Subgroups — C₄₇×C₄⋊#401 #26054852

Order 12032.

1106 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#401	C₂	1	2	yes	maximal
2	C₄₇×#1443	C₂	1	6	yes	maximal
3	C₄₇×C₄⋊#95	C₂	1	3	yes	maximal
4	C₄₇×C₄⋊#95	C₂	1	3	yes	maximal
5	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊C₄×C₄₇	C₂²	1	3	yes	—
7	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄²×C₄₇	C₂²	1	3	yes	—
9	C₄₇×#401	—	2	8	no	—
10	C₂×#95×C₄₇	C₂²	1	6	yes	—
11	C₂×#95×C₄₇	C₂²	1	6	yes	—
12	C₂×#95×C₄₇	C₂²	1	3	yes	—
13	C₂×#95×C₄₇	C₂²	1	6	yes	—
14	C₂×#95×C₄₇	C₂²	1	6	yes	—
15	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
17	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
18	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
19	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
20	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₄₇	—	2	6	no	—
22	C₂×C₄⋊C₄×C₄₇	—	2	6	no	—
23	C₂×C₄⋊C₄×C₄₇	—	2	6	no	—
24	C₂×C₄⋊C₄×C₄₇	—	2	6	no	—
25	C₂×C₄²×C₄₇	—	2	6	no	—
26	C₂×C₄²×C₄₇	—	2	6	no	—
27	C₂×C₄²×C₄₇	—	2	6	no	—
28	#95×C₄₇	—	2	12	no	—
29	#95×C₄₇	—	2	12	no	—
30	#95×C₄₇	—	2	6	no	—
31	#95×C₄₇	—	2	12	no	—
32	#95×C₄₇	—	4	6	no	—
33	#95×C₄₇	D₄	1	4	yes	—
34	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
35	C₂²×C₄×C₄₇	—	2	3	no	—
36	C₂²×C₄×C₄₇	—	2	3	no	—
37	C₂²×C₄×C₄₇	—	2	3	no	—
38	C₂²×C₄×C₄₇	—	2	3	no	—
39	C₂²×C₄×C₄₇	—	2	3	no	—
40	C₂²×C₄×C₄₇	—	2	3	no	—
41	C₂²×C₄×C₄₇	—	2	3	no	—
42	C₂²×C₄×C₄₇	—	2	3	no	—
43	C₂²×C₄×C₄₇	—	2	3	no	—
44	C₂²×C₄×C₄₇	—	2	3	no	—
45	C₂²×C₄×C₄₇	—	2	3	no	—
46	C₂²×C₄×C₄₇	—	2	3	no	—
47	C₂²×C₄×C₄₇	—	2	2	no	—
48	C₂²×C₄×C₄₇	—	2	6	no	—
49	C₂²×C₄×C₄₇	—	2	6	no	—
50	C₂²×C₄×C₄₇	—	2	6	no	—
51	C₂²×C₄×C₄₇	—	2	6	no	—
52	C₂²×C₄×C₄₇	—	2	6	no	—
53	C₂²×C₄×C₄₇	—	2	6	no	—
54	C₂²×C₄×C₄₇	—	2	6	no	—
55	C₂²×C₄×C₄₇	—	2	6	no	—
56	C₂²×C₄×C₄₇	—	2	6	no	—
57	C₂²×C₄×C₄₇	C₂×D₄	1	6	yes	—
58	C₂²×C₄×C₄₇	#41	1	6	yes	—
59	C₂²×C₄×C₄₇	#41	1	6	yes	—
60	C₂²×C₄×C₄₇	#41	1	6	yes	—
61	C₂²×C₄×C₄₇	#41	1	2	yes	—
62	C₄⋊C₄×C₄₇	—	4	4	no	—
63	C₄⋊C₄×C₄₇	—	4	12	no	—
64	C₄²×C₄₇	—	4	12	no	—
65	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
66	C₂³×C₄₇	C₂×#41	1	3	yes	—
67	C₂³×C₄₇	C₂×#41	1	3	yes	—
68	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
69	C₂³×C₄₇	C₂×#41	1	3	yes	—
70	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
71	C₂³×C₄₇	2₋¹⁺⁴	1	3	yes	—
72	C₂×C₄×C₄₇	—	2	6	no	—
73	C₂×C₄×C₄₇	—	2	6	no	—
74	C₂×C₄×C₄₇	—	2	6	no	—
75	C₂×C₄×C₄₇	—	2	6	no	—
76	C₂×C₄×C₄₇	—	2	6	no	—
77	C₂×C₄×C₄₇	—	2	6	no	—
78	C₂×C₄×C₄₇	—	4	3	no	—
79	C₂×C₄×C₄₇	—	4	3	no	—
80	C₂×C₄×C₄₇	—	4	3	no	—
81	C₂×C₄×C₄₇	—	4	3	no	—
