Subgroups — C₄₇×#20705 #26060403

Order 12032.

1470 conjugacy classes of subgroups.

The subgroup lattice has 438 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	C₂×C₄₇×#407	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2280	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1826	C₂	1	8	yes	maximal, complemented
5	C₄₇×#1733	C₂	1	4	yes	maximal, complemented
6	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
8	C₂×#117×C₄₇	—	2	2	no	—
9	C₂×#117×C₄₇	—	2	1	no	—
10	C₂×#117×C₄₇	—	2	2	no	—
11	C₂×#117×C₄₇	—	2	1	no	—
12	C₂×#117×C₄₇	C₄	1	4	yes	complemented
13	C₂×#117×C₄₇	C₄	1	2	yes	complemented
14	C₂×#117×C₄₇	C₂²	1	4	yes	—
15	C₂×#117×C₄₇	C₂²	1	2	yes	—
16	C₂×#117×C₄₇	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	complemented
18	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
19	C₂²×C₄²×C₄₇	—	2	1	no	—
20	C₄₇×#407	—	2	1	no	—
21	C₄₇×#407	—	2	1	no	—
22	C₄₇×#407	C₂²	1	4	yes	—
23	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
24	C₄₇×#381	—	2	1	no	—
25	C₄₇×#380	—	2	2	no	—
26	C₄₇×#379	—	2	1	no	—
27	C₄×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
28	C₄₇×#339	C₂²	1	16	yes	complemented
29	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₇	—	2	8	no	—
31	C₂³×C₄×C₄₇	—	2	2	no	—
32	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
34	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₇	D₄	1	2	yes	—
36	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	D₄	1	2	yes	—
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂×M₁₆×C₄₇	—	2	2	no	—
43	C₂×M₁₆×C₄₇	—	2	8	no	—
44	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
45	C₂²×C₈×C₄₇	—	2	2	no	—
46	#117×C₄₇	—	2	4	no	—
47	#117×C₄₇	—	2	4	no	—
48	#117×C₄₇	—	2	4	no	—
49	#117×C₄₇	—	2	4	no	—
50	#117×C₄₇	—	2	2	no	—
51	#117×C₄₇	—	2	4	no	—
52	#117×C₄₇	—	2	2	no	—
53	#117×C₄₇	—	2	8	no	—
54	#117×C₄₇	C₂×C₄	1	8	yes	—
55	#117×C₄₇	C₂×C₄	1	4	yes	—
56	#117×C₄₇	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
70	C₂×C₄²×C₄₇	—	2	2	no	—
71	C₂×C₄²×C₄₇	—	2	4	no	—
72	C₂×C₄²×C₄₇	—	2	4	no	—
73	C₂×C₄²×C₄₇	—	2	2	no	—
74	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
75	C₂²⋊C₈×C₄₇	—	2	4	no	—
76	C₂²⋊C₈×C₄₇	—	2	4	no	—
77	#95×C₄₇	—	2	4	no	—
78	C₂⁴×C₄₇	—	2	4	no	—
79	C₂⁴×C₄₇	—	4	4	no	—
80	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
82	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
84	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	8	no	—
89	C₂²×C₄×C₄₇	—	2	8	no	—
90	C₂²×C₄×C₄₇	—	2	8	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	8	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	4	8	no	—
99	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	#41	1	8	yes	—
117	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
118	M₁₆×C₄₇	—	2	8	no	—
119	M₁₆×C₄₇	—	4	4	no	—
120	C₂×C₈×C₄₇	—	2	4	no	—
121	C₂×C₈×C₄₇	—	4	4	no	—
122	C₄⋊C₄×C₄₇	—	2	4	no	—
123	C₄⋊C₄×C₄₇	—	2	4	no	—
124	C₄⋊C₄×C₄₇	—	2	4	no	—
125	C₄⋊C₄×C₄₇	—	4	4	no	—
126	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
127	C₂²⋊C₄×C₄₇	—	2	8	no	—
128	C₂²⋊C₄×C₄₇	—	2	4	no	—
129	C₂²⋊C₄×C₄₇	—	2	4	no	—
130	C₂²⋊C₄×C₄₇	—	4	8	no	—
131	C₂²⋊C₄×C₄₇	—	4	4	no	—
132	C₄²×C₄₇	—	2	8	no	—
133	C₄²×C₄₇	—	2	4	no	—
134	C₄²×C₄₇	—	2	4	no	—
135	C₄²×C₄₇	—	2	8	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	4	no	—
138	C₂³×C₄₇	—	2	4	no	—
139	C₂³×C₄₇	—	2	4	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	4	no	—
142	C₂³×C₄₇	—	2	4	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	—	4	2	no	—
145	C₂³×C₄₇	—	4	2	no	—
146	C₂³×C₄₇	—	4	2	no	—
147	C₂³×C₄₇	—	4	16	no	—
148	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂³×C₄₇	#123	1	4	yes	—
153	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	8	no	—
