Subgroups — #27080673

Order 12032.

1882 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#533×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20252340	C₂	1	4	yes	maximal, complemented
3	Q₈×#10625324	C₂	1	4	yes	maximal, complemented
4	#20252336	C₂	1	4	yes	maximal, complemented
5	#20252330	C₂	1	4	yes	maximal, complemented
6	#20252327	C₂	1	2	yes	maximal, complemented
7	#20252326	C₂	1	2	yes	maximal, complemented
8	#20252323	C₂	1	1	yes	maximal, characteristic, complemented
9	#20252322	C₂	1	1	yes	maximal, characteristic, complemented
10	#20252318	C₂	1	1	yes	maximal, characteristic, complemented
11	#20251949	C₂	1	2	yes	maximal
12	#423×D₄₇	C₂	1	1	yes	maximal, characteristic
13	#20251804	C₂	1	2	yes	maximal
14	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	1	yes	characteristic
17	C₂²×#10625324	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
19	#15689680	C₂²	1	1	yes	characteristic
20	#15689679	C₄	1	2	yes	—
21	#15689678	C₄	1	2	yes	—
22	#15689677	C₂²	1	4	yes	—
23	#15689676	C₂²	1	2	yes	—
24	#15689675	C₄	1	4	yes	—
25	C₄⋊Q₈×D₄₇	C₄	1	2	yes	—
26	#125×D₄₇	C₄	1	2	yes	—
27	C₂²⋊Q₈×D₄₇	C₄	1	4	yes	—
28	C₄×Q₈×D₄₇	C₂²	1	4	yes	—
29	#117×D₄₇	C₂²	1	2	yes	—
30	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
31	#15689254	C₂²	1	4	yes	complemented
32	#15689253	C₂²	1	4	yes	complemented
33	#15689253	C₂²	1	8	yes	complemented
34	#15689252	C₂²	1	8	yes	complemented
35	#15689251	C₂²	1	8	yes	complemented
36	#15689250	C₂²	1	4	yes	complemented
37	#15689250	C₂²	1	8	yes	complemented
38	Q₈×C₄₇⋊C₈	C₂²	1	4	yes	complemented
39	C₈×Dic₉₄	C₂²	1	4	yes	complemented
40	#15689247	C₂²	1	4	yes	complemented
41	#15689151	C₂²	1	2	yes	—
42	#15689150	C₂²	1	2	yes	—
43	#15689149	C₂²	1	2	yes	—
44	#15689148	C₂²	1	8	yes	—
45	#15689147	C₂²	1	1	yes	characteristic
46	#15689146	C₂²	1	2	yes	—
47	#15689145	C₂²	1	4	yes	—
48	#15689145	C₂²	1	8	yes	—
49	C₄⋊C₈×D₄₇	C₂²	1	4	yes	—
50	#15689081	C₂²	1	2	yes	—
51	#15689080	C₂²	1	4	yes	—
52	#15689079	C₂²	1	2	yes	—
53	#15689078	C₂²	1	2	yes	—
54	#15689077	C₂²	1	4	yes	—
55	#15689075	C₂²	1	4	yes	—
56	C₄×#10625324	C₂²	1	2	yes	—
57	C₄×#10625324	C₂²	1	2	yes	—
58	C₄×#10625324	C₂²	1	2	yes	—
59	C₄×#10625324	C₂²	1	2	yes	—
60	C₄×#10625324	C₂²	1	4	yes	—
61	C₂×#13093934	C₂²	1	1	yes	characteristic
62	C₂×#13093934	C₂²	1	1	yes	characteristic
63	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
64	C₄₇×#533	C₂²	1	1	yes	characteristic
65	C₄₇×#446	C₂²	1	4	yes	complemented
66	C₈×Q₈×C₄₇	C₂²	1	4	yes	complemented
67	C₄₇×#424	C₂²	1	2	yes	—
68	C₄₇×#423	C₂²	1	1	yes	characteristic
69	C₄₇×#405	C₂²	1	2	yes	—
70	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
71	C₂×Q₈×D₄₇	C₂×C₄	1	4	yes	—
72	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
73	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
74	C₂×#10625329	C₂³	1	2	yes	—
75	C₂×#10625324	—	2	4	no	—
76	C₂×#10625324	Q₈	1	8	yes	complemented
