Subgroups — #26235199

Order 12032.

812 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689251	C₂	1	2	yes	maximal
2	C₄²×Dic₉₄	C₂	1	1	yes	maximal, characteristic
3	#20244111	C₂	1	2	yes	maximal
4	#20244108	C₂	1	2	yes	maximal
5	#20244103	C₂	1	2	yes	maximal
6	#20243505	C₂	1	1	yes	maximal, characteristic
7	#20243503	C₂	1	1	yes	maximal, characteristic
8	#20243503	C₂	1	1	yes	maximal, characteristic
9	#20243240	C₂	1	1	yes	maximal, characteristic
10	#20243236	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1767	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₉₄	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₉₄	C₄	1	1	yes	characteristic
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	#15689251	—	2	8	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
20	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×#13093934	C₂²	1	2	yes	—
22	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
23	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
24	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
25	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
26	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
27	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
28	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
30	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
33	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
34	#15688878	C₂²	1	1	yes	characteristic
35	#15688878	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	2	yes	—
40	C₂×#97×C₄₇	C₂²	1	2	yes	—
41	C₄³×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	1	yes	characteristic
43	C₄₇×#336	C₂²	1	1	yes	characteristic
44	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₄×Dic₉₄	—	2	4	no	—
48	C₄×Dic₉₄	—	2	4	no	—
49	C₄×Dic₉₄	D₄	1	4	yes	—
50	C₄×Dic₉₄	Q₈	1	4	yes	—
51	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×Dic₄₇⋊C₄	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	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
73	Dic₄₇⋊C₈	—	2	4	no	—
74	Dic₄₇⋊C₈	—	2	4	no	—
75	Dic₄₇⋊C₈	—	2	4	no	—
76	Dic₄₇⋊C₈	—	2	4	no	—
77	#13093934	—	2	4	no	—
78	C₈×Dic₄₇	—	2	4	no	—
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	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
83	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
84	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
86	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
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	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₄₇	—	2	4	no	—
95	#97×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
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	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×Dic₉₄	—	2	2	no	—
112	C₂×Dic₉₄	—	2	2	no	—
113	C₂×Dic₉₄	C₄⋊C₄	1	4	yes	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	#41	1	4	yes	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	—	4	1	no	—
126	C₄²×C₄₇	C₂×D₄	1	2	yes	—
127	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
131	Dic₄₇⋊C₄	—	2	2	no	—
132	Dic₄₇⋊C₄	—	2	2	no	—
133	Dic₄₇⋊C₄	—	2	2	no	—
134	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
135	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
136	Dic₄₇⋊C₄	M₁₆	1	4	yes	—
137	C₄×Dic₄₇	—	2	2	no	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	4	1	no	—
145	C₄×Dic₄₇	—	4	1	no	—
146	C₄×Dic₄₇	M₁₆	1	4	yes	—
147	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
148	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
149	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
150	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	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	—	2	2	no	—
157	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	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	1	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	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
172	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
175	C₂×C₄×C₄₇	#131	1	2	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
