Subgroups — C₄×C₄₇⋊#338 #26121445

Order 12032.

858 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625329	C₂	1	2	yes	maximal
2	C₂×C₄₇⋊#338	C₂	1	4	yes	maximal
3	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10625329	C₂²	1	4	yes	—
5	C₄×#10625329	—	2	4	no	—
6	C₄×#10625329	—	2	4	no	—
7	C₂×#13093935	C₄	1	4	yes	—
8	C₂×C₄×C₄₇⋊C₈	C₄	1	4	yes	—
9	C₄₇⋊#338	C₄	1	16	yes	direct product factor
10	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
11	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
12	C₄×M₁₆×C₄₇	—	2	4	no	—
13	C₂×#97×C₄₇	C₄	1	2	yes	—
14	C₂×C₄×C₈×C₄₇	C₄	1	2	yes	—
15	C₂×#10625329	—	2	4	no	—
16	C₂×#10625329	—	2	4	no	—
17	C₂×#10625329	—	2	8	no	—
18	C₂×#10625329	C₂×C₄	1	16	yes	—
19	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
20	#13093935	—	2	8	no	—
21	C₄×C₄₇⋊C₈	—	2	8	no	—
22	C₂³×C₄×C₄₇	Q₈	1	2	yes	—
23	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
24	C₂×M₁₆×C₄₇	—	2	4	no	—
25	C₂×M₁₆×C₄₇	—	2	4	no	—
26	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	—
27	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
28	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₄₇	D₄	1	2	yes	—
33	C₂×C₄²×C₄₇	D₄	1	4	yes	—
34	#97×C₄₇	—	2	4	no	—
35	C₄×C₈×C₄₇	—	2	4	no	—
36	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
37	C₂²×C₄×C₄₇	—	4	4	no	—
38	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
39	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
40	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
41	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
42	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
43	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
44	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
45	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
47	C₂²×C₄×C₄₇	#41	1	4	yes	—
48	M₁₆×C₄₇	—	2	16	no	—
49	C₂×C₈×C₄₇	—	2	4	no	—
50	C₂×C₈×C₄₇	—	2	4	no	—
51	C₂×C₈×C₄₇	C₄²	1	8	yes	—
52	C₄²×C₄₇	C₄²	1	2	yes	—
53	C₄²×C₄₇	C₄²	1	1	yes	characteristic
54	C₄²×C₄₇	C₄²	1	1	yes	characteristic
55	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
56	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
57	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
58	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
59	#10625329	—	2	16	no	—
60	#10625329	—	2	16	no	—
61	C₂×C₄₇⋊C₈	—	2	8	no	—
62	C₂×C₄₇⋊C₈	—	2	8	no	—
63	C₂×C₄₇⋊C₈	C₄²	1	16	yes	—
64	C₂³×C₄₇	—	4	2	no	—
65	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
66	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
67	C₂³×C₄₇	C₄×Q₈	1	4	yes	—
68	C₂×C₄×C₄₇	—	2	8	no	—
69	C₂×C₄×C₄₇	—	2	4	no	—
70	C₂×C₄×C₄₇	—	4	4	no	—
71	C₂×C₄×C₄₇	—	4	2	no	—
72	C₂×C₄×C₄₇	#95	1	4	yes	—
73	C₂×C₄×C₄₇	#95	1	2	yes	—
74	C₂×C₄×C₄₇	#95	1	2	yes	—
75	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
76	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
77	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
78	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
79	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₄₇	#117	1	4	yes	—
81	C₂×C₄×C₄₇	#117	1	2	yes	—
82	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
83	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
84	C₈×C₄₇	—	2	8	no	—
85	C₄₇⋊C₈	—	2	16	no	—
86	C₄×#338	—	47	1	no	maximal, Sylow
87	C₂²×C₄₇	—	2	4	no	—
88	C₂²×C₄₇	—	2	2	no	—
89	C₂²×C₄₇	—	4	4	no	—
90	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
91	C₂²×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
92	C₂²×C₄₇	C₄×C₄⋊C₄	1	4	yes	—
93	C₄×C₄₇	—	2	4	no	—
94	C₄×C₄₇	—	2	2	no	—
95	C₄×C₄₇	#338	1	4	yes	complemented
96	C₄×C₄₇	C₄³	1	1	yes	characteristic
97	C₄×C₄₇	#376	1	1	yes	characteristic
98	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
99	C₄×C₄₇	C₄×C₂²⋊C₄	1	4	yes	—
100	C₂×C₄×M₁₆	—	47	2	no	—
101	C₂×C₄×M₁₆	D₄₇	1	1	yes	characteristic
102	C₂×#338	—	47	4	no	—
103	C₂×C₄₇	—	2	2	no	—
104	C₂×C₄₇	—	2	4	no	—
105	C₂×C₄₇	C₄×#95	1	1	yes	characteristic
106	C₂×C₄₇	C₂×#338	1	2	yes	—
107	C₂²×M₁₆	—	47	4	no	—
108	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
