Subgroups — C₄₇×#20699 #26060397

Order 12032.

1502 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2280	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1825	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1824	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1823	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1735	C₂	1	4	yes	maximal, complemented
8	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
10	C₂×#117×C₄₇	—	2	4	no	—
11	C₂×#117×C₄₇	—	2	1	no	—
12	C₂×#117×C₄₇	—	2	1	no	—
13	C₂×#117×C₄₇	C₄	1	8	yes	complemented
14	C₂×#117×C₄₇	C₂²	1	2	yes	—
15	C₂×#117×C₄₇	C₂²	1	2	yes	—
16	C₂×#117×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
20	C₂²×C₄²×C₄₇	—	2	1	no	—
21	C₂×C₂²⋊C₈×C₄₇	—	2	4	no	—
22	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
24	C₄₇×#381	—	2	1	no	—
25	C₄₇×#380	C₂²	1	2	yes	—
26	C₄₇×#380	C₂²	1	2	yes	—
27	C₄₇×#379	—	2	1	no	—
28	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
29	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
30	C₄₇×#340	C₂²	1	8	yes	complemented
31	C₄₇×#340	C₂²	1	8	yes	complemented
32	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₇	—	2	8	no	—
34	C₂³×C₄×C₄₇	—	2	1	no	—
35	C₂³×C₄×C₄₇	—	2	1	no	—
36	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	D₄	1	4	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₇	—	2	4	no	—
45	C₂²×C₈×C₄₇	—	2	8	no	—
46	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
47	#117×C₄₇	—	2	8	no	—
48	#117×C₄₇	—	2	8	no	—
49	#117×C₄₇	—	2	4	no	—
50	#117×C₄₇	—	2	4	no	—
51	#117×C₄₇	—	2	8	no	—
52	#117×C₄₇	C₂×C₄	1	8	yes	—
53	#117×C₄₇	C₂×C₄	1	8	yes	—
54	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
60	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	—	2	8	no	—
70	C₂×C₄²×C₄₇	—	2	2	no	—
71	C₂×C₄²×C₄₇	—	2	2	no	—
72	C₂×C₄²×C₄₇	—	2	2	no	—
73	C₂²⋊C₈×C₄₇	—	2	4	no	—
74	C₂²⋊C₈×C₄₇	—	2	4	no	—
75	#95×C₄₇	—	2	2	no	—
76	#95×C₄₇	—	2	2	no	—
77	C₂⁴×C₄₇	—	2	4	no	—
78	C₂⁴×C₄₇	—	2	4	no	—
79	C₂⁴×C₄₇	—	4	2	no	—
80	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
81	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	16	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	16	no	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	4	4	no	—
97	C₂²×C₄×C₄₇	—	4	4	no	—
98	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
99	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
110	C₂²×C₄×C₄₇	#41	1	8	yes	—
111	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₄₇	—	2	4	no	—
113	C₂×C₈×C₄₇	—	2	8	no	—
114	C₂×C₈×C₄₇	—	4	8	no	—
115	C₄⋊C₄×C₄₇	—	2	4	no	—
116	C₄⋊C₄×C₄₇	—	2	4	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	8	no	—
120	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
121	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
122	C₂²⋊C₄×C₄₇	—	2	8	no	—
123	C₂²⋊C₄×C₄₇	—	2	8	no	—
124	C₂²⋊C₄×C₄₇	—	4	4	no	—
125	C₂²⋊C₄×C₄₇	—	4	4	no	—
126	C₂²⋊C₄×C₄₇	—	4	4	no	—
127	C₄²×C₄₇	—	2	8	no	—
128	C₄²×C₄₇	—	2	8	no	—
129	C₄²×C₄₇	—	4	4	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	2	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	8	no	—
138	C₂³×C₄₇	—	2	8	no	—
139	C₂³×C₄₇	—	4	4	no	—
140	C₂³×C₄₇	—	4	16	no	—
141	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂³×C₄₇	#123	1	4	yes	—
145	C₂³×C₄₇	#135	1	4	yes	—
146	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	8	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	8	no	—
155	C₂×C₄×C₄₇	—	2	8	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	4	8	no	—
