Subgroups — #26214261

Order 12032.

1130 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689148	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689080	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689080	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
5	#20245868	C₂	1	1	yes	maximal, characteristic
6	#20243260	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243259	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243259	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243258	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243256	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243083	C₂	1	1	yes	maximal, characteristic
14	#336×D₄₇	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	1	yes	characteristic
17	C₂²×#10625324	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
20	C₂×#13093981	C₂²	1	1	yes	characteristic
21	C₂×#13093981	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
23	#15689148	C₄	1	8	yes	complemented
24	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	#15689080	—	2	4	no	—
28	#15689080	C₄	1	8	yes	complemented
29	C₄×#10625324	—	2	4	no	—
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×#13093934	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
39	#15689020	C₄	1	2	yes	—
40	#15689018	C₄	1	2	yes	—
41	#15688997	C₄	1	2	yes	—
42	#15688994	C₄	1	2	yes	—
43	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
46	#15688878	C₂²	1	1	yes	characteristic
47	#15688878	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	#15688877	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
54	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
57	C₄₇×#336	C₂²	1	1	yes	characteristic
58	C₄₇×#336	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
60	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
61	C₂×#10625324	—	2	2	no	—
62	C₂×#10625324	—	2	2	no	—
63	C₂×#10625324	C₂×C₄	1	4	yes	—
64	C₂×#10625324	C₂×C₄	1	4	yes	—
65	C₂×#10625324	D₄	1	4	yes	—
66	C₂×#10625324	Q₈	1	4	yes	—
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₂×C₈×D₄₇	—	2	2	no	—
72	C₂×C₈×D₄₇	—	2	2	no	—
73	C₂×C₈×D₄₇	—	2	2	no	—
74	C₂×C₈×D₄₇	—	2	2	no	—
75	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
76	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
77	#13093981	—	2	2	no	—
78	#13093981	—	2	2	no	—
79	#13093981	C₂×C₄	1	4	yes	—
80	#13093981	C₂×C₄	1	4	yes	—
81	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
82	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
83	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
84	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
85	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
88	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
91	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
93	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
94	C₄²×D₄₇	—	2	2	no	—
95	C₄²×D₄₇	—	2	2	no	—
96	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
97	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
98	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
99	#13093934	—	2	2	no	—
100	#13093934	—	2	2	no	—
101	#13093934	—	2	2	no	—
102	#13093934	C₂×C₄	1	4	yes	complemented
103	C₄×C₄₇⋊C₈	—	2	2	no	—
104	C₄×C₄₇⋊C₈	—	2	2	no	—
105	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
106	C₈×Dic₄₇	—	2	2	no	—
107	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
108	C₄₇⋊#95	C₂×C₄	1	2	yes	—
109	C₄₇⋊#95	C₂×C₄	1	2	yes	—
