Subgroups — #26216783

Order 12032.

854 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689181	C₂	1	2	yes	maximal
2	#117×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20243541	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243541	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243503	C₂	1	2	yes	maximal, complemented
6	#20243372	C₂	1	1	yes	maximal, characteristic
7	#20243366	C₂	1	2	yes	maximal
8	#20243244	C₂	1	2	yes	maximal, complemented
9	#20243243	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1798	C₂	1	1	yes	maximal, characteristic
12	C₂×#13093983	C₂²	1	1	yes	characteristic
13	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
14	#15689181	—	2	8	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
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×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
22	C₂×#13093934	C₂²	1	2	yes	—
23	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
24	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
25	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
26	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
27	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
28	#15688969	C₂²	1	1	yes	characteristic
29	#15688969	C₂²	1	1	yes	characteristic
30	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
31	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688878	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#336	C₂²	1	2	yes	—
40	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
41	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
43	#13093983	D₄	1	4	yes	—
44	#13093983	Q₈	1	4	yes	—
45	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
46	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄×Dic₄₇	—	2	2	no	—
48	C₂×C₄×Dic₄₇	—	2	2	no	—
49	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
51	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
60	Dic₄₇⋊C₈	—	2	4	no	—
61	Dic₄₇⋊C₈	—	2	4	no	—
62	Dic₄₇⋊C₈	—	2	4	no	—
63	Dic₄₇⋊C₈	—	2	4	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
65	#13093934	—	2	4	no	—
66	C₈×Dic₄₇	—	2	4	no	—
67	C₄₇⋊#95	C₂×C₄	1	2	yes	—
68	C₄₇⋊#95	C₂×C₄	1	2	yes	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₄₇⋊#95	C₂×C₄	1	2	yes	—
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
74	#117×C₄₇	—	2	2	no	—
75	#117×C₄₇	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₄₇	—	2	2	no	—
83	C₄⋊C₈×C₄₇	—	2	2	no	—
84	C₂²⋊C₈×C₄₇	—	2	4	no	—
85	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₄₇	—	2	4	no	—
99	C₂²×Dic₄₇	—	2	4	no	—
100	C₂²×Dic₄₇	—	4	2	no	—
101	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₂²⋊C₄×C₄₇	—	2	2	no	—
114	C₂²⋊C₄×C₄₇	—	2	2	no	—
115	C₄²×C₄₇	—	2	1	no	—
116	C₄²×C₄₇	—	2	1	no	—
117	C₄²×C₄₇	#41	1	2	yes	—
118	C₄²×C₄₇	#41	1	2	yes	—
119	C₂²⋊Dic₄₇	C₄⋊C₄	1	8	yes	—
120	C₄⋊Dic₄₇	C₄⋊C₄	1	8	yes	—
121	C₄×Dic₄₇	—	2	1	no	—
122	C₄×Dic₄₇	—	2	1	no	—
123	C₄×Dic₄₇	—	2	4	no	—
124	C₄×Dic₄₇	—	2	4	no	—
125	C₄×Dic₄₇	—	2	4	no	—
126	C₄×Dic₄₇	—	4	2	no	—
127	C₄×Dic₄₇	—	4	2	no	—
128	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
129	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
130	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
131	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
132	C₄×Dic₄₇	#41	1	2	yes	—
133	C₄×Dic₄₇	#41	1	2	yes	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂³×C₄₇	—	2	1	no	—