159	C₂×C₄×C₄₇	—	4	4	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	—	4	8	no	—
162	C₂×C₄×C₄₇	—	4	4	no	—
163	C₂×C₄×C₄₇	—	4	4	no	—
164	C₂×C₄×C₄₇	—	4	4	no	—
165	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₇	#117	1	8	yes	—
169	C₂×C₄×C₄₇	#123	1	8	yes	—
170	C₂×C₄×C₄₇	#123	1	4	yes	—
171	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
174	C₈×C₄₇	—	4	4	no	—
175	#20699	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₄₇	—	2	8	no	—
177	C₂²×C₄₇	—	2	8	no	—
178	C₂²×C₄₇	—	2	2	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	—	4	16	no	—
186	C₂²×C₄₇	—	4	4	no	—
187	C₂²×C₄₇	#381	1	4	yes	—
188	C₂²×C₄₇	#416	1	4	yes	—
189	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
190	C₂²×C₄₇	C₂×#123	1	2	yes	—
191	C₂²×C₄₇	C₂×#135	1	2	yes	—
192	C₂²×C₄₇	#575	1	2	yes	—
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	2	2	no	—
195	C₄×C₄₇	—	4	4	no	—
196	C₄×C₄₇	—	4	4	no	—
197	C₄×C₄₇	—	8	4	no	—
198	C₄×C₄₇	#381	1	4	yes	—
199	C₄×C₄₇	C₂×#117	1	2	yes	—
200	C₄×C₄₇	C₂×#123	1	2	yes	—
201	C₂²×#117	C₂×C₄₇	1	1	yes	characteristic
202	C₂²×C₂²⋊C₈	C₂×C₄₇	1	1	yes	characteristic
203	#2280	C₂×C₄₇	1	1	yes	characteristic
204	#1825	C₂×C₄₇	1	4	yes	complemented
205	#1824	C₂×C₄₇	1	2	yes	complemented
206	#1823	C₂×C₄₇	1	2	yes	complemented
207	#1735	C₂×C₄₇	1	4	yes	complemented
208	C₂×C₄₇	—	2	4	no	—
209	C₂×C₄₇	—	2	4	no	—
210	C₂×C₄₇	—	4	2	no	—
211	C₂×C₄₇	C₂×#381	1	1	yes	characteristic
212	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
213	C₂×C₄₇	#2896	1	1	yes	characteristic
214	C₂×C₄₇	#3091	1	4	yes	—
215	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
216	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
217	C₂×#117	—	2	4	no	—
218	C₂×#117	—	2	1	no	—
219	C₂×#117	—	2	1	no	—
220	C₂×#117	C₄×C₄₇	1	8	yes	complemented
221	C₂×#117	C₂²×C₄₇	1	2	yes	—
222	C₂×#117	C₂²×C₄₇	1	2	yes	—
223	C₂×#117	C₂²×C₄₇	1	2	yes	—
224	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
226	C₂²×C₂²⋊C₄	—	2	1	no	—
227	C₂²×C₄²	—	2	1	no	—
228	C₂×C₂²⋊C₈	—	2	4	no	—
229	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
230	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
231	#381	—	2	1	no	—
232	#380	C₂²×C₄₇	1	2	yes	—
233	#380	C₂²×C₄₇	1	2	yes	—
234	#379	—	2	1	no	—
235	C₄×C₂²⋊C₄	—	2	1	no	—
236	C₄×C₂²⋊C₄	—	2	1	no	—
237	#340	C₂²×C₄₇	1	8	yes	complemented
238	#340	C₂²×C₄₇	1	8	yes	complemented
239	C₄₇	#20699	1	1	yes	characteristic, direct product factor, Sylow
240	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
241	C₂³×C₄	—	2	8	no	—
242	C₂³×C₄	—	2	1	no	—
243	C₂³×C₄	—	2	1	no	—
244	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
245	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
246	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
247	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
248	C₂³×C₄	D₄×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	C₂²×C₈	—	2	4	no	—
253	C₂²×C₈	—	2	8	no	—
254	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
255	#117	—	2	8	no	—
256	#117	—	2	8	no	—
257	#117	—	2	4	no	—
258	#117	—	2	4	no	—
259	#117	—	2	8	no	—
260	#117	C₂×C₄×C₄₇	1	8	yes	—
261	#117	C₂×C₄×C₄₇	1	8	yes	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
267	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
268	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
269	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	8	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	—	2	8	no	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂²⋊C₈	—	2	4	no	—
