Subgroups — #26234064

Order 12032.

916 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244104	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243945	C₂	1	2	yes	maximal, complemented
5	#20243943	C₂	1	2	yes	maximal, complemented
6	#20243367	C₂	1	2	yes	maximal
7	#20243365	C₂	1	1	yes	maximal, characteristic
8	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×(C₂×D₄₇)⋊C₈	C₂	1	1	yes	maximal, characteristic
10	C₄×(C₂×D₄₇)⋊C₈	C₂	1	2	yes	maximal
11	C₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊C₄×D₄₇	C₄	1	1	yes	characteristic
13	C₂×C₄⋊C₄×D₄₇	C₄	1	1	yes	characteristic
14	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄²×D₄₇	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
24	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
25	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
26	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
27	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
28	#15688974	C₄	1	2	yes	—
29	#95×D₄₇	C₄	1	2	yes	—
30	#15688878	C₂²	1	2	yes	—
31	#15688877	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	1	yes	characteristic
35	#15688877	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
43	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
45	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
53	C₄⋊C₄×D₄₇	—	2	4	no	—
54	C₄⋊C₄×D₄₇	C₈	1	8	yes	complemented
55	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	C₄²×D₄₇	—	2	2	no	—
62	C₄²×D₄₇	—	2	2	no	—
63	C₄²×D₄₇	—	4	2	no	—
64	C₄²×D₄₇	—	4	2	no	—
65	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
66	Dic₄₇⋊C₈	—	4	2	no	—
67	Dic₄₇⋊C₈	—	4	2	no	—
68	(C₂×D₄₇)⋊C₈	—	2	4	no	—
69	(C₂×D₄₇)⋊C₈	—	2	2	no	—
70	(C₂×D₄₇)⋊C₈	Q₈	1	4	yes	—
71	C₄×C₄₇⋊C₈	—	2	2	no	—
72	C₄×C₄₇⋊C₈	—	4	2	no	—
73	C₄₇⋊#95	C₂×C₄	1	2	yes	—
74	C₄₇⋊#95	C₂×C₄	1	2	yes	—
75	C₄₇⋊#95	C₂×C₄	1	2	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₇	—	2	2	no	—
84	C₄×C₈×C₄₇	—	2	2	no	—
85	C₄×C₈×C₄₇	—	4	2	no	—
86	#95×C₄₇	C₂×C₄	1	2	yes	—
87	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₄₇	—	2	2	no	—
99	C₂×C₄×D₄₇	—	2	2	no	—
100	C₂×C₄×D₄₇	—	2	1	no	—
101	C₂×C₄×D₄₇	—	2	1	no	—
102	C₂×C₄×D₄₇	—	2	1	no	—
103	C₂×C₄×D₄₇	—	2	1	no	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	—	2	4	no	—
106	C₂×C₄×D₄₇	—	2	2	no	—
107	C₂×C₄×D₄₇	—	2	4	no	—
108	C₂×C₄×D₄₇	—	4	2	no	—
109	C₂×C₄×D₄₇	—	4	2	no	—
110	C₂×C₄×D₄₇	—	4	2	no	—
111	C₂×C₄×D₄₇	—	4	1	no	—
112	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
113	C₂×C₄×D₄₇	C₂×C₈	1	8	yes	—
114	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
115	C₂×C₄×D₄₇	#41	1	2	yes	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	—	2	1	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
125	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	—
126	C₄⋊C₄×C₄₇	M₁₆	1	4	yes	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	#41	1	2	yes	—
130	C₄²×C₄₇	#41	1	2	yes	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	—
133	Dic₄₇⋊C₄	—	2	4	no	—
134	Dic₄₇⋊C₄	C₂×C₈	1	8	yes	—
135	C₄×Dic₄₇	—	2	2	no	—
136	C₄×Dic₄₇	—	2	2	no	—
137	C₄×Dic₄₇	—	2	1	no	—
138	C₄×Dic₄₇	—	2	1	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	4	2	no	—
