Subgroups — #26221084

Order 12032.

854 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×#15689175	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
3	#20245784	C₂	1	1	yes	maximal, characteristic
4	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244104	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243572	C₂	1	2	yes	maximal
8	#20243569	C₂	1	2	yes	maximal
9	#20243247	C₂	1	2	yes	maximal, complemented
10	#20243244	C₂	1	2	yes	maximal, complemented
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	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
15	#15689175	—	2	4	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
21	C₄×#10625324	—	2	4	no	—
22	C₂×#13093934	C₂²	1	1	yes	characteristic
23	C₂×#13093934	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
26	#15688990	C₄	1	2	yes	—
27	#15688988	C₄	1	1	yes	characteristic
28	#15688988	C₄	1	1	yes	characteristic
29	#15688985	C₄	1	2	yes	—
30	#15688980	C₄	1	1	yes	characteristic
31	#15688980	C₄	1	1	yes	characteristic
32	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
33	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
34	#15688969	C₂²	1	2	yes	—
35	#15688878	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
46	C₂×#10625324	—	2	2	no	—
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	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
53	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	C₂³	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×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	C₄²×D₄₇	D₄	1	4	yes	—
64	C₄²×D₄₇	Q₈	1	4	yes	—
65	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
66	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
67	Dic₄₇⋊C₈	—	2	4	no	—
68	Dic₄₇⋊C₈	—	2	4	no	—
69	(C₂×D₄₇)⋊C₈	—	2	4	no	—
70	#13093934	—	2	2	no	—
71	#13093934	—	2	2	no	—
72	C₄×C₄₇⋊C₈	—	2	2	no	—
73	C₈×Dic₄₇	—	2	4	no	—
74	C₄₇⋊#95	C₂×C₄	1	2	yes	—
75	C₄₇⋊#95	C₂×C₄	1	2	yes	—
76	C₄₇⋊#95	C₂×C₄	1	2	yes	—
77	C₄₇⋊#95	C₂×C₄	1	2	yes	—
78	C₄₇⋊#95	C₂×C₄	1	2	yes	—
79	C₄₇⋊#95	C₂×C₄	1	2	yes	—
80	C₄₇⋊#95	C₂×C₄	1	2	yes	—
81	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	—	2	4	no	—
89	C₄⋊C₈×C₄₇	—	2	2	no	—
90	C₄×C₈×C₄₇	—	2	2	no	—
91	#95×C₄₇	C₂×C₄	1	2	yes	—
92	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₄₇	—	2	2	no	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	—	2	1	no	—
106	C₂×C₄×D₄₇	—	2	1	no	—
107	C₂×C₄×D₄₇	—	2	1	no	—
108	C₂×C₄×D₄₇	—	2	1	no	—
109	C₂×C₄×D₄₇	—	4	1	no	—
110	C₂×C₄×D₄₇	—	4	1	no	—
111	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
112	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
113	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
114	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	—	2	1	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	#41	1	2	yes	—
123	C₂×C₈×C₄₇	#41	1	2	yes	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	C₂×D₄	1	2	yes	—
129	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
130	(C₂×D₄₇)⋊C₄	—	4	2	no	—
131	(C₂×D₄₇)⋊C₄	—	4	2	no	—
132	C₄⋊Dic₄₇	—	2	2	no	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄×Dic₄₇	—	2	2	no	—
