Subgroups — C₄²×Dic₄₇⋊C₄ #26137358

Order 12032.

2478 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₄₇⋊C₄	C₂	1	6	yes	maximal
2	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄₇⋊#95	C₂	1	6	yes	maximal
5	C₂×C₄³×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₄₇⋊C₄	C₂²	1	4	yes	—
7	C₂²×C₄×Dic₄₇	C₂²	1	3	yes	—
8	C₂²×C₄×Dic₄₇	C₂²	1	6	yes	—
9	C₂²×C₄×Dic₄₇	C₂²	1	3	yes	—
10	C₄×Dic₄₇⋊C₄	C₄	1	48	yes	direct product factor
11	C₂×C₄₇⋊#95	C₂²	1	12	yes	—
12	C₄²×Dic₄₇	—	2	4	no	—
13	C₄²×Dic₄₇	C₄	1	8	yes	complemented
14	C₂²×C₄²×C₄₇	C₂²	1	6	yes	—
15	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₄³×C₄₇	—	2	4	no	—
17	C₂³×Dic₄₇	C₂³	1	3	yes	—
18	C₂³×Dic₄₇	C₂³	1	4	yes	—
19	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
20	C₂×Dic₄₇⋊C₄	C₂×C₄	1	48	yes	—
21	C₂×C₄×Dic₄₇	—	2	12	no	—
22	C₂×C₄×Dic₄₇	—	2	12	no	—
23	C₂×C₄×Dic₄₇	—	2	12	no	—
24	C₂×C₄×Dic₄₇	C₂×C₄	1	12	yes	—
25	C₂×C₄×Dic₄₇	C₂×C₄	1	24	yes	—
26	C₂×C₄×Dic₄₇	C₂×C₄	1	12	yes	—
27	C₂×C₄×Dic₄₇	C₂×C₄	1	24	yes	—
28	C₄₇⋊#95	C₂×C₄	1	48	yes	—
29	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
30	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
31	C₂×C₄²×C₄₇	—	2	12	no	—
32	C₂×C₄²×C₄₇	—	2	12	no	—
33	C₂×C₄²×C₄₇	C₂×C₄	1	24	yes	—
34	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
35	C₂×C₄²×C₄₇	D₄	1	4	yes	—
36	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
37	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
38	C₂²×C₄×C₄₇	—	2	4	no	—
39	C₂²×C₄×C₄₇	—	2	12	no	—
40	C₂²×C₄×C₄₇	C₂²×C₄	1	24	yes	—
41	C₂²×C₄×C₄₇	C₂²×C₄	1	6	yes	—
42	C₂²×C₄×C₄₇	C₂²×C₄	1	12	yes	—
43	C₂²×C₄×C₄₇	C₂×D₄	1	6	yes	—
44	C₂²×C₄×C₄₇	C₂×Q₈	1	6	yes	—
45	C₂²×C₄×C₄₇	#41	1	12	yes	—
46	C₂²×Dic₄₇	—	2	4	no	—
47	C₂²×Dic₄₇	—	2	12	no	—
48	C₂²×Dic₄₇	—	2	12	no	—
49	C₂²×Dic₄₇	C₂²×C₄	1	12	yes	—
50	C₂²×Dic₄₇	C₂²×C₄	1	24	yes	—
51	C₂²×Dic₄₇	C₂²×C₄	1	6	yes	—
52	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
53	C₂²×Dic₄₇	C₂²×C₄	1	12	yes	—
54	C₄²×C₄₇	—	2	48	no	—
55	C₄²×C₄₇	C₄⋊C₄	1	16	yes	complemented
56	Dic₄₇⋊C₄	C₄²	1	64	yes	direct product factor
57	C₄×Dic₄₇	—	2	24	no	—
58	C₄×Dic₄₇	—	2	48	no	—
59	C₄×Dic₄₇	C₄²	1	48	yes	complemented
60	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
61	C₂³×C₄₇	C₂³×C₄	1	6	yes	—
62	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
63	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
64	C₂³×C₄₇	C₂×#41	1	6	yes	—
65	C₂×C₄×C₄₇	—	2	24	no	—
66	C₂×C₄×C₄₇	—	2	24	no	—
