Subgroups — #27079700

Order 12032.

3178 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689888	C₂	1	1	yes	maximal, characteristic
2	C₂×#131×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20256587	C₂	1	1	yes	maximal, characteristic
4	#20251815	C₂	1	3	yes	maximal, complemented
5	#20251814	C₂	1	1	yes	maximal, characteristic, complemented
6	#20251813	C₂	1	3	yes	maximal, complemented
7	C₄×#13094032	C₂	1	3	yes	maximal, complemented
8	C₄×#13094031	C₂	1	1	yes	maximal, characteristic, complemented
9	#20251810	C₂	1	3	yes	maximal, complemented
10	#131×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	#20251805	C₂	1	3	yes	maximal, complemented
12	#20251804	C₂	1	3	yes	maximal, complemented
13	C₂×#15689080	C₂	1	3	yes	maximal, complemented
14	#405×D₄₇	C₂	1	3	yes	maximal, complemented
15	C₄₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×D₄₇	C₂²	1	1	yes	characteristic
17	#15689888	C₄	1	16	yes	complemented
18	C₂×#13094032	C₂²	1	3	yes	—
19	C₂×#13094032	C₂²	1	3	yes	—
20	C₂×#13094031	C₂²	1	1	yes	characteristic
21	C₂×#13094031	C₂²	1	1	yes	characteristic
22	C₂×#13094030	C₂²	1	3	yes	—
23	C₂×#13094030	C₂²	1	3	yes	—
24	#131×D₄₇	C₄	1	16	yes	complemented
25	C₂²×#10625324	C₂²	1	3	yes	—
26	C₂×M₁₆×D₄₇	C₂²	1	3	yes	—
27	C₂×M₁₆×D₄₇	C₂²	1	3	yes	—
28	C₂²×C₈×D₄₇	C₂²	1	3	yes	—
29	#15689605	C₄	1	2	yes	—
30	#15689602	C₄	1	6	yes	—
31	#15689599	C₄	1	2	yes	—
32	#15689595	C₄	1	6	yes	—
33	#41×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₄×#10625350	C₂²	1	3	yes	—
35	#15689591	C₂²	1	3	yes	—
36	C₂×#13093981	C₂²	1	3	yes	—
37	#117×D₄₇	C₂²	1	3	yes	—
38	#15689081	C₂²	1	3	yes	complemented
39	#15689081	C₂²	1	3	yes	complemented
40	#15689080	C₂²	1	3	yes	—
41	#15689080	C₂²	1	1	yes	characteristic
42	#15689080	C₂²	1	3	yes	—
43	#15689080	C₂²	1	3	yes	—
44	#15689080	C₂²	1	3	yes	complemented
45	#15689080	C₂²	1	3	yes	complemented
46	#15689080	C₂²	1	3	yes	complemented
47	#15689080	C₂²	1	3	yes	complemented
48	#15689080	C₂²	1	6	yes	complemented
49	#15689079	C₂²	1	3	yes	complemented
50	#15689079	C₂²	1	3	yes	complemented
51	#15689078	C₂²	1	3	yes	complemented
52	#15689078	C₂²	1	3	yes	complemented
53	#15689077	C₂²	1	6	yes	—
54	#15689077	C₂²	1	6	yes	complemented
55	C₄×#10625329	C₂²	1	3	yes	complemented
56	#15689075	C₂²	1	6	yes	complemented
57	M₁₆×Dic₄₇	C₂²	1	3	yes	complemented
58	M₁₆×Dic₄₇	C₂²	1	3	yes	complemented
59	C₄×#10625324	C₂²	1	6	yes	complemented
60	C₂×#13093934	C₂²	1	3	yes	complemented
61	#97×D₄₇	C₂²	1	6	yes	complemented
62	C₂×C₄×C₄₇⋊C₈	C₂²	1	3	yes	complemented
63	C₂×C₈×Dic₄₇	C₂²	1	3	yes	complemented
