Subgroups — #26214651

Order 12032.

1102 conjugacy classes of subgroups.

The subgroup lattice has 584 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	1	yes	maximal, characteristic
2	C₂×#15689081	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245853	C₂	1	1	yes	maximal, characteristic
5	#20243265	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243260	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243243	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243174	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243169	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243167	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243164	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243156	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243156	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₇×#435	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	C₂×#13093983	C₂²	1	1	yes	characteristic
20	#15689195	C₄	1	8	yes	complemented
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	#15689081	—	2	4	no	—
25	#15689078	—	2	4	no	—
26	C₂×#13093935	C₂²	1	1	yes	characteristic
27	C₂×#13093934	C₂²	1	1	yes	characteristic
28	C₂×#13093934	C₂²	1	1	yes	characteristic
29	C₂×#13093934	C₂²	1	1	yes	characteristic
30	C₂×#13093934	C₂²	1	1	yes	characteristic
31	C₂×#13093934	C₂²	1	1	yes	characteristic
32	C₂×#13093934	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
37	#15689026	C₄	1	2	yes	—
38	#15689022	C₄	1	2	yes	—
39	#15689016	C₄	1	2	yes	—
40	#15689016	C₄	1	2	yes	—
41	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
44	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
45	#15688877	C₂²	1	1	yes	characteristic
46	#15688877	C₂²	1	1	yes	characteristic
47	#15688877	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
52	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
54	C₄₇×#435	C₄	1	8	yes	complemented
55	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
58	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
59	C₂×#10625329	—	2	2	no	—
60	C₂×#10625329	—	2	2	no	—
61	C₂×#10625329	C₂×C₄	1	4	yes	—
62	C₂²×C₄₇⋊C₈	—	2	2	no	—
63	C₂²×C₄₇⋊C₈	—	2	2	no	—
64	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
65	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	#13093983	—	2	2	no	—
70	#13093983	—	2	2	no	—
71	#13093983	—	2	2	no	—
72	#13093983	—	2	2	no	—
73	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
79	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
80	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
81	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
87	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
88	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
89	#13093935	C₂×C₄	1	4	yes	—
90	#13093934	—	2	2	no	—
91	#13093934	—	2	2	no	—
92	#13093934	—	2	2	no	—
93	#13093934	—	2	2	no	—
94	#13093934	—	2	2	no	—
95	#13093934	—	2	2	no	—
96	C₈×Dic₄₇	—	2	2	no	—
97	C₈×Dic₄₇	—	2	2	no	—
98	C₈×Dic₄₇	—	2	2	no	—
99	C₈×Dic₄₇	D₄	1	4	yes	complemented
100	C₄₇⋊#95	C₂×C₄	1	2	yes	—
101	C₄₇⋊#95	C₂×C₄	1	2	yes	—
102	C₄₇⋊#95	C₂×C₄	1	2	yes	—
103	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
104	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
106	C₂×M₁₆×C₄₇	—	2	2	no	—
107	C₂×M₁₆×C₄₇	—	2	2	no	—
108	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
109	C₂²×C₈×C₄₇	—	2	2	no	—
110	C₂²×C₈×C₄₇	—	2	2	no	—
111	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