82	C₂×C₄×C₄₇	—	4	3	no	—
83	C₂×C₄×C₄₇	—	4	3	no	—
84	C₂×C₄×C₄₇	—	4	3	no	—
85	C₂×C₄×C₄₇	—	4	3	no	—
86	C₂×C₄×C₄₇	—	4	2	no	—
87	C₂×C₄×C₄₇	—	4	6	no	—
88	C₂×C₄×C₄₇	—	4	6	no	—
89	C₂×C₄×C₄₇	—	4	6	no	—
90	C₂×C₄×C₄₇	—	4	6	no	—
91	C₂×C₄×C₄₇	—	4	6	no	—
92	C₂×C₄×C₄₇	—	4	6	no	—
93	C₂×C₄×C₄₇	—	4	6	no	—
94	C₂×C₄×C₄₇	—	4	6	no	—
95	C₂×C₄×C₄₇	—	4	6	no	—
96	C₂×C₄×C₄₇	#126	1	12	yes	—
97	C₂×C₄×C₄₇	#126	1	4	yes	—
98	C₂×C₄×C₄₇	#126	1	12	yes	—
99	C₄⋊#401	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
100	C₂²×C₄₇	C₂×#126	1	1	yes	characteristic
101	C₂²×C₄₇	C₂×#126	1	3	yes	—
102	C₂²×C₄₇	C₂×#126	1	3	yes	—
103	C₂²×C₄₇	#529	1	3	yes	—
104	C₂²×C₄₇	#532	1	3	yes	—
105	C₂²×C₄₇	#541	1	3	yes	—
106	C₂²×C₄₇	#542	1	3	yes	—
107	C₂²×C₄₇	#547	1	3	yes	—
108	C₂²×C₄₇	#550	1	1	yes	characteristic
109	C₂²×C₄₇	#552	1	3	yes	—
110	C₂²×C₄₇	#553	1	3	yes	—
111	C₂²×C₄₇	#556	1	3	yes	—
112	C₂²×C₄₇	#556	1	3	yes	—
113	C₄×C₄₇	—	4	6	no	—
114	C₄×C₄₇	—	4	6	no	—
115	C₄×C₄₇	—	8	2	no	—
116	C₄×C₄₇	—	8	6	no	—
117	C₄×C₄₇	#401	1	8	yes	complemented
118	C₂×#401	C₂×C₄₇	1	2	yes	—
119	#1443	C₂×C₄₇	1	6	yes	—
120	C₄⋊#95	C₂×C₄₇	1	3	yes	—
121	C₄⋊#95	C₂×C₄₇	1	3	yes	—
122	C₄×#95	C₂×C₄₇	1	1	yes	characteristic
123	C₂×C₄₇	C₂×#401	1	1	yes	characteristic
124	C₂×C₄₇	#2494	1	3	yes	—
125	C₂×C₄₇	#2496	1	3	yes	—
126	C₂×C₄₇	#2512	1	3	yes	—
127	C₂×C₄₇	#2514	1	3	yes	—
128	C₂×C₄₇	#2645	1	1	yes	characteristic
129	C₂×C₄₇	#2860	1	1	yes	characteristic
130	C₂²×C₄⋊C₄	C₂²×C₄₇	1	3	yes	—
131	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
132	C₂²×C₄²	C₂²×C₄₇	1	3	yes	—
133	#401	—	2	8	no	—
134	C₂×#95	C₂²×C₄₇	1	6	yes	—
135	C₂×#95	C₂²×C₄₇	1	6	yes	—
136	C₂×#95	C₂²×C₄₇	1	3	yes	—
137	C₂×#95	C₂²×C₄₇	1	6	yes	—
138	C₂×#95	C₂²×C₄₇	1	6	yes	—
139	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
140	C₄₇	C₄⋊#401	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
142	C₂³×C₄	C₂³×C₄₇	1	6	yes	—
143	C₂³×C₄	C₂³×C₄₇	1	3	yes	—
144	C₂³×C₄	C₂³×C₄₇	1	3	yes	—
145	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
146	C₂×C₄⋊C₄	—	2	6	no	—
147	C₂×C₄⋊C₄	—	2	6	no	—
148	C₂×C₄⋊C₄	—	2	6	no	—
149	C₂×C₄⋊C₄	—	2	6	no	—
150	C₂×C₄²	—	2	6	no	—
151	C₂×C₄²	—	2	6	no	—
152	C₂×C₄²	—	2	6	no	—
153	#95	—	2	12	no	—
154	#95	—	2	12	no	—
155	#95	—	2	6	no	—
156	#95	—	2	12	no	—
157	#95	—	4	6	no	—
158	#95	D₄×C₄₇	1	4	yes	—
159	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
160	C₂²×C₄	—	2	3	no	—
161	C₂²×C₄	—	2	3	no	—
162	C₂²×C₄	—	2	3	no	—
163	C₂²×C₄	—	2	3	no	—
164	C₂²×C₄	—	2	3	no	—
165	C₂²×C₄	—	2	3	no	—
166	C₂²×C₄	—	2	3	no	—
167	C₂²×C₄	—	2	3	no	—
168	C₂²×C₄	—	2	3	no	—
