Subgroups — C₄₇×#10741 #26050439

Order 12032.

1186 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#519	C₂	1	1	yes	maximal, characteristic
2	C₂²×#101×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2310	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1733	C₂	1	2	yes	maximal
5	C₂×C₄₇×H(3,ℤ/4)	C₂	1	2	yes	maximal
6	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
8	C₄₇×#519	—	2	2	no	—
9	C₄₇×#519	—	2	4	no	—
10	C₄₇×#519	C₄	1	4	yes	complemented
11	C₂×C₄×Q₈×C₄₇	—	2	4	no	—
12	C₂×#117×C₄₇	—	2	2	no	—
13	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₇	C₂²	1	2	yes	—
16	C₂×#101×C₄₇	—	2	2	no	—
17	C₂×#101×C₄₇	—	2	2	no	—
18	C₂×#101×C₄₇	C₄	1	4	yes	complemented
19	C₄₇×#391	—	2	2	no	—
20	C₄₇×#391	C₄	1	4	yes	complemented
21	C₄₇×#381	—	2	2	no	—
22	C₄₇×#339	—	2	4	no	—
23	C₄₇×H(3,ℤ/4)	—	2	4	no	—
24	C₂²×Q₈×C₄₇	—	2	2	no	—
25	C₂²×Q₈×C₄₇	—	2	2	no	—
26	C₂²×Q₈×C₄₇	—	2	2	no	—
27	C₂²×Q₈×C₄₇	—	2	2	no	—
28	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
29	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
30	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
31	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
32	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
33	C₂²×Q₈×C₄₇	Q₈	1	2	yes	—
34	C₂³×C₄×C₄₇	D₄	1	2	yes	—
35	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₄₇	—	2	2	no	—
37	C₂×M₁₆×C₄₇	—	2	2	no	—
38	C₂×M₁₆×C₄₇	—	2	2	no	—
39	C₂×M₁₆×C₄₇	—	2	2	no	—
40	C₂×M₁₆×C₄₇	—	2	2	no	—
41	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
42	C₂²×C₈×C₄₇	—	2	2	no	—
43	C₄×Q₈×C₄₇	—	2	16	no	—
44	C₄×Q₈×C₄₇	—	2	16	no	—
45	#117×C₄₇	—	2	8	no	—
46	#117×C₄₇	—	2	8	no	—
47	#117×C₄₇	—	2	2	no	—
48	#117×C₄₇	—	2	2	no	—
49	#117×C₄₇	—	2	2	no	—
50	#117×C₄₇	—	2	2	no	—
51	#117×C₄₇	—	2	2	no	—
52	#117×C₄₇	—	2	2	no	—
53	#117×C₄₇	C₂×C₄	1	4	yes	—
54	#117×C₄₇	D₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄²×C₄₇	—	2	4	no	—
63	C₂×C₄²×C₄₇	—	2	1	no	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₄₇	D₄	1	4	yes	—
66	#101×C₄₇	—	2	8	no	—
67	#95×C₄₇	—	2	8	no	—
68	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₂×Q₈×C₄₇	—	2	4	no	—
70	C₂×Q₈×C₄₇	—	2	4	no	—
71	C₂×Q₈×C₄₇	—	2	4	no	—
72	C₂×Q₈×C₄₇	—	2	4	no	—
73	C₂×Q₈×C₄₇	—	2	4	no	—
74	C₂×Q₈×C₄₇	—	2	4	no	—
75	C₂×Q₈×C₄₇	—	2	4	no	—
76	C₂×Q₈×C₄₇	—	2	4	no	—
77	C₂×Q₈×C₄₇	—	2	4	no	—
78	C₂×Q₈×C₄₇	—	2	4	no	—
79	C₂×Q₈×C₄₇	—	2	4	no	—
80	C₂×Q₈×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	C₄²	1	4	yes	—
82	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
83	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
84	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
94	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂²×C₄×C₄₇	#41	1	2	yes	—
105	M₁₆×C₄₇	—	2	4	no	—
106	M₁₆×C₄₇	—	2	4	no	—
107	M₁₆×C₄₇	—	4	2	no	—
108	M₁₆×C₄₇	—	4	2	no	—
109	C₂×C₈×C₄₇	—	2	4	no	—
110	C₂×C₈×C₄₇	—	4	2	no	—
111	C₂×C₈×C₄₇	—	4	2	no	—
112	C₄⋊C₄×C₄₇	—	2	16	no	—
113	C₄⋊C₄×C₄₇	—	2	4	no	—
114	C₄⋊C₄×C₄₇	—	2	4	no	—
115	C₄⋊C₄×C₄₇	—	2	4	no	—
116	C₄⋊C₄×C₄₇	—	4	2	no	—
117	C₂²⋊C₄×C₄₇	—	2	4	no	—
118	C₂²⋊C₄×C₄₇	—	2	4	no	—
119	C₂²⋊C₄×C₄₇	—	4	1	no	—
120	C₂²⋊C₄×C₄₇	—	4	1	no	—
121	C₂²⋊C₄×C₄₇	—	4	1	no	—
122	C₂²⋊C₄×C₄₇	—	4	1	no	—
123	C₄²×C₄₇	—	2	16	no	—
124	C₄²×C₄₇	—	2	4	no	—
125	C₄²×C₄₇	—	2	4	no	—
126	C₄²×C₄₇	—	4	2	no	—
127	C₄²×C₄₇	C₂²⋊C₄	1	8	yes	—
128	C₂³×C₄₇	—	4	2	no	—
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂³×C₄₇	#120	1	1	yes	characteristic
133	C₂³×C₄₇	#120	1	1	yes	characteristic
134	C₂³×C₄₇	#123	1	1	yes	characteristic
