Subgroups — #26222318

Order 12032.

1110 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689195	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244183	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244003	C₂	1	2	yes	maximal, complemented
7	#20243686	C₂	1	2	yes	maximal, complemented
8	#20243368	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243257	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243166	C₂	1	2	yes	maximal, complemented
11	C₄×#121×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂²×#10625329	C₂²	1	1	yes	characteristic
14	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
15	#15689195	—	2	8	no	—
16	D₄×C₄₇⋊C₈	—	2	4	no	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
22	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
23	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
24	C₄×#10625329	—	2	4	no	—
25	C₂×#13093935	C₂²	1	1	yes	characteristic
26	C₂×#13093935	C₂²	1	2	yes	—
27	C₂×#13093935	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	#15688878	C₂²	1	2	yes	—
31	#15688878	C₂²	1	2	yes	—
32	#15688878	C₂²	1	2	yes	—
33	C₂×#121×C₄₇	C₄	1	1	yes	characteristic
34	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
36	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#390	C₄	1	1	yes	characteristic
38	C₄₇×#389	C₄	1	1	yes	characteristic
39	C₄₇×#388	C₄	1	2	yes	—
40	C₄₇×#386	C₄	1	2	yes	—
41	C₄₇×#380	C₄	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
44	C₂×#10625329	—	2	2	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂×#10625329	—	2	2	no	—
47	C₂×#10625329	—	2	2	no	—
48	C₂×#10625329	—	2	2	no	—
49	C₂×#10625329	D₄	1	4	yes	complemented
50	C₂²×C₄₇⋊C₈	—	2	4	no	—
51	C₂²×C₄₇⋊C₈	—	2	4	no	—
52	C₂²×C₄₇⋊C₈	—	2	4	no	—
53	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
54	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
62	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
66	#13093935	—	2	2	no	—
67	#13093935	—	2	2	no	—
68	#13093935	—	2	4	no	—
69	C₄×C₄₇⋊C₈	—	2	2	no	—
70	C₄×C₄₇⋊C₈	D₄	1	4	yes	complemented
71	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
77	#121×C₄₇	—	2	4	no	—
78	C₄×D₄×C₄₇	—	2	4	no	—
79	C₄×D₄×C₄₇	—	2	4	no	—
80	C₄×D₄×C₄₇	—	2	2	no	—
81	C₄×D₄×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
88	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
90	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
91	C₂×C₄²×C₄₇	—	2	2	no	—
92	C₂×C₄²×C₄₇	—	2	2	no	—
93	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	#95×C₄₇	C₂×C₄	1	2	yes	—
99	#95×C₄₇	C₂×C₄	1	2	yes	—
100	#95×C₄₇	C₂×C₄	1	2	yes	—
101	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂×D₄×C₄₇	—	2	4	no	—
104	C₂×D₄×C₄₇	—	2	4	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	4	2	no	—
108	C₂×D₄×C₄₇	M₁₆	1	4	yes	complemented
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	4	1	no	—
124	C₂²×C₄×C₄₇	—	4	1	no	—
125	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₄₇	#41	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
136	C₄⋊C₄×C₄₇	—	2	4	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₂²⋊C₄×C₄₇	—	2	4	no	—
141	C₂²⋊C₄×C₄₇	—	2	4	no	—
142	C₂²⋊C₄×C₄₇	—	2	4	no	—
143	C₂²⋊C₄×C₄₇	—	2	4	no	—
144	C₂²⋊C₄×C₄₇	—	4	2	no	—
145	C₄²×C₄₇	—	2	2	no	—
146	C₄²×C₄₇	—	2	2	no	—
147	C₄²×C₄₇	—	2	1	no	—
148	C₄²×C₄₇	—	2	2	no	—
149	C₄²×C₄₇	—	2	1	no	—
150	C₄²×C₄₇	—	2	2	no	—
151	C₄²×C₄₇	C₂×D₄	1	2	yes	—
152	C₄²×C₄₇	#41	1	2	yes	—
153	#10625329	—	2	8	no	—
154	#10625329	—	2	8	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	2	1	no	—
157	C₂×C₄₇⋊C₈	—	2	1	no	—
158	C₂×C₄₇⋊C₈	—	2	1	no	—
