Subgroups — #27161477

Order 12608.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263326	C₂	1	2	yes	maximal
2	#20263258	C₂	1	4	yes	maximal
3	C₄×C₈×C₁₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₉₄	—	2	2	no	—
5	C₄⋊Dic₁₉₇	—	2	2	no	—
6	C₄⋊Dic₁₉₇	C₂²	1	4	yes	—
7	C₂×C₈×C₁₉₇	C₂²	1	2	yes	—
8	C₄²×C₁₉₇	C₂²	1	1	yes	characteristic
9	Dic₃₉₄	—	4	4	no	—
10	C₂×Dic₁₉₇	—	2	4	no	—
11	C₂×C₄×C₁₉₇	D₄	1	2	yes	—
12	C₂×C₄×C₁₉₇	C₂³	1	1	yes	characteristic
13	C₈×C₁₉₇	Q₈	1	4	yes	complemented
14	C₂²×C₁₉₇	C₂×D₄	1	1	yes	characteristic
15	C₄×C₁₉₇	SD₁₆	1	4	yes	—
16	C₄×C₁₉₇	C₂×Q₈	1	2	yes	—
17	Dic₁₉₇	—	4	4	no	—
18	C₂×C₁₉₇	C₄⋊Q₈	1	1	yes	characteristic
19	C₂×C₁₉₇	C₂×SD₁₆	1	2	yes	—
20	C₁₉₇	#498	1	1	yes	characteristic, complemented, Sylow
21	#498	—	197	1	no	maximal, Sylow
22	C₄⋊Q₈	—	197	2	no	—
23	#106	—	197	4	no	—
24	C₄×C₈	D₁₉₇	1	1	yes	characteristic
25	C₂×Q₈	—	394	2	no	—
26	C₂×C₈	C₂×D₁₉₇	1	2	yes	—
27	C₄⋊C₄	—	394	2	no	—
28	C₄⋊C₄	—	197	4	no	—
29	C₄²	C₂×D₁₉₇	1	1	yes	characteristic
30	Q₈	—	788	4	no	—
31	C₂×C₄	—	394	4	no	—
32	C₂×C₄	D₇₈₈	1	2	yes	—
33	C₂×C₄	C₂²×D₁₉₇	1	1	yes	characteristic
34	C₈	Dic₃₉₄	1	4	yes	complemented
35	C₂²	C₂×D₇₈₈	1	1	yes	characteristic
36	C₄	—	788	4	no	—
37	C₄	#15691347	1	4	yes	—
38	C₄	C₂×Dic₃₉₄	1	2	yes	—
39	C₂	#20263326	1	1	yes	characteristic
40	C₂	C₂×#15691347	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.