112	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
116	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
117	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
118	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
123	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
124	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
125	#97×C₄₇	C₂×C₄	1	4	yes	—
126	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₄₇	—	4	2	no	—
129	C₂×D₄×C₄₇	C₄²	1	4	yes	—
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	1	no	—
133	C₂²×C₄×C₄₇	—	2	1	no	—
134	C₂²×C₄×C₄₇	—	2	1	no	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	—	2	1	no	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
147	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
148	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
149	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
150	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
151	M₁₆×C₄₇	—	2	8	no	—
152	C₂×C₈×C₄₇	—	2	1	no	—
153	C₂×C₈×C₄₇	—	2	1	no	—
154	C₂×C₈×C₄₇	—	2	1	no	—
155	C₂×C₈×C₄₇	—	2	1	no	—
156	C₂×C₈×C₄₇	—	2	1	no	—
157	C₂×C₈×C₄₇	—	2	1	no	—
158	C₂×C₈×C₄₇	—	2	8	no	—
159	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
160	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
162	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
163	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₄₇	#41	1	2	yes	—
165	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
166	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
167	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
168	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
169	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
170	C₂²⋊Dic₄₇	—	2	4	no	—
171	C₂²⋊Dic₄₇	—	2	4	no	—
172	C₂²⋊Dic₄₇	—	4	2	no	—
173	C₂²⋊Dic₄₇	—	4	2	no	—
174	C₄⋊Dic₄₇	—	2	4	no	—
175	C₄⋊Dic₄₇	—	2	4	no	—
176	C₄⋊Dic₄₇	—	4	2	no	—
177	C₄×Dic₄₇	—	2	1	no	—
178	C₄×Dic₄₇	—	2	1	no	—
179	C₄×Dic₄₇	—	2	1	no	—
180	C₄×Dic₄₇	—	2	1	no	—
181	C₄×Dic₄₇	—	2	1	no	—
182	C₄×Dic₄₇	—	2	1	no	—
183	C₄×Dic₄₇	—	4	2	no	—
184	C₄×Dic₄₇	—	4	2	no	—
185	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
186	C₄×Dic₄₇	#41	1	2	yes	—
187	#10625329	—	2	8	no	—
188	C₂×C₄₇⋊C₈	—	2	1	no	—
189	C₂×C₄₇⋊C₈	—	2	1	no	—
190	C₂×C₄₇⋊C₈	—	2	1	no	—
191	C₂×C₄₇⋊C₈	—	2	1	no	—
192	C₂×C₄₇⋊C₈	—	2	1	no	—
193	C₂×C₄₇⋊C₈	—	2	1	no	—
194	C₂×C₄₇⋊C₈	—	2	8	no	—
195	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
196	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
197	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
198	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
199	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
200	C₂×C₄₇⋊C₈	#41	1	2	yes	—
201	C₂³×C₄₇	—	2	1	no	—
202	C₂³×C₄₇	—	2	1	no	—
203	C₂³×C₄₇	—	2	1	no	—
204	C₂³×C₄₇	—	2	1	no	—
205	C₂³×C₄₇	—	2	2	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	—	2	2	no	—
208	C₂³×C₄₇	—	2	2	no	—
209	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
210	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
211	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
212	D₄×C₄₇	—	4	4	no	—
213	C₂×C₄×C₄₇	—	2	1	no	—
214	C₂×C₄×C₄₇	—	2	1	no	—
215	C₂×C₄×C₄₇	—	2	1	no	—
216	C₂×C₄×C₄₇	—	2	1	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
228	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
229	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
230	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
