Subgroups — #89285

Order 448.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#107	C₂	1	1	yes	maximal, characteristic
2	#6392	C₂	1	1	yes	maximal, characteristic
3	C₂×C₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×C₇×C₈	C₂²	1	1	yes	characteristic
5	C₇×C₄⋊C₄	—	2	1	no	—
6	C₄⋊Dic₇	—	2	1	no	—
7	C₇⋊C₁₆	C₄	1	2	yes	complemented
8	#367	—	7	1	no	maximal, Sylow
9	C₂×C₄×C₇	—	4	1	no	—
10	C₂×C₄×C₇	D₄	1	1	yes	characteristic
11	C₂×Dic₇	—	4	1	no	—
12	C₇×C₈	C₂×C₄	1	1	yes	characteristic
13	C₇×C₈	Q₈	1	1	yes	characteristic
14	C₂×C₁₆	—	7	1	no	—
15	#107	—	7	1	no	—
16	#107	D₇	1	1	yes	characteristic
17	C₂²×C₇	D₈	1	1	yes	characteristic
18	C₄×C₇	—	8	1	no	—
19	C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
20	C₄×C₇	Q₁₆	1	1	yes	characteristic
21	Dic₇	—	8	1	no	—
22	C₂×C₈	C₂×D₇	1	1	yes	characteristic
23	C₄⋊C₄	—	2	1	no	—
24	C₄⋊C₄	—	14	1	no	—
25	C₁₆	—	7	2	no	—
26	C₂×C₇	#107	1	1	yes	characteristic
27	C₂×C₇	SD₃₂	1	1	yes	characteristic
28	C₂×C₇	SD₃₂	1	1	yes	characteristic
29	C₂×C₄	—	4	1	no	—
30	C₂×C₄	—	28	1	no	—
31	C₂×C₄	C₂²⋊D₇	1	1	yes	characteristic
32	C₈	Dic₁₄	1	1	yes	characteristic
33	C₈	C₄×D₇	1	1	yes	characteristic
34	C₇	#367	1	1	yes	characteristic, complemented, Sylow
35	C₂²	#1141	1	1	yes	characteristic
36	C₄	—	8	1	no	—
37	C₄	—	56	1	no	—
38	C₄	Dic₇⋊C₄	1	1	yes	characteristic
39	C₄	#1144	1	1	yes	characteristic
40	C₂	#6381	1	1	yes	characteristic
41	C₂	#6401	1	1	yes	characteristic
42	C₂	#6402	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. C₇⋊C₁₆	C₄	semidirect
34. C₇	#367	semidirect

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