Subgroups — C₄₇×#23484 #26063182

Order 12032.

1418 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#419	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#103×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄₇×#408	C₂	1	1	yes	maximal, characteristic
6	C₄₇×#2311	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#2036	C₂	1	4	yes	maximal, complemented
8	C₄₇×#2035	C₂	1	4	yes	maximal, complemented
9	C₄₇×#1735	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₄₇×#536	—	2	4	no	—
15	C₄₇×#536	—	2	4	no	—
16	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
17	C₂×#124×C₄₇	—	2	1	no	—
18	C₂×#123×C₄₇	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
21	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#428	—	2	4	no	—
25	C₂×#107×C₄₇	C₂²	1	2	yes	—
26	C₂×#106×C₄₇	C₂²	1	2	yes	—
27	C₄₇×#419	—	2	4	no	—
28	C₂×#103×C₄₇	—	2	4	no	—
29	C₂×#103×C₄₇	C₂²	1	4	yes	—
30	C₂×#103×C₄₇	C₂²	1	4	yes	—
31	C₄₇×#408	—	2	4	no	—
32	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
33	C₄₇×#391	—	2	1	no	—
34	C₄₇×#390	—	2	1	no	—
35	C₄₇×#386	—	2	2	no	—
36	C₄₇×#380	C₂²	1	4	yes	—
37	C₄₇×#340	C₂²	1	2	yes	—
38	C₄₇×#340	C₂²	1	2	yes	—
39	C₂×#41×C₄₇	—	2	2	no	—
40	C₂×#41×C₄₇	—	2	2	no	—
41	C₂×#41×C₄₇	—	2	2	no	—
42	C₂×#41×C₄₇	—	2	2	no	—
43	C₂×#41×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	—	2	2	no	—
45	C₂²×Q₈×C₄₇	—	2	1	no	—
46	C₂²×Q₈×C₄₇	—	2	2	no	—
47	C₂²×Q₈×C₄₇	—	2	2	no	—
48	C₂²×Q₈×C₄₇	—	2	2	no	—
49	C₂²×Q₈×C₄₇	—	2	2	no	—
50	C₂²×Q₈×C₄₇	—	2	2	no	—
51	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
52	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
53	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
54	C₂²×D₄×C₄₇	D₄	1	2	yes	—
55	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	—	2	1	no	—
57	C₂³×C₄×C₄₇	—	2	1	no	—
58	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
59	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
60	C₂×M₁₆×C₄₇	—	2	2	no	—
61	C₂×M₁₆×C₄₇	—	2	2	no	—
62	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
63	C₂²×C₈×C₄₇	—	2	2	no	—
64	C₂²×C₈×C₄₇	—	2	2	no	—
65	C₂²×C₈×C₄₇	—	2	2	no	—
66	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
67	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₄₇	—	2	8	no	—
69	#124×C₄₇	—	2	8	no	—
70	#123×C₄₇	—	2	16	no	—
71	C₂²⋊Q₈×C₄₇	—	2	4	no	—
72	C₂²⋊Q₈×C₄₇	—	2	4	no	—
73	C₂²⋊Q₈×C₄₇	—	2	4	no	—
74	C₂²⋊Q₈×C₄₇	—	2	4	no	—
75	#117×C₄₇	—	2	2	no	—
76	#117×C₄₇	—	2	2	no	—
77	#117×C₄₇	—	2	2	no	—
78	#117×C₄₇	D₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
93	C₂×C₄²×C₄₇	—	2	1	no	—
94	C₂×C₄²×C₄₇	—	2	1	no	—
95	#107×C₄₇	—	2	4	no	—
96	#106×C₄₇	—	2	4	no	—
97	#103×C₄₇	—	2	8	no	—
98	#103×C₄₇	—	2	8	no	—
99	C₂²⋊C₈×C₄₇	—	2	8	no	—
100	#95×C₄₇	—	2	4	no	—
101	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
102	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
