Subgroups — #26213774

Order 12032.

1042 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689080	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689077	C₂	1	1	yes	maximal, characteristic
3	#20245727	C₂	1	1	yes	maximal, characteristic
4	#20243140	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243138	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243138	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243136	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243135	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243133	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243132	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243083	C₂	1	1	yes	maximal, characteristic
12	#20243083	C₂	1	1	yes	maximal, characteristic
13	#20243080	C₂	1	1	yes	maximal, characteristic
14	#336×D₄₇	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1746	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	1	yes	characteristic
17	C₂²×#10625324	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
20	C₂×#13093981	C₂²	1	1	yes	characteristic
21	C₂×#13093981	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
23	#15689080	C₄	1	8	yes	complemented
24	#15689077	C₄	1	8	yes	complemented
25	C₂×#13093935	C₂²	1	1	yes	characteristic
26	C₂×#13093934	C₂²	1	1	yes	characteristic
27	C₂×#13093934	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688974	C₄	1	2	yes	—
32	#15688974	C₄	1	2	yes	—
33	#15688970	C₄	1	2	yes	—
34	#15688970	C₄	1	2	yes	—
35	#15688969	C₂²	1	1	yes	characteristic
36	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
37	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
38	#15688878	C₂²	1	1	yes	characteristic
39	#15688878	C₂²	1	1	yes	characteristic
40	#15688878	C₂²	1	1	yes	characteristic
41	#15688878	C₂²	1	1	yes	characteristic
42	#15688877	C₂²	1	1	yes	characteristic
43	#15688877	C₂²	1	1	yes	characteristic
44	#15688877	C₂²	1	1	yes	characteristic
45	#15688877	C₂²	1	1	yes	characteristic
46	#15688877	C₂²	1	1	yes	characteristic
47	#15688877	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
52	C₄₇×#376	C₂²	1	1	yes	characteristic
53	C₄₇×#336	C₂²	1	1	yes	characteristic
54	C₄₇×#336	C₂²	1	1	yes	characteristic
55	C₄₇×#336	C₂²	1	1	yes	characteristic
56	C₄₇×#336	C₂²	1	1	yes	characteristic
57	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
58	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
59	C₂×#10625324	—	2	2	no	—
60	C₂×#10625324	—	2	2	no	—
61	C₂×#10625324	—	2	2	no	—
62	C₂×#10625324	—	2	2	no	—
63	C₂×#10625324	C₂×C₄	1	4	yes	—
64	C₂×#10625324	C₂×C₄	1	4	yes	—
65	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₂×C₈×D₄₇	—	2	2	no	—
70	C₂×C₈×D₄₇	—	2	2	no	—
71	C₂×C₈×D₄₇	—	2	2	no	—
72	C₂×C₈×D₄₇	—	2	2	no	—
73	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
74	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
75	#13093981	—	2	2	no	—
76	#13093981	—	2	2	no	—
77	#13093981	C₂×C₄	1	4	yes	—
78	#13093981	C₂×C₄	1	4	yes	—
79	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
80	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
83	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
86	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
87	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
