Subgroups — C₄₇×#18787 #26058485

Order 12032.

1206 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1637	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1635	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1631	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1629	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1486	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₇	—	2	1	no	—
13	C₄₇×#550	C₂²	1	1	yes	characteristic
14	D₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₄₇×#548	—	2	1	no	—
16	C₄₇×#547	—	2	1	no	—
17	C₄₇×#547	C₂²	1	1	yes	characteristic
18	C₄₇×#546	—	2	2	no	—
19	C₄₇×#546	—	2	1	no	—
20	D₄²×C₄₇	—	2	1	no	—
21	D₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#532	—	2	1	no	—
23	C₄₇×#532	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
25	C₄₇×#525	—	2	2	no	—
26	C₄₇×#525	—	2	1	no	—
27	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₄₇	—	2	1	no	—
29	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#492	C₂²	1	2	yes	complemented
31	C₄₇×#487	C₂²	1	2	yes	complemented
32	C₄₇×#477	C₂²	1	2	yes	complemented
33	C₄₇×#476	—	2	1	no	—
34	C₄₇×#476	—	2	1	no	—
35	C₄₇×#476	C₂²	1	2	yes	—
36	C₄₇×#476	C₂²	1	2	yes	complemented
37	C₄₇×#476	C₂²	1	2	yes	complemented
38	C₄₇×#475	—	2	1	no	—
39	C₄₇×#474	—	2	1	no	—
40	C₄₇×#461	—	2	2	no	—
41	C₄₇×#448	—	2	2	no	—
42	C₄₇×#431	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×#428	—	2	1	no	—
44	C₂×#106×C₄₇	—	2	1	no	—
45	C₄₇×#423	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
47	C₄₇×#417	—	2	1	no	—
48	C₂×#102×C₄₇	—	2	1	no	—
49	C₄₇×#332	C₂²	1	2	yes	complemented
50	C₄₇×#331	C₂²	1	2	yes	complemented
51	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
53	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
54	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
55	C₂×#41×C₄₇	—	2	2	no	—
56	C₂×#41×C₄₇	—	2	2	no	—
57	C₂×#41×C₄₇	—	2	1	no	—
58	C₂×#41×C₄₇	—	2	1	no	—
59	C₂×#41×C₄₇	—	2	1	no	—
60	C₂×#41×C₄₇	—	4	4	no	—
61	C₂×#41×C₄₇	—	4	4	no	—
62	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
63	C₂²×Q₈×C₄₇	—	2	1	no	—
64	C₂²×Q₈×C₄₇	—	2	1	no	—
65	C₂²×D₄×C₄₇	—	2	2	no	—
66	C₂²×D₄×C₄₇	—	2	1	no	—
67	C₂²×D₄×C₄₇	—	2	1	no	—
68	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₄₇	—	2	2	no	—
70	C₂³×C₄×C₄₇	—	2	1	no	—
71	C₂×SD₁₆×C₄₇	—	2	4	no	—
72	C₂×M₁₆×C₄₇	—	2	1	no	—
73	C₂²×C₈×C₄₇	—	2	1	no	—
74	C₄⋊Q₈×C₄₇	—	2	1	no	—
75	C₄⋊Q₈×C₄₇	—	2	1	no	—
76	C₄⋊Q₈×C₄₇	—	2	1	no	—
77	C₄⋊Q₈×C₄₇	—	2	1	no	—
78	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
79	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	#127×C₄₇	—	2	1	no	—
81	#127×C₄₇	C₂³	1	1	yes	characteristic
82	#124×C₄₇	—	2	2	no	—
83	#124×C₄₇	—	2	1	no	—
84	#123×C₄₇	—	2	2	no	—
85	#123×C₄₇	—	2	2	no	—
86	#123×C₄₇	—	2	2	no	—
87	C₂²⋊Q₈×C₄₇	—	2	2	no	—