103	#41×C₄₇	—	4	4	no	—
104	#41×C₄₇	—	4	4	no	—
105	#41×C₄₇	—	4	4	no	—
106	#41×C₄₇	—	4	4	no	—
107	C₂×Q₈×C₄₇	—	2	4	no	—
108	C₂×Q₈×C₄₇	—	2	2	no	—
109	C₂×Q₈×C₄₇	—	2	2	no	—
110	C₂×Q₈×C₄₇	—	2	2	no	—
111	C₂×Q₈×C₄₇	—	2	2	no	—
112	C₂×Q₈×C₄₇	—	2	8	no	—
113	C₂×Q₈×C₄₇	—	2	8	no	—
114	C₂×Q₈×C₄₇	—	2	2	no	—
115	C₂×Q₈×C₄₇	—	2	2	no	—
116	C₂×Q₈×C₄₇	—	2	2	no	—
117	C₂×Q₈×C₄₇	—	2	2	no	—
118	C₂×Q₈×C₄₇	—	4	2	no	—
119	C₂×Q₈×C₄₇	—	4	4	no	—
120	C₂×Q₈×C₄₇	—	4	2	no	—
121	C₂×Q₈×C₄₇	—	4	4	no	—
122	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
123	C₂×D₄×C₄₇	—	2	4	no	—
124	C₂×D₄×C₄₇	—	2	4	no	—
125	C₂×D₄×C₄₇	—	2	4	no	—
126	C₂×D₄×C₄₇	—	2	2	no	—
127	C₂×D₄×C₄₇	—	2	2	no	—
128	C₂×D₄×C₄₇	—	2	2	no	—
129	C₂²×C₄×C₄₇	—	2	4	no	—
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	2	2	no	—
136	C₂²×C₄×C₄₇	—	2	2	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	2	2	no	—
140	C₂²×C₄×C₄₇	—	2	2	no	—
141	C₂²×C₄×C₄₇	—	4	2	no	—
142	C₂²×C₄×C₄₇	—	4	2	no	—
143	C₂²×C₄×C₄₇	—	4	2	no	—
144	C₂²×C₄×C₄₇	—	8	2	no	—
145	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₄₇	#41	1	2	yes	—
151	C₂²×C₄×C₄₇	#41	1	2	yes	—
152	C₂²×C₄×C₄₇	#41	1	2	yes	—
153	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
154	M₁₆×C₄₇	—	2	8	no	—
155	C₂×C₈×C₄₇	—	2	2	no	—
156	C₂×C₈×C₄₇	—	2	2	no	—
157	C₂×C₈×C₄₇	—	2	2	no	—
158	C₂×C₈×C₄₇	—	2	2	no	—
159	C₂×C₈×C₄₇	—	2	2	no	—
160	C₂×C₈×C₄₇	—	4	4	no	—
161	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
162	C₄⋊C₄×C₄₇	—	2	8	no	—
163	C₄⋊C₄×C₄₇	—	2	8	no	—
164	C₄⋊C₄×C₄₇	—	2	1	no	—
165	C₄⋊C₄×C₄₇	—	2	1	no	—
166	C₄⋊C₄×C₄₇	—	2	2	no	—
167	C₄⋊C₄×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	—	2	2	no	—
169	C₄⋊C₄×C₄₇	—	2	2	no	—
170	C₄⋊C₄×C₄₇	—	4	2	no	—
171	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
172	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
173	C₂²⋊C₄×C₄₇	—	2	8	no	—
174	C₂²⋊C₄×C₄₇	—	2	8	no	—
175	C₂²⋊C₄×C₄₇	—	2	4	no	—
176	C₂²⋊C₄×C₄₇	—	4	2	no	—
177	C₂²⋊C₄×C₄₇	—	8	4	no	—
178	C₄²×C₄₇	—	2	4	no	—
179	C₄²×C₄₇	—	4	2	no	—
180	C₂³×C₄₇	—	2	2	no	—
181	C₂³×C₄₇	—	2	2	no	—
182	C₂³×C₄₇	—	2	2	no	—
183	C₂³×C₄₇	—	2	2	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	2	4	no	—
186	C₂³×C₄₇	—	2	4	no	—
187	C₂³×C₄₇	#120	1	2	yes	—
188	C₂³×C₄₇	#121	1	2	yes	—
189	C₂³×C₄₇	#123	1	2	yes	—
190	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₄₇	—	2	4	no	—
192	Q₈×C₄₇	—	2	4	no	—
193	Q₈×C₄₇	—	4	2	no	—
194	Q₈×C₄₇	—	4	2	no	—
195	Q₈×C₄₇	—	4	8	no	—
196	Q₈×C₄₇	—	4	4	no	—
197	D₄×C₄₇	—	4	8	no	—
198	D₄×C₄₇	—	4	4	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	4	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	—	4	2	no	—
206	C₂×C₄×C₄₇	—	4	2	no	—
207	C₂×C₄×C₄₇	—	4	2	no	—
208	C₂×C₄×C₄₇	—	4	2	no	—
209	C₂×C₄×C₄₇	—	4	8	no	—
210	C₂×C₄×C₄₇	—	4	2	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	2	no	—
