Subgroups — #26221694

Order 12032.

858 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13093983	C₂	1	1	yes	maximal, characteristic
2	#20243997	C₂	1	2	yes	maximal
3	#20243991	C₂	1	2	yes	maximal
4	#20243946	C₂	1	2	yes	maximal, complemented
5	#20243944	C₂	1	2	yes	maximal, complemented
6	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
9	#20243133	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#13093983	C₄	1	1	yes	characteristic
13	C₂×#13093983	C₄	1	1	yes	characteristic
14	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
20	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
21	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
22	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
23	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊Dic₄₇	C₄	1	1	yes	characteristic
26	C₄×C₂²⋊Dic₄₇	C₄	1	1	yes	characteristic
27	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	#15688969	C₄	1	1	yes	characteristic
30	#15688969	C₄	1	1	yes	characteristic
31	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
32	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
33	#15688878	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	#13093983	—	2	4	no	—
46	#13093983	C₈	1	8	yes	complemented
47	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₄₇	C₂×C₄	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×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
64	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
67	Dic₄₇⋊C₈	—	2	4	no	—
68	Dic₄₇⋊C₈	—	2	4	no	—
69	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
70	C₄×C₄₇⋊C₈	—	2	2	no	—
71	C₄×C₄₇⋊C₈	—	2	2	no	—
72	C₈×Dic₄₇	—	2	4	no	—
73	C₈×Dic₄₇	—	2	4	no	—
74	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
75	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
76	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
77	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
78	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
79	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
80	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
81	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
86	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄²×C₄₇	—	2	2	no	—
88	C₂×C₄²×C₄₇	—	2	2	no	—
89	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₂²⋊C₈×C₄₇	—	2	4	no	—
94	C₄×C₈×C₄₇	—	2	2	no	—
95	C₄×C₈×C₄₇	—	2	2	no	—
96	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	—	2	2	no	—
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	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	#41	1	4	yes	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	1	no	—
130	C₄²×C₄₇	—	2	1	no	—
131	C₄²×C₄₇	#41	1	2	yes	—
132	C₄²×C₄₇	#41	1	2	yes	—
133	C₂²⋊Dic₄₇	—	2	2	no	—
134	C₂²⋊Dic₄₇	—	2	2	no	—
135	C₂²⋊Dic₄₇	C₂×C₈	1	4	yes	—
136	C₂²⋊Dic₄₇	C₂×C₈	1	4	yes	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	—
140	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	—	2	2	no	—
146	C₄×Dic₄₇	—	2	2	no	—
147	C₄×Dic₄₇	—	2	2	no	—
148	C₄×Dic₄₇	—	2	2	no	—
149	C₄×Dic₄₇	—	2	2	no	—
150	C₄×Dic₄₇	C₂×C₈	1	4	yes	—
151	C₄×Dic₄₇	C₂×C₈	1	4	yes	—
152	C₄×Dic₄₇	M₁₆	1	4	yes	—
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	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	#41	1	4	yes	—