141	C₂³×C₄₇	—	2	1	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
145	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₇	#117	1	2	yes	—
160	C₂×C₄×C₄₇	#117	1	2	yes	—
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	4	8	no	—
176	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
177	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
178	C₂×Dic₄₇	#117	1	4	yes	—
179	C₂×Dic₄₇	#131	1	4	yes	—
180	C₈×C₄₇	—	4	2	no	—
181	C₈×C₄₇	—	4	2	no	—
182	C₄₇⋊C₈	—	4	2	no	—
183	C₄₇⋊C₈	—	4	2	no	—
184	#20813	—	47	1	no	maximal, Sylow
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	4	1	no	—
188	C₂²×C₄₇	—	4	1	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×#131	1	2	yes	—
194	C₂²×C₄₇	#568	1	2	yes	—
195	C₄×C₄₇	—	2	2	no	—
196	C₄×C₄₇	—	2	2	no	—
197	C₄×C₄₇	—	2	2	no	—
198	C₄×C₄₇	—	4	1	no	—
199	C₄×C₄₇	—	4	1	no	—
200	C₄×C₄₇	#532	1	1	yes	characteristic
201	C₄×C₄₇	#532	1	1	yes	characteristic
202	C₄×C₄₇	#533	1	1	yes	characteristic
203	C₄×C₄₇	#533	1	1	yes	characteristic
204	Dic₄₇	—	2	4	no	—
205	Dic₄₇	—	2	4	no	—
206	Dic₄₇	—	2	4	no	—
207	Dic₄₇	—	2	4	no	—
208	C₂×#433	—	47	2	no	—
209	C₄×#117	—	47	1	no	—
210	#1843	—	47	1	no	—
211	#1843	—	47	1	no	—
212	#1831	—	47	2	no	—
213	#1798	—	47	1	no	—
214	#1798	D₄₇	1	1	yes	characteristic
215	#1797	—	47	2	no	—
216	#1768	—	47	2	no	—
217	#1767	—	47	1	no	—
218	C₄×C₄⋊C₈	—	47	1	no	—
219	C₂×C₄₇	—	4	2	no	—
220	C₂×C₄₇	#2285	1	1	yes	characteristic
221	C₂×C₄₇	#2906	1	2	yes	—
222	C₂×C₄₇	#2922	1	1	yes	characteristic
223	C₂×C₄₇	#2923	1	1	yes	characteristic
224	C₂×C₄₇	#2924	1	2	yes	—
225	C₂×#117	—	47	1	no	—
226	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
227	C₂²×C₄²	—	47	1	no	—
228	#433	—	94	8	no	—
229	C₂×C₄⋊C₈	—	47	2	no	—
230	C₂×C₄⋊C₈	—	47	2	no	—
231	C₂×C₄⋊C₈	—	47	2	no	—
232	C₂×C₄⋊C₈	—	47	2	no	—
233	C₂×C₄⋊C₈	—	47	1	no	—
234	C₂×C₄⋊C₈	—	47	1	no	—
235	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
236	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
237	C₂×C₂²⋊C₈	—	47	2	no	—
238	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
239	C₂×#97	—	47	2	no	—
240	C₂×C₄×C₈	—	47	2	no	—
241	C₄×C₄⋊C₄	—	47	2	no	—
242	C₄×C₄⋊C₄	—	47	2	no	—
243	C₄×C₂²⋊C₄	—	47	2	no	—
244	C₄×C₂²⋊C₄	—	47	2	no	—
245	#376	—	47	1	no	—
246	#376	—	47	1	no	—
247	C₄³	—	47	1	no	—
248	C₄³	—	47	1	no	—
249	#336	—	47	2	no	—
250	#336	—	47	2	no	—
251	#336	—	47	2	no	—
252	#336	C₂×D₄₇	1	2	yes	—
253	C₄₇	#20813	1	1	yes	characteristic, complemented, Sylow
254	C₂³×C₄	—	47	2	no	—
255	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
256	C₂²×C₈	—	47	2	no	—
257	C₂²×C₈	—	47	2	no	—
258	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
259	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	—	47	4	no	—
263	#117	—	47	4	no	—
264	C₂×C₄⋊C₄	—	47	2	no	—
265	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	47	2	no	—
268	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
270	C₂×C₄²	—	47	1	no	—
271	C₂×C₄²	—	47	1	no	—
272	C₂×C₄²	—	47	1	no	—
273	C₂×C₄²	—	47	2	no	—
274	C₂×C₄²	—	47	2	no	—
275	C₂×C₄²	—	47	2	no	—
276	C₂×C₄²	—	47	1	no	—
277	C₂×C₄²	—	47	2	no	—
278	C₂×C₄²	—	47	2	no	—
279	C₂×C₄²	—	94	2	no	—
280	C₂×C₄²	—	94	2	no	—
281	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
282	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	94	4	no	—
286	C₄⋊C₈	—	94	4	no	—
287	C₄⋊C₈	—	94	4	no	—
288	C₄⋊C₈	—	94	4	no	—
289	C₄⋊C₈	—	94	2	no	—
290	C₄⋊C₈	—	94	2	no	—
291	C₂²⋊C₈	—	2	4	no	—
292	C₂²⋊C₈	—	94	4	no	—
