Subgroups — #26369480

Order 12032.

692 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689541	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252082	C₂	1	1	yes	maximal, characteristic
3	#20245218	C₂	1	2	yes	maximal, complemented
4	#20245213	C₂	1	2	yes	maximal, complemented
5	#20245211	C₂	1	2	yes	maximal, complemented
6	C₁₆×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
7	#20245148	C₂	1	1	yes	maximal, characteristic, complemented
8	#20245003	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂²⋊(C₄₇⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
10	#20244987	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×M₃₂×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094030	C₂²	1	1	yes	characteristic
13	#15689634	C₄	1	1	yes	characteristic
14	#15689541	—	2	4	no	—
15	C₂×#13093963	C₂²	1	2	yes	complemented
16	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₄₇	C₂²	1	2	yes	complemented
19	#15689194	C₄	1	2	yes	—
20	#15689194	C₄	1	2	yes	—
21	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
22	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
23	#15689149	C₄	1	1	yes	characteristic
24	#15689089	C₄	1	1	yes	characteristic
25	#15689087	C₄	1	1	yes	characteristic
26	#15689078	C₂²	1	1	yes	characteristic
27	Dic₄₇⋊C₁₆	C₂²	1	2	yes	complemented
28	Dic₄₇⋊C₁₆	C₂²	1	2	yes	complemented
29	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic
30	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic
31	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic
32	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic
33	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	complemented
34	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	complemented
35	#15688898	C₂²	1	2	yes	complemented
36	C₁₆×Dic₄₇	C₂²	1	2	yes	complemented
37	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×M₃₂×C₄₇	—	2	4	no	—
39	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
41	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×C₁₆×C₄₇	C₂²	1	2	yes	—
43	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
44	#13094030	—	2	2	no	—
45	#13094030	—	2	2	no	—
46	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
47	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
48	C₂×#10625324	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₄₇	C₂³	1	2	yes	—
50	#13094007	C₈	1	2	yes	—
51	#13094003	C₈	1	1	yes	characteristic
52	#13094003	C₈	1	1	yes	characteristic
53	#13093998	C₈	1	1	yes	characteristic
54	#13093998	C₈	1	1	yes	characteristic
55	#13093993	C₈	1	2	yes	—
56	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
57	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
58	#13093983	C₂×C₄	1	1	yes	characteristic
59	#13093963	—	2	4	no	—
60	C₂×C₄₇⋊C₁₆	—	2	2	no	—
61	C₂×C₄₇⋊C₁₆	—	2	2	no	—
62	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
64	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
65	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
66	C₁₆×D₄₇	—	2	4	no	—
67	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
68	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
69	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
70	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
71	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
72	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
73	#13093934	C₂×C₄	1	2	yes	—
74	C₈×Dic₄₇	C₂³	1	2	yes	—
75	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₄₇	—	2	2	no	—
77	C₂²×C₈×C₄₇	—	2	2	no	—
78	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	M₃₂×C₄₇	—	2	2	no	—
85	M₃₂×C₄₇	—	2	4	no	—
86	M₃₂×C₄₇	D₄	1	4	yes	complemented
87	C₂×C₁₆×C₄₇	—	2	4	no	—
88	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
89	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
90	C₂⁴×C₄₇	C₂×C₈	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊D₄₇	C₂×C₈	1	2	yes	—
100	C₂×C₂²⋊D₄₇	C₂×C₈	1	2	yes	—
101	C₂×C₂²⋊D₄₇	C₂×C₈	1	2	yes	—
102	#10625350	—	2	2	no	—
103	#10625350	—	2	2	no	—
104	C₂×D₁₈₈	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
106	C₂×Dic₉₄	C₂×C₈	1	1	yes	characteristic
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	1	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	#41	1	2	yes	—
119	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
121	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
