Subgroups — #89709

Order 448.

138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
2	C₇⋊#95	C₂	1	6	yes	maximal
3	C₂²×C₄×C₇	C₂²	1	3	yes	—
4	C₂²×Dic₇	C₂²	1	4	yes	—
5	C₄²×C₇	C₄	1	4	yes	complemented
6	#383	—	7	1	no	maximal, Sylow
7	C₂³×C₇	C₂³	1	1	yes	characteristic
8	C₂×C₄×C₇	—	2	6	no	—
9	C₂×C₄×C₇	C₂×C₄	1	6	yes	—
10	C₂×Dic₇	—	2	12	no	—
11	C₂×C₄²	D₇	1	1	yes	characteristic
12	#95	—	7	6	no	—
13	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
14	C₂²×C₇	#41	1	6	yes	—
15	C₄×C₇	—	2	6	no	—
16	Dic₇	—	4	4	no	—
17	C₂²×C₄	—	7	4	no	—
18	C₂²×C₄	C₂×D₇	1	3	yes	—
19	C₄²	Dic₇	1	4	yes	complemented
20	C₂×C₇	#117	1	3	yes	—
21	C₂×C₇	#126	1	4	yes	—
22	C₂³	C₂²×D₇	1	1	yes	characteristic
23	C₂×C₄	—	2	6	no	—
24	C₂×C₄	—	14	12	no	—
25	C₂×C₄	C₂×Dic₇	1	6	yes	—
26	C₇	#383	1	1	yes	characteristic, complemented, Sylow
27	C₂²	#1157	1	6	yes	—
28	C₂²	C₂²×Dic₇	1	1	yes	characteristic
29	C₄	—	2	6	no	—
30	C₄	—	28	4	no	—
31	C₂	#6439	1	4	yes	—
32	C₂	#6489	1	3	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.