Subgroups — #26121555

Order 12032.

1822 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688885	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×Dic₄₇	—	2	1	no	—
6	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	—	2	8	no	—
8	C₂²×C₄⋊Dic₄₇	—	2	2	no	—
9	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
10	C₂²×C₄⋊Dic₄₇	C₄	1	4	yes	complemented
11	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
12	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
13	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
14	C₂×C₂²⋊(C₄₇⋊C₈)	C₄	1	4	yes	complemented
15	#15688885	—	2	8	no	—
16	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
19	C₄₇×#380	—	2	2	no	—
20	C₄₇×#380	C₄	1	4	yes	complemented
21	C₂×#95×C₄₇	—	2	1	no	—
22	C₂³×Dic₄₇	—	2	8	no	—
23	C₂³×Dic₄₇	—	2	4	no	—
24	C₂³×Dic₄₇	—	2	2	no	—
25	C₂³×Dic₄₇	—	4	4	no	—
26	C₂³×Dic₄₇	—	4	2	no	—
27	C₂³×Dic₄₇	—	4	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	2	no	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂²×C₄₇⋊C₈	—	2	4	no	—
31	C₂²×C₄₇⋊C₈	—	2	4	no	—
32	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
33	C₂×C₄⋊Dic₄₇	—	2	8	no	—
34	C₂×C₄⋊Dic₄₇	—	2	16	no	—
35	C₂×C₄⋊Dic₄₇	—	2	4	no	—
36	C₂×C₄⋊Dic₄₇	—	2	4	no	—
37	C₂×C₄⋊Dic₄₇	—	2	2	no	—
38	C₂×C₄⋊Dic₄₇	—	2	16	no	—
39	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
40	C₂×C₄⋊Dic₄₇	D₄	1	8	yes	—
41	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
42	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	—	2	4	no	—
44	C₂³×C₄×C₄₇	—	2	4	no	—
45	C₂³×C₄×C₄₇	—	2	2	no	—
46	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	D₄	1	2	yes	—
51	C₂³×C₄×C₄₇	D₄	1	2	yes	—
52	C₂³×C₄×C₄₇	Q₈	1	2	yes	—
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	complemented
58	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
60	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
61	#95×C₄₇	—	2	4	no	—
62	C₂⁴×C₄₇	—	2	2	no	—
63	C₂⁴×C₄₇	—	2	2	no	—
64	C₂⁴×C₄₇	—	2	2	no	—
65	C₂⁴×C₄₇	—	2	2	no	—
66	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
67	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
68	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
69	C₂⁴×C₄₇	D₈	1	2	yes	—
70	C₂⁴×C₄₇	SD₁₆	1	2	yes	—
71	C₂⁴×C₄₇	SD₁₆	1	2	yes	—
72	C₂⁴×C₄₇	Q₁₆	1	2	yes	—
73	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	4	no	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	8	no	—
79	C₂²×C₄×C₄₇	—	2	8	no	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	8	no	—
82	C₂²×C₄×C₄₇	—	2	8	no	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	4	2	no	—
86	C₂²×C₄×C₄₇	—	4	2	no	—
87	C₂²×C₄×C₄₇	—	4	2	no	—
88	C₂²×C₄×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	—	4	2	no	—
90	C₂²×C₄×C₄₇	—	4	2	no	—
91	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
95	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	4	yes	—
106	C₂²×Dic₄₇	—	2	16	no	—
107	C₂²×Dic₄₇	—	2	4	no	—
108	C₂²×Dic₄₇	—	2	8	no	—
109	C₂²×Dic₄₇	—	4	8	no	—
110	C₂²×Dic₄₇	—	4	16	no	—