77	C₂×#10625324	C₂³	1	2	yes	—
78	C₂×#10625324	C₂³	1	2	yes	—
79	C₂×#10625324	C₂³	1	4	yes	—
80	C₂×#10625324	C₂³	1	1	yes	characteristic
81	C₂×#10625324	C₂³	1	1	yes	characteristic
82	C₂×#10625324	C₂³	1	1	yes	characteristic
83	C₂×#10625324	C₂³	1	1	yes	characteristic
84	M₁₆×D₄₇	—	2	8	no	—
85	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×C₈×D₄₇	C₂³	1	4	yes	—
88	#13094024	C₂×C₄	1	2	yes	—
89	#13094023	C₂×C₄	1	4	yes	—
90	#13094023	C₂×C₄	1	4	yes	—
91	#13094022	C₂×C₄	1	4	yes	—
92	#13094016	C₂×C₄	1	2	yes	—
93	#13094015	C₂×C₄	1	4	yes	—
94	#13094014	C₂×C₄	1	8	yes	—
95	#13094004	C₂×C₄	1	4	yes	—
96	#13094003	C₂×C₄	1	4	yes	—
97	#13094002	C₂×C₄	1	8	yes	—
98	#13094001	C₂×C₄	1	8	yes	—
99	#13094000	C₂×C₄	1	4	yes	—
100	Q₈×Dic₄₇	C₂×C₄	1	4	yes	—
101	C₄×Dic₉₄	C₂³	1	4	yes	—
102	C₄×Dic₉₄	C₂³	1	8	yes	—
103	#13093989	C₂×C₄	1	4	yes	—
104	#13093989	C₂×C₄	1	8	yes	—
105	#13093983	C₂³	1	2	yes	—
106	#13093982	C₂×C₄	1	4	yes	—
107	#13093981	C₂³	1	4	yes	—
108	#13093980	C₂×C₄	1	4	yes	—
109	C₄⋊C₄×D₄₇	C₂×C₄	1	4	yes	—
110	C₄⋊C₄×D₄₇	C₂×C₄	1	8	yes	—
111	C₄⋊C₄×D₄₇	C₂×C₄	1	4	yes	—
112	C₂²⋊C₄×D₄₇	C₂×C₄	1	4	yes	—
113	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
114	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
115	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
116	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
117	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
118	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
119	C₄²×D₄₇	C₂³	1	2	yes	—
120	C₄²×D₄₇	C₂³	1	2	yes	—
121	C₄²×D₄₇	C₂³	1	4	yes	—
122	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
123	C₄⋊(C₄₇⋊C₈)	C₂³	1	8	yes	—
124	Dic₄₇⋊C₈	C₂³	1	8	yes	—
125	Dic₄₇⋊C₈	C₂³	1	8	yes	—
126	Dic₄₇⋊C₈	C₂³	1	8	yes	—
127	#13093935	C₂³	1	4	yes	—
128	#13093934	C₂³	1	2	yes	—
129	#13093934	C₂³	1	4	yes	—
130	#13093934	C₂³	1	2	yes	—
131	#13093934	C₂³	1	2	yes	—
132	#13093934	C₂³	1	2	yes	—
133	#13093934	C₂³	1	4	yes	—
134	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
135	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
136	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
137	C₈×Dic₄₇	C₂³	1	4	yes	—
138	C₈×Dic₄₇	C₂³	1	4	yes	—
139	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
140	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
142	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
143	#125×C₄₇	C₂×C₄	1	2	yes	—
144	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
145	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
146	#117×C₄₇	C₂³	1	2	yes	—
147	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
148	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
149	C₄⋊C₈×C₄₇	C₂³	1	8	yes	—
150	#97×C₄₇	C₂³	1	4	yes	—
151	C₄×C₈×C₄₇	C₂³	1	2	yes	—
152	C₄×C₈×C₄₇	C₂³	1	2	yes	—
153	C₄×C₈×C₄₇	C₂³	1	4	yes	—
154	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
156	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