159	C₂×C₄₇⋊C₈	—	2	1	no	—
160	C₂×C₄₇⋊C₈	—	2	1	no	—
161	C₂×C₄₇⋊C₈	—	2	2	no	—
162	C₂×C₄₇⋊C₈	—	2	2	no	—
163	C₂×C₄₇⋊C₈	—	2	2	no	—
164	C₂×C₄₇⋊C₈	—	2	2	no	—
165	C₂×C₄₇⋊C₈	—	2	2	no	—
166	C₂×C₄₇⋊C₈	—	2	2	no	—
167	C₂×C₄₇⋊C₈	—	4	8	no	—
168	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
169	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
170	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
171	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
172	C₂×C₄₇⋊C₈	#41	1	2	yes	—
173	C₂×C₄₇⋊C₈	#41	1	2	yes	—
174	C₂³×C₄₇	—	2	2	no	—
175	C₂³×C₄₇	—	2	2	no	—
176	C₂³×C₄₇	—	2	1	no	—
177	C₂³×C₄₇	—	2	2	no	—
178	C₂³×C₄₇	—	2	1	no	—
179	C₂³×C₄₇	—	2	1	no	—
180	C₂³×C₄₇	—	2	1	no	—
181	C₂³×C₄₇	—	2	2	no	—
182	C₂³×C₄₇	—	2	2	no	—
183	C₂³×C₄₇	—	2	1	no	—
184	C₂³×C₄₇	—	2	1	no	—
185	C₂³×C₄₇	—	2	2	no	—
186	C₂³×C₄₇	C₄×D₄	1	2	yes	—
187	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
188	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
189	D₄×C₄₇	—	2	8	no	—
190	D₄×C₄₇	—	4	8	no	—
191	C₂×C₄×C₄₇	—	2	1	no	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	2	1	no	—
194	C₂×C₄×C₄₇	—	2	1	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	1	no	—
200	C₂×C₄×C₄₇	—	2	1	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	1	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	1	no	—
210	C₂×C₄×C₄₇	—	2	1	no	—
211	C₂×C₄×C₄₇	—	2	2	no	—
212	C₂×C₄×C₄₇	—	2	1	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	4	4	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	2	no	—
217	C₂×C₄×C₄₇	—	4	2	no	—
218	C₂×C₄×C₄₇	—	4	2	no	—
219	C₂×C₄×C₄₇	—	4	4	no	—
220	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
221	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
222	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
223	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
224	C₂×C₄×C₄₇	#131	1	2	yes	—
225	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
231	C₄₇⋊C₈	—	2	2	no	—
232	C₄₇⋊C₈	—	2	2	no	—
233	C₄₇⋊C₈	—	2	2	no	—
234	C₄₇⋊C₈	—	4	2	no	—
235	C₄₇⋊C₈	—	4	2	no	—
236	C₄₇⋊C₈	#121	1	4	yes	complemented
237	#21486	—	47	1	no	maximal, Sylow
238	C₂²×C₄₇	—	2	4	no	—
239	C₂²×C₄₇	—	2	2	no	—
240	C₂²×C₄₇	—	2	4	no	—
241	C₂²×C₄₇	—	2	2	no	—
242	C₂²×C₄₇	—	2	4	no	—
243	C₂²×C₄₇	—	2	2	no	—
244	C₂²×C₄₇	—	4	1	no	—
245	C₂²×C₄₇	—	4	1	no	—
246	C₂²×C₄₇	—	4	2	no	—
247	C₂²×C₄₇	—	4	2	no	—
248	C₂²×C₄₇	—	4	1	no	—
249	C₂²×C₄₇	—	4	2	no	—
250	C₂²×C₄₇	—	4	1	no	—
251	C₂²×C₄₇	—	4	2	no	—
252	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
255	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
256	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
257	C₂²×C₄₇	#568	1	1	yes	characteristic
258	C₂²×C₄₇	#568	1	1	yes	characteristic
259	C₄×C₄₇	—	2	2	no	—
260	C₄×C₄₇	—	2	2	no	—
261	C₄×C₄₇	—	4	1	no	—
262	C₄×C₄₇	—	4	1	no	—
263	C₄×C₄₇	—	4	2	no	—
264	C₄×C₄₇	—	4	2	no	—
265	C₄×C₄₇	—	4	2	no	—
266	C₄×C₄₇	#435	1	4	yes	complemented
267	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
268	C₄×C₄₇	#525	1	1	yes	characteristic
269	C₄×C₄₇	#529	1	1	yes	characteristic
270	C₄×C₄₇	#532	1	1	yes	characteristic
271	C₂×#435	—	47	2	no	—
272	C₂×C₈×D₄	—	47	1	no	—
273	C₂×C₄×M₁₆	—	47	1	no	—
274	C₄×#121	D₄₇	1	1	yes	characteristic
275	#1954	—	47	1	no	—
276	#1939	—	47	1	no	—
277	#1924	—	47	2	no	—
278	#1870	—	47	2	no	—
279	#1797	—	47	1	no	—
280	#1770	—	47	1	no	—
281	#1752	—	47	2	no	—
282	C₂×C₄₇	—	4	4	no	—
283	C₂×C₄₇	—	4	2	no	—
284	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
285	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
286	C₂×C₄₇	#2930	1	1	yes	characteristic
287	C₂×C₄₇	D₄×M₁₆	1	1	yes	characteristic