88	C₂²⋊Q₈×C₄₇	—	2	1	no	—
89	C₂²⋊Q₈×C₄₇	—	2	2	no	—
90	C₂²⋊Q₈×C₄₇	—	2	1	no	—
91	#121×C₄₇	—	2	2	no	—
92	#121×C₄₇	—	2	2	no	—
93	#121×C₄₇	—	2	2	no	—
94	#121×C₄₇	—	2	1	no	—
95	#121×C₄₇	—	2	1	no	—
96	#121×C₄₇	—	2	1	no	—
97	#121×C₄₇	—	2	1	no	—
98	#121×C₄₇	—	2	1	no	—
99	#121×C₄₇	D₄	1	2	yes	—
100	#120×C₄₇	—	2	2	no	—
101	#120×C₄₇	—	2	2	no	—
102	#120×C₄₇	—	2	2	no	—
103	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
104	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₄₇	—	2	2	no	—
106	C₄×D₄×C₄₇	—	2	2	no	—
107	C₄×D₄×C₄₇	—	2	2	no	—
108	C₄×D₄×C₄₇	—	2	1	no	—
109	C₄×D₄×C₄₇	—	2	1	no	—
110	C₄×D₄×C₄₇	—	2	1	no	—
111	C₄×D₄×C₄₇	—	2	1	no	—
112	C₄×D₄×C₄₇	—	2	1	no	—
113	C₄×D₄×C₄₇	—	2	1	no	—
114	C₄×D₄×C₄₇	—	2	1	no	—
115	C₄×D₄×C₄₇	D₄	1	2	yes	—
116	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
117	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
118	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
119	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
121	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
122	#117×C₄₇	—	2	1	no	—
123	#117×C₄₇	D₄	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
125	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
129	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
130	C₂×C₄²×C₄₇	—	2	1	no	—
131	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
132	#107×C₄₇	—	2	2	no	—
133	#106×C₄₇	—	2	2	no	—
134	#106×C₄₇	—	2	2	no	—
135	#106×C₄₇	—	2	2	no	—
136	C₄⋊C₈×C₄₇	—	2	1	no	—
137	C₄⋊C₈×C₄₇	—	2	1	no	—
138	C₄⋊C₈×C₄₇	—	2	1	no	—
139	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
140	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
141	#103×C₄₇	—	2	2	no	—
142	#103×C₄₇	—	2	4	no	—
143	#102×C₄₇	—	2	2	no	—
144	#102×C₄₇	—	2	2	no	—
145	#102×C₄₇	—	2	2	no	—
146	C₂²⋊C₈×C₄₇	—	2	1	no	—
147	C₄×C₈×C₄₇	C₂³	1	2	yes	—
148	C₂⁴×C₄₇	—	2	2	no	—
149	C₂⁴×C₄₇	—	2	1	no	—
150	#41×C₄₇	—	2	2	no	—
151	#41×C₄₇	—	4	8	no	—
152	#41×C₄₇	—	4	8	no	—
153	#41×C₄₇	—	4	2	no	—
154	#41×C₄₇	—	4	2	no	—
155	#41×C₄₇	—	4	2	no	—
156	#41×C₄₇	—	4	2	no	—
157	#41×C₄₇	—	4	2	no	—
158	#41×C₄₇	—	4	2	no	—
159	#41×C₄₇	SD₁₆	1	4	yes	complemented
160	C₂×Q₈×C₄₇	—	2	2	no	—
161	C₂×Q₈×C₄₇	—	2	1	no	—
162	C₂×Q₈×C₄₇	—	2	2	no	—
163	C₂×Q₈×C₄₇	—	4	2	no	—
164	C₂×Q₈×C₄₇	—	4	2	no	—
165	C₂×Q₈×C₄₇	—	4	1	no	—
166	C₂×Q₈×C₄₇	—	8	2	no	—
167	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
168	C₂×D₄×C₄₇	—	2	1	no	—
169	C₂×D₄×C₄₇	—	2	2	no	—
170	C₂×D₄×C₄₇	—	2	2	no	—
171	C₂×D₄×C₄₇	—	2	2	no	—
172	C₂×D₄×C₄₇	—	2	2	no	—
173	C₂×D₄×C₄₇	—	2	2	no	—
174	C₂×D₄×C₄₇	—	2	2	no	—
175	C₂×D₄×C₄₇	—	2	2	no	—
176	C₂×D₄×C₄₇	—	2	1	no	—
177	C₂×D₄×C₄₇	—	2	1	no	—
178	C₂×D₄×C₄₇	—	2	1	no	—
179	C₂×D₄×C₄₇	—	4	1	no	—
180	C₂×D₄×C₄₇	—	4	2	no	—
181	C₂×D₄×C₄₇	—	4	8	no	—
182	C₂×D₄×C₄₇	—	4	2	no	—
183	C₂×D₄×C₄₇	—	4	2	no	—