169	C₂²×C₄	—	2	3	no	—
170	C₂²×C₄	—	2	3	no	—
171	C₂²×C₄	—	2	3	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	6	no	—
174	C₂²×C₄	—	2	6	no	—
175	C₂²×C₄	—	2	6	no	—
176	C₂²×C₄	—	2	6	no	—
177	C₂²×C₄	—	2	6	no	—
178	C₂²×C₄	—	2	6	no	—
179	C₂²×C₄	—	2	6	no	—
180	C₂²×C₄	—	2	6	no	—
181	C₂²×C₄	—	2	6	no	—
182	C₂²×C₄	C₂×D₄×C₄₇	1	6	yes	—
183	C₂²×C₄	#41×C₄₇	1	6	yes	—
184	C₂²×C₄	#41×C₄₇	1	6	yes	—
185	C₂²×C₄	#41×C₄₇	1	6	yes	—
186	C₂²×C₄	#41×C₄₇	1	2	yes	—
187	C₄⋊C₄	—	4	4	no	—
188	C₄⋊C₄	—	4	12	no	—
189	C₄²	—	4	12	no	—
190	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
191	C₂³	C₂×#41×C₄₇	1	3	yes	—
192	C₂³	C₂×#41×C₄₇	1	3	yes	—
193	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
194	C₂³	C₂×#41×C₄₇	1	3	yes	—
195	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
196	C₂³	2₋¹⁺⁴×C₄₇	1	3	yes	—
197	C₂×C₄	—	2	6	no	—
198	C₂×C₄	—	2	6	no	—
199	C₂×C₄	—	2	6	no	—
200	C₂×C₄	—	2	6	no	—
201	C₂×C₄	—	2	6	no	—
202	C₂×C₄	—	2	6	no	—
203	C₂×C₄	—	4	3	no	—
204	C₂×C₄	—	4	3	no	—
205	C₂×C₄	—	4	3	no	—
206	C₂×C₄	—	4	3	no	—
207	C₂×C₄	—	4	3	no	—
208	C₂×C₄	—	4	3	no	—
209	C₂×C₄	—	4	3	no	—
210	C₂×C₄	—	4	3	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	4	6	no	—
213	C₂×C₄	—	4	6	no	—
214	C₂×C₄	—	4	6	no	—
215	C₂×C₄	—	4	6	no	—
216	C₂×C₄	—	4	6	no	—
217	C₂×C₄	—	4	6	no	—
218	C₂×C₄	—	4	6	no	—
219	C₂×C₄	—	4	6	no	—
220	C₂×C₄	—	4	6	no	—
221	C₂×C₄	#126×C₄₇	1	12	yes	—
222	C₂×C₄	#126×C₄₇	1	4	yes	—
223	C₂×C₄	#126×C₄₇	1	12	yes	—
224	C₂²	C₂×#126×C₄₇	1	1	yes	characteristic
225	C₂²	C₂×#126×C₄₇	1	3	yes	—
226	C₂²	C₂×#126×C₄₇	1	3	yes	—
227	C₂²	C₄₇×#529	1	3	yes	—
228	C₂²	C₄₇×#532	1	3	yes	—
229	C₂²	C₄₇×#541	1	3	yes	—
230	C₂²	C₄₇×#542	1	3	yes	—
231	C₂²	C₄₇×#547	1	3	yes	—
232	C₂²	C₄₇×#550	1	1	yes	characteristic
233	C₂²	C₄₇×#552	1	3	yes	—
234	C₂²	C₄₇×#553	1	3	yes	—
235	C₂²	C₄₇×#556	1	3	yes	—
236	C₂²	C₄₇×#556	1	3	yes	—
237	C₄	—	4	6	no	—
238	C₄	—	4	6	no	—
239	C₄	—	8	2	no	—
240	C₄	—	8	6	no	—
241	C₄	C₄₇×#401	1	8	yes	complemented
242	C₂	C₂×C₄₇×#401	1	1	yes	characteristic
243	C₂	C₄₇×#2494	1	3	yes	—
244	C₂	C₄₇×#2496	1	3	yes	—
245	C₂	C₄₇×#2512	1	3	yes	—
246	C₂	C₄₇×#2514	1	3	yes	—
247	C₂	C₄₇×#2645	1	1	yes	characteristic
248	C₂	C₄₇×#2860	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
99. C₄⋊#401	C₄₇	direct (N × H)
117. C₄×C₄₇	#401	semidirect
140. C₄₇	C₄⋊#401	direct (N × H)
241. C₄	C₄₇×#401	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#401	2
C₄₇×#1443	2
C₄₇×C₄⋊#95	2
C₄×#95×C₄₇	2
C₄⋊#401	47

Subgroups — C47×C4⋊#401 #26054852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×C₄⋊#401 #26054852