Subgroups — #26124460

Order 12032.

846 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688877	C₂	1	2	yes	maximal
3	C₂×#15688877	C₂	1	2	yes	maximal
4	C₄×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
8	C₂×C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
10	C₂×C₄₇⋊#95	C₄	1	2	yes	—
11	C₂×C₄₇⋊#95	C₄	1	1	yes	characteristic
12	C₂×C₄₇⋊#95	C₄	1	1	yes	characteristic
13	#15688877	—	2	4	no	—
14	#15688877	—	2	4	no	—
15	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#336	—	2	2	no	—
19	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
20	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
21	C₂²×C₄₇⋊C₈	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	2	2	no	—
27	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
28	C₂×C₄×Dic₄₇	—	2	2	no	—
29	C₂×C₄×Dic₄₇	—	2	2	no	—
30	C₂×C₄×Dic₄₇	—	2	2	no	—
31	C₂×C₄×Dic₄₇	—	2	2	no	—
32	C₂×C₄×Dic₄₇	—	2	2	no	—
33	C₂×C₄×Dic₄₇	—	2	2	no	—
34	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
35	C₄₇⋊#95	—	2	2	no	—
36	C₄₇⋊#95	—	2	4	no	—
37	C₄₇⋊#95	C₈	1	4	yes	complemented
38	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₄₇	—	2	1	no	—
42	C₂²×C₈×C₄₇	—	2	1	no	—
43	C₂²×C₈×C₄₇	—	2	2	no	—
44	C₂²×C₈×C₄₇	—	2	1	no	—
45	C₂²×C₈×C₄₇	—	2	2	no	—
46	C₂²×C₈×C₄₇	—	2	1	no	—
47	C₂²×C₈×C₄₇	—	2	2	no	—
48	C₂²×C₈×C₄₇	—	2	2	no	—
49	C₂²×C₈×C₄₇	D₄	1	2	yes	—
50	C₂²×C₈×C₄₇	Q₈	1	2	yes	—
51	C₂×C₄²×C₄₇	—	2	2	no	—
52	C₂×C₄²×C₄₇	—	2	2	no	—
53	C₂×C₄²×C₄₇	D₄	1	2	yes	—
54	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
55	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	—	2	2	no	—
57	C₂²×C₄×C₄₇	—	2	2	no	—
58	C₂²×C₄×C₄₇	—	2	2	no	—
59	C₂²×C₄×C₄₇	—	2	2	no	—
60	C₂²×C₄×C₄₇	—	2	1	no	—
61	C₂²×C₄×C₄₇	—	2	1	no	—
62	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
63	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
65	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
66	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
67	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	#41	1	2	yes	—
73	C₂²×C₄×C₄₇	#41	1	2	yes	—
74	C₂²×C₄×C₄₇	#41	1	2	yes	—
75	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
76	C₂²×Dic₄₇	—	2	2	no	—
77	C₂²×Dic₄₇	—	2	2	no	—
78	C₂²×Dic₄₇	—	2	2	no	—
79	C₂²×Dic₄₇	—	2	2	no	—
80	C₂²×Dic₄₇	—	2	2	no	—
81	C₂²×Dic₄₇	—	2	2	no	—
82	C₂²×Dic₄₇	—	2	2	no	—
83	C₂²×Dic₄₇	—	2	2	no	—
84	C₂²×Dic₄₇	—	2	2	no	—
85	C₂²×Dic₄₇	—	2	2	no	—
86	C₂²×Dic₄₇	—	2	2	no	—
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₂²×Dic₄₇	C₂×C₈	1	4	yes	—
89	C₂²×Dic₄₇	M₁₆	1	4	yes	—
90	C₂×C₈×C₄₇	—	2	2	no	—
91	C₂×C₈×C₄₇	—	2	4	no	—
92	C₂×C₈×C₄₇	—	2	2	no	—
93	C₂×C₈×C₄₇	—	2	4	no	—
94	C₂×C₈×C₄₇	—	4	1	no	—
95	C₂×C₈×C₄₇	—	4	1	no	—
96	C₂×C₈×C₄₇	—	4	2	no	—
97	C₂×C₈×C₄₇	—	4	1	no	—
98	C₂×C₈×C₄₇	—	4	1	no	—
99	C₂×C₈×C₄₇	—	4	2	no	—
100	C₄²×C₄₇	—	2	2	no	—
101	C₄²×C₄₇	—	2	4	no	—
102	C₄²×C₄₇	—	2	2	no	—
103	C₄×Dic₄₇	—	4	2	no	—
104	C₄×Dic₄₇	—	4	2	no	—
105	C₄×Dic₄₇	—	4	2	no	—
106	C₄×Dic₄₇	—	4	2	no	—
107	C₂×C₄₇⋊C₈	—	2	4	no	—
108	C₂×C₄₇⋊C₈	—	2	4	no	—
109	C₂×C₄₇⋊C₈	—	2	4	no	—
110	C₂×C₄₇⋊C₈	—	4	2	no	—
111	C₂×C₄₇⋊C₈	—	4	2	no	—
112	C₂×C₄₇⋊C₈	—	4	2	no	—
113	C₂×C₄₇⋊C₈	—	4	2	no	—
114	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₂³×C₄₇	#117	1	2	yes	—
