Subgroups — C₇×#329 #89371

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	C₇×#97	C₂	1	2	yes	maximal, complemented
3	C₂×C₇×Q₈	C₄	1	1	yes	characteristic
4	C₂×C₇×D₄	C₄	1	1	yes	characteristic
5	C₂×C₇×C₈	—	2	2	no	—
6	C₇×C₂²⋊C₄	—	2	2	no	—
7	C₄²×C₇	C₂²	1	1	yes	characteristic
8	#329	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₂³×C₇	—	2	1	no	—
10	C₇×Q₈	—	4	1	no	—
11	C₇×D₄	—	4	1	no	—
12	C₂×C₄×C₇	—	2	1	no	—
13	C₂×C₄×C₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₇	D₄	1	2	yes	—
15	C₇×C₈	—	2	4	no	—
16	#124	C₂×C₇	1	1	yes	characteristic
17	#97	C₂×C₇	1	2	yes	complemented
18	C₂²×C₇	—	4	1	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	—	2	2	no	—
23	C₄×C₇	—	4	1	no	—
24	C₂×Q₈	C₄×C₇	1	1	yes	characteristic
25	C₂×D₄	C₄×C₇	1	1	yes	characteristic
26	C₂×C₈	—	2	2	no	—
27	C₂²⋊C₄	—	2	2	no	—
28	C₄²	C₂²×C₇	1	1	yes	characteristic
29	C₂×C₇	—	8	1	no	—
30	C₂×C₇	#100	1	1	yes	characteristic
31	C₂×C₇	#104	1	2	yes	—
32	C₂³	—	2	1	no	—
33	Q₈	—	4	1	no	—
34	D₄	—	4	1	no	—
35	C₂×C₄	—	2	1	no	—
36	C₂×C₄	C₂×C₄×C₇	1	1	yes	characteristic
37	C₂×C₄	C₇×D₄	1	2	yes	—
38	C₈	—	2	4	no	—
39	C₇	#329	1	1	yes	characteristic, direct product factor, Sylow
40	C₂²	—	4	1	no	—
41	C₂²	—	4	2	no	—
42	C₂²	C₇×C₂²⋊C₄	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	2	2	no	—
45	C₄	—	4	1	no	—
46	C₂	—	8	1	no	—
47	C₂	C₇×#100	1	1	yes	characteristic
48	C₂	C₇×#104	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.