Subgroups — C₂×#120×Dic₄₇ #26374693

Order 12032.

8582 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×Dic₄₇	C₂	1	3	yes	maximal, complemented
3	#120×Dic₄₇	C₂	1	16	yes	maximal, direct product factor
4	C₂×#15689003	C₂	1	3	yes	maximal, complemented
5	C₂×#15688998	C₂	1	3	yes	maximal, complemented
6	C₂×#15688979	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂²⋊C₄×Dic₄₇	C₂	1	3	yes	maximal, complemented
8	C₂²×#120×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂⁴×Dic₄₇	—	2	24	no	—
10	C₂⁴×Dic₄₇	C₂²	1	3	yes	—
11	C₂⁴×Dic₄₇	C₂²	1	3	yes	—
12	C₂⁴×Dic₄₇	C₂²	1	8	yes	complemented
13	C₂⁴×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
14	C₂×D₄×Dic₄₇	—	2	24	no	—
15	C₂×D₄×Dic₄₇	C₂²	1	24	yes	complemented
16	C₂²×C₄⋊Dic₄₇	C₂²	1	3	yes	complemented
17	C₂²×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
18	C₂²×C₂²⋊Dic₄₇	C₂²	1	3	yes	—
19	C₂²×C₂²⋊Dic₄₇	C₂²	1	3	yes	complemented
20	C₂²×C₄×Dic₄₇	C₂²	1	3	yes	complemented
21	#15689003	C₂²	1	24	yes	complemented
22	#15688998	C₂²	1	24	yes	complemented
23	#15688979	C₂²	1	8	yes	complemented
24	C₂²⋊C₄×Dic₄₇	C₂²	1	24	yes	complemented
25	C₂×C₄₇⋊#95	C₂²	1	6	yes	complemented
26	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
27	C₂³×D₄×C₄₇	C₂²	1	3	yes	—
28	C₂×#120×C₄₇	C₄	1	16	yes	complemented
29	C₂×#120×C₄₇	C₂²	1	8	yes	—
30	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	3	yes	—
31	C₂³×Dic₄₇	—	2	128	no	—
32	C₂³×Dic₄₇	—	2	12	no	—
33	C₂³×Dic₄₇	—	2	24	no	—
34	C₂³×Dic₄₇	—	2	24	no	—
35	C₂³×Dic₄₇	—	2	96	no	—
36	C₂³×Dic₄₇	—	2	12	no	—
37	C₂³×Dic₄₇	D₄	1	24	yes	complemented
38	C₂³×Dic₄₇	C₂³	1	3	yes	—
39	C₂³×Dic₄₇	C₂³	1	12	yes	—
40	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
41	C₂³×Dic₄₇	C₂³	1	3	yes	—
42	C₂³×Dic₄₇	C₂³	1	12	yes	—
43	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
44	C₂³×Dic₄₇	C₂³	1	4	yes	complemented
45	D₄×Dic₄₇	—	2	96	no	—
46	C₂×C₄⋊Dic₄₇	—	2	12	no	—
47	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	complemented
48	C₂×C₂²⋊Dic₄₇	—	2	12	no	—
49	C₂×C₂²⋊Dic₄₇	—	2	12	no	—
50	C₂×C₂²⋊Dic₄₇	—	2	12	no	—
51	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	—
52	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	—
53	C₂×C₂²⋊Dic₄₇	C₂³	1	12	yes	complemented
54	C₂×C₄×Dic₄₇	—	2	12	no	—
55	C₂×C₄×Dic₄₇	C₂³	1	12	yes	complemented
56	C₄₇⋊#95	C₂³	1	24	yes	complemented
57	C₂⁵×C₄₇	—	2	12	no	—
58	C₂⁵×C₄₇	—	2	12	no	—
59	C₂⁵×C₄₇	C₂×C₄	1	8	yes	complemented
60	C₂⁵×C₄₇	C₂³	1	4	yes	—
