Subgroups — #26124173

Order 12032.

778 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688892	C₂	1	2	yes	maximal
3	C₂×#15688892	C₂	1	2	yes	maximal
4	#20243082	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×#10625329	C₂²	1	2	yes	—
8	#15689147	—	2	4	no	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
11	#15688892	—	2	4	no	—
12	#15688892	—	2	4	no	—
13	#15688878	—	2	1	no	—
14	#15688878	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#389	—	2	1	no	—
20	C₄₇×#389	—	2	1	no	—
21	C₄₇×#389	—	2	1	no	—
22	C₄₇×#389	—	2	1	no	—
23	C₂×#95×C₄₇	C₄	1	2	yes	—
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	2	no	—
34	C₂×#10625329	D₄	1	4	yes	—
35	C₂×#10625329	Q₈	1	4	yes	—
36	C₂²×C₄₇⋊C₈	—	2	2	no	—
37	C₂²×C₄₇⋊C₈	—	2	2	no	—
38	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
39	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
40	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
56	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₇	Q₈	1	2	yes	—
58	C₂×C₄²×C₄₇	—	2	2	no	—
59	C₂×C₄²×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
64	#95×C₄₇	—	2	2	no	—
65	#95×C₄₇	—	2	2	no	—
66	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	4	no	—
75	C₂²×C₄×C₄₇	—	4	1	no	—
76	C₂²×C₄×C₄₇	—	4	1	no	—
77	C₂²×C₄×C₄₇	—	4	2	no	—
78	C₂²×C₄×C₄₇	—	4	2	no	—
79	C₂²×C₄×C₄₇	—	4	2	no	—
80	C₂²×C₄×C₄₇	—	4	2	no	—
81	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
86	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	#41	1	2	yes	—
95	C₂²×C₄×C₄₇	#41	1	2	yes	—
96	C₄⋊C₄×C₄₇	—	2	2	no	—
97	C₄⋊C₄×C₄₇	—	2	2	no	—
98	C₄⋊C₄×C₄₇	—	2	2	no	—
99	C₄⋊C₄×C₄₇	—	2	2	no	—
100	C₄⋊C₄×C₄₇	—	4	4	no	—
101	C₄⋊C₄×C₄₇	—	4	4	no	—
102	C₄⋊C₄×C₄₇	—	4	1	no	—
103	C₄⋊C₄×C₄₇	—	4	2	no	—
104	C₄⋊C₄×C₄₇	—	4	1	no	—
105	C₄²×C₄₇	—	2	1	no	—
106	C₄²×C₄₇	—	2	1	no	—
107	C₄²×C₄₇	—	2	2	no	—
108	C₄²×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	2	1	no	—
110	C₄²×C₄₇	—	2	1	no	—
111	#10625329	—	2	4	no	—
112	#10625329	—	2	4	no	—
113	#10625329	—	2	4	no	—
114	#10625329	—	2	4	no	—
115	#10625329	—	4	2	no	—
116	#10625329	—	4	2	no	—
117	#10625329	—	4	2	no	—
118	#10625329	—	4	2	no	—
119	C₂×C₄₇⋊C₈	—	2	4	no	—
120	C₂×C₄₇⋊C₈	—	2	4	no	—
121	C₂×C₄₇⋊C₈	—	4	2	no	—
122	C₂×C₄₇⋊C₈	—	4	2	no	—
123	C₂×C₄₇⋊C₈	—	4	2	no	—
124	C₂×C₄₇⋊C₈	—	4	2	no	—
125	C₂³×C₄₇	—	2	1	no	—
126	C₂³×C₄₇	—	2	1	no	—
127	C₂³×C₄₇	—	2	1	no	—
128	C₂³×C₄₇	—	2	1	no	—
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂³×C₄₇	#117	1	1	yes	characteristic
132	C₂³×C₄₇	C₄×D₄	1	2	yes	—
133	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	8	4	no	—
155	C₂×C₄×C₄₇	#100	1	2	yes	—
156	C₂×C₄×C₄₇	#101	1	2	yes	—
157	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#121	1	2	yes	—
159	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#121	1	2	yes	—
162	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
163	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
164	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
167	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#123	1	2	yes	—
169	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
170	C₂×C₄×C₄₇	#125	1	2	yes	—
171	C₂×C₄×C₄₇	#125	1	2	yes	—
172	C₂×C₄×C₄₇	#126	1	2	yes	—
173	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
