Subgroups — C₄₇×#13847 #26053545

Order 12032.

2574 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₇×#376	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1445	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1439	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1438	C₂	1	2	yes	maximal
8	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₄₇	—	2	4	no	—
11	C₂×C₄×D₄×C₄₇	—	2	4	no	—
12	C₂×C₄×D₄×C₄₇	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	—
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
21	C₄×C₂²⋊C₄×C₄₇	—	2	16	no	—
22	C₄₇×#376	—	2	4	no	—
23	C₂×#95×C₄₇	C₂²	1	2	yes	—
24	C₂×#95×C₄₇	C₂²	1	2	yes	—
25	C₂×#95×C₄₇	C₂²	1	8	yes	—
26	C₂×#95×C₄₇	C₂²	1	2	yes	—
27	C₂⁵×C₄₇	C₂³	1	2	yes	—
28	C₂²×D₄×C₄₇	—	2	8	no	—
29	C₂²×D₄×C₄₇	—	2	2	no	—
30	C₂²×D₄×C₄₇	—	2	2	no	—
31	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
32	C₂³×C₄×C₄₇	—	2	4	no	—
33	C₂³×C₄×C₄₇	—	2	4	no	—
34	C₂³×C₄×C₄₇	—	2	8	no	—
35	C₂³×C₄×C₄₇	—	2	8	no	—
36	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	—
37	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₄×D₄×C₄₇	—	2	32	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
48	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
49	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
50	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
51	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
54	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
55	C₂×C₄²×C₄₇	—	2	4	no	—
56	C₂×C₄²×C₄₇	—	2	4	no	—
57	C₂×C₄²×C₄₇	—	2	8	no	—
58	C₂×C₄²×C₄₇	—	2	4	no	—
59	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₄²×C₄₇	D₄	1	4	yes	—
61	C₂×C₄²×C₄₇	D₄	1	4	yes	—
62	C₂×C₄²×C₄₇	D₄	1	8	yes	complemented
63	#95×C₄₇	—	2	4	no	—
64	#95×C₄₇	—	2	4	no	—
65	#95×C₄₇	—	2	16	no	—
66	#95×C₄₇	—	2	4	no	—
67	C₂⁴×C₄₇	—	2	4	no	—
68	C₂⁴×C₄₇	—	2	2	no	—
69	C₂⁴×C₄₇	—	2	2	no	—
70	C₂⁴×C₄₇	—	2	8	no	—
71	C₂⁴×C₄₇	—	2	4	no	—
72	C₂⁴×C₄₇	—	2	4	no	—
73	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
74	C₂⁴×C₄₇	#41	1	8	yes	—
75	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
76	C₂×D₄×C₄₇	—	2	16	no	—
77	C₂×D₄×C₄₇	—	2	16	no	—
78	C₂×D₄×C₄₇	—	2	16	no	—
79	C₂×D₄×C₄₇	—	2	8	no	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	8	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	8	no	—
90	C₂²×C₄×C₄₇	—	2	8	no	—
91	C₂²×C₄×C₄₇	—	2	8	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	16	no	—
95	C₂²×C₄×C₄₇	—	2	32	no	—
96	C₂²×C₄×C₄₇	—	4	16	no	—
97	C₂²×C₄×C₄₇	—	4	8	no	—
98	C₂²×C₄×C₄₇	—	4	8	no	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₄₇	#41	1	8	yes	—
112	C₂²×C₄×C₄₇	#41	1	4	yes	—
113	C₄⋊C₄×C₄₇	—	2	16	no	—
114	C₄⋊C₄×C₄₇	—	2	8	no	—
115	C₂²⋊C₄×C₄₇	—	2	64	no	—
116	C₂²⋊C₄×C₄₇	—	2	16	no	—
117	C₄²×C₄₇	—	2	16	no	—
118	C₄²×C₄₇	—	4	8	no	—
119	C₄²×C₄₇	C₂²⋊C₄	1	16	yes	complemented
120	C₂³×C₄₇	—	2	4	no	—
121	C₂³×C₄₇	—	2	4	no	—
122	C₂³×C₄₇	—	2	8	no	—
123	C₂³×C₄₇	—	2	8	no	—
124	C₂³×C₄₇	—	2	16	no	—
125	C₂³×C₄₇	—	2	8	no	—
126	C₂³×C₄₇	—	2	8	no	—