293	#97	—	94	4	no	—
294	C₄×C₈	—	94	4	no	—
295	#95	—	47	2	no	—
296	#95	—	47	2	no	—
297	#95	—	47	2	no	—
298	#95	—	47	2	no	—
299	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	47	2	no	—
305	C₂²×C₄	—	47	2	no	—
306	C₂²×C₄	—	47	2	no	—
307	C₂²×C₄	—	47	2	no	—
308	C₂²×C₄	—	94	4	no	—
309	C₂²×C₄	—	94	4	no	—
310	C₂²×C₄	—	188	2	no	—
311	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
316	C₂²×C₄	D₄×D₄₇	1	2	yes	—
317	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
318	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	—	94	2	no	—
329	C₂×C₈	—	94	2	no	—
330	C₂×C₈	—	94	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	47	8	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	47	8	no	—
337	C₄²	—	2	1	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	47	2	no	—
340	C₄²	—	47	2	no	—
341	C₄²	—	47	2	no	—
342	C₄²	—	47	2	no	—
343	C₄²	—	47	2	no	—
344	C₄²	—	47	2	no	—
345	C₄²	—	94	4	no	—
346	C₄²	—	94	4	no	—
347	C₄²	—	94	4	no	—
348	C₄²	—	94	1	no	—
349	C₄²	—	94	1	no	—
350	C₄²	—	188	2	no	—
351	C₄²	—	188	2	no	—
352	C₄²	#10625352	1	2	yes	—
353	C₄²	#10625352	1	2	yes	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
359	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	47	4	no	—
373	C₂×C₄	—	47	4	no	—
374	C₂×C₄	—	47	4	no	—
375	C₂×C₄	—	47	4	no	—
376	C₂×C₄	—	94	2	no	—
377	C₂×C₄	—	94	2	no	—
378	C₂×C₄	—	94	2	no	—
379	C₂×C₄	—	94	2	no	—
380	C₂×C₄	—	94	2	no	—
381	C₂×C₄	—	94	2	no	—
382	C₂×C₄	—	94	2	no	—
383	C₂×C₄	—	94	2	no	—
384	C₂×C₄	—	188	8	no	—
385	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
386	C₂×C₄	#13093980	1	2	yes	—
387	C₂×C₄	#13093980	1	2	yes	—
388	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
390	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
391	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
393	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
394	C₈	—	4	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	188	2	no	—
397	C₈	—	188	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	4	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	2	no	—
403	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
404	C₂²	#117×D₄₇	1	1	yes	characteristic
405	C₂²	C₂×#13093980	1	1	yes	characteristic
406	C₂²	#131×D₄₇	1	2	yes	—
407	C₂²	#15689888	1	2	yes	—
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	94	4	no	—
414	C₄	—	94	4	no	—
415	C₄	—	94	4	no	—
416	C₄	—	94	4	no	—
417	C₄	#15689668	1	1	yes	characteristic
418	C₄	#15689668	1	1	yes	characteristic
419	C₄	#15689675	1	1	yes	characteristic
420	C₄	#15689675	1	1	yes	characteristic
421	C₂	—	4	2	no	—
422	C₂	#20245790	1	1	yes	characteristic
423	C₂	#20251955	1	2	yes	—
424	C₂	#20252028	1	1	yes	characteristic
425	C₂	#20252035	1	1	yes	characteristic
426	C₂	#20252044	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1798	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1798	D₄₇
hypocenter	C₄₇	#20813
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1798

Complements

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

N	H ≅ G/N	type
3. #20243541	C₂	semidirect
4. #20243541	C₂	semidirect
5. #20243503	C₂	semidirect
8. #20243244	C₂	semidirect
9. #20243243	C₂	semidirect
10. C₄⋊C₈×Dic₄₇	C₂	semidirect
253. C₄₇	#20813	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689181	2
#117×Dic₄₇	2
#20243541	2
#20243503	2
#20243372	2
#20243366	2
#20243244	2
#20243243	2
C₄⋊C₈×Dic₄₇	2
C₄₇×#1798	2
#20813	47