288	C₂×C₄₇	#2935	1	1	yes	characteristic
289	C₂×C₄₇	#2969	1	1	yes	characteristic
290	C₂×C₄₇	#2970	1	1	yes	characteristic
291	C₂²×M₁₆	—	47	1	no	—
292	C₂²×M₁₆	—	47	1	no	—
293	C₂³×C₈	—	47	2	no	—
294	C₂×#121	Dic₄₇	1	1	yes	characteristic
295	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
296	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
297	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
298	#435	—	94	8	no	—
299	C₈×D₄	—	94	4	no	—
300	C₂×C₄⋊C₈	—	47	1	no	—
301	C₂×C₄⋊C₈	—	47	1	no	—
302	C₂×C₄⋊C₈	—	47	2	no	—
303	C₂×C₂²⋊C₈	—	47	2	no	—
304	C₂×C₂²⋊C₈	—	47	2	no	—
305	C₂×C₂²⋊C₈	—	47	2	no	—
306	C₂×C₂²⋊C₈	—	47	2	no	—
307	C₄×M₁₆	—	94	4	no	—
308	C₂×#97	—	47	1	no	—
309	C₂×#97	—	47	1	no	—
310	C₂×#97	—	47	2	no	—
311	C₂×C₄×C₈	—	47	1	no	—
312	C₂×C₄×C₈	—	47	1	no	—
313	#390	Dic₄₇	1	1	yes	characteristic
314	#389	Dic₄₇	1	1	yes	characteristic
315	#388	Dic₄₇	1	2	yes	—
316	#386	Dic₄₇	1	2	yes	—
317	#380	Dic₄₇	1	1	yes	characteristic
318	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
319	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
320	#336	—	47	2	no	—
321	#336	—	47	2	no	—
322	#336	—	47	2	no	—
323	C₄₇	#21486	1	1	yes	characteristic, complemented, Sylow
324	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
325	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
326	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
327	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
328	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
329	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
330	C₂×M₁₆	—	47	4	no	—
331	C₂×M₁₆	—	94	2	no	—
332	C₂×M₁₆	—	94	2	no	—
333	C₂×M₁₆	—	94	2	no	—
334	C₂×M₁₆	—	94	2	no	—
335	C₂×M₁₆	—	94	2	no	—
336	C₂²×C₈	—	47	1	no	—
337	C₂²×C₈	—	47	1	no	—
338	C₂²×C₈	—	47	1	no	—
339	C₂²×C₈	—	47	1	no	—
340	C₂²×C₈	—	47	2	no	—
341	C₂²×C₈	—	47	2	no	—
342	C₂²×C₈	—	94	4	no	—
343	C₂²×C₈	—	94	4	no	—
344	C₂²×C₈	—	94	4	no	—
345	#121	—	2	4	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	4	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
352	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
355	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
357	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
362	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
363	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
364	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
365	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
366	C₄⋊C₈	—	94	4	no	—
367	C₄⋊C₈	—	94	2	no	—
368	C₄⋊C₈	—	94	2	no	—
369	C₂²⋊C₈	—	94	4	no	—
370	C₂²⋊C₈	—	94	4	no	—
371	C₂²⋊C₈	—	94	4	no	—
372	C₂²⋊C₈	—	94	4	no	—
373	#97	—	94	2	no	—
374	#97	—	94	2	no	—
375	#97	—	94	4	no	—
376	C₄×C₈	—	47	4	no	—
377	C₄×C₈	—	94	2	no	—
378	#95	C₂×Dic₄₇	1	2	yes	—
379	#95	C₂×Dic₄₇	1	2	yes	—
380	#95	C₂×Dic₄₇	1	2	yes	—
381	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
382	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	#10625329	1	4	yes	complemented
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	D₄×D₄₇	1	2	yes	—
406	C₂²×C₄	#10625352	1	2	yes	—
407	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
408	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
409	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
410	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
411	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
412	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
413	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
414	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
