Subgroups — C₇×#356 #89398

Order 448.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₇×#101	C₂	1	2	yes	maximal
3	C₂×C₇×Q₈	C₄	1	1	yes	characteristic
4	C₂×C₇×Q₈	C₂²	1	1	yes	characteristic
5	C₇×M₁₆	—	2	2	no	—
6	C₇×C₄⋊C₄	—	2	2	no	—
7	C₄²×C₇	C₄	1	1	yes	characteristic
8	#356	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₇×Q₈	—	4	1	no	—
10	C₇×Q₈	—	4	1	no	—
11	C₂×C₄×C₇	—	2	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	—	4	2	no	—
16	C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic
17	#101	C₂×C₇	1	2	yes	—
18	C₂²×C₇	C₂²⋊C₄	1	1	yes	characteristic
19	C₄×C₇	—	2	2	no	—
20	C₄×C₇	—	2	2	no	—
21	C₄×C₇	—	2	1	no	—
22	C₄×C₇	—	4	1	no	—
23	C₂×Q₈	C₄×C₇	1	1	yes	characteristic
24	C₂×Q₈	C₂²×C₇	1	1	yes	characteristic
25	M₁₆	—	2	2	no	—
26	C₄⋊C₄	—	2	2	no	—
27	C₄²	C₄×C₇	1	1	yes	characteristic
28	C₂×C₇	—	2	1	no	—
29	C₂×C₇	#99	1	1	yes	characteristic
30	Q₈	—	4	1	no	—
31	Q₈	—	4	1	no	—
32	C₂×C₄	—	2	1	no	—
33	C₂×C₄	—	2	1	no	—
34	C₂×C₄	C₂×C₄×C₇	1	1	yes	characteristic
35	C₂×C₄	C₇×D₄	1	2	yes	—
36	C₈	—	4	2	no	—
37	C₇	#356	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²	C₇×C₂²⋊C₄	1	1	yes	characteristic
39	C₄	—	2	2	no	—
40	C₄	—	2	2	no	—
41	C₄	—	2	1	no	—
42	C₄	—	4	1	no	—
43	C₂	—	2	1	no	—
44	C₂	C₇×#99	1	1	yes	characteristic

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

N	H ≅ G/N	type
8. #356	C₇	direct (N × H)
37. C₇	#356	direct (N × H)

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