61	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
62	C₂⁵×C₄₇	C₂³	1	3	yes	—
63	C₂²×D₄×C₄₇	—	2	12	no	—
64	C₂²×D₄×C₄₇	—	2	12	no	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	24	yes	complemented
66	C₂²×D₄×C₄₇	C₂³	1	12	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
68	#120×C₄₇	C₂×C₄	1	64	yes	complemented
69	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	24	yes	complemented
70	C₂×C₂²⋊C₄×C₄₇	C₂³	1	12	yes	—
71	C₂⁴×C₄₇	—	2	96	no	—
72	C₂⁴×C₄₇	—	2	32	no	—
73	C₂⁴×C₄₇	—	2	96	no	—
74	C₂⁴×C₄₇	—	2	24	no	—
75	C₂⁴×C₄₇	—	2	12	no	—
76	C₂⁴×C₄₇	—	2	24	no	—
77	C₂⁴×C₄₇	—	2	12	no	—
78	C₂⁴×C₄₇	—	2	6	no	—
79	C₂⁴×C₄₇	—	2	6	no	—
80	C₂⁴×C₄₇	C₂²×C₄	1	12	yes	—
81	C₂⁴×C₄₇	C₂²×C₄	1	16	yes	complemented
82	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	complemented
83	C₂⁴×C₄₇	C₂×D₄	1	12	yes	—
84	C₂⁴×C₄₇	#41	1	12	yes	—
85	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
86	C₂⁴×C₄₇	C₂⁴	1	6	yes	—
87	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
88	C₂×D₄×C₄₇	—	2	96	no	—
89	C₂×D₄×C₄₇	—	2	24	no	—
90	C₂×D₄×C₄₇	—	2	24	no	—
91	C₂×D₄×C₄₇	C₂²×C₄	1	48	yes	complemented
92	C₂²×C₄×C₄₇	—	2	6	no	—
93	C₂²×C₄×C₄₇	—	2	6	no	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	12	yes	complemented
95	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
96	C₂²×Dic₄₇	—	2	96	no	—
97	C₂²×Dic₄₇	—	2	256	no	—
98	C₂²×Dic₄₇	—	2	24	no	—
99	C₂²×Dic₄₇	—	2	12	no	—
100	C₂²×Dic₄₇	—	2	96	no	—
101	C₂²×Dic₄₇	—	2	48	no	—
102	C₂²×Dic₄₇	—	2	48	no	—
103	C₂²×Dic₄₇	—	2	6	no	—
104	C₂²×Dic₄₇	—	2	6	no	—
105	C₂²×Dic₄₇	—	2	12	no	—
106	C₂²×Dic₄₇	—	2	24	no	—
107	C₂²×Dic₄₇	—	4	16	no	—
108	C₂²×Dic₄₇	C₂×D₄	1	12	yes	—
109	C₂²×Dic₄₇	C₂×D₄	1	12	yes	—
110	C₂²×Dic₄₇	C₂×D₄	1	48	yes	complemented
111	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
112	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
113	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
114	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
115	C₂²⋊C₄×C₄₇	C₂²×C₄	1	48	yes	complemented
116	C₂²⋊Dic₄₇	—	2	24	no	—
117	C₂²⋊Dic₄₇	—	2	24	no	—
118	C₂²⋊Dic₄₇	—	2	24	no	—
119	C₄⋊Dic₄₇	—	2	24	no	—
120	C₄×Dic₄₇	—	2	24	no	—
121	C₂³×C₄₇	—	2	32	no	—
122	C₂³×C₄₇	—	2	96	no	—
123	C₂³×C₄₇	—	2	256	no	—
124	C₂³×C₄₇	—	2	48	no	—
125	C₂³×C₄₇	—	2	96	no	—
126	C₂³×C₄₇	—	2	24	no	—
127	C₂³×C₄₇	—	2	24	no	—
128	C₂³×C₄₇	—	2	48	no	—
129	C₂³×C₄₇	—	2	12	no	—
130	C₂³×C₄₇	—	2	12	no	—
131	C₂³×C₄₇	—	2	24	no	—
132	C₂³×C₄₇	—	2	6	no	—