116	C₂³×C₄₇	C₄×D₄	1	2	yes	—
117	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
118	C₂³×C₄₇	C₄×Q₈	1	1	yes	characteristic
119	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
120	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
121	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
122	C₂³×C₄₇	#131	1	1	yes	characteristic
123	C₂³×C₄₇	#131	1	1	yes	characteristic
124	C₂³×C₄₇	#131	1	2	yes	—
125	C₂×C₄×C₄₇	—	2	2	no	—
126	C₂×C₄×C₄₇	—	2	2	no	—
127	C₂×C₄×C₄₇	—	2	4	no	—
128	C₂×C₄×C₄₇	—	2	4	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	4	2	no	—
133	C₂×C₄×C₄₇	—	4	2	no	—
134	C₂×C₄×C₄₇	C₄⋊C₈	1	4	yes	—
135	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
136	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
137	C₂×C₄×C₄₇	#121	1	2	yes	—
138	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
139	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
140	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#123	1	2	yes	—
143	C₂×C₄×C₄₇	#123	1	2	yes	—
144	C₂×C₄×C₄₇	#124	1	2	yes	—
145	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#125	1	2	yes	—
148	C₂×C₄×C₄₇	#125	1	2	yes	—
149	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#126	1	2	yes	—
151	C₂×C₄×C₄₇	#126	1	2	yes	—
152	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
153	C₂×Dic₄₇	—	2	4	no	—
154	C₂×Dic₄₇	—	2	4	no	—
155	C₂×Dic₄₇	—	2	4	no	—
156	C₂×Dic₄₇	—	2	4	no	—
157	C₂×Dic₄₇	—	2	4	no	—
158	C₂×Dic₄₇	—	2	4	no	—
159	C₂×Dic₄₇	—	4	2	no	—
160	C₂×Dic₄₇	—	4	2	no	—
161	C₂×Dic₄₇	—	4	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	C₂×Dic₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₈×C₄₇	—	4	2	no	—
168	C₈×C₄₇	—	4	2	no	—
169	C₄₇⋊C₈	—	4	4	no	—
170	#11255	—	47	1	no	maximal, Sylow
171	C₂²×C₄₇	#382	1	1	yes	characteristic
172	C₂²×C₄₇	#385	1	1	yes	characteristic
173	C₂²×C₄₇	#387	1	2	yes	—
174	C₂²×C₄₇	#388	1	2	yes	—
175	C₂²×C₄₇	#389	1	1	yes	characteristic
176	C₂²×C₄₇	C₂×C₄⋊C₈	1	1	yes	characteristic
177	C₂²×C₄₇	#423	1	1	yes	characteristic
178	C₂²×C₄₇	#424	1	1	yes	characteristic
179	C₂²×C₄₇	#424	1	1	yes	characteristic
180	C₂²×C₄₇	#431	1	2	yes	—
181	C₂²×C₄₇	#432	1	2	yes	—
182	C₂²×C₄₇	#433	1	2	yes	—
183	C₂²×C₄₇	#433	1	2	yes	—
184	C₂²×C₄₇	C₈×D₄	1	2	yes	—
185	C₂²×C₄₇	C₈×D₄	1	1	yes	characteristic
186	C₂²×C₄₇	#435	1	2	yes	—
187	C₂²×C₄₇	#435	1	2	yes	—
188	C₂²×C₄₇	#435	1	2	yes	—
189	C₂²×C₄₇	#436	1	2	yes	—
190	C₂²×C₄₇	#436	1	1	yes	characteristic
191	C₂²×C₄₇	C₈×Q₈	1	1	yes	characteristic
192	C₂²×C₄₇	#446	1	2	yes	—
193	C₂²×C₄₇	#446	1	1	yes	characteristic
194	C₄×C₄₇	—	2	4	no	—
195	C₄×C₄₇	—	4	2	no	—
196	C₄×C₄₇	#393	1	1	yes	characteristic
197	C₄×C₄₇	#394	1	1	yes	characteristic
198	C₄×C₄₇	#397	1	1	yes	characteristic
199	C₄×C₄₇	#398	1	2	yes	—
200	C₄×C₄₇	#400	1	1	yes	characteristic
201	C₄×C₄₇	#400	1	2	yes	—
202	Dic₄₇	—	4	4	no	—
203	Dic₄₇	—	4	4	no	—
204	C₂²×C₄⋊C₈	—	47	1	no	—
205	C₂×#336	—	47	2	no	—
206	C₂×#336	—	47	2	no	—
207	C₂×#336	D₄₇	1	1	yes	characteristic
208	C₄×#95	—	47	1	no	—
209	C₂×C₄₇	#1442	1	1	yes	characteristic
210	C₂×C₄₇	#1831	1	1	yes	characteristic
211	C₂×C₄₇	#1832	1	1	yes	characteristic
212	C₂×C₄₇	#1850	1	1	yes	characteristic