110	C₄₇⋊#95	C₂×C₄	1	2	yes	—
111	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
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	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
116	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
119	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
120	#97×C₄₇	—	2	2	no	—
121	#97×C₄₇	C₂×C₄	1	4	yes	complemented
122	C₄×C₈×C₄₇	—	2	2	no	—
123	#95×C₄₇	C₂×C₄	1	2	yes	—
124	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
130	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
131	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
132	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₄₇	—	2	4	no	—
136	C₂×C₄×D₄₇	—	2	4	no	—
137	C₂×C₄×D₄₇	—	4	2	no	—
138	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
139	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
140	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
141	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
142	C₂×C₄×D₄₇	#41	1	2	yes	—
143	C₂×C₄×D₄₇	#41	1	2	yes	—
144	C₂×C₈×C₄₇	—	2	1	no	—
145	C₂×C₈×C₄₇	—	2	1	no	—
146	C₂×C₈×C₄₇	—	2	1	no	—
147	C₂×C₈×C₄₇	—	2	1	no	—
148	C₂×C₈×C₄₇	—	2	1	no	—
149	C₂×C₈×C₄₇	—	2	1	no	—
150	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
156	C₄⋊C₄×C₄₇	—	2	4	no	—
157	C₄²×C₄₇	—	2	1	no	—
158	C₄²×C₄₇	—	2	1	no	—
159	C₄²×C₄₇	—	2	1	no	—
160	C₄²×C₄₇	—	2	1	no	—
161	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
162	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
163	(C₂×D₄₇)⋊C₄	—	2	4	no	—
164	(C₂×D₄₇)⋊C₄	C₄²	1	4	yes	—
165	(C₂×D₄₇)⋊C₄	C₄²	1	4	yes	—
166	C₄⋊Dic₄₇	—	4	2	no	—
167	Dic₄₇⋊C₄	—	2	4	no	—
168	Dic₄₇⋊C₄	—	2	4	no	—
169	Dic₄₇⋊C₄	—	4	2	no	—
170	Dic₄₇⋊C₄	C₄²	1	4	yes	—
171	Dic₄₇⋊C₄	C₄²	1	4	yes	—
172	C₄×Dic₄₇	—	2	1	no	—
173	C₄×Dic₄₇	—	2	1	no	—
174	C₄×Dic₄₇	—	2	1	no	—
175	C₄×Dic₄₇	—	2	1	no	—
176	C₄×Dic₄₇	—	2	4	no	—
177	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
178	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
179	C₂×C₄₇⋊C₈	—	2	1	no	—
180	C₂×C₄₇⋊C₈	—	2	1	no	—
181	C₂×C₄₇⋊C₈	—	2	1	no	—
182	C₂×C₄₇⋊C₈	—	2	1	no	—
183	C₂×C₄₇⋊C₈	—	2	1	no	—
184	C₂×C₄₇⋊C₈	—	2	1	no	—
185	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
186	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
187	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
188	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
189	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
190	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
191	#10625324	—	2	8	no	—
192	#10625324	C₄⋊C₄	1	16	yes	complemented
193	C₈×D₄₇	—	2	8	no	—
194	C₈×D₄₇	—	2	8	no	—
195	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
196	C₂²×D₄₇	—	2	2	no	—
197	C₂²×D₄₇	—	2	2	no	—
198	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
199	C₂²×D₄₇	C₄×D₄	1	2	yes	—
200	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
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	2	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
209	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
210	C₂×C₄×C₄₇	#131	1	4	yes	—
211	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
217	C₂×Dic₄₇	—	2	2	no	—
218	C₂×Dic₄₇	—	2	2	no	—
219	C₂×Dic₄₇	—	2	2	no	—
220	C₂×Dic₄₇	—	2	2	no	—
221	C₂×Dic₄₇	—	2	2	no	—
222	C₂×Dic₄₇	—	2	2	no	—
223	C₂×Dic₄₇	—	2	2	no	—
224	C₂×Dic₄₇	—	2	2	no	—
225	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
226	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
