Subgroups — #26232820

Order 12032.

1036 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689254	C₂	1	2	yes	maximal, complemented
2	#20244329	C₂	1	2	yes	maximal, complemented
3	#20244329	C₂	1	2	yes	maximal, complemented
4	#20244325	C₂	1	2	yes	maximal, complemented
5	#20243372	C₂	1	2	yes	maximal
6	#20243368	C₂	1	1	yes	maximal, characteristic
7	#20243154	C₂	1	2	yes	maximal
8	#20243150	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
10	#15689254	—	2	8	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#13093935	C₂²	1	2	yes	—
18	C₂×#13093935	C₂²	1	2	yes	—
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
20	#15688878	C₂²	1	1	yes	characteristic
21	#15688878	C₂²	1	2	yes	—
22	#15688878	C₂²	1	2	yes	—
23	#15688878	C₂²	1	2	yes	—
24	#15688878	C₂²	1	1	yes	characteristic
25	#15688878	C₂²	1	2	yes	—
26	#15688878	C₂²	1	2	yes	—
27	C₄₇×#533	—	2	8	no	—
28	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
29	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
30	C₂×#125×C₄₇	C₄	1	2	yes	—
31	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
32	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
33	C₂×C₂²⋊Q₈×C₄₇	C₄	1	2	yes	—
34	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₄₇	C₂²	1	2	yes	—
38	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
40	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
41	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
44	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
45	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
46	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
47	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
48	C₂²⋊(C₄₇⋊C₈)	Q₈	1	4	yes	complemented
49	#13093935	—	2	4	no	—
50	#13093935	—	2	4	no	—
51	C₄×C₄₇⋊C₈	—	2	4	no	—
52	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
53	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
58	C₄⋊Q₈×C₄₇	—	2	4	no	—
59	C₄⋊Q₈×C₄₇	—	2	4	no	—
60	#125×C₄₇	—	2	8	no	—
61	C₂²⋊Q₈×C₄₇	—	2	4	no	—
62	C₂²⋊Q₈×C₄₇	—	2	4	no	—
63	C₂²⋊Q₈×C₄₇	—	2	8	no	—
64	C₄×Q₈×C₄₇	—	2	4	no	—
65	C₄×Q₈×C₄₇	—	2	4	no	—
66	C₄×Q₈×C₄₇	—	2	4	no	—
67	C₄×Q₈×C₄₇	D₄	1	8	yes	—
68	#117×C₄₇	—	2	4	no	—
69	#117×C₄₇	—	2	4	no	—
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₄₇	—	2	4	no	—
82	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
88	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂×Q₈×C₄₇	—	2	4	no	—
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	—	2	4	no	—
92	C₂×Q₈×C₄₇	—	4	1	no	—
93	C₂×Q₈×C₄₇	—	4	1	no	—
94	C₂×Q₈×C₄₇	—	4	2	no	—
95	C₂×Q₈×C₄₇	—	4	1	no	—
96	C₂×Q₈×C₄₇	—	4	1	no	—
97	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	4	1	no	—
104	C₂²×C₄×C₄₇	—	4	1	no	—
105	C₂²×C₄×C₄₇	—	4	1	no	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
116	C₂²×C₄×C₄₇	#41	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
118	C₄⋊C₄×C₄₇	—	2	4	no	—
119	C₄⋊C₄×C₄₇	—	2	4	no	—
120	C₄⋊C₄×C₄₇	—	2	4	no	—
121	C₄⋊C₄×C₄₇	—	2	4	no	—
122	C₄⋊C₄×C₄₇	—	2	4	no	—
123	C₄⋊C₄×C₄₇	—	2	4	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
126	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
127	C₂²⋊C₄×C₄₇	—	2	4	no	—
128	C₂²⋊C₄×C₄₇	—	2	4	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	C₂×D₄	1	4	yes	—
135	C₄²×C₄₇	C₂×D₄	1	4	yes	—
136	C₄²×C₄₇	C₂×D₄	1	4	yes	—
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	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
149	C₂³×C₄₇	—	2	1	no	—
150	C₂³×C₄₇	—	2	1	no	—
151	C₂³×C₄₇	—	2	1	no	—
152	C₂³×C₄₇	—	2	1	no	—
153	C₂³×C₄₇	—	2	1	no	—
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
156	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
157	Q₈×C₄₇	—	4	4	no	—
158	Q₈×C₄₇	—	4	8	no	—
159	Q₈×C₄₇	—	4	4	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	4	4	no	—
184	C₂×C₄×C₄₇	—	4	4	no	—
