Subgroups — D₇×#14524212 #44476607

Order 30324.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊#14524212	C₂	1	1	yes	maximal, characteristic, complemented
2	D₇×#11762246	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#14524212	C₂	1	1	yes	maximal, characteristic, complemented
4	D₇×C₁₉×D₁₉	—	3	1	no	maximal, Hall
5	C₇×#11762246	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₁₃₃	—	3	1	no	—
7	D₇×C₁₉²	D₃	1	1	yes	characteristic, complemented
8	C₇×C₁₉×D₁₉	—	3	1	no	—
9	C₂×#14524212	—	7	1	no	maximal, Hall
10	C₇×C₁₉²	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×#11762246	—	7	1	no	—
12	#14524212	—	7	1	no	—
13	#14524212	D₇	1	1	yes	characteristic, direct product factor
14	C₂×C₁₉×D₁₉	—	21	1	no	Hall
15	#11762246	C₂×D₇	1	1	yes	characteristic, complemented, Hall
16	D₇×C₁₉⋊C₃	—	38	1	no	—
17	C₂×C₁₉²	—	7	1	no	—
18	C₁₉×D₁₉	—	3	1	no	—
19	C₁₉×D₁₉	—	21	1	no	—
20	C₂×D₇×C₁₉	—	57	1	no	—
21	D₇×D₁₉	—	3	1	no	—
22	C₇×C₁₉⋊C₃	—	38	1	no	—
23	C₁₉²	D₃×D₇	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₇×C₁₉	—	57	1	no	—
25	D₁₃₃	—	3	1	no	—
26	C₇×D₁₉	—	3	1	no	—
27	D₇×C₁₉	—	2	1	no	—
28	D₇×C₁₉	—	3	1	no	—
29	D₇×C₁₉	—	6	1	no	—
30	D₇×C₁₉	—	6	2	no	—
31	D₇×C₁₉	—	57	1	no	—
32	C₇×C₁₉	—	2	1	no	—
33	C₇×C₁₉	—	3	1	no	—
34	C₇×C₁₉	—	6	1	no	—
35	C₇×C₁₉	—	6	2	no	—
36	C₂×C₁₉⋊C₃	—	266	1	no	—
37	D₃×D₇	—	361	1	no	maximal, Hall
38	C₂²×C₁₉	—	399	1	no	—
39	C₂×D₁₉	—	21	1	no	—
40	C₁₉⋊C₃	—	38	1	no	—
41	D₂₁	—	361	1	no	—
42	C₃×D₇	—	722	1	no	—
43	D₃×C₇	—	361	1	no	—
44	C₂×C₁₉	—	14	1	no	—
45	C₂×C₁₉	—	21	1	no	—
46	C₂×C₁₉	—	21	1	no	—
47	C₂×C₁₉	—	42	2	no	—
48	C₂×C₁₉	—	57	1	no	—
49	C₂×C₁₉	—	399	1	no	—
50	D₁₉	—	3	1	no	—
51	D₁₉	—	21	1	no	—
52	C₂×D₇	—	57	1	no	Hall
53	C₃×C₇	—	722	1	no	Hall
54	C₁₉	—	2	1	no	—
55	C₁₉	—	3	1	no	—
56	C₁₉	—	3	1	no	—
57	C₁₉	—	6	2	no	—
58	C₂×C₇	—	57	1	no	—
59	D₇	—	57	1	no	—
60	D₇	#14524212	1	1	yes	characteristic, direct product factor
61	C₂×D₃	—	2527	1	no	Hall
62	C₇	C₂×#14524212	1	1	yes	characteristic, complemented, Sylow
63	C₂×C₃	—	5054	1	no	—
64	D₃	—	361	1	no	—
65	D₃	—	2527	1	no	—
66	C₂²	—	399	1	no	Sylow
67	C₃	—	722	1	no	Sylow
68	C₂	—	7	1	no	—
69	C₂	—	57	1	no	—
70	C₂	—	399	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₇×#11762246	C₂²
Fitting, socle	C₇×C₁₉²	C₂×D₃
LCS	G ▷ C₇×#11762246
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇⋊#14524212	C₂	semidirect
2. D₇×#11762246	C₂	semidirect
3. C₇×#14524212	C₂	semidirect
5. C₇×#11762246	C₂²	semidirect
7. D₇×C₁₉²	D₃	semidirect
10. C₇×C₁₉²	C₂×D₃	semidirect
13. #14524212	D₇	direct (N × H)
15. #11762246	C₂×D₇	semidirect
23. C₁₉²	D₃×D₇	semidirect
60. D₇	#14524212	direct (N × H)
62. C₇	C₂×#14524212	semidirect

Maximal subgroups

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

subgroup	index
C₇⋊#14524212	2
D₇×#11762246	2
C₇×#14524212	2
D₇×C₁₉×D₁₉	3
C₂×#14524212	7
D₃×D₇	361

Subgroups — D7×#14524212 #44476607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#14524212 #44476607