88	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
89	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
90	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
93	C₄²×D₄₇	—	2	2	no	—
94	C₄²×D₄₇	—	2	2	no	—
95	#13093935	C₂×C₄	1	4	yes	complemented
96	#13093934	C₂×C₄	1	4	yes	complemented
97	#13093934	C₂×C₄	1	4	yes	complemented
98	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
99	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
100	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
101	C₄₇⋊#95	C₂×C₄	1	2	yes	—
102	C₄₇⋊#95	C₂×C₄	1	2	yes	—
103	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
110	#97×C₄₇	C₂×C₄	1	4	yes	complemented
111	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
112	#95×C₄₇	C₂×C₄	1	2	yes	—
113	#95×C₄₇	C₂×C₄	1	2	yes	—
114	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
121	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
124	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₄₇	—	2	4	no	—
126	C₂×C₄×D₄₇	—	2	4	no	—
127	C₂×C₄×D₄₇	—	4	2	no	—
128	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
129	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
130	C₂×C₄×D₄₇	#41	1	2	yes	—
131	C₂×C₄×D₄₇	#41	1	2	yes	—
132	C₂×C₄×D₄₇	#41	1	2	yes	—
133	C₂×C₄×D₄₇	#41	1	2	yes	—
134	C₂×C₈×C₄₇	—	2	1	no	—
135	C₂×C₈×C₄₇	—	2	1	no	—
136	C₂×C₈×C₄₇	—	2	1	no	—
137	C₂×C₈×C₄₇	—	2	1	no	—
138	C₂×C₈×C₄₇	—	2	1	no	—
139	C₂×C₈×C₄₇	—	2	1	no	—
140	C₂×C₈×C₄₇	—	2	1	no	—
141	C₂×C₈×C₄₇	—	2	1	no	—
142	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
146	C₄²×C₄₇	—	2	1	no	—
147	C₄²×C₄₇	—	2	1	no	—
148	C₄²×C₄₇	—	2	1	no	—
149	C₄²×C₄₇	—	2	1	no	—
150	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
151	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
152	(C₂×D₄₇)⋊C₄	—	2	4	no	—
153	(C₂×D₄₇)⋊C₄	C₄²	1	4	yes	—
154	(C₂×D₄₇)⋊C₄	C₄²	1	4	yes	—
155	Dic₄₇⋊C₄	—	2	4	no	—
156	Dic₄₇⋊C₄	C₄²	1	4	yes	—
157	Dic₄₇⋊C₄	C₄²	1	4	yes	—
158	C₄×Dic₄₇	—	2	1	no	—
159	C₄×Dic₄₇	—	2	1	no	—
160	C₄×Dic₄₇	—	2	1	no	—
161	C₄×Dic₄₇	—	2	1	no	—
162	C₄×Dic₄₇	—	2	4	no	—
163	C₄×Dic₄₇	—	2	4	no	—
164	C₄×Dic₄₇	—	2	4	no	—
165	C₄×Dic₄₇	—	4	2	no	—
166	C₄×Dic₄₇	—	4	2	no	—
167	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
168	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
169	C₂×C₄₇⋊C₈	—	2	1	no	—
170	C₂×C₄₇⋊C₈	—	2	1	no	—
171	C₂×C₄₇⋊C₈	—	2	1	no	—
172	C₂×C₄₇⋊C₈	—	2	1	no	—
173	C₂×C₄₇⋊C₈	—	2	1	no	—
174	C₂×C₄₇⋊C₈	—	2	1	no	—
175	C₂×C₄₇⋊C₈	—	2	1	no	—
176	C₂×C₄₇⋊C₈	—	2	1	no	—
177	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
178	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
179	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
180	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
181	#10625324	—	2	8	no	—
182	#10625324	—	2	8	no	—
183	C₈×D₄₇	—	2	8	no	—
184	C₈×D₄₇	—	2	8	no	—
185	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
186	C₂²×D₄₇	—	2	2	no	—
187	C₂²×D₄₇	—	2	2	no	—
188	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
189	C₂²×D₄₇	#117	1	2	yes	—
190	C₂²×D₄₇	#117	1	2	yes	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
200	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
201	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
207	C₂×Dic₄₇	—	2	2	no	—
208	C₂×Dic₄₇	—	2	2	no	—