135	C₂³×C₄₇	#123	1	1	yes	characteristic
136	Q₈×C₄₇	—	2	8	no	—
137	Q₈×C₄₇	—	2	8	no	—
138	Q₈×C₄₇	—	2	8	no	—
139	Q₈×C₄₇	—	2	8	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	8	no	—
147	C₂×C₄×C₄₇	—	4	8	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	#95	1	8	yes	—
153	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#117	1	2	yes	—
159	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₄₇	#120	1	2	yes	—
164	C₂×C₄×C₄₇	#121	1	2	yes	—
165	C₂×C₄×C₄₇	#121	1	2	yes	—
166	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
167	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
168	C₂×C₄×C₄₇	#123	1	2	yes	—
169	C₈×C₄₇	—	4	4	no	—
170	#10741	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₄₇	—	2	2	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	4	1	no	—
175	C₂²×C₄₇	—	4	1	no	—
176	C₂²×C₄₇	—	4	1	no	—
177	C₂²×C₄₇	—	4	1	no	—
178	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
179	C₂²×C₄₇	#379	1	1	yes	characteristic
180	C₂²×C₄₇	#381	1	1	yes	characteristic
181	C₂²×C₄₇	#385	1	1	yes	characteristic
182	C₂²×C₄₇	#385	1	1	yes	characteristic
183	C₂²×C₄₇	#386	1	1	yes	characteristic
184	C₂²×C₄₇	#386	1	1	yes	characteristic
185	C₄×C₄₇	—	2	8	no	—
186	C₄×C₄₇	—	4	8	no	—
187	C₄×C₄₇	—	8	2	no	—
188	C₄×C₄₇	—	8	2	no	—
189	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
190	C₄×C₄₇	#380	1	2	yes	—
191	C₄×C₄₇	#385	1	2	yes	—
192	C₄×C₄₇	#386	1	2	yes	—
193	C₂×#519	C₂×C₄₇	1	1	yes	characteristic
194	C₂²×#101	C₂×C₄₇	1	1	yes	characteristic
195	#2310	C₂×C₄₇	1	1	yes	characteristic
196	#1733	C₂×C₄₇	1	2	yes	—
197	C₂×H(3,ℤ/4)	C₂×C₄₇	1	2	yes	—
198	C₂×C₄₇	—	2	1	no	—
199	C₂×C₄₇	—	2	1	no	—
200	C₂×C₄₇	—	2	1	no	—
201	C₂×C₄₇	—	2	1	no	—
202	C₂×C₄₇	—	2	1	no	—
203	C₂×C₄₇	—	2	1	no	—
204	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
205	C₂×C₄₇	#1912	1	2	yes	—
206	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
207	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
208	#519	—	2	2	no	—
209	#519	—	2	4	no	—
210	#519	C₄×C₄₇	1	4	yes	complemented
211	C₂×C₄×Q₈	—	2	4	no	—
212	C₂×#117	—	2	2	no	—
213	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
214	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
215	C₂×#117	C₂²×C₄₇	1	2	yes	—
216	C₂×#101	—	2	2	no	—
217	C₂×#101	—	2	2	no	—
218	C₂×#101	C₄×C₄₇	1	4	yes	complemented
219	#391	—	2	2	no	—
220	#391	C₄×C₄₇	1	4	yes	complemented
221	#381	—	2	2	no	—
222	#339	—	2	4	no	—
223	H(3,ℤ/4)	—	2	4	no	—
224	C₄₇	#10741	1	1	yes	characteristic, direct product factor, Sylow
225	C₂²×Q₈	—	2	2	no	—
226	C₂²×Q₈	—	2	2	no	—
227	C₂²×Q₈	—	2	2	no	—
228	C₂²×Q₈	—	2	2	no	—
229	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
230	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
231	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
232	C₂²×Q₈	D₄×C₄₇	1	2	yes	—
233	C₂²×Q₈	D₄×C₄₇	1	2	yes	—
234	C₂²×Q₈	Q₈×C₄₇	1	2	yes	—
235	C₂³×C₄	D₄×C₄₇	1	2	yes	—
236	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
243	C₂²×C₈	—	2	2	no	—
244	C₄×Q₈	—	2	16	no	—
245	C₄×Q₈	—	2	16	no	—
246	#117	—	2	8	no	—
247	#117	—	2	8	no	—
248	#117	—	2	2	no	—
249	#117	—	2	2	no	—
250	#117	—	2	2	no	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	#117	C₂×C₄×C₄₇	1	4	yes	—
255	#117	D₄×C₄₇	1	4	yes	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₄²	—	2	4	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
266	C₂×C₄²	D₄×C₄₇	1	4	yes	—
267	#101	—	2	8	no	—
268	#95	—	2	8	no	—
269	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	4	no	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	2	4	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	C₄²×C₄₇	1	4	yes	—
