083443	C₂	1	1	yes	maximal, characteristic
3	#15667734	—	2	2	no	—
4	C₂×#13083443	—	2	2	no	—
5	C₂×#13083443	C₄	1	1	yes	characteristic
6	C₂×#13083443	C₂²	1	1	yes	characteristic
7	C₂²×D₃₅₃	C₄	1	1	yes	characteristic
8	C₂²×C₃₅₃	C₈	1	1	yes	characteristic, complemented
9	C₂×D₃₅₃	—	2	1	no	—
10	C₂×D₃₅₃	—	2	1	no	—
11	C₂×D₃₅₃	C₈	1	1	yes	characteristic, complemented
12	C₂×D₃₅₃	C₂×C₄	1	1	yes	characteristic
13	#13083443	—	2	1	no	—
14	#13083443	D₄	1	2	yes	—
15	C₂×C₃₅₃	—	2	1	no	—
16	C₂×C₃₅₃	C₂×C₈	1	1	yes	characteristic
17	D₃₅₃	—	2	1	no	—
18	D₃₅₃	C₂²⋊C₄	1	1	yes	characteristic
19	D₃₅₃	M₁₆	1	1	yes	characteristic
20	C₃₅₃	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
21	C₂²⋊C₈	—	353	1	no	maximal, Sylow
22	C₂²×C₄	—	353	1	no	—
23	C₂×C₈	—	353	2	no	—
24	C₂³	—	353	1	no	—
25	C₂×C₄	—	353	1	no	—
26	C₂×C₄	—	353	1	no	—
27	C₂×C₄	—	706	2	no	—
28	C₈	—	706	2	no	—
29	C₂²	—	353	1	no	—
30	C₂²	—	353	1	no	—
31	C₂²	—	706	1	no	—
32	C₂²	—	706	1	no	—
33	C₂²	#15667734	1	1	yes	characteristic, complemented
34	C₄	—	353	2	no	—
35	C₄	—	706	1	no	—
36	C₂	—	2	1	no	—
37	C₂	—	353	1	no	—
38	C₂	—	353	1	no	—
39	C₂	—	706	1	no	—
40	C₂	C₂×#15667734	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.