127	C₂³×C₄₇	—	2	16	no	—
128	C₂³×C₄₇	—	4	4	no	—
129	C₂³×C₄₇	—	4	8	no	—
130	C₂³×C₄₇	—	4	4	no	—
131	C₂³×C₄₇	—	4	2	no	—
132	C₂³×C₄₇	—	4	8	no	—
133	C₂³×C₄₇	—	4	2	no	—
134	C₂³×C₄₇	—	4	4	no	—
135	C₂³×C₄₇	#117	1	8	yes	—
136	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
137	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
138	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
140	C₂³×C₄₇	C₂×#41	1	4	yes	—
141	C₂³×C₄₇	C₂×#41	1	2	yes	—
142	C₂³×C₄₇	C₂×#41	1	4	yes	—
143	D₄×C₄₇	—	2	32	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	8	no	—
152	C₂×C₄×C₄₇	—	2	8	no	—
153	C₂×C₄×C₄₇	—	2	16	no	—
154	C₂×C₄×C₄₇	—	2	16	no	—
155	C₂×C₄×C₄₇	—	2	8	no	—
156	C₂×C₄×C₄₇	—	4	4	no	—
157	C₂×C₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	—	4	8	no	—
159	C₂×C₄×C₄₇	—	4	4	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	8	no	—
162	C₂×C₄×C₄₇	—	4	4	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	4	no	—
165	C₂×C₄×C₄₇	—	4	32	no	—
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
167	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
168	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
169	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
170	C₂×C₄×C₄₇	#121	1	8	yes	—
171	C₂×C₄×C₄₇	#124	1	4	yes	—
172	C₂×C₄×C₄₇	#127	1	4	yes	—
173	#13847	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₇	—	2	8	no	—
175	C₂²×C₄₇	—	2	16	no	—
176	C₂²×C₄₇	—	4	16	no	—
177	C₂²×C₄₇	—	4	8	no	—
178	C₂²×C₄₇	—	4	8	no	—
179	C₂²×C₄₇	—	4	8	no	—
180	C₂²×C₄₇	—	4	4	no	—
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×#117	1	2	yes	—
184	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
185	C₂²×C₄₇	C₄×#41	1	2	yes	—
186	C₂²×C₄₇	C₂×#121	1	2	yes	—
187	C₂²×C₄₇	#525	1	2	yes	—
188	C₂²×C₄₇	#525	1	8	yes	—
189	C₂²×C₄₇	#525	1	2	yes	—
190	C₂²×C₄₇	#525	1	2	yes	—
191	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
192	C₂²×C₄₇	#529	1	8	yes	—
193	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
194	C₂²×C₄₇	#532	1	2	yes	—
195	C₄×C₄₇	—	2	4	no	—
196	C₄×C₄₇	—	2	4	no	—
197	C₄×C₄₇	—	4	8	no	—
198	C₄×C₄₇	—	4	8	no	—
199	C₄×C₄₇	—	4	4	no	—
200	C₄×C₄₇	#390	1	8	yes	—
201	C₂²×C₄×D₄	C₂×C₄₇	1	1	yes	characteristic
202	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
203	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	4	yes	complemented
204	C₂×#376	C₂×C₄₇	1	1	yes	characteristic, complemented
205	#1445	C₂×C₄₇	1	2	yes	complemented
206	#1439	C₂×C₄₇	1	4	yes	complemented
207	#1438	C₂×C₄₇	1	2	yes	—
208	C₂×C₄₇	—	4	8	no	—
209	C₂×C₄₇	#2280	1	1	yes	characteristic
210	C₂×C₄₇	#2290	1	4	yes	—
211	C₂×C₄₇	C₂×#390	1	1	yes	characteristic
212	C₂×C₄₇	#2297	1	1	yes	characteristic
213	C₂×C₄₇	#2392	1	4	yes	—
214	C₂×C₄₇	#2397	1	2	yes	—
215	C₂×C₄₇	#2398	1	2	yes	—
216	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
217	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
218	C₂×C₄×D₄	—	2	4	no	—
219	C₂×C₄×D₄	—	2	4	no	—
220	C₂×C₄×D₄	C₄×C₄₇	1	8	yes	complemented
221	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
