Subgroups — C₂×C₄×C₄₇⋊#95 #26137347

Order 12032.

4462 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×Dic₄₇	C₂	1	2	yes	maximal
2	C₂²×C₄₇⋊#95	C₂	1	4	yes	maximal
3	C₄×C₄₇⋊#95	C₂	1	8	yes	maximal, direct product factor
4	C₂³×C₄²×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×Dic₄₇	C₂²	1	4	yes	—
6	C₂²×C₄×Dic₄₇	—	2	8	no	—
7	C₂²×C₄×Dic₄₇	—	2	8	no	—
8	C₂²×C₄×Dic₄₇	C₄	1	16	yes	complemented
9	C₂²×C₄×Dic₄₇	C₂²	1	8	yes	—
10	C₂×C₄₇⋊#95	C₄	1	32	yes	direct product factor
11	C₂×C₄₇⋊#95	C₂²	1	16	yes	—
12	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₄₇	—	2	8	no	—
15	C₂²×C₄²×C₄₇	C₄	1	8	yes	complemented
16	C₂²×C₄²×C₄₇	C₂²	1	4	yes	—
17	C₂³×Dic₄₇	—	2	8	no	—
18	C₂³×Dic₄₇	—	2	8	no	—
19	C₂³×Dic₄₇	—	2	16	no	—
20	C₂³×Dic₄₇	C₂×C₄	1	32	yes	—
21	C₂³×Dic₄₇	C₂×C₄	1	16	yes	—
22	C₂³×Dic₄₇	C₂³	1	8	yes	—
23	C₂×C₄×Dic₄₇	—	2	64	no	—
24	C₂×C₄×Dic₄₇	—	2	16	no	—
25	C₂×C₄×Dic₄₇	—	2	16	no	—
26	C₂×C₄×Dic₄₇	C₂×C₄	1	32	yes	complemented
27	C₄₇⋊#95	C₂×C₄	1	64	yes	direct product factor
28	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
29	C₂³×C₄×C₄₇	—	2	8	no	—
30	C₂³×C₄×C₄₇	—	2	8	no	—
31	C₂³×C₄×C₄₇	C₂×C₄	1	16	yes	—
32	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
33	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
34	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
35	C₂³×C₄×C₄₇	D₄	1	4	yes	—
36	C₂³×C₄×C₄₇	D₄	1	8	yes	—
37	C₂³×C₄×C₄₇	Q₈	1	4	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
40	C₂×C₄²×C₄₇	—	2	32	no	—
41	C₂×C₄²×C₄₇	—	2	16	no	—
42	C₂×C₄²×C₄₇	C₂×C₄	1	16	yes	complemented
43	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
44	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
45	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
46	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
47	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
48	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
49	C₂⁴×C₄₇	#41	1	8	yes	—
50	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	—	2	16	no	—
52	C₂²×C₄×C₄₇	—	2	16	no	—
53	C₂²×C₄×C₄₇	—	2	64	no	—
54	C₂²×C₄×C₄₇	—	2	8	no	—
55	C₂²×C₄×C₄₇	—	2	8	no	—
56	C₂²×C₄×C₄₇	C₄²	1	16	yes	—
57	C₂²×C₄×C₄₇	C₄²	1	32	yes	complemented
58	C₂²×C₄×C₄₇	C₂²⋊C₄	1	32	yes	—
59	C₂²×C₄×C₄₇	C₂²⋊C₄	1	16	yes	—
60	C₂²×C₄×C₄₇	C₄⋊C₄	1	32	yes	—
61	C₂²×C₄×C₄₇	C₄⋊C₄	1	16	yes	—
62	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	—
63	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
64	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
65	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
66	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
67	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
68	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
69	C₂²×Dic₄₇	—	2	32	no	—
70	C₂²×Dic₄₇	—	2	32	no	—
71	C₂²×Dic₄₇	—	2	64	no	—
72	C₂²×Dic₄₇	—	2	64	no	—
73	C₂²×Dic₄₇	—	2	8	no	—
74	C₂²×Dic₄₇	—	2	8	no	—
75	C₂²×Dic₄₇	—	2	16	no	—
76	C₂²×Dic₄₇	C₄²	1	64	yes	complemented
77	C₂²×Dic₄₇	C₂²×C₄	1	32	yes	—
78	C₂²×Dic₄₇	C₂²×C₄	1	16	yes	—
79	C₄²×C₄₇	—	2	32	no	—
80	C₄×Dic₄₇	—	2	64	no	—
81	C₂³×C₄₇	C₂×C₄²	1	16	yes	—
82	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
83	C₂³×C₄₇	C₂×C₄²	1	8	yes	—
84	C₂³×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
85	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
86	C₂³×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
87	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
88	C₂³×C₄₇	#117	1	16	yes	—
89	C₂³×C₄₇	#117	1	8	yes	—
90	C₂³×C₄₇	C₄×D₄	1	32	yes	—
91	C₂³×C₄₇	C₄×D₄	1	16	yes	—
92	C₂³×C₄₇	C₄×Q₈	1	16	yes	—
93	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