209	C₂×Dic₄₇	—	2	2	no	—
210	C₂×Dic₄₇	—	2	2	no	—
211	C₂×Dic₄₇	—	2	2	no	—
212	C₂×Dic₄₇	—	2	2	no	—
213	C₂×Dic₄₇	—	2	2	no	—
214	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
215	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
216	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
217	C₂×Dic₄₇	#117	1	2	yes	—
218	C₂×Dic₄₇	#117	1	2	yes	—
219	C₂×Dic₄₇	#131	1	4	yes	—
220	C₄×D₄₇	—	4	8	no	—
221	C₄×D₄₇	#117	1	4	yes	—
222	C₄×D₄₇	#117	1	4	yes	—
223	C₄×D₄₇	#117	1	4	yes	—
224	C₄×D₄₇	#117	1	4	yes	—
225	C₈×C₄₇	—	2	2	no	—
226	C₈×C₄₇	—	2	2	no	—
227	C₈×C₄₇	—	2	2	no	—
228	C₈×C₄₇	—	2	2	no	—
229	C₄₇⋊C₈	—	2	2	no	—
230	C₄₇⋊C₈	—	2	2	no	—
231	C₄₇⋊C₈	—	2	2	no	—
232	C₄₇⋊C₈	—	2	2	no	—
233	#20368	—	47	1	no	maximal, Sylow
234	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
235	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
236	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
237	C₂²×C₄₇	C₂×#131	1	2	yes	—
238	C₂²×C₄₇	#568	1	2	yes	—
239	C₂×D₄₇	—	2	2	no	—
240	C₂×D₄₇	—	2	2	no	—
241	C₂×D₄₇	—	2	4	no	—
242	C₂×D₄₇	—	2	4	no	—
243	C₂×D₄₇	#376	1	4	yes	—
244	C₄×C₄₇	—	2	2	no	—
245	C₄×C₄₇	—	2	2	no	—
246	C₄×C₄₇	—	4	2	no	—
247	C₄×C₄₇	—	4	2	no	—
248	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
249	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
250	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
251	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
252	Dic₄₇	—	2	2	no	—
253	Dic₄₇	—	2	2	no	—
254	Dic₄₇	—	2	4	no	—
255	Dic₄₇	—	4	2	no	—
256	Dic₄₇	#376	1	4	yes	—
257	C₂×#405	—	47	1	no	—
258	C₂×#405	—	47	1	no	—
259	C₄×#117	—	47	1	no	—
260	#1746	—	47	1	no	—
261	#1746	—	47	1	no	—
262	#1746	—	47	1	no	—
263	#1746	D₄₇	1	1	yes	characteristic, complemented
264	#1745	—	47	1	no	—
265	#1745	—	47	1	no	—
266	#1744	—	47	1	no	—
267	#1744	—	47	1	no	—
268	#1729	—	47	1	no	—
269	#1729	—	47	1	no	—
270	#1728	—	47	1	no	—
271	C₂×#336	—	47	1	no	—
272	C₂×C₄₇	C₂×#376	1	1	yes	characteristic
273	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
274	C₂×C₄₇	#2875	1	1	yes	characteristic
275	C₂×C₄₇	#2924	1	2	yes	—
276	C₂×C₄₇	#2925	1	2	yes	—
277	D₄₇	—	2	4	no	—
278	C₂²×M₁₆	—	47	1	no	—
279	C₂²×M₁₆	—	47	1	no	—
280	C₂³×C₈	—	47	1	no	—
281	C₂³×C₈	—	47	1	no	—
282	C₂×#117	—	47	1	no	—
283	C₂×#117	—	47	1	no	—
284	C₂²×C₄²	—	47	1	no	—
285	#405	—	47	8	no	—
286	#405	—	47	8	no	—
287	C₂×#97	—	47	1	no	—
288	C₂×#97	—	47	1	no	—
289	C₂×#97	—	47	1	no	—
290	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
291	C₂×C₄×C₈	—	47	1	no	—
292	C₂×C₄×C₈	—	47	1	no	—
293	C₂×C₄×C₈	—	47	1	no	—
294	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
295	C₄×C₄⋊C₄	—	47	2	no	—
296	C₄×C₄⋊C₄	—	47	2	no	—
297	C₄×C₂²⋊C₄	—	47	2	no	—
298	C₄×C₂²⋊C₄	—	47	2	no	—
299	#376	—	47	1	no	—
300	#376	C₂×D₄₇	1	1	yes	characteristic
301	C₄³	—	47	1	no	—
302	C₄³	—	47	1	no	—
303	#336	—	47	1	no	—
304	#336	—	47	1	no	—
305	#336	—	47	1	no	—
306	#336	—	47	1	no	—
307	#336	—	47	1	no	—
308	#336	—	47	1	no	—
309	#336	—	47	1	no	—
310	#336	—	47	1	no	—
311	#336	—	47	1	no	—
312	#336	—	47	1	no	—
313	#336	—	47	1	no	—
314	#336	—	47	1	no	—
315	#336	C₂×D₄₇	1	1	yes	characteristic
316	#336	C₂×D₄₇	1	1	yes	characteristic
317	#336	C₂×D₄₇	1	1	yes	characteristic
318	#336	C₂×D₄₇	1	1	yes	characteristic