231	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
237	C₂×Dic₄₇	—	2	2	no	—
238	C₂×Dic₄₇	—	2	2	no	—
239	C₂×Dic₄₇	—	2	2	no	—
240	C₂×Dic₄₇	—	2	2	no	—
241	C₂×Dic₄₇	—	2	2	no	—
242	C₂×Dic₄₇	—	2	2	no	—
243	C₂×Dic₄₇	—	2	2	no	—
244	C₂×Dic₄₇	—	2	2	no	—
245	C₂×Dic₄₇	—	2	2	no	—
246	C₂×Dic₄₇	—	2	2	no	—
247	C₂×Dic₄₇	—	2	2	no	—
248	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
249	C₈×C₄₇	—	2	2	no	—
250	C₈×C₄₇	—	2	2	no	—
251	C₈×C₄₇	—	2	2	no	—
252	C₈×C₄₇	C₄×D₄	1	4	yes	—
253	C₄₇⋊C₈	—	2	2	no	—
254	C₄₇⋊C₈	—	2	2	no	—
255	C₄₇⋊C₈	—	2	2	no	—
256	C₄₇⋊C₈	C₄×D₄	1	4	yes	—
257	#20488	—	47	1	no	maximal, Sylow
258	C₂²×C₄₇	—	2	2	no	—
259	C₂²×C₄₇	—	2	2	no	—
260	C₂²×C₄₇	—	2	2	no	—
261	C₂²×C₄₇	—	2	2	no	—
262	C₂²×C₄₇	—	2	2	no	—
263	C₂²×C₄₇	—	2	2	no	—
264	C₂²×C₄₇	—	4	2	no	—
265	C₂²×C₄₇	—	4	2	no	—
266	C₂²×C₄₇	—	4	2	no	—
267	C₂²×C₄₇	—	4	2	no	—
268	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
269	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
270	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
271	C₂²×C₄₇	#568	1	2	yes	—
272	C₂²×C₄₇	#568	1	2	yes	—
273	C₄×C₄₇	—	2	2	no	—
274	C₄×C₄₇	—	2	2	no	—
275	C₄×C₄₇	—	2	2	no	—
276	C₄×C₄₇	—	2	2	no	—
277	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
278	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
279	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
280	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
281	Dic₄₇	—	2	4	no	—
282	Dic₄₇	—	4	2	no	—
283	Dic₄₇	—	4	2	no	—
284	Dic₄₇	—	4	2	no	—
285	C₂×#435	—	47	1	no	—
286	C₂×#435	D₄₇	1	1	yes	characteristic
287	C₂×#405	—	47	1	no	—
288	C₂×#405	—	47	1	no	—
289	#2293	—	47	1	no	—
290	#1771	—	47	1	no	—
291	#1771	—	47	1	no	—
292	#1767	—	47	1	no	—
293	#1753	—	47	1	no	—
294	#1753	—	47	1	no	—
295	#1752	—	47	1	no	—
296	#1752	—	47	1	no	—
297	#1750	—	47	1	no	—
298	#1750	—	47	1	no	—
299	C₄×#97	—	47	1	no	—
300	C₂×C₄₇	—	4	2	no	—
301	C₂×C₄₇	—	4	2	no	—
302	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
303	C₂×C₄₇	#2873	1	1	yes	characteristic
304	C₂×C₄₇	#2875	1	1	yes	characteristic
305	C₂×C₄₇	#2932	1	2	yes	—
306	C₂×C₄₇	#2967	1	2	yes	—
307	C₂²×M₁₆	—	47	1	no	—
308	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
309	C₂³×C₈	—	47	1	no	—
310	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
311	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
312	C₂×#117	—	47	1	no	—
313	C₂×#117	—	47	1	no	—
314	#435	—	47	8	no	—
315	#435	Dic₄₇	1	8	yes	complemented
316	C₂×C₄⋊C₈	—	47	1	no	—
317	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
318	C₂×C₂²⋊C₈	—	47	1	no	—
319	C₂×C₂²⋊C₈	—	47	1	no	—
320	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
321	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
322	#405	—	94	4	no	—
323	#405	—	94	4	no	—
324	C₂×#97	—	47	1	no	—
325	C₂×#97	—	47	1	no	—
326	C₂×#97	—	47	1	no	—
327	C₂×#97	—	47	1	no	—
328	C₂×#97	—	47	1	no	—
329	C₂×#97	—	47	1	no	—
330	C₂×#97	—	47	1	no	—
331	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
332	C₂×C₄×C₈	—	47	1	no	—
333	C₂×C₄×C₈	—	47	1	no	—
334	C₂×C₄×C₈	—	47	1	no	—
335	C₂×C₄×C₈	—	47	1	no	—
336	#390	—	47	2	no	—
337	#389	—	47	2	no	—
338	#388	—	47	2	no	—
339	#388	—	47	2	no	—
340	C₄×C₄⋊C₄	—	47	1	no	—
341	C₄×C₂²⋊C₄	—	47	1	no	—
342	C₄×C₂²⋊C₄	—	47	1	no	—
343	C₄³	—	47	1	no	—
344	#336	—	47	1	no	—
345	#336	—	47	1	no	—
346	#336	—	47	1	no	—
347	#336	—	47	1	no	—
348	#336	—	47	1	no	—
349	#336	—	47	1	no	—
350	C₄₇	#20488	1	1	yes	characteristic, complemented, Sylow