282	C₂²⋊C₈	—	2	4	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	C₂⁴	—	2	4	no	—
286	C₂⁴	—	2	4	no	—
287	C₂⁴	—	4	2	no	—
288	C₂⁴	C₂²⋊C₄×C₄₇	1	4	yes	—
289	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
290	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
291	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	16	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	16	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
307	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
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	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
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	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
318	C₂²×C₄	#41×C₄₇	1	8	yes	—
319	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	—	2	8	no	—
322	C₂×C₈	—	4	8	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
329	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	8	no	—
332	C₂²⋊C₄	—	4	4	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₄²	—	2	8	no	—
336	C₄²	—	2	8	no	—
337	C₄²	—	4	4	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	8	no	—
346	C₂³	—	2	8	no	—
347	C₂³	—	4	4	no	—
348	C₂³	—	4	16	no	—
349	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
350	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
351	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
352	C₂³	#123×C₄₇	1	4	yes	—
353	C₂³	#135×C₄₇	1	4	yes	—
354	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	4	8	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	8	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
374	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
375	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
376	C₂×C₄	#117×C₄₇	1	8	yes	—
377	C₂×C₄	#123×C₄₇	1	8	yes	—
378	C₂×C₄	#123×C₄₇	1	4	yes	—
379	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
382	C₈	—	4	4	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	2	8	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	4	16	no	—
393	C₂²	—	4	4	no	—
394	C₂²	C₄₇×#381	1	4	yes	—
395	C₂²	C₄₇×#416	1	4	yes	—
396	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
397	C₂²	C₂×#123×C₄₇	1	2	yes	—
398	C₂²	C₂×#135×C₄₇	1	2	yes	—
399	C₂²	C₄₇×#575	1	2	yes	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	8	4	no	—
405	C₄	C₄₇×#381	1	4	yes	—
406	C₄	C₂×#117×C₄₇	1	2	yes	—
407	C₄	C₂×#123×C₄₇	1	2	yes	—
408	C₂	—	2	4	no	—
409	C₂	—	2	4	no	—
410	C₂	—	4	2	no	—
411	C₂	C₂×C₄₇×#381	1	1	yes	characteristic
412	C₂	C₂×C₄₇×#416	1	1	yes	characteristic
413	C₂	C₄₇×#2896	1	1	yes	characteristic
414	C₂	C₄₇×#3091	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁵×C₄₇	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ C₂⁴×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₇×#1825	C₂	semidirect
5. C₄₇×#1824	C₂	semidirect
6. C₄₇×#1823	C₂	semidirect
7. C₄₇×#1735	C₂	semidirect
13. C₂×#117×C₄₇	C₄	semidirect
30. C₄₇×#340	C₂²	semidirect
31. C₄₇×#340	C₂²	semidirect
175. #20699	C₄₇	direct (N × H)
204. #1825	C₂×C₄₇	semidirect
205. #1824	C₂×C₄₇	semidirect
206. #1823	C₂×C₄₇	semidirect
207. #1735	C₂×C₄₇	semidirect
220. C₂×#117	C₄×C₄₇	semidirect
237. #340	C₂²×C₄₇	semidirect
238. #340	C₂²×C₄₇	semidirect
239. C₄₇	#20699	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#117×C₄₇	2
C₂²×C₂²⋊C₈×C₄₇	2
C₄₇×#2280	2
C₄₇×#1825	2
C₄₇×#1824	2
C₄₇×#1823	2
C₄₇×#1735	2
#20699	47

Subgroups — C47×#20699 #26060397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20699 #26060397