184	C₂×D₄×C₄₇	—	4	2	no	—
185	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
186	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
187	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
188	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₄₇	—	2	1	no	—
190	C₂²×C₄×C₄₇	—	2	2	no	—
191	C₂²×C₄×C₄₇	—	2	2	no	—
192	C₂²×C₄×C₄₇	—	2	2	no	—
193	C₂²×C₄×C₄₇	—	2	1	no	—
194	C₂²×C₄×C₄₇	—	2	1	no	—
195	C₂²×C₄×C₄₇	—	2	2	no	—
196	C₂²×C₄×C₄₇	—	2	1	no	—
197	C₂²×C₄×C₄₇	—	2	1	no	—
198	C₂²×C₄×C₄₇	—	2	1	no	—
199	C₂²×C₄×C₄₇	—	2	1	no	—
200	C₂²×C₄×C₄₇	—	2	1	no	—
201	C₂²×C₄×C₄₇	—	4	8	no	—
202	C₂²×C₄×C₄₇	—	4	2	no	—
203	C₂²×C₄×C₄₇	—	4	2	no	—
204	C₂²×C₄×C₄₇	—	4	1	no	—
205	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
208	SD₁₆×C₄₇	—	8	4	no	—
209	M₁₆×C₄₇	—	4	2	no	—
210	C₂×C₈×C₄₇	—	2	2	no	—
211	C₂×C₈×C₄₇	—	2	2	no	—
212	C₂×C₈×C₄₇	—	2	2	no	—
213	C₂×C₈×C₄₇	—	4	2	no	—
214	C₄⋊C₄×C₄₇	—	2	2	no	—
215	C₄⋊C₄×C₄₇	—	2	2	no	—
216	C₄⋊C₄×C₄₇	—	2	1	no	—
217	C₄⋊C₄×C₄₇	—	2	1	no	—
218	C₄⋊C₄×C₄₇	—	2	1	no	—
219	C₄⋊C₄×C₄₇	—	2	1	no	—
220	C₄⋊C₄×C₄₇	—	2	2	no	—
221	C₄⋊C₄×C₄₇	—	2	2	no	—
222	C₄⋊C₄×C₄₇	—	4	1	no	—
223	C₄⋊C₄×C₄₇	—	4	1	no	—
224	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
225	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
226	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
227	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
228	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
229	C₂²⋊C₄×C₄₇	—	2	2	no	—
230	C₂²⋊C₄×C₄₇	—	2	2	no	—
231	C₂²⋊C₄×C₄₇	—	2	2	no	—
232	C₂²⋊C₄×C₄₇	—	2	2	no	—
233	C₂²⋊C₄×C₄₇	—	2	1	no	—
234	C₂²⋊C₄×C₄₇	—	2	1	no	—
235	C₂²⋊C₄×C₄₇	—	2	2	no	—
236	C₂²⋊C₄×C₄₇	—	2	1	no	—
237	C₂²⋊C₄×C₄₇	—	2	1	no	—
238	C₂²⋊C₄×C₄₇	—	2	2	no	—
239	C₂²⋊C₄×C₄₇	—	2	1	no	—
240	C₂²⋊C₄×C₄₇	—	2	1	no	—
241	C₂²⋊C₄×C₄₇	—	2	1	no	—
242	C₄²×C₄₇	—	2	1	no	—
243	C₄²×C₄₇	—	2	1	no	—
244	C₄²×C₄₇	—	2	1	no	—
245	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
246	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
247	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
248	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
249	C₂³×C₄₇	—	2	1	no	—
250	C₂³×C₄₇	—	2	1	no	—
251	C₂³×C₄₇	—	2	1	no	—
252	C₂³×C₄₇	—	2	2	no	—
253	C₂³×C₄₇	—	4	2	no	—
254	C₂³×C₄₇	—	4	4	no	—
255	C₂³×C₄₇	—	4	4	no	—
256	C₂³×C₄₇	—	4	2	no	—
257	C₂³×C₄₇	—	8	1	no	—
258	C₂³×C₄₇	—	8	2	no	—
259	C₂³×C₄₇	#120	1	1	yes	characteristic
260	Q₈×C₄₇	—	2	1	no	—
261	Q₈×C₄₇	—	4	4	no	—
262	Q₈×C₄₇	—	4	4	no	—
263	Q₈×C₄₇	—	4	1	no	—
264	Q₈×C₄₇	—	4	1	no	—
265	Q₈×C₄₇	—	8	2	no	—
266	Q₈×C₄₇	C₂×SD₁₆	1	2	yes	—
267	D₄×C₄₇	—	2	4	no	—
268	D₄×C₄₇	—	2	1	no	—
269	D₄×C₄₇	—	2	1	no	—
270	D₄×C₄₇	—	2	1	no	—
271	D₄×C₄₇	—	2	1	no	—
272	D₄×C₄₇	—	4	2	no	—
273	D₄×C₄₇	—	4	2	no	—
274	D₄×C₄₇	—	4	4	no	—
275	D₄×C₄₇	—	4	4	no	—
276	D₄×C₄₇	—	4	4	no	—
277	D₄×C₄₇	—	4	4	no	—