142	C₄×Dic₄₇	—	4	2	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
152	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂²×D₄₇	—	2	1	no	—
154	C₂²×D₄₇	—	2	1	no	—
155	C₂²×D₄₇	—	2	1	no	—
156	C₂²×D₄₇	—	2	1	no	—
157	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
158	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
159	C₂²×D₄₇	#131	1	2	yes	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	#117	1	2	yes	—
167	C₂×C₄×C₄₇	#117	1	2	yes	—
168	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
169	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
170	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
171	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
172	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	1	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	2	2	no	—
187	C₂×Dic₄₇	—	2	1	no	—
188	C₂×Dic₄₇	—	2	2	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
191	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
192	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
193	C₄×D₄₇	—	2	2	no	—
194	C₄×D₄₇	—	2	2	no	—
195	C₄×D₄₇	—	2	2	no	—
196	C₄×D₄₇	—	2	2	no	—
197	C₄×D₄₇	—	2	8	no	—
198	C₄×D₄₇	—	4	8	no	—
199	C₄×D₄₇	—	4	4	no	—
200	C₄×D₄₇	—	4	8	no	—
201	C₈×C₄₇	—	2	2	no	—
202	C₈×C₄₇	—	4	1	no	—
203	C₈×C₄₇	—	4	2	no	—
204	C₄₇⋊C₈	—	2	2	no	—
205	C₄₇⋊C₈	—	4	2	no	—
206	C₄₇⋊C₈	—	4	1	no	—
207	#22625	—	47	1	no	maximal, Sylow
208	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
210	C₂²×C₄₇	#518	1	1	yes	characteristic
211	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
212	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
214	C₂²×C₄₇	#568	1	1	yes	characteristic
215	C₂×D₄₇	—	2	2	no	—
216	C₂×D₄₇	—	2	2	no	—
217	C₂×D₄₇	—	2	2	no	—
218	C₂×D₄₇	—	2	2	no	—
219	C₂×D₄₇	—	2	2	no	—
220	C₂×D₄₇	—	2	2	no	—
221	C₂×D₄₇	C₈×Q₈	1	4	yes	—
222	C₄×C₄₇	—	2	2	no	—
223	C₄×C₄₇	—	2	4	no	—
224	C₄×C₄₇	—	2	4	no	—
225	C₄×C₄₇	#431	1	4	yes	—
226	C₄×C₄₇	#553	1	1	yes	characteristic
227	C₄×C₄₇	#553	1	1	yes	characteristic
228	C₄×C₄₇	#554	1	1	yes	characteristic
229	C₄×C₄₇	#554	1	1	yes	characteristic
230	Dic₄₇	—	2	2	no	—
231	Dic₄₇	—	2	2	no	—
232	Dic₄₇	—	2	4	no	—
233	Dic₄₇	—	4	1	no	—
234	Dic₄₇	—	4	2	no	—
235	C₂×C₄×C₄⋊C₄	—	47	1	no	—
236	#1939	—	47	1	no	—
237	#1939	—	47	1	no	—
238	#1916	—	47	2	no	—
239	#1916	—	47	2	no	—
240	#1797	—	47	1	no	—
241	#1797	—	47	2	no	—
242	C₈×C₄⋊C₄	—	47	1	no	—
243	C₈×C₄⋊C₄	D₄₇	1	1	yes	characteristic, complemented
244	C₄×C₂²⋊C₈	—	47	1	no	—
245	C₄×C₂²⋊C₈	—	47	2	no	—
246	C₂×C₄₇	#2345	1	1	yes	characteristic
247	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
248	C₂×C₄₇	#2924	1	1	yes	characteristic
249	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
250	C₂×C₄₇	Q₈×M₁₆	1	1	yes	characteristic
251	C₂×C₄₇	#2972	1	1	yes	characteristic
252	C₂×C₄₇	#2974	1	1	yes	characteristic
253	D₄₇	—	2	4	no	—
254	C₂²×C₄⋊C₄	—	47	1	no	—
255	C₂²×C₄⋊C₄	—	47	1	no	—
256	C₂²×C₄²	—	47	1	no	—
257	C₂²×C₄²	—	47	2	no	—
258	C₂×C₄⋊C₈	—	47	1	no	—
259	C₂×C₄⋊C₈	—	47	2	no	—
260	C₂×C₄⋊C₈	—	47	2	no	—
261	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
262	C₂×C₂²⋊C₈	—	47	1	no	—
263	C₂×C₂²⋊C₈	—	47	2	no	—
264	C₂×C₂²⋊C₈	—	47	1	no	—
265	C₂×C₄×C₈	—	47	1	no	—
266	C₂×C₄×C₈	—	47	2	no	—