159	C₂³×C₄₇	—	2	1	no	—
160	C₂³×C₄₇	—	2	1	no	—
161	C₂³×C₄₇	—	2	1	no	—
162	C₂³×C₄₇	—	2	1	no	—
163	C₂³×C₄₇	—	2	1	no	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
166	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	8	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	4	no	—
179	C₂×C₄×C₄₇	#117	1	2	yes	—
180	C₂×C₄×C₄₇	#117	1	2	yes	—
181	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
182	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
183	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
184	C₂×C₄×C₄₇	#131	1	2	yes	—
185	C₂×C₄×C₄₇	#131	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
187	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	1	no	—
192	C₂×Dic₄₇	—	2	1	no	—
193	C₂×Dic₄₇	—	2	1	no	—
194	C₂×Dic₄₇	—	2	1	no	—
195	C₂×Dic₄₇	—	2	1	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	1	no	—
198	C₂×Dic₄₇	—	2	1	no	—
199	C₂×Dic₄₇	—	2	1	no	—
200	C₂×Dic₄₇	—	2	1	no	—
201	C₂×Dic₄₇	—	2	1	no	—
202	C₂×Dic₄₇	—	2	1	no	—
203	C₂×Dic₄₇	—	2	1	no	—
204	C₂×Dic₄₇	—	2	1	no	—
205	C₂×Dic₄₇	—	2	1	no	—
206	C₂×Dic₄₇	—	2	1	no	—
207	C₂×Dic₄₇	—	2	1	no	—
208	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
209	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
210	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
211	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
212	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
213	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
214	C₈×C₄₇	—	2	4	no	—
215	C₈×C₄₇	—	4	2	no	—
216	C₄₇⋊C₈	—	2	4	no	—
217	C₄₇⋊C₈	—	4	2	no	—
218	#21430	—	47	1	no	maximal, Sylow
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	2	2	no	—
222	C₂²×C₄₇	—	4	1	no	—
223	C₂²×C₄₇	—	4	1	no	—
224	C₂²×C₄₇	—	4	1	no	—
225	C₂²×C₄₇	—	4	1	no	—
226	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
227	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
228	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
229	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
230	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
231	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
232	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
233	C₄×C₄₇	—	2	2	no	—
234	C₄×C₄₇	—	4	1	no	—
235	C₄×C₄₇	—	4	1	no	—
236	C₄×C₄₇	#431	1	4	yes	—
237	C₄×C₄₇	#433	1	4	yes	—
238	C₄×C₄₇	#529	1	2	yes	—
239	C₄×C₄₇	#529	1	2	yes	—
240	Dic₄₇	—	2	2	no	—
241	Dic₄₇	—	2	2	no	—
242	Dic₄₇	—	2	2	no	—
243	Dic₄₇	—	2	2	no	—
244	Dic₄₇	—	2	2	no	—
245	Dic₄₇	—	2	2	no	—
246	Dic₄₇	—	4	1	no	—
247	Dic₄₇	—	4	1	no	—
248	C₄×#117	—	47	1	no	—
249	#1923	—	47	2	no	—
250	#1923	—	47	2	no	—
251	#1916	—	47	2	no	—
252	#1916	—	47	2	no	—
253	C₄×C₄⋊C₈	—	47	1	no	—
254	C₄×C₄⋊C₈	—	47	1	no	—
255	C₄×C₂²⋊C₈	—	47	1	no	—
256	C₄×C₂²⋊C₈	D₄₇	1	1	yes	characteristic
257	#1744	—	47	1	no	—
258	C₄²×C₈	—	47	1	no	—
259	C₂×C₄₇	—	4	2	no	—
260	C₂×C₄₇	#2298	1	1	yes	characteristic
261	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
262	C₂×C₄₇	C₂×#433	1	1	yes	characteristic
263	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
264	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
265	C₂×C₄₇	#2965	1	1	yes	characteristic
266	C₂×C₄₇	#2965	1	1	yes	characteristic