227	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
228	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
229	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
230	C₄×D₄₇	—	4	8	no	—
231	C₄×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
232	C₄×D₄₇	#117	1	4	yes	—
233	C₄×D₄₇	C₄×D₄	1	4	yes	—
234	C₄×D₄₇	C₄×Q₈	1	4	yes	—
235	C₈×C₄₇	—	2	2	no	—
236	C₈×C₄₇	—	2	2	no	—
237	C₈×C₄₇	—	2	2	no	—
238	C₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
239	C₄₇⋊C₈	—	2	2	no	—
240	C₄₇⋊C₈	—	2	2	no	—
241	C₄₇⋊C₈	—	2	2	no	—
242	C₄₇⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
243	#20439	—	47	1	no	maximal, Sylow
244	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
245	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
247	C₂²×C₄₇	C₂×#131	1	2	yes	—
248	C₂²×C₄₇	#568	1	2	yes	—
249	C₂×D₄₇	—	2	2	no	—
250	C₂×D₄₇	—	2	2	no	—
251	C₂×D₄₇	—	2	4	no	—
252	C₂×D₄₇	—	2	4	no	—
253	C₂×D₄₇	C₄×C₄⋊C₄	1	4	yes	—
254	C₄×C₄₇	—	2	2	no	—
255	C₄×C₄₇	—	2	2	no	—
256	C₄×C₄₇	—	2	4	no	—
257	C₄×C₄₇	—	4	2	no	—
258	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
259	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
260	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
261	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
262	Dic₄₇	—	2	2	no	—
263	Dic₄₇	—	2	2	no	—
264	Dic₄₇	—	4	2	no	—
265	Dic₄₇	—	4	2	no	—
266	Dic₄₇	C₄×C₄⋊C₄	1	4	yes	—
267	C₂×#424	—	47	1	no	—
268	C₂×#405	—	47	1	no	—
269	C₂×#405	—	47	1	no	—
270	C₂×C₄×M₁₆	—	47	1	no	—
271	#2296	—	47	1	no	—
272	#1771	—	47	1	no	—
273	#1771	—	47	1	no	—
274	#1771	—	47	1	no	—
275	#1771	D₄₇	1	1	yes	characteristic, complemented
276	#1770	—	47	1	no	—
277	#1770	—	47	1	no	—
278	C₈×C₄⋊C₄	—	47	1	no	—
279	C₈×C₄⋊C₄	—	47	1	no	—
280	#1729	—	47	1	no	—
281	C₂×#336	—	47	1	no	—
282	C₂×C₄₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
283	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
284	C₂×C₄₇	#2875	1	1	yes	characteristic
285	C₂×C₄₇	#2933	1	2	yes	—
286	C₂×C₄₇	#2962	1	2	yes	—
287	D₄₇	—	2	4	no	—
288	C₂²×M₁₆	—	47	1	no	—
289	C₂²×M₁₆	—	47	1	no	—
290	C₂³×C₈	—	47	1	no	—
291	C₂³×C₈	—	47	1	no	—
292	C₂×#117	—	47	1	no	—
293	C₂×#117	—	47	1	no	—
294	C₂²×C₄²	—	47	1	no	—
295	#424	—	47	8	no	—
296	C₂×C₄⋊C₈	—	47	1	no	—
297	C₂×C₄⋊C₈	—	47	1	no	—
298	C₂×C₄⋊C₈	—	47	1	no	—
299	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
300	#405	—	47	8	no	—
301	#405	—	94	4	no	—
302	C₄×M₁₆	—	94	4	no	—
303	C₂×#97	—	47	1	no	—
304	C₂×#97	—	47	1	no	—
305	C₂×#97	—	47	1	no	—
306	C₂×#97	—	47	1	no	—
307	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
308	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
309	C₂×C₄×C₈	—	47	1	no	—
310	C₂×C₄×C₈	—	47	1	no	—
311	C₂×C₄×C₈	—	47	1	no	—
312	C₂×C₄×C₈	—	47	1	no	—
313	C₂×C₄×C₈	—	47	1	no	—
314	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
315	#389	—	47	2	no	—
316	#389	—	47	2	no	—
317	#385	—	47	2	no	—
318	#385	—	47	2	no	—
319	C₄×C₄⋊C₄	—	47	1	no	—
320	C₄×C₄⋊C₄	—	47	1	no	—
321	C₄×C₄⋊C₄	—	47	1	no	—
322	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
323	#336	—	47	1	no	—
324	#336	—	47	1	no	—
325	#336	—	47	1	no	—
326	#336	—	47	1	no	—
327	#336	—	47	1	no	—
328	#336	—	47	1	no	—
329	#336	C₂×D₄₇	1	1	yes	characteristic
330	#336	C₂×D₄₇	1	1	yes	characteristic
331	C₄₇	#20439	1	1	yes	characteristic, complemented, Sylow
332	C₂³×C₄	—	47	1	no	—
333	C₂³×C₄	—	47	2	no	—
334	C₂×M₁₆	—	47	4	no	—
335	C₂×M₁₆	—	47	4	no	—
336	C₂×M₁₆	—	47	4	no	—
337	C₂×M₁₆	—	47	4	no	—
338	C₂×M₁₆	—	94	2	no	—