175	C₄₇⋊C₈	—	4	4	no	—
176	C₄₇⋊C₈	—	4	4	no	—
177	#11204	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	2	no	—
184	C₂²×C₄₇	—	2	2	no	—
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	#380	1	1	yes	characteristic
187	C₂²×C₄₇	#386	1	1	yes	characteristic
188	C₂²×C₄₇	#387	1	2	yes	—
189	C₂²×C₄₇	#389	1	2	yes	—
190	C₂²×C₄₇	#391	1	1	yes	characteristic
191	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
193	C₂²×C₄₇	#413	1	1	yes	characteristic
194	C₂²×C₄₇	#413	1	1	yes	characteristic
195	C₄×C₄₇	—	2	2	no	—
196	C₄×C₄₇	—	2	2	no	—
197	C₄×C₄₇	—	4	4	no	—
198	C₄×C₄₇	—	4	1	no	—
199	C₄×C₄₇	—	4	1	no	—
200	C₄×C₄₇	—	8	2	no	—
201	C₄×C₄₇	#394	1	1	yes	characteristic
202	C₄×C₄₇	#395	1	1	yes	characteristic
203	C₄×C₄₇	#396	1	2	yes	—
204	C₄×C₄₇	#398	1	1	yes	characteristic
205	C₄×C₄₇	#398	1	2	yes	—
206	C₄×C₄₇	#400	1	1	yes	characteristic
207	C₂×#423	—	47	1	no	—
208	C₂×#389	D₄₇	1	1	yes	characteristic
209	C₂×#343	—	47	2	no	—
210	C₂×#343	—	47	2	no	—
211	#1728	—	47	1	no	—
212	C₂×C₄₇	—	2	2	no	—
213	C₂×C₄₇	—	2	2	no	—
214	C₂×C₄₇	#1441	1	1	yes	characteristic
215	C₂×C₄₇	#1800	1	1	yes	characteristic
216	C₂×C₄₇	#1801	1	1	yes	characteristic
217	C₂×C₄₇	#1900	1	1	yes	characteristic
218	C₂×C₄₇	#1901	1	1	yes	characteristic
219	C₂×C₄₇	#1997	1	1	yes	characteristic
220	C₂×C₄₇	#1998	1	1	yes	characteristic
221	C₂²×M₁₆	—	47	2	no	—
222	C₂²×M₁₆	—	47	2	no	—
223	C₂²×C₄⋊C₄	Dic₄₇	1	2	yes	—
224	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
226	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
227	#423	—	94	4	no	—
228	C₂×C₄⋊C₈	—	94	1	no	—
229	C₂×C₄⋊C₈	—	94	1	no	—
230	#389	—	2	1	no	—
231	#389	—	2	1	no	—
232	#389	—	2	1	no	—
233	#389	—	2	1	no	—
234	C₂×#95	Dic₄₇	1	2	yes	—
235	#343	—	94	4	no	—
236	#343	—	94	4	no	—
237	#336	—	94	1	no	—
238	#336	—	94	1	no	—
239	C₄₇	#11204	1	1	yes	characteristic, complemented, Sylow
240	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
241	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
242	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
243	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
244	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
245	C₂×M₁₆	—	47	4	no	—
246	C₂×M₁₆	—	47	4	no	—
247	C₂×M₁₆	—	94	2	no	—
248	C₂×M₁₆	—	94	2	no	—
249	C₂×M₁₆	—	94	2	no	—
250	C₂×M₁₆	—	94	2	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂×M₁₆	—	94	2	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂×M₁₆	—	94	2	no	—
255	C₂×M₁₆	—	94	2	no	—
256	C₂×M₁₆	—	94	2	no	—
257	C₂²×C₈	—	94	2	no	—
258	C₂²×C₈	—	94	2	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	4	4	no	—
270	C₂×C₄⋊C₄	Dic₉₄	1	2	yes	—
271	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
275	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
276	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
277	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
278	C₄⋊C₈	—	94	4	no	—
279	C₄⋊C₈	—	94	4	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	4	1	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
298	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
302	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
304	C₂²×C₄	#10625350	1	1	yes	characteristic
305	C₂²×C₄	#10625350	1	1	yes	characteristic