213	C₂×C₄₇	#1851	1	1	yes	characteristic
214	C₂×C₄₇	#1916	1	2	yes	—
215	C₂×C₄₇	#1917	1	2	yes	—
216	C₂×C₄₇	#1923	1	2	yes	—
217	C₂×C₄₇	#1924	1	2	yes	—
218	C₂×C₄₇	#1939	1	1	yes	characteristic
219	C₂×C₄₇	#1940	1	1	yes	characteristic
220	C₂³×C₈	—	47	2	no	—
221	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
222	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
223	C₂²×C₄²	—	47	2	no	—
224	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
225	C₂×C₄⋊C₈	—	94	4	no	—
226	C₂×C₄⋊C₈	—	94	2	no	—
227	C₂×#95	—	47	1	no	—
228	C₂×#95	—	47	2	no	—
229	C₂×#95	—	47	1	no	—
230	#336	—	2	2	no	—
231	#336	—	94	4	no	—
232	#336	—	94	4	no	—
233	C₄₇	#11255	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₄	—	47	2	no	—
235	C₂³×C₄	—	47	2	no	—
236	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
237	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
238	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	47	4	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₂²×C₈	—	94	2	no	—
250	C₂²×C₈	—	94	2	no	—
251	C₂²×C₈	—	94	2	no	—
252	C₂²×C₈	—	94	2	no	—
253	C₂²×C₈	—	94	2	no	—
254	C₂²×C₈	Dic₉₄	1	2	yes	—
255	C₂²×C₈	D₁₈₈	1	2	yes	—
256	C₂×C₄²	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	94	2	no	—
259	C₂×C₄²	—	94	2	no	—
260	C₂×C₄²	—	94	2	no	—
261	C₂×C₄²	—	94	2	no	—
262	C₂×C₄²	—	94	2	no	—
263	C₂×C₄²	—	94	2	no	—
264	C₂×C₄²	Dic₉₄	1	2	yes	—
265	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
266	C₄⋊C₈	—	94	8	no	—
267	#95	—	47	4	no	—
268	#95	—	94	4	no	—
269	#95	—	94	2	no	—
270	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	47	4	no	—
278	C₂²×C₄	—	47	4	no	—
279	C₂²×C₄	—	94	2	no	—
280	C₂²×C₄	—	94	2	no	—
281	C₂²×C₄	—	94	2	no	—
282	C₂²×C₄	—	94	2	no	—
283	C₂²×C₄	—	94	2	no	—
284	C₂²×C₄	—	94	2	no	—
285	C₂²×C₄	—	94	2	no	—
286	C₂²×C₄	—	94	2	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	—	94	2	no	—
291	C₂²×C₄	C₈×D₄₇	1	2	yes	—
292	C₂²×C₄	#10625324	1	2	yes	—
293	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
294	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
295	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
296	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
298	C₂²×C₄	#10625350	1	1	yes	characteristic
299	C₂²×C₄	#10625350	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₄₇	1	2	yes	—
301	C₂²×C₄	#10625352	1	2	yes	—
302	C₂²×C₄	#10625352	1	2	yes	—
303	C₂²×C₄	#10625354	1	2	yes	—
304	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	4	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	2	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	94	4	no	—
316	C₂×C₈	—	94	4	no	—
317	C₂×C₈	—	94	4	no	—
318	C₂×C₈	—	188	2	no	—
319	C₂×C₈	—	188	2	no	—
320	C₂×C₈	—	188	2	no	—
321	C₂×C₈	—	188	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	4	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	188	2	no	—
326	C₄²	—	188	2	no	—
327	C₄²	—	188	2	no	—
328	C₄²	—	188	2	no	—
329	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
330	C₂³	#13093982	1	2	yes	—
331	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
332	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
333	C₂³	C₄×Dic₉₄	1	1	yes	characteristic
