Subgroups — #15690872

Order 3104.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊#87604	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×D₉₇	—	2	1	no	—
5	C₂×#87604	—	2	1	no	—
6	D₄×C₉₇	C₄	1	1	yes	characteristic, complemented
7	C₂²⋊D₉₇	—	2	1	no	—
8	D₃₈₈	C₄	1	1	yes	characteristic, complemented
9	C₄×D₉₇	C₂²	1	1	yes	characteristic
10	#11715897	—	2	1	no	—
11	C₂²×C₉₇	—	2	1	no	—
12	C₂×D₉₇	—	2	1	no	—
13	C₂×D₉₇	—	4	1	no	—
14	C₂×D₉₇	—	4	1	no	—
15	C₂×D₉₇	D₄	1	1	yes	characteristic
16	#87604	—	4	1	no	—
17	C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
18	Dic₉₇	D₄	1	1	yes	characteristic
19	C₂×C₉₇	—	4	1	no	—
20	C₂×C₉₇	C₂²⋊C₄	1	1	yes	characteristic
21	D₉₇	—	4	1	no	—
22	D₉₇	D₈	1	1	yes	characteristic
23	D₉₇	SD₁₆	1	1	yes	characteristic
24	C₉₇	#102	1	1	yes	characteristic, complemented, Sylow
25	#102	—	97	1	no	maximal, Sylow
26	C₂×D₄	—	97	1	no	—
27	C₂×C₈	—	97	1	no	—
28	C₄⋊C₄	—	97	1	no	—
29	C₂³	—	194	1	no	—
30	D₄	—	97	1	no	—
31	D₄	—	194	1	no	—
32	D₄	#87604	1	1	yes	characteristic, complemented
33	C₂×C₄	—	97	1	no	—
34	C₂×C₄	—	194	1	no	—
35	C₈	—	194	1	no	—
36	C₂²	—	2	1	no	—
37	C₂²	—	97	1	no	—
38	C₂²	—	388	1	no	—
39	C₂²	—	388	1	no	—
40	C₂²	—	194	1	no	—
41	C₄	—	97	1	no	—
42	C₄	—	388	1	no	—
43	C₄	C₂×#87604	1	1	yes	characteristic
44	C₂	—	4	1	no	—
45	C₂	—	97	1	no	—
46	C₂	—	97	1	no	—
47	C₂	—	388	1	no	—
48	C₂	C₂²⋊#87604	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.