351	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
352	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
353	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
354	C₂×M₁₆	—	2	2	no	—
355	C₂×M₁₆	—	2	2	no	—
356	C₂×M₁₆	—	47	4	no	—
357	C₂×M₁₆	—	94	2	no	—
358	C₂×M₁₆	—	94	2	no	—
359	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
360	C₂²×C₈	—	2	2	no	—
361	C₂²×C₈	—	2	2	no	—
362	C₂²×C₈	—	47	1	no	—
363	C₂²×C₈	—	47	4	no	—
364	C₂²×C₈	—	47	1	no	—
365	C₂²×C₈	—	47	1	no	—
366	C₂²×C₈	—	47	1	no	—
367	C₂²×C₈	—	94	2	no	—
368	C₂²×C₈	—	94	2	no	—
369	C₂²×C₈	C₂×Dic₄₇	1	4	yes	—
370	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
371	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
372	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
373	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
374	C₄×D₄	C₄×D₄₇	1	4	yes	—
375	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
376	#117	—	94	2	no	—
377	#117	—	94	2	no	—
378	#117	—	94	2	no	—
379	#117	—	94	2	no	—
380	C₂×C₄⋊C₄	—	47	2	no	—
381	C₂×C₄⋊C₄	—	47	2	no	—
382	C₂×C₄⋊C₄	—	47	2	no	—
383	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	—	47	2	no	—
385	C₂×C₂²⋊C₄	—	47	2	no	—
386	C₂×C₂²⋊C₄	—	47	2	no	—
387	C₂×C₂²⋊C₄	—	47	2	no	—
388	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
390	C₂×C₄²	—	47	1	no	—
391	C₂×C₄²	—	47	1	no	—
392	C₂×C₄²	—	47	1	no	—
393	C₂×C₄²	—	47	1	no	—
394	C₂×C₄²	—	47	2	no	—
395	C₂×C₄²	—	47	2	no	—
396	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
397	C₄⋊C₈	—	47	4	no	—
398	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	—
399	C₂²⋊C₈	—	47	4	no	—
400	C₂²⋊C₈	—	47	4	no	—
401	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	—
402	C₂²⋊C₈	C₂×Dic₄₇	1	4	yes	—
403	#97	—	47	4	no	—
404	#97	—	94	2	no	—
405	#97	—	94	2	no	—
406	#97	—	94	2	no	—
407	#97	—	94	2	no	—
408	#97	—	94	2	no	—
409	#97	—	94	2	no	—
410	#97	C₂×Dic₄₇	1	4	yes	—
411	C₄×C₈	—	47	4	no	—
412	C₄×C₈	—	94	2	no	—
413	C₄×C₈	—	94	2	no	—
414	C₄×C₈	—	94	2	no	—
415	#95	—	47	2	no	—
416	#95	—	47	2	no	—
417	#95	—	47	2	no	—
418	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
419	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
420	C₂×D₄	—	4	2	no	—
421	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	47	2	no	—
431	C₂²×C₄	—	47	2	no	—
432	C₂²×C₄	—	47	2	no	—
433	C₂²×C₄	—	47	2	no	—
434	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
439	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
440	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
441	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
442	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
443	M₁₆	—	2	8	no	—
444	M₁₆	—	94	8	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	8	no	—
452	C₂×C₈	—	47	2	no	—
453	C₂×C₈	—	47	2	no	—
454	C₂×C₈	—	47	2	no	—
455	C₂×C₈	—	47	2	no	—
456	C₂×C₈	—	47	2	no	—
457	C₂×C₈	—	47	2	no	—
458	C₂×C₈	—	94	8	no	—
459	C₂×C₈	—	94	1	no	—
460	C₂×C₈	—	94	1	no	—
461	C₂×C₈	—	94	1	no	—
462	C₂×C₈	—	94	1	no	—
463	C₂×C₈	—	94	1	no	—
464	C₂×C₈	—	94	1	no	—
465	C₂×C₈	D₄×D₄₇	1	2	yes	—
466	C₂×C₈	#10625352	1	2	yes	—
467	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
468	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
469	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
470	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
471	C₄⋊C₄	—	94	4	no	—
472	C₄⋊C₄	—	94	4	no	—
473	C₄⋊C₄	—	188	2	no	—
474	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
