Subgroups — #26105719

Order 12032.

922 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	#20252021	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20241220	C₂	1	4	yes	maximal, complemented
4	C₄₇×#2920	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×Dic₄₇	—	2	1	no	—
6	C₂²×C₄×Dic₄₇	—	2	1	no	—
7	C₂²×C₄×Dic₄₇	C₄	1	2	yes	—
8	#15689180	—	2	1	no	—
9	#15689180	C₄	1	2	yes	complemented
10	#15689176	—	2	1	no	—
11	#15689176	C₂²	1	2	yes	—
12	#15689147	C₄	1	2	yes	complemented
13	#15689087	—	2	1	no	—
14	C₄×#10625329	—	2	1	no	—
15	C₄²×Dic₄₇	—	2	1	no	—
16	C₄²×Dic₄₇	—	2	1	no	—
17	C₄²×Dic₄₇	C₄	1	2	yes	—
18	C₄²×Dic₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#432	—	2	1	no	—
21	C₄₇×#432	C₄	1	2	yes	complemented
22	C₄₇×#431	—	2	1	no	—
23	C₄₇×#431	C₂²	1	2	yes	—
24	C₄₇×#423	C₄	1	2	yes	complemented
25	C₄₇×#407	—	2	1	no	—
26	C₄×M₁₆×C₄₇	—	2	1	no	—
27	C₂³×Dic₄₇	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×C₄×Dic₄₇	—	2	8	no	—
30	C₂×C₄×Dic₄₇	—	2	8	no	—
31	C₂×C₄×Dic₄₇	—	2	2	no	—
32	C₂×C₄×Dic₄₇	—	2	2	no	—
33	C₂×C₄×Dic₄₇	—	2	2	no	—
34	C₂×C₄×Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	2	8	no	—
37	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
38	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
39	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
40	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
42	#13093935	—	2	2	no	—
43	C₄×C₄₇⋊C₈	—	2	2	no	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂×M₁₆×C₄₇	—	2	2	no	—
48	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₇	Q₈	1	1	yes	characteristic
58	C₂×C₄²×C₄₇	Q₈	1	1	yes	characteristic
59	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
60	C₄⋊C₈×C₄₇	—	2	2	no	—
61	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
62	C₂²⋊C₈×C₄₇	—	2	2	no	—
63	C₂²⋊C₈×C₄₇	—	2	2	no	—
64	#97×C₄₇	—	2	2	no	—
65	C₄×C₈×C₄₇	—	2	2	no	—
66	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	—	2	4	no	—
68	C₂²×C₄×C₄₇	—	2	4	no	—
69	C₂²×C₄×C₄₇	—	2	4	no	—
70	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×Dic₄₇	—	2	8	no	—
89	C₂²×Dic₄₇	—	2	8	no	—
90	C₂²×Dic₄₇	—	2	8	no	—
91	C₂²×Dic₄₇	—	2	4	no	—
92	M₁₆×C₄₇	—	4	4	no	—
93	C₂×C₈×C₄₇	—	2	4	no	—
94	C₄²×C₄₇	C₄²	1	1	yes	characteristic
95	C₄²×C₄₇	C₄²	1	1	yes	characteristic
96	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
110	C₄×Dic₄₇	—	2	8	no	—
111	C₄×Dic₄₇	—	2	8	no	—
112	C₄×Dic₄₇	—	2	8	no	—
113	C₄×Dic₄₇	—	2	8	no	—
114	C₄×Dic₄₇	—	2	8	no	—
115	C₄×Dic₄₇	—	2	4	no	—
116	C₄×Dic₄₇	M₁₆	1	8	yes	complemented
117	#10625329	—	4	4	no	—
118	C₂×C₄₇⋊C₈	—	2	4	no	—
119	C₂³×C₄₇	—	2	2	no	—
120	C₂³×C₄₇	—	2	2	no	—
121	C₂³×C₄₇	—	2	2	no	—
122	C₂³×C₄₇	#95	1	1	yes	characteristic
123	C₂³×C₄₇	#95	1	1	yes	characteristic
124	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₄₇	—	2	2	no	—
126	C₂×C₄×C₄₇	—	2	2	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
143	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
144	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
145	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#104	1	4	yes	—
147	C₂×C₄×C₄₇	#104	1	4	yes	—
148	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
155	C₂×Dic₄₇	—	2	8	no	—
156	C₂×Dic₄₇	—	2	8	no	—
157	C₂×Dic₄₇	—	2	32	no	—
158	C₂×Dic₄₇	—	2	8	no	—
159	C₈×C₄₇	—	4	4	no	—
160	C₄₇⋊C₈	—	4	4	no	—
161	#7867	—	47	1	no	maximal, Sylow
162	C₂²×C₄₇	—	2	8	no	—
163	C₂²×C₄₇	—	2	1	no	—
164	C₂²×C₄₇	—	2	1	no	—
165	C₂²×C₄₇	—	2	1	no	—
