Subgroups — C₂×C₇×C₄⋊C₃₂ #13190842

Order 1792.

230 conjugacy classes of subgroups.

The subgroup lattice has 130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₃₂	C₂	1	2	yes	maximal
2	C₂×C₄×C₇×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₇×C₄⋊C₃₂	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₇×C₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₇×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₇×C₈	C₄	1	1	yes	characteristic
7	C₂×C₇×C₃₂	—	2	4	no	—
8	C₂×C₇×C₃₂	C₂²	1	4	yes	—
9	C₄×C₇×C₁₆	C₄	1	2	yes	—
10	C₄×C₇×C₁₆	C₂²	1	2	yes	—
11	C₂×C₄⋊C₃₂	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂²×C₇×C₈	C₈	1	1	yes	characteristic
13	C₂²×C₇×C₈	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄²×C₇	C₈	1	1	yes	characteristic
15	C₂×C₇×C₁₆	—	2	2	no	—
16	C₂×C₇×C₁₆	C₂×C₄	1	2	yes	—
17	C₂×C₇×C₁₆	C₂×C₄	1	1	yes	characteristic
18	C₂×C₇×C₁₆	D₄	1	2	yes	—
19	C₂×C₇×C₁₆	Q₈	1	2	yes	—
20	C₂×C₇×C₁₆	C₂³	1	1	yes	characteristic
21	C₄×C₇×C₈	C₈	1	2	yes	—
22	C₄×C₇×C₈	C₂×C₄	1	2	yes	—
23	C₇×C₃₂	—	2	4	no	—
24	C₂²×C₃₂	C₂×C₇	1	2	yes	—
25	C₂×C₄×C₁₆	C₂×C₇	1	1	yes	characteristic
26	C₄⋊C₃₂	C₂×C₇	1	4	yes	direct product factor
27	C₂²×C₄×C₇	C₁₆	1	1	yes	characteristic
28	C₂²×C₄×C₇	C₁₆	1	1	yes	characteristic
29	C₂²×C₄×C₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₇×C₈	—	2	2	no	—
31	C₂×C₇×C₈	C₄⋊C₄	1	2	yes	—
32	C₂×C₇×C₈	C₂×C₈	1	2	yes	—
33	C₂×C₇×C₈	C₂×C₈	1	1	yes	characteristic
34	C₂×C₇×C₈	M₁₆	1	2	yes	—
35	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
36	C₄²×C₇	C₁₆	1	2	yes	—
37	C₄²×C₇	C₂×C₈	1	2	yes	—
38	C₇×C₁₆	—	2	2	no	—
39	C₇×C₁₆	C₄⋊C₄	1	2	yes	—
40	C₇×C₁₆	C₂×D₄	1	1	yes	characteristic
41	C₇×C₁₆	C₂×Q₈	1	1	yes	characteristic
42	C₂²×C₁₆	C₄×C₇	1	1	yes	characteristic
43	C₂²×C₁₆	C₂²×C₇	1	1	yes	characteristic
44	C₂×C₄×C₈	C₄×C₇	1	1	yes	characteristic
45	C₂×C₃₂	—	2	4	no	—
46	C₂×C₃₂	C₂²×C₇	1	4	yes	—
47	C₄×C₁₆	C₄×C₇	1	2	yes	—
48	C₄×C₁₆	C₂²×C₇	1	2	yes	—
49	C₂³×C₇	C₂×C₁₆	1	1	yes	characteristic
50	C₂×C₄×C₇	—	2	2	no	—
51	C₂×C₄×C₇	C₃₂	1	4	yes	complemented
52	C₂×C₄×C₇	C₄⋊C₈	1	2	yes	—
53	C₂×C₄×C₇	C₂×C₁₆	1	2	yes	—
54	C₂×C₄×C₇	C₂×C₁₆	1	1	yes	characteristic
55	C₂×C₄×C₇	C₂×C₁₆	1	2	yes	—
56	C₂×C₄×C₇	M₃₂	1	2	yes	—
57	C₂×C₄×C₇	C₂²×C₈	1	1	yes	characteristic
58	C₇×C₈	—	2	2	no	—
59	C₇×C₈	C₄⋊C₈	1	2	yes	—
60	C₇×C₈	C₂×C₄⋊C₄	1	1	yes	characteristic
61	C₇×C₈	C₂×M₁₆	1	1	yes	characteristic
62	C₂²×C₈	C₇×C₈	1	1	yes	characteristic
63	C₂²×C₈	C₂×C₄×C₇	1	1	yes	characteristic
64	C₂×C₄²	C₇×C₈	1	1	yes	characteristic
65	C₂×C₁₆	—	2	2	no	—
66	C₂×C₁₆	C₂×C₄×C₇	1	2	yes	—
67	C₂×C₁₆	C₂×C₄×C₇	1	1	yes	characteristic
68	C₂×C₁₆	C₇×D₄	1	2	yes	—
69	C₂×C₁₆	C₇×Q₈	1	2	yes	—
70	C₂×C₁₆	C₂³×C₇	1	1	yes	characteristic
71	C₄×C₈	C₇×C₈	1	2	yes	—
72	C₄×C₈	C₂×C₄×C₇	1	2	yes	—
