Subgroups — #17984146

Order 4384.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#10587739	C₂	1	2	yes	maximal, complemented
2	C₂×C₂²⋊D₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#10587739	—	2	2	no	—
4	C₂²×D₁₃₇	C₂²	1	1	yes	characteristic
5	C₂²⋊D₁₃₇	—	2	2	no	—
6	C₂×Dic₁₃₇	C₄	1	1	yes	characteristic, complemented
7	C₂³×C₁₃₇	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₁₃₇	—	2	1	no	—
9	C₂²×C₁₃₇	—	4	1	no	—
10	C₂²×C₁₃₇	C₂×C₄	1	1	yes	characteristic
11	C₂×D₁₃₇	—	4	1	no	—
12	C₂×D₁₃₇	D₄	1	2	yes	—
13	#10587739	—	4	2	no	—
14	Dic₁₃₇	—	2	1	no	—
15	C₂×C₁₃₇	—	2	1	no	—
16	C₂×C₁₃₇	—	4	1	no	—
17	C₂×C₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
18	D₁₃₇	—	2	2	no	—
19	C₁₃₇	#99	1	1	yes	characteristic, complemented, Sylow
20	#99	—	137	1	no	maximal, Sylow
21	C₂×D₄	—	137	1	no	—
22	C₂²⋊C₄	—	137	2	no	—
23	C₂³	—	137	1	no	—
24	C₂³	#10587739	1	1	yes	characteristic, complemented
25	D₄	—	274	2	no	—
26	C₂×C₄	—	274	2	no	—
27	C₂×C₄	—	137	1	no	—
28	C₂²	—	2	1	no	—
29	C₂²	—	4	1	no	—
30	C₂²	—	548	1	no	—
31	C₂²	—	137	2	no	—
32	C₂²	C₂×#10587739	1	1	yes	characteristic
33	C₄	—	274	1	no	—
34	C₄	—	548	2	no	—
35	C₂	—	2	1	no	—
36	C₂	—	4	1	no	—
37	C₂	—	274	2	no	—
38	C₂	C₂²⋊#10587739	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.