Subgroups — C₄₇×#17328 #26057026

Order 12032.

750 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2965	C₂	1	1	yes	maximal, characteristic
2	C₈×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2922	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1454	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1453	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1452	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1451	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1450	C₂	1	2	yes	maximal, complemented
9	C₈×M₁₆×C₄₇	C₂	1	2	yes	maximal, complemented
10	C₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
13	C₄₇×#446	C₄	1	2	yes	—
14	C₈×Q₈×C₄₇	C₄	1	2	yes	—
15	C₄₇×#436	C₄	1	2	yes	—
16	C₄₇×#435	C₄	1	4	yes	—
17	C₈×D₄×C₄₇	C₄	1	2	yes	—
18	C₈×D₄×C₄₇	C₄	1	4	yes	—
19