Subgroups — #26214614

Order 12032.

1150 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689201	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689078	C₂	1	2	yes	maximal, complemented
3	#20245853	C₂	1	1	yes	maximal, characteristic
4	#20243258	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243243	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243174	C₂	1	2	yes	maximal, complemented
8	C₈×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
9	#20243156	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂×#13093983	C₂²	1	2	yes	—
14	#15689201	C₄	1	8	yes	complemented
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	#15689078	—	2	8	no	—
18	C₂×#13093934	C₂²	1	2	yes	—
19	C₂×#13093934	C₂²	1	2	yes	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
22	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	#15689026	C₄	1	2	yes	—
27	#15689022	C₄	1	2	yes	—
28	#15689016	C₄	1	4	yes	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
31	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₈×D₄×C₄₇	C₄	1	8	yes	complemented
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#10625329	—	2	4	no	—
42	C₂×#10625329	—	2	4	no	—
43	C₂×#10625329	C₂×C₄	1	8	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	#13093983	—	2	4	no	—
48	#13093983	—	2	4	no	—
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
51	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
52	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
53	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
57	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
58	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
59	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	—
60	#13093934	—	2	4	no	—
61	#13093934	—	2	4	no	—
62	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
63	C₈×Dic₄₇	—	2	4	no	—
64	C₈×Dic₄₇	—	2	2	no	—
65	C₈×Dic₄₇	—	2	2	no	—
66	C₈×Dic₄₇	—	2	2	no	—
67	C₈×Dic₄₇	D₄	1	4	yes	complemented
68	C₄₇⋊#95	C₂×C₄	1	4	yes	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
72	C₂²×C₈×C₄₇	—	2	4	no	—
73	C₂²×C₈×C₄₇	—	2	4	no	—
74	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
77	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
79	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
80	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
84	C₂²⋊C₈×C₄₇	C₂×C₄	1	8	yes	—
85	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
86	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	C₄²	1	4	yes	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
99	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
100	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	—	2	16	no	—
107	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₄₇	#41	1	2	yes	—
112	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
113	C₂²⋊C₄×C₄₇	C₄²	1	8	yes	—
114	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
115	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²⋊Dic₄₇	—	2	8	no	—
117	C₂²⋊Dic₄₇	—	2	8	no	—
118	C₄⋊Dic₄₇	—	2	4	no	—
119	C₄⋊Dic₄₇	—	2	8	no	—
120	C₄×Dic₄₇	—	2	4	no	—
121	C₄×Dic₄₇	—	2	2	no	—
122	C₄×Dic₄₇	—	2	1	no	—
123	C₄×Dic₄₇	—	2	1	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₄×Dic₄₇	—	2	4	no	—
126	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
127	C₄×Dic₄₇	#41	1	2	yes	—
128	#10625329	—	2	16	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
134	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
135	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
137	C₂×C₄₇⋊C₈	#41	1	2	yes	—
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	—	2	2	no	—
140	C₂³×C₄₇	—	2	4	no	—
141	C₂³×C₄₇	—	2	4	no	—
142	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
143	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
144	D₄×C₄₇	—	2	8	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