158	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
159	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
160	Q₈×D₄₇	—	4	8	no	—
161	C₂×C₄×D₄₇	—	4	4	no	—
162	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
163	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
164	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
165	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
166	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
167	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
170	C₂×C₄×D₄₇	#41	1	4	yes	—
171	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
173	C₂×Dic₉₄	C₂²×C₄	1	4	yes	—
174	C₂×Dic₉₄	C₂²×C₄	1	8	yes	—
175	M₁₆×C₄₇	—	2	4	no	—
176	C₂×C₈×C₄₇	—	2	2	no	—
177	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	complemented
178	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
179	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
180	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
181	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
182	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
183	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
184	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
185	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
186	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
188	C₄²×C₄₇	C₂⁴	1	2	yes	—
189	C₄²×C₄₇	C₂⁴	1	4	yes	—
190	C₂²⋊Dic₄₇	C₂²×C₄	1	4	yes	—
191	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	8	yes	—
192	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
193	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
194	C₄⋊Dic₄₇	C₂²×C₄	1	8	yes	—
195	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
196	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
197	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
198	Dic₄₇⋊C₄	C₂²×C₄	1	8	yes	—
199	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
201	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
202	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
203	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
204	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
205	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
206	C₄×Dic₄₇	C₂⁴	1	4	yes	—
207	C₄×Dic₄₇	C₂⁴	1	2	yes	—
208	#10625329	—	2	4	no	—
209	C₂×C₄₇⋊C₈	—	2	2	no	—
210	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	complemented
211	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
212	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
213	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
214	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
215	#10625324	—	2	8	no	—
216	#10625324	—	2	4	no	—
217	#10625324	—	2	4	no	—
218	#10625324	C₂×Q₈	1	4	yes	—
219	#10625324	C₂×Q₈	1	4	yes	—
220	#10625324	C₂×Q₈	1	4	yes	complemented
221	#10625324	C₂×Q₈	1	4	yes	complemented
222	C₈×D₄₇	—	2	8	no	—