267	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
269	C₄×C₄⋊C₄	—	47	1	no	—
270	C₄×C₄⋊C₄	—	47	1	no	—
271	C₄×C₄⋊C₄	—	47	1	no	—
272	C₄×C₄⋊C₄	—	47	2	no	—
273	C₄×C₄⋊C₄	—	47	2	no	—
274	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
275	C₂×#95	—	47	2	no	—
276	#336	—	47	2	no	—
277	#336	—	47	1	no	—
278	#336	—	47	1	no	—
279	#336	—	47	2	no	—
280	#336	—	47	2	no	—
281	#336	—	47	2	no	—
282	#336	C₂×D₄₇	1	2	yes	—
283	C₄₇	#22625	1	1	yes	characteristic, complemented, Sylow
284	C₂³×C₄	—	47	1	no	—
285	C₂³×C₄	—	47	1	no	—
286	C₂³×C₄	—	47	2	no	—
287	C₂³×C₄	—	47	2	no	—
288	C₂³×C₄	—	47	1	no	—
289	C₂²×C₈	—	47	1	no	—
290	C₂²×C₈	—	47	1	no	—
291	C₂²×C₈	—	47	2	no	—
292	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
293	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
294	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	—	47	2	no	—
296	C₂×C₄⋊C₄	—	47	1	no	—
297	C₂×C₄⋊C₄	—	47	8	no	—
298	C₂×C₄⋊C₄	—	47	2	no	—
299	C₂×C₄⋊C₄	—	47	1	no	—
300	C₂×C₄⋊C₄	—	94	4	no	—
301	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
303	C₂×C₄²	—	47	1	no	—
304	C₂×C₄²	—	47	1	no	—
305	C₂×C₄²	—	47	1	no	—
306	C₂×C₄²	—	47	2	no	—
307	C₂×C₄²	—	47	2	no	—
308	C₂×C₄²	—	47	2	no	—
309	C₂×C₄²	—	94	2	no	—
310	C₂×C₄²	—	94	2	no	—
311	C₂×C₄²	—	188	2	no	—
312	C₂×C₄²	—	188	2	no	—
313	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
314	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
315	C₄⋊C₈	—	2	2	no	—
316	C₄⋊C₈	—	94	2	no	—
317	C₄⋊C₈	—	188	2	no	—
318	C₄⋊C₈	—	188	2	no	—
319	C₂²⋊C₈	—	47	4	no	—
320	C₂²⋊C₈	—	94	2	no	—
321	C₂²⋊C₈	—	94	4	no	—
322	C₄×C₈	—	2	2	no	—
323	C₄×C₈	—	4	2	no	—
324	C₄×C₈	—	94	2	no	—
325	C₄×C₈	—	188	2	no	—
326	#95	—	47	2	no	—
327	#95	—	47	2	no	—
328	#95	—	47	2	no	—
329	#95	C₄×D₄₇	1	2	yes	—
330	C₂⁴	—	47	1	no	—
331	C₂²×C₄	—	47	2	no	—
332	C₂²×C₄	—	47	1	no	—
333	C₂²×C₄	—	47	1	no	—
334	C₂²×C₄	—	47	4	no	—
335	C₂²×C₄	—	47	2	no	—
336	C₂²×C₄	—	47	2	no	—
337	C₂²×C₄	—	47	8	no	—
338	C₂²×C₄	—	47	1	no	—
339	C₂²×C₄	—	47	2	no	—
340	C₂²×C₄	—	94	4	no	—
341	C₂²×C₄	—	94	2	no	—
342	C₂²×C₄	—	94	2	no	—
343	C₂²×C₄	—	94	2	no	—
344	C₂²×C₄	—	94	1	no	—
345	C₂²×C₄	—	94	1	no	—
346	C₂²×C₄	—	94	1	no	—
347	C₂²×C₄	—	94	1	no	—
348	C₂²×C₄	—	94	2	no	—
349	C₂²×C₄	—	94	4	no	—
350	C₂²×C₄	—	188	2	no	—
351	C₂²×C₄	—	188	2	no	—
352	C₂²×C₄	—	188	2	no	—
353	C₂²×C₄	—	188	1	no	—
354	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
356	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
357	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
358	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	47	2	no	—
368	C₂×C₈	—	94	1	no	—
369	C₂×C₈	—	94	1	no	—
370	C₂×C₈	—	94	2	no	—
371	C₂×C₈	—	94	1	no	—
372	C₂×C₈	—	94	1	no	—
373	C₂×C₈	—	94	2	no	—
374	C₂×C₈	—	94	1	no	—
375	C₂×C₈	—	94	2	no	—
376	C₂×C₈	Q₈×D₄₇	1	2	yes	—
377	C₄⋊C₄	—	47	8	no	—
378	C₄⋊C₄	—	47	4	no	—
379	C₄⋊C₄	—	94	4	no	—
380	C₄⋊C₄	—	94	2	no	—
381	C₄⋊C₄	C₈×D₄₇	1	4	yes	—
382	C₄⋊C₄	#10625324	1	4	yes	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	94	2	no	—
386	C₄²	—	94	2	no	—
387	C₄²	—	94	1	no	—
388	C₄²	—	94	1	no	—
389	C₄²	—	94	2	no	—
390	C₄²	—	94	2	no	—
391	C₄²	—	188	2	no	—
392	C₄²	—	188	2	no	—
393	C₄²	#10625350	1	2	yes	—