111	C₂²×Dic₄₇	—	4	16	no	—
112	C₂²×Dic₄₇	—	4	8	no	—
113	C₂²×Dic₄₇	—	4	2	no	—
114	C₂²×Dic₄₇	—	4	2	no	—
115	C₂²×Dic₄₇	—	4	4	no	—
116	C₄⋊C₄×C₄₇	—	2	8	no	—
117	C₄⋊C₄×C₄₇	—	4	4	no	—
118	C₂²⋊C₄×C₄₇	—	4	8	no	—
119	C₄⋊Dic₄₇	—	2	16	no	—
120	C₄⋊Dic₄₇	—	2	4	no	—
121	C₄⋊Dic₄₇	—	2	8	no	—
122	C₄⋊Dic₄₇	C₂²⋊C₄	1	8	yes	complemented
123	C₂×C₄₇⋊C₈	—	2	4	no	—
124	C₂×C₄₇⋊C₈	—	2	8	no	—
125	C₂×C₄₇⋊C₈	—	4	2	no	—
126	C₂×C₄₇⋊C₈	—	4	4	no	—
127	C₂×C₄₇⋊C₈	—	4	2	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	4	no	—
131	C₂³×C₄₇	—	2	4	no	—
132	C₂³×C₄₇	—	2	4	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	4	no	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	—	2	4	no	—
138	C₂³×C₄₇	—	2	4	no	—
139	C₂³×C₄₇	—	2	4	no	—
140	C₂³×C₄₇	—	2	4	no	—
141	C₂³×C₄₇	—	2	4	no	—
142	C₂³×C₄₇	—	2	4	no	—
143	C₂³×C₄₇	—	2	4	no	—
144	C₂³×C₄₇	#95	1	4	yes	—
145	C₂³×C₄₇	#102	1	4	yes	—
146	C₂³×C₄₇	#102	1	4	yes	—
147	C₂³×C₄₇	#103	1	4	yes	—
148	C₂³×C₄₇	#103	1	4	yes	—
149	C₂³×C₄₇	#106	1	4	yes	—
150	C₂³×C₄₇	#107	1	4	yes	—
151	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂³×C₄₇	#120	1	2	yes	—
155	C₂³×C₄₇	#123	1	2	yes	—
156	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
157	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
158	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
159	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
160	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
161	C₂³×C₄₇	#137	1	2	yes	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	8	no	—
167	C₂×C₄×C₄₇	—	2	8	no	—
168	C₂×C₄×C₄₇	—	2	8	no	—
169	C₂×C₄×C₄₇	—	2	8	no	—
170	C₂×C₄×C₄₇	—	4	4	no	—
171	C₂×C₄×C₄₇	—	4	4	no	—
172	C₂×C₄×C₄₇	—	4	4	no	—
173	C₂×C₄×C₄₇	—	8	2	no	—
174	C₂×C₄×C₄₇	—	8	2	no	—
175	C₂×C₄×C₄₇	—	8	2	no	—
176	C₂×C₄×C₄₇	—	8	2	no	—
177	C₂×C₄×C₄₇	#95	1	4	yes	—
178	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	#117	1	2	yes	—
184	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
185	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
186	C₂×C₄×C₄₇	#120	1	2	yes	—
187	C₂×C₄×C₄₇	#121	1	4	yes	—
188	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
189	C₂×C₄×C₄₇	#123	1	2	yes	—
190	C₂×Dic₄₇	—	2	8	no	—
191	C₂×Dic₄₇	—	4	32	no	—
192	C₂×Dic₄₇	—	4	4	no	—
193	C₂×Dic₄₇	—	4	4	no	—
194	C₂×Dic₄₇	—	4	8	no	—
195	C₂×Dic₄₇	—	4	8	no	—
196	C₄₇⋊C₈	—	4	4	no	—
197	#10730	—	47	1	no	maximal, Sylow
198	C₂²×C₄₇	—	2	4	no	—
199	C₂²×C₄₇	—	2	4	no	—
200	C₂²×C₄₇	—	2	8	no	—
201	C₂²×C₄₇	—	2	8	no	—
202	C₂²×C₄₇	—	2	8	no	—
203	C₂²×C₄₇	—	2	8	no	—
204	C₂²×C₄₇	—	2	4	no	—
205	C₂²×C₄₇	—	2	4	no	—
206	C₂²×C₄₇	—	2	4	no	—
207	C₂²×C₄₇	—	2	4	no	—
208	C₂²×C₄₇	#340	1	8	yes	complemented
209	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
210	C₂²×C₄₇	#379	1	1	yes	characteristic
211	C₂²×C₄₇	#381	1	1	yes	characteristic
212	C₂²×C₄₇	#385	1	2	yes	—
213	C₂²×C₄₇	#386	1	2	yes	—
214	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
215	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
216	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