64	C₄×C₈×D₄₇	C₂²	1	6	yes	complemented
65	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
66	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
67	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
68	C₄₇×#405	C₂²	1	3	yes	complemented
69	C₄₇×#405	C₂²	1	3	yes	complemented
70	C₄×M₁₆×C₄₇	C₂²	1	3	yes	complemented
71	C₂×#97×C₄₇	C₂²	1	3	yes	complemented
72	C₂×#10625354	C₂×C₄	1	1	yes	characteristic
73	C₂×#10625350	C₂³	1	3	yes	—
74	C₂×#10625352	C₂×C₄	1	3	yes	—
75	#41×D₄₇	C₂×C₄	1	8	yes	—
76	#41×D₄₇	C₂×C₄	1	8	yes	—
77	C₂×Q₈×D₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×D₄×D₄₇	C₂×C₄	1	3	yes	—
79	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
80	#13094032	C₂×C₄	1	24	yes	complemented
81	#13094032	C₂×C₄	1	24	yes	complemented
82	#13094031	C₂×C₄	1	8	yes	complemented
83	#13094031	C₂×C₄	1	8	yes	complemented
84	#13094030	C₂×C₄	1	24	yes	complemented
85	#13094030	C₂×C₄	1	24	yes	complemented
86	C₂×#10625329	C₂³	1	3	yes	—
87	C₂×#10625329	C₂³	1	3	yes	—
88	C₂×#10625324	C₂×C₄	1	24	yes	complemented
89	C₂×#10625324	C₂³	1	3	yes	—
90	C₂×#10625324	C₂³	1	6	yes	—
91	C₂×#10625324	C₂³	1	3	yes	—
92	C₂×#10625324	C₂³	1	3	yes	—
93	C₂×#10625324	C₂³	1	1	yes	characteristic
94	M₁₆×D₄₇	C₂×C₄	1	24	yes	complemented
95	M₁₆×D₄₇	C₂×C₄	1	24	yes	complemented
96	C₂²×C₄₇⋊C₈	C₂³	1	3	yes	—
97	C₂²×C₄₇⋊C₈	C₂³	1	3	yes	—
98	C₂×C₈×D₄₇	C₂×C₄	1	24	yes	complemented
99	C₂×C₈×D₄₇	C₂³	1	3	yes	—
100	C₂×C₈×D₄₇	C₂³	1	6	yes	—
101	C₂×C₈×D₄₇	C₂³	1	3	yes	—
102	C₂×C₈×D₄₇	C₂³	1	3	yes	—
103	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
104	Q₈×Dic₄₇	C₂×C₄	1	2	yes	—
105	C₄×Dic₉₄	C₂×C₄	1	6	yes	—
106	#13093989	C₂×C₄	1	6	yes	—
107	C₄×D₁₈₈	C₂×C₄	1	6	yes	—
108	D₄×Dic₄₇	C₂×C₄	1	6	yes	—
109	#13093986	C₂×C₄	1	6	yes	—
110	C₄×C₂²⋊D₄₇	C₂×C₄	1	12	yes	—
111	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	12	yes	—
112	#13093983	C₂³	1	3	yes	—
113	#13093982	C₂×C₄	1	6	yes	—
114	#13093981	C₂×C₄	1	6	yes	—
115	#13093981	C₂×C₄	1	6	yes	—
116	#13093981	C₂³	1	3	yes	—
117	#13093981	C₂³	1	1	yes	characteristic
118	#13093981	C₂³	1	3	yes	—
119	#13093981	C₂³	1	3	yes	—
120	#13093980	C₂×C₄	1	6	yes	—
121	C₂×Dic₄₇⋊C₄	C₂×C₄	1	6	yes	—
122	C₄⋊C₄×D₄₇	C₂×C₄	1	6	yes	—
123	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	6	yes	—
124	C₂²⋊C₄×D₄₇	C₂×C₄	1	6	yes	—
125	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
126	C₄²×D₄₇	C₂³	1	6	yes	—
127	#13093935	C₂³	1	6	yes	—
128	#13093934	C₂³	1	3	yes	—
129	#13093934	C₂³	1	6	yes	—
130	#13093934	C₂³	1	1	yes	characteristic
131	#13093934	C₂³	1	3	yes	—
132	#13093934	C₂³	1	3	yes	—