278	D₄×C₄₇	—	4	4	no	—
279	D₄×C₄₇	—	4	1	no	—
280	D₄×C₄₇	—	4	1	no	—
281	D₄×C₄₇	—	4	1	no	—
282	D₄×C₄₇	—	4	1	no	—
283	D₄×C₄₇	—	8	2	no	—
284	D₄×C₄₇	C₂×SD₁₆	1	2	yes	—
285	D₄×C₄₇	#137	1	2	yes	—
286	C₂×C₄×C₄₇	—	2	1	no	—
287	C₂×C₄×C₄₇	—	2	1	no	—
288	C₂×C₄×C₄₇	—	2	1	no	—
289	C₂×C₄×C₄₇	—	2	4	no	—
290	C₂×C₄×C₄₇	—	2	1	no	—
291	C₂×C₄×C₄₇	—	2	1	no	—
292	C₂×C₄×C₄₇	—	2	1	no	—
293	C₂×C₄×C₄₇	—	2	2	no	—
294	C₂×C₄×C₄₇	—	2	1	no	—
295	C₂×C₄×C₄₇	—	4	1	no	—
296	C₂×C₄×C₄₇	—	4	4	no	—
297	C₂×C₄×C₄₇	—	4	4	no	—
298	C₂×C₄×C₄₇	—	4	4	no	—
299	C₂×C₄×C₄₇	—	4	2	no	—
300	C₂×C₄×C₄₇	—	4	1	no	—
301	C₂×C₄×C₄₇	—	4	1	no	—
302	C₂×C₄×C₄₇	—	4	1	no	—
303	C₂×C₄×C₄₇	—	4	1	no	—
304	C₂×C₄×C₄₇	—	4	1	no	—
305	C₂×C₄×C₄₇	—	4	1	no	—
306	C₂×C₄×C₄₇	—	4	2	no	—
307	C₂×C₄×C₄₇	—	4	4	no	—
308	C₂×C₄×C₄₇	—	4	2	no	—
309	C₂×C₄×C₄₇	—	4	2	no	—
310	C₂×C₄×C₄₇	—	8	1	no	—
311	C₂×C₄×C₄₇	—	8	2	no	—
312	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
313	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
314	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
315	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
316	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
317	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
320	C₈×C₄₇	—	4	2	no	—
321	C₈×C₄₇	—	4	2	no	—
322	C₈×C₄₇	—	4	2	no	—
323	#18787	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
324	C₂²×C₄₇	—	2	1	no	—
325	C₂²×C₄₇	—	2	1	no	—
326	C₂²×C₄₇	—	2	2	no	—
327	C₂²×C₄₇	—	2	2	no	—
328	C₂²×C₄₇	—	4	1	no	—
329	C₂²×C₄₇	—	4	1	no	—
330	C₂²×C₄₇	—	4	1	no	—
331	C₂²×C₄₇	—	4	1	no	—
332	C₂²×C₄₇	—	4	2	no	—
333	C₂²×C₄₇	—	4	1	no	—
334	C₂²×C₄₇	—	4	1	no	—
335	C₂²×C₄₇	—	4	2	no	—
336	C₂²×C₄₇	—	4	2	no	—
337	C₂²×C₄₇	—	4	1	no	—
338	C₂²×C₄₇	—	8	4	no	—
339	C₂²×C₄₇	—	8	8	no	—
340	C₂²×C₄₇	#450	1	2	yes	—
341	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
342	C₄×C₄₇	—	2	2	no	—
343	C₄×C₄₇	—	2	1	no	—
344	C₄×C₄₇	—	2	1	no	—
345	C₄×C₄₇	—	2	1	no	—
346	C₄×C₄₇	—	4	1	no	—
347	C₄×C₄₇	—	4	2	no	—
348	C₄×C₄₇	—	4	1	no	—
349	C₄×C₄₇	—	4	1	no	—
350	C₄×C₄₇	—	4	1	no	—
351	C₄×C₄₇	—	8	2	no	—
352	C₄×C₄₇	#450	1	2	yes	—
353	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
354	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
355	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
356	C₄×C₄₇	#575	1	1	yes	characteristic
357	D₄×#41	C₂×C₄₇	1	1	yes	characteristic
358	#3206	C₂×C₄₇	1	1	yes	characteristic, complemented
359	#3079	C₂×C₄₇	1	1	yes	characteristic, complemented
360	C₂×#476	C₂×C₄₇	1	1	yes	characteristic, complemented
361	#1637	C₂×C₄₇	1	2	yes	complemented
362	#1635	C₂×C₄₇	1	2	yes	complemented
363	#1631	C₂×C₄₇	1	2	yes	complemented
364	#1629	C₂×C₄₇	1	2	yes	complemented
365	#1547	C₂×C₄₇	1	1	yes	characteristic, complemented
366	#1486	C₂×C₄₇	1	1	yes	characteristic, complemented
