Subgroups — C₂×C₄×Dic₄₇⋊C₄ #20245724

Order 6016.

928 conjugacy classes of subgroups.

The subgroup lattice has 180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
4. C₄×Dic₄₇⋊C₄	C₂	direct (N × H)
10. C₂×Dic₄₇⋊C₄	C₄	direct (N × H)
13. C₂×C₄×Dic₄₇	C₄	semidirect
41. Dic₄₇⋊C₄	C₂×C₄	direct (N × H)
43. C₄×Dic₄₇	C₂×C₄	semidirect
53. C₂×C₄×C₄₇	C₄⋊C₄	semidirect
63. C₂×Dic₄₇	C₄²	semidirect
79. C₄×C₄₇	C₂×C₄⋊C₄	semidirect
82. Dic₄₇	C₂×C₄²	semidirect
84. C₂×C₄₇	C₄×C₄⋊C₄	semidirect
96. C₄₇	C₂×C₄×C₄⋊C₄	semidirect
153. C₂×C₄	Dic₄₇⋊C₄	direct (N × H)
172. C₄	C₂×Dic₄₇⋊C₄	direct (N × H)
173. C₂	C₄×Dic₄₇⋊C₄	direct (N × H)

Subgroups — C2×C4×Dic47⋊C4 #20245724

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₄×Dic₄₇⋊C₄ #20245724