217	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
218	C₂²×C₄₇	#417	1	2	yes	—
219	C₂²×C₄₇	#418	1	1	yes	characteristic
220	C₂²×C₄₇	#419	1	1	yes	characteristic
221	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
222	C₂²×C₄₇	C₂×#107	1	1	yes	characteristic
223	C₂²×C₄₇	#428	1	2	yes	—
224	C₂²×C₄₇	#447	1	2	yes	—
225	C₂²×C₄₇	#448	1	2	yes	—
226	C₂²×C₄₇	#450	1	2	yes	—
227	C₂²×C₄₇	#451	1	2	yes	—
228	C₂²×C₄₇	#480	1	2	yes	—
229	C₂²×C₄₇	#481	1	2	yes	—
230	C₂²×C₄₇	#483	1	2	yes	—
231	C₂²×C₄₇	#484	1	2	yes	—
232	C₄×C₄₇	—	2	4	no	—
233	C₄×C₄₇	—	8	4	no	—
234	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
235	C₄×C₄₇	#380	1	2	yes	—
236	C₄×C₄₇	#385	1	2	yes	—
237	C₄×C₄₇	#386	1	2	yes	—
238	Dic₄₇	—	4	8	no	—
239	C₂³×C₄⋊C₄	—	47	1	no	—
240	C₂²×C₂²⋊C₈	—	47	1	no	—
241	C₂×#380	D₄₇	1	1	yes	characteristic
242	C₂×#340	—	47	4	no	—
243	C₂×C₄₇	—	2	8	no	—
244	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
245	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
246	C₂×C₄₇	#1736	1	1	yes	characteristic
247	C₂×C₄₇	#1786	1	1	yes	characteristic
248	C₂×C₄₇	#1787	1	1	yes	characteristic
249	C₂×C₄₇	#1823	1	1	yes	characteristic
250	C₂×C₄₇	#1824	1	1	yes	characteristic
251	C₂×C₄₇	#1852	1	2	yes	—
252	C₂×C₄₇	#1853	1	2	yes	—
253	C₂×C₄₇	#1872	1	2	yes	—
254	C₂×C₄₇	#1874	1	2	yes	—
255	C₂⁴×C₄	—	94	1	no	—
256	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
257	C₂³×C₈	—	47	2	no	—
258	C₂²×C₄⋊C₄	—	47	2	no	—
259	C₂²×C₄⋊C₄	—	47	4	no	—
260	C₂²×C₄⋊C₄	—	94	8	no	—
261	C₂²×C₄⋊C₄	—	94	2	no	—
262	C₂²×C₄⋊C₄	—	94	1	no	—
263	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
264	C₂²×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₈	—	47	4	no	—
266	C₂×C₂²⋊C₈	—	94	2	no	—
267	C₂×C₂²⋊C₈	—	94	2	no	—
268	#380	—	2	2	no	—
269	#380	Dic₄₇	1	4	yes	complemented
270	C₂×#95	—	2	1	no	—
271	#340	—	94	8	no	—
272	C₄₇	#10730	1	1	yes	characteristic, complemented, Sylow
273	C₂⁵	C₂²⋊D₄₇	1	1	yes	characteristic
274	C₂³×C₄	—	2	4	no	—
275	C₂³×C₄	—	2	4	no	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	—	94	8	no	—
278	C₂³×C₄	—	94	4	no	—
279	C₂³×C₄	—	94	2	no	—
280	C₂³×C₄	—	188	4	no	—
281	C₂³×C₄	—	188	2	no	—
282	C₂³×C₄	—	188	2	no	—
283	C₂³×C₄	Dic₉₄	1	2	yes	—
284	C₂³×C₄	C₄×D₄₇	1	2	yes	—
285	C₂³×C₄	C₄×D₄₇	1	2	yes	—
286	C₂³×C₄	D₁₈₈	1	2	yes	—
287	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
288	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
289	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
290	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
291	C₂²×C₈	—	47	4	no	—
292	C₂²×C₈	—	94	2	no	—
293	C₂²×C₈	—	94	4	no	—
294	C₂²×C₈	—	94	4	no	—
295	C₂²×C₈	—	94	2	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	47	4	no	—
300	C₂×C₄⋊C₄	—	47	8	no	—
301	C₂×C₄⋊C₄	—	94	16	no	—
302	C₂×C₄⋊C₄	—	94	8	no	—
303	C₂×C₄⋊C₄	—	94	16	no	—
304	C₂×C₄⋊C₄	—	94	4	no	—
305	C₂×C₄⋊C₄	—	94	2	no	—
306	C₂×C₄⋊C₄	—	94	4	no	—
307	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	complemented