109	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
110	C₄×M₁₆	—	2	4	no	—
111	C₄×M₁₆	—	94	4	no	—
112	C₄×M₁₆	—	94	4	no	—
113	C₂×#97	—	47	4	no	—
114	C₂×#97	Dic₄₇	1	2	yes	—
115	C₂×C₄×C₈	—	47	4	no	—
116	C₂×C₄×C₈	Dic₄₇	1	2	yes	—
117	#338	—	47	16	no	—
118	C₄₇	C₄×#338	1	1	yes	characteristic, complemented, Sylow
119	C₂³×C₄	Dic₉₄	1	2	yes	—
120	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
121	C₂×M₁₆	—	2	4	no	—
122	C₂×M₁₆	—	2	4	no	—
123	C₂×M₁₆	—	47	16	no	—
124	C₂×M₁₆	—	94	4	no	—
125	C₂×M₁₆	—	94	8	no	—
126	C₂×M₁₆	—	94	4	no	—
127	C₂×M₁₆	C₄×D₄₇	1	8	yes	—
128	C₂²×C₈	—	47	8	no	—
129	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
130	C₂×C₄²	C₄×D₄₇	1	2	yes	—
131	C₂×C₄²	C₄×D₄₇	1	2	yes	—
132	C₂×C₄²	D₁₈₈	1	2	yes	—
133	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
134	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
135	C₂×C₄²	C₂²⋊D₄₇	1	4	yes	—
136	#97	—	2	4	no	—
137	#97	—	94	8	no	—
138	C₄×C₈	—	2	4	no	—
139	C₄×C₈	—	94	8	no	—
140	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
141	C₂²×C₄	—	4	4	no	—
142	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
143	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
144	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
145	C₂²×C₄	C₄⋊Dic₄₇	1	2	yes	—
146	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
147	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
148	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
149	C₂²×C₄	#10625350	1	4	yes	—
150	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
152	M₁₆	—	2	16	no	—
153	M₁₆	—	94	16	no	—
154	M₁₆	—	94	16	no	—
155	C₂×C₈	—	2	4	no	—
156	C₂×C₈	—	2	4	no	—
157	C₂×C₈	—	47	16	no	—
158	C₂×C₈	—	94	8	no	—
159	C₂×C₈	—	94	8	no	—
160	C₂×C₈	C₄×Dic₄₇	1	8	yes	—
161	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
162	C₄²	C₄×Dic₄₇	1	2	yes	—
163	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
164	C₄²	(C₂×D₄₇)⋊C₄	1	4	yes	—
165	C₄²	(C₂×D₄₇)⋊C₄	1	4	yes	—
166	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
167	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
168	C₂³	—	4	2	no	—
169	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
170	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
171	C₂³	C₄×Dic₉₄	1	4	yes	—
172	C₂×C₄	—	2	8	no	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	—	4	2	no	—
176	C₂×C₄	C₄₇⋊#95	1	4	yes	—
177	C₂×C₄	C₄₇⋊#95	1	2	yes	—
178	C₂×C₄	C₄₇⋊#95	1	2	yes	—
179	C₂×C₄	C₄²×D₄₇	1	4	yes	—
180	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
181	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
182	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
183	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
184	C₂×C₄	#13093981	1	4	yes	—
185	C₂×C₄	#13093983	1	2	yes	—
186	C₂×C₄	C₄×C₂²⋊D₄₇	1	8	yes	—
187	C₂×C₄	C₄×D₁₈₈	1	4	yes	—
188	C₈	—	2	8	no	—
189	C₈	—	94	16	no	—
190	C₂²	—	2	4	no	—
191	C₂²	—	2	2	no	—
192	C₂²	—	4	4	no	—
193	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
194	C₂²	C₄×C₄⋊Dic₄₇	1	2	yes	—
195	C₂²	C₄×Dic₄₇⋊C₄	1	4	yes	—
196	C₄	—	2	4	no	—
197	C₄	—	2	2	no	—
198	C₄	C₄₇⋊#338	1	4	yes	direct product factor
199	C₄	C₄²×Dic₄₇	1	1	yes	characteristic
200	C₄	#15688969	1	1	yes	characteristic
201	C₄	C₄×C₂²⋊Dic₄₇	1	2	yes	—
202	C₄	C₄×(C₂×D₄₇)⋊C₄	1	4	yes	—
203	C₂	—	2	2	no	—
204	C₂	—	2	4	no	—
205	C₂	C₄×C₄₇⋊#95	1	1	yes	characteristic
206	C₂	C₂×C₄₇⋊#338	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄×Dic₄₇
commutator	C₄×C₄₇	C₄³
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂⁴×C₄₇	C₂×Q₈
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×C₄×M₁₆	D₄₇
hypocenter	C₄₇	C₄×#338
LCS	G ▷ C₄×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
9. C₄₇⋊#338	C₄	direct (N × H)
95. C₄×C₄₇	#338	semidirect
118. C₄₇	C₄×#338	semidirect
198. C₄	C₄₇⋊#338	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×#10625329	2
C₂×C₄₇⋊#338	2
C₂×C₄×M₁₆×C₄₇	2
C₄×#338	47

Subgroups — C4×C47⋊#338 #26121445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₇⋊#338 #26121445