223	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	—
224	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
225	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
226	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
227	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
228	C₄×C₄⋊C₄	—	2	4	no	—
229	C₄×C₂²⋊C₄	—	2	16	no	—
230	#376	—	2	4	no	—
231	C₂×#95	C₂²×C₄₇	1	2	yes	—
232	C₂×#95	C₂²×C₄₇	1	2	yes	—
233	C₂×#95	C₂²×C₄₇	1	2	yes	—
234	C₂×#95	C₂²×C₄₇	1	8	yes	—
235	C₄₇	#13847	1	1	yes	characteristic, direct product factor, Sylow
236	C₂⁵	C₂³×C₄₇	1	2	yes	—
237	C₂²×D₄	—	2	8	no	—
238	C₂²×D₄	—	2	2	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
241	C₂³×C₄	—	2	4	no	—
242	C₂³×C₄	—	2	4	no	—
243	C₂³×C₄	—	2	8	no	—
244	C₂³×C₄	—	2	8	no	—
245	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	—
246	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
247	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
248	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
249	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
252	C₄×D₄	—	2	32	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	8	no	—
257	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
258	C₂×C₂²⋊C₄	—	2	16	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	—	2	4	no	—
261	C₂×C₂²⋊C₄	—	2	16	no	—
262	C₂×C₂²⋊C₄	—	2	16	no	—
263	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	8	yes	—
264	C₂×C₄²	—	2	4	no	—
265	C₂×C₄²	—	2	4	no	—
266	C₂×C₄²	—	2	8	no	—
267	C₂×C₄²	—	2	4	no	—
268	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
269	C₂×C₄²	D₄×C₄₇	1	4	yes	—
270	C₂×C₄²	D₄×C₄₇	1	4	yes	—
271	C₂×C₄²	D₄×C₄₇	1	8	yes	complemented
272	#95	—	2	4	no	—
273	#95	—	2	4	no	—
274	#95	—	2	16	no	—
275	#95	—	2	4	no	—
276	C₂⁴	—	2	4	no	—
277	C₂⁴	—	2	2	no	—
278	C₂⁴	—	2	2	no	—
279	C₂⁴	—	2	8	no	—
280	C₂⁴	—	2	4	no	—
281	C₂⁴	—	2	4	no	—
282	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
283	C₂⁴	#41×C₄₇	1	8	yes	—
284	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
285	C₂×D₄	—	2	16	no	—
286	C₂×D₄	—	2	16	no	—
287	C₂×D₄	—	2	16	no	—
288	C₂×D₄	—	2	8	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	8	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	16	no	—
304	C₂²×C₄	—	2	32	no	—
305	C₂²×C₄	—	4	16	no	—
306	C₂²×C₄	—	4	8	no	—
307	C₂²×C₄	—	4	8	no	—
308	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
309	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
313	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
320	C₂²×C₄	#41×C₄₇	1	8	yes	—
321	C₂²×C₄	#41×C₄₇	1	4	yes	—
322	C₄⋊C₄	—	2	16	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	2	64	no	—
325	C₂²⋊C₄	—	2	16	no	—
326	C₄²	—	2	16	no	—
327	C₄²	—	4	8	no	—
328	C₄²	C₂²⋊C₄×C₄₇	1	16	yes	complemented
329	C₂³	—	2	4	no	—
330	C₂³	—	2	4	no	—
331	C₂³	—	2	8	no	—
332	C₂³	—	2	8	no	—
333	C₂³	—	2	16	no	—
334	C₂³	—	2	8	no	—
335	C₂³	—	2	8	no	—