167	C₂×C₄×C₄₇	—	4	8	no	—
168	C₂×C₄×C₄₇	—	4	8	no	—
169	C₂×C₄×C₄₇	—	4	8	no	—
170	C₂×C₄×C₄₇	—	4	8	no	—
171	C₂×C₄×C₄₇	—	4	4	no	—
172	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	#117	1	4	yes	—
177	C₂×C₄×C₄₇	#117	1	4	yes	—
178	C₂×C₄×C₄₇	#123	1	4	yes	—
179	C₂×C₄×C₄₇	#123	1	4	yes	—
180	C₂×C₄×C₄₇	#123	1	4	yes	—
181	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
184	C₈×C₄₇	—	4	4	no	—
185	#20705	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₇	—	2	8	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	2	2	no	—
189	C₂²×C₄₇	—	2	2	no	—
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	2	2	no	—
192	C₂²×C₄₇	—	2	2	no	—
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	4	4	no	—
196	C₂²×C₄₇	—	4	8	no	—
197	C₂²×C₄₇	—	4	8	no	—
198	C₂²×C₄₇	—	4	4	no	—
199	C₂²×C₄₇	#381	1	2	yes	—
200	C₂²×C₄₇	#381	1	2	yes	—
201	C₂²×C₄₇	#421	1	4	yes	—
202	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
203	C₂²×C₄₇	C₂×#123	1	2	yes	—
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	4	8	no	—
207	C₄×C₄₇	—	8	4	no	—
208	C₄×C₄₇	#381	1	2	yes	—
209	C₄×C₄₇	#381	1	2	yes	—
210	C₄×C₄₇	C₂×#117	1	2	yes	—
211	C₄×C₄₇	C₂×#123	1	2	yes	—
212	C₂²×#117	C₂×C₄₇	1	1	yes	characteristic
213	C₂×#407	C₂×C₄₇	1	1	yes	characteristic
214	#2280	C₂×C₄₇	1	1	yes	characteristic
215	#1826	C₂×C₄₇	1	8	yes	complemented
216	#1733	C₂×C₄₇	1	4	yes	complemented
217	C₂×C₄₇	—	2	2	no	—
218	C₂×C₄₇	—	2	2	no	—
219	C₂×C₄₇	—	2	4	no	—
220	C₂×C₄₇	—	2	2	no	—
221	C₂×C₄₇	—	4	2	no	—
222	C₂×C₄₇	C₂×#381	1	1	yes	characteristic
223	C₂×C₄₇	C₂×#421	1	2	yes	—
224	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
225	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
226	C₂×#117	—	2	2	no	—
227	C₂×#117	—	2	1	no	—
228	C₂×#117	—	2	2	no	—
229	C₂×#117	—	2	1	no	—
230	C₂×#117	C₄×C₄₇	1	4	yes	complemented
231	C₂×#117	C₄×C₄₇	1	2	yes	complemented
232	C₂×#117	C₂²×C₄₇	1	4	yes	—
233	C₂×#117	C₂²×C₄₇	1	2	yes	—
234	C₂×#117	C₂²×C₄₇	1	2	yes	—
235	C₂²×C₄⋊C₄	C₄×C₄₇	1	2	yes	complemented
236	C₂²×C₂²⋊C₄	—	2	1	no	—
237	C₂²×C₄²	—	2	1	no	—
238	#407	—	2	1	no	—
239	#407	—	2	1	no	—
240	#407	C₂²×C₄₇	1	4	yes	—
241	C₂×C₂²⋊C₈	—	2	2	no	—
242	#381	—	2	1	no	—
243	#380	—	2	2	no	—
244	#379	—	2	1	no	—
245	C₄×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
246	#339	C₂²×C₄₇	1	16	yes	complemented
247	C₄₇	#20705	1	1	yes	characteristic, direct product factor, Sylow
248	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
249	C₂³×C₄	—	2	8	no	—
250	C₂³×C₄	—	2	2	no	—
251	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
252	C₂³×C₄	C₂×C₄×C₄₇	1	2	yes	—
253	C₂³×C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
254	C₂³×C₄	D₄×C₄₇	1	2	yes	—
255	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
256	C₂³×C₄	D₄×C₄₇	1	2	yes	—
257	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
258	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
260	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	2	8	no	—
263	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
264	C₂²×C₈	—	2	2	no	—
265	#117	—	2	4	no	—
266	#117	—	2	4	no	—
267	#117	—	2	4	no	—
268	#117	—	2	4	no	—
269	#117	—	2	2	no	—
270	#117	—	2	4	no	—
271	#117	—	2	2	no	—
272	#117	—	2	8	no	—
273	#117	C₂×C₄×C₄₇	1	8	yes	—
274	#117	C₂×C₄×C₄₇	1	4	yes	—
275	#117	C₂³×C₄₇	1	4	yes	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
281	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
282	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
283	C₂×C₂²⋊C₄	—	2	4	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	4	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	—	2	4	no	—
291	C₂×C₄²	—	2	4	no	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