319	C₄₇	#20368	1	1	yes	characteristic, complemented, Sylow
320	C₂³×C₄	—	47	1	no	—
321	C₂³×C₄	—	47	2	no	—
322	C₂×M₁₆	—	47	4	no	—
323	C₂×M₁₆	—	47	4	no	—
324	C₂×M₁₆	—	94	2	no	—
325	C₂×M₁₆	—	94	2	no	—
326	C₂×M₁₆	—	94	2	no	—
327	C₂×M₁₆	—	94	2	no	—
328	C₂²×C₈	—	47	1	no	—
329	C₂²×C₈	—	47	1	no	—
330	C₂²×C₈	—	47	1	no	—
331	C₂²×C₈	—	47	1	no	—
332	C₂²×C₈	—	47	4	no	—
333	C₂²×C₈	—	47	4	no	—
334	C₂²×C₈	—	94	2	no	—
335	C₂²×C₈	—	94	2	no	—
336	C₂²×C₈	—	94	2	no	—
337	C₂²×C₈	—	94	2	no	—
338	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
339	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
340	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
341	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
342	#117	—	47	4	no	—
343	#117	—	47	4	no	—
344	#117	—	94	2	no	—
345	#117	—	94	2	no	—
346	C₂×C₄⋊C₄	—	47	1	no	—
347	C₂×C₄⋊C₄	—	47	1	no	—
348	C₂×C₄⋊C₄	—	47	2	no	—
349	C₂×C₂²⋊C₄	—	47	1	no	—
350	C₂×C₂²⋊C₄	—	47	1	no	—
351	C₂×C₂²⋊C₄	—	47	2	no	—
352	C₂×C₄²	—	47	1	no	—
353	C₂×C₄²	—	47	2	no	—
354	C₂×C₄²	—	47	2	no	—
355	C₂×C₄²	—	47	2	no	—
356	C₂×C₄²	—	47	1	no	—
357	C₂×C₄²	—	47	1	no	—
358	C₂×C₄²	—	47	2	no	—
359	C₂×C₄²	—	47	2	no	—
360	C₂×C₄²	—	94	2	no	—
361	C₂×C₄²	—	94	2	no	—
362	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
363	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
364	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
365	#97	—	47	4	no	—
366	#97	—	47	4	no	—
367	#97	—	47	4	no	—
368	#97	C₄×D₄₇	1	4	yes	complemented
369	C₄×C₈	—	47	4	no	—
370	C₄×C₈	—	47	4	no	—
371	C₄×C₈	—	47	4	no	—
372	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
373	#95	—	47	2	no	—
374	#95	—	47	2	no	—
375	#95	C₄×D₄₇	1	2	yes	—
376	#95	C₄×D₄₇	1	2	yes	—
377	C₂⁴	—	47	1	no	—
378	C₂²×C₄	—	47	1	no	—
379	C₂²×C₄	—	47	2	no	—
380	C₂²×C₄	—	47	2	no	—
381	C₂²×C₄	—	47	2	no	—
382	C₂²×C₄	—	47	2	no	—
383	C₂²×C₄	—	47	2	no	—
384	C₂²×C₄	—	47	2	no	—
385	C₂²×C₄	—	47	1	no	—
386	C₂²×C₄	—	47	1	no	—
387	C₂²×C₄	—	47	2	no	—
388	C₂²×C₄	—	47	2	no	—
389	C₂²×C₄	—	94	4	no	—
390	C₂²×C₄	—	94	4	no	—
391	C₂²×C₄	—	188	2	no	—
392	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
393	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
394	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
396	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
397	M₁₆	—	94	8	no	—
398	M₁₆	—	94	8	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	47	2	no	—
408	C₂×C₈	—	47	2	no	—
409	C₂×C₈	—	47	2	no	—
410	C₂×C₈	—	47	2	no	—
411	C₂×C₈	—	94	8	no	—
412	C₂×C₈	—	94	8	no	—
413	C₂×C₈	—	94	1	no	—
414	C₂×C₈	—	94	1	no	—
415	C₂×C₈	—	94	1	no	—
416	C₂×C₈	—	94	1	no	—
417	C₂×C₈	—	94	1	no	—
418	C₂×C₈	—	94	1	no	—
419	C₂×C₈	—	94	1	no	—
420	C₂×C₈	—	94	1	no	—
421	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
422	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
423	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
424	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
425	C₄⋊C₄	—	47	4	no	—
426	C₄⋊C₄	—	47	4	no	—
427	C₄⋊C₄	—	94	4	no	—
428	C₂²⋊C₄	—	47	4	no	—
429	C₂²⋊C₄	—	47	4	no	—
430	C₂²⋊C₄	—	94	4	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	—	2	1	no	—
435	C₄²	—	47	2	no	—
436	C₄²	—	47	2	no	—
437	C₄²	—	94	4	no	—
438	C₄²	—	94	4	no	—
439	C₄²	—	94	4	no	—
440	C₄²	—	94	1	no	—
441	C₄²	—	94	1	no	—
