Subgroups — #27163817

Order 12736.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263874	C₂	1	2	yes	maximal
2	C₄⋊Q₈×C₁₉₉	C₂	1	1	yes	maximal, characteristic
3	#15691870	—	2	2	no	—
4	C₂×Q₈×C₁₉₉	C₄	1	1	yes	characteristic
5	C₂×Q₈×C₁₉₉	C₂²	1	1	yes	characteristic
6	C₄⋊C₄×C₁₉₉	—	2	2	no	—
7	C₄²×C₁₉₉	C₄	1	1	yes	characteristic
8	C₁₉₉⋊C₈	—	4	2	no	—
9	Q₈×C₁₉₉	—	4	1	no	—
10	Q₈×C₁₉₉	—	4	1	no	—
11	C₂×C₄×C₁₉₉	—	2	1	no	—
12	C₂×C₄×C₁₉₉	—	2	1	no	—
13	C₂×C₄×C₁₉₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₁₉₉	D₄	1	2	yes	—
15	C₂²×C₁₉₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₁₉₉	—	2	2	no	—
17	C₄×C₁₉₉	—	2	1	no	—
18	C₄×C₁₉₉	—	2	2	no	—
19	C₄×C₁₉₉	—	4	1	no	—
20	C₂×C₁₉₉	—	2	1	no	—
21	C₂×C₁₉₉	#99	1	1	yes	characteristic
22	C₁₉₉	#356	1	1	yes	characteristic, complemented, Sylow
23	#356	—	199	1	no	maximal, Sylow
24	C₄⋊Q₈	D₁₉₉	1	1	yes	characteristic
25	#101	—	199	2	no	—
26	C₂×Q₈	Dic₁₉₉	1	1	yes	characteristic
27	C₂×Q₈	C₂×D₁₉₉	1	1	yes	characteristic
28	M₁₆	—	398	2	no	—
29	C₄⋊C₄	—	2	2	no	—
30	C₄²	Dic₁₉₉	1	1	yes	characteristic
31	Q₈	—	4	1	no	—
32	Q₈	—	4	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	C₂×Dic₁₉₉	1	1	yes	characteristic
36	C₂×C₄	C₂²⋊D₁₉₉	1	2	yes	—
37	C₈	—	796	2	no	—
38	C₂²	C₂²⋊Dic₁₉₉	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	2	2	no	—
41	C₄	—	2	1	no	—
42	C₄	—	4	1	no	—
43	C₂	—	2	1	no	—
44	C₂	#20263870	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₁₉₉	#356	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.