306	C₂²×C₄	D₄×D₄₇	1	2	yes	—
307	C₂²×C₄	#10625352	1	2	yes	—
308	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
309	C₂²×C₄	#10625354	1	2	yes	—
310	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
312	M₁₆	—	94	4	no	—
313	M₁₆	—	94	4	no	—
314	M₁₆	—	94	4	no	—
315	M₁₆	—	94	4	no	—
316	M₁₆	—	188	2	no	—
317	M₁₆	—	188	2	no	—
318	M₁₆	—	188	2	no	—
319	M₁₆	—	188	2	no	—
320	C₂×C₈	—	94	4	no	—
321	C₂×C₈	—	94	4	no	—
322	C₂×C₈	—	188	2	no	—
323	C₂×C₈	—	188	2	no	—
324	C₂×C₈	—	188	2	no	—
325	C₂×C₈	—	188	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	4	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	2	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄²	—	2	1	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
346	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
347	C₂³	#13093983	1	1	yes	characteristic
348	C₂³	D₄×Dic₄₇	1	2	yes	—
349	C₂³	Q₈×Dic₄₇	1	2	yes	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	8	4	no	—
371	C₂×C₄	#13093941	1	2	yes	—
372	C₂×C₄	#13093943	1	2	yes	—
373	C₂×C₄	#13093992	1	1	yes	characteristic
374	C₂×C₄	#13093996	1	2	yes	—
375	C₂×C₄	#13093998	1	1	yes	characteristic
376	C₂×C₄	#13093998	1	1	yes	characteristic
377	C₂×C₄	#13093999	1	2	yes	—
378	C₂×C₄	#13094000	1	2	yes	—
379	C₂×C₄	#13094002	1	2	yes	—
380	C₂×C₄	#13094003	1	1	yes	characteristic
381	C₂×C₄	#13094003	1	1	yes	characteristic
382	C₂×C₄	#13094004	1	2	yes	—
383	C₂×C₄	#13094005	1	1	yes	characteristic
384	C₂×C₄	#13094009	1	2	yes	—
385	C₂×C₄	#13094013	1	1	yes	characteristic
386	C₂×C₄	#13094014	1	2	yes	—
387	C₂×C₄	#13094015	1	2	yes	—
388	C₂×C₄	#13094019	1	2	yes	—
389	C₂×C₄	#13094022	1	1	yes	characteristic
390	C₂×C₄	#13094023	1	2	yes	—
391	C₈	—	188	4	no	—
392	C₈	—	188	4	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	#15688983	1	1	yes	characteristic
402	C₂²	#15689003	1	1	yes	characteristic
403	C₂²	#15689009	1	2	yes	—
404	C₂²	#15689022	1	2	yes	—
405	C₂²	#15689030	1	1	yes	characteristic
406	C₂²	C₂×#13093941	1	1	yes	characteristic
407	C₂²	C₂×#13093943	1	1	yes	characteristic
408	C₂²	#15689107	1	1	yes	characteristic
409	C₂²	#15689107	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	2	no	—
416	C₄	#15689040	1	1	yes	characteristic
417	C₄	#15689043	1	1	yes	characteristic
418	C₄	#15689045	1	2	yes	—
419	C₄	#15689053	1	1	yes	characteristic
420	C₄	#15689056	1	2	yes	—
421	C₄	#15689062	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	2	2	no	—
424	C₂	#20241641	1	1	yes	characteristic
425	C₂	#20243380	1	1	yes	characteristic
426	C₂	#20243384	1	1	yes	characteristic
427	C₂	#20243852	1	1	yes	characteristic
428	C₂	#20243857	1	1	yes	characteristic
429	C₂	#20244378	1	1	yes	characteristic
430	C₂	#20244382	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator, prime radical	C₂⁴×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#389	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#389	D₄₇
hypocenter	C₄₇	#11204
LCS	G ▷ C₂⁴×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#389

Complements

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

N	H ≅ G/N	type
239. C₄₇	#11204	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₂×#15688892	2
#20243082	2
C₂×C₄₇×#389	2
#11204	47