133	C₄×C₄₇⋊C₈	C₂³	1	3	yes	—
134	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
135	C₄×C₄₇⋊C₈	C₂³	1	3	yes	—
136	C₄×C₄₇⋊C₈	C₂³	1	3	yes	—
137	C₈×Dic₄₇	C₂³	1	3	yes	—
138	C₈×Dic₄₇	C₂³	1	6	yes	—
139	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
140	C₈×Dic₄₇	C₂³	1	3	yes	—
141	C₈×Dic₄₇	C₂³	1	3	yes	—
142	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
143	#131×C₄₇	C₂×C₄	1	8	yes	complemented
144	#131×C₄₇	C₂×C₄	1	8	yes	complemented
145	C₂×M₁₆×C₄₇	C₂³	1	3	yes	—
146	C₂×M₁₆×C₄₇	C₂³	1	3	yes	—
147	C₂²×C₈×C₄₇	C₂³	1	3	yes	—
148	C₂²×C₈×C₄₇	C₂³	1	3	yes	—
149	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
150	C₄×D₄×C₄₇	C₂×C₄	1	6	yes	—
151	#117×C₄₇	C₂³	1	3	yes	—
152	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
153	#97×C₄₇	C₂³	1	3	yes	—
154	#97×C₄₇	C₂³	1	3	yes	—
155	#97×C₄₇	C₂³	1	1	yes	characteristic
156	#97×C₄₇	C₂³	1	3	yes	—
157	C₄×C₈×C₄₇	C₂³	1	6	yes	—
158	C₂³×D₄₇	C₂²×C₄	1	3	yes	—
159	#41×C₄₇	C₂²×C₄	1	4	yes	—
160	#41×C₄₇	C₂²×C₄	1	4	yes	—
161	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₂×D₄×C₄₇	C₂²×C₄	1	3	yes	—
163	C₂²×C₄×C₄₇	C₂²×C₄	1	6	yes	—
164	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
165	C₂×C₂²⋊D₄₇	C₂²×C₄	1	6	yes	—
166	C₂²×Dic₄₇	C₂²×C₄	1	6	yes	—
167	C₂²×Dic₄₇	C₂²×C₄	1	3	yes	—
168	#10625354	C₄²	1	8	yes	—
169	Q₈×D₄₇	C₄²	1	8	yes	—
170	#10625352	C₄²	1	24	yes	—
171	D₄×D₄₇	C₄²	1	24	yes	—
172	#10625350	C₂²×C₄	1	12	yes	—
173	#10625350	C₂²×C₄	1	12	yes	—
174	C₂×D₁₈₈	C₂²×C₄	1	3	yes	—
175	C₂×C₄×D₄₇	C₂²×C₄	1	12	yes	—
176	C₂×C₄×D₄₇	C₂²×C₄	1	3	yes	—
177	C₂×C₄×D₄₇	C₂²×C₄	1	3	yes	—
178	C₂×C₄×D₄₇	C₂²×C₄	1	12	yes	—
179	C₂×C₄×D₄₇	C₂²×C₄	1	12	yes	—
180	C₂×C₄×D₄₇	C₂⁴	1	3	yes	—
181	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
182	C₂×Dic₉₄	C₂²×C₄	1	3	yes	—
183	M₁₆×C₄₇	C₂²×C₄	1	12	yes	—
184	M₁₆×C₄₇	C₂²×C₄	1	12	yes	—
185	C₂×C₈×C₄₇	C₂²×C₄	1	12	yes	—
186	C₂×C₈×C₄₇	C₂²×C₄	1	12	yes	—
187	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
188	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
189	C₂×C₈×C₄₇	C₂⁴	1	3	yes	—
190	C₂×C₈×C₄₇	C₂⁴	1	3	yes	—
191	C₄⋊C₄×C₄₇	C₂²×C₄	1	6	yes	—
192	C₂²⋊C₄×C₄₇	C₂²×C₄	1	6	yes	—
193	C₄²×C₄₇	C₂²×C₄	1	6	yes	—
194	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
195	C₄²×C₄₇	C₂⁴	1	3	yes	—
196	C₂²⋊Dic₄₇	C₂²×C₄	1	6	yes	—
197	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	6	yes	—
198	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	2	yes	—
199	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	6	yes	—
200	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	6	yes	—
201	C₄⋊Dic₄₇	C₂²×C₄	1	6	yes	—