135	C₄×Dic₄₇	—	2	2	no	—
136	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
137	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
138	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
139	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	#41	1	2	yes	—
148	C₂×C₄₇⋊C₈	#41	1	2	yes	—
149	#10625324	—	2	8	no	—
150	#10625324	—	2	8	no	—
151	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂²×D₄₇	—	2	1	no	—
153	C₂²×D₄₇	—	2	1	no	—
154	C₂²×D₄₇	—	2	1	no	—
155	C₂²×D₄₇	—	2	1	no	—
156	C₂²×D₄₇	—	2	1	no	—
157	C₂²×D₄₇	—	2	1	no	—
158	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
169	C₂×C₄×C₄₇	#131	1	2	yes	—
170	C₂×C₄×C₄₇	#131	1	2	yes	—
171	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	1	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	1	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	—	2	2	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	2	2	no	—
189	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
190	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
191	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
192	C₄×D₄₇	—	2	2	no	—
193	C₄×D₄₇	—	2	2	no	—
194	C₄×D₄₇	—	2	2	no	—
195	C₄×D₄₇	—	2	2	no	—
196	C₄×D₄₇	—	2	8	no	—
197	C₄×D₄₇	—	4	4	no	—
198	C₈×C₄₇	—	2	2	no	—
199	C₈×C₄₇	—	2	2	no	—
200	C₈×C₄₇	—	4	2	no	—
201	C₄₇⋊C₈	—	2	2	no	—
202	C₄₇⋊C₈	—	2	2	no	—
203	C₄₇⋊C₈	—	4	2	no	—
204	#21354	—	47	1	no	maximal, Sylow
205	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
206	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
207	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
210	C₂²×C₄₇	#568	1	1	yes	characteristic
211	C₂²×C₄₇	#568	1	1	yes	characteristic
212	C₂×D₄₇	—	2	2	no	—
213	C₂×D₄₇	—	2	2	no	—
214	C₂×D₄₇	—	2	2	no	—
215	C₂×D₄₇	—	4	1	no	—
216	C₂×D₄₇	—	4	1	no	—
217	C₂×D₄₇	—	4	1	no	—
218	C₂×D₄₇	—	4	1	no	—
219	C₄×C₄₇	—	2	2	no	—
220	C₄×C₄₇	—	4	2	no	—
221	C₄×C₄₇	—	4	2	no	—
222	C₄×C₄₇	#424	1	4	yes	—
223	C₄×C₄₇	#525	1	1	yes	characteristic
224	C₄×C₄₇	#525	1	1	yes	characteristic
225	C₄×C₄₇	#533	1	1	yes	characteristic
226	C₄×C₄₇	#533	1	1	yes	characteristic
227	Dic₄₇	—	2	2	no	—
228	Dic₄₇	—	2	2	no	—
229	Dic₄₇	—	2	2	no	—
230	Dic₄₇	—	4	2	no	—
231	Dic₄₇	—	4	2	no	—
232	C₂×#431	—	47	1	no	—
233	C₂×C₄×M₁₆	—	47	1	no	—
234	#2283	—	47	1	no	—
235	#1939	—	47	1	no	—
236	#1939	—	47	1	no	—
237	#1939	—	47	1	no	—
238	#1939	D₄₇	1	1	yes	characteristic, complemented
239	#1851	—	47	2	no	—
240	#1851	—	47	2	no	—
241	#1768	—	47	2	no	—
242	#1768	—	47	2	no	—
243	C₂×C₄₇	#2296	1	1	yes	characteristic
244	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
245	C₂×C₄₇	#2905	1	1	yes	characteristic
246	C₂×C₄₇	#2969	1	1	yes	characteristic
247	C₂×C₄₇	#2969	1	1	yes	characteristic
248	C₂×C₄₇	#2969	1	1	yes	characteristic
249	C₂×C₄₇	#2969	1	1	yes	characteristic
250	D₄₇	—	4	2	no	—
251	C₂²×M₁₆	—	47	1	no	—
252	C₂²×M₁₆	—	47	1	no	—
253	C₂²×C₄²	—	47	1	no	—
254	#431	—	94	4	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	1	no	—
259	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
260	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
261	C₂×C₂²⋊C₈	—	47	2	no	—
