Subgroups — #27163159

Order 12704.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₉₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#13097544	C₂	1	1	yes	maximal, characteristic
3	Q₈×D₃₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#13097544	—	2	1	no	—
5	#15691794	—	2	1	no	—
6	Dic₇₉₄	—	2	1	no	—
7	Dic₇₉₄	C₄	1	1	yes	characteristic, complemented
8	C₄×D₃₉₇	—	2	1	no	—
9	C₄×D₃₉₇	C₂²	1	1	yes	characteristic
10	Q₈×C₃₉₇	C₄	1	1	yes	characteristic, complemented
11	C₂×D₃₉₇	D₄	1	1	yes	characteristic
12	#13097544	—	4	1	no	—
13	C₄×C₃₉₇	—	2	1	no	—
14	C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
15	Dic₃₉₇	—	2	1	no	—
16	Dic₃₉₇	D₄	1	1	yes	characteristic
17	C₂×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
18	D₃₉₇	SD₁₆	1	1	yes	characteristic
19	D₃₉₇	Q₁₆	1	1	yes	characteristic
20	C₃₉₇	#103	1	1	yes	characteristic, complemented, Sylow
21	#103	—	397	1	no	maximal, Sylow
22	C₂×Q₈	—	397	1	no	—
23	C₂×C₈	—	397	1	no	—
24	C₄⋊C₄	—	397	1	no	—
25	Q₈	—	794	1	no	—
26	Q₈	—	397	1	no	—
27	Q₈	#13097544	1	1	yes	characteristic, complemented
28	C₂×C₄	—	794	1	no	—
29	C₂×C₄	—	794	1	no	—
30	C₂×C₄	—	397	1	no	—
31	C₈	—	794	1	no	—
32	C₂²	—	397	1	no	—
33	C₄	—	2	1	no	—
34	C₄	—	794	1	no	—
35	C₄	—	1588	1	no	—
36	C₄	—	397	1	no	—
37	C₄	C₂×#13097544	1	1	yes	characteristic
38	C₂	—	397	1	no	—
39	C₂	—	397	1	no	—
40	C₂	C₂²⋊#13097544	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.