67	C₂×C₄×C₄₇	C₂×C₄²	1	16	yes	—
68	C₂×C₄×C₄₇	C₂×C₄²	1	12	yes	—
69	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	12	yes	—
70	C₂×C₄×C₄₇	#117	1	12	yes	—
71	C₂×C₄×C₄₇	C₄×D₄	1	24	yes	—
72	C₂×C₄×C₄₇	C₄×Q₈	1	24	yes	—
73	C₂×Dic₄₇	—	2	12	no	—
74	C₂×Dic₄₇	—	2	24	no	—
75	C₂×Dic₄₇	—	2	24	no	—
76	C₂×Dic₄₇	—	2	24	no	—
77	C₂×Dic₄₇	C₂×C₄²	1	12	yes	—
78	C₂×Dic₄₇	C₂×C₄²	1	16	yes	—
79	C₂×Dic₄₇	C₂×C₄²	1	12	yes	—
80	C₂×Dic₄₇	C₂×C₄²	1	16	yes	—
81	C₄²×C₄⋊C₄	—	47	1	no	maximal, Sylow
82	C₂²×C₄₇	C₂²×C₄²	1	3	yes	—
83	C₂²×C₄₇	C₂²×C₄²	1	4	yes	—
84	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄₇	C₂×#117	1	3	yes	—
86	C₂²×C₄₇	C₂×C₄×D₄	1	6	yes	—
87	C₂²×C₄₇	C₂×C₄×Q₈	1	6	yes	—
88	C₂²×C₄₇	C₄×#41	1	12	yes	—
89	C₄×C₄₇	—	2	16	no	—
90	C₄×C₄₇	C₄×C₄⋊C₄	1	24	yes	complemented
91	Dic₄₇	—	2	12	no	—
92	Dic₄₇	—	2	16	no	—
93	Dic₄₇	C₄³	1	8	yes	complemented
94	C₂×C₄×C₄⋊C₄	—	47	6	no	—
95	C₂×C₄³	—	47	1	no	—
96	C₂×C₄³	—	47	1	no	—
97	C₂×C₄³	D₄₇	1	1	yes	characteristic
98	C₄×#95	—	47	6	no	—
99	C₂×C₄₇	C₂×C₄³	1	1	yes	characteristic
100	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	3	yes	—
101	C₂×C₄₇	C₄×#117	1	3	yes	—
102	C₂×C₄₇	C₄²×D₄	1	4	yes	—
103	C₂×C₄₇	C₄²×Q₈	1	4	yes	—
104	C₂²×C₄⋊C₄	—	47	4	no	—
105	C₂²×C₄²	—	47	3	no	—
106	C₂²×C₄²	—	47	3	no	—
107	C₂²×C₄²	—	47	6	no	—
108	C₂²×C₄²	C₂×D₄₇	1	6	yes	—
109	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
110	C₄×C₄⋊C₄	—	47	48	no	—
111	C₂×#95	—	47	12	no	—
112	C₄³	—	2	4	no	—
113	C₄³	—	47	8	no	—
114	C₄³	—	94	4	no	—
115	C₄₇	C₄²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
116	C₂³×C₄	—	47	1	no	—
117	C₂³×C₄	—	47	4	no	—
118	C₂³×C₄	—	47	3	no	—
119	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
120	C₂³×C₄	C₂²×D₄₇	1	3	yes	—
121	C₂×C₄⋊C₄	—	47	48	no	—
122	C₂×C₄²	—	2	12	no	—
123	C₂×C₄²	—	2	12	no	—
124	C₂×C₄²	—	47	12	no	—
125	C₂×C₄²	—	47	24	no	—
126	C₂×C₄²	—	47	12	no	—
127	C₂×C₄²	—	47	24	no	—
128	C₂×C₄²	—	94	12	no	—
129	C₂×C₄²	—	94	12	no	—
130	C₂×C₄²	—	94	12	no	—
131	C₂×C₄²	Dic₉₄	1	4	yes	—
132	C₂×C₄²	C₄×D₄₇	1	24	yes	—
133	C₂×C₄²	C₄×D₄₇	1	4	yes	—
134	C₂×C₄²	C₂²⋊D₄₇	1	4	yes	—
135	#95	—	47	48	no	—
136	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
137	C₂²×C₄	—	2	4	no	—
138	C₂²×C₄	—	2	12	no	—
139	C₂²×C₄	—	47	2	no	—
140	C₂²×C₄	—	47	12	no	—
141	C₂²×C₄	—	47	12	no	—
142	C₂²×C₄	—	47	24	no	—
143	C₂²×C₄	—	47	6	no	—
144	C₂²×C₄	—	94	4	no	—
145	C₂²×C₄	—	94	12	no	—
146	C₂²×C₄	—	94	12	no	—
147	C₂²×C₄	C₂×Dic₉₄	1	6	yes	—