262	C₄×M₁₆	—	94	4	no	—
263	C₂×#97	—	47	1	no	—
264	C₂×#97	—	47	1	no	—
265	C₂×C₄×C₈	—	47	2	no	—
266	C₂×C₄×C₈	—	47	1	no	—
267	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
268	#383	—	47	2	no	—
269	#382	—	47	1	no	—
270	#382	—	47	1	no	—
271	#381	—	47	2	no	—
272	#380	—	47	1	no	—
273	#380	—	47	1	no	—
274	C₄×C₄⋊C₄	—	47	1	no	—
275	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
276	C₄×C₂²⋊C₄	—	47	2	no	—
277	#376	—	47	2	no	—
278	#336	—	47	2	no	—
279	#336	—	47	2	no	—
280	#336	—	47	2	no	—
281	#336	C₂×D₄₇	1	2	yes	—
282	C₄₇	#21354	1	1	yes	characteristic, complemented, Sylow
283	C₂³×C₄	—	47	1	no	—
284	C₂³×C₄	—	47	1	no	—
285	C₂³×C₄	—	47	1	no	—
286	C₂×M₁₆	—	94	2	no	—
287	C₂×M₁₆	—	94	2	no	—
288	C₂×M₁₆	—	94	2	no	—
289	C₂×M₁₆	—	94	2	no	—
290	C₂×M₁₆	—	94	2	no	—
291	C₂×M₁₆	—	94	2	no	—
292	C₂²×C₈	—	47	1	no	—
293	C₂²×C₈	—	47	1	no	—
294	C₂²×C₈	—	47	2	no	—
295	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
296	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
297	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	—	47	1	no	—
299	C₂×C₄⋊C₄	—	47	1	no	—
300	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	—	47	2	no	—
303	C₂×C₂²⋊C₄	—	47	2	no	—
304	C₂×C₄²	—	47	1	no	—
305	C₂×C₄²	—	47	1	no	—
306	C₂×C₄²	—	47	1	no	—
307	C₂×C₄²	—	47	4	no	—
308	C₂×C₄²	—	47	4	no	—
309	C₂×C₄²	—	47	2	no	—
310	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
311	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
312	C₄⋊C₈	—	2	4	no	—
313	C₄⋊C₈	—	2	2	no	—
314	C₄⋊C₈	—	94	4	no	—
315	C₄⋊C₈	—	94	4	no	—
316	C₄⋊C₈	—	94	4	no	—
317	C₄⋊C₈	—	94	2	no	—
318	C₂²⋊C₈	—	94	4	no	—
319	#97	—	94	2	no	—
320	#97	—	94	2	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	94	4	no	—
323	C₄×C₈	—	94	2	no	—
324	#95	—	47	2	no	—
325	#95	—	47	2	no	—
326	#95	—	47	2	no	—
327	#95	—	47	2	no	—
328	#95	—	47	2	no	—
329	#95	—	47	2	no	—
330	#95	—	47	2	no	—
331	#95	C₄×D₄₇	1	2	yes	—
332	C₂⁴	—	47	1	no	—
333	C₂²×C₄	—	47	1	no	—
334	C₂²×C₄	—	47	1	no	—
335	C₂²×C₄	—	47	1	no	—
336	C₂²×C₄	—	47	4	no	—
337	C₂²×C₄	—	47	2	no	—
338	C₂²×C₄	—	47	2	no	—
339	C₂²×C₄	—	47	4	no	—
340	C₂²×C₄	—	47	2	no	—
341	C₂²×C₄	—	47	2	no	—
342	C₂²×C₄	—	94	2	no	—
343	C₂²×C₄	—	94	2	no	—
344	C₂²×C₄	—	94	1	no	—
345	C₂²×C₄	—	94	1	no	—
346	C₂²×C₄	—	94	1	no	—
347	C₂²×C₄	—	94	1	no	—
348	C₂²×C₄	—	188	1	no	—
349	C₂²×C₄	—	188	1	no	—
350	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
351	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
352	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
354	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
355	M₁₆	—	94	8	no	—
356	M₁₆	—	94	8	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	47	2	no	—
365	C₂×C₈	—	47	2	no	—
366	C₂×C₈	—	94	1	no	—
367	C₂×C₈	—	94	1	no	—
368	C₂×C₈	—	94	1	no	—
369	C₂×C₈	—	94	1	no	—
370	C₂×C₈	—	94	2	no	—
371	C₂×C₈	—	94	2	no	—
372	C₂×C₈	—	94	2	no	—
373	C₂×C₈	#10625352	1	2	yes	—
374	C₂×C₈	#10625354	1	2	yes	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	94	2	no	—
378	C₄⋊C₄	—	94	2	no	—
379	C₂²⋊C₄	—	188	2	no	—
380	C₂²⋊C₄	—	188	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	47	4	no	—