94	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
95	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
96	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
97	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
98	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
99	C₂³×C₄₇	C₂×#41	1	4	yes	—
100	C₂×C₄×C₄₇	—	2	8	no	—
101	C₂×C₄×C₄₇	—	2	8	no	—
102	C₂×C₄×C₄₇	—	2	32	no	—
103	C₂×C₄×C₄₇	—	2	64	no	—
104	C₂×C₄×C₄₇	#95	1	64	yes	complemented
105	C₂×C₄×C₄₇	C₂×C₄²	1	8	yes	—
106	C₂×C₄×C₄₇	C₂×C₄²	1	16	yes	complemented
107	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	16	yes	—
108	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
109	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	16	yes	—
110	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	8	yes	—
111	C₂×Dic₄₇	—	2	16	no	—
112	C₂×Dic₄₇	—	2	16	no	—
113	C₂×Dic₄₇	—	2	32	no	—
114	C₂×Dic₄₇	—	2	32	no	—
115	C₂×Dic₄₇	—	2	128	no	—
116	C₂×Dic₄₇	C₂×C₄²	1	32	yes	complemented
117	C₂×C₄×#95	—	47	1	no	maximal, Sylow
118	C₂²×C₄₇	C₄³	1	8	yes	—
119	C₂²×C₄₇	C₂×#95	1	8	yes	—
120	C₂²×C₄₇	#376	1	8	yes	—
121	C₂²×C₄₇	C₄×C₂²⋊C₄	1	16	yes	—
122	C₂²×C₄₇	C₄×C₂²⋊C₄	1	32	yes	—
123	C₂²×C₄₇	C₄×C₄⋊C₄	1	16	yes	—
124	C₂²×C₄₇	C₄×C₄⋊C₄	1	32	yes	—
125	C₂²×C₄₇	C₂²×C₄²	1	4	yes	—
126	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
127	C₂²×C₄₇	C₂²×C₄²	1	2	yes	—
128	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	2	yes	—
129	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄₇	C₂²×C₄⋊C₄	1	2	yes	—
131	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
132	C₂²×C₄₇	C₂×#117	1	4	yes	—
133	C₂²×C₄₇	C₂×#117	1	2	yes	—
134	C₂²×C₄₇	C₂×C₄×D₄	1	8	yes	—
135	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
136	C₂²×C₄₇	C₂×C₄×Q₈	1	4	yes	—
137	C₄×C₄₇	—	2	16	no	—
138	C₄×C₄₇	C₂×#95	1	16	yes	complemented
139	Dic₄₇	—	2	32	no	—
140	C₂³×C₄²	—	47	2	no	—
141	C₂³×C₄²	D₄₇	1	1	yes	characteristic
142	C₂²×#95	—	47	4	no	—
143	C₄×#95	—	47	8	no	—
144	C₂×C₄₇	C₄×#95	1	16	yes	complemented
145	C₂×C₄₇	C₂×C₄³	1	1	yes	characteristic
146	C₂×C₄₇	C₂²×#95	1	1	yes	characteristic
147	C₂×C₄₇	C₂×#376	1	1	yes	characteristic
148	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	4	yes	—
150	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	2	yes	—
151	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	4	yes	—
152	C₂⁴×C₄	—	47	4	no	—
153	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
154	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
155	C₂²×C₄²	—	2	8	no	—
156	C₂²×C₄²	—	47	16	no	—
157	C₂²×C₄²	—	47	8	no	—
158	C₂²×C₄²	—	94	8	no	—
159	C₂²×C₄²	—	94	8	no	—
160	C₂²×C₄²	Dic₄₇	1	8	yes	complemented
161	C₂²×C₄²	C₂×D₄₇	1	4	yes	—
162	C₂×#95	—	47	32	no	—
163	C₂×#95	—	47	16	no	—
164	C₄₇	C₂×C₄×#95	1	1	yes	characteristic, complemented, Sylow
165	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
166	C₂³×C₄	—	2	8	no	—
167	C₂³×C₄	—	2	8	no	—
168	C₂³×C₄	—	47	32	no	—
169	C₂³×C₄	—	47	16	no	—
170	C₂³×C₄	—	47	8	no	—
171	C₂³×C₄	—	94	8	no	—
172	C₂³×C₄	—	94	16	no	—
173	C₂³×C₄	—	94	8	no	—
174	C₂³×C₄	Dic₉₄	1	4	yes	—
175	C₂³×C₄	C₄×D₄₇	1	16	yes	—
176	C₂³×C₄	C₄×D₄₇	1	8	yes	—
177	C₂³×C₄	D₁₈₈	1	4	yes	—
178	C₂³×C₄	C₂×Dic₄₇	1	8	yes	—
179	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
180	C₂³×C₄	C₂²⋊D₄₇	1	8	yes	—
181	C₂³×C₄	C₂²×D₄₇	1	4	yes	—
182	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
183	C₂×C₄²	—	2	32	no	—
184	C₂×C₄²	—	2	16	no	—
185	C₂×C₄²	—	47	32	no	—
186	C₂×C₄²	—	94	64	no	—
187	C₂×C₄²	—	94	16	no	—
188	C₂×C₄²	—	94	16	no	—
189	C₂×C₄²	C₂×Dic₄₇	1	16	yes	complemented
190	#95	—	47	64	no	—
191	C₂⁴	C₂×Dic₉₄	1	2	yes	—