185	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
188	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
189	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
190	C₂×C₄×C₄₇	#131	1	2	yes	—
191	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
195	C₄₇⋊C₈	—	2	4	no	—
196	C₄₇⋊C₈	—	4	2	no	—
197	C₄₇⋊C₈	—	4	2	no	—
198	C₄₇⋊C₈	—	4	2	no	—
199	#22511	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	2	2	no	—
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	4	1	no	—
204	C₂²×C₄₇	—	4	1	no	—
205	C₂²×C₄₇	—	4	1	no	—
206	C₂²×C₄₇	—	4	1	no	—
207	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
209	C₂²×C₄₇	#519	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
211	C₂²×C₄₇	#568	1	1	yes	characteristic
212	C₂²×C₄₇	#568	1	1	yes	characteristic
213	C₂²×C₄₇	#568	1	1	yes	characteristic
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	2	4	no	—
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	2	2	no	—
219	C₄×C₄₇	—	2	4	no	—
220	C₄×C₄₇	—	4	1	no	—
221	C₄×C₄₇	—	4	2	no	—
222	C₄×C₄₇	—	4	2	no	—
223	C₄×C₄₇	#548	1	2	yes	—
224	C₄×C₄₇	D₄×Q₈	1	2	yes	—
225	C₂×#533	D₄₇	1	1	yes	characteristic
226	C₂×#446	—	47	2	no	—
227	#1985	—	47	2	no	—
228	#1985	—	47	2	no	—
229	#1984	—	47	2	no	—
230	#1798	—	47	2	no	—
231	#1797	—	47	1	no	—
232	#1750	—	47	2	no	—
233	#1749	—	47	1	no	—
234	C₂×C₄₇	—	4	2	no	—
235	C₂×C₄₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄₇	#2879	1	1	yes	characteristic
237	C₂×C₄₇	#2880	1	1	yes	characteristic
238	C₂×C₄₇	#2961	1	1	yes	characteristic
239	C₂×C₄₇	#2962	1	1	yes	characteristic
240	C₂×C₄₇	#2985	1	1	yes	characteristic
241	C₂×C₄₇	#2987	1	1	yes	characteristic
242	#533	—	2	8	no	—
243	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic
244	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic
245	C₂×#125	Dic₄₇	1	2	yes	—
246	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	Dic₄₇	1	2	yes	—
249	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
250	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
252	C₂×#117	C₂×D₄₇	1	2	yes	—
253	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
254	#446	—	94	8	no	—
255	C₂×C₄⋊C₈	—	47	2	no	—
256	C₂×C₄⋊C₈	—	47	2	no	—
257	C₂×C₄⋊C₈	—	47	2	no	—
258	C₂×C₂²⋊C₈	—	47	1	no	—
259	C₂×C₂²⋊C₈	—	47	2	no	—
260	C₂×C₂²⋊C₈	—	47	1	no	—
261	C₂×#97	—	47	2	no	—
262	C₂×#97	—	47	2	no	—
263	C₂×C₄×C₈	—	47	2	no	—
264	#336	—	47	1	no	—
265	#336	—	47	1	no	—
266	#336	—	47	2	no	—
267	#336	—	47	2	no	—
268	#336	—	47	2	no	—
269	#336	—	47	2	no	—
270	#336	—	47	2	no	—
271	C₄₇	#22511	1	1	yes	characteristic, complemented, Sylow
272	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
273	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
274	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
275	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
276	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
277	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
278	C₂²×C₈	—	47	2	no	—
279	C₂²×C₈	—	47	2	no	—
280	C₂²×C₈	—	47	2	no	—
281	C₂²×C₈	—	47	2	no	—
282	C₄⋊Q₈	—	2	4	no	—
283	C₄⋊Q₈	—	2	4	no	—
284	#125	—	2	8	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	—	2	4	no	—
287	C₂²⋊Q₈	—	2	8	no	—
288	C₄×Q₈	—	2	4	no	—
289	C₄×Q₈	—	2	4	no	—
290	C₄×Q₈	—	2	4	no	—
291	C₄×Q₈	C₂²⋊D₄₇	1	8	yes	—
292	#117	—	2	4	no	—
293	#117	—	2	4	no	—
294	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
295	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
296	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
297	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
298	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
299	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
302	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
305	C₂×C₄²	—	2	4	no	—
306	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