223	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
224	C₂²×D₄₇	—	4	2	no	—
225	C₂²×D₄₇	C₄×Q₈	1	4	yes	—
226	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
227	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
228	Q₈×C₄₇	—	2	8	no	—
229	C₂×C₄×C₄₇	—	2	4	no	—
230	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
231	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
232	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
234	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
235	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
236	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
237	C₂×Dic₄₇	—	4	2	no	—
238	C₂×Dic₄₇	C₄×Q₈	1	4	yes	—
239	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
240	C₂×Dic₄₇	C₂³×C₄	1	2	yes	—
241	C₂×Dic₄₇	C₂³×C₄	1	8	yes	—
242	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
243	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
244	C₄×D₄₇	—	2	4	no	—
245	C₄×D₄₇	—	2	4	no	—
246	C₄×D₄₇	—	4	2	no	—
247	C₄×D₄₇	—	4	2	no	—
248	C₄×D₄₇	—	4	8	no	—
249	C₄×D₄₇	C₄×Q₈	1	4	yes	—
250	C₄×D₄₇	C₄×Q₈	1	4	yes	—
251	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
252	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
253	C₄×D₄₇	C₂×#41	1	2	yes	—
254	C₄×D₄₇	C₂×#41	1	2	yes	—
255	Dic₉₄	—	2	8	no	—
256	Dic₉₄	—	4	8	no	—
257	C₈×C₄₇	—	2	4	no	—
258	C₈×C₄₇	—	2	2	no	—
259	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
260	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
261	C₄₇⋊C₈	—	2	4	no	—
262	C₄₇⋊C₈	—	2	2	no	—
263	C₄₇⋊C₈	C₂²×Q₈	1	2	yes	—
264	C₄₇⋊C₈	C₂²×Q₈	1	2	yes	—
265	#60192	—	47	1	no	maximal, Sylow
266	C₂²×C₄₇	—	2	2	no	—
267	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
268	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
269	C₂×D₄₇	—	2	2	no	—
270	C₂×D₄₇	—	2	2	no	—
271	C₂×D₄₇	—	4	4	no	—
272	C₂×D₄₇	C₂×C₄×Q₈	1	2	yes	—
273	C₂×D₄₇	C₂×C₄×Q₈	1	2	yes	—
274	C₄×C₄₇	—	2	8	no	—
275	C₄×C₄₇	—	2	2	no	—
276	C₄×C₄₇	C₂×C₄×Q₈	1	2	yes	—
277	C₄×C₄₇	#568	1	4	yes	—
278	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
279	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
280	Dic₄₇	—	2	8	no	—
281	Dic₄₇	—	2	2	no	—
282	Dic₄₇	—	2	2	no	—
283	Dic₄₇	C₂×C₄×Q₈	1	2	yes	—
284	Dic₄₇	C₂×C₄×Q₈	1	2	yes	—
285	C₂×#533	—	47	1	no	—
286	Q₈×M₁₆	—	47	4	no	—
287	Q₈×M₁₆	—	47	4	no	—
288	#2962	—	47	4	no	—
289	#2962	—	47	4	no	—
290	#2961	—	47	2	no	—
291	#2961	—	47	2	no	—
292	#2960	—	47	1	no	—
293	#2960	—	47	1	no	—
294	#2960	—	47	1	no	—
295	#2960	D₄₇	1	1	yes	characteristic, complemented
296	#2905	—	47	2	no	—
297	C₂×#423	—	47	1	no	—
298	#2873	—	47	2	no	—
299	C₂×C₄×M₁₆	—	47	1	no	—
300	C₂×C₄₇	—	2	2	no	—
301	C₂×C₄₇	C₂²×C₄×Q₈	1	1	yes	characteristic
302	C₂×C₄₇	C₂×#568	1	2	yes	—
303	D₄₇	—	2	2	no	—
304	D₄₇	—	2	2	no	—
305	C₂²×M₁₆	—	47	2	no	—
306	C₂²×M₁₆	—	47	1	no	—
307	C₂²×M₁₆	—	47	1	no	—
308	#533	—	47	2	no	—
309	#533	—	47	2	no	—
310	#533	—	47	4	no	—
311	#533	—	47	4	no	—
