Subgroups — #26219563

Order 12032.

1010 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689148	C₂	1	2	yes	maximal
2	C₂×C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
4	#20245792	C₂	1	1	yes	maximal, characteristic
5	#20244110	C₂	1	2	yes	maximal, complemented
6	#20244108	C₂	1	2	yes	maximal, complemented
7	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244104	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243083	C₂	1	2	yes	maximal
11	C₄₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×#10625324	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
15	C₂×#13093981	C₂²	1	2	yes	—
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	#15689148	—	2	8	no	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
20	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
22	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
23	C₄⋊C₈×D₄₇	—	2	4	no	—
24	C₄×#10625324	—	2	4	no	—
25	C₂×#13093934	C₂²	1	1	yes	characteristic
26	C₂×#13093934	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	#15688992	C₄	1	1	yes	characteristic
29	#15688992	C₄	1	1	yes	characteristic
30	#15688987	C₄	1	2	yes	—
31	#15688982	C₄	1	2	yes	—
32	#15688980	C₄	1	1	yes	characteristic
33	#15688980	C₄	1	1	yes	characteristic
34	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
35	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
36	#15688878	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	#15688877	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#336	C₂²	1	2	yes	—
44	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
47	C₂×#10625324	—	2	2	no	—
48	C₂×#10625324	—	2	2	no	—
49	C₂×#10625324	—	2	2	no	—
50	C₂×#10625324	—	2	2	no	—
51	C₂×#10625324	D₄	1	4	yes	—
52	C₂×#10625324	Q₈	1	4	yes	—
53	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
54	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₄₇	—	2	4	no	—
57	C₂×C₈×D₄₇	—	2	4	no	—
58	C₂×C₈×D₄₇	—	2	4	no	—
59	#13093981	—	2	4	no	—
60	#13093981	—	2	4	no	—
61	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
72	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
73	C₄²×D₄₇	D₄	1	4	yes	—
74	C₄²×D₄₇	Q₈	1	4	yes	—
75	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
76	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
77	Dic₄₇⋊C₈	—	2	4	no	—
78	Dic₄₇⋊C₈	—	2	4	no	—
79	Dic₄₇⋊C₈	—	2	4	no	—
80	#13093934	—	2	2	no	—
81	#13093934	—	2	2	no	—
82	C₄×C₄₇⋊C₈	—	2	2	no	—
83	C₄₇⋊#95	C₂×C₄	1	2	yes	—
84	C₄₇⋊#95	C₂×C₄	1	2	yes	—
85	C₄₇⋊#95	C₂×C₄	1	2	yes	—
86	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
87	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₇	—	2	4	no	—
94	C₄⋊C₈×C₄₇	—	2	2	no	—
95	C₄×C₈×C₄₇	—	2	2	no	—
96	#95×C₄₇	C₂×C₄	1	2	yes	—
97	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₄₇	—	2	2	no	—
109	C₂×C₄×D₄₇	—	2	2	no	—
110	C₂×C₄×D₄₇	—	4	1	no	—
111	C₂×C₄×D₄₇	—	4	1	no	—
112	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
113	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
114	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
115	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
116	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
117	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
118	C₂×C₄×D₄₇	#41	1	2	yes	—
119	C₂×C₄×D₄₇	#41	1	2	yes	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	C₂×D₄	1	2	yes	—
134	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
