Subgroups — #27160828

Order 12608.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#13096802	C₂	1	2	yes	maximal
2	C₄⋊Q₈×C₁₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#13096802	—	2	2	no	—
4	C₂×Q₈×C₁₉₇	C₄	1	2	yes	—
5	C₄⋊C₄×C₁₉₇	—	2	2	no	—
6	C₄²×C₁₉₇	C₂²	1	1	yes	characteristic
7	#13096802	—	4	2	no	—
8	Q₈×C₁₉₇	—	4	2	no	—
9	C₂×C₄×C₁₉₇	—	2	2	no	—
10	C₂×C₄×C₁₉₇	C₂×C₄	1	1	yes	characteristic
11	C₂×C₄×C₁₉₇	D₄	1	2	yes	—
12	C₂²×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
13	C₄×C₁₉₇	—	2	1	no	—
14	C₄×C₁₉₇	—	4	2	no	—
15	C₄×C₁₉₇	SD₁₆	1	2	yes	—
16	C₄×C₁₉₇	Q₁₆	1	2	yes	—
17	C₂×C₁₉₇	#100	1	1	yes	characteristic
18	C₂×C₁₉₇	#103	1	2	yes	—
19	C₁₉₇	#333	1	1	yes	characteristic, complemented, Sylow
20	#333	—	197	1	no	maximal, Sylow
21	C₄⋊Q₈	D₁₉₇	1	1	yes	characteristic
22	C₄⋊C₈	—	197	2	no	—
23	C₂×Q₈	Dic₁₉₇	1	2	yes	—
24	C₂×C₈	—	394	2	no	—
25	C₄⋊C₄	—	2	2	no	—
26	C₄²	C₂×D₁₉₇	1	1	yes	characteristic
27	Q₈	—	4	2	no	—
28	C₂×C₄	—	2	2	no	—
29	C₂×C₄	C₂×Dic₁₉₇	1	1	yes	characteristic
30	C₂×C₄	C₂²⋊D₁₉₇	1	2	yes	—
31	C₈	—	788	2	no	—
32	C₂²	C₂²⋊Dic₁₉₇	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	4	2	no	—
35	C₄	#15691345	1	2	yes	—
36	C₄	#15691348	1	2	yes	—
37	C₂	#20263243	1	1	yes	characteristic
38	C₂	#20263250	1	2	yes	—

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
19. C₁₉₇	#333	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.