Subgroups — #26014980

Order 11296.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₀₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₄₁₂	C₂	1	1	yes	maximal, characteristic
3	#19150714	C₂	1	4	yes	maximal, complemented
4	C₄²×C₃₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₃₅₃	C₂²	1	2	yes	—
6	Dic₇₀₆	—	2	2	no	—
7	D₁₄₁₂	—	2	2	no	—
8	C₂×Dic₃₅₃	C₂²	1	2	yes	—
9	C₂×C₄×C₃₅₃	C₂²	1	2	yes	—
10	C₂×C₄×C₃₅₃	C₂²	1	1	yes	characteristic
11	C₂²×C₃₅₃	C₂³	1	1	yes	characteristic
12	C₂×D₃₅₃	—	2	2	no	—
13	C₂×D₃₅₃	—	2	4	no	—
14	C₄×C₃₅₃	—	2	2	no	—
15	C₄×C₃₅₃	D₄	1	2	yes	—
16	Dic₃₅₃	—	2	2	no	—
17	C₂×C₃₅₃	C₂×D₄	1	1	yes	characteristic
18	C₂×C₃₅₃	#41	1	2	yes	—
19	D₃₅₃	—	4	2	no	—
20	C₃₅₃	#124	1	1	yes	characteristic, complemented, Sylow
21	#124	—	353	1	no	maximal, Sylow
22	C₂×Q₈	—	353	1	no	—
23	C₂×D₄	—	353	1	no	—
24	C₂²⋊C₄	—	353	4	no	—
25	C₄²	D₃₅₃	1	1	yes	characteristic, complemented
26	C₂³	—	353	2	no	—
27	Q₈	—	706	2	no	—
28	D₄	—	706	2	no	—
29	C₂×C₄	—	353	2	no	—
30	C₂×C₄	C₂×D₃₅₃	1	2	yes	—
31	C₂×C₄	C₂×D₃₅₃	1	1	yes	characteristic
32	C₂²	—	706	2	no	—
33	C₂²	—	706	4	no	—
34	C₂²	C₂²×D₃₅₃	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	706	2	no	—
37	C₄	D₁₄₁₂	1	2	yes	—
38	C₂	—	1412	2	no	—
39	C₂	C₂×D₁₄₁₂	1	1	yes	characteristic
40	C₂	#19150737	1	2	yes	—

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.