214	C₂×C₄×C₄₇	—	4	2	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	2	no	—
217	C₂×C₄×C₄₇	—	4	4	no	—
218	C₂×C₄×C₄₇	—	4	2	no	—
219	C₂×C₄×C₄₇	—	8	4	no	—
220	C₂×C₄×C₄₇	#120	1	2	yes	—
221	C₂×C₄×C₄₇	#121	1	4	yes	—
222	C₂×C₄×C₄₇	#121	1	4	yes	—
223	C₂×C₄×C₄₇	#121	1	2	yes	—
224	C₂×C₄×C₄₇	#123	1	4	yes	—
225	C₂×C₄×C₄₇	#123	1	2	yes	—
226	C₂×C₄×C₄₇	#124	1	4	yes	—
227	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
233	C₈×C₄₇	—	2	4	no	—
234	C₈×C₄₇	—	4	2	no	—
235	#23484	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂²×C₄₇	—	2	4	no	—
237	C₂²×C₄₇	—	2	2	no	—
238	C₂²×C₄₇	—	2	2	no	—
239	C₂²×C₄₇	—	2	4	no	—
240	C₂²×C₄₇	—	4	4	no	—
241	C₂²×C₄₇	—	4	2	no	—
242	C₂²×C₄₇	—	4	2	no	—
243	C₂²×C₄₇	—	4	2	no	—
244	C₂²×C₄₇	—	4	4	no	—
245	C₂²×C₄₇	#394	1	4	yes	—
246	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
247	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
248	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
249	C₂²×C₄₇	#577	1	2	yes	—
250	C₂²×C₄₇	#578	1	2	yes	—
251	C₄×C₄₇	—	4	2	no	—
252	C₄×C₄₇	—	4	4	no	—
253	C₄×C₄₇	—	4	2	no	—
254	C₄×C₄₇	—	4	2	no	—
255	C₄×C₄₇	—	8	2	no	—
256	C₄×C₄₇	—	8	2	no	—
257	C₄×C₄₇	#394	1	4	yes	—
258	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
259	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
260	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
261	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
262	C₂×#536	C₂×C₄₇	1	1	yes	characteristic
263	C₂×#428	C₂×C₄₇	1	1	yes	characteristic, complemented
264	C₂×#419	C₂×C₄₇	1	1	yes	characteristic, complemented
265	C₂²×#103	C₂×C₄₇	1	1	yes	characteristic, complemented
266	C₂×#408	C₂×C₄₇	1	1	yes	characteristic
267	#2311	C₂×C₄₇	1	1	yes	characteristic
268	#2036	C₂×C₄₇	1	4	yes	complemented
269	#2035	C₂×C₄₇	1	4	yes	complemented
270	#1735	C₂×C₄₇	1	1	yes	characteristic, complemented
271	C₂×C₄₇	—	2	4	no	—
272	C₂×C₄₇	—	8	2	no	—
273	C₂×C₄₇	C₂×#394	1	1	yes	characteristic
274	C₂×C₄₇	#3010	1	1	yes	characteristic
275	C₂×C₄₇	#3011	1	1	yes	characteristic
276	C₂×C₄₇	#3063	1	2	yes	—
277	C₂×C₄₇	#3097	1	2	yes	—
278	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
279	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
280	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
281	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
282	#536	—	2	4	no	—
283	#536	—	2	4	no	—
284	C₂×C₄⋊Q₈	—	2	1	no	—
285	C₂×#124	—	2	1	no	—
286	C₂×#123	—	2	2	no	—
287	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
288	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
289	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
290	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
292	#428	—	2	4	no	—
293	C₂×#107	C₂²×C₄₇	1	2	yes	—
294	C₂×#106	C₂²×C₄₇	1	2	yes	—
295	#419	—	2	4	no	—
296	C₂×#103	—	2	4	no	—
297	C₂×#103	C₂²×C₄₇	1	4	yes	—
298	C₂×#103	C₂²×C₄₇	1	4	yes	—
299	#408	—	2	4	no	—