312	#533	—	47	2	no	—
313	#533	—	47	1	no	—
314	#533	C₂×D₄₇	1	1	yes	characteristic
315	C₂×C₄⋊Q₈	—	47	2	no	—
316	C₂×#125	—	47	2	no	—
317	C₂×C₂²⋊Q₈	—	47	4	no	—
318	C₂×C₄×Q₈	—	47	4	no	—
319	C₂×#117	—	47	2	no	—
320	C₂²×C₄²	—	47	1	no	—
321	#446	—	47	4	no	—
322	#446	—	47	4	no	—
323	#446	—	47	8	no	—
324	#446	—	47	8	no	—
325	#446	—	47	8	no	—
326	#446	—	47	4	no	—
327	#446	—	47	8	no	—
328	#446	C₂×D₄₇	1	4	yes	complemented
329	C₈×Q₈	—	47	4	no	—
330	C₈×Q₈	—	47	4	no	—
331	C₈×Q₈	—	47	4	no	—
332	C₈×Q₈	C₂×D₄₇	1	4	yes	complemented
333	#424	—	47	2	no	—
334	#424	—	47	2	no	—
335	#424	—	47	2	no	—
336	#424	—	47	8	no	—
337	#424	C₂×D₄₇	1	2	yes	—
338	#423	—	47	2	no	—
339	#423	—	47	1	no	—
340	#423	—	47	4	no	—
341	#423	—	47	8	no	—
342	#423	C₂×D₄₇	1	1	yes	characteristic
343	C₂×C₄⋊C₈	—	47	4	no	—
344	#405	—	47	2	no	—
345	#405	—	47	2	no	—
346	#405	—	47	2	no	—
347	#405	—	47	4	no	—
348	#405	—	47	4	no	—
349	#405	C₂×D₄₇	1	2	yes	—
350	C₄×M₁₆	—	47	4	no	—
351	C₄×M₁₆	—	47	2	no	—
352	C₄×M₁₆	—	47	2	no	—
353	C₄×M₁₆	—	47	2	no	—
354	C₄×M₁₆	—	47	2	no	—
355	C₄×M₁₆	—	47	4	no	—
356	C₂×#97	—	47	1	no	—
357	C₂×#97	—	47	1	no	—
358	C₂×C₄×C₈	—	47	1	no	—
359	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
360	C₄₇	#60192	1	1	yes	characteristic, complemented, Sylow
361	C₂²×Q₈	—	47	4	no	—
362	C₂³×C₄	—	47	1	no	—
363	C₂³×C₄	—	47	2	no	—
364	C₂×M₁₆	—	47	2	no	—
365	C₂×M₁₆	—	47	8	no	—
366	C₂×M₁₆	—	47	1	no	—
367	C₂×M₁₆	—	47	1	no	—
368	C₂×M₁₆	—	47	1	no	—
369	C₂×M₁₆	—	47	1	no	—
370	C₂×M₁₆	—	47	4	no	—
371	C₂×M₁₆	—	47	2	no	—
372	C₂×M₁₆	—	47	2	no	—
373	C₂×M₁₆	—	94	4	no	—
374	C₂×M₁₆	—	94	8	no	—
375	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
376	C₂²×C₈	—	47	1	no	—
377	C₂²×C₈	—	47	1	no	—
378	C₂²×C₈	—	47	4	no	—
379	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
380	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
381	C₄⋊Q₈	—	47	4	no	—
382	C₄⋊Q₈	—	47	4	no	—
383	C₄⋊Q₈	—	47	4	no	—
384	C₄⋊Q₈	—	47	2	no	—
385	C₄⋊Q₈	C₄×D₄₇	1	2	yes	—
386	#125	—	47	8	no	—
387	#125	—	47	4	no	—
388	#125	—	47	2	no	—
389	#125	C₄×D₄₇	1	2	yes	—
390	C₂²⋊Q₈	—	47	4	no	—
391	C₂²⋊Q₈	—	47	4	no	—
392	C₂²⋊Q₈	—	47	8	no	—
393	C₂²⋊Q₈	—	47	4	no	—
394	C₂²⋊Q₈	—	47	8	no	—
395	C₂²⋊Q₈	C₄×D₄₇	1	4	yes	—
396	C₄×Q₈	—	47	4	no	—
397	C₄×Q₈	—	47	4	no	—
398	C₄×Q₈	—	47	8	no	—
399	C₄×Q₈	—	47	4	no	—
400	C₄×Q₈	—	47	8	no	—
401	C₄×Q₈	C₂²×D₄₇	1	4	yes	—
402	#117	—	47	2	no	—
403	#117	—	47	4	no	—
404	#117	—	47	4	no	—
405	#117	—	47	4	no	—
406	#117	C₂²×D₄₇	1	2	yes	—
407	C₂×C₄⋊C₄	—	47	4	no	—
408	C₂×C₄⋊C₄	—	47	8	no	—
409	C₂×C₄⋊C₄	—	47	4	no	—
410	C₂×C₂²⋊C₄	—	47	4	no	—
411	C₂×C₄²	—	47	2	no	—
412	C₂×C₄²	—	47	1	no	—
413	C₂×C₄²	—	47	1	no	—
414	C₂×C₄²	—	47	1	no	—
415	C₂×C₄²	—	47	1	no	—
416	C₂×C₄²	—	47	1	no	—
417	C₂×C₄²	—	47	4	no	—
418	C₂×C₄²	—	47	2	no	—
419	C₂×C₄²	—	47	2	no	—
420	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
421	C₄⋊C₈	—	47	8	no	—
422	C₄⋊C₈	—	47	8	no	—
423	C₄⋊C₈	—	47	8	no	—
