Subgroups — #17986367

Order 4544.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14556120	C₂	1	1	yes	maximal, characteristic
2	#14556052	C₂	1	4	yes	maximal
3	#14556039	C₂	1	1	yes	maximal, characteristic
4	C₄⋊Q₈×C₇₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₇₁⋊C₈	C₂²	1	2	yes	—
6	C₄⋊Dic₇₁	C₂²	1	2	yes	—
7	Dic₇₁⋊C₄	—	2	2	no	—
8	C₂×Q₈×C₇₁	C₂²	1	2	yes	—
9	C₄⋊C₄×C₇₁	—	2	2	no	—
10	C₄²×C₇₁	C₂²	1	1	yes	characteristic
11	Q₈×C₇₁	—	2	4	no	—
12	C₂×C₄×C₇₁	—	2	2	no	—
13	C₂×C₄×C₇₁	D₄	1	2	yes	—
14	C₂×C₄×C₇₁	C₂³	1	1	yes	characteristic
15	C₂×Dic₇₁	—	2	2	no	—
16	C₇₁⋊C₈	—	2	2	no	—
17	C₂²×C₇₁	C₂×D₄	1	1	yes	characteristic
18	C₄×C₇₁	—	2	2	no	—
19	C₄×C₇₁	—	4	2	no	—
20	C₄×C₇₁	#41	1	2	yes	—
21	Dic₇₁	—	4	2	no	—
22	C₂×C₇₁	#124	1	1	yes	characteristic
23	C₂×C₇₁	#137	1	2	yes	—
24	C₇₁	#491	1	1	yes	characteristic, complemented, Sylow
25	#491	—	71	1	no	maximal, Sylow
26	C₄⋊Q₈	D₇₁	1	1	yes	characteristic
27	#125	—	71	1	no	—
28	#103	—	71	4	no	—
29	#97	—	71	1	no	—
30	C₂×Q₈	C₂×D₇₁	1	2	yes	—
31	C₂×C₈	—	71	2	no	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	71	2	no	—
34	C₄⋊C₄	—	142	2	no	—
35	C₄²	C₂×D₇₁	1	1	yes	characteristic
36	Q₈	—	2	4	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	142	2	no	—
39	C₂×C₄	C₂²⋊D₇₁	1	2	yes	—
40	C₂×C₄	C₂²×D₇₁	1	1	yes	characteristic
41	C₈	—	142	2	no	—
42	C₂²	C₂×C₂²⋊D₇₁	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	284	2	no	—
46	C₄	#11765864	1	2	yes	—
47	C₂	#14556115	1	1	yes	characteristic
48	C₂	#14556159	1	2	yes	—

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

N	H ≅ G/N	type
24. C₇₁	#491	semidirect

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