300	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
301	#391	—	2	1	no	—
302	#390	—	2	1	no	—
303	#386	—	2	2	no	—
304	#380	C₂²×C₄₇	1	4	yes	—
305	#340	C₂²×C₄₇	1	2	yes	—
306	#340	C₂²×C₄₇	1	2	yes	—
307	C₄₇	#23484	1	1	yes	characteristic, direct product factor, Sylow
308	C₂×#41	—	2	2	no	—
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	2	2	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	—	2	2	no	—
314	C₂²×Q₈	—	2	1	no	—
315	C₂²×Q₈	—	2	2	no	—
316	C₂²×Q₈	—	2	2	no	—
317	C₂²×Q₈	—	2	2	no	—
318	C₂²×Q₈	—	2	2	no	—
319	C₂²×Q₈	—	2	2	no	—
320	C₂²×Q₈	D₄×C₄₇	1	4	yes	—
321	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
322	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
323	C₂²×D₄	D₄×C₄₇	1	2	yes	—
324	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	—	2	1	no	—
327	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
328	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
329	C₂×M₁₆	—	2	2	no	—
330	C₂×M₁₆	—	2	2	no	—
331	C₂×M₁₆	D₄×C₄₇	1	4	yes	—
332	C₂²×C₈	—	2	2	no	—
333	C₂²×C₈	—	2	2	no	—
334	C₂²×C₈	—	2	2	no	—
335	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
336	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
337	C₄⋊Q₈	—	2	8	no	—
338	#124	—	2	8	no	—
339	#123	—	2	16	no	—
340	C₂²⋊Q₈	—	2	4	no	—
341	C₂²⋊Q₈	—	2	4	no	—
342	C₂²⋊Q₈	—	2	4	no	—
343	C₂²⋊Q₈	—	2	4	no	—
344	#117	—	2	2	no	—
345	#117	—	2	2	no	—
346	#117	—	2	2	no	—
347	#117	D₄×C₄₇	1	4	yes	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	—	2	4	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	—	2	1	no	—
364	#107	—	2	4	no	—
365	#106	—	2	4	no	—
366	#103	—	2	8	no	—
367	#103	—	2	8	no	—
368	C₂²⋊C₈	—	2	8	no	—
369	#95	—	2	4	no	—
370	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
371	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
372	#41	—	4	4	no	—
373	#41	—	4	4	no	—
374	#41	—	4	4	no	—
375	#41	—	4	4	no	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	2	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	2	8	no	—
382	C₂×Q₈	—	2	8	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	2	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	4	2	no	—
388	C₂×Q₈	—	4	4	no	—
389	C₂×Q₈	—	4	2	no	—
390	C₂×Q₈	—	4	4	no	—
391	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
392	C₂×D₄	—	2	4	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	2	no	—
413	C₂²×C₄	—	8	2	no	—
414	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
417	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
419	C₂²×C₄	#41×C₄₇	1	2	yes	—
420	C₂²×C₄	#41×C₄₇	1	2	yes	—
421	C₂²×C₄	#41×C₄₇	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
423	M₁₆	—	2	8	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	4	4	no	—
430	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	4	2	no	—
440	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