307	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
308	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
309	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
310	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
311	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
312	C₄⋊C₈	—	94	4	no	—
313	C₄⋊C₈	—	94	4	no	—
314	C₄⋊C₈	—	94	4	no	—
315	C₂²⋊C₈	—	47	4	no	—
316	C₂²⋊C₈	—	94	4	no	—
317	C₂²⋊C₈	—	94	2	no	—
318	#97	—	94	4	no	—
319	#97	—	94	4	no	—
320	C₄×C₈	—	94	4	no	—
321	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
322	C₂×Q₈	—	2	4	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	4	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	4	1	no	—
327	C₂×Q₈	—	4	2	no	—
328	C₂×Q₈	—	4	1	no	—
329	C₂×Q₈	—	4	1	no	—
330	C₂×Q₈	C₂²⋊Dic₄₇	1	4	yes	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
340	C₂²×C₄	#10625354	1	2	yes	—
341	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
342	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
343	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
344	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
345	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
347	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
348	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
351	C₂×C₈	—	47	4	no	—
352	C₂×C₈	—	94	2	no	—
353	C₂×C₈	—	94	2	no	—
354	C₂×C₈	—	94	2	no	—
355	C₂×C₈	—	94	2	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	94	2	no	—
358	C₂×C₈	—	94	2	no	—
359	C₂×C₈	—	94	2	no	—
360	C₂×C₈	—	94	2	no	—
361	C₂×C₈	—	94	2	no	—
362	C₂×C₈	—	94	2	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	C₂²⋊Dic₄₇	1	8	yes	—
371	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
380	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
381	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	Q₈×Dic₄₇	1	2	yes	—
389	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
390	Q₈	—	4	4	no	—
391	Q₈	—	4	8	no	—
392	Q₈	—	4	4	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
419	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
420	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
421	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
422	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
423	C₂×C₄	#13094031	1	2	yes	—
424	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
425	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
427	C₂×C₄	#13094072	1	2	yes	—
428	C₈	—	94	4	no	—
429	C₈	—	188	2	no	—
430	C₈	—	188	2	no	—
431	C₈	—	188	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
440	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
441	C₂²	#15689601	1	1	yes	characteristic
442	C₂²	C₂×#13094031	1	1	yes	characteristic
443	C₂²	#15689890	1	1	yes	characteristic
444	C₂²	#15689890	1	1	yes	characteristic
445	C₂²	#15689890	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	4	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	1	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	#15689784	1	2	yes	—
456	C₄	Q₈×C₂²⋊D₄₇	1	2	yes	—
457	C₂	—	4	2	no	—
458	C₂	Q₈×C₂²⋊Dic₄₇	1	1	yes	characteristic
459	C₂	#20251833	1	1	yes	characteristic
460	C₂	#20251837	1	1	yes	characteristic
461	C₂	#20252329	1	1	yes	characteristic
462	C₂	#20252337	1	1	yes	characteristic
463	C₂	#20252483	1	1	yes	characteristic
464	C₂	#20252494	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₂×C₄₇×#533	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	#22511
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. C₂×#15689254	C₂	semidirect
2. #20244329	C₂	semidirect
3. #20244329	C₂	semidirect
4. #20244325	C₂	semidirect
48. C₂²⋊(C₄₇⋊C₈)	Q₈	semidirect
271. C₄₇	#22511	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689254	2
#20244329	2
#20244325	2
#20243372	2
#20243368	2
#20243154	2
#20243150	2
C₂×C₄₇×#533	2
#22511	47