Subgroups — D₄₉×D₁₁₇ #37524113

Order 22932.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₇₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₉×D₁₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×C₁₃×D₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃₉×D₄₉	—	3	1	no	maximal
5	C₉×C₁₃×C₄₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₉₁₁	—	3	1	no	—
7	C₄₉×D₃₉	—	3	1	no	—
8	C₃×C₁₃×D₄₉	D₃	1	1	yes	characteristic
9	D₇×D₁₁₇	—	7	1	no	maximal
10	D₁₃×D₄₉	—	9	1	no	Hall
11	C₃×C₁₃×C₄₉	C₂×D₃	1	1	yes	characteristic
12	D₉×D₄₉	—	13	1	no	maximal, Hall
13	D₈₁₉	—	7	1	no	—
14	C₇×D₁₁₇	D₇	1	1	yes	characteristic
15	C₉×C₁₃×D₇	—	7	1	no	—
16	D₆₃₇	—	9	1	no	—
17	D₁₃×C₄₉	—	9	1	no	—
18	C₁₃×D₄₉	D₉	1	1	yes	characteristic, complemented
19	D₇×D₃₉	—	21	1	no	—
20	D₄₄₁	—	13	1	no	—
21	C₉×D₄₉	D₁₃	1	1	yes	characteristic, complemented
22	D₉×C₄₉	—	13	1	no	—
23	C₇×C₉×C₁₃	C₂×D₇	1	1	yes	characteristic
24	C₁₃×C₄₉	C₂×D₉	1	1	yes	characteristic, complemented, Hall
25	D₃×D₄₉	—	39	1	no	—
26	D₂₇₃	—	21	1	no	—
27	C₇×D₃₉	—	3	1	no	—
28	C₃×C₁₃×D₇	—	7	1	no	—
29	C₂×D₁₁₇	—	49	1	no	Hall
30	C₉×C₄₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	D₇×D₁₃	—	63	1	no	—
32	D₁₄₇	—	39	1	no	—
33	C₃×D₄₉	D₃₉	1	1	yes	characteristic
34	D₃×C₄₉	—	39	1	no	—
35	C₃×C₇×C₁₃	D₃×D₇	1	1	yes	characteristic
36	D₇×D₉	—	91	1	no	—
37	C₂×C₉×C₁₃	—	49	1	no	—
38	D₁₁₇	—	49	1	no	—
39	D₁₁₇	D₄₉	1	1	yes	characteristic, direct product factor
40	C₂×D₄₉	—	117	1	no	Hall
41	D₉₁	—	63	1	no	—
42	C₇×D₁₃	—	9	1	no	—
43	C₁₃×D₇	—	7	1	no	—
44	C₂×D₃₉	—	147	1	no	—
45	C₃×C₄₉	C₂×D₃₉	1	1	yes	characteristic
46	D₆₃	—	91	1	no	—
47	C₉×D₇	—	7	1	no	—
48	C₇×D₉	—	13	1	no	—
49	C₉×C₁₃	C₂×D₄₉	1	1	yes	characteristic, complemented, Hall
50	C₂×C₄₉	—	117	1	no	—
51	D₄₉	—	117	1	no	—
52	D₄₉	D₁₁₇	1	1	yes	characteristic, direct product factor
53	C₇×C₁₃	D₇×D₉	1	1	yes	characteristic
54	D₃×D₇	—	273	1	no	—
55	C₂×C₃×C₁₃	—	49	1	no	—
56	D₃₉	—	3	1	no	—
57	D₃₉	—	147	1	no	—
58	C₇×C₉	D₇×D₁₃	1	1	yes	characteristic
59	C₂×D₁₃	—	441	1	no	Hall
60	C₄₉	C₂×D₁₁₇	1	1	yes	characteristic, complemented, Sylow
61	D₂₁	—	273	1	no	—
62	C₃×D₇	—	7	1	no	—
63	D₃×C₇	—	39	1	no	—
64	C₃×C₁₃	D₃×D₄₉	1	1	yes	characteristic
65	C₂×D₉	—	637	1	no	Hall
66	C₂×D₇	—	819	1	no	—
67	C₂×C₁₃	—	49	1	no	—
68	D₁₃	—	9	1	no	—
69	D₁₃	—	441	1	no	—
70	C₃×C₇	D₇×D₃₉	1	1	yes	characteristic
71	C₂×C₉	—	49	1	no	—
72	D₉	—	13	1	no	—
73	D₉	—	637	1	no	—
74	C₂×C₇	—	117	1	no	—
75	D₇	—	7	1	no	—
76	D₇	—	819	1	no	—
77	C₁₃	D₉×D₄₉	1	1	yes	characteristic, complemented, Sylow
78	C₂×D₃	—	1911	1	no	—
79	C₉	D₁₃×D₄₉	1	1	yes	characteristic, complemented, Sylow
80	C₇	D₇×D₁₁₇	1	1	yes	characteristic
81	C₂×C₃	—	49	1	no	—
82	D₃	—	39	1	no	—
83	D₃	—	1911	1	no	—
84	C₂²	—	5733	1	no	Sylow
85	C₃	D₃₉×D₄₉	1	1	yes	characteristic
86	C₂	—	49	1	no	—
87	C₂	—	5733	1	no	—
88	C₂	—	117	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₃×C₄₉	C₂²
Frattini	C₃×C₇	D₇×D₃₉
socle	C₃×C₇×C₁₃	D₃×D₇
LCS	G ▷ C₉×C₁₃×C₄₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₅₇₃₃	C₂	semidirect
2. C₄₉×D₁₁₇	C₂	semidirect
3. C₉×C₁₃×D₄₉	C₂	semidirect
5. C₉×C₁₃×C₄₉	C₂²	semidirect
18. C₁₃×D₄₉	D₉	semidirect
21. C₉×D₄₉	D₁₃	semidirect
24. C₁₃×C₄₉	C₂×D₉	semidirect
30. C₉×C₄₉	C₂×D₁₃	semidirect
39. D₁₁₇	D₄₉	direct (N × H)
49. C₉×C₁₃	C₂×D₄₉	semidirect
52. D₄₉	D₁₁₇	direct (N × H)
60. C₄₉	C₂×D₁₁₇	semidirect
77. C₁₃	D₉×D₄₉	semidirect
79. C₉	D₁₃×D₄₉	semidirect

Maximal subgroups

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

subgroup	index
D₅₇₃₃	2
C₄₉×D₁₁₇	2
C₉×C₁₃×D₄₉	2
D₃₉×D₄₉	3
D₇×D₁₁₇	7
D₉×D₄₉	13

Subgroups — D49×D117 #37524113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₉×D₁₁₇ #37524113