441	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₂²⋊C₄	—	8	4	no	—
447	C₄²	—	2	4	no	—
448	C₄²	—	4	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	2	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	4	no	—
456	C₂³	#120×C₄₇	1	2	yes	—
457	C₂³	#121×C₄₇	1	2	yes	—
458	C₂³	#123×C₄₇	1	2	yes	—
459	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
460	Q₈	—	2	4	no	—
461	Q₈	—	2	4	no	—
462	Q₈	—	4	2	no	—
463	Q₈	—	4	2	no	—
464	Q₈	—	4	8	no	—
465	Q₈	—	4	4	no	—
466	D₄	—	4	8	no	—
467	D₄	—	4	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	8	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	8	4	no	—
489	C₂×C₄	#120×C₄₇	1	2	yes	—
490	C₂×C₄	#121×C₄₇	1	4	yes	—
491	C₂×C₄	#121×C₄₇	1	4	yes	—
492	C₂×C₄	#121×C₄₇	1	2	yes	—
493	C₂×C₄	#123×C₄₇	1	4	yes	—
494	C₂×C₄	#123×C₄₇	1	2	yes	—
495	C₂×C₄	#124×C₄₇	1	4	yes	—
496	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
499	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
500	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
501	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
502	C₈	—	2	4	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	C₄₇×#394	1	4	yes	—
514	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
515	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
516	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
517	C₂²	C₄₇×#577	1	2	yes	—
518	C₂²	C₄₇×#578	1	2	yes	—
519	C₄	—	4	2	no	—
520	C₄	—	4	4	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	8	2	no	—
524	C₄	—	8	2	no	—
525	C₄	C₄₇×#394	1	4	yes	—
526	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
527	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
528	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
529	C₄	C₂×#124×C₄₇	1	1	yes	characteristic
530	C₂	—	2	4	no	—
531	C₂	—	8	2	no	—
532	C₂	C₂×C₄₇×#394	1	1	yes	characteristic
533	C₂	C₄₇×#3010	1	1	yes	characteristic
534	C₂	C₄₇×#3011	1	1	yes	characteristic
535	C₂	C₄₇×#3063	1	2	yes	—
536	C₂	C₄₇×#3097	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×#41×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×#41×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#428	C₂	semidirect
3. C₂×C₄₇×#419	C₂	semidirect
4. C₂²×#103×C₄₇	C₂	semidirect
7. C₄₇×#2036	C₂	semidirect
8. C₄₇×#2035	C₂	semidirect
9. C₄₇×#1735	C₂	semidirect
235. #23484	C₄₇	direct (N × H)
263. C₂×#428	C₂×C₄₇	semidirect
264. C₂×#419	C₂×C₄₇	semidirect
265. C₂²×#103	C₂×C₄₇	semidirect
268. #2036	C₂×C₄₇	semidirect
269. #2035	C₂×C₄₇	semidirect
270. #1735	C₂×C₄₇	semidirect
307. C₄₇	#23484	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#536	2
C₂×C₄₇×#428	2
C₂×C₄₇×#419	2
C₂²×#103×C₄₇	2
C₂×C₄₇×#408	2
C₄₇×#2311	2
C₄₇×#2036	2
C₄₇×#2035	2
C₄₇×#1735	2
#23484	47

Subgroups — C47×#23484 #26063182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#23484 #26063182