202	Dic₄₇⋊C₄	C₂²×C₄	1	6	yes	—
203	Dic₄₇⋊C₄	C₂²×C₄	1	2	yes	—
204	Dic₄₇⋊C₄	C₂²×C₄	1	6	yes	—
205	Dic₄₇⋊C₄	C₂²×C₄	1	6	yes	—
206	C₄×Dic₄₇	C₂²×C₄	1	12	yes	—
207	C₄×Dic₄₇	C₂²×C₄	1	6	yes	—
208	C₄×Dic₄₇	C₂⁴	1	3	yes	—
209	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
210	#10625329	C₂²×C₄	1	12	yes	—
211	#10625329	C₂²×C₄	1	12	yes	—
212	C₂×C₄₇⋊C₈	C₂²×C₄	1	12	yes	—
213	C₂×C₄₇⋊C₈	C₂²×C₄	1	12	yes	—
214	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
215	C₂×C₄₇⋊C₈	C₂⁴	1	3	yes	—
216	C₂×C₄₇⋊C₈	C₂⁴	1	3	yes	—
217	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
218	#10625324	C₂²×C₄	1	12	yes	—
219	#10625324	C₂²×C₄	1	24	yes	—
220	#10625324	C₂²×C₄	1	4	yes	—
221	#10625324	C₂²×C₄	1	12	yes	—
222	#10625324	C₂²×C₄	1	12	yes	—
223	C₈×D₄₇	C₂²×C₄	1	4	yes	—
224	C₈×D₄₇	C₂²×C₄	1	12	yes	—
225	C₈×D₄₇	C₂²×C₄	1	12	yes	—
226	C₈×D₄₇	C₂²×C₄	1	12	yes	—
227	C₈×D₄₇	C₂²×C₄	1	24	yes	—
228	C₂³×C₄₇	C₂³×C₄	1	3	yes	—
229	C₂²×D₄₇	—	4	6	no	—
230	C₂²×D₄₇	C₂×C₄²	1	12	yes	—
231	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
232	C₂²×D₄₇	C₂³×C₄	1	3	yes	—
233	Q₈×C₄₇	C₂×C₄²	1	4	yes	—
234	D₄×C₄₇	C₂×C₄²	1	12	yes	—
235	C₂×C₄×C₄₇	—	4	6	no	—
236	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
237	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
238	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
239	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
240	C₂×C₄×C₄₇	C₂³×C₄	1	3	yes	—
241	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
242	C₂²⋊D₄₇	C₂×C₄²	1	24	yes	—
243	C₂×Dic₄₇	—	4	6	no	—
244	C₂×Dic₄₇	C₂×C₄²	1	12	yes	—
245	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
246	C₂×Dic₄₇	C₂³×C₄	1	6	yes	—
247	C₂×Dic₄₇	C₂³×C₄	1	3	yes	—
248	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
249	D₁₈₈	C₂×C₄²	1	12	yes	—
250	C₄×D₄₇	—	4	12	no	—
251	C₄×D₄₇	C₂×C₄²	1	12	yes	—
252	C₄×D₄₇	C₂×C₄²	1	12	yes	—
253	C₄×D₄₇	C₂³×C₄	1	2	yes	—
254	C₄×D₄₇	C₂³×C₄	1	6	yes	—
255	C₄×D₄₇	C₂³×C₄	1	6	yes	—
256	C₄×D₄₇	C₂³×C₄	1	2	yes	—
257	Dic₉₄	C₂×C₄²	1	12	yes	—
258	C₈×C₄₇	C₂³×C₄	1	2	yes	—
259	C₈×C₄₇	C₂³×C₄	1	6	yes	—
260	C₈×C₄₇	C₂³×C₄	1	6	yes	—
261	C₈×C₄₇	C₂³×C₄	1	2	yes	—
262	C₄₇⋊C₈	C₂³×C₄	1	2	yes	—
263	C₄₇⋊C₈	C₂³×C₄	1	6	yes	—
264	C₄₇⋊C₈	C₂³×C₄	1	6	yes	—
265	C₄₇⋊C₈	C₂³×C₄	1	2	yes	—
266	#60058	—	47	1	no	maximal, Sylow
267	C₂²×C₄₇	—	2	6	no	—
268	C₂²×C₄₇	C₂²×C₄²	1	6	yes	—
269	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
270	C₂×D₄₇	—	2	6	no	—
271	C₂×D₄₇	—	2	2	no	—
272	C₂×D₄₇	—	4	12	no	—
273	C₂×D₄₇	C₂²×C₄²	1	2	yes	—
274	C₂×D₄₇	C₂²×C₄²	1	6	yes	—
275	C₄×C₄₇	—	2	6	no	—
276	C₄×C₄₇	—	2	2	no	—
277	C₄×C₄₇	C₂²×C₄²	1	6	yes	—