367	#1477	C₂×C₄₇	1	1	yes	characteristic, complemented
368	C₂×C₄₇	—	2	2	no	—
369	C₂×C₄₇	—	4	2	no	—
370	C₂×C₄₇	—	4	2	no	—
371	C₂×C₄₇	—	8	1	no	—
372	C₂×C₄₇	—	8	2	no	—
373	C₂×C₄₇	C₂×#450	1	1	yes	characteristic
374	C₂×C₄₇	#3007	1	1	yes	characteristic
375	C₂×C₄₇	#3021	1	1	yes	characteristic
376	C₂²×#41	—	2	1	no	—
377	#550	C₂²×C₄₇	1	1	yes	characteristic
378	D₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
379	#548	—	2	1	no	—
380	#547	—	2	1	no	—
381	#547	C₂²×C₄₇	1	1	yes	characteristic
382	#546	—	2	2	no	—
383	#546	—	2	1	no	—
384	D₄²	—	2	1	no	—
385	D₄²	C₂²×C₄₇	1	1	yes	characteristic
386	#532	—	2	1	no	—
387	#532	C₂²×C₄₇	1	1	yes	characteristic
388	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
389	#525	—	2	2	no	—
390	#525	—	2	1	no	—
391	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
392	C₂×C₄×D₄	—	2	1	no	—
393	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
394	#492	C₂²×C₄₇	1	2	yes	complemented
395	#487	C₂²×C₄₇	1	2	yes	complemented
396	#477	C₂²×C₄₇	1	2	yes	complemented
397	#476	—	2	1	no	—
398	#476	—	2	1	no	—
399	#476	C₂²×C₄₇	1	2	yes	—
400	#476	C₂²×C₄₇	1	2	yes	complemented
401	#476	C₂²×C₄₇	1	2	yes	complemented
402	#475	—	2	1	no	—
403	#474	—	2	1	no	—
404	#461	—	2	2	no	—
405	#448	—	2	2	no	—
406	#431	C₂²×C₄₇	1	1	yes	characteristic, complemented
407	#428	—	2	1	no	—
408	C₂×#106	—	2	1	no	—
409	#423	C₂²×C₄₇	1	1	yes	characteristic, complemented
410	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
411	#417	—	2	1	no	—
412	C₂×#102	—	2	1	no	—
413	#332	C₂²×C₄₇	1	2	yes	complemented
414	#331	C₂²×C₄₇	1	2	yes	complemented
415	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	complemented
416	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
417	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
418	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
419	C₄₇	#18787	1	1	yes	characteristic, direct product factor, Sylow
420	C₂×#41	—	2	2	no	—
421	C₂×#41	—	2	2	no	—
422	C₂×#41	—	2	1	no	—
423	C₂×#41	—	2	1	no	—
424	C₂×#41	—	2	1	no	—
425	C₂×#41	—	4	4	no	—
426	C₂×#41	—	4	4	no	—
427	C₂×#41	D₄×C₄₇	1	1	yes	characteristic
428	C₂²×Q₈	—	2	1	no	—
429	C₂²×Q₈	—	2	1	no	—
430	C₂²×D₄	—	2	2	no	—
431	C₂²×D₄	—	2	1	no	—
432	C₂²×D₄	—	2	1	no	—
433	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
434	C₂³×C₄	—	2	2	no	—
435	C₂³×C₄	—	2	1	no	—
436	C₂×SD₁₆	—	2	4	no	—
437	C₂×M₁₆	—	2	1	no	—
438	C₂²×C₈	—	2	1	no	—
439	C₄⋊Q₈	—	2	1	no	—
440	C₄⋊Q₈	—	2	1	no	—
441	C₄⋊Q₈	—	2	1	no	—
442	C₄⋊Q₈	—	2	1	no	—
443	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
444	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
445	#127	—	2	1	no	—
446	#127	C₂³×C₄₇	1	1	yes	characteristic
447	#124	—	2	2	no	—
448	#124	—	2	1	no	—
449	#123	—	2	2	no	—
450	#123	—	2	2	no	—
