Subgroups — C₇×#498 #90144

Order 448.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₄⋊Q₈	C₂	1	2	yes	maximal
2	C₇×#106	C₂	1	4	yes	maximal
3	C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×Q₈	—	2	2	no	—
5	C₂×C₇×C₈	C₂²	1	2	yes	—
6	C₇×C₄⋊C₄	—	2	2	no	—
7	C₇×C₄⋊C₄	C₂²	1	4	yes	—
8	C₄²×C₇	C₂²	1	1	yes	characteristic
9	#498	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
10	C₇×Q₈	—	4	4	no	—
11	C₂×C₄×C₇	—	2	4	no	—
12	C₂×C₄×C₇	D₄	1	2	yes	—
13	C₂×C₄×C₇	C₂³	1	1	yes	characteristic
14	C₇×C₈	Q₈	1	4	yes	complemented
15	C₄⋊Q₈	C₂×C₇	1	2	yes	—
16	#106	C₂×C₇	1	4	yes	—
17	C₄×C₈	C₂×C₇	1	1	yes	characteristic
18	C₂²×C₇	C₂×D₄	1	1	yes	characteristic
19	C₄×C₇	—	4	4	no	—
20	C₄×C₇	SD₁₆	1	4	yes	—
21	C₄×C₇	C₂×Q₈	1	2	yes	—
22	C₂×Q₈	—	2	2	no	—
23	C₂×C₈	C₂²×C₇	1	2	yes	—
24	C₄⋊C₄	—	2	2	no	—
25	C₄⋊C₄	C₂²×C₇	1	4	yes	—
26	C₄²	C₂²×C₇	1	1	yes	characteristic
27	C₂×C₇	C₄⋊Q₈	1	1	yes	characteristic
28	C₂×C₇	C₂×SD₁₆	1	2	yes	—
29	Q₈	—	4	4	no	—
30	C₂×C₄	—	2	4	no	—
31	C₂×C₄	C₇×D₄	1	2	yes	—
32	C₂×C₄	C₂³×C₇	1	1	yes	characteristic
33	C₈	C₇×Q₈	1	4	yes	complemented
34	C₇	#498	1	1	yes	characteristic, direct product factor, Sylow
35	C₂²	C₂×C₇×D₄	1	1	yes	characteristic
36	C₄	—	4	4	no	—
37	C₄	C₇×SD₁₆	1	4	yes	—
38	C₄	C₂×C₇×Q₈	1	2	yes	—
39	C₂	C₇×C₄⋊Q₈	1	1	yes	characteristic
40	C₂	C₂×C₇×SD₁₆	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄²×C₇ ◁ G

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.