294	C₂²⋊C₈	—	2	4	no	—
295	C₂²⋊C₈	—	2	4	no	—
296	#95	—	2	4	no	—
297	C₂⁴	—	2	4	no	—
298	C₂⁴	—	4	4	no	—
299	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
300	C₂⁴	C₂²⋊C₄×C₄₇	1	2	yes	—
301	C₂⁴	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
302	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
303	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	4	8	no	—
318	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
320	C₂²×C₄	C₂²⋊C₄×C₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
322	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
323	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
324	C₂²×C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
325	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
326	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
327	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
328	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
329	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
331	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
335	C₂²×C₄	#41×C₄₇	1	8	yes	—
336	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
337	M₁₆	—	2	8	no	—
338	M₁₆	—	4	4	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	4	4	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
346	C₂²⋊C₄	—	2	8	no	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	4	8	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₄²	—	2	8	no	—
352	C₄²	—	2	4	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	2	8	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	16	no	—
367	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
368	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
369	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
370	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
371	C₂³	#123×C₄₇	1	4	yes	—
372	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	4	8	no	—
387	C₂×C₄	—	4	8	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
392	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
393	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
395	C₂×C₄	#117×C₄₇	1	4	yes	—
396	C₂×C₄	#117×C₄₇	1	4	yes	—
397	C₂×C₄	#123×C₄₇	1	4	yes	—
398	C₂×C₄	#123×C₄₇	1	4	yes	—
399	C₂×C₄	#123×C₄₇	1	4	yes	—
400	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
403	C₈	—	4	4	no	—
404	C₂²	—	2	8	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	4	no	—
414	C₂²	—	4	8	no	—
415	C₂²	—	4	8	no	—
416	C₂²	—	4	4	no	—
417	C₂²	C₄₇×#381	1	2	yes	—
418	C₂²	C₄₇×#381	1	2	yes	—
419	C₂²	C₄₇×#421	1	4	yes	—
420	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
421	C₂²	C₂×#123×C₄₇	1	2	yes	—
422	C₄	—	2	2	no	—
423	C₄	—	2	2	no	—
424	C₄	—	4	8	no	—
425	C₄	—	8	4	no	—
426	C₄	C₄₇×#381	1	2	yes	—
427	C₄	C₄₇×#381	1	2	yes	—
428	C₄	C₂×#117×C₄₇	1	2	yes	—
429	C₄	C₂×#123×C₄₇	1	2	yes	—
430	C₂	—	2	2	no	—
431	C₂	—	2	2	no	—
432	C₂	—	2	4	no	—
433	C₂	—	2	2	no	—
434	C₂	—	4	2	no	—
435	C₂	C₂×C₄₇×#381	1	1	yes	characteristic
436	C₂	C₂×C₄₇×#421	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₄₇×#1826	C₂	semidirect
5. C₄₇×#1733	C₂	semidirect
12. C₂×#117×C₄₇	C₄	semidirect
13. C₂×#117×C₄₇	C₄	semidirect
17. C₂²×C₄⋊C₄×C₄₇	C₄	semidirect
28. C₄₇×#339	C₂²	semidirect
185. #20705	C₄₇	direct (N × H)
215. #1826	C₂×C₄₇	semidirect
216. #1733	C₂×C₄₇	semidirect
230. C₂×#117	C₄×C₄₇	semidirect
231. C₂×#117	C₄×C₄₇	semidirect
235. C₂²×C₄⋊C₄	C₄×C₄₇	semidirect
246. #339	C₂²×C₄₇	semidirect
247. C₄₇	#20705	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
C₂×C₄₇×#407	2
C₄₇×#2280	2
C₄₇×#1826	2
C₄₇×#1733	2
#20705	47

Subgroups — C47×#20705 #26060403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20705 #26060403