451	#123	—	2	2	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	2	1	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	1	no	—
456	#121	—	2	2	no	—
457	#121	—	2	2	no	—
458	#121	—	2	2	no	—
459	#121	—	2	1	no	—
460	#121	—	2	1	no	—
461	#121	—	2	1	no	—
462	#121	—	2	1	no	—
463	#121	—	2	1	no	—
464	#121	D₄×C₄₇	1	2	yes	—
465	#120	—	2	2	no	—
466	#120	—	2	2	no	—
467	#120	—	2	2	no	—
468	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
469	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
470	C₄×D₄	—	2	2	no	—
471	C₄×D₄	—	2	2	no	—
472	C₄×D₄	—	2	2	no	—
473	C₄×D₄	—	2	1	no	—
474	C₄×D₄	—	2	1	no	—
475	C₄×D₄	—	2	1	no	—
476	C₄×D₄	—	2	1	no	—
477	C₄×D₄	—	2	1	no	—
478	C₄×D₄	—	2	1	no	—
479	C₄×D₄	—	2	1	no	—
480	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
481	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
482	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
483	C₄×D₄	D₄×C₄₇	1	2	yes	—
484	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
485	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
486	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
487	#117	—	2	1	no	—
488	#117	D₄×C₄₇	1	1	yes	characteristic
489	C₂×C₄⋊C₄	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	1	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	—	2	2	no	—
494	C₂×C₂²⋊C₄	—	2	1	no	—
495	C₂×C₄²	—	2	1	no	—
496	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
497	#107	—	2	2	no	—
498	#106	—	2	2	no	—
499	#106	—	2	2	no	—
500	#106	—	2	2	no	—
501	C₄⋊C₈	—	2	1	no	—
502	C₄⋊C₈	—	2	1	no	—
503	C₄⋊C₈	—	2	1	no	—
504	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
505	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
506	#103	—	2	2	no	—
507	#103	—	2	4	no	—
508	#102	—	2	2	no	—
509	#102	—	2	2	no	—
510	#102	—	2	2	no	—
511	C₂²⋊C₈	—	2	1	no	—
512	C₄×C₈	C₂³×C₄₇	1	2	yes	—
513	C₂⁴	—	2	2	no	—
514	C₂⁴	—	2	1	no	—
515	#41	—	2	2	no	—
516	#41	—	4	8	no	—
517	#41	—	4	8	no	—
518	#41	—	4	2	no	—
519	#41	—	4	2	no	—
520	#41	—	4	2	no	—
521	#41	—	4	2	no	—
522	#41	—	4	2	no	—
523	#41	—	4	2	no	—
524	#41	SD₁₆×C₄₇	1	4	yes	complemented
525	C₂×Q₈	—	2	2	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	4	2	no	—
529	C₂×Q₈	—	4	2	no	—
530	C₂×Q₈	—	4	1	no	—
531	C₂×Q₈	—	8	2	no	—
532	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
533	C₂×D₄	—	2	1	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	2	2	no	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	2	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	4	1	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	8	no	—
547	C₂×D₄	—	4	2	no	—
548	C₂×D₄	—	4	2	no	—
549	C₂×D₄	—	4	2	no	—
550	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
551	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
552	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
553	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	1	no	—