308	C₂×C₂²⋊C₄	—	2	4	no	—
309	C₂×C₂²⋊C₄	—	4	2	no	—
310	C₂×C₂²⋊C₄	—	4	2	no	—
311	C₂²⋊C₈	—	94	8	no	—
312	#95	—	2	4	no	—
313	C₂⁴	—	2	2	no	—
314	C₂⁴	—	2	2	no	—
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	Dic₄₇⋊C₄	1	2	yes	—
318	C₂⁴	(C₂×D₄₇)⋊C₄	1	2	yes	—
319	C₂⁴	#10625334	1	2	yes	—
320	C₂⁴	#10625335	1	2	yes	—
321	C₂⁴	#10625336	1	2	yes	—
322	C₂⁴	#10625337	1	2	yes	—
323	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
324	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	94	16	no	—
343	C₂²×C₄	—	94	4	no	—
344	C₂²×C₄	—	94	8	no	—
345	C₂²×C₄	—	188	16	no	—
346	C₂²×C₄	—	188	16	no	—
347	C₂²×C₄	—	188	8	no	—
348	C₂²×C₄	—	188	8	no	—
349	C₂²×C₄	—	188	2	no	—
350	C₂²×C₄	—	188	2	no	—
351	C₂²×C₄	—	188	4	no	—
352	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
353	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
354	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
355	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
356	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
357	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
358	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
359	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
363	C₂²×C₄	D₄×D₄₇	1	4	yes	—
364	C₂²×C₄	#10625352	1	4	yes	—
365	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
367	C₂×C₈	—	94	4	no	—
368	C₂×C₈	—	94	8	no	—
369	C₂×C₈	—	188	2	no	—
370	C₂×C₈	—	188	4	no	—
371	C₂×C₈	—	188	2	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	4	4	no	—
374	C₄⋊C₄	—	47	8	no	—
375	C₄⋊C₄	—	94	16	no	—
376	C₄⋊C₄	—	94	4	no	—
377	C₄⋊C₄	—	94	8	no	—
378	C₂²⋊C₄	—	4	8	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	4	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	4	no	—
394	C₂³	—	2	4	no	—
395	C₂³	C₄₇⋊#95	1	4	yes	—
396	C₂³	#13093944	1	4	yes	—
397	C₂³	#13093945	1	4	yes	—
398	C₂³	#13093947	1	4	yes	—
399	C₂³	#13093948	1	4	yes	—
400	C₂³	#13093955	1	4	yes	—
401	C₂³	#13093957	1	4	yes	—
402	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
403	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
404	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
405	C₂³	#13093992	1	2	yes	—
406	C₂³	#13094005	1	2	yes	—
407	C₂³	C₂×#10625334	1	1	yes	characteristic
408	C₂³	C₂×#10625336	1	1	yes	characteristic
409	C₂³	C₂×#10625335	1	1	yes	characteristic
410	C₂³	C₂×#10625337	1	1	yes	characteristic
411	C₂³	#13094049	1	2	yes	—
412	C₂³	#13094054	1	2	yes	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	8	2	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	—	8	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	—	94	8	no	—
429	C₂×C₄	—	188	32	no	—
430	C₂×C₄	—	188	8	no	—
431	C₂×C₄	—	188	8	no	—
432	C₂×C₄	—	188	4	no	—
433	C₂×C₄	—	188	4	no	—
434	C₂×C₄	C₄₇⋊#95	1	4	yes	—
435	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
436	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
437	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