278	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
279	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
280	Dic₄₇	—	2	6	no	—
281	Dic₄₇	—	2	2	no	—
282	Dic₄₇	C₂²×C₄²	1	6	yes	—
283	Dic₄₇	C₂²×C₄²	1	2	yes	—
284	C₂×#568	—	47	1	no	—
285	C₂²×#131	—	47	1	no	—
286	#3428	—	47	1	no	—
287	#2875	—	47	3	no	—
288	#2875	—	47	3	no	—
289	#2875	—	47	1	no	—
290	#2875	D₄₇	1	1	yes	characteristic, complemented
291	C₄×#131	—	47	3	no	—
292	C₄×#131	—	47	3	no	—
293	C₄×#131	—	47	1	no	—
294	C₄×#131	—	47	1	no	—
295	#2873	—	47	3	no	—
296	#2873	—	47	3	no	—
297	C₂×#405	—	47	3	no	—
298	C₂×#405	—	47	3	no	—
299	C₂×C₄₇	—	2	6	no	—
300	C₂×C₄₇	C₂³×C₄²	1	1	yes	characteristic
301	C₂×C₄₇	#3573	1	2	yes	—
302	D₄₇	—	2	2	no	—
303	D₄₇	—	2	6	no	—
304	C₂²×#41	—	47	1	no	—
305	#568	—	47	16	no	—
306	C₂×#131	—	47	1	no	—
307	C₂×#131	—	47	1	no	—
308	C₂×#131	—	47	16	no	—
309	C₂×#131	—	47	3	no	—
310	C₂×#131	—	47	3	no	—
311	C₂×#131	—	47	3	no	—
312	C₂×#131	—	47	3	no	—
313	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
314	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
315	C₂²×M₁₆	—	47	3	no	—
316	C₂²×M₁₆	—	47	3	no	—
317	C₂²×M₁₆	—	47	3	no	—
318	C₂³×C₈	—	47	3	no	—
319	#520	—	47	2	no	—
320	#520	—	47	6	no	—
321	#519	—	47	2	no	—
322	#518	—	47	6	no	—
323	C₄×#41	—	47	1	no	—
324	C₄×#41	—	47	3	no	—
325	C₄×#41	—	47	3	no	—
326	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
327	C₂×#117	—	47	3	no	—
328	C₂×#117	—	47	3	no	—
329	#405	—	47	3	no	—
330	#405	—	47	3	no	—
331	#405	—	47	3	no	—
332	#405	—	47	3	no	—
333	#405	—	47	3	no	—
334	#405	—	47	3	no	—
335	#405	—	47	3	no	—
336	#405	—	47	1	no	—
337	#405	—	47	3	no	—
338	#405	—	47	3	no	—
339	#405	—	47	3	no	—
340	#405	—	47	3	no	—
341	#405	—	47	3	no	—
342	#405	—	47	3	no	—
343	#405	—	47	6	no	—
344	#405	—	47	6	no	—
345	#405	—	47	6	no	—
346	#405	C₂×D₄₇	1	3	yes	complemented
347	#405	C₂×D₄₇	1	3	yes	complemented
348	C₄×M₁₆	—	47	3	no	—
349	C₄×M₁₆	—	47	3	no	—
350	C₄×M₁₆	—	47	3	no	—
351	C₄×M₁₆	—	47	6	no	—
352	C₄×M₁₆	—	47	6	no	—
353	C₄×M₁₆	C₂×D₄₇	1	3	yes	complemented
354	C₂×#97	—	47	3	no	—
355	C₂×#97	—	47	6	no	—
356	C₂×#97	C₂×D₄₇	1	3	yes	complemented
357	C₂×C₄×C₈	—	47	3	no	—
358	C₂×C₄×C₈	—	47	3	no	—
359	C₂×C₄×C₈	—	47	6	no	—
360	C₄₇	#60058	1	1	yes	characteristic, complemented, Sylow
361	C₂×#41	—	47	8	no	—
362	C₂×#41	—	47	8	no	—
363	C₂×#41	—	47	1	no	—
364	C₂×#41	—	47	3	no	—
365	C₂×#41	—	47	3	no	—
366	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
367	C₂²×Q₈	—	47	1	no	—
368	C₂²×D₄	—	47	3	no	—
369	C₂³×C₄	—	47	3	no	—
370	#131	—	47	8	no	—
371	#131	—	47	8	no	—
372	#131	—	47	24	no	—