339	C₂×M₁₆	—	94	2	no	—
340	C₂²×C₈	—	47	1	no	—
341	C₂²×C₈	—	47	1	no	—
342	C₂²×C₈	—	47	1	no	—
343	C₂²×C₈	—	47	1	no	—
344	C₂²×C₈	—	47	4	no	—
345	C₂²×C₈	—	47	4	no	—
346	C₂²×C₈	—	94	2	no	—
347	C₂²×C₈	—	94	2	no	—
348	C₂²×C₈	—	94	2	no	—
349	C₂²×C₈	—	94	2	no	—
350	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
351	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
352	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
353	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
354	#117	—	47	4	no	—
355	#117	—	47	4	no	—
356	#117	—	94	2	no	—
357	#117	—	94	2	no	—
358	C₂×C₄⋊C₄	—	47	1	no	—
359	C₂×C₄⋊C₄	—	47	1	no	—
360	C₂×C₄⋊C₄	—	47	2	no	—
361	C₂×C₄⋊C₄	—	47	2	no	—
362	C₂×C₄⋊C₄	—	47	2	no	—
363	C₂×C₄⋊C₄	—	47	2	no	—
364	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
365	C₂×C₂²⋊C₄	—	47	1	no	—
366	C₂×C₂²⋊C₄	—	47	1	no	—
367	C₂×C₂²⋊C₄	—	47	2	no	—
368	C₂×C₄²	—	47	1	no	—
369	C₂×C₄²	—	47	2	no	—
370	C₂×C₄²	—	47	1	no	—
371	C₂×C₄²	—	47	1	no	—
372	C₂×C₄²	—	94	2	no	—
373	C₂×C₄²	—	94	2	no	—
374	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
375	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
376	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
377	C₄⋊C₈	—	47	4	no	—
378	C₄⋊C₈	—	47	4	no	—
379	C₄⋊C₈	—	47	4	no	—
380	C₄⋊C₈	C₄×D₄₇	1	4	yes	complemented
381	#97	—	2	2	no	—
382	#97	—	47	4	no	—
383	#97	—	94	2	no	—
384	#97	—	94	2	no	—
385	#97	—	94	2	no	—
386	#97	C₄×D₄₇	1	4	yes	complemented
387	C₄×C₈	—	2	2	no	—
388	C₄×C₈	—	47	4	no	—
389	C₄×C₈	—	47	4	no	—
390	C₄×C₈	—	94	2	no	—
391	C₄×C₈	—	94	2	no	—
392	C₄×C₈	—	94	2	no	—
393	#95	—	47	2	no	—
394	#95	—	47	2	no	—
395	#95	—	47	2	no	—
396	#95	C₄×D₄₇	1	2	yes	—
397	C₂⁴	—	47	1	no	—
398	C₂²×C₄	—	47	1	no	—
399	C₂²×C₄	—	47	2	no	—
400	C₂²×C₄	—	47	2	no	—
401	C₂²×C₄	—	47	2	no	—
402	C₂²×C₄	—	47	2	no	—
403	C₂²×C₄	—	47	2	no	—
404	C₂²×C₄	—	47	2	no	—
405	C₂²×C₄	—	47	1	no	—
406	C₂²×C₄	—	47	1	no	—
407	C₂²×C₄	—	47	2	no	—
408	C₂²×C₄	—	47	2	no	—
409	C₂²×C₄	—	94	4	no	—
410	C₂²×C₄	—	94	4	no	—
411	C₂²×C₄	—	188	2	no	—
412	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
413	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
414	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
415	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
416	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
417	M₁₆	—	47	16	no	—
418	M₁₆	—	94	8	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	47	2	no	—
426	C₂×C₈	—	47	2	no	—
427	C₂×C₈	—	47	2	no	—
428	C₂×C₈	—	47	2	no	—
429	C₂×C₈	—	47	2	no	—
430	C₂×C₈	—	47	2	no	—
431	C₂×C₈	—	94	8	no	—
432	C₂×C₈	—	94	8	no	—
433	C₂×C₈	—	94	1	no	—
434	C₂×C₈	—	94	1	no	—
435	C₂×C₈	—	94	1	no	—
436	C₂×C₈	—	94	1	no	—
437	C₂×C₈	—	94	1	no	—
438	C₂×C₈	—	94	1	no	—
439	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
440	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
441	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
442	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
443	C₂×C₈	D₄×D₄₇	1	2	yes	—
444	C₂×C₈	Q₈×D₄₇	1	2	yes	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	47	4	no	—
447	C₄⋊C₄	—	47	4	no	—
448	C₄⋊C₄	—	94	4	no	—
449	C₄⋊C₄	—	94	4	no	—
450	C₄⋊C₄	—	188	2	no	—
451	C₄⋊C₄	—	188	2	no	—
452	C₂²⋊C₄	—	47	4	no	—
453	C₂²⋊C₄	—	47	4	no	—
454	C₂²⋊C₄	—	94	4	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	47	2	no	—
460	C₄²	—	47	2	no	—
461	C₄²	—	94	4	no	—
462	C₄²	—	94	1	no	—
463	C₄²	—	94	1	no	—
464	C₄²	—	94	1	no	—
465	C₄²	—	94	1	no	—
466	C₄²	C₂×C₄×D₄₇	1	2	yes	—