135	(C₂×D₄₇)⋊C₄	—	2	4	no	—
136	(C₂×D₄₇)⋊C₄	—	2	4	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	Dic₄₇⋊C₄	—	2	4	no	—
140	Dic₄₇⋊C₄	—	2	4	no	—
141	Dic₄₇⋊C₄	—	4	2	no	—
142	Dic₄₇⋊C₄	—	4	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
146	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
147	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
148	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
157	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
158	#10625324	—	2	8	no	—
159	#10625324	—	2	8	no	—
160	C₈×D₄₇	—	4	8	no	—
161	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
162	C₂²×D₄₇	—	2	1	no	—
163	C₂²×D₄₇	—	2	1	no	—
164	C₂²×D₄₇	—	2	1	no	—
165	C₂²×D₄₇	—	2	1	no	—
166	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
167	C₂²×D₄₇	C₄×D₄	1	2	yes	—
168	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
179	C₂×C₄×C₄₇	#131	1	2	yes	—
180	C₂×C₄×C₄₇	#131	1	2	yes	—
181	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂×Dic₄₇	—	2	1	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	2	2	no	—
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	—	2	2	no	—
195	C₂×Dic₄₇	—	2	2	no	—
196	C₂×Dic₄₇	—	2	2	no	—
197	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
198	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
199	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
200	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
201	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
202	C₄×D₄₇	—	2	8	no	—
203	C₄×D₄₇	—	4	4	no	—
204	C₄×D₄₇	#121	1	4	yes	—
205	C₄×D₄₇	C₂²⋊Q₈	1	4	yes	—
206	C₄×D₄₇	#125	1	4	yes	—
207	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
208	C₈×C₄₇	—	2	2	no	—
209	C₈×C₄₇	—	2	2	no	—
210	C₈×C₄₇	—	4	2	no	—
211	C₄₇⋊C₈	—	2	2	no	—
212	C₄₇⋊C₈	—	2	2	no	—
213	C₄₇⋊C₈	—	4	2	no	—
214	#21145	—	47	1	no	maximal, Sylow
215	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
217	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
220	C₂²×C₄₇	#568	1	1	yes	characteristic
221	C₂²×C₄₇	#568	1	1	yes	characteristic
222	C₂×D₄₇	—	2	2	no	—
223	C₂×D₄₇	—	2	2	no	—
224	C₂×D₄₇	—	2	2	no	—
225	C₂×D₄₇	—	2	2	no	—
226	C₂×D₄₇	—	2	2	no	—
227	C₂×D₄₇	—	2	2	no	—
228	C₂×D₄₇	#389	1	4	yes	—
229	C₄×C₄₇	—	2	2	no	—
230	C₄×C₄₇	—	4	2	no	—
231	C₄×C₄₇	—	4	2	no	—
232	C₄×C₄₇	#424	1	4	yes	complemented
233	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
234	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
235	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
236	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
237	Dic₄₇	—	2	2	no	—
238	Dic₄₇	—	2	2	no	—
239	Dic₄₇	—	4	2	no	—
240	Dic₄₇	—	4	2	no	—
241	Dic₄₇	#389	1	4	yes	—
242	C₂×#424	—	47	2	no	—
243	C₂²×C₄⋊C₈	—	47	1	no	—
244	C₂×C₄×M₁₆	—	47	1	no	—
245	#2285	—	47	1	no	—
246	#1940	—	47	2	no	—
247	#1940	—	47	2	no	—
248	#1939	—	47	1	no	—
249	#1939	—	47	1	no	—
250	#1939	—	47	1	no	—
251	#1939	D₄₇	1	1	yes	characteristic, complemented
252	#1729	—	47	2	no	—
253	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
254	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
255	C₂×C₄₇	#2905	1	1	yes	characteristic
256	C₂×C₄₇	#2935	1	1	yes	characteristic
257	C₂×C₄₇	#2935	1	1	yes	characteristic
258	C₂×C₄₇	#2962	1	1	yes	characteristic
259	C₂×C₄₇	#2962	1	1	yes	characteristic
260	D₄₇	—	2	4	no	—
261	C₂²×M₁₆	—	47	1	no	—
262	C₂²×M₁₆	—	47	1	no	—
263	C₂³×C₈	—	47	2	no	—