334	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
335	C₂³	M₁₆×D₄₇	1	2	yes	—
336	C₂³	C₂×#10625324	1	1	yes	characteristic
337	C₂³	#13094030	1	1	yes	characteristic
338	C₂³	#13094030	1	1	yes	characteristic
339	C₂³	#13094032	1	2	yes	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	94	4	no	—
350	C₂×C₄	—	94	4	no	—
351	C₂×C₄	—	94	4	no	—
352	C₂×C₄	—	94	4	no	—
353	C₂×C₄	—	94	4	no	—
354	C₂×C₄	—	94	4	no	—
355	C₂×C₄	—	188	2	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	—	188	2	no	—
358	C₂×C₄	—	188	2	no	—
359	C₂×C₄	—	188	2	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	Dic₄₇⋊C₈	1	4	yes	—
364	C₂×C₄	#13093992	1	1	yes	characteristic
365	C₂×C₄	#13093998	1	1	yes	characteristic
366	C₂×C₄	#13093999	1	2	yes	—
367	C₂×C₄	#13094001	1	2	yes	—
368	C₂×C₄	#13094001	1	2	yes	—
369	C₂×C₄	#13094003	1	1	yes	characteristic
370	C₂×C₄	#13094005	1	1	yes	characteristic
371	C₂×C₄	#13094008	1	2	yes	—
372	C₂×C₄	#13094009	1	2	yes	—
373	C₂×C₄	#13094010	1	2	yes	—
374	C₂×C₄	#13094011	1	1	yes	characteristic
375	C₂×C₄	#13094013	1	1	yes	characteristic
376	C₂×C₄	#13094015	1	2	yes	—
377	C₂×C₄	#13094015	1	2	yes	—
378	C₂×C₄	#13094016	1	1	yes	characteristic
379	C₂×C₄	#13094017	1	2	yes	—
380	C₂×C₄	#13094019	1	2	yes	—
381	C₂×C₄	#13094024	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	188	4	no	—
385	C₂²	#15688988	1	1	yes	characteristic
386	C₂²	#15688995	1	1	yes	characteristic
387	C₂²	#15689010	1	2	yes	—
388	C₂²	#15689015	1	2	yes	—
389	C₂²	#15689021	1	1	yes	characteristic
390	C₂²	C₂×Dic₄₇⋊C₈	1	1	yes	characteristic
391	C₂²	#15689146	1	1	yes	characteristic
392	C₂²	#15689149	1	1	yes	characteristic
393	C₂²	#15689151	1	1	yes	characteristic
394	C₂²	#15689175	1	2	yes	—
395	C₂²	#15689179	1	2	yes	—
396	C₂²	#15689183	1	2	yes	—
397	C₂²	#15689183	1	2	yes	—
398	C₂²	(C₂²⋊D₄₇)⋊C₈	1	2	yes	—
399	C₂²	C₈×D₁₈₈	1	1	yes	characteristic
400	C₂²	#15689191	1	2	yes	—
401	C₂²	#15689196	1	2	yes	—
402	C₂²	#15689197	1	2	yes	—
403	C₂²	#15689198	1	2	yes	—
404	C₂²	#15689202	1	1	yes	characteristic
405	C₂²	C₈×Dic₉₄	1	1	yes	characteristic
406	C₂²	#15689251	1	2	yes	—
407	C₂²	#15689253	1	1	yes	characteristic
408	C₄	—	2	4	no	—
409	C₄	—	4	2	no	—
410	C₄	—	188	4	no	—
411	C₄	—	188	4	no	—
412	C₄	#15689035	1	1	yes	characteristic
413	C₄	#15689040	1	1	yes	characteristic
414	C₄	#15689048	1	1	yes	characteristic
415	C₄	#15689055	1	2	yes	—
416	C₄	#15689062	1	1	yes	characteristic
417	C₄	#15689065	1	2	yes	—
418	C₂	#20241644	1	1	yes	characteristic
419	C₂	#20243504	1	1	yes	characteristic
420	C₂	#20243507	1	1	yes	characteristic
421	C₂	#20243565	1	1	yes	characteristic
422	C₂	#20243570	1	1	yes	characteristic
423	C₂	#20243948	1	2	yes	—
424	C₂	#20243955	1	2	yes	—
425	C₂	#20243995	1	2	yes	—
426	C₂	#20244002	1	2	yes	—
427	C₂	#20244106	1	1	yes	characteristic
428	C₂	#20244111	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂²×C₈
Fitting	C₂×C₄₇×#336	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	#11255
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
37. C₄₇⋊#95	C₈	semidirect
233. C₄₇	#11255	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₂×#15688877	2
C₄×C₄₇⋊#95	2
C₂×C₄₇×#336	2
#11255	47