267	C₂×#117	—	47	1	no	—
268	C₂×#117	—	47	1	no	—
269	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
270	C₂×C₄⋊C₈	—	47	2	no	—
271	C₂×C₄⋊C₈	—	47	2	no	—
272	C₂×C₂²⋊C₈	—	47	2	no	—
273	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
274	C₂×C₄×C₈	—	47	2	no	—
275	C₂×C₄×C₈	—	47	2	no	—
276	C₂×C₄×C₈	—	47	1	no	—
277	C₂×C₄×C₈	—	47	1	no	—
278	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
280	C₄×C₄⋊C₄	—	47	1	no	—
281	C₄×C₄⋊C₄	—	47	1	no	—
282	C₄×C₄⋊C₄	—	47	1	no	—
283	C₄×C₄⋊C₄	—	47	1	no	—
284	C₄×C₂²⋊C₄	—	47	1	no	—
285	C₄×C₂²⋊C₄	—	47	1	no	—
286	C₄×C₂²⋊C₄	—	47	1	no	—
287	C₄×C₂²⋊C₄	—	47	1	no	—
288	#376	—	47	1	no	—
289	#376	—	47	1	no	—
290	C₄³	—	47	1	no	—
291	C₄³	—	47	1	no	—
292	#336	—	47	2	no	—
293	#336	—	47	2	no	—
294	#336	—	47	2	no	—
295	#336	—	47	2	no	—
296	#336	—	47	2	no	—
297	#336	C₂×D₄₇	1	2	yes	—
298	C₄₇	#21430	1	1	yes	characteristic, complemented, Sylow
299	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
300	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
301	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
302	C₂²×C₈	—	47	2	no	—
303	C₂²×C₈	—	47	2	no	—
304	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
305	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
306	#117	—	47	8	no	—
307	#117	—	94	4	no	—
308	C₂×C₄⋊C₄	—	47	1	no	—
309	C₂×C₄⋊C₄	—	47	1	no	—
310	C₂×C₄⋊C₄	—	47	1	no	—
311	C₂×C₄⋊C₄	—	47	1	no	—
312	C₂×C₂²⋊C₄	—	47	1	no	—
313	C₂×C₂²⋊C₄	—	47	1	no	—
314	C₂×C₂²⋊C₄	—	47	1	no	—
315	C₂×C₂²⋊C₄	—	47	1	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	47	1	no	—
319	C₂×C₄²	—	47	1	no	—
320	C₂×C₄²	—	47	1	no	—
321	C₂×C₄²	—	47	1	no	—
322	C₂×C₄²	—	47	1	no	—
323	C₂×C₄²	—	47	1	no	—
324	C₂×C₄²	—	47	1	no	—
325	C₂×C₄²	—	47	1	no	—
326	C₂×C₄²	—	47	1	no	—
327	C₂×C₄²	—	47	1	no	—
328	C₂×C₄²	—	47	1	no	—
329	C₂×C₄²	—	47	1	no	—
330	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
331	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
332	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
333	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
334	C₄⋊C₈	—	94	4	no	—
335	C₄⋊C₈	—	94	4	no	—
336	C₂²⋊C₈	—	2	4	no	—
337	C₂²⋊C₈	—	94	4	no	—
338	C₄×C₈	—	2	2	no	—
339	C₄×C₈	—	2	2	no	—
340	C₄×C₈	—	94	4	no	—
341	C₄×C₈	—	94	4	no	—
342	C₄×C₈	—	94	2	no	—
343	C₄×C₈	—	94	2	no	—
344	#95	—	47	1	no	—
345	#95	—	47	1	no	—
346	#95	—	47	1	no	—
347	#95	—	47	1	no	—
348	#95	—	47	1	no	—
349	#95	—	47	1	no	—
350	#95	—	47	1	no	—
351	#95	—	47	1	no	—
352	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	47	1	no	—
363	C₂²×C₄	—	47	1	no	—
364	C₂²×C₄	—	47	1	no	—
365	C₂²×C₄	—	47	1	no	—
366	C₂²×C₄	—	47	1	no	—
367	C₂²×C₄	—	47	1	no	—
368	C₂²×C₄	—	47	1	no	—
369	C₂²×C₄	—	47	1	no	—
370	C₂²×C₄	C₈×D₄₇	1	4	yes	—
371	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
376	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	47	4	no	—
383	C₂×C₈	—	94	2	no	—
384	C₂×C₈	—	94	2	no	—
385	C₂×C₈	—	94	2	no	—
386	C₂×C₈	—	94	2	no	—
387	C₂×C₈	—	94	2	no	—
388	C₂×C₈	#10625350	1	4	yes	—
389	C₄⋊C₄	—	47	4	no	—
390	C₄⋊C₄	—	47	4	no	—
391	C₄⋊C₄	—	94	2	no	—
392	C₄⋊C₄	—	94	2	no	—
393	C₂²⋊C₄	—	47	4	no	—
394	C₂²⋊C₄	—	47	4	no	—
395	C₂²⋊C₄	—	94	2	no	—
396	C₂²⋊C₄	—	94	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	47	4	no	—
