Subgroups — C₃×Dic₇⋊C₁₆ #13051161

Order 1344.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₈×Dic₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	Dic₇⋊C₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₇×C₈	C₂²	1	1	yes	characteristic
6	C₃×C₄×Dic₇	C₄	1	1	yes	characteristic
7	C₂×C₃×C₇⋊C₈	C₄	1	1	yes	characteristic
8	C₃×C₇×C₁₆	—	2	1	no	—
9	C₃×C₇⋊C₁₆	—	2	1	no	—
10	C₂×C₇×C₁₆	C₂×C₃	1	1	yes	characteristic
11	C₈×Dic₇	C₂×C₃	1	1	yes	characteristic
12	C₂×C₇⋊C₁₆	C₂×C₃	1	1	yes	characteristic
13	C₃×C₄⋊C₁₆	—	7	1	no	maximal, Hall
14	C₂×C₃×C₄×C₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₃×Dic₇	C₈	1	1	yes	characteristic
16	C₂×C₃×Dic₇	C₈	1	1	yes	characteristic
17	C₃×C₇×C₈	D₄	1	1	yes	characteristic
18	C₃×C₇×C₈	Q₈	1	1	yes	characteristic
19	C₃×C₇⋊C₈	—	2	1	no	—
20	C₂×C₇×C₈	C₂²×C₃	1	1	yes	characteristic
21	C₄×Dic₇	C₃×C₄	1	1	yes	characteristic
22	C₂×C₇⋊C₈	C₃×C₄	1	1	yes	characteristic
23	C₇×C₁₆	—	2	1	no	—
24	C₇⋊C₁₆	—	2	1	no	—
25	C₂×C₃×C₁₆	—	7	1	no	—
26	C₂×C₃×C₁₆	D₇	1	1	yes	characteristic
27	C₃×C₄×C₈	—	7	1	no	—
28	C₂²×C₃×C₇	C₂×C₈	1	1	yes	characteristic
29	C₃×C₄×C₇	C₄⋊C₄	1	1	yes	characteristic
30	C₃×C₄×C₇	M₁₆	1	1	yes	characteristic
31	C₃×Dic₇	—	2	1	no	—
32	C₃×Dic₇	C₁₆	1	2	yes	complemented
33	C₄⋊C₁₆	—	7	1	no	Sylow
34	C₂×C₄×C₇	C₂×C₃×C₄	1	1	yes	characteristic
35	C₂×Dic₇	C₃×C₈	1	1	yes	characteristic
36	C₂×Dic₇	C₃×C₈	1	1	yes	characteristic
37	C₇×C₈	C₃×D₄	1	1	yes	characteristic
38	C₇×C₈	C₃×Q₈	1	1	yes	characteristic
39	C₇⋊C₈	—	2	1	no	—
40	C₂×C₃×C₈	—	7	1	no	—
41	C₂×C₃×C₈	C₂×D₇	1	1	yes	characteristic
42	C₃×C₄²	—	7	1	no	—
43	C₃×C₁₆	—	2	1	no	—
44	C₃×C₁₆	—	14	1	no	—
45	C₂×C₃×C₇	C₄⋊C₈	1	1	yes	characteristic
46	C₂×C₃×C₇	C₂×C₁₆	1	1	yes	characteristic
47	C₂×C₃×C₇	M₃₂	1	1	yes	characteristic
48	C₂×C₁₆	—	7	1	no	—
49	C₂×C₁₆	C₃×D₇	1	1	yes	characteristic
50	C₄×C₈	—	7	1	no	—
51	C₂²×C₇	C₂×C₃×C₈	1	1	yes	characteristic
52	C₄×C₇	C₃×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₇	C₃×M₁₆	1	1	yes	characteristic
54	Dic₇	—	2	1	no	—
55	Dic₇	C₃×C₁₆	1	2	yes	complemented
56	C₂×C₃×C₄	—	7	1	no	—
57	C₂×C₃×C₄	—	7	1	no	—