192	C₂⁴	C₂×C₄×D₄₇	1	4	yes	—
193	C₂⁴	C₂×C₄×D₄₇	1	8	yes	—
194	C₂⁴	C₂×D₁₈₈	1	2	yes	—
195	C₂⁴	#10625350	1	8	yes	—
196	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
197	C₂⁴	C₂×C₂²⋊D₄₇	1	4	yes	—
198	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
199	C₂²×C₄	—	2	16	no	—
200	C₂²×C₄	—	2	16	no	—
201	C₂²×C₄	—	2	64	no	—
202	C₂²×C₄	—	2	8	no	—
203	C₂²×C₄	—	2	8	no	—
204	C₂²×C₄	—	47	64	no	—
205	C₂²×C₄	—	47	32	no	—
206	C₂²×C₄	—	47	16	no	—
207	C₂²×C₄	—	94	32	no	—
208	C₂²×C₄	—	94	32	no	—
209	C₂²×C₄	—	94	64	no	—
210	C₂²×C₄	—	94	64	no	—
211	C₂²×C₄	—	94	8	no	—
212	C₂²×C₄	—	94	8	no	—
213	C₂²×C₄	—	94	16	no	—
214	C₂²×C₄	C₄×Dic₄₇	1	16	yes	—
215	C₂²×C₄	C₄×Dic₄₇	1	32	yes	complemented
216	C₂²×C₄	Dic₄₇⋊C₄	1	32	yes	—
217	C₂²×C₄	C₄⋊Dic₄₇	1	16	yes	—
218	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	32	yes	—
219	C₂²×C₄	C₂²⋊Dic₄₇	1	16	yes	—
220	C₂²×C₄	C₂×Dic₉₄	1	4	yes	—
221	C₂²×C₄	C₂×C₄×D₄₇	1	16	yes	—
222	C₂²×C₄	C₂×C₄×D₄₇	1	8	yes	—
223	C₂²×C₄	C₂×D₁₈₈	1	4	yes	—
224	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
225	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
226	C₂²×C₄	C₂×C₂²⋊D₄₇	1	8	yes	—
227	C₄²	—	2	32	no	—
228	C₄²	—	94	64	no	—
229	C₂³	C₄²×D₄₇	1	16	yes	—
230	C₂³	C₂×C₄×Dic₄₇	1	4	yes	—
231	C₂³	C₂×C₄×Dic₄₇	1	8	yes	—
232	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	8	yes	—
233	C₂³	C₂×C₂²⋊Dic₄₇	1	4	yes	—
234	C₂³	C₂×Dic₄₇⋊C₄	1	8	yes	—
235	C₂³	C₂×C₄⋊Dic₄₇	1	4	yes	—
236	C₂³	#13093981	1	16	yes	—
237	C₂³	#13093983	1	8	yes	—
238	C₂³	C₄×C₂²⋊D₄₇	1	32	yes	—
239	C₂³	C₄×D₁₈₈	1	16	yes	—
240	C₂³	C₄×Dic₉₄	1	16	yes	—
241	C₂³	C₂²×C₄×D₄₇	1	2	yes	—
242	C₂³	C₂²×C₄×D₄₇	1	4	yes	—
243	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
244	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
245	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
246	C₂³	C₂²×Dic₉₄	1	1	yes	characteristic
247	C₂³	C₂×#10625350	1	4	yes	—
248	C₂×C₄	—	2	64	no	—
249	C₂×C₄	—	2	8	no	—
250	C₂×C₄	—	2	8	no	—
251	C₂×C₄	—	2	32	no	—
252	C₂×C₄	—	47	32	no	—
253	C₂×C₄	—	94	128	no	—
254	C₂×C₄	—	94	16	no	—
255	C₂×C₄	—	94	16	no	—
256	C₂×C₄	—	94	32	no	—
257	C₂×C₄	—	94	32	no	—
258	C₂×C₄	C₄₇⋊#95	1	64	yes	direct product factor
259	C₂×C₄	C₂×C₄×Dic₄₇	1	8	yes	—
260	C₂×C₄	C₂×C₄×Dic₄₇	1	16	yes	complemented
261	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	16	yes	—
262	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	8	yes	—
263	C₂×C₄	C₂×Dic₄₇⋊C₄	1	16	yes	—
264	C₂×C₄	C₂×C₄⋊Dic₄₇	1	8	yes	—
265	C₂²	C₄²×Dic₄₇	1	8	yes	—
266	C₂²	C₂×C₄₇⋊#95	1	8	yes	—
267	C₂²	#15688969	1	8	yes	—
268	C₂²	C₄×C₂²⋊Dic₄₇	1	16	yes	—
269	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	32	yes	—
270	C₂²	C₄×C₄⋊Dic₄₇	1	16	yes	—
271	C₂²	C₄×Dic₄₇⋊C₄	1	32	yes	—
272	C₂²	C₂×C₄²×D₄₇	1	4	yes	—
273	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
274	C₂²	C₂²×C₄×Dic₄₇	1	2	yes	—
275	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	2	yes	—
276	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
277	C₂²	C₂²×Dic₄₇⋊C₄	1	2	yes	—
278	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
279	C₂²	C₂×#13093981	1	4	yes	—
280	C₂²	C₂×#13093983	1	2	yes	—
281	C₂²	C₂×C₄×C₂²⋊D₄₇	1	8	yes	—
282	C₂²	C₂×C₄×D₁₈₈	1	4	yes	—
283	C₂²	C₂×C₄×Dic₉₄	1	4	yes	—
284	C₄	—	2	16	no	—
285	C₄	—	94	32	no	—
286	C₄	C₂×C₄₇⋊#95	1	16	yes	direct product factor
287	C₂	C₄×C₄₇⋊#95	1	16	yes	direct product factor
288	C₂	C₂×C₄²×Dic₄₇	1	1	yes	characteristic
289	C₂	C₂²×C₄₇⋊#95	1	1	yes	characteristic
290	C₂	C₂×#15688969	1	1	yes	characteristic
291	C₂	C₂×C₄×C₂²⋊Dic₄₇	1	2	yes	—
292	C₂	C₂×C₄×(C₂×D₄₇)⋊C₄	1	4	yes	—
293	C₂	C₂×C₄×C₄⋊Dic₄₇	1	2	yes	—
294	C₂	C₂×C₄×Dic₄₇⋊C₄	1	4	yes	—

