Subgroups — #26181937

Order 12032.

836 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252021	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689176	C₂	1	1	yes	maximal, characteristic
3	#20241685	C₂	1	4	yes	maximal, complemented
4	#20241677	C₂	1	2	yes	maximal, complemented
5	#20241675	C₂	1	2	yes	maximal, complemented
6	C₈×#10625329	C₂	1	2	yes	maximal, complemented
7	M₁₆×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
9	#15689180	C₄	1	2	yes	—
10	#15689180	C₄	1	2	yes	—
11	#15689176	C₄	1	2	yes	—
12	#15689176	C₄	1	2	yes	—
13	#15689176	C₂²	1	2	yes	—
14	#15689176	C₂²	1	1	yes	characteristic
15	#15689176	C₂²	1	1	yes	characteristic
16	#15689176	C₂²	1	2	yes	—
17	#15689176	C₂²	1	2	yes	—
18	#15689147	C₄	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	2	yes	—
20	#15689087	C₄	1	2	yes	—
21	C₂×C₂²⋊(C₄₇⋊C₈)	C₄	1	2	yes	—
22	C₄×#10625329	C₂²	1	2	yes	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
24	#15688845	C₂²	1	4	yes	complemented
25	#15688845	C₂²	1	4	yes	complemented
26	#15688844	C₂²	1	4	yes	complemented
27	C₈×C₄₇⋊C₈	C₂²	1	4	yes	complemented
28	C₂²×M₁₆×C₄₇	C₄	1	2	yes	—
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₄×M₁₆×C₄₇	C₄	1	2	yes	—
31	C₄×M₁₆×C₄₇	C₄	1	2	yes	—
32	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
33	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
34	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
35	C₂×#97×C₄₇	C₄	1	2	yes	—
36	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
37	C₂×#10625329	C₂×C₄	1	4	yes	—
38	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
39	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
40	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
41	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
42	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
43	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
44	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
45	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
46	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
47	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
48	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
49	#13093935	C₂×C₄	1	4	yes	—
50	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
51	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
52	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
53	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
54	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×M₁₆×C₄₇	—	2	8	no	—
58	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
59	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
60	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
61	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	#97×C₄₇	C₂×C₄	1	2	yes	—
75	#97×C₄₇	C₂×C₄	1	4	yes	—
76	#97×C₄₇	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
78	C₄×C₈×C₄₇	C₂³	1	2	yes	—
79	C₄×C₈×C₄₇	C₂³	1	2	yes	—
80	C₂⁴×C₄₇	C₄²	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	4	2	no	—
84	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₄²	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	C₂²×C₄	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	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	M₁₆×C₄₇	—	2	4	no	—
103	M₁₆×C₄₇	—	2	8	no	—
104	M₁₆×C₄₇	M₁₆	1	8	yes	complemented
105	C₂×C₈×C₄₇	—	2	8	no	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
108	C₄²×C₄₇	C₄²	1	1	yes	characteristic
109	C₄²×C₄₇	C₄²	1	1	yes	characteristic
110	C₄²×C₄₇	C₄²	1	1	yes	characteristic
111	C₄²×C₄₇	C₄²	1	1	yes	characteristic
112	C₄²×C₄₇	C₄²	1	1	yes	characteristic
113	C₄²×C₄₇	C₄²	1	1	yes	characteristic
114	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
124	#10625329	—	2	8	no	—
125	C₂×C₄₇⋊C₈	—	4	4	no	—
126	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
127	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
128	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	4	1	no	—
132	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
133	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
134	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	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	—	4	1	no	—
149	C₂×C₄×C₄₇	—	4	1	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
161	C₂×C₄×C₄₇	#131	1	4	yes	—
162	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₈×C₄₇	—	2	4	no	—
166	C₈×C₄₇	C₂×M₁₆	1	8	yes	—
167	C₄₇⋊C₈	—	2	8	no	—
168	C₄₇⋊C₈	—	2	4	no	—
169	C₄₇⋊C₈	—	2	4	no	—
170	#17327	—	47	1	no	maximal, Sylow
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	—	2	1	no	—
173	C₂²×C₄₇	—	2	1	no	—
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	1	no	—
178	C₂²×C₄₇	—	4	4	no	—
179	C₂²×C₄₇	C₄×M₁₆	1	2	yes	—
180	C₂²×C₄₇	#405	1	2	yes	—
181	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
182	C₄×C₄₇	—	2	1	no	—
183	C₄×C₄₇	—	2	1	no	—
184	C₄×C₄₇	—	2	1	no	—
185	C₄×C₄₇	—	2	1	no	—
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	C₄×M₁₆	1	2	yes	—
190	C₄×C₄₇	#405	1	2	yes	—
191	C₄×C₄₇	C₂²×M₁₆	1	2	yes	—
192	C₄×C₄₇	C₂×#131	1	2	yes	—
193	C₄×C₄₇	#568	1	2	yes	—
194	#2920	—	47	1	no	—
195	C₂×#431	—	47	1	no	—
196	C₂×C₄×M₁₆	D₄₇	1	1	yes	characteristic
197	#1453	—	47	4	no	—
198	#1451	—	47	2	no	—
199	#1451	—	47	2	no	—
200	C₈×M₁₆	—	47	2	no	—
201	C₈×M₁₆	—	47	2	no	—
202	C₂×C₄₇	—	2	2	no	—
203	C₂×C₄₇	—	2	2	no	—
204	C₂×C₄₇	—	4	1	no	—
205	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
206	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
207	C₂×C₄₇	#2873	1	1	yes	characteristic
208	C₂²×M₁₆	Dic₄₇	1	2	yes	—
209	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
210	#432	—	47	2	no	—
211	#432	—	47	2	no	—
212	#431	—	47	2	no	—
213	#431	—	47	2	no	—
214	#431	—	47	1	no	—
215	#431	—	47	1	no	—
216	#431	—	47	2	no	—
217	#431	—	47	2	no	—
218	#431	—	47	2	no	—
219	#423	—	47	2	no	—