438	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
439	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
440	C₂×C₄	#13093980	1	2	yes	—
441	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	4	yes	—
442	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
443	C₂×C₄	#13093994	1	2	yes	—
444	C₂×C₄	#13093996	1	4	yes	—
445	C₂×C₄	#13094001	1	4	yes	—
446	C₂×C₄	#13094008	1	2	yes	—
447	C₈	—	188	4	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	2	8	no	—
452	C₂²	—	2	4	no	—
453	C₂²	—	2	8	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	8	no	—
457	C₂²	—	2	8	no	—
458	C₂²	#15688885	1	8	yes	complemented
459	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
460	C₂²	#15688978	1	1	yes	characteristic
461	C₂²	#15688984	1	1	yes	characteristic
462	C₂²	#15688995	1	2	yes	—
463	C₂²	#15689003	1	2	yes	—
464	C₂²	C₂×#13093944	1	1	yes	characteristic
465	C₂²	C₂×#13093945	1	1	yes	characteristic
466	C₂²	C₂×#13093947	1	1	yes	characteristic
467	C₂²	C₂×#13093948	1	1	yes	characteristic
468	C₂²	#15689124	1	2	yes	—
469	C₂²	#15689127	1	1	yes	characteristic
470	C₂²	#15689131	1	1	yes	characteristic
471	C₂²	C₂×#13093955	1	1	yes	characteristic
472	C₂²	C₂×#13093957	1	1	yes	characteristic
473	C₂²	#15689166	1	2	yes	—
474	C₂²	#15689256	1	2	yes	—
475	C₂²	#15689261	1	2	yes	—
476	C₂²	#15689273	1	2	yes	—
477	C₂²	#15689278	1	2	yes	—
478	C₂²	#15689434	1	2	yes	—
479	C₂²	#15689439	1	2	yes	—
480	C₂²	#15689451	1	2	yes	—
481	C₂²	#15689456	1	2	yes	—
482	C₄	—	2	4	no	—
483	C₄	—	8	4	no	—
484	C₄	—	188	8	no	—
485	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
486	C₄	#15688981	1	2	yes	—
487	C₄	#15688998	1	2	yes	—
488	C₄	#15689000	1	2	yes	—
489	C₂	—	2	8	no	—
490	C₂	#20241610	1	1	yes	characteristic
491	C₂	C₂×#15688885	1	1	yes	characteristic
492	C₂	#20243109	1	1	yes	characteristic
493	C₂	#20243318	1	1	yes	characteristic
494	C₂	#20243322	1	1	yes	characteristic
495	C₂	#20243472	1	1	yes	characteristic
496	C₂	#20243476	1	1	yes	characteristic
497	C₂	#20243575	1	2	yes	—
498	C₂	#20243580	1	2	yes	—
499	C₂	#20243696	1	2	yes	—
500	C₂	#20243706	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#380	C₂
socle	C₂⁴×C₄₇	C₂×D₄
prime radical	C₂⁵×C₄₇	D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#380	D₄₇
hypocenter	C₄₇	#10730
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂×#380

Complements

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

N	H ≅ G/N	type
3. C₂×#15688885	C₂	semidirect
10. C₂²×C₄⋊Dic₄₇	C₄	semidirect
14. C₂×C₂²⋊(C₄₇⋊C₈)	C₄	semidirect
20. C₄₇×#380	C₄	semidirect
32. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
57. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
122. C₄⋊Dic₄₇	C₂²⋊C₄	semidirect
208. C₂²×C₄₇	#340	semidirect
269. #380	Dic₄₇	semidirect
272. C₄₇	#10730	semidirect
307. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
458. C₂²	#15688885	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊Dic₄₇	2
C₂²×C₂²⋊(C₄₇⋊C₈)	2
C₂×#15688885	2
C₂×C₄₇×#380	2
#10730	47