Subgroups — #89336

Order 448.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#124	C₂	1	1	yes	maximal, characteristic
2	#6408	C₂	1	2	yes	maximal
3	C₂×C₇×Q₈	C₄	1	1	yes	characteristic, complemented
4	C₂×C₇×D₄	C₂²	1	1	yes	characteristic
5	C₇×C₂²⋊C₄	—	2	2	no	—
6	C₄²×C₇	C₄	1	1	yes	characteristic, complemented
7	C₂²⋊Dic₇	—	2	2	no	—
8	#354	—	7	1	no	maximal, Sylow
9	C₂³×C₇	D₄	1	2	yes	—
10	C₇×Q₈	—	4	1	no	—
11	C₇×D₄	—	4	1	no	—
12	C₂×C₄×C₇	—	2	1	no	—
13	C₂×C₄×C₇	—	2	1	no	—
14	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
15	C₂×Dic₇	—	4	2	no	—
16	#124	D₇	1	1	yes	characteristic
17	#99	—	7	2	no	—
18	C₂²×C₇	—	2	2	no	—
19	C₂²×C₇	—	4	2	no	—
20	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₇	—	2	1	no	—
22	C₄×C₇	—	4	1	no	—
23	C₄×C₇	—	4	1	no	—
24	Dic₇	—	8	2	no	—
25	C₂×Q₈	Dic₇	1	1	yes	characteristic, complemented
26	C₂×D₄	C₂×D₇	1	1	yes	characteristic
27	C₂²⋊C₄	—	2	2	no	—
28	C₂²⋊C₄	—	14	2	no	—
29	C₄²	Dic₇	1	1	yes	characteristic, complemented
30	C₂×C₇	—	2	1	no	—
31	C₂×C₇	—	4	2	no	—
32	C₂×C₇	#99	1	1	yes	characteristic
33	C₂³	C₂²⋊D₇	1	2	yes	—
34	Q₈	—	4	1	no	—
35	D₄	—	4	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	—	28	2	no	—
39	C₂×C₄	C₂×Dic₇	1	1	yes	characteristic
40	C₇	#354	1	1	yes	characteristic, complemented, Sylow
41	C₂²	—	2	2	no	—
42	C₂²	—	4	2	no	—
43	C₂²	C₂²⋊Dic₇	1	1	yes	characteristic
44	C₄	—	2	1	no	—
45	C₄	—	4	1	no	—
46	C₄	—	4	1	no	—
47	C₄	—	56	2	no	—
48	C₂	—	2	1	no	—
49	C₂	—	4	2	no	—
50	C₂	#6408	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.