336	C₂³	—	2	16	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	4	8	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	8	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	4	no	—
344	C₂³	#117×C₄₇	1	8	yes	—
345	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
346	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
347	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
348	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
349	C₂³	C₂×#41×C₄₇	1	4	yes	—
350	C₂³	C₂×#41×C₄₇	1	2	yes	—
351	C₂³	C₂×#41×C₄₇	1	4	yes	—
352	D₄	—	2	32	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	16	no	—
363	C₂×C₄	—	2	16	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	32	no	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
376	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
377	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
378	C₂×C₄	C₄×D₄×C₄₇	1	8	yes	—
379	C₂×C₄	#121×C₄₇	1	8	yes	—
380	C₂×C₄	#124×C₄₇	1	4	yes	—
381	C₂×C₄	#127×C₄₇	1	4	yes	—
382	C₂²	—	2	8	no	—
383	C₂²	—	2	16	no	—
384	C₂²	—	4	8	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	4	16	no	—
388	C₂²	—	4	8	no	—
389	C₂²	—	4	8	no	—
390	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
391	C₂²	C₂×#117×C₄₇	1	2	yes	—
392	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
393	C₂²	C₄×#41×C₄₇	1	2	yes	—
394	C₂²	C₂×#121×C₄₇	1	2	yes	—
395	C₂²	C₄₇×#525	1	2	yes	—
396	C₂²	C₄₇×#525	1	2	yes	—
397	C₂²	C₄₇×#525	1	8	yes	—
398	C₂²	C₄₇×#525	1	2	yes	—
399	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
400	C₂²	C₄₇×#529	1	8	yes	—
401	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
402	C₂²	C₄₇×#532	1	2	yes	—
403	C₄	—	2	4	no	—
404	C₄	—	2	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	8	no	—
407	C₄	—	4	8	no	—
408	C₄	C₄₇×#390	1	8	yes	—
409	C₂	—	4	8	no	—
410	C₂	C₄₇×#2280	1	1	yes	characteristic
411	C₂	C₄₇×#2290	1	4	yes	—
412	C₂	C₂×C₄₇×#390	1	1	yes	characteristic
413	C₂	C₄₇×#2297	1	1	yes	characteristic
414	C₂	C₄₇×#2392	1	4	yes	—
415	C₂	C₄₇×#2397	1	2	yes	—
416	C₂	C₄₇×#2398	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₇	C₂³
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
socle	C₂⁴×C₄₇	C₂⁴
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₄⋊C₄×C₄₇	C₂	semidirect
3. C₂×C₄×C₂²⋊C₄×C₄₇	C₂	semidirect
4. C₂×C₄₇×#376	C₂	semidirect
5. C₄₇×#1445	C₂	semidirect
6. C₄₇×#1439	C₂	semidirect
12. C₂×C₄×D₄×C₄₇	C₄	semidirect
62. C₂×C₄²×C₄₇	D₄	semidirect
119. C₄²×C₄₇	C₂²⋊C₄	semidirect
173. #13847	C₄₇	direct (N × H)
202. C₂×C₄×C₄⋊C₄	C₂×C₄₇	semidirect
203. C₂×C₄×C₂²⋊C₄	C₂×C₄₇	semidirect
204. C₂×#376	C₂×C₄₇	semidirect
205. #1445	C₂×C₄₇	semidirect
206. #1439	C₂×C₄₇	semidirect
220. C₂×C₄×D₄	C₄×C₄₇	semidirect
235. C₄₇	#13847	direct (N × H)
271. C₂×C₄²	D₄×C₄₇	semidirect
328. C₄²	C₂²⋊C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₇	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₂×C₄₇×#376	2
C₄₇×#1445	2
C₄₇×#1439	2
C₄₇×#1438	2
#13847	47

Subgroups — C47×#13847 #26053545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#13847 #26053545