384	C₄²	—	47	4	no	—
385	C₄²	—	47	2	no	—
386	C₄²	—	47	2	no	—
387	C₄²	—	94	2	no	—
388	C₄²	—	94	2	no	—
389	C₄²	D₄×D₄₇	1	2	yes	—
390	C₄²	Q₈×D₄₇	1	2	yes	—
391	C₂³	—	47	2	no	—
392	C₂³	—	94	1	no	—
393	C₂³	—	94	1	no	—
394	C₂³	—	94	1	no	—
395	C₂³	—	94	1	no	—
396	C₂³	—	94	1	no	—
397	C₂³	—	94	1	no	—
398	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	47	2	no	—
408	C₂×C₄	—	47	2	no	—
409	C₂×C₄	—	47	2	no	—
410	C₂×C₄	—	94	1	no	—
411	C₂×C₄	—	94	1	no	—
412	C₂×C₄	—	94	1	no	—
413	C₂×C₄	—	94	1	no	—
414	C₂×C₄	—	94	1	no	—
415	C₂×C₄	—	94	1	no	—
416	C₂×C₄	—	94	2	no	—
417	C₂×C₄	—	94	2	no	—
418	C₂×C₄	—	94	8	no	—
419	C₂×C₄	—	94	2	no	—
420	C₂×C₄	—	94	2	no	—
421	C₂×C₄	—	94	2	no	—
422	C₂×C₄	—	94	2	no	—
423	C₂×C₄	—	94	2	no	—
424	C₂×C₄	—	94	2	no	—
425	C₂×C₄	—	94	2	no	—
426	C₂×C₄	—	94	2	no	—
427	C₂×C₄	—	188	4	no	—
428	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
429	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
430	C₂×C₄	#13094030	1	2	yes	—
431	C₂×C₄	#13094032	1	2	yes	—
432	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
433	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
434	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
435	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
436	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
437	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	2	2	no	—
440	C₈	—	4	2	no	—
441	C₈	—	94	2	no	—
442	C₈	—	94	2	no	—
443	C₈	—	188	2	no	—
444	C₂²	—	94	2	no	—
445	C₂²	—	94	2	no	—
446	C₂²	—	94	2	no	—
447	C₂²	—	188	1	no	—
448	C₂²	—	188	1	no	—
449	C₂²	—	188	1	no	—
450	C₂²	—	188	1	no	—
451	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
452	C₂²	C₄×#10625352	1	1	yes	characteristic
453	C₂²	C₄×#10625354	1	1	yes	characteristic
454	C₂²	C₂×#13094030	1	1	yes	characteristic
455	C₂²	C₂×#13094032	1	1	yes	characteristic
456	C₂²	#15689888	1	1	yes	characteristic
457	C₂²	#15689888	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	4	2	no	—
460	C₄	—	4	2	no	—
461	C₄	—	94	2	no	—
462	C₄	—	94	2	no	—
463	C₄	—	94	2	no	—
464	C₄	—	188	2	no	—
465	C₄	—	188	2	no	—
466	C₄	#15689148	1	4	yes	—
467	C₄	#15689633	1	1	yes	characteristic
468	C₄	#15689636	1	1	yes	characteristic
469	C₄	#15689678	1	1	yes	characteristic
470	C₄	#15689679	1	1	yes	characteristic
471	C₂	—	188	2	no	—
472	C₂	#20245869	1	1	yes	characteristic
473	C₂	C₂×#15689148	1	1	yes	characteristic
474	C₂	#20251949	1	1	yes	characteristic
475	C₂	#20252389	1	1	yes	characteristic
476	C₂	#20252391	1	1	yes	characteristic
477	C₂	#20252394	1	1	yes	characteristic
478	C₂	#20252395	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	#21354
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
4. #20244107	C₂	semidirect
5. #20244106	C₂	semidirect
6. #20244104	C₂	semidirect
9. #20243247	C₂	semidirect
10. #20243244	C₂	semidirect
11. C₄₇×#1939	C₂	semidirect
238. #1939	D₄₇	semidirect
282. C₄₇	#21354	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689175	2
C₂×C₄×#10625324	2
#20245784	2
#20244107	2
#20244106	2
#20244104	2
#20243572	2
#20243569	2
#20243247	2
#20243244	2
C₄₇×#1939	2
#21354	47