122	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
123	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
124	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
125	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
127	Dic₄₇⋊C₄	C₂×C₈	1	2	yes	—
128	Dic₄₇⋊C₄	C₂×C₈	1	2	yes	—
129	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
130	#10625329	—	2	2	no	—
131	#10625329	—	2	2	no	—
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
134	#10625324	—	2	4	no	—
135	C₈×D₄₇	—	2	2	no	—
136	C₈×D₄₇	—	2	2	no	—
137	C₁₆×C₄₇	—	2	2	no	—
138	C₁₆×C₄₇	C₂×D₄	1	4	yes	—
139	C₄₇⋊C₁₆	—	2	1	no	—
140	C₄₇⋊C₁₆	—	2	1	no	—
141	C₄₇⋊C₁₆	—	2	1	no	—
142	C₄₇⋊C₁₆	—	2	1	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	—	4	1	no	—
146	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
147	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
148	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#131	1	2	yes	—
162	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
163	C₂²⋊D₄₇	—	2	4	no	—
164	C₂²⋊D₄₇	—	2	4	no	—
165	C₂²⋊D₄₇	—	4	2	no	—
166	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
167	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
168	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
169	D₁₈₈	—	2	2	no	—
170	C₄×D₄₇	—	2	2	no	—
171	C₄×D₄₇	—	2	2	no	—
172	Dic₉₄	—	2	2	no	—
173	C₈×C₄₇	—	2	1	no	—
174	C₈×C₄₇	—	2	1	no	—
175	C₈×C₄₇	C₄×D₄	1	2	yes	—
176	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
178	C₄₇⋊C₈	—	2	2	no	—
179	C₄₇⋊C₈	—	2	2	no	—
180	#33436	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	2	1	no	—
186	C₂²×C₄₇	—	2	1	no	—
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	4	4	no	—
189	C₂²×C₄₇	C₈×D₄	1	2	yes	—
190	C₂²×C₄₇	#504	1	2	yes	complemented
191	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
192	C₂×D₄₇	—	2	2	no	—
193	C₂×D₄₇	—	2	2	no	—
194	C₂×D₄₇	—	2	2	no	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	C₈×D₄	1	2	yes	—
198	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
200	Dic₄₇	—	2	2	no	—
201	Dic₄₇	—	2	2	no	—
202	Dic₄₇	—	2	2	no	—
203	C₂×#504	—	47	1	no	—
204	C₂²×M₃₂	D₄₇	1	1	yes	characteristic, complemented
205	#2929	—	47	1	no	—
206	#2169	—	47	2	no	—
207	#2168	—	47	2	no	—
208	#2168	—	47	2	no	—
209	D₄×C₁₆	—	47	2	no	—
210	#2151	—	47	1	no	—
211	#2113	—	47	1	no	—
212	C₂×C₂²⋊C₁₆	—	47	1	no	—
213	#2108	—	47	1	no	—
214	C₂×C₄₇	—	2	2	no	—
215	C₂×C₄₇	—	2	2	no	—
216	C₂×C₄₇	—	4	1	no	—
217	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#504	1	1	yes	characteristic
219	C₂×C₄₇	#3407	1	1	yes	characteristic
220	D₄₇	—	4	2	no	—
221	C₂×#131	—	47	1	no	—
222	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
223	#525	—	47	1	no	—
224	#504	—	94	4	no	—
225	C₂×M₃₂	—	2	4	no	—
226	C₂×M₃₂	—	47	2	no	—
227	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
228	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
229	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic
230	C₂²×C₁₆	—	47	1	no	—
231	C₂²×C₁₆	—	47	1	no	—
232	C₂²×C₁₆	—	47	2	no	—
233	C₂²×C₁₆	C₂×D₄₇	1	2	yes	—
234	#435	—	47	2	no	—
235	#435	—	47	2	no	—
236	C₈×D₄	—	47	2	no	—
237	C₈×D₄	—	47	2	no	—
238	#424	—	47	1	no	—
239	#408	—	47	1	no	—
240	#407	—	47	1	no	—
241	#405	—	47	1	no	—
242	C₄⋊C₁₆	—	47	2	no	—
243	C₄⋊C₁₆	—	47	2	no	—
244	C₂²⋊C₁₆	—	47	1	no	—
245	C₂²⋊C₁₆	—	47	1	no	—
246	C₂²⋊C₁₆	—	47	1	no	—
247	C₂²⋊C₁₆	—	47	1	no	—
248	C₂²⋊C₁₆	—	47	2	no	—
249	C₂²⋊C₁₆	—	47	2	no	—
250	#346	—	47	2	no	—
251	C₄×C₁₆	—	47	2	no	—
252	C₄₇	#33436	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	—	47	1	no	—
254	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
255	#131	—	94	2	no	—
256	#131	—	94	2	no	—
257	C₂×M₁₆	—	47	1	no	—
258	C₂×M₁₆	—	47	1	no	—
259	C₂×M₁₆	—	47	2	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	47	2	no	—
263	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
265	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
269	#123	—	47	2	no	—
270	C₂²⋊Q₈	—	47	1	no	—
271	C₂²⋊Q₈	—	47	1	no	—
272	#121	—	47	1	no	—
273	#121	—	47	1	no	—
274	#120	—	47	2	no	—
275	C₄×D₄	—	47	2	no	—
276	C₄×D₄	—	47	2	no	—
277	#117	—	47	1	no	—
278	M₃₂	—	2	2	no	—
279	M₃₂	—	2	4	no	—
280	M₃₂	—	94	4	no	—
281	M₃₂	C₂²⋊D₄₇	1	4	yes	complemented
282	C₂×C₁₆	—	2	4	no	—
283	C₂×C₁₆	—	47	1	no	—
284	C₂×C₁₆	—	47	1	no	—
285	C₂×C₁₆	—	47	1	no	—
286	C₂×C₁₆	—	47	1	no	—
287	C₂×C₁₆	—	94	2	no	—
288	C₂×C₁₆	—	94	2	no	—