264	C₂×#117	—	47	2	no	—
265	C₂²×C₄²	—	47	1	no	—
266	#424	—	94	8	no	—
267	C₂×C₄⋊C₈	—	47	2	no	—
268	C₂×C₄⋊C₈	—	47	2	no	—
269	C₂×C₄⋊C₈	—	47	2	no	—
270	C₂×C₄⋊C₈	—	47	1	no	—
271	C₂×C₄⋊C₈	—	47	2	no	—
272	C₂×C₄⋊C₈	—	94	4	no	—
273	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
275	C₄×M₁₆	—	94	4	no	—
276	C₂×#97	—	47	1	no	—
277	C₂×#97	—	47	1	no	—
278	C₂×C₄×C₈	—	47	1	no	—
279	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
280	#384	—	47	1	no	—
281	#384	—	47	1	no	—
282	#382	—	47	2	no	—
283	#380	—	47	1	no	—
284	#380	—	47	1	no	—
285	#380	—	47	2	no	—
286	C₄×C₄⋊C₄	—	47	1	no	—
287	C₄×C₄⋊C₄	—	47	2	no	—
288	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
289	#336	—	47	2	no	—
290	#336	—	47	2	no	—
291	#336	—	47	2	no	—
292	#336	C₂×D₄₇	1	2	yes	—
293	C₄₇	#21145	1	1	yes	characteristic, complemented, Sylow
294	C₂³×C₄	—	47	1	no	—
295	C₂³×C₄	—	47	1	no	—
296	C₂³×C₄	—	47	1	no	—
297	C₂×M₁₆	—	47	4	no	—
298	C₂×M₁₆	—	47	4	no	—
299	C₂×M₁₆	—	94	2	no	—
300	C₂×M₁₆	—	94	2	no	—
301	C₂×M₁₆	—	94	2	no	—
302	C₂×M₁₆	—	94	2	no	—
303	C₂²×C₈	—	47	1	no	—
304	C₂²×C₈	—	47	1	no	—
305	C₂²×C₈	—	47	2	no	—
306	C₂²×C₈	—	94	4	no	—
307	C₂²×C₈	—	94	4	no	—
308	C₂²×C₈	—	94	4	no	—
309	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
310	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
311	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
312	#117	—	94	4	no	—
313	#117	—	94	4	no	—
314	C₂×C₄⋊C₄	—	47	2	no	—
315	C₂×C₄⋊C₄	—	47	2	no	—
316	C₂×C₄⋊C₄	—	47	1	no	—
317	C₂×C₄⋊C₄	—	47	1	no	—
318	C₂×C₄⋊C₄	—	47	2	no	—
319	C₂×C₄⋊C₄	—	47	2	no	—
320	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	—	47	2	no	—
323	C₂×C₂²⋊C₄	—	47	2	no	—
324	C₂×C₄²	—	47	1	no	—
325	C₂×C₄²	—	47	1	no	—
326	C₂×C₄²	—	47	1	no	—
327	C₂×C₄²	—	47	4	no	—
328	C₂×C₄²	—	47	4	no	—
329	C₂×C₄²	—	47	2	no	—
330	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
331	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
332	C₄⋊C₈	—	2	4	no	—
333	C₄⋊C₈	—	2	2	no	—
334	C₄⋊C₈	—	94	4	no	—
335	C₄⋊C₈	—	94	4	no	—
336	C₄⋊C₈	—	94	4	no	—
337	C₄⋊C₈	—	94	4	no	—
338	C₄⋊C₈	—	94	2	no	—
339	#97	—	94	2	no	—
340	#97	—	94	2	no	—
341	C₄×C₈	—	2	2	no	—
342	C₄×C₈	—	94	2	no	—
343	#95	—	47	2	no	—
344	#95	—	47	2	no	—
345	#95	—	47	2	no	—
346	#95	C₄×D₄₇	1	2	yes	—
347	C₂⁴	—	47	1	no	—
348	C₂²×C₄	—	47	1	no	—
349	C₂²×C₄	—	47	2	no	—
350	C₂²×C₄	—	47	2	no	—
351	C₂²×C₄	—	47	2	no	—
352	C₂²×C₄	—	47	2	no	—
353	C₂²×C₄	—	47	2	no	—
354	C₂²×C₄	—	47	2	no	—
355	C₂²×C₄	—	47	1	no	—
356	C₂²×C₄	—	47	1	no	—
357	C₂²×C₄	—	47	4	no	—
358	C₂²×C₄	—	47	4	no	—
359	C₂²×C₄	—	47	2	no	—
360	C₂²×C₄	—	47	2	no	—
361	C₂²×C₄	—	94	2	no	—
362	C₂²×C₄	—	94	2	no	—
363	C₂²×C₄	—	188	1	no	—
364	C₂²×C₄	—	188	1	no	—
365	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
366	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
367	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
370	M₁₆	—	94	8	no	—
371	M₁₆	—	94	8	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	47	2	no	—
380	C₂×C₈	—	47	2	no	—
381	C₂×C₈	—	94	1	no	—
382	C₂×C₈	—	94	1	no	—
383	C₂×C₈	—	94	1	no	—
384	C₂×C₈	—	94	1	no	—
385	C₂×C₈	—	94	2	no	—
386	C₂×C₈	—	94	2	no	—
387	C₂×C₈	—	94	2	no	—
388	C₂×C₈	—	188	8	no	—
389	C₂×C₈	D₄×D₄₇	1	2	yes	—
390	C₂×C₈	Q₈×D₄₇	1	2	yes	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	94	4	no	—
394	C₄⋊C₄	—	94	4	no	—
395	C₄⋊C₄	—	94	2	no	—
396	C₄⋊C₄	—	94	2	no	—
397	C₄⋊C₄	—	188	2	no	—