179	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
180	C₂×Dic₄₇	—	2	1	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	1	no	—
183	C₂×Dic₄₇	—	2	1	no	—
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	1	no	—
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	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	C₂×C₄⋊C₄	1	2	yes	—
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	C₂×M₁₆	1	2	yes	—
201	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
202	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
203	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
204	Dic₉₄	—	2	8	no	—
205	C₈×C₄₇	—	2	4	no	—
206	C₈×C₄₇	—	4	2	no	—
207	C₄₇⋊C₈	—	4	2	no	—
208	C₄₇⋊C₈	—	4	2	no	—
209	#22736	—	47	1	no	maximal, Sylow
210	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
211	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
212	C₂²×C₄₇	#519	1	1	yes	characteristic
213	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
214	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
215	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
216	C₂²×C₄₇	#568	1	1	yes	characteristic
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	2	2	no	—
219	C₄×C₄₇	—	2	2	no	—
220	C₄×C₄₇	—	2	2	no	—
221	C₄×C₄₇	—	2	2	no	—
222	C₄×C₄₇	—	4	1	no	—
223	C₄×C₄₇	#548	1	2	yes	—
224	C₄×C₄₇	#557	1	2	yes	—
225	Dic₄₇	—	2	2	no	—
226	Dic₄₇	—	2	2	no	—
227	Dic₄₇	—	2	2	no	—
228	Dic₄₇	—	2	2	no	—
229	Dic₄₇	—	2	2	no	—
230	Dic₄₇	—	4	1	no	—
231	Dic₄₇	—	4	1	no	—
232	Dic₄₇	#423	1	4	yes	—
233	C₂×#446	—	47	2	no	—
234	C₄²×Q₈	—	47	1	no	—
235	#1940	—	47	2	no	—
236	#1940	—	47	2	no	—
237	#1939	—	47	2	no	—
238	#1831	—	47	1	no	—
239	#1831	—	47	1	no	—
240	#1831	—	47	1	no	—
241	#1767	—	47	1	no	—
242	#1767	D₄₇	1	1	yes	characteristic
243	C₄×C₄⋊C₈	—	47	1	no	—
244	C₂×C₄₇	#2351	1	1	yes	characteristic
245	C₂×C₄₇	C₂×#423	1	1	yes	characteristic
246	C₂×C₄₇	#2906	1	1	yes	characteristic
247	C₂×C₄₇	#2965	1	1	yes	characteristic
248	C₂×C₄₇	#2970	1	1	yes	characteristic
249	C₂×C₄₇	#2983	1	1	yes	characteristic
250	C₂×C₄₇	#2984	1	1	yes	characteristic
251	C₂×C₄×Q₈	—	47	1	no	—
252	C₂×C₄×Q₈	—	47	1	no	—
253	C₂×C₄×Q₈	—	47	1	no	—
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×C₄⋊C₈	—	47	2	no	—
259	C₂×C₄⋊C₈	—	47	2	no	—
260	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
261	C₂×#97	—	47	2	no	—
262	C₂×#97	C₂×D₄₇	1	2	yes	—
263	C₂×C₄×C₈	—	47	2	no	—
264	C₄×C₄⋊C₄	—	47	1	no	—
265	C₄×C₄⋊C₄	—	47	1	no	—
266	C₄×C₄⋊C₄	—	47	1	no	—
267	C₄×C₄⋊C₄	—	47	1	no	—
268	C₄×C₄⋊C₄	—	47	1	no	—
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	1	no	—
273	C₄³	—	47	1	no	—
274	C₄³	—	47	1	no	—
275	C₄³	C₂×D₄₇	1	1	yes	characteristic
276	#336	—	47	2	no	—
277	#336	—	47	2	no	—
278	#336	—	47	1	no	—
279	#336	—	47	1	no	—
280	#336	—	47	2	no	—
281	#336	C₂×D₄₇	1	1	yes	characteristic
282	#336	C₂×D₄₇	1	1	yes	characteristic
283	C₄₇	#22736	1	1	yes	characteristic, complemented, Sylow
284	C₂²×Q₈	—	47	1	no	—
285	C₂²×C₈	—	47	2	no	—
286	C₂²×C₈	—	47	2	no	—
287	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
288	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
289	C₄×Q₈	—	47	4	no	—
290	C₄×Q₈	—	47	4	no	—
291	C₄×Q₈	—	94	4	no	—
292	C₄×Q₈	—	94	4	no	—
293	C₂×C₄⋊C₄	—	47	1	no	—
294	C₂×C₄⋊C₄	—	47	1	no	—
295	C₂×C₄⋊C₄	—	47	1	no	—
296	C₂×C₄⋊C₄	—	47	1	no	—
297	C₂×C₄⋊C₄	—	47	1	no	—
298	C₂×C₄⋊C₄	—	47	1	no	—
299	C₂×C₄⋊C₄	—	47	1	no	—
300	C₂×C₄⋊C₄	—	47	1	no	—
301	C₂×C₄⋊C₄	—	47	1	no	—
302	C₂×C₄²	—	47	1	no	—
303	C₂×C₄²	—	47	1	no	—
304	C₂×C₄²	—	47	1	no	—
305	C₂×C₄²	—	47	1	no	—
306	C₂×C₄²	—	47	1	no	—
307	C₂×C₄²	—	47	1	no	—
308	C₂×C₄²	—	47	1	no	—
309	C₂×C₄²	—	47	1	no	—
310	C₂×C₄²	—	47	1	no	—
311	C₂×C₄²	—	47	1	no	—
312	C₂×C₄²	—	47	1	no	—
313	C₂×C₄²	—	47	1	no	—
314	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
315	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
316	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
317	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
318	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
319	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