133	C₂³×C₄₇	—	2	6	no	—
134	C₂³×C₄₇	—	4	4	no	—
135	C₂³×C₄₇	—	4	12	no	—
136	C₂³×C₄₇	C₄×D₄	1	48	yes	complemented
137	C₂³×C₄₇	C₂³×C₄	1	12	yes	—
138	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
139	C₂³×C₄₇	C₂³×C₄	1	4	yes	complemented
140	C₂³×C₄₇	C₂²×D₄	1	12	yes	—
141	C₂³×C₄₇	C₂²×D₄	1	6	yes	—
142	C₂³×C₄₇	C₂×#41	1	12	yes	—
143	C₂³×C₄₇	C₂×#41	1	6	yes	—
144	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
145	D₄×C₄₇	—	2	96	no	—
146	C₂×C₄×C₄₇	—	2	24	no	—
147	C₂×C₄×C₄₇	—	2	6	no	—
148	C₂×C₄×C₄₇	—	2	6	no	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	12	yes	complemented
150	C₂×Dic₄₇	—	2	96	no	—
151	C₂×Dic₄₇	—	2	24	no	—
152	C₂×Dic₄₇	—	2	12	no	—
153	C₂×Dic₄₇	—	2	96	no	—
154	C₂×Dic₄₇	—	2	6	no	—
155	C₂×Dic₄₇	—	2	6	no	—
156	C₂×Dic₄₇	—	2	12	no	—
157	C₂×Dic₄₇	—	4	4	no	—
158	C₂×Dic₄₇	—	4	12	no	—
159	C₂×Dic₄₇	—	4	16	no	—
160	C₂×Dic₄₇	#120	1	16	yes	direct product factor
161	C₂×Dic₄₇	C₂²×D₄	1	12	yes	—
162	C₂×Dic₄₇	C₂²×D₄	1	12	yes	—
163	C₂×C₄×#120	—	47	1	no	maximal, Sylow
164	C₂²×C₄₇	—	2	128	no	—
165	C₂²×C₄₇	—	2	24	no	—
166	C₂²×C₄₇	—	2	12	no	—
167	C₂²×C₄₇	—	2	12	no	—
168	C₂²×C₄₇	—	2	24	no	—
169	C₂²×C₄₇	—	2	96	no	—
170	C₂²×C₄₇	—	2	12	no	—
171	C₂²×C₄₇	—	4	2	no	—
172	C₂²×C₄₇	—	4	6	no	—
173	C₂²×C₄₇	—	4	16	no	—
174	C₂²×C₄₇	C₂×C₄×D₄	1	12	yes	—
175	C₂²×C₄₇	C₂×C₄×D₄	1	24	yes	complemented
176	C₂²×C₄₇	C₂×#120	1	4	yes	—
177	C₂²×C₄₇	#525	1	12	yes	—
178	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
179	C₂²×C₄₇	C₂³×D₄	1	3	yes	—
180	C₂²×C₄₇	C₂²×#41	1	3	yes	—
181	C₄×C₄₇	—	2	12	no	—
182	Dic₄₇	—	2	12	no	—
183	Dic₄₇	—	4	2	no	—
184	Dic₄₇	—	4	6	no	—
185	Dic₄₇	C₂×#120	1	8	yes	direct product factor
186	C₂⁵×C₄	—	47	1	no	—
187	C₂²×#120	D₄₇	1	1	yes	characteristic
188	C₂²×C₄×D₄	—	47	3	no	—
189	C₄×#120	—	47	16	no	—
190	C₂×#386	—	47	3	no	—
191	C₂×#385	—	47	3	no	—
192	C₂×#379	—	47	1	no	—
193	C₂×C₄×C₂²⋊C₄	—	47	3	no	—
194	C₂×C₄₇	—	2	24	no	—
195	C₂×C₄₇	—	4	4	no	—
196	C₂×C₄₇	C₄×#120	1	8	yes	complemented
197	C₂×C₄₇	C₂²×C₄×D₄	1	3	yes	—
198	C₂×C₄₇	C₂²×#120	1	1	yes	characteristic
199	C₂×C₄₇	C₂×#525	1	3	yes	—
200	C₂⁶	C₂×D₄₇	1	1	yes	characteristic
201	C₂³×D₄	C₂×D₄₇	1	3	yes	—
202	C₂⁴×C₄	—	47	3	no	—
203	C₂⁴×C₄	—	47	3	no	—
204	C₂⁴×C₄	—	47	8	no	—
205	C₂⁴×C₄	—	47	1	no	—
206	C₂⁴×C₄	—	94	24	no	—
207	C₂×#120	Dic₄₇	1	16	yes	direct product factor
208	C₂×#120	C₂×D₄₇	1	8	yes	—
209	C₂×C₄×D₄	—	47	24	no	—
210	C₂×C₄×D₄	—	94	24	no	—
211	C₂²×C₄⋊C₄	—	47	3	no	—
212	C₂²×C₂²⋊C₄	—	47	3	no	—