424	C₄⋊C₈	—	47	4	no	—
425	C₄⋊C₈	—	47	8	no	—
426	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
427	C₄⋊C₈	C₂²×D₄₇	1	8	yes	—
428	#97	—	47	2	no	—
429	#97	—	47	2	no	—
430	#97	—	47	2	no	—
431	#97	—	47	2	no	—
432	#97	—	47	4	no	—
433	#97	—	47	4	no	—
434	#97	—	47	4	no	—
435	#97	C₂²×D₄₇	1	4	yes	—
436	C₄×C₈	—	47	4	no	—
437	C₄×C₈	—	47	4	no	—
438	C₄×C₈	—	47	2	no	—
439	C₄×C₈	—	47	2	no	—
440	C₄×C₈	—	47	4	no	—
441	C₄×C₈	C₂²×D₄₇	1	2	yes	—
442	C₄×C₈	C₂²×D₄₇	1	2	yes	—
443	C₄×C₈	C₂²×D₄₇	1	4	yes	—
444	C₂⁴	—	47	1	no	—
445	C₂×Q₈	—	47	4	no	—
446	C₂×Q₈	—	47	8	no	—
447	C₂×Q₈	—	188	8	no	—
448	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
449	C₂²×C₄	—	47	1	no	—
450	C₂²×C₄	—	47	1	no	—
451	C₂²×C₄	—	47	1	no	—
452	C₂²×C₄	—	47	4	no	—
453	C₂²×C₄	—	47	4	no	—
454	C₂²×C₄	—	47	1	no	—
455	C₂²×C₄	—	47	1	no	—
456	C₂²×C₄	—	47	2	no	—
457	C₂²×C₄	—	47	2	no	—
458	C₂²×C₄	—	47	2	no	—
459	C₂²×C₄	—	47	2	no	—
460	C₂²×C₄	—	47	2	no	—
461	C₂²×C₄	—	47	8	no	—
462	C₂²×C₄	—	188	4	no	—
463	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
464	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
465	M₁₆	—	2	4	no	—
466	M₁₆	—	47	4	no	—
467	M₁₆	—	47	4	no	—
468	M₁₆	—	47	4	no	—
469	M₁₆	—	47	4	no	—
470	M₁₆	—	94	4	no	—
471	M₁₆	—	94	4	no	—
472	M₁₆	—	94	8	no	—
473	M₁₆	—	94	4	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	47	4	no	—
476	C₂×C₈	—	47	1	no	—
477	C₂×C₈	—	47	1	no	—
478	C₂×C₈	—	47	4	no	—
479	C₂×C₈	—	47	2	no	—
480	C₂×C₈	—	94	8	no	—
481	C₂×C₈	—	94	2	no	—
482	C₂×C₈	Q₈×D₄₇	1	4	yes	complemented
483	C₂×C₈	C₂³×D₄₇	1	4	yes	—
484	C₂×C₈	C₂³×D₄₇	1	2	yes	—
485	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
486	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
487	C₄⋊C₄	—	47	8	no	—
488	C₄⋊C₄	—	47	8	no	—
489	C₄⋊C₄	—	47	8	no	—
490	C₄⋊C₄	—	47	8	no	—
491	C₄⋊C₄	—	47	4	no	—
492	C₄⋊C₄	—	47	8	no	—
493	C₄⋊C₄	—	47	4	no	—
494	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
495	C₄⋊C₄	C₂×C₄×D₄₇	1	8	yes	—
496	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
497	C₂²⋊C₄	—	47	4	no	—
498	C₂²⋊C₄	—	47	8	no	—
499	C₂²⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
500	C₄²	—	47	2	no	—
501	C₄²	—	47	2	no	—
502	C₄²	—	47	2	no	—
503	C₄²	—	47	1	no	—
504	C₄²	—	47	2	no	—
505	C₄²	—	47	1	no	—
506	C₄²	—	47	8	no	—
507	C₄²	—	47	4	no	—
508	C₄²	—	47	2	no	—
509	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
510	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
511	C₄²	C₂³×D₄₇	1	2	yes	—
512	C₄²	C₂³×D₄₇	1	4	yes	—
513	C₂³	—	47	1	no	—
514	C₂³	—	47	1	no	—
515	C₂³	—	47	4	no	—
516	C₂³	—	188	2	no	—
517	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
518	Q₈	—	2	8	no	—
519	Q₈	—	94	8	no	—
520	Q₈	—	188	8	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	47	4	no	—
523	C₂×C₄	—	47	1	no	—
524	C₂×C₄	—	47	1	no	—
525	C₂×C₄	—	47	4	no	—
526	C₂×C₄	—	47	4	no	—
527	C₂×C₄	—	47	2	no	—
528	C₂×C₄	—	47	2	no	—
529	C₂×C₄	—	47	2	no	—
