Subgroups — #4294×C₇⋊Dic₇ #45691515

Order 33516.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇²×#4294	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×C₇⋊Dic₇	C₃	1	1	yes	maximal, characteristic
3	C₇²×#4294	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₇²×C₁₉	C₂×C₃	1	1	yes	characteristic
5	Dic₇×#4294	—	7	8	no	maximal
6	C₁₉×C₇⋊Dic₇	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₇²×C₁₉	C₃×C₄	1	1	yes	characteristic
8	C₂×C₇×#4294	D₇	1	8	yes	—
9	C₂×C₇²×C₁₉	C₂×C₉	1	1	yes	characteristic
10	C₉×C₇⋊Dic₇	—	19	1	no	maximal, Hall
11	C₃×C₁₉×Dic₇	—	7	8	no	—
12	C₇×#4294	Dic₇	1	8	yes	complemented
13	C₇²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇²×C₉	—	19	1	no	—
15	C₂×C₃×C₇×C₁₉	C₃×D₇	1	8	yes	—
16	C₄×#4294	—	49	1	no	Hall
17	C₃×C₇⋊Dic₇	C₁₉⋊C₃	1	1	yes	characteristic
18	C₁₉×Dic₇	—	7	8	no	—
19	C₇²×C₉	—	19	1	no	Hall
20	C₃×C₇×C₁₉	C₃×Dic₇	1	8	yes	—
21	C₂×#4294	C₇⋊D₇	1	1	yes	characteristic
22	C₂×C₃×C₇²	C₂×C₁₉⋊C₃	1	1	yes	characteristic
23	C₂×C₇×C₁₉	C₉×D₇	1	8	yes	—
24	C₉×Dic₇	—	133	8	no	—
25	C₃×C₄×C₁₉	—	49	1	no	—
26	C₇⋊Dic₇	#4294	1	1	yes	characteristic, direct product factor, Hall
27	#4294	C₇⋊Dic₇	1	1	yes	characteristic, direct product factor, Hall
28	C₃×C₇²	C₄×C₁₉⋊C₃	1	1	yes	characteristic
29	C₇×C₁₉	C₉×Dic₇	1	8	yes	complemented
30	C₂×C₇×C₉	—	19	8	no	—
31	C₂×C₃×C₁₉	C₃×C₇⋊D₇	1	1	yes	characteristic
32	C₂×C₇²	C₂×#4294	1	1	yes	characteristic
33	C₃×Dic₇	—	7	8	no	—
34	C₄×C₁₉	—	49	1	no	Hall
35	C₇×C₉	—	19	8	no	—
36	C₃×C₁₉	C₃×C₇⋊Dic₇	1	1	yes	characteristic
37	C₇²	C₄×#4294	1	1	yes	characteristic, complemented, Sylow
38	C₂×C₃×C₇	D₇×C₁₉⋊C₃	1	8	yes	—
39	C₂×C₁₉	C₉×C₇⋊D₇	1	1	yes	characteristic
40	C₄×C₉	—	931	1	no	Hall
41	Dic₇	—	7	8	no	—
42	C₃×C₇	Dic₇×C₁₉⋊C₃	1	8	yes	—
43	C₁₉	C₉×C₇⋊Dic₇	1	1	yes	characteristic, complemented, Sylow
44	C₂×C₉	—	19	1	no	—
45	C₂×C₇	D₇×#4294	1	8	yes	—
46	C₃×C₄	—	49	1	no	—
47	C₉	—	19	1	no	Sylow
48	C₇	Dic₇×#4294	1	8	yes	complemented
49	C₂×C₃	C₁₉⋊C₃×C₇⋊D₇	1	1	yes	characteristic
50	C₄	—	49	1	no	Sylow
51	C₃	C₁₉⋊C₃×C₇⋊Dic₇	1	1	yes	characteristic
52	C₂	C₇⋊D₇×#4294	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂×C₃	C₁₉⋊C₃×C₇⋊D₇
commutator, hypocenter	C₇²×C₁₉	C₄×C₉
Fitting, socle, prime radical, cosocle	C₂×C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²×C₁₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
3. C₇²×#4294	C₄	semidirect
6. C₁₉×C₇⋊Dic₇	C₉	semidirect
12. C₇×#4294	Dic₇	semidirect
13. C₇²×C₁₉	C₄×C₉	semidirect
26. C₇⋊Dic₇	#4294	direct (N × H)
27. #4294	C₇⋊Dic₇	direct (N × H)
29. C₇×C₁₉	C₉×Dic₇	semidirect
37. C₇²	C₄×#4294	semidirect
43. C₁₉	C₉×C₇⋊Dic₇	semidirect
48. C₇	Dic₇×#4294	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₇²×#4294	2
C₃×C₁₉×C₇⋊Dic₇	3
Dic₇×#4294	7
C₉×C₇⋊Dic₇	19

Subgroups — #4294×C7⋊Dic7 #45691515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #4294×C₇⋊Dic₇ #45691515