559	C₂²×C₄	—	2	1	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	1	no	—
562	C₂²×C₄	—	2	1	no	—
563	C₂²×C₄	—	2	1	no	—
564	C₂²×C₄	—	2	1	no	—
565	C₂²×C₄	—	2	1	no	—
566	C₂²×C₄	—	4	8	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	2	no	—
569	C₂²×C₄	—	4	1	no	—
570	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
573	SD₁₆	—	8	4	no	—
574	M₁₆	—	4	2	no	—
575	C₂×C₈	—	2	2	no	—
576	C₂×C₈	—	2	2	no	—
577	C₂×C₈	—	2	2	no	—
578	C₂×C₈	—	4	2	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	4	1	no	—
588	C₄⋊C₄	—	4	1	no	—
589	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
590	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
591	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
592	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
593	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	2	1	no	—
609	C₄²	—	2	1	no	—
610	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
611	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
612	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
613	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
614	C₂³	—	2	1	no	—
615	C₂³	—	2	1	no	—
616	C₂³	—	2	1	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	4	2	no	—
619	C₂³	—	4	4	no	—
620	C₂³	—	4	4	no	—
621	C₂³	—	4	2	no	—
622	C₂³	—	8	1	no	—
623	C₂³	—	8	2	no	—
624	C₂³	#120×C₄₇	1	1	yes	characteristic
625	Q₈	—	2	1	no	—
626	Q₈	—	4	4	no	—
627	Q₈	—	4	4	no	—
628	Q₈	—	4	1	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	8	2	no	—
631	Q₈	C₂×SD₁₆×C₄₇	1	2	yes	—
632	D₄	—	2	4	no	—
633	D₄	—	2	1	no	—
634	D₄	—	2	1	no	—
635	D₄	—	2	1	no	—
636	D₄	—	2	1	no	—
637	D₄	—	4	2	no	—
638	D₄	—	4	2	no	—
639	D₄	—	4	4	no	—
640	D₄	—	4	4	no	—
641	D₄	—	4	4	no	—
642	D₄	—	4	4	no	—
643	D₄	—	4	4	no	—
644	D₄	—	4	1	no	—
645	D₄	—	4	1	no	—
646	D₄	—	4	1	no	—
647	D₄	—	4	1	no	—
648	D₄	—	8	2	no	—
649	D₄	C₂×SD₁₆×C₄₇	1	2	yes	—
650	D₄	#137×C₄₇	1	2	yes	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	4	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	4	4	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	2	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	4	1	no	—
674	C₂×C₄	—	4	2	no	—
675	C₂×C₄	—	8	1	no	—
676	C₂×C₄	—	8	2	no	—
677	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
678	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
679	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
680	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
681	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
682	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
683	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
684	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
685	C₈	—	4	2	no	—
686	C₈	—	4	2	no	—