373	#131	—	47	24	no	—
374	#131	—	47	24	no	—
375	#131	—	47	24	no	—
376	#131	C₄×D₄₇	1	8	yes	complemented
377	#131	C₄×D₄₇	1	8	yes	complemented
378	C₂×M₁₆	—	47	3	no	—
379	C₂×M₁₆	—	47	3	no	—
380	C₂×M₁₆	—	47	24	no	—
381	C₂×M₁₆	—	47	24	no	—
382	C₂×M₁₆	—	47	24	no	—
383	C₂×M₁₆	—	47	1	no	—
384	C₂×M₁₆	—	47	3	no	—
385	C₂×M₁₆	—	47	3	no	—
386	C₂×M₁₆	—	47	6	no	—
387	C₂×M₁₆	—	47	3	no	—
388	C₂×M₁₆	C₂²×D₄₇	1	3	yes	—
389	C₂×M₁₆	C₂²×D₄₇	1	3	yes	—
390	C₂²×C₈	—	47	3	no	—
391	C₂²×C₈	—	47	3	no	—
392	C₂²×C₈	—	47	24	no	—
393	C₂²×C₈	—	47	1	no	—
394	C₂²×C₈	—	47	3	no	—
395	C₂²×C₈	—	47	3	no	—
396	C₂²×C₈	—	47	3	no	—
397	C₂²×C₈	—	47	6	no	—
398	C₂²×C₈	C₂²×D₄₇	1	3	yes	—
399	C₂²×C₈	C₂²×D₄₇	1	3	yes	—
400	C₄×Q₈	—	47	2	no	—
401	C₄×Q₈	—	47	6	no	—
402	C₄×Q₈	—	47	6	no	—
403	C₄×Q₈	C₄×D₄₇	1	2	yes	—
404	C₄×D₄	—	47	6	no	—
405	C₄×D₄	—	47	12	no	—
406	C₄×D₄	—	47	6	no	—
407	C₄×D₄	—	47	12	no	—
408	C₄×D₄	—	47	6	no	—
409	C₄×D₄	C₄×D₄₇	1	6	yes	—
410	#117	—	47	3	no	—
411	#117	—	47	6	no	—
412	#117	—	47	6	no	—
413	#117	—	47	6	no	—
414	#117	—	47	6	no	—
415	#117	—	47	1	no	—
416	#117	—	47	3	no	—
417	#117	—	47	3	no	—
418	#117	—	47	3	no	—
419	#117	C₂²×D₄₇	1	3	yes	—
420	C₂×C₄⋊C₄	—	47	6	no	—
421	C₂×C₄⋊C₄	—	47	6	no	—
422	C₂×C₂²⋊C₄	—	47	6	no	—
423	C₂×C₂²⋊C₄	—	47	6	no	—
424	C₂×C₄²	—	47	3	no	—
425	C₂×C₄²	—	47	6	no	—
426	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
427	#97	—	47	3	no	—
428	#97	—	47	1	no	—
429	#97	—	47	6	no	—
430	#97	—	47	3	no	—
431	#97	—	47	3	no	—
432	#97	—	47	6	no	—
433	#97	C₂²×D₄₇	1	3	yes	—
434	#97	C₂²×D₄₇	1	1	yes	characteristic
435	#97	C₂²×D₄₇	1	3	yes	—
436	#97	C₂²×D₄₇	1	3	yes	—
437	C₄×C₈	—	47	1	no	—
438	C₄×C₈	—	47	3	no	—
439	C₄×C₈	—	47	3	no	—
440	C₄×C₈	—	47	6	no	—
441	C₄×C₈	—	47	3	no	—
442	C₄×C₈	—	47	1	no	—
443	C₄×C₈	—	47	3	no	—
444	C₄×C₈	—	47	3	no	—
445	C₄×C₈	—	47	3	no	—
446	C₄×C₈	C₂²×D₄₇	1	6	yes	—
447	C₂⁴	—	47	3	no	—
448	#41	—	47	8	no	—
449	#41	—	47	24	no	—
450	#41	—	47	12	no	—
451	#41	—	47	12	no	—
452	#41	C₂×C₄×D₄₇	1	4	yes	—
453	#41	C₂×C₄×D₄₇	1	4	yes	—
454	C₂×Q₈	—	47	8	no	—
455	C₂×Q₈	—	47	3	no	—
456	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
457	C₂×D₄	—	47	6	no	—
458	C₂×D₄	—	47	24	no	—
459	C₂×D₄	—	47	3	no	—
460	C₂×D₄	C₂×C₄×D₄₇	1	3	yes	—
461	C₂²×C₄	—	47	3	no	—
462	C₂²×C₄	—	47	3	no	—
463	C₂²×C₄	—	47	3	no	—
464	C₂²×C₄	—	47	12	no	—
465	C₂²×C₄	—	47	12	no	—
466	C₂²×C₄	—	47	3	no	—
467	C₂²×C₄	—	47	1	no	—
468	C₂²×C₄	—	47	6	no	—
469	C₂²×C₄	—	47	12	no	—
470	C₂²×C₄	C₂×C₄×D₄₇	1	6	yes	—
471	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
472	M₁₆	—	47	12	no	—
473	M₁₆	—	47	12	no	—
474	M₁₆	—	47	12	no	—
