Subgroups — #49088447

Order 35744.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊Dic₁₁₁₇	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×C₁₁₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₁₁₁₇	—	2	2	no	—
4	C₂³×C₁₁₁₇	C₄	1	1	yes	characteristic, complemented
5	C₂³×C₁₁₁₇	C₂²	1	1	yes	characteristic
6	D₄×C₁₁₁₇	—	2	2	no	—
7	C₂×C₄×C₁₁₁₇	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₁₁₁₇	—	2	1	no	—
9	C₂²×C₁₁₁₇	—	4	1	no	—
10	C₂²×C₁₁₁₇	—	4	1	no	—
11	C₂²×C₁₁₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₁₁₁₇	D₄	1	2	yes	—
13	C₄×C₁₁₁₇	—	2	1	no	—
14	Dic₁₁₁₇	—	4	2	no	—
15	C₂×C₁₁₁₇	—	2	2	no	—
16	C₂×C₁₁₁₇	—	2	1	no	—
17	C₂×C₁₁₁₇	—	4	1	no	—
18	C₂×C₁₁₁₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₁₁₁₇	#99	1	1	yes	characteristic, complemented, Sylow
20	#99	—	1117	1	no	maximal, Sylow
21	C₂×D₄	D₁₁₁₇	1	1	yes	characteristic
22	C₂²⋊C₄	—	1117	2	no	—
23	C₂³	Dic₁₁₁₇	1	1	yes	characteristic, complemented
24	C₂³	C₂×D₁₁₁₇	1	1	yes	characteristic
25	D₄	—	2	2	no	—
26	C₂×C₄	—	2234	2	no	—
27	C₂×C₄	Dic₁₁₁₇	1	1	yes	characteristic, complemented
28	C₂²	—	2	1	no	—
29	C₂²	—	4	1	no	—
30	C₂²	—	4	1	no	—
31	C₂²	C₂×Dic₁₁₁₇	1	1	yes	characteristic
32	C₂²	C₂²⋊D₁₁₁₇	1	2	yes	—
33	C₄	—	2	1	no	—
34	C₄	—	4468	2	no	—
35	C₂	—	2	2	no	—
36	C₂	—	2	1	no	—
37	C₂	—	4	1	no	—
38	C₂	C₂²⋊Dic₁₁₁₇	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.