213	C₂²×C₂²⋊C₄	—	47	3	no	—
214	C₂²×C₂²⋊C₄	—	47	3	no	—
215	C₂²×C₂²⋊C₄	C₂×D₄₇	1	3	yes	—
216	C₂²×C₄²	—	47	3	no	—
217	#386	—	47	24	no	—
218	#385	—	47	24	no	—
219	#379	—	47	8	no	—
220	C₄×C₂²⋊C₄	—	47	24	no	—
221	C₂×#95	—	47	6	no	—
222	C₄₇	C₂×C₄×#120	1	1	yes	characteristic, complemented, Sylow
223	C₂⁵	—	2	12	no	—
224	C₂⁵	—	2	12	no	—
225	C₂⁵	C₂×Dic₄₇	1	8	yes	complemented
226	C₂⁵	C₂²×D₄₇	1	4	yes	—
227	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
228	C₂⁵	C₂²×D₄₇	1	3	yes	—
229	C₂²×D₄	—	2	12	no	—
230	C₂²×D₄	—	2	12	no	—
231	C₂²×D₄	C₂×Dic₄₇	1	24	yes	complemented
232	C₂²×D₄	C₂²×D₄₇	1	12	yes	—
233	C₂³×C₄	—	47	1	no	—
234	C₂³×C₄	—	47	24	no	—
235	C₂³×C₄	—	47	12	no	—
236	C₂³×C₄	—	47	3	no	—
237	C₂³×C₄	—	47	4	no	—
238	C₂³×C₄	—	47	12	no	—
239	C₂³×C₄	—	47	3	no	—
240	C₂³×C₄	—	47	1	no	—
241	C₂³×C₄	—	94	24	no	—
242	C₂³×C₄	—	94	24	no	—
243	C₂³×C₄	—	94	96	no	—
244	C₂³×C₄	—	94	12	no	—
245	C₂³×C₄	—	94	128	no	—
246	C₂³×C₄	—	94	12	no	—
247	C₂³×C₄	C₂²×D₄₇	1	3	yes	—
248	#120	C₂×Dic₄₇	1	64	yes	direct product factor
249	C₄×D₄	—	94	96	no	—
250	C₂×C₄⋊C₄	—	47	12	no	—
251	C₂×C₄⋊C₄	—	94	12	no	—
252	C₂×C₂²⋊C₄	—	47	12	no	—
253	C₂×C₂²⋊C₄	—	47	12	no	—
254	C₂×C₂²⋊C₄	—	47	12	no	—
255	C₂×C₂²⋊C₄	—	94	12	no	—
256	C₂×C₂²⋊C₄	—	94	12	no	—
257	C₂×C₂²⋊C₄	—	94	12	no	—
258	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	24	yes	complemented
259	C₂×C₂²⋊C₄	C₂²×D₄₇	1	12	yes	—
260	C₂×C₄²	—	47	12	no	—
261	C₂×C₄²	—	94	12	no	—
262	#95	—	47	24	no	—
263	C₂⁴	—	2	32	no	—
264	C₂⁴	—	2	96	no	—
265	C₂⁴	—	2	96	no	—
266	C₂⁴	—	2	24	no	—
267	C₂⁴	—	2	12	no	—
268	C₂⁴	—	2	24	no	—
269	C₂⁴	—	2	12	no	—
270	C₂⁴	—	2	6	no	—
271	C₂⁴	—	2	6	no	—
272	C₂⁴	D₄×D₄₇	1	12	yes	—
273	C₂⁴	#10625352	1	12	yes	—
274	C₂⁴	C₂²×Dic₄₇	1	12	yes	—
275	C₂⁴	C₂²×Dic₄₇	1	16	yes	complemented
276	C₂⁴	C₂²×Dic₄₇	1	4	yes	complemented
277	C₂⁴	C₂³×D₄₇	1	2	yes	—
278	C₂⁴	C₂³×D₄₇	1	6	yes	—
279	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
280	C₂×D₄	—	2	96	no	—
281	C₂×D₄	—	2	24	no	—
282	C₂×D₄	—	2	24	no	—
283	C₂×D₄	C₂²×Dic₄₇	1	48	yes	complemented
284	C₂²×C₄	—	2	6	no	—
285	C₂²×C₄	—	2	6	no	—
286	C₂²×C₄	—	47	12	no	—
287	C₂²×C₄	—	47	2	no	—
288	C₂²×C₄	—	47	12	no	—
289	C₂²×C₄	—	47	48	no	—
290	C₂²×C₄	—	47	6	no	—
291	C₂²×C₄	—	47	6	no	—
292	C₂²×C₄	—	47	2	no	—
293	C₂²×C₄	—	94	96	no	—
294	C₂²×C₄	—	94	48	no	—
295	C₂²×C₄	—	94	48	no	—
296	C₂²×C₄	—	94	24	no	—
297	C₂²×C₄	—	94	256	no	—
298	C₂²×C₄	—	94	96	no	—
299	C₂²×C₄	—	94	24	no	—
300	C₂²×C₄	—	94	12	no	—