166	C₂²×C₄₇	—	2	1	no	—
167	C₂²×C₄₇	—	2	1	no	—
168	C₂²×C₄₇	—	2	1	no	—
169	C₂²×C₄₇	#339	1	2	yes	—
170	C₂²×C₄₇	#339	1	2	yes	—
171	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
172	C₂²×C₄₇	#407	1	2	yes	—
173	C₄×C₄₇	—	2	1	no	—
174	C₄×C₄₇	—	2	1	no	—
175	C₄×C₄₇	—	2	1	no	—
176	C₄×C₄₇	—	2	1	no	—
177	C₄×C₄₇	—	2	1	no	—
178	C₄×C₄₇	—	2	1	no	—
179	C₄×C₄₇	#339	1	2	yes	—
180	C₄×C₄₇	#339	1	2	yes	—
181	C₄×C₄₇	C₄×M₁₆	1	2	yes	—
182	C₄×C₄₇	C₂×#104	1	2	yes	—
183	C₄×C₄₇	C₂×#104	1	2	yes	—
184	C₄×C₄₇	#423	1	2	yes	—
185	Dic₄₇	—	2	16	no	—
186	#2920	—	47	1	no	—
187	#2920	D₄₇	1	1	yes	characteristic
188	C₂×C₄³	—	47	1	no	—
189	#1276	—	47	4	no	—
190	C₂×C₄₇	—	2	2	no	—
191	C₂×C₄₇	—	2	2	no	—
192	C₂×C₄₇	—	2	2	no	—
193	C₂×C₄₇	#1728	1	1	yes	characteristic
194	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
195	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
196	C₂²×C₄²	—	47	2	no	—
197	C₂²×C₄²	—	94	1	no	—
198	C₂²×C₄²	—	94	1	no	—
199	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
200	#432	—	2	1	no	—
201	#432	—	47	2	no	—
202	#432	—	94	1	no	—
203	#432	Dic₄₇	1	2	yes	complemented
204	#431	—	2	1	no	—
205	#431	—	47	2	no	—
206	#431	—	94	1	no	—
207	#431	C₂×D₄₇	1	2	yes	—
208	#423	—	47	2	no	—
209	#423	Dic₄₇	1	2	yes	complemented
210	#407	—	2	1	no	—
211	#407	—	94	1	no	—
212	C₄×M₁₆	—	2	1	no	—
213	C₄×M₁₆	—	94	1	no	—
214	C₄³	—	47	2	no	—
215	C₄³	—	47	2	no	—
216	C₄³	—	94	1	no	—
217	C₄³	—	94	1	no	—
218	C₄₇	#7867	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₄	—	94	2	no	—
220	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
221	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
222	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	94	2	no	—
225	C₂×C₄²	—	47	4	no	—
226	C₂×C₄²	—	94	8	no	—
227	C₂×C₄²	—	94	8	no	—
228	C₂×C₄²	—	94	8	no	—
229	C₂×C₄²	—	94	2	no	—
230	C₂×C₄²	—	94	2	no	—
231	C₂×C₄²	—	94	2	no	—
232	C₂×C₄²	—	94	2	no	—
233	C₂×C₄²	—	94	2	no	—
234	C₂×C₄²	Dic₉₄	1	1	yes	characteristic
235	C₂×C₄²	Dic₉₄	1	1	yes	characteristic
236	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
237	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
238	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
239	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
241	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
244	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
245	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
246	C₄⋊C₈	—	2	2	no	—
247	C₄⋊C₈	—	47	4	no	—
248	C₄⋊C₈	—	94	2	no	—
249	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
250	C₂²⋊C₈	—	2	2	no	—
251	C₂²⋊C₈	—	2	2	no	—
252	C₂²⋊C₈	—	94	2	no	—
253	C₂²⋊C₈	—	94	2	no	—
254	#97	—	2	2	no	—
255	#97	—	94	2	no	—
256	C₄×C₈	—	2	2	no	—
257	C₄×C₈	—	94	2	no	—
258	C₂⁴	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	94	8	no	—
263	C₂²×C₄	—	94	8	no	—
264	C₂²×C₄	—	94	8	no	—
265	C₂²×C₄	—	94	4	no	—
266	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
267	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
268	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	Dic₄₇⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
273	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
274	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
275	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
276	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
277	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