402	C₄²	—	47	4	no	—
403	C₄²	—	47	4	no	—
404	C₄²	—	94	2	no	—
405	C₄²	—	94	2	no	—
406	C₄²	—	94	2	no	—
407	C₄²	—	94	2	no	—
408	C₄²	—	94	2	no	—
409	C₄²	—	94	2	no	—
410	C₄²	—	94	2	no	—
411	C₄²	—	94	2	no	—
412	C₄²	—	94	2	no	—
413	C₄²	#10625352	1	2	yes	—
414	C₄²	#10625352	1	2	yes	—
415	C₂³	—	2	1	no	—
416	C₂³	—	2	1	no	—
417	C₂³	—	2	1	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	C₂×C₈×D₄₇	1	2	yes	—
422	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	47	2	no	—
436	C₂×C₄	—	47	2	no	—
437	C₂×C₄	—	47	2	no	—
438	C₂×C₄	—	47	2	no	—
439	C₂×C₄	—	47	2	no	—
440	C₂×C₄	—	47	2	no	—
441	C₂×C₄	—	94	1	no	—
442	C₂×C₄	—	94	1	no	—
443	C₂×C₄	—	94	1	no	—
444	C₂×C₄	—	94	1	no	—
445	C₂×C₄	—	94	1	no	—
446	C₂×C₄	—	94	1	no	—
447	C₂×C₄	—	94	1	no	—
448	C₂×C₄	—	94	1	no	—
449	C₂×C₄	—	94	1	no	—
450	C₂×C₄	—	94	1	no	—
451	C₂×C₄	—	94	1	no	—
452	C₂×C₄	—	94	1	no	—
453	C₂×C₄	—	94	1	no	—
454	C₂×C₄	—	94	1	no	—
455	C₂×C₄	—	94	1	no	—
456	C₂×C₄	—	94	1	no	—
457	C₂×C₄	—	94	1	no	—
458	C₂×C₄	—	94	1	no	—
459	C₂×C₄	#13093980	1	2	yes	—
460	C₂×C₄	#13093980	1	2	yes	—
461	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
462	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
463	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
464	C₂×C₄	#13094030	1	2	yes	—
465	C₂×C₄	#13094032	1	2	yes	—
466	C₂×C₄	#41×D₄₇	1	2	yes	—
467	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
468	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
469	C₂×C₄	C₂×#10625350	1	2	yes	—
470	C₈	—	2	4	no	—
471	C₈	—	4	2	no	—
472	C₈	—	94	4	no	—
473	C₈	—	188	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	C₂×#13093980	1	1	yes	characteristic
482	C₂²	#15689591	1	1	yes	characteristic
483	C₂²	C₄×#10625350	1	1	yes	characteristic
484	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
485	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
486	C₂²	C₂×#13094030	1	1	yes	characteristic
487	C₂²	C₂×#13094032	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	1	no	—
491	C₄	—	94	2	no	—
492	C₄	—	94	2	no	—
493	C₄	—	94	2	no	—
494	C₄	—	94	2	no	—
495	C₄	—	94	2	no	—
496	C₄	—	94	2	no	—
497	C₄	—	188	1	no	—
498	C₄	—	188	1	no	—
499	C₄	#15689173	1	4	yes	—
500	C₄	#15689181	1	4	yes	—
501	C₄	#15689653	1	2	yes	—
502	C₄	#15689655	1	2	yes	—
503	C₂	—	4	2	no	—
504	C₂	#20245884	1	1	yes	characteristic
505	C₂	C₂×#15689173	1	1	yes	characteristic
506	C₂	C₂×#15689181	1	1	yes	characteristic
507	C₂	#20252344	1	1	yes	characteristic
508	C₂	C₈×#10625350	1	1	yes	characteristic
509	C₂	#20252350	1	1	yes	characteristic
510	C₂	#20252352	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×C₂²⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₂²⋊C₈	D₄₇
hypocenter	C₄₇	#21430
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₄×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
4. #20243946	C₂	semidirect
5. #20243944	C₂	semidirect
6. C₄×Dic₄₇⋊C₈	C₂	semidirect
7. C₄×Dic₄₇⋊C₈	C₂	semidirect
9. #20243133	C₂	semidirect
10. C₄×C₈×Dic₄₇	C₂	semidirect
46. #13093983	C₈	semidirect
298. C₄₇	#21430	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13093983	2
#20243997	2
#20243991	2
#20243946	2
#20243944	2
C₄×Dic₄₇⋊C₈	2
C₄×C₂²⋊(C₄₇⋊C₈)	2
#20243133	2
C₄×C₈×Dic₄₇	2
C₄×C₂²⋊C₈×C₄₇	2
#21430	47