154	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
155	C₂×C₄×C₄₇	#131	1	4	yes	—
156	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	4	no	—
167	C₂×Dic₄₇	—	2	4	no	—
168	C₂×Dic₄₇	—	2	4	no	—
169	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
170	C₂×Dic₄₇	#131	1	4	yes	—
171	C₈×C₄₇	—	2	4	no	—
172	C₈×C₄₇	—	2	2	no	—
173	C₈×C₄₇	C₄×D₄	1	4	yes	—
174	C₄₇⋊C₈	—	2	4	no	—
175	C₄₇⋊C₈	—	2	2	no	—
176	C₄₇⋊C₈	C₄×D₄	1	4	yes	—
177	#20485	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	2	4	no	—
179	C₂²×C₄₇	—	2	4	no	—
180	C₂²×C₄₇	—	2	4	no	—
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	—	4	4	no	—
183	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#131	1	2	yes	—
187	C₂²×C₄₇	C₂×#131	1	2	yes	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	2	4	no	—
190	C₄×C₄₇	#405	1	4	yes	complemented
191	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
194	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
195	Dic₄₇	—	2	4	no	—
196	Dic₄₇	—	2	4	no	—
197	Dic₄₇	—	4	4	no	—
198	C₂×#436	—	47	1	no	—
199	C₂×C₈×D₄	D₄₇	1	1	yes	characteristic
200	C₂×#405	—	47	2	no	—
201	#2293	—	47	1	no	—
202	#1770	—	47	1	no	—
203	C₈×C₄⋊C₄	—	47	1	no	—
204	#1767	—	47	1	no	—
205	#1753	—	47	2	no	—
206	C₈×C₂²⋊C₄	—	47	2	no	—
207	#1750	—	47	2	no	—
208	C₄²×C₈	—	47	1	no	—
209	C₂×C₄₇	—	4	4	no	—
210	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
212	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
213	C₂×C₄₇	#2931	1	2	yes	—
214	C₂×C₄₇	#2966	1	2	yes	—
215	C₂²×M₁₆	—	47	2	no	—
216	C₂³×C₈	C₂×D₄₇	1	2	yes	—
217	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
218	C₂×#117	—	47	2	no	—
219	#436	—	47	8	no	—
220	C₈×D₄	Dic₄₇	1	8	yes	complemented
221	C₂×C₄⋊C₈	—	47	1	no	—
222	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
223	C₂×C₂²⋊C₈	—	47	2	no	—
224	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
225	#405	—	94	8	no	—
226	C₂×#97	—	47	2	no	—
227	C₂×#97	—	47	2	no	—
228	C₂×C₄×C₈	—	47	1	no	—
229	C₂×C₄×C₈	—	47	1	no	—
230	C₂×C₄×C₈	—	47	1	no	—
231	C₂×C₄×C₈	—	47	1	no	—
232	C₂×C₄×C₈	—	47	2	no	—
233	C₂×C₄×C₈	—	47	1	no	—
234	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
235	#390	—	47	2	no	—
236	#389	—	47	2	no	—
237	#388	—	47	4	no	—
238	C₄×C₄⋊C₄	—	47	1	no	—
239	C₄×C₂²⋊C₄	—	47	2	no	—
240	C₄³	—	47	1	no	—
241	#336	—	47	2	no	—
242	#336	—	47	2	no	—
243	#336	—	47	2	no	—
244	C₄₇	#20485	1	1	yes	characteristic, complemented, Sylow
245	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
246	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
247	C₂×M₁₆	—	47	8	no	—
248	C₂×M₁₆	—	94	4	no	—
249	C₂×M₁₆	—	94	4	no	—
250	C₂²×C₈	—	2	4	no	—
251	C₂²×C₈	—	2	4	no	—
252	C₂²×C₈	—	47	1	no	—
253	C₂²×C₈	—	47	2	no	—
254	C₂²×C₈	—	47	1	no	—
255	C₂²×C₈	C₂×Dic₄₇	1	8	yes	—
256	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
257	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
258	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
259	C₄×D₄	C₄×D₄₇	1	4	yes	—
260	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
261	#117	—	94	4	no	—
262	#117	—	94	4	no	—
263	C₂×C₄⋊C₄	—	47	4	no	—
264	C₂×C₄⋊C₄	—	47	2	no	—
265	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
266	C₂×C₂²⋊C₄	—	47	4	no	—
267	C₂×C₂²⋊C₄	—	47	4	no	—
268	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
269	C₂×C₄²	—	47	1	no	—
270	C₂×C₄²	—	47	2	no	—
271	C₂×C₄²	—	47	2	no	—
272	C₂×C₄²	—	47	2	no	—
273	C₂×C₄²	—	47	1	no	—
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	C₄⋊C₈	—	47	4	no	—
276	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	—
277	C₂²⋊C₈	—	47	8	no	—
278	C₂²⋊C₈	C₂×Dic₄₇	1	8	yes	—
279	#97	—	94	4	no	—
280	#97	—	94	4	no	—
281	C₄×C₈	—	47	4	no	—
282	C₄×C₈	—	47	4	no	—
283	C₄×C₈	—	94	2	no	—
284	C₄×C₈	—	94	2	no	—
285	C₄×C₈	—	94	4	no	—
286	C₄×C₈	—	94	2	no	—
287	C₄×C₈	C₂×Dic₄₇	1	4	yes	—
288	#95	—	47	4	no	—