58	C₂×C₃×C₄	C₄×D₇	1	1	yes	characteristic
59	C₃×C₈	—	14	1	no	—
60	C₃×C₈	Dic₁₄	1	1	yes	characteristic
61	C₃×C₈	C₂²⋊D₇	1	1	yes	characteristic
62	C₃×C₇	C₄⋊C₁₆	1	1	yes	characteristic, complemented, Hall
63	C₂×C₈	—	7	1	no	—
64	C₂×C₈	C₂×C₃×D₇	1	1	yes	characteristic
65	C₄²	—	7	1	no	—
66	C₁₆	—	2	1	no	—
67	C₁₆	—	14	1	no	—
68	C₂×C₇	C₃×C₄⋊C₈	1	1	yes	characteristic
69	C₂×C₇	C₂×C₃×C₁₆	1	1	yes	characteristic
70	C₂×C₇	C₃×M₃₂	1	1	yes	characteristic
71	C₂²×C₃	C₈×D₇	1	1	yes	characteristic
72	C₃×C₄	—	7	2	no	—
73	C₃×C₄	—	14	1	no	—
74	C₃×C₄	#1131	1	1	yes	characteristic
75	C₃×C₄	Dic₇⋊C₄	1	1	yes	characteristic
76	C₂×C₄	—	7	1	no	—
77	C₂×C₄	—	7	1	no	—
78	C₂×C₄	C₃×C₄×D₇	1	1	yes	characteristic
79	C₈	—	14	1	no	—
80	C₈	C₃×Dic₁₄	1	1	yes	characteristic
81	C₈	C₃×C₂²⋊D₇	1	1	yes	characteristic
82	C₇	C₃×C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
83	C₂×C₃	D₇×C₁₆	1	1	yes	characteristic
84	C₂×C₃	#6372	1	1	yes	characteristic
85	C₂×C₃	Dic₇⋊C₈	1	1	yes	characteristic
86	C₂²	C₃×C₈×D₇	1	1	yes	characteristic
87	C₄	—	7	2	no	—
88	C₄	—	14	1	no	—
89	C₄	C₃×#1131	1	1	yes	characteristic
90	C₄	C₃×Dic₇⋊C₄	1	1	yes	characteristic
91	C₃	Dic₇⋊C₁₆	1	1	yes	characteristic, direct product factor, Sylow
92	C₂	C₃×D₇×C₁₆	1	1	yes	characteristic
93	C₂	C₃×#6372	1	1	yes	characteristic
94	C₂	C₃×Dic₇⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₈	C₂×D₇
commutator	C₂×C₇	C₂×C₃×C₁₆
Frattini	C₂×C₈	C₂×C₃×D₇
Fitting	C₂×C₃×C₇×C₁₆	C₂
socle, prime radical	C₂²×C₃×C₇	C₂×C₈
cosocle	C₂×C₇×C₈	C₂²×C₃
hypercenter	C₂×C₃×C₁₆	D₇
hypocenter	C₇	C₃×C₄⋊C₁₆
LCS	G ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₈ ◁ C₂×C₃×C₁₆

Complements

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

N	H ≅ G/N	type
4. Dic₇⋊C₁₆	C₃	direct (N × H)
32. C₃×Dic₇	C₁₆	semidirect
55. Dic₇	C₃×C₁₆	semidirect
62. C₃×C₇	C₄⋊C₁₆	semidirect
82. C₇	C₃×C₄⋊C₁₆	semidirect
91. C₃	Dic₇⋊C₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₇×C₁₆	2
C₃×C₈×Dic₇	2
C₂×C₃×C₇⋊C₁₆	2
Dic₇⋊C₁₆	3
C₃×C₄⋊C₁₆	7

Subgroups — C3×Dic7⋊C16 #13051161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₇⋊C₁₆ #13051161