415	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
416	M₁₆	—	94	8	no	—
417	M₁₆	—	94	8	no	—
418	C₂×C₈	—	47	2	no	—
419	C₂×C₈	—	47	2	no	—
420	C₂×C₈	—	47	2	no	—
421	C₂×C₈	—	47	2	no	—
422	C₂×C₈	—	47	2	no	—
423	C₂×C₈	—	47	2	no	—
424	C₂×C₈	—	94	1	no	—
425	C₂×C₈	—	94	1	no	—
426	C₂×C₈	—	94	1	no	—
427	C₂×C₈	—	94	1	no	—
428	C₂×C₈	—	94	1	no	—
429	C₂×C₈	—	94	1	no	—
430	C₂×C₈	—	94	2	no	—
431	C₂×C₈	—	94	2	no	—
432	C₂×C₈	—	94	2	no	—
433	C₂×C₈	—	94	2	no	—
434	C₂×C₈	—	94	2	no	—
435	C₂×C₈	—	94	2	no	—
436	C₂×C₈	—	188	8	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	2	no	—
452	C₄²	D₄×D₄₇	1	2	yes	—
453	C₄²	#10625352	1	2	yes	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	D₄×Dic₄₇	1	2	yes	—
467	C₂³	C₂×#10625329	1	4	yes	—
468	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
469	D₄	—	2	8	no	—
470	D₄	—	4	8	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
501	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
502	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
503	C₂×C₄	C₂×#10625329	1	2	yes	—
504	C₂×C₄	#13094031	1	2	yes	—
505	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
506	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
507	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
508	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
509	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
510	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
511	C₈	—	47	4	no	—
512	C₈	—	94	2	no	—
513	C₈	—	94	2	no	—
514	C₈	—	94	2	no	—
515	C₈	—	188	2	no	—
516	C₈	—	188	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	1	no	—
531	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
532	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
533	C₂²	#41×Dic₄₇	1	1	yes	characteristic
534	C₂²	C₂²×#10625329	1	1	yes	characteristic
535	C₂²	C₂×#13094031	1	1	yes	characteristic
536	C₂²	#15689890	1	1	yes	characteristic
537	C₂²	#15689890	1	1	yes	characteristic
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	#15689195	1	4	yes	complemented
546	C₄	#121×D₄₇	1	1	yes	characteristic
547	C₄	#15689633	1	1	yes	characteristic
548	C₄	#15689654	1	1	yes	characteristic
549	C₄	#15689668	1	1	yes	characteristic
550	C₂	—	4	2	no	—
551	C₂	—	4	4	no	—
552	C₂	#121×Dic₄₇	1	1	yes	characteristic
553	C₂	C₂×#15689195	1	1	yes	characteristic
554	C₂	#20252092	1	1	yes	characteristic
555	C₂	D₄×#10625329	1	1	yes	characteristic
556	C₂	#20252132	1	1	yes	characteristic
557	C₂	#20252393	1	1	yes	characteristic
558	C₂	#20252402	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄×#121×C₄₇	C₂
prime radical	C₂×#121×C₄₇	C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#121	D₄₇
hypocenter	C₄₇	#21486
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#121

Complements

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

N	H ≅ G/N	type
1. C₂×#15689195	C₂	semidirect
2. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
3. C₂×C₄×#10625329	C₂	semidirect
4. #20244183	C₂	semidirect
5. #20244107	C₂	semidirect
6. #20244003	C₂	semidirect
7. #20243686	C₂	semidirect
8. #20243368	C₂	semidirect
9. #20243257	C₂	semidirect
10. #20243166	C₂	semidirect
49. C₂×#10625329	D₄	semidirect
70. C₄×C₄₇⋊C₈	D₄	semidirect
108. C₂×D₄×C₄₇	M₁₆	semidirect
236. C₄₇⋊C₈	#121	semidirect
266. C₄×C₄₇	#435	semidirect
323. C₄₇	#21486	semidirect
388. C₂×D₄	#10625329	semidirect
545. C₄	#15689195	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689195	2
C₂×D₄×C₄₇⋊C₈	2
C₂×C₄×#10625329	2
#20244183	2
#20244107	2
#20244003	2
#20243686	2
#20243368	2
#20243257	2
#20243166	2
C₄×#121×C₄₇	2
#21486	47