475	C₂²⋊C₄	—	94	4	no	—
476	C₂²⋊C₄	—	94	4	no	—
477	C₂²⋊C₄	—	188	2	no	—
478	C₂²⋊C₄	—	188	2	no	—
479	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
480	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
481	C₄²	—	47	2	no	—
482	C₄²	—	47	2	no	—
483	C₄²	—	94	1	no	—
484	C₄²	—	94	1	no	—
485	C₄²	—	94	1	no	—
486	C₄²	—	94	1	no	—
487	C₄²	—	94	1	no	—
488	C₄²	—	94	1	no	—
489	C₄²	—	188	2	no	—
490	C₄²	—	188	2	no	—
491	C₄²	C₂×C₄×D₄₇	1	2	yes	—
492	C₄²	C₂²×Dic₄₇	1	2	yes	—
493	C₂³	—	2	1	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
502	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
503	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
504	D₄	—	4	4	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	47	4	no	—
520	C₂×C₄	—	94	2	no	—
521	C₂×C₄	—	94	2	no	—
522	C₂×C₄	—	94	2	no	—
523	C₂×C₄	—	94	2	no	—
524	C₂×C₄	—	94	2	no	—
525	C₂×C₄	—	94	2	no	—
526	C₂×C₄	—	94	2	no	—
527	C₂×C₄	—	94	2	no	—
528	C₂×C₄	—	94	2	no	—
529	C₂×C₄	—	94	2	no	—
530	C₂×C₄	—	94	2	no	—
531	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
532	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
533	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
534	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
535	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
536	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
537	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
538	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
539	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
540	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
541	C₈	—	2	2	no	—
542	C₈	—	2	2	no	—
543	C₈	—	2	2	no	—
544	C₈	—	47	4	no	—
545	C₈	—	94	2	no	—
546	C₈	—	94	2	no	—
547	C₈	—	94	2	no	—
548	C₈	D₄×Dic₄₇	1	4	yes	—
549	C₂²	—	2	2	no	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
560	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
561	C₂²	C₄×#10625352	1	1	yes	characteristic
562	C₂²	#15689888	1	2	yes	—
563	C₂²	#15689889	1	2	yes	—
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	94	4	no	—
569	C₄	—	188	2	no	—
570	C₄	—	188	2	no	—
571	C₄	—	188	2	no	—
572	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
573	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
574	C₄	C₄×#10625352	1	1	yes	characteristic
575	C₄	#41×Dic₄₇	1	1	yes	characteristic
576	C₂	—	4	2	no	—
577	C₂	—	4	2	no	—
578	C₂	C₄×D₄×Dic₄₇	1	1	yes	characteristic
579	C₂	#20251806	1	1	yes	characteristic
580	C₂	#20251814	1	1	yes	characteristic
581	C₂	#20252102	1	2	yes	—
582	C₂	#20252370	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₂×C₄₇×#435	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#435	D₄₇
hypocenter	C₄₇	#20488
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
2. C₂×#15689081	C₂	semidirect
3. C₂×#15689078	C₂	semidirect
5. #20243265	C₂	semidirect
6. #20243260	C₂	semidirect
7. #20243243	C₂	semidirect
8. #20243174	C₂	semidirect
9. #20243169	C₂	semidirect
10. #20243167	C₂	semidirect
11. #20243164	C₂	semidirect
12. #20243156	C₂	semidirect
13. #20243156	C₂	semidirect
14. #97×Dic₄₇	C₂	semidirect
20. #15689195	C₄	semidirect
54. C₄₇×#435	C₄	semidirect
99. C₈×Dic₄₇	D₄	semidirect
315. #435	Dic₄₇	semidirect
350. C₄₇	#20488	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×#15689081	2
C₂×#15689078	2
#20245853	2
#20243265	2
#20243260	2
#20243243	2
#20243174	2
#20243169	2
#20243167	2
#20243164	2
#20243156	2
#97×Dic₄₇	2
C₂×C₄₇×#435	2
#20488	47