Subgroups — Q₁₆×D₃₉₇ #27163112

Order 12704.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₃₉₇	C₂	1	2	yes	maximal
2	Dic₁₅₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20263721	C₂	1	2	yes	maximal, complemented
4	C₈×D₃₉₇	C₂	1	1	yes	maximal, characteristic
5	Q₁₆×C₃₉₇	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₇₉₄	—	2	2	no	—
7	Dic₇₉₄	C₂²	1	2	yes	—
8	C₄×D₃₉₇	—	2	2	no	—
9	C₄×D₃₉₇	C₂²	1	1	yes	characteristic
10	#15691787	C₂²	1	1	yes	characteristic
11	Q₈×C₃₉₇	C₂²	1	2	yes	—
12	C₈×C₃₉₇	C₂²	1	1	yes	characteristic
13	C₂×D₃₉₇	D₄	1	1	yes	characteristic
14	C₄×C₃₉₇	—	2	2	no	—
15	C₄×C₃₉₇	C₂³	1	1	yes	characteristic
16	Dic₃₉₇	—	2	2	no	—
17	Dic₃₉₇	D₄	1	1	yes	characteristic
18	C₂×C₃₉₇	C₂×D₄	1	1	yes	characteristic
19	D₃₉₇	Q₁₆	1	2	yes	direct product factor
20	C₃₉₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₁₆	—	397	1	no	maximal, Sylow
22	C₂×Q₈	—	397	2	no	—
23	Q₁₆	—	397	2	no	—
24	Q₁₆	—	397	1	no	—
25	Q₁₆	D₃₉₇	1	1	yes	characteristic, direct product factor
26	C₂×C₈	—	397	1	no	—
27	Q₈	—	794	2	no	—
28	Q₈	—	397	2	no	—
29	Q₈	C₂×D₃₉₇	1	2	yes	—
30	C₂×C₄	—	794	2	no	—
31	C₂×C₄	—	397	1	no	—
32	C₈	—	397	1	no	—
33	C₈	C₂×D₃₉₇	1	1	yes	characteristic
34	C₂²	—	397	1	no	—
35	C₄	—	2	2	no	—
36	C₄	—	794	2	no	—
37	C₄	—	397	1	no	—
38	C₄	C₂²×D₃₉₇	1	1	yes	characteristic
39	C₂	—	397	2	no	—
40	C₂	D₄×D₃₉₇	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.