320	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
321	C₄⋊C₈	—	2	4	no	—
322	C₄⋊C₈	—	94	4	no	—
323	C₄⋊C₈	—	94	4	no	—
324	C₄⋊C₈	—	94	4	no	—
325	C₄⋊C₈	—	94	4	no	—
326	C₄⋊C₈	—	94	4	no	—
327	#97	—	2	4	no	—
328	#97	—	94	4	no	—
329	C₄×C₈	—	94	4	no	—
330	#95	—	47	1	no	—
331	#95	—	47	1	no	—
332	#95	—	47	1	no	—
333	#95	—	47	1	no	—
334	#95	—	47	1	no	—
335	#95	—	47	1	no	—
336	C₂×Q₈	—	47	4	no	—
337	C₂×Q₈	—	94	2	no	—
338	C₂×Q₈	—	94	2	no	—
339	C₂²×C₄	—	47	1	no	—
340	C₂²×C₄	—	47	1	no	—
341	C₂²×C₄	—	47	1	no	—
342	C₂²×C₄	—	47	1	no	—
343	C₂²×C₄	—	47	1	no	—
344	C₂²×C₄	—	47	1	no	—
345	C₂²×C₄	—	47	1	no	—
346	C₂²×C₄	—	47	1	no	—
347	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	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	C₂×C₈	—	94	2	no	—
364	C₂×C₈	—	94	2	no	—
365	C₂×C₈	#10625350	1	4	yes	—
366	C₄⋊C₄	—	47	4	no	—
367	C₄⋊C₄	—	47	4	no	—
368	C₄⋊C₄	—	47	4	no	—
369	C₄⋊C₄	—	47	4	no	—
370	C₄⋊C₄	—	94	2	no	—
371	C₄⋊C₄	—	94	2	no	—
372	C₄⋊C₄	—	94	2	no	—
373	C₄⋊C₄	—	94	2	no	—
374	C₄⋊C₄	—	94	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	4	1	no	—
381	C₄²	—	47	4	no	—
382	C₄²	—	47	2	no	—
383	C₄²	—	47	2	no	—
384	C₄²	—	47	2	no	—
385	C₄²	—	47	2	no	—
386	C₄²	—	94	2	no	—
387	C₄²	—	94	2	no	—
388	C₄²	—	94	2	no	—
389	C₄²	—	94	2	no	—
390	C₄²	—	94	2	no	—
391	C₄²	—	94	2	no	—
392	C₄²	—	94	2	no	—
393	C₄²	—	188	1	no	—
394	C₄²	—	188	1	no	—
395	C₄²	D₄×D₄₇	1	2	yes	—
396	C₄²	Q₈×D₄₇	1	2	yes	—
397	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
398	Q₈	—	94	8	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	47	2	no	—
413	C₂×C₄	—	47	2	no	—
414	C₂×C₄	—	47	2	no	—
415	C₂×C₄	—	47	2	no	—
416	C₂×C₄	—	47	2	no	—
417	C₂×C₄	—	47	2	no	—
418	C₂×C₄	—	47	2	no	—
419	C₂×C₄	—	47	2	no	—
420	C₂×C₄	—	94	1	no	—
421	C₂×C₄	—	94	1	no	—
422	C₂×C₄	—	94	1	no	—
423	C₂×C₄	—	94	1	no	—
424	C₂×C₄	—	94	1	no	—
425	C₂×C₄	—	94	1	no	—
426	C₂×C₄	—	94	1	no	—
427	C₂×C₄	—	94	1	no	—
428	C₂×C₄	—	94	1	no	—
429	C₂×C₄	—	94	1	no	—
430	C₂×C₄	—	94	1	no	—
431	C₂×C₄	—	94	1	no	—
432	C₂×C₄	—	94	1	no	—
433	C₂×C₄	—	94	1	no	—
434	C₂×C₄	—	94	1	no	—
435	C₂×C₄	—	94	1	no	—
436	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
437	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
438	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
439	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
440	C₂×C₄	#13094032	1	2	yes	—
441	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
442	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
443	C₂×C₄	C₂×#10625350	1	2	yes	—
444	C₂×C₄	#13094071	1	2	yes	—
445	C₈	—	2	4	no	—
446	C₈	—	4	2	no	—
447	C₈	—	188	2	no	—
448	C₈	—	188	2	no	—
449	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
450	C₂²	C₄×#10625350	1	1	yes	characteristic
451	C₂²	#15689600	1	1	yes	characteristic
452	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
453	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
454	C₂²	C₂×#13094032	1	1	yes	characteristic
455	C₂²	#15689889	1	1	yes	characteristic
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	4	1	no	—
462	C₄	—	47	4	no	—
463	C₄	—	94	2	no	—
464	C₄	—	94	2	no	—
465	C₄	—	94	2	no	—
466	C₄	—	94	2	no	—
467	C₄	—	94	2	no	—
468	C₄	—	188	1	no	—
469	C₄	—	188	1	no	—
470	C₄	#15689782	1	2	yes	—
471	C₄	#15689851	1	2	yes	—
472	C₂	#20246308	1	1	yes	characteristic
473	C₂	#423×D₄₇	1	1	yes	characteristic
474	C₂	#20251957	1	1	yes	characteristic
475	C₂	#20252350	1	1	yes	characteristic
476	C₂	#20252399	1	1	yes	characteristic
477	C₂	#20252472	1	1	yes	characteristic
478	C₂	#20252478	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle, prime radical	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1767	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1767	D₄₇
hypocenter	C₄₇	#22736
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1767

Complements

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

N	H ≅ G/N	type
283. C₄₇	#22736	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689251	2
C₄²×Dic₉₄	2
#20244111	2
#20244108	2
#20244103	2
#20243505	2
#20243503	2
#20243240	2
#20243236	2
C₄₇×#1767	2
#22736	47