Subgroups — #36383990

Order 22688.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26015403	C₂	1	1	yes	maximal, characteristic, complemented
2	#26015402	C₂	1	2	yes	maximal, complemented
3	D₇₀₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19150893	C₂	1	2	yes	maximal, complemented
5	#26015392	C₂	1	1	yes	maximal, characteristic
6	#19150893	C₂²	1	1	yes	characteristic
7	#19150893	C₂²	1	2	yes	—
8	#19150893	C₂²	1	1	yes	characteristic
9	Dic₁₄₁₈	C₄	1	1	yes	characteristic
10	C₂²⋊D₇₀₉	C₄	1	2	yes	—
11	C₂×Dic₇₀₉	C₂²	1	2	yes	—
12	C₄×D₇₀₉	C₂²	1	1	yes	characteristic
13	D₄×C₇₀₉	C₄	1	1	yes	characteristic
14	C₂²×C₇₀₉	C₂×C₄	1	2	yes	—
15	C₂×D₇₀₉	C₂×C₄	1	1	yes	characteristic
16	C₄×C₇₀₉	C₂×C₄	1	1	yes	characteristic
17	Dic₇₀₉	C₂×C₄	1	2	yes	—
18	Dic₇₀₉	C₂³	1	1	yes	characteristic
19	C₂×C₇₀₉	—	2	2	no	—
20	C₂×C₇₀₉	C₂²×C₄	1	1	yes	characteristic
21	D₇₀₉	—	2	1	no	—
22	C₇₀₉	#131	1	1	yes	characteristic, complemented, Sylow
23	#131	—	709	1	no	maximal, Sylow
24	#41	—	709	1	no	—
25	M₁₆	—	709	2	no	—
26	M₁₆	—	709	1	no	—
27	C₂×C₈	—	709	2	no	—
28	C₂×C₈	—	709	1	no	—
29	Q₈	—	709	1	no	—
30	D₄	—	709	2	no	—
31	D₄	#15667778	1	1	yes	characteristic
32	C₂×C₄	—	709	2	no	—
33	C₂×C₄	—	709	1	no	—
34	C₈	—	709	1	no	—
35	C₈	—	709	2	no	—
36	C₈	—	709	1	no	—
37	C₂²	—	709	1	no	—
38	C₂²	C₂×#15667778	1	2	yes	—
39	C₄	—	709	1	no	—
40	C₄	—	709	2	no	—
41	C₄	C₂×#15667778	1	1	yes	characteristic
42	C₂	—	2	2	no	—
43	C₂	—	1418	1	no	—
44	C₂	C₂²×#15667778	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.