394	C₄²	#10625350	1	2	yes	—
395	C₂³	—	47	2	no	—
396	C₂³	—	47	2	no	—
397	C₂³	—	47	2	no	—
398	C₂³	—	94	1	no	—
399	C₂³	—	94	1	no	—
400	C₂³	—	94	1	no	—
401	C₂³	—	94	1	no	—
402	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	47	2	no	—
410	C₂×C₄	—	47	2	no	—
411	C₂×C₄	—	47	4	no	—
412	C₂×C₄	—	94	1	no	—
413	C₂×C₄	—	94	1	no	—
414	C₂×C₄	—	94	2	no	—
415	C₂×C₄	—	94	1	no	—
416	C₂×C₄	—	94	1	no	—
417	C₂×C₄	—	94	2	no	—
418	C₂×C₄	—	94	2	no	—
419	C₂×C₄	—	94	2	no	—
420	C₂×C₄	—	94	2	no	—
421	C₂×C₄	—	94	2	no	—
422	C₂×C₄	—	94	8	no	—
423	C₂×C₄	—	94	1	no	—
424	C₂×C₄	—	94	2	no	—
425	C₂×C₄	—	94	2	no	—
426	C₂×C₄	—	94	2	no	—
427	C₂×C₄	—	94	1	no	—
428	C₂×C₄	—	94	1	no	—
429	C₂×C₄	—	188	8	no	—
430	C₂×C₄	—	188	8	no	—
431	C₂×C₄	—	188	4	no	—
432	C₂×C₄	#13093981	1	2	yes	—
433	C₂×C₄	#13093981	1	2	yes	—
434	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
435	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
436	C₂×C₄	C₂×#10625324	1	4	yes	—
437	C₂×C₄	C₂×#10625324	1	2	yes	—
438	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
439	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
440	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
441	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
442	C₂×C₄	#13094069	1	1	yes	characteristic
443	C₂×C₄	#13094070	1	1	yes	characteristic
444	C₈	—	2	2	no	—
445	C₈	—	4	1	no	—
446	C₈	—	4	2	no	—
447	C₈	—	94	2	no	—
448	C₈	—	188	2	no	—
449	C₈	—	188	1	no	—
450	C₂²	—	47	4	no	—
451	C₂²	—	94	2	no	—
452	C₂²	—	94	2	no	—
453	C₂²	—	94	2	no	—
454	C₂²	—	94	2	no	—
455	C₂²	—	94	2	no	—
456	C₂²	—	94	2	no	—
457	C₂²	C₂×#13093981	1	1	yes	characteristic
458	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
459	C₂²	#15689595	1	1	yes	characteristic
460	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
461	C₂²	C₂²×#10625324	1	1	yes	characteristic
462	C₂²	#131×D₄₇	1	1	yes	characteristic
463	C₂²	#15689888	1	1	yes	characteristic
464	C₄	—	2	4	no	—
465	C₄	—	2	2	no	—
466	C₄	—	2	4	no	—
467	C₄	—	94	2	no	—
468	C₄	—	94	2	no	—
469	C₄	—	94	4	no	—
470	C₄	—	188	2	no	—
471	C₄	—	188	1	no	—
472	C₄	#15689174	1	4	yes	—
473	C₄	#15689817	1	1	yes	characteristic
474	C₄	#15689823	1	1	yes	characteristic
475	C₄	#15689828	1	1	yes	characteristic
476	C₄	#15689833	1	1	yes	characteristic
477	C₂	—	94	4	no	—
478	C₂	#20246261	1	1	yes	characteristic
479	C₂	C₂×#15689174	1	1	yes	characteristic
480	C₂	#20252043	1	1	yes	characteristic
481	C₂	C₈×Q₈×D₄₇	1	1	yes	characteristic
482	C₂	Q₈×#10625324	1	1	yes	characteristic
483	C₂	#20252409	1	1	yes	characteristic
484	C₂	#20252421	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₈×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#22625
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #20244106	C₂	semidirect
3. #20244104	C₂	semidirect
4. #20243945	C₂	semidirect
5. #20243943	C₂	semidirect
8. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₇	C₂	semidirect
54. C₄⋊C₄×D₄₇	C₈	semidirect
243. C₈×C₄⋊C₄	D₄₇	semidirect
283. C₄₇	#22625	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊C₄×D₄₇	2
#20244106	2
#20244104	2
#20243945	2
#20243943	2
#20243367	2
#20243365	2
C₄⋊C₄×C₄₇⋊C₈	2
C₄×(C₂×D₄₇)⋊C₈	2
C₈×C₄⋊C₄×C₄₇	2
#22625	47