289	#95	—	47	2	no	—
290	C₂⁴	C₂×C₄×D₄₇	1	2	yes	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	47	2	no	—
298	C₂²×C₄	—	47	2	no	—
299	C₂²×C₄	—	47	4	no	—
300	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
302	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
303	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
305	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
306	M₁₆	—	94	16	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	16	no	—
312	C₂×C₈	—	47	2	no	—
313	C₂×C₈	—	47	2	no	—
314	C₂×C₈	—	47	2	no	—
315	C₂×C₈	—	47	2	no	—
316	C₂×C₈	—	47	4	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	94	1	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	94	1	no	—
321	C₂×C₈	D₄×D₄₇	1	2	yes	—
322	C₂×C₈	#10625352	1	2	yes	—
323	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
324	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
325	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
326	C₄⋊C₄	—	94	8	no	—
327	C₄⋊C₄	—	94	4	no	—
328	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
329	C₂²⋊C₄	—	94	8	no	—
330	C₂²⋊C₄	—	94	8	no	—
331	C₂²⋊C₄	C₄×Dic₄₇	1	8	yes	—
332	C₄²	—	47	2	no	—
333	C₄²	—	47	2	no	—
334	C₄²	—	94	4	no	—
335	C₄²	—	94	4	no	—
336	C₄²	—	94	2	no	—
337	C₄²	—	94	1	no	—
338	C₄²	—	94	2	no	—
339	C₄²	—	94	1	no	—
340	C₄²	C₂×C₄×D₄₇	1	2	yes	—
341	C₄²	C₂²×Dic₄₇	1	2	yes	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	4	no	—
346	C₂³	C₂×C₄×Dic₄₇	1	4	yes	—
347	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
348	D₄	—	2	8	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	47	4	no	—
357	C₂×C₄	—	47	4	no	—
358	C₂×C₄	—	94	2	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	—	94	4	no	—
363	C₂×C₄	—	94	4	no	—
364	C₂×C₄	—	94	4	no	—
365	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
366	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
367	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
368	C₂×C₄	#13094030	1	4	yes	—
369	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
372	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
373	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	2	2	no	—
377	C₈	—	47	4	no	—
378	C₈	—	94	4	no	—
379	C₈	—	94	2	no	—
380	C₈	D₄×Dic₄₇	1	4	yes	—
381	C₂²	—	2	4	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
387	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
388	C₂²	C₄×#10625352	1	1	yes	characteristic
389	C₂²	#131×D₄₇	1	2	yes	—
390	C₂²	C₂×#13094030	1	2	yes	—
391	C₄	—	2	2	no	—
392	C₄	—	2	4	no	—
393	C₄	—	94	4	no	—
394	C₄	—	94	4	no	—
395	C₄	—	188	4	no	—
396	C₄	#15689078	1	4	yes	complemented
397	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
398	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
399	C₄	C₄×#10625352	1	1	yes	characteristic
400	C₄	#41×Dic₄₇	1	1	yes	characteristic
401	C₂	—	4	4	no	—
402	C₂	C₄×D₄×Dic₄₇	1	1	yes	characteristic
403	C₂	C₂×#15689078	1	1	yes	characteristic
404	C₂	#131×Dic₄₇	1	1	yes	characteristic
405	C₂	#20252095	1	2	yes	—
406	C₂	#20252360	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₈×D₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₈×D₄	D₄₇
hypocenter	C₄₇	#20485
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#15689078	C₂	semidirect
4. #20243258	C₂	semidirect
5. C₈×C₄⋊Dic₄₇	C₂	semidirect
6. #20243243	C₂	semidirect
7. #20243174	C₂	semidirect
8. C₈×C₂²⋊Dic₄₇	C₂	semidirect
9. #20243156	C₂	semidirect
10. C₄×C₈×Dic₄₇	C₂	semidirect
14. #15689201	C₄	semidirect
37. C₈×D₄×C₄₇	C₄	semidirect
67. C₈×Dic₄₇	D₄	semidirect
190. C₄×C₄₇	#405	semidirect
220. C₈×D₄	Dic₄₇	semidirect
244. C₄₇	#20485	semidirect
396. C₄	#15689078	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689201	2
C₂×#15689078	2
#20245853	2
#20243258	2
C₈×C₄⋊Dic₄₇	2
#20243243	2
#20243174	2
C₈×C₂²⋊Dic₄₇	2
#20243156	2
C₄×C₈×Dic₄₇	2
C₂×C₈×D₄×C₄₇	2
#20485	47