687	C₈	—	4	2	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	2	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	8	4	no	—
703	C₂²	—	8	8	no	—
704	C₂²	C₄₇×#450	1	2	yes	—
705	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
706	C₄	—	2	2	no	—
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	2	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	—	8	2	no	—
716	C₄	C₄₇×#450	1	2	yes	—
717	C₄	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
718	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
719	C₄	C₂×#137×C₄₇	1	1	yes	characteristic
720	C₄	C₄₇×#575	1	1	yes	characteristic
721	C₂	—	2	2	no	—
722	C₂	—	4	2	no	—
723	C₂	—	4	2	no	—
724	C₂	—	8	1	no	—
725	C₂	—	8	2	no	—
726	C₂	C₂×C₄₇×#450	1	1	yes	characteristic
727	C₂	C₄₇×#3007	1	1	yes	characteristic
728	C₂	C₄₇×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
prime radical	D₄×#41×C₄₇	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#3206	C₂	semidirect
3. C₄₇×#3079	C₂	semidirect
4. C₂×C₄₇×#476	C₂	semidirect
5. C₄₇×#1637	C₂	semidirect
6. C₄₇×#1635	C₂	semidirect
7. C₄₇×#1631	C₂	semidirect
8. C₄₇×#1629	C₂	semidirect
9. C₄₇×#1547	C₂	semidirect
10. C₄₇×#1486	C₂	semidirect
11. C₄₇×#1477	C₂	semidirect
24. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
30. C₄₇×#492	C₂²	semidirect
31. C₄₇×#487	C₂²	semidirect
32. C₄₇×#477	C₂²	semidirect
36. C₄₇×#476	C₂²	semidirect
37. C₄₇×#476	C₂²	semidirect
42. C₄₇×#431	C₂²	semidirect
45. C₄₇×#423	C₂²	semidirect
46. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
49. C₄₇×#332	C₂²	semidirect
50. C₄₇×#331	C₂²	semidirect
51. C₄₇×Q₈⋊C₈	C₂²	semidirect
53. C₄₇×D₄⋊C₈	C₂²	semidirect
54. C₄₇×D₄⋊C₈	C₂²	semidirect
159. #41×C₄₇	SD₁₆	semidirect
323. #18787	C₄₇	direct (N × H)
358. #3206	C₂×C₄₇	semidirect
359. #3079	C₂×C₄₇	semidirect
360. C₂×#476	C₂×C₄₇	semidirect
361. #1637	C₂×C₄₇	semidirect
362. #1635	C₂×C₄₇	semidirect
363. #1631	C₂×C₄₇	semidirect
364. #1629	C₂×C₄₇	semidirect
365. #1547	C₂×C₄₇	semidirect
366. #1486	C₂×C₄₇	semidirect
367. #1477	C₂×C₄₇	semidirect
388. C₂×C₄⋊Q₈	C₂²×C₄₇	semidirect
394. #492	C₂²×C₄₇	semidirect
395. #487	C₂²×C₄₇	semidirect
396. #477	C₂²×C₄₇	semidirect
400. #476	C₂²×C₄₇	semidirect
401. #476	C₂²×C₄₇	semidirect
406. #431	C₂²×C₄₇	semidirect
409. #423	C₂²×C₄₇	semidirect
410. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
413. #332	C₂²×C₄₇	semidirect
414. #331	C₂²×C₄₇	semidirect
415. Q₈⋊C₈	C₂²×C₄₇	semidirect
417. D₄⋊C₈	C₂²×C₄₇	semidirect
418. D₄⋊C₈	C₂²×C₄₇	semidirect
419. C₄₇	#18787	direct (N × H)
524. #41	SD₁₆×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
D₄×#41×C₄₇	2
C₄₇×#3206	2
C₄₇×#3079	2
C₂×C₄₇×#476	2
C₄₇×#1637	2
C₄₇×#1635	2
C₄₇×#1631	2
C₄₇×#1629	2
C₄₇×#1547	2
C₄₇×#1486	2
C₄₇×#1477	2
#18787	47

Subgroups — C47×#18787 #26058485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18787 #26058485