283	C₂×Q₈	C₂²⋊C₄×C₄₇	1	4	yes	—
284	C₂×Q₈	C₄⋊C₄×C₄₇	1	4	yes	—
285	C₂×Q₈	C₄⋊C₄×C₄₇	1	4	yes	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
294	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
295	C₂²×C₄	C₄⋊C₄×C₄₇	1	4	yes	—
296	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
303	C₂²×C₄	C₂×Q₈×C₄₇	1	1	yes	characteristic
304	C₂²×C₄	#41×C₄₇	1	2	yes	—
305	C₂²×C₄	#41×C₄₇	1	2	yes	—
306	M₁₆	—	2	4	no	—
307	M₁₆	—	2	4	no	—
308	M₁₆	—	4	2	no	—
309	M₁₆	—	4	2	no	—
310	C₂×C₈	—	2	4	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	—	4	2	no	—
313	C₄⋊C₄	—	2	16	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	2	4	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	4	1	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₄²	—	2	16	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	2	4	no	—
327	C₄²	—	4	2	no	—
328	C₄²	C₂²⋊C₄×C₄₇	1	8	yes	—
329	C₂³	—	4	2	no	—
330	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
331	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
332	C₂³	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
333	C₂³	#120×C₄₇	1	1	yes	characteristic
334	C₂³	#120×C₄₇	1	1	yes	characteristic
335	C₂³	#123×C₄₇	1	1	yes	characteristic
336	C₂³	#123×C₄₇	1	1	yes	characteristic
337	Q₈	—	2	8	no	—
338	Q₈	—	2	8	no	—
339	Q₈	—	2	8	no	—
340	Q₈	—	2	8	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	#95×C₄₇	1	8	yes	—
354	C₂×C₄	C₂×C₄²×C₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
356	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
359	C₂×C₄	#117×C₄₇	1	2	yes	—
360	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
361	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
362	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
363	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
364	C₂×C₄	#120×C₄₇	1	2	yes	—
365	C₂×C₄	#121×C₄₇	1	2	yes	—
366	C₂×C₄	#121×C₄₇	1	2	yes	—
367	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
368	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
369	C₂×C₄	#123×C₄₇	1	2	yes	—
370	C₈	—	4	4	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	C₂×#95×C₄₇	1	1	yes	characteristic
379	C₂²	C₄₇×#379	1	1	yes	characteristic
380	C₂²	C₄₇×#381	1	1	yes	characteristic
381	C₂²	C₄₇×#385	1	1	yes	characteristic
382	C₂²	C₄₇×#385	1	1	yes	characteristic
383	C₂²	C₄₇×#386	1	1	yes	characteristic
384	C₂²	C₄₇×#386	1	1	yes	characteristic
385	C₄	—	2	8	no	—
386	C₄	—	4	8	no	—
387	C₄	—	8	2	no	—
388	C₄	—	8	2	no	—
389	C₄	C₄×C₂²⋊C₄×C₄₇	1	2	yes	—
390	C₄	C₄₇×#380	1	2	yes	—
391	C₄	C₄₇×#385	1	2	yes	—
392	C₄	C₄₇×#386	1	2	yes	—
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	—	2	1	no	—
397	C₂	—	2	1	no	—
398	C₂	—	2	1	no	—
399	C₂	C₄₇×C₂²⋊#95	1	1	yes	characteristic
400	C₂	C₄₇×#1912	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	#386
commutator	C₂×C₄	C₂×C₄²×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
prime radical	C₂⁴×C₄₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₄₇×#519	C₄	semidirect
18. C₂×#101×C₄₇	C₄	semidirect
20. C₄₇×#391	C₄	semidirect
170. #10741	C₄₇	direct (N × H)
210. #519	C₄×C₄₇	semidirect
218. C₂×#101	C₄×C₄₇	semidirect
220. #391	C₄×C₄₇	semidirect
224. C₄₇	#10741	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#519	2
C₂²×#101×C₄₇	2
C₄₇×#2310	2
C₄₇×#1733	2
C₂×C₄₇×H(3,ℤ/4)	2
#10741	47

Subgroups — C47×#10741 #26050439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10741 #26050439