398	C₄⋊C₄	—	188	2	no	—
399	C₂²⋊C₄	—	94	4	no	—
400	C₂²⋊C₄	—	94	4	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	47	4	no	—
404	C₄²	—	47	4	no	—
405	C₄²	—	47	2	no	—
406	C₄²	—	47	2	no	—
407	C₄²	—	94	2	no	—
408	C₄²	—	94	2	no	—
409	C₄²	D₄×D₄₇	1	2	yes	—
410	C₄²	Q₈×D₄₇	1	2	yes	—
411	C₂³	—	47	2	no	—
412	C₂³	—	47	2	no	—
413	C₂³	—	47	2	no	—
414	C₂³	—	94	1	no	—
415	C₂³	—	94	1	no	—
416	C₂³	—	94	1	no	—
417	C₂³	—	94	1	no	—
418	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	47	2	no	—
428	C₂×C₄	—	47	2	no	—
429	C₂×C₄	—	47	2	no	—
430	C₂×C₄	—	47	4	no	—
431	C₂×C₄	—	47	4	no	—
432	C₂×C₄	—	47	4	no	—
433	C₂×C₄	—	47	4	no	—
434	C₂×C₄	—	47	2	no	—
435	C₂×C₄	—	47	2	no	—
436	C₂×C₄	—	94	1	no	—
437	C₂×C₄	—	94	1	no	—
438	C₂×C₄	—	94	1	no	—
439	C₂×C₄	—	94	1	no	—
440	C₂×C₄	—	94	8	no	—
441	C₂×C₄	—	94	2	no	—
442	C₂×C₄	—	94	2	no	—
443	C₂×C₄	—	94	2	no	—
444	C₂×C₄	—	94	2	no	—
445	C₂×C₄	—	94	2	no	—
446	C₂×C₄	—	94	2	no	—
447	C₂×C₄	—	188	4	no	—
448	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
449	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
450	C₂×C₄	#13094030	1	2	yes	—
451	C₂×C₄	#13094032	1	2	yes	—
452	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
454	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
455	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
456	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
457	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
458	C₈	—	2	2	no	—
459	C₈	—	2	2	no	—
460	C₈	—	4	2	no	—
461	C₈	—	94	2	no	—
462	C₈	—	94	2	no	—
463	C₈	—	188	2	no	—
464	C₂²	—	47	4	no	—
465	C₂²	—	94	2	no	—
466	C₂²	—	94	2	no	—
467	C₂²	—	94	2	no	—
468	C₂²	—	94	2	no	—
469	C₂²	—	94	2	no	—
470	C₂²	—	94	2	no	—
471	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
472	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
473	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
474	C₂²	C₂×#13094030	1	1	yes	characteristic
475	C₂²	C₂×#13094032	1	1	yes	characteristic
476	C₂²	#15689888	1	1	yes	characteristic
477	C₂²	#15689888	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	47	4	no	—
482	C₄	—	94	2	no	—
483	C₄	—	94	2	no	—
484	C₄	—	188	2	no	—
485	C₄	—	188	2	no	—
486	C₄	#15689148	1	4	yes	complemented
487	C₄	#121×D₄₇	1	1	yes	characteristic
488	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
489	C₄	#125×D₄₇	1	1	yes	characteristic
490	C₄	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
491	C₂	—	94	4	no	—
492	C₂	#389×D₄₇	1	1	yes	characteristic
493	C₂	C₂×#15689148	1	1	yes	characteristic
494	C₂	#20251949	1	1	yes	characteristic
495	C₂	#20252127	1	1	yes	characteristic
496	C₂	#20252133	1	1	yes	characteristic
497	C₂	#20252330	1	1	yes	characteristic
498	C₂	#20252336	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1939	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1939	D₄₇
hypocenter	C₄₇	#21145
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
5. #20244110	C₂	semidirect
6. #20244108	C₂	semidirect
7. #20244107	C₂	semidirect
8. #20244106	C₂	semidirect
9. #20244104	C₂	semidirect
11. C₄₇×#1939	C₂	semidirect
232. C₄×C₄₇	#424	semidirect
251. #1939	D₄₇	semidirect
293. C₄₇	#21145	semidirect
486. C₄	#15689148	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689148	2
C₂×C₄⋊C₈×D₄₇	2
C₂×C₄×#10625324	2
#20245792	2
#20244110	2
#20244108	2
#20244107	2
#20244106	2
#20244104	2
#20243083	2
C₄₇×#1939	2
#21145	47