Subgroups — #20261115

Order 6208.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₈₈	C₂	1	4	yes	maximal
2	#15690810	C₂	1	2	yes	maximal
3	C₄×C₈×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₉₄	C₂²	1	4	yes	—
5	Dic₃₈₈	—	2	8	no	—
6	C₄⋊Dic₉₇	—	2	4	no	—
7	C₂×C₈×C₉₇	C₂²	1	2	yes	—
8	C₄²×C₉₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₉₇	D₄	1	2	yes	—
10	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
11	C₂×Dic₉₇	—	2	4	no	—
12	Dic₁₉₄	—	2	8	no	—
13	C₈×C₉₇	D₄	1	4	yes	—
14	C₂²×C₉₇	C₂×D₄	1	1	yes	characteristic
15	C₄×C₉₇	Q₁₆	1	4	yes	complemented
16	C₄×C₉₇	C₂×D₄	1	2	yes	—
17	Dic₉₇	—	4	4	no	—
18	C₂×C₉₇	#127	1	1	yes	characteristic
19	C₂×C₉₇	C₂×Q₁₆	1	2	yes	—
20	C₉₇	#494	1	1	yes	characteristic, complemented, Sylow
21	#494	—	97	1	no	maximal, Sylow
22	C₂×Q₁₆	—	97	4	no	—
23	C₄⋊Q₈	—	97	2	no	—
24	C₄×C₈	D₉₇	1	1	yes	characteristic
25	C₂×Q₈	—	97	4	no	—
26	Q₁₆	—	194	8	no	—
27	C₂×C₈	C₂×D₉₇	1	2	yes	—
28	C₄⋊C₄	—	194	4	no	—
29	C₄²	C₂×D₉₇	1	1	yes	characteristic
30	Q₈	—	194	8	no	—
31	C₂×C₄	—	194	4	no	—
32	C₂×C₄	D₃₈₈	1	2	yes	—
33	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
34	C₈	D₃₈₈	1	4	yes	—
35	C₂²	C₂×D₃₈₈	1	1	yes	characteristic
36	C₄	—	388	4	no	—
37	C₄	Dic₃₈₈	1	4	yes	complemented
38	C₄	C₂×D₃₈₈	1	2	yes	—
39	C₂	#15690807	1	1	yes	characteristic
40	C₂	C₂×Dic₃₈₈	1	2	yes	—

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