467	C₄²	C₂×C₄×D₄₇	1	2	yes	—
468	C₂³	—	47	2	no	—
469	C₂³	—	47	2	no	—
470	C₂³	—	47	2	no	—
471	C₂³	—	94	2	no	—
472	C₂³	—	94	2	no	—
473	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
474	C₂×C₄	—	2	2	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	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	47	2	no	—
482	C₂×C₄	—	47	2	no	—
483	C₂×C₄	—	47	2	no	—
484	C₂×C₄	—	47	4	no	—
485	C₂×C₄	—	47	4	no	—
486	C₂×C₄	—	47	4	no	—
487	C₂×C₄	—	47	4	no	—
488	C₂×C₄	—	47	2	no	—
489	C₂×C₄	—	47	2	no	—
490	C₂×C₄	—	94	2	no	—
491	C₂×C₄	—	94	2	no	—
492	C₂×C₄	—	94	2	no	—
493	C₂×C₄	—	94	2	no	—
494	C₂×C₄	—	94	2	no	—
495	C₂×C₄	—	94	2	no	—
496	C₂×C₄	—	94	2	no	—
497	C₂×C₄	—	94	2	no	—
498	C₂×C₄	—	188	8	no	—
499	C₂×C₄	C₄²×D₄₇	1	2	yes	—
500	C₂×C₄	C₄²×D₄₇	1	2	yes	—
501	C₂×C₄	#13094032	1	4	yes	—
502	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
503	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
504	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
505	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
506	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
507	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
508	C₈	—	2	2	no	—
509	C₈	—	2	2	no	—
510	C₈	—	2	2	no	—
511	C₈	—	47	4	no	—
512	C₈	—	94	2	no	—
513	C₈	—	94	2	no	—
514	C₈	—	94	2	no	—
515	C₈	C₄⋊C₄×D₄₇	1	4	yes	—
516	C₂²	—	47	4	no	—
517	C₂²	—	94	2	no	—
518	C₂²	—	94	2	no	—
519	C₂²	—	94	4	no	—
520	C₂²	—	94	4	no	—
521	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
522	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
523	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
524	C₂²	C₂×#13094032	1	2	yes	—
525	C₂²	#15689888	1	2	yes	—
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	2	4	no	—
529	C₄	—	4	2	no	—
530	C₄	—	47	4	no	—
531	C₄	—	94	2	no	—
532	C₄	—	94	2	no	—
533	C₄	—	188	2	no	—
534	C₄	—	188	2	no	—
535	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
536	C₄	#117×D₄₇	1	1	yes	characteristic
537	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
538	C₄	C₄×Q₈×D₄₇	1	1	yes	characteristic
539	C₂	—	94	4	no	—
540	C₂	C₄×C₄⋊C₄×D₄₇	1	1	yes	characteristic
541	C₂	C₄×#13094032	1	1	yes	characteristic
542	C₂	#20251815	1	1	yes	characteristic
543	C₂	#20252114	1	2	yes	—
544	C₂	#20252336	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1771	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1771	D₄₇
hypocenter	C₄₇	#20439
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
6. #20243260	C₂	semidirect
7. #20243259	C₂	semidirect
8. #20243259	C₂	semidirect
9. #20243258	C₂	semidirect
10. #20243256	C₂	semidirect
11. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
12. C₈×Dic₄₇⋊C₄	C₂	semidirect
15. C₄₇×#1771	C₂	semidirect
23. #15689148	C₄	semidirect
28. #15689080	C₄	semidirect
96. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
97. Dic₄₇⋊C₈	C₂×C₄	semidirect
98. Dic₄₇⋊C₈	C₂×C₄	semidirect
102. #13093934	C₂×C₄	semidirect
105. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
107. C₈×Dic₄₇	C₂×C₄	semidirect
119. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
121. #97×C₄₇	C₂×C₄	semidirect
192. #10625324	C₄⋊C₄	semidirect
275. #1771	D₄₇	semidirect
331. C₄₇	#20439	semidirect
380. C₄⋊C₈	C₄×D₄₇	semidirect
386. #97	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689148	2
C₂×#15689080	2
C₂×C₄×#10625324	2
#20245868	2
#20243260	2
#20243259	2
#20243258	2
#20243256	2
C₄⋊C₄×C₄₇⋊C₈	2
C₈×Dic₄₇⋊C₄	2
#20243083	2
#336×D₄₇	2
C₄₇×#1771	2
#20439	47