278	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
284	M₁₆	—	4	4	no	—
285	M₁₆	—	188	4	no	—
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	94	4	no	—
288	C₄²	—	47	8	no	—
289	C₄²	—	94	8	no	—
290	C₄²	—	94	8	no	—
291	C₄²	—	94	8	no	—
292	C₄²	—	94	8	no	—
293	C₄²	—	94	8	no	—
294	C₄²	—	94	4	no	—
295	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
296	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
297	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
298	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
299	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
300	C₄²	Dic₄₇⋊C₄	1	1	yes	characteristic
301	C₄²	C₄⋊Dic₄₇	1	1	yes	characteristic
302	C₄²	C₄⋊Dic₄₇	1	1	yes	characteristic
303	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
304	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
305	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
306	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
307	C₄²	C₂×Dic₉₄	1	1	yes	characteristic
308	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
309	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
310	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	C₄₇⋊#95	1	1	yes	characteristic
315	C₂³	C₄₇⋊#95	1	1	yes	characteristic
316	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	94	8	no	—
333	C₂×C₄	—	94	8	no	—
334	C₂×C₄	—	94	32	no	—
335	C₂×C₄	—	94	8	no	—
336	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
337	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
338	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
339	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
340	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
341	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
342	C₂×C₄	#13093950	1	4	yes	—
343	C₂×C₄	#13093951	1	4	yes	—
344	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
345	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
347	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
348	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
350	C₂×C₄	M₁₆×D₄₇	1	4	yes	—
351	C₈	—	4	4	no	—
352	C₈	—	188	4	no	—
353	C₂²	—	2	8	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	#15688882	1	2	yes	—
361	C₂²	#15688884	1	2	yes	—
362	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
363	C₂²	#15689086	1	2	yes	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	2	1	no	—
370	C₄	—	94	16	no	—
371	C₄	#15688882	1	2	yes	—
372	C₄	#15688884	1	2	yes	—
373	C₄	M₁₆×Dic₄₇	1	2	yes	—
374	C₄	C₂×#13093950	1	2	yes	—
375	C₄	C₂×#13093951	1	2	yes	—
376	C₄	#15689146	1	2	yes	—
377	C₂	—	2	2	no	—
378	C₂	—	2	2	no	—
379	C₂	—	2	2	no	—
380	C₂	#20243081	1	1	yes	characteristic
381	C₂	C₂×#15688882	1	1	yes	characteristic
382	C₂	C₂×#15688884	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#2920	C₂
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#2920	D₄₇
hypocenter	C₄₇	#7867
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #20241220	C₂	semidirect
9. #15689180	C₄	semidirect
12. #15689147	C₄	semidirect
21. C₄₇×#432	C₄	semidirect
24. C₄₇×#423	C₄	semidirect
39. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
61. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
116. C₄×Dic₄₇	M₁₆	semidirect
203. #432	Dic₄₇	semidirect
209. #423	Dic₄₇	semidirect
218. C₄₇	#7867	semidirect
249. C₄⋊C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252021	2
C₂×C₄²×Dic₄₇	2
#20241220	2
C₄₇×#2920	2
#7867	47