530	C₂×C₄	—	47	2	no	—
531	C₂×C₄	—	47	2	no	—
532	C₂×C₄	—	47	2	no	—
533	C₂×C₄	—	47	8	no	—
534	C₂×C₄	—	94	4	no	—
535	C₂×C₄	—	94	4	no	—
536	C₂×C₄	—	188	2	no	—
537	C₂×C₄	—	188	2	no	—
538	C₂×C₄	—	188	8	no	—
539	C₂×C₄	—	188	2	no	—
540	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
541	C₂×C₄	C₂²×C₄×D₄₇	1	8	yes	—
542	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
543	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
544	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
545	C₂×C₄	#41×D₄₇	1	2	yes	—
546	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
547	C₈	—	2	2	no	—
548	C₈	—	2	4	no	—
549	C₈	—	47	2	no	—
550	C₈	—	47	2	no	—
551	C₈	—	94	4	no	—
552	C₈	—	94	2	no	—
553	C₈	C₂×Q₈×D₄₇	1	2	yes	—
554	C₈	C₂×Q₈×D₄₇	1	2	yes	—
555	C₂²	—	2	2	no	—
556	C₂²	—	47	2	no	—
557	C₂²	—	47	2	no	—
558	C₂²	—	94	2	no	—
559	C₂²	—	94	2	no	—
560	C₂²	—	188	4	no	—
561	C₂²	C₄×Q₈×D₄₇	1	2	yes	—
562	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
563	C₄	—	2	2	no	—
564	C₄	—	2	8	no	—
565	C₄	—	47	2	no	—
566	C₄	—	47	2	no	—
567	C₄	—	94	2	no	—
568	C₄	—	94	2	no	—
569	C₄	—	94	8	no	—
570	C₄	C₄×Q₈×D₄₇	1	2	yes	—
571	C₄	#15689888	1	4	yes	—
572	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
573	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
574	C₂	—	2	2	no	—
575	C₂	—	94	2	no	—
576	C₂	—	94	2	no	—
577	C₂	C₂×C₄×Q₈×D₄₇	1	1	yes	characteristic
578	C₂	C₂×#15689888	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2960	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2960	D₄₇
hypocenter	C₄₇	#60192
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2960

Complements

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

N	H ≅ G/N	type
2. #20252340	C₂	semidirect
3. Q₈×#10625324	C₂	semidirect
4. #20252336	C₂	semidirect
5. #20252330	C₂	semidirect
6. #20252327	C₂	semidirect
7. #20252326	C₂	semidirect
8. #20252323	C₂	semidirect
9. #20252322	C₂	semidirect
10. #20252318	C₂	semidirect
15. C₄₇×#2960	C₂	semidirect
31. #15689254	C₂²	semidirect
32. #15689253	C₂²	semidirect
33. #15689253	C₂²	semidirect
34. #15689252	C₂²	semidirect
35. #15689251	C₂²	semidirect
36. #15689250	C₂²	semidirect
37. #15689250	C₂²	semidirect
38. Q₈×C₄₇⋊C₈	C₂²	semidirect
39. C₈×Dic₉₄	C₂²	semidirect
40. #15689247	C₂²	semidirect
65. C₄₇×#446	C₂²	semidirect
66. C₈×Q₈×C₄₇	C₂²	semidirect
76. C₂×#10625324	Q₈	semidirect
177. C₂×C₈×C₄₇	C₂×Q₈	semidirect
210. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
220. #10625324	C₂×Q₈	semidirect
221. #10625324	C₂×Q₈	semidirect
295. #2960	D₄₇	semidirect
328. #446	C₂×D₄₇	semidirect
332. C₈×Q₈	C₂×D₄₇	semidirect
360. C₄₇	#60192	semidirect
482. C₂×C₈	Q₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#533×D₄₇	2
#20252340	2
Q₈×#10625324	2
#20252336	2
#20252330	2
#20252327	2
#20252326	2
#20252323	2
#20252322	2
#20252318	2
#20251949	2
#423×D₄₇	2
#20251804	2
C₂×C₄×#10625324	2
C₄₇×#2960	2
#60192	47