Subgroups — #20263246

Order 6304.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₈₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#13096802	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₄×C₁₉₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₁₉₇	—	2	1	no	—
5	D₇₈₈	—	2	1	no	—
6	D₇₈₈	C₄	1	2	yes	complemented
7	#13096802	—	2	1	no	—
8	C₂×C₄×C₁₉₇	—	2	1	no	—
9	C₂×C₄×C₁₉₇	C₂²	1	1	yes	characteristic
10	C₂²×C₁₉₇	D₄	1	1	yes	characteristic
11	C₂×D₁₉₇	—	2	2	no	—
12	C₂×D₁₉₇	—	4	1	no	—
13	C₂×D₁₉₇	—	4	1	no	—
14	C₄×C₁₉₇	—	4	1	no	—
15	C₄×C₁₉₇	C₂×C₄	1	1	yes	characteristic
16	C₄×C₁₉₇	D₄	1	1	yes	characteristic
17	C₂×C₁₉₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₁₉₇	D₈	1	1	yes	characteristic
19	C₂×C₁₉₇	SD₁₆	1	1	yes	characteristic
20	D₁₉₇	—	4	2	no	—
21	C₁₉₇	#102	1	1	yes	characteristic, complemented, Sylow
22	#102	—	197	1	no	maximal, Sylow
23	C₂×D₄	—	197	1	no	—
24	C₂×C₈	—	197	1	no	—
25	C₄⋊C₄	D₁₉₇	1	1	yes	characteristic, complemented
26	C₂³	—	394	1	no	—
27	D₄	—	394	1	no	—
28	D₄	—	197	2	no	—
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	C₂×D₁₉₇	1	1	yes	characteristic
31	C₈	—	394	1	no	—
32	C₂²	—	788	1	no	—
33	C₂²	—	788	1	no	—
34	C₂²	—	394	2	no	—
35	C₂²	C₂²⋊D₁₉₇	1	1	yes	characteristic
36	C₄	—	4	1	no	—
37	C₄	C₄×D₁₉₇	1	1	yes	characteristic
38	C₄	D₇₈₈	1	1	yes	characteristic
39	C₂	—	788	2	no	—
40	C₂	#15691335	1	1	yes	characteristic
41	C₂	#15691343	1	1	yes	characteristic
42	C₂	#15691345	1	1	yes	characteristic

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