Subgroups — C₇×#384 #90030

Order 448.

186 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×C₄⋊C₄	C₂	1	6	yes	maximal
2	C₂×C₄²×C₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₇	C₂²	1	4	yes	—
4	C₂²×C₄×C₇	C₂²	1	3	yes	—
5	C₇×C₄⋊C₄	—	2	12	no	—
6	C₄²×C₇	C₄	1	4	yes	complemented
7	#384	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
8	C₂³×C₇	C₂³	1	1	yes	characteristic
9	C₂×C₄×C₇	—	2	12	no	—
10	C₂×C₄×C₇	C₂×C₄	1	6	yes	—
11	C₂×C₄×C₇	D₄	1	6	yes	—
12	C₂×C₄×C₇	Q₈	1	6	yes	—
13	C₂×C₄⋊C₄	C₂×C₇	1	6	yes	—
14	C₂×C₄²	C₂×C₇	1	1	yes	characteristic
15	C₂²×C₇	C₂²×C₄	1	1	yes	characteristic
16	C₂²×C₇	C₂×D₄	1	3	yes	—
17	C₂²×C₇	C₂×Q₈	1	3	yes	—
18	C₄×C₇	—	4	4	no	—
19	C₄×C₇	C₄⋊C₄	1	12	yes	complemented
20	C₂²×C₄	C₂²×C₇	1	4	yes	—
21	C₂²×C₄	C₂²×C₇	1	3	yes	—
22	C₄⋊C₄	—	2	12	no	—
23	C₄²	C₄×C₇	1	4	yes	complemented
24	C₂×C₇	C₂×C₄⋊C₄	1	3	yes	—
25	C₂×C₇	#127	1	1	yes	characteristic
26	C₂×C₇	C₄⋊Q₈	1	3	yes	—
27	C₂³	C₂³×C₇	1	1	yes	characteristic
28	C₂×C₄	—	2	12	no	—
29	C₂×C₄	C₂×C₄×C₇	1	6	yes	—
30	C₂×C₄	C₇×D₄	1	6	yes	—
31	C₂×C₄	C₇×Q₈	1	6	yes	—
32	C₇	#384	1	1	yes	characteristic, direct product factor, Sylow
33	C₂²	C₂²×C₄×C₇	1	1	yes	characteristic
34	C₂²	C₂×C₇×D₄	1	3	yes	—
35	C₂²	C₂×C₇×Q₈	1	3	yes	—
36	C₄	—	4	4	no	—
37	C₄	C₇×C₄⋊C₄	1	12	yes	complemented
38	C₂	C₂×C₇×C₄⋊C₄	1	3	yes	—
39	C₂	C₇×#127	1	1	yes	characteristic
40	C₂	C₇×C₄⋊Q₈	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.