301	C₂²×C₄	—	94	6	no	—
302	C₂²×C₄	—	94	6	no	—
303	C₂²×C₄	—	94	12	no	—
304	C₂²×C₄	—	188	16	no	—
305	C₂²×C₄	C₂²×Dic₄₇	1	12	yes	complemented
306	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
307	C₄⋊C₄	—	94	24	no	—
308	C₂²⋊C₄	—	94	24	no	—
309	C₂²⋊C₄	—	94	24	no	—
310	C₂²⋊C₄	—	94	24	no	—
311	C₂²⋊C₄	C₂²×Dic₄₇	1	48	yes	complemented
312	C₄²	—	94	24	no	—
313	C₂³	—	2	32	no	—
314	C₂³	—	2	96	no	—
315	C₂³	—	2	256	no	—
316	C₂³	—	2	48	no	—
317	C₂³	—	2	96	no	—
318	C₂³	—	2	24	no	—
319	C₂³	—	2	24	no	—
320	C₂³	—	2	48	no	—
321	C₂³	—	2	12	no	—
322	C₂³	—	2	12	no	—
323	C₂³	—	2	24	no	—
324	C₂³	—	2	6	no	—
325	C₂³	—	2	6	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	4	12	no	—
328	C₂³	D₄×Dic₄₇	1	48	yes	complemented
329	C₂³	C₂³×Dic₄₇	1	12	yes	—
330	C₂³	C₂³×Dic₄₇	1	2	yes	—
331	C₂³	C₂³×Dic₄₇	1	4	yes	complemented
332	C₂³	C₂×D₄×D₄₇	1	12	yes	—
333	C₂³	C₂×D₄×D₄₇	1	6	yes	—
334	C₂³	C₂×#10625352	1	12	yes	—
335	C₂³	C₂×#10625352	1	6	yes	—
336	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
337	D₄	—	2	96	no	—
338	C₂×C₄	—	2	24	no	—
339	C₂×C₄	—	2	6	no	—
340	C₂×C₄	—	2	6	no	—
341	C₂×C₄	—	47	16	no	—
342	C₂×C₄	—	47	12	no	—
343	C₂×C₄	—	47	12	no	—
344	C₂×C₄	—	94	96	no	—
345	C₂×C₄	—	94	96	no	—
346	C₂×C₄	—	94	24	no	—
347	C₂×C₄	—	94	12	no	—
348	C₂×C₄	—	94	6	no	—
349	C₂×C₄	—	94	6	no	—
350	C₂×C₄	—	94	12	no	—
351	C₂×C₄	—	188	16	no	—
352	C₂×C₄	—	188	4	no	—
353	C₂×C₄	—	188	12	no	—
354	C₂×C₄	C₂³×Dic₄₇	1	12	yes	complemented
355	C₂²	—	2	128	no	—
356	C₂²	—	2	24	no	—
357	C₂²	—	2	12	no	—
358	C₂²	—	2	12	no	—
359	C₂²	—	2	24	no	—
360	C₂²	—	2	96	no	—
361	C₂²	—	2	12	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	6	no	—
364	C₂²	—	4	16	no	—
365	C₂²	C₂×D₄×Dic₄₇	1	12	yes	—
366	C₂²	C₂×D₄×Dic₄₇	1	24	yes	complemented
367	C₂²	#120×D₄₇	1	4	yes	—
368	C₂²	#15689629	1	12	yes	—
369	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
370	C₂²	C₂²×D₄×D₄₇	1	3	yes	—
371	C₂²	C₂²×#10625352	1	3	yes	—
372	C₄	—	2	12	no	—
373	C₄	—	47	8	no	—
374	C₄	—	94	12	no	—
375	C₄	—	188	2	no	—
376	C₄	—	188	6	no	—
377	C₂	—	2	24	no	—
378	C₂	—	4	4	no	—
379	C₂	#120×Dic₄₇	1	8	yes	direct product factor
380	C₂	C₂²×D₄×Dic₄₇	1	3	yes	—
381	C₂	C₂×#120×D₄₇	1	1	yes	characteristic
382	C₂	C₂×#15689629	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting, prime radical	C₂²×#120×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
cosocle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#120	D₄₇
hypocenter	C₄₇	C₂×C₄×#120
