Subgroups — #26121469

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689081	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689079	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688887	C₂	1	1	yes	maximal, characteristic
5	#20243104	C₂	1	1	yes	maximal, characteristic
6	C₂×#15688883	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₇×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10625329	C₂²	1	1	yes	characteristic
9	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#13093983	C₂²	1	1	yes	characteristic
12	#15689081	—	2	2	no	—
13	#15689081	C₄	1	4	yes	complemented
14	#15689079	—	2	2	no	—
15	#15689079	C₄	1	4	yes	complemented
16	C₂×#13093935	—	2	1	no	—
17	C₂×#13093934	—	2	1	no	—
18	C₂×C₄×C₄₇⋊C₈	—	2	2	no	—
19	C₂×C₄×C₄₇⋊C₈	—	2	2	no	—
20	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
21	C₂×C₄×C₄₇⋊C₈	C₄	1	4	yes	complemented
22	C₂×C₈×Dic₄₇	—	2	1	no	—
23	#15688887	C₄	1	4	yes	complemented
24	#15688885	C₄	1	4	yes	complemented
25	#15688883	C₄	1	4	yes	complemented
26	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#339	C₄	1	4	yes	complemented
30	C₂×#10625329	—	2	1	no	—
31	C₂×#10625329	—	2	1	no	—
32	C₂×#10625329	—	2	1	no	—
33	C₂×#10625329	C₂×C₄	1	2	yes	—
34	C₂×#10625329	C₂×C₄	1	2	yes	—
35	C₂×#10625329	C₂×C₄	1	2	yes	—
36	C₂²×C₄₇⋊C₈	—	2	1	no	—
37	C₂²×C₄₇⋊C₈	—	2	1	no	—
38	C₂²×C₄₇⋊C₈	—	2	1	no	—
39	C₂²×C₄₇⋊C₈	—	2	1	no	—
40	C₂²×C₄₇⋊C₈	—	2	1	no	—
41	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
47	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
49	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
50	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
51	C₂²×C₄₇⋊C₈	Q₈	1	2	yes	—
52	#13093983	—	2	1	no	—
53	#13093983	—	2	1	no	—
54	#13093983	C₂×C₄	1	2	yes	—
55	#13093983	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
58	C₂×C₄×Dic₄₇	—	2	1	no	—
59	#13093935	—	2	4	no	—
60	#13093934	—	2	4	no	—
61	C₄×C₄₇⋊C₈	—	2	8	no	—
62	C₄×C₄₇⋊C₈	—	2	4	no	—
63	C₈×Dic₄₇	—	2	4	no	—
64	C₂³×C₄×C₄₇	—	2	1	no	—
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₄₇	—	2	1	no	—
67	C₂×M₁₆×C₄₇	—	2	1	no	—
68	C₂×M₁₆×C₄₇	—	2	1	no	—
69	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₄₇	—	2	1	no	—
73	#117×C₄₇	—	2	1	no	—
74	#117×C₄₇	—	2	1	no	—
75	#117×C₄₇	C₂×C₄	1	2	yes	—
76	#117×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	—	2	1	no	—
80	C₂×C₄²×C₄₇	—	2	1	no	—
81	C₂×C₄²×C₄₇	—	2	1	no	—
82	C₂×C₄²×C₄₇	—	2	1	no	—
83	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
84	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
85	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
86	C₂⁴×C₄₇	#41	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	—	2	8	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
106	C₂²×Dic₄₇	—	2	2	no	—
107	M₁₆×C₄₇	—	2	2	no	—
108	M₁₆×C₄₇	—	2	2	no	—
109	M₁₆×C₄₇	—	2	2	no	—
110	M₁₆×C₄₇	C₄²	1	4	yes	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
116	C₂²⋊C₄×C₄₇	—	2	2	no	—
117	C₂²⋊C₄×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	—	2	2	no	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	C₄²	1	4	yes	—
124	C₂²⋊Dic₄₇	—	2	2	no	—
125	C₂²⋊Dic₄₇	—	2	2	no	—
126	C₄⋊Dic₄₇	—	2	2	no	—
127	C₄⋊Dic₄₇	C₄²	1	4	yes	—
128	C₄×Dic₄₇	—	2	2	no	—
129	C₄×Dic₄₇	—	2	2	no	—
130	#10625329	—	2	2	no	—