475	M₁₆	—	47	4	no	—
476	M₁₆	—	47	24	no	—
477	M₁₆	—	47	12	no	—
478	M₁₆	—	47	12	no	—
479	M₁₆	C₂×C₄×D₄₇	1	12	yes	—
480	M₁₆	C₂×C₄×D₄₇	1	12	yes	—
481	C₂×C₈	—	47	12	no	—
482	C₂×C₈	—	47	12	no	—
483	C₂×C₈	—	47	1	no	—
484	C₂×C₈	—	47	3	no	—
485	C₂×C₈	—	47	3	no	—
486	C₂×C₈	—	47	1	no	—
487	C₂×C₈	—	47	4	no	—
488	C₂×C₈	—	47	12	no	—
489	C₂×C₈	—	47	12	no	—
490	C₂×C₈	—	47	12	no	—
491	C₂×C₈	—	47	24	no	—
492	C₂×C₈	C₂×C₄×D₄₇	1	12	yes	—
493	C₂×C₈	C₂×C₄×D₄₇	1	12	yes	—
494	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
495	C₂×C₈	C₂³×D₄₇	1	3	yes	—
496	C₂×C₈	C₂³×D₄₇	1	3	yes	—
497	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
498	C₄⋊C₄	—	47	6	no	—
499	C₄⋊C₄	—	47	2	no	—
500	C₄⋊C₄	—	47	6	no	—
501	C₄⋊C₄	—	47	6	no	—
502	C₄⋊C₄	—	47	6	no	—
503	C₄⋊C₄	C₂×C₄×D₄₇	1	6	yes	—
504	C₂²⋊C₄	—	47	6	no	—
505	C₂²⋊C₄	—	47	6	no	—
506	C₂²⋊C₄	—	47	2	no	—
507	C₂²⋊C₄	—	47	6	no	—
508	C₂²⋊C₄	—	47	6	no	—
509	C₂²⋊C₄	C₂×C₄×D₄₇	1	6	yes	—
510	C₄²	—	47	12	no	—
511	C₄²	—	47	6	no	—
512	C₄²	—	47	3	no	—
513	C₄²	—	47	1	no	—
514	C₄²	C₂×C₄×D₄₇	1	6	yes	—
515	C₄²	C₂³×D₄₇	1	1	yes	characteristic
516	C₄²	C₂³×D₄₇	1	3	yes	—
517	C₂³	—	47	1	no	—
518	C₂³	—	47	3	no	—
519	C₂³	—	47	12	no	—
520	C₂³	—	188	6	no	—
521	C₂³	C₂²×C₄×D₄₇	1	3	yes	—
522	Q₈	—	47	12	no	—
523	Q₈	C₄²×D₄₇	1	4	yes	—
524	D₄	—	47	24	no	—
525	D₄	—	47	12	no	—
526	D₄	C₄²×D₄₇	1	12	yes	—
527	C₂×C₄	—	4	6	no	—
528	C₂×C₄	—	47	12	no	—
529	C₂×C₄	—	47	3	no	—
530	C₂×C₄	—	47	1	no	—
531	C₂×C₄	—	47	12	no	—
532	C₂×C₄	—	47	12	no	—
533	C₂×C₄	—	47	2	no	—
534	C₂×C₄	—	47	6	no	—
535	C₂×C₄	—	47	6	no	—
536	C₂×C₄	—	47	2	no	—
537	C₂×C₄	—	47	2	no	—
538	C₂×C₄	—	47	6	no	—
539	C₂×C₄	—	188	12	no	—
540	C₂×C₄	—	188	6	no	—
541	C₂×C₄	C₂²×C₄×D₄₇	1	6	yes	—
542	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
543	C₂×C₄	C₂²×C₄×D₄₇	1	3	yes	—
544	C₂×C₄	C₂²×C₄×D₄₇	1	6	yes	—
545	C₂×C₄	C₂²×C₄×D₄₇	1	6	yes	—
546	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
547	C₈	—	47	2	no	—
548	C₈	—	47	6	no	—
549	C₈	—	47	6	no	—
550	C₈	—	47	2	no	—
551	C₈	C₂²×C₄×D₄₇	1	2	yes	—
552	C₈	C₂²×C₄×D₄₇	1	6	yes	—
553	C₈	C₂²×C₄×D₄₇	1	6	yes	—
554	C₈	C₂²×C₄×D₄₇	1	2	yes	—
555	C₂²	—	2	6	no	—
556	C₂²	—	47	2	no	—
557	C₂²	—	47	6	no	—
558	C₂²	—	94	6	no	—
559	C₂²	—	94	2	no	—
560	C₂²	—	188	12	no	—
561	C₂²	C₂×C₄²×D₄₇	1	6	yes	—
562	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
563	C₄	—	2	2	no	—
564	C₄	—	2	6	no	—
565	C₄	—	47	2	no	—
566	C₄	—	47	6	no	—
567	C₄	—	94	6	no	—
568	C₄	—	94	2	no	—
569	C₄	C₂×C₄²×D₄₇	1	6	yes	—
570	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
571	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