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#120

Complements

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

N	H ≅ G/N	type
1. C₂⁵×Dic₄₇	C₂	semidirect
2. C₂²×D₄×Dic₄₇	C₂	semidirect
3. #120×Dic₄₇	C₂	direct (N × H)
4. C₂×#15689003	C₂	semidirect
5. C₂×#15688998	C₂	semidirect
6. C₂×#15688979	C₂	semidirect
7. C₂×C₂²⋊C₄×Dic₄₇	C₂	semidirect
12. C₂⁴×Dic₄₇	C₂²	semidirect
13. C₂⁴×Dic₄₇	C₂²	semidirect
15. C₂×D₄×Dic₄₇	C₂²	semidirect
16. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
19. C₂²×C₂²⋊Dic₄₇	C₂²	semidirect
20. C₂²×C₄×Dic₄₇	C₂²	semidirect
21. #15689003	C₂²	semidirect
22. #15688998	C₂²	semidirect
23. #15688979	C₂²	semidirect
24. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
25. C₂×C₄₇⋊#95	C₂²	semidirect
28. C₂×#120×C₄₇	C₄	semidirect
37. C₂³×Dic₄₇	D₄	semidirect
44. C₂³×Dic₄₇	C₂³	semidirect
47. C₂×C₄⋊Dic₄₇	C₂³	semidirect
53. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
55. C₂×C₄×Dic₄₇	C₂³	semidirect
56. C₄₇⋊#95	C₂³	semidirect
59. C₂⁵×C₄₇	C₂×C₄	semidirect
65. C₂²×D₄×C₄₇	C₂×C₄	semidirect
68. #120×C₄₇	C₂×C₄	semidirect
69. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
81. C₂⁴×C₄₇	C₂²×C₄	semidirect
82. C₂⁴×C₄₇	C₂²×C₄	semidirect
91. C₂×D₄×C₄₇	C₂²×C₄	semidirect
94. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
110. C₂²×Dic₄₇	C₂×D₄	semidirect
115. C₂²⋊C₄×C₄₇	C₂²×C₄	semidirect
136. C₂³×C₄₇	C₄×D₄	semidirect
139. C₂³×C₄₇	C₂³×C₄	semidirect
149. C₂×C₄×C₄₇	C₂³×C₄	semidirect
160. C₂×Dic₄₇	#120	direct (N × H)
175. C₂²×C₄₇	C₂×C₄×D₄	semidirect
185. Dic₄₇	C₂×#120	direct (N × H)
196. C₂×C₄₇	C₄×#120	semidirect
207. C₂×#120	Dic₄₇	direct (N × H)
222. C₄₇	C₂×C₄×#120	semidirect
225. C₂⁵	C₂×Dic₄₇	semidirect
231. C₂²×D₄	C₂×Dic₄₇	semidirect
248. #120	C₂×Dic₄₇	direct (N × H)
258. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
275. C₂⁴	C₂²×Dic₄₇	semidirect
276. C₂⁴	C₂²×Dic₄₇	semidirect
283. C₂×D₄	C₂²×Dic₄₇	semidirect
305. C₂²×C₄	C₂²×Dic₄₇	semidirect
311. C₂²⋊C₄	C₂²×Dic₄₇	semidirect
328. C₂³	D₄×Dic₄₇	semidirect
331. C₂³	C₂³×Dic₄₇	semidirect
354. C₂×C₄	C₂³×Dic₄₇	semidirect
366. C₂²	C₂×D₄×Dic₄₇	semidirect
379. C₂	#120×Dic₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×Dic₄₇	2
C₂²×D₄×Dic₄₇	2
#120×Dic₄₇	2
C₂×#15689003	2
C₂×#15688998	2
C₂×#15688979	2
C₂×C₂²⋊C₄×Dic₄₇	2
C₂²×#120×C₄₇	2
C₂×C₄×#120	47

Subgroups — C2×#120×Dic47 #26374693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#120×Dic₄₇ #26374693