131	#10625329	—	2	2	no	—
132	#10625329	—	2	2	no	—
133	#10625329	C₄²	1	4	yes	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	C₄²	1	4	yes	—
144	C₂×C₄₇⋊C₈	C₄²	1	4	yes	—
145	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
146	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
147	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
148	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
149	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
150	C₂×C₄₇⋊C₈	C₄⋊C₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₄⋊C₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	C₄⋊C₄	1	4	yes	—
153	C₂×C₄₇⋊C₈	C₄⋊C₄	1	4	yes	—
154	C₂³×C₄₇	—	2	4	no	—
155	C₂³×C₄₇	#117	1	1	yes	characteristic
156	C₂³×C₄₇	#117	1	1	yes	characteristic
157	C₂³×C₄₇	#117	1	1	yes	characteristic
158	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
159	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
160	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
161	C₂³×C₄₇	C₄×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₇	—	2	8	no	—
163	C₂×C₄×C₄₇	—	2	8	no	—
164	C₂×C₄×C₄₇	—	2	8	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	4	4	no	—
168	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
182	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
183	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
196	C₂×Dic₄₇	—	2	4	no	—
197	C₂×Dic₄₇	—	4	4	no	—
198	C₈×C₄₇	—	2	4	no	—
199	C₄₇⋊C₈	—	2	4	no	—
200	C₄₇⋊C₈	—	2	4	no	—
201	C₄₇⋊C₈	#95	1	4	yes	—
202	C₄₇⋊C₈	#95	1	4	yes	—
203	#10706	—	47	1	no	maximal, Sylow
204	C₂²×C₄₇	—	2	2	no	—
205	C₂²×C₄₇	—	2	2	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	2	2	no	—
208	C₂²×C₄₇	—	2	2	no	—
209	C₂²×C₄₇	—	2	2	no	—
210	C₂²×C₄₇	#376	1	1	yes	characteristic
211	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
213	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
215	C₂²×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
217	C₂²×C₄₇	#443	1	4	yes	—
218	C₄×C₄₇	—	2	8	no	—
219	C₄×C₄₇	—	4	4	no	—
220	C₄×C₄₇	C₄³	1	1	yes	characteristic
221	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
222	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
223	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
224	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
225	C₄×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
226	C₄×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
227	C₄×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
228	Dic₄₇	—	4	4	no	—
229	C₂×#405	—	47	1	no	—
230	C₂×#405	—	47	1	no	—
231	C₂²×C₄×C₈	—	47	1	no	—
232	C₂×#341	—	47	1	no	—
233	#1735	—	47	1	no	—
234	C₂×#339	—	47	1	no	—
235	C₂×#339	D₄₇	1	1	yes	characteristic
236	C₂×C₄₇	—	2	1	no	—
237	C₂×C₄₇	—	2	1	no	—
238	C₂×C₄₇	—	2	1	no	—
239	C₂×C₄₇	—	2	1	no	—
240	C₂×C₄₇	C₄×#95	1	1	yes	characteristic
241	C₂×C₄₇	#1764	1	2	yes	—
242	C₂×C₄₇	#1764	1	2	yes	—
243	C₂×C₄₇	#1772	1	2	yes	—
244	C₂²×M₁₆	—	47	1	no	—
245	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
246	C₂³×C₈	—	47	1	no	—
247	C₂³×C₈	—	47	1	no	—
248	C₂×#117	—	47	1	no	—
249	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
250	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
251	#405	—	47	4	no	—
252	#405	—	47	4	no	—
253	#405	—	94	2	no	—
254	#405	—	94	2	no	—