	subgroup	G/H
center	C₂⁴×C₄	C₂×D₄₇
commutator	C₂×C₄₇	C₂×C₄³
Frattini	C₂⁴	C₂³×D₄₇
Fitting	C₂³×C₄²×C₄₇	C₂
socle, prime radical	C₂⁵×C₄₇	C₂³
cosocle	C₂⁴×C₄₇	C₂⁴
hypercenter	C₂³×C₄²	D₄₇
hypocenter	C₄₇	C₂×C₄×#95
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴×C₄ ◁ C₂³×C₄²

Complements

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

N	H ≅ G/N	type
3. C₄×C₄₇⋊#95	C₂	direct (N × H)
8. C₂²×C₄×Dic₄₇	C₄	semidirect
10. C₂×C₄₇⋊#95	C₄	direct (N × H)
15. C₂²×C₄²×C₄₇	C₄	semidirect
26. C₂×C₄×Dic₄₇	C₂×C₄	semidirect
27. C₄₇⋊#95	C₂×C₄	direct (N × H)
42. C₂×C₄²×C₄₇	C₂×C₄	semidirect
57. C₂²×C₄×C₄₇	C₄²	semidirect
76. C₂²×Dic₄₇	C₄²	semidirect
104. C₂×C₄×C₄₇	#95	semidirect
106. C₂×C₄×C₄₇	C₂×C₄²	semidirect
116. C₂×Dic₄₇	C₂×C₄²	semidirect
138. C₄×C₄₇	C₂×#95	semidirect
144. C₂×C₄₇	C₄×#95	semidirect
160. C₂²×C₄²	Dic₄₇	semidirect
164. C₄₇	C₂×C₄×#95	semidirect
189. C₂×C₄²	C₂×Dic₄₇	semidirect
215. C₂²×C₄	C₄×Dic₄₇	semidirect
258. C₂×C₄	C₄₇⋊#95	direct (N × H)
260. C₂×C₄	C₂×C₄×Dic₄₇	semidirect
286. C₄	C₂×C₄₇⋊#95	direct (N × H)
287. C₂	C₄×C₄₇⋊#95	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×Dic₄₇	2
C₂²×C₄₇⋊#95	2
C₄×C₄₇⋊#95	2
C₂³×C₄²×C₄₇	2
C₂×C₄×#95	47

Subgroups — C2×C4×C47⋊#95 #26137347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₄₇⋊#95 #26137347