73	C₃₂	—	2	4	no	—
74	C₂²×C₇	C₄⋊C₁₆	1	2	yes	—
75	C₂²×C₇	C₂×C₃₂	1	2	yes	—
76	C₂²×C₇	M₆₄	1	2	yes	—
77	C₂²×C₇	C₂²×C₁₆	1	1	yes	characteristic
78	C₄×C₇	—	2	2	no	—
79	C₄×C₇	C₄⋊C₁₆	1	2	yes	—
80	C₄×C₇	C₂×C₃₂	1	4	yes	complemented
81	C₄×C₇	C₂×C₄⋊C₈	1	1	yes	characteristic
82	C₄×C₇	C₂×M₃₂	1	1	yes	characteristic
83	C₂²×C₄	C₇×C₁₆	1	1	yes	characteristic
84	C₂²×C₄	C₇×C₁₆	1	1	yes	characteristic
85	C₂²×C₄	C₂×C₇×C₈	1	1	yes	characteristic
86	C₂×C₈	—	2	2	no	—
87	C₂×C₈	C₇×C₄⋊C₄	1	2	yes	—
88	C₂×C₈	C₂×C₇×C₈	1	2	yes	—
89	C₂×C₈	C₂×C₇×C₈	1	1	yes	characteristic
90	C₂×C₈	C₇×M₁₆	1	2	yes	—
91	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
92	C₄²	C₇×C₁₆	1	2	yes	—
93	C₄²	C₂×C₇×C₈	1	2	yes	—
94	C₁₆	—	2	2	no	—
95	C₁₆	C₇×C₄⋊C₄	1	2	yes	—
96	C₁₆	C₂×C₇×D₄	1	1	yes	characteristic
97	C₁₆	C₂×C₇×Q₈	1	1	yes	characteristic
98	C₂×C₇	C₄⋊C₃₂	1	4	yes	direct product factor
99	C₂×C₇	C₂×C₄⋊C₁₆	1	1	yes	characteristic
100	C₂×C₇	C₂²×C₃₂	1	1	yes	characteristic
101	C₂×C₇	C₂×M₆₄	1	1	yes	characteristic
102	C₂³	C₂×C₇×C₁₆	1	1	yes	characteristic
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	C₇×C₃₂	1	4	yes	complemented
105	C₂×C₄	C₇×C₄⋊C₈	1	2	yes	—
106	C₂×C₄	C₂×C₇×C₁₆	1	2	yes	—
107	C₂×C₄	C₂×C₇×C₁₆	1	1	yes	characteristic
108	C₂×C₄	C₂×C₇×C₁₆	1	2	yes	—
109	C₂×C₄	C₇×M₃₂	1	2	yes	—
110	C₂×C₄	C₂²×C₇×C₈	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	C₇×C₄⋊C₈	1	2	yes	—
113	C₈	C₂×C₇×C₄⋊C₄	1	1	yes	characteristic
114	C₈	C₂×C₇×M₁₆	1	1	yes	characteristic
115	C₇	C₂×C₄⋊C₃₂	1	1	yes	characteristic, direct product factor, Sylow
116	C₂²	C₇×C₄⋊C₁₆	1	2	yes	—
117	C₂²	C₂×C₇×C₃₂	1	2	yes	—
118	C₂²	C₇×M₆₄	1	2	yes	—
119	C₂²	C₂²×C₇×C₁₆	1	1	yes	characteristic
120	C₄	—	2	2	no	—
121	C₄	C₇×C₄⋊C₁₆	1	2	yes	—
122	C₄	C₂×C₇×C₃₂	1	4	yes	complemented
123	C₄	C₂×C₇×C₄⋊C₈	1	1	yes	characteristic
124	C₄	C₂×C₇×M₃₂	1	1	yes	characteristic
125	C₂	C₇×C₄⋊C₃₂	1	4	yes	direct product factor
126	C₂	C₂×C₇×C₄⋊C₁₆	1	1	yes	characteristic
127	C₂	C₂²×C₇×C₃₂	1	1	yes	characteristic
128	C₂	C₂×C₇×M₆₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₇×C₁₆	C₂²
commutator	C₂	C₂²×C₇×C₃₂
Frattini, cosocle	C₂×C₁₆	C₂³×C₇
socle, prime radical	C₂³×C₇	C₂×C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇×C₄⋊C₃₂	C₂	direct (N × H)
11. C₂×C₄⋊C₃₂	C₇	direct (N × H)
26. C₄⋊C₃₂	C₂×C₇	direct (N × H)
51. C₂×C₄×C₇	C₃₂	semidirect
80. C₄×C₇	C₂×C₃₂	semidirect
98. C₂×C₇	C₄⋊C₃₂	direct (N × H)
104. C₂×C₄	C₇×C₃₂	semidirect
115. C₇	C₂×C₄⋊C₃₂	direct (N × H)
122. C₄	C₂×C₇×C₃₂	semidirect
125. C₂	C₇×C₄⋊C₃₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₇×C₃₂	2
C₂×C₄×C₇×C₁₆	2
C₇×C₄⋊C₃₂	2
C₂×C₄⋊C₃₂	7

Subgroups — C2×C7×C4⋊C32 #13190842

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇×C₄⋊C₃₂ #13190842