220	C₂×C₄⋊C₈	—	47	2	no	—
221	#407	—	47	2	no	—
222	C₂×C₂²⋊C₈	—	47	2	no	—
223	C₄×M₁₆	—	47	2	no	—
224	C₄×M₁₆	Dic₄₇	1	2	yes	—
225	C₄×M₁₆	Dic₄₇	1	2	yes	—
226	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
227	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
228	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
229	C₂×#97	Dic₄₇	1	2	yes	—
230	C₂×C₄×C₈	—	47	2	no	—
231	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
232	#322	—	47	4	no	—
233	#322	—	47	4	no	—
234	#322	—	47	4	no	—
235	C₈²	—	47	4	no	—
236	C₄₇	#17327	1	1	yes	characteristic, complemented, Sylow
237	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
238	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
239	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
240	C₂×M₁₆	—	2	8	no	—
241	C₂×M₁₆	—	47	4	no	—
242	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
243	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
244	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
245	C₂²×C₈	—	47	4	no	—
246	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
247	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
248	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
249	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
250	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
251	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
252	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
253	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
254	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
255	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
256	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
257	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
258	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
259	C₄⋊C₈	—	47	2	no	—
260	C₄⋊C₈	—	47	2	no	—
261	C₄⋊C₈	—	47	4	no	—
262	C₄⋊C₈	—	47	4	no	—
263	C₄⋊C₈	—	47	4	no	—
264	C₂²⋊C₈	—	47	2	no	—
265	C₂²⋊C₈	—	47	2	no	—
266	C₂²⋊C₈	—	47	4	no	—
267	C₂²⋊C₈	—	47	4	no	—
268	C₂²⋊C₈	—	47	4	no	—
269	#97	—	47	4	no	—
270	#97	C₂×Dic₄₇	1	2	yes	—
271	#97	C₂×Dic₄₇	1	4	yes	—
272	#97	C₂×Dic₄₇	1	2	yes	—
273	C₄×C₈	—	47	4	no	—
274	C₄×C₈	—	47	2	no	—
275	C₄×C₈	—	47	4	no	—
276	C₄×C₈	—	47	2	no	—
277	C₄×C₈	C₂×Dic₄₇	1	4	yes	—
278	C₄×C₈	C₂²×D₄₇	1	2	yes	—
279	C₄×C₈	C₂²×D₄₇	1	2	yes	—
280	C₂⁴	C₄×Dic₄₇	1	1	yes	characteristic
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
289	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
291	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₄×D₄₇	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	M₁₆	—	2	4	no	—
303	M₁₆	—	2	8	no	—
304	M₁₆	—	94	8	no	—
305	M₁₆	#10625329	1	8	yes	complemented
306	C₂×C₈	—	2	8	no	—
307	C₂×C₈	—	47	4	no	—
308	C₂×C₈	—	47	4	no	—
309	C₂×C₈	—	47	8	no	—
310	C₂×C₈	—	188	4	no	—
311	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
312	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
313	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
314	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
315	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
316	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
317	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
318	C₄²	C₄×Dic₄₇	1	1	yes	characteristic
319	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
320	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
321	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
322	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
323	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
324	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
325	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
326	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
327	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
328	C₄²	C₂³×D₄₇	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	4	1	no	—
332	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
333	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
334	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
354	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
358	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂×#10625329	1	4	yes	—
361	C₂×C₄	#13094032	1	4	yes	—
362	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
363	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
365	C₈	—	2	4	no	—
366	C₈	—	94	8	no	—
367	C₈	—	94	4	no	—
368	C₈	—	94	4	no	—
369	C₈	C₂×#10625329	1	8	yes	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	4	4	no	—
378	C₂²	C₄×#10625329	1	2	yes	—
379	C₂²	#15689081	1	2	yes	—
380	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	2	1	no	—
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	C₄×#10625329	1	2	yes	—
389	C₄	#15689081	1	2	yes	—
390	C₄	C₂²×#10625329	1	2	yes	—
391	C₄	C₂×#13094032	1	2	yes	—
392	C₄	#15689889	1	2	yes	—
393	C₂	—	2	2	no	—
394	C₂	—	2	2	no	—
395	C₂	—	4	1	no	—
396	C₂	C₂×C₄×#10625329	1	1	yes	characteristic
397	C₂	C₂×#15689081	1	1	yes	characteristic
398	C₂	#20251806	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂²×C₄²
Fitting	C₂×C₄×M₁₆×C₄₇	C₂
prime radical	C₂⁴×C₄₇	C₄²
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₄₇
hypocenter	C₄₇	#17327
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #20241685	C₂	semidirect
4. #20241677	C₂	semidirect
5. #20241675	C₂	semidirect
6. C₈×#10625329	C₂	semidirect
7. M₁₆×C₄₇⋊C₈	C₂	semidirect
24. #15688845	C₂²	semidirect
25. #15688845	C₂²	semidirect
26. #15688844	C₂²	semidirect
27. C₈×C₄₇⋊C₈	C₂²	semidirect
104. M₁₆×C₄₇	M₁₆	semidirect
236. C₄₇	#17327	semidirect
305. M₁₆	#10625329	semidirect

Maximal subgroups

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

subgroup	index
#20252021	2
C₂×#15689176	2
#20241685	2
#20241677	2
#20241675	2
C₈×#10625329	2
M₁₆×C₄₇⋊C₈	2
C₂×C₄×M₁₆×C₄₇	2
#17327	47