Subgroups — #6440

Order 224.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₇	C₂	1	1	yes	maximal, characteristic
2	C₇×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊Dic₇	C₂	1	1	yes	maximal, characteristic
4	Dic₇⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₄×Dic₇	C₂	1	2	yes	maximal, complemented
6	C₂³×C₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₇	C₂²	1	2	yes	—
8	C₂×Dic₇	C₄	1	4	yes	complemented
9	C₂×Dic₇	C₂²	1	2	yes	—
10	C₂×Dic₇	C₂²	1	1	yes	characteristic
11	C₂×Dic₇	C₂²	1	1	yes	characteristic
12	#117	—	7	1	no	maximal, Sylow
13	C₂²×C₇	—	2	2	no	—
14	C₂²×C₇	C₂×C₄	1	2	yes	—
15	C₂²×C₇	C₂³	1	1	yes	characteristic
16	C₄×C₇	—	2	2	no	—
17	Dic₇	—	2	2	no	—
18	Dic₇	C₂×C₄	1	2	yes	—
19	Dic₇	C₂×C₄	1	2	yes	—
20	C₂²×C₄	—	7	1	no	—
21	C₄⋊C₄	—	7	2	no	—
22	C₂²⋊C₄	—	7	1	no	—
23	C₂²⋊C₄	D₇	1	1	yes	characteristic
24	C₄²	—	7	2	no	—
25	C₂×C₇	—	2	2	no	—
26	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×C₇	#41	1	2	yes	—
28	C₂³	C₂×D₇	1	1	yes	characteristic
29	C₂×C₄	—	7	4	no	—
30	C₂×C₄	—	7	1	no	—
31	C₂×C₄	—	7	1	no	—
32	C₂×C₄	—	7	2	no	—
33	C₂×C₄	C₂×D₇	1	2	yes	—
34	C₇	#117	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	2	2	no	—
36	C₂²	C₄×D₇	1	2	yes	—
37	C₂²	C₂²×D₇	1	1	yes	characteristic
38	C₄	—	2	2	no	—
39	C₄	—	7	2	no	—
40	C₄	—	7	2	no	—
41	C₄	—	14	2	no	—
42	C₂	—	2	2	no	—
43	C₂	C₂×C₄×D₇	1	1	yes	characteristic
44	C₂	#1159	1	2	yes	—

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.