572	C₂	—	2	6	no	—
573	C₂	—	94	2	no	—
574	C₂	—	94	6	no	—
575	C₂	C₂²×C₄²×D₄₇	1	1	yes	characteristic
576	C₂	#20258101	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator	C₂×C₄₇	C₂³×C₄²
Fitting	C₄₇×#2875	C₂
socle	C₂²×C₄₇	C₂⁴×C₄
prime radical	C₂×#41×D₄₇	C₂²
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2875	D₄₇
hypocenter	C₄₇	#60058
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2875

Complements

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

N	H ≅ G/N	type
4. #20251815	C₂	semidirect
5. #20251814	C₂	semidirect
6. #20251813	C₂	semidirect
7. C₄×#13094032	C₂	semidirect
8. C₄×#13094031	C₂	semidirect
9. #20251810	C₂	semidirect
10. #131×Dic₄₇	C₂	semidirect
11. #20251805	C₂	semidirect
12. #20251804	C₂	semidirect
13. C₂×#15689080	C₂	semidirect
14. #405×D₄₇	C₂	semidirect
15. C₄₇×#2875	C₂	semidirect
17. #15689888	C₄	semidirect
24. #131×D₄₇	C₄	semidirect
38. #15689081	C₂²	semidirect
39. #15689081	C₂²	semidirect
44. #15689080	C₂²	semidirect
45. #15689080	C₂²	semidirect
46. #15689080	C₂²	semidirect
47. #15689080	C₂²	semidirect
48. #15689080	C₂²	semidirect
49. #15689079	C₂²	semidirect
50. #15689079	C₂²	semidirect
51. #15689078	C₂²	semidirect
52. #15689078	C₂²	semidirect
54. #15689077	C₂²	semidirect
55. C₄×#10625329	C₂²	semidirect
56. #15689075	C₂²	semidirect
57. M₁₆×Dic₄₇	C₂²	semidirect
58. M₁₆×Dic₄₇	C₂²	semidirect
59. C₄×#10625324	C₂²	semidirect
60. C₂×#13093934	C₂²	semidirect
61. #97×D₄₇	C₂²	semidirect
62. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
63. C₂×C₈×Dic₄₇	C₂²	semidirect
64. C₄×C₈×D₄₇	C₂²	semidirect
68. C₄₇×#405	C₂²	semidirect
69. C₄₇×#405	C₂²	semidirect
70. C₄×M₁₆×C₄₇	C₂²	semidirect
71. C₂×#97×C₄₇	C₂²	semidirect
80. #13094032	C₂×C₄	semidirect
81. #13094032	C₂×C₄	semidirect
82. #13094031	C₂×C₄	semidirect
83. #13094031	C₂×C₄	semidirect
84. #13094030	C₂×C₄	semidirect
85. #13094030	C₂×C₄	semidirect
88. C₂×#10625324	C₂×C₄	semidirect
94. M₁₆×D₄₇	C₂×C₄	semidirect
95. M₁₆×D₄₇	C₂×C₄	semidirect
98. C₂×C₈×D₄₇	C₂×C₄	semidirect
143. #131×C₄₇	C₂×C₄	semidirect
144. #131×C₄₇	C₂×C₄	semidirect
290. #2875	D₄₇	semidirect
346. #405	C₂×D₄₇	semidirect
347. #405	C₂×D₄₇	semidirect
353. C₄×M₁₆	C₂×D₄₇	semidirect
356. C₂×#97	C₂×D₄₇	semidirect
360. C₄₇	#60058	semidirect
376. #131	C₄×D₄₇	semidirect
377. #131	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×#15689888	2
C₂×#131×D₄₇	2
#20256587	2
#20251815	2
#20251814	2
#20251813	2
C₄×#13094032	2
C₄×#13094031	2
#20251810	2
#131×Dic₄₇	2
#20251805	2
#20251804	2
C₂×#15689080	2
#405×D₄₇	2
C₄₇×#2875	2
#60058	47