289	C₂×C₁₆	—	94	4	no	—
290	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
291	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
292	C₄⋊C₈	—	47	2	no	—
293	C₄⋊C₈	—	47	2	no	—
294	C₂²⋊C₈	—	47	2	no	—
295	C₂²⋊C₈	—	47	2	no	—
296	C₂²⋊C₈	—	47	2	no	—
297	C₂²⋊C₈	—	47	2	no	—
298	#97	—	47	2	no	—
299	C₄×C₈	—	47	2	no	—
300	C₂⁴	C₈×D₄₇	1	1	yes	characteristic
301	#41	—	94	2	no	—
302	#41	—	94	2	no	—
303	C₂×Q₈	—	47	1	no	—
304	C₂×D₄	—	47	2	no	—
305	C₂×D₄	—	47	2	no	—
306	C₂×D₄	—	47	2	no	—
307	C₂×D₄	—	47	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	47	2	no	—
311	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
312	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₈×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	C₂×C₄×D₄₇	1	1	yes	characteristic
317	M₁₆	—	94	2	no	—
318	M₁₆	—	94	2	no	—
319	M₁₆	—	94	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	47	2	no	—
328	C₂×C₈	—	47	2	no	—
329	C₂×C₈	—	94	2	no	—
330	C₂×C₈	—	94	2	no	—
331	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
332	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂×C₈	#10625350	1	2	yes	—
335	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
336	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
337	C₄⋊C₄	—	47	2	no	—
338	C₄⋊C₄	—	47	2	no	—
339	C₄⋊C₄	—	47	1	no	—
340	C₄⋊C₄	—	47	1	no	—
341	C₂²⋊C₄	—	47	2	no	—
342	C₂²⋊C₄	—	47	2	no	—
343	C₂²⋊C₄	—	47	2	no	—
344	C₂²⋊C₄	—	47	2	no	—
345	C₂²⋊C₄	—	47	2	no	—
346	C₄²	—	47	2	no	—
347	C₁₆	—	2	2	no	—
348	C₁₆	—	94	1	no	—
349	C₁₆	—	94	1	no	—
350	C₁₆	—	94	1	no	—
351	C₁₆	—	94	1	no	—
352	C₁₆	C₂×C₂²⋊D₄₇	1	4	yes	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	47	2	no	—
357	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
358	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
359	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
360	Q₈	—	94	2	no	—
361	D₄	—	94	4	no	—
362	D₄	—	94	4	no	—
363	D₄	—	94	2	no	—
364	D₄	—	188	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	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	2	no	—
373	C₂×C₄	—	47	2	no	—
374	C₂×C₄	—	47	2	no	—
375	C₂×C₄	—	94	2	no	—
376	C₂×C₄	—	94	2	no	—
377	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
378	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
381	C₂×C₄	#13094030	1	2	yes	—
382	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	94	2	no	—
386	C₈	—	94	2	no	—
387	C₈	C₄×C₂²⋊D₄₇	1	2	yes	—
388	C₈	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
389	C₈	C₂×#10625350	1	1	yes	characteristic
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	4	4	no	—
398	C₂²	—	94	2	no	—
399	C₂²	—	94	2	no	—
400	C₂²	—	94	2	no	—
401	C₂²	C₈×C₂²⋊D₄₇	1	2	yes	—
402	C₂²	#15689541	1	2	yes	complemented
403	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	94	2	no	—
407	C₄	—	94	2	no	—
408	C₄	—	94	2	no	—
409	C₄	C₈×C₂²⋊D₄₇	1	2	yes	—
410	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
411	C₄	C₂×#13094030	1	1	yes	characteristic
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	—	4	1	no	—
415	C₂	—	188	2	no	—
416	C₂	C₂×C₈×C₂²⋊D₄₇	1	1	yes	characteristic
417	C₂	C₂×#15689541	1	1	yes	characteristic
418	C₂	#20256490	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₈
Fitting	C₂²×M₃₂×C₄₇	C₂
prime radical	#15689634	C₄
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	C₂²×M₃₂	D₄₇
hypocenter	C₄₇	#33436
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×#15689541	C₂	semidirect
3. #20245218	C₂	semidirect
4. #20245213	C₂	semidirect
5. #20245211	C₂	semidirect
6. C₁₆×C₂²⋊D₄₇	C₂	semidirect
7. #20245148	C₂	semidirect
8. #20245003	C₂	semidirect
9. C₂×C₂²⋊(C₄₇⋊C₁₆)	C₂	semidirect
10. #20244987	C₂	semidirect
11. C₂²×M₃₂×C₄₇	C₂	semidirect
15. C₂×#13093963	C₂²	semidirect
18. C₂×C₁₆×D₄₇	C₂²	semidirect
27. Dic₄₇⋊C₁₆	C₂²	semidirect
28. Dic₄₇⋊C₁₆	C₂²	semidirect
33. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
34. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
35. #15688898	C₂²	semidirect
36. C₁₆×Dic₄₇	C₂²	semidirect
86. M₃₂×C₄₇	D₄	semidirect
190. C₂²×C₄₇	#504	semidirect
204. C₂²×M₃₂	D₄₇	semidirect
252. C₄₇	#33436	semidirect
281. M₃₂	C₂²⋊D₄₇	semidirect
402. C₂²	#15689541	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689541	2
#20252082	2
#20245218	2
#20245213	2
#20245211	2
C₁₆×C₂²⋊D₄₇	2
#20245148	2
#20245003	2
C₂×C₂²⋊(C₄₇⋊C₁₆)	2
#20244987	2
C₂²×M₃₂×C₄₇	2
#33436	47