255	C₂×#97	—	94	1	no	—
256	C₂×#97	—	94	1	no	—
257	C₂×C₄×C₈	—	47	4	no	—
258	C₂×C₄×C₈	—	94	2	no	—
259	C₂×C₄×C₈	—	94	2	no	—
260	C₂×C₄×C₈	—	94	1	no	—
261	C₂×C₄×C₈	—	94	1	no	—
262	#341	—	47	4	no	—
263	#340	—	47	4	no	—
264	#339	—	47	4	no	—
265	#339	Dic₄₇	1	4	yes	complemented
266	C₄₇	#10706	1	1	yes	characteristic, complemented, Sylow
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	47	2	no	—
273	C₂×M₁₆	—	47	2	no	—
274	C₂×M₁₆	—	47	2	no	—
275	C₂×M₁₆	—	94	1	no	—
276	C₂×M₁₆	—	94	1	no	—
277	C₂×M₁₆	—	94	1	no	—
278	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
279	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
280	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	47	2	no	—
283	C₂²×C₈	—	47	2	no	—
284	C₂²×C₈	—	47	2	no	—
285	C₂²×C₈	—	47	2	no	—
286	C₂²×C₈	—	47	2	no	—
287	C₂²×C₈	—	47	1	no	—
288	C₂²×C₈	—	47	1	no	—
289	C₂²×C₈	—	47	2	no	—
290	C₂²×C₈	—	47	2	no	—
291	C₂²×C₈	—	47	2	no	—
292	C₂²×C₈	—	47	2	no	—
293	C₂²×C₈	—	94	1	no	—
294	C₂²×C₈	—	94	1	no	—
295	C₂²×C₈	—	94	1	no	—
296	C₂²×C₈	—	94	1	no	—
297	C₂²×C₈	—	94	1	no	—
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	—	47	2	no	—
301	#117	—	47	2	no	—
302	#117	—	94	1	no	—
303	#117	—	94	1	no	—
304	#117	C₄×D₄₇	1	2	yes	—
305	#117	C₂×Dic₄₇	1	2	yes	—
306	C₂×C₄⋊C₄	—	47	2	no	—
307	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	94	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	94	1	no	—
315	C₂×C₄²	C₄×D₄₇	1	2	yes	—
316	C₂×C₄²	C₄×D₄₇	1	2	yes	—
317	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
318	#97	—	94	4	no	—
319	#97	—	94	4	no	—
320	C₄×C₈	—	94	8	no	—
321	C₄×C₈	—	94	4	no	—
322	C₄×C₈	—	94	4	no	—
323	C₂⁴	#10625352	1	1	yes	characteristic
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	94	2	no	—
330	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
337	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
338	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
339	C₂²×C₄	#10625352	1	1	yes	characteristic
340	C₂²×C₄	#10625352	1	1	yes	characteristic
341	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
342	C₂²×C₄	#10625354	1	1	yes	characteristic
343	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	47	4	no	—
348	M₁₆	—	94	2	no	—
349	M₁₆	—	94	2	no	—
350	M₁₆	—	94	2	no	—
351	M₁₆	C₄×Dic₄₇	1	4	yes	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	47	4	no	—
356	C₂×C₈	—	47	4	no	—
357	C₂×C₈	—	47	2	no	—
358	C₂×C₈	—	47	2	no	—
359	C₂×C₈	—	47	2	no	—
360	C₂×C₈	—	47	2	no	—
361	C₂×C₈	—	47	4	no	—
362	C₂×C₈	—	47	4	no	—
363	C₂×C₈	—	47	2	no	—
364	C₂×C₈	—	47	2	no	—
365	C₂×C₈	—	47	4	no	—
366	C₂×C₈	—	94	2	no	—
367	C₂×C₈	—	94	2	no	—
368	C₂×C₈	—	94	2	no	—
369	C₂×C₈	—	94	2	no	—
370	C₂×C₈	—	94	2	no	—
371	C₂×C₈	—	94	2	no	—
372	C₂×C₈	—	94	2	no	—
373	C₂×C₈	—	94	2	no	—
374	C₂×C₈	—	94	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	47	4	no	—
377	C₄⋊C₄	—	94	2	no	—
378	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	94	2	no	—
382	C₂²⋊C₄	—	94	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	94	2	no	—
389	C₄²	—	94	2	no	—
390	C₄²	C₄×Dic₄₇	1	4	yes	—
391	C₂³	—	2	4	no	—
392	C₂³	#13093980	1	1	yes	characteristic
393	C₂³	#13093980	1	1	yes	characteristic
394	C₂³	#13093982	1	1	yes	characteristic
395	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