442	C₄²	—	94	1	no	—
443	C₄²	—	94	1	no	—
444	C₄²	—	188	2	no	—
445	C₄²	—	188	2	no	—
446	C₄²	C₂×C₄×D₄₇	1	2	yes	—
447	C₄²	C₂×C₄×D₄₇	1	2	yes	—
448	C₂³	—	47	2	no	—
449	C₂³	—	47	2	no	—
450	C₂³	—	47	2	no	—
451	C₂³	—	94	2	no	—
452	C₂³	—	94	2	no	—
453	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	47	2	no	—
463	C₂×C₄	—	47	2	no	—
464	C₂×C₄	—	47	2	no	—
465	C₂×C₄	—	47	4	no	—
466	C₂×C₄	—	47	4	no	—
467	C₂×C₄	—	47	4	no	—
468	C₂×C₄	—	47	4	no	—
469	C₂×C₄	—	47	2	no	—
470	C₂×C₄	—	47	2	no	—
471	C₂×C₄	—	47	4	no	—
472	C₂×C₄	—	94	2	no	—
473	C₂×C₄	—	94	2	no	—
474	C₂×C₄	—	94	2	no	—
475	C₂×C₄	—	94	2	no	—
476	C₂×C₄	—	94	2	no	—
477	C₂×C₄	—	94	2	no	—
478	C₂×C₄	—	94	2	no	—
479	C₂×C₄	—	188	8	no	—
480	C₂×C₄	C₄²×D₄₇	1	2	yes	—
481	C₂×C₄	C₄²×D₄₇	1	2	yes	—
482	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
483	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
484	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
485	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
486	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
487	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
488	C₈	—	2	2	no	—
489	C₈	—	2	2	no	—
490	C₈	—	2	2	no	—
491	C₈	—	2	2	no	—
492	C₈	—	94	2	no	—
493	C₈	—	94	2	no	—
494	C₈	—	94	2	no	—
495	C₈	—	94	2	no	—
496	C₂²	—	47	4	no	—
497	C₂²	—	94	4	no	—
498	C₂²	—	94	4	no	—
499	C₂²	—	94	2	no	—
500	C₂²	—	94	2	no	—
501	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
502	C₂²	#117×D₄₇	1	1	yes	characteristic
503	C₂²	#117×D₄₇	1	1	yes	characteristic
504	C₂²	#131×D₄₇	1	2	yes	—
505	C₂²	#15689888	1	2	yes	—
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	2	no	—
510	C₄	—	47	4	no	—
511	C₄	—	94	4	no	—
512	C₄	—	94	2	no	—
513	C₄	—	94	2	no	—
514	C₄	—	188	2	no	—
515	C₄	#117×D₄₇	1	1	yes	characteristic
516	C₄	#117×D₄₇	1	1	yes	characteristic
517	C₄	#117×D₄₇	1	1	yes	characteristic
518	C₄	#117×D₄₇	1	1	yes	characteristic
519	C₂	—	94	4	no	—
520	C₂	#376×D₄₇	1	1	yes	characteristic
521	C₂	#20251810	1	1	yes	characteristic
522	C₂	#20251815	1	1	yes	characteristic
523	C₂	#20252044	1	2	yes	—
524	C₂	#20252051	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1746	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1746	D₄₇
hypocenter	C₄₇	#20368
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1746

Complements

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

N	H ≅ G/N	type
4. #20243140	C₂	semidirect
5. #20243138	C₂	semidirect
6. #20243138	C₂	semidirect
7. #20243136	C₂	semidirect
8. #20243135	C₂	semidirect
9. #20243133	C₂	semidirect
10. #20243132	C₂	semidirect
15. C₄₇×#1746	C₂	semidirect
23. #15689080	C₄	semidirect
24. #15689077	C₄	semidirect
95. #13093935	C₂×C₄	semidirect
96. #13093934	C₂×C₄	semidirect
97. #13093934	C₂×C₄	semidirect
98. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
99. C₈×Dic₄₇	C₂×C₄	semidirect
100. C₈×Dic₄₇	C₂×C₄	semidirect
110. #97×C₄₇	C₂×C₄	semidirect
111. C₄×C₈×C₄₇	C₂×C₄	semidirect
263. #1746	D₄₇	semidirect
319. C₄₇	#20368	semidirect
368. #97	C₄×D₄₇	semidirect
372. C₄×C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689080	2
C₂×#15689077	2
#20245727	2
#20243140	2
#20243138	2
#20243136	2
#20243135	2
#20243133	2
#20243132	2
#20243083	2
#20243080	2
#336×D₄₇	2
C₄₇×#1746	2
#20368	47