148	C₂²×C₄	C₂×C₄×D₄₇	1	24	yes	—
149	C₂²×C₄	C₂×C₄×D₄₇	1	6	yes	—
150	C₂²×C₄	C₂×C₄×D₄₇	1	12	yes	—
151	C₂²×C₄	#10625350	1	12	yes	—
152	C₂²×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
153	C₄⋊C₄	—	47	64	no	—
154	C₄²	—	2	48	no	—
155	C₄²	—	47	48	no	—
156	C₄²	—	94	24	no	—
157	C₄²	—	94	48	no	—
158	C₄²	Dic₄₇⋊C₄	1	16	yes	direct product factor
159	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
160	C₂³	C₂²×C₄×D₄₇	1	6	yes	—
161	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
162	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
163	C₂³	C₂×#10625350	1	6	yes	—
164	C₂×C₄	—	2	24	no	—
165	C₂×C₄	—	2	24	no	—
166	C₂×C₄	—	47	12	no	—
167	C₂×C₄	—	47	16	no	—
168	C₂×C₄	—	47	12	no	—
169	C₂×C₄	—	47	16	no	—
170	C₂×C₄	—	94	12	no	—
171	C₂×C₄	—	94	24	no	—
172	C₂×C₄	—	94	24	no	—
173	C₂×C₄	—	94	24	no	—
174	C₂×C₄	C₄²×D₄₇	1	16	yes	—
175	C₂×C₄	C₄²×D₄₇	1	12	yes	—
176	C₂×C₄	C₂×Dic₄₇⋊C₄	1	12	yes	—
177	C₂×C₄	#13093981	1	12	yes	—
178	C₂×C₄	C₄×C₂²⋊D₄₇	1	24	yes	—
179	C₂×C₄	C₄×Dic₉₄	1	24	yes	—
180	C₂²	C₂×C₄²×D₄₇	1	3	yes	—
181	C₂²	C₂×C₄²×D₄₇	1	4	yes	—
182	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
183	C₂²	C₂×#13093981	1	3	yes	—
184	C₂²	C₂×C₄×C₂²⋊D₄₇	1	6	yes	—
185	C₂²	C₂×C₄×Dic₉₄	1	6	yes	—
186	C₂²	C₄×#10625350	1	12	yes	—
187	C₄	—	2	16	no	—
188	C₄	—	47	8	no	—
189	C₄	—	94	12	no	—
190	C₄	—	94	16	no	—
191	C₄	C₄×Dic₄₇⋊C₄	1	24	yes	direct product factor
192	C₂	C₄³×D₄₇	1	1	yes	characteristic
193	C₂	C₂×C₄×Dic₄₇⋊C₄	1	3	yes	—
194	C₂	C₄×#13093981	1	3	yes	—
195	C₂	C₄²×C₂²⋊D₄₇	1	4	yes	—
196	C₂	C₄²×Dic₉₄	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄²	C₂×D₄₇
commutator	C₂×C₄₇	C₂×C₄³
Frattini	C₂⁴	C₂³×D₄₇
Fitting	C₂×C₄³×C₄₇	C₂
socle, prime radical, cosocle	C₂⁴×C₄₇	C₂⁴
hypercenter	C₂×C₄³	D₄₇
hypocenter	C₄₇	C₄²×C₄⋊C₄
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄² ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
10. C₄×Dic₄₇⋊C₄	C₄	direct (N × H)
13. C₄²×Dic₄₇	C₄	semidirect
55. C₄²×C₄₇	C₄⋊C₄	semidirect
56. Dic₄₇⋊C₄	C₄²	direct (N × H)
59. C₄×Dic₄₇	C₄²	semidirect
90. C₄×C₄₇	C₄×C₄⋊C₄	semidirect
93. Dic₄₇	C₄³	semidirect
115. C₄₇	C₄²×C₄⋊C₄	semidirect
158. C₄²	Dic₄₇⋊C₄	direct (N × H)
191. C₄	C₄×Dic₄₇⋊C₄	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×C₄×Dic₄₇⋊C₄	2
C₂×C₄²×Dic₄₇	2
C₄×C₄₇⋊#95	2
C₂×C₄³×C₄₇	2
C₄²×C₄⋊C₄	47

Subgroups — C42×Dic47⋊C4 #26137358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×Dic₄₇⋊C₄ #26137358