396	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
397	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
398	C₂³	#13093989	1	1	yes	characteristic
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	94	4	no	—
406	C₂×C₄	—	188	4	no	—
407	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
408	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
409	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
410	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
417	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
418	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
419	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
420	C₂×C₄	#13093980	1	1	yes	characteristic
421	C₂×C₄	#13093982	1	1	yes	characteristic
422	C₂×C₄	#13093982	1	1	yes	characteristic
423	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
424	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
425	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
426	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
427	C₂×C₄	#13093986	1	1	yes	characteristic
428	C₂×C₄	#13093986	1	1	yes	characteristic
429	C₂×C₄	#13093986	1	1	yes	characteristic
430	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
431	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
432	C₂×C₄	#13093989	1	1	yes	characteristic
433	C₂×C₄	#13093989	1	1	yes	characteristic
434	C₂×C₄	Q₈×Dic₄₇	1	1	yes	characteristic
435	C₈	—	2	4	no	—
436	C₈	—	47	4	no	—
437	C₈	—	47	4	no	—
438	C₈	—	94	4	no	—
439	C₈	—	94	4	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	#15688968	1	1	yes	characteristic
447	C₂²	#15688970	1	1	yes	characteristic
448	C₂²	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
449	C₂²	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
450	C₂²	#15688974	1	1	yes	characteristic
451	C₂²	#15688974	1	1	yes	characteristic
452	C₂²	C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
453	C₂²	#15689237	1	4	yes	—
454	C₄	—	2	8	no	—
455	C₄	—	4	4	no	—
456	C₄	—	188	4	no	—
457	C₄	C₄²×Dic₄₇	1	1	yes	characteristic
458	C₄	#95×D₄₇	1	1	yes	characteristic
459	C₄	#15688970	1	1	yes	characteristic
460	C₄	#15688970	1	1	yes	characteristic
461	C₄	C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
462	C₄	#15688974	1	1	yes	characteristic
463	C₄	C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
464	C₄	C₄⋊C₄×Dic₄₇	1	1	yes	characteristic
465	C₂	—	2	1	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	#95×Dic₄₇	1	1	yes	characteristic
470	C₂	#20243222	1	2	yes	—
471	C₂	#20243226	1	2	yes	—
472	C₂	#20243266	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₄³
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#339	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂⁴×C₄₇	#41
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#339	D₄₇
hypocenter	C₄₇	#10706
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
13. #15689081	C₄	semidirect
15. #15689079	C₄	semidirect
21. C₂×C₄×C₄₇⋊C₈	C₄	semidirect
23. #15688887	C₄	semidirect
24. #15688885	C₄	semidirect
25. #15688883	C₄	semidirect
29. C₄₇×#339	C₄	semidirect
265. #339	Dic₄₇	semidirect
266. C₄₇	#10706	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689081	2
C₂×#15689079	2
C₂²×C₄×C₄₇⋊C₈	2
C₂×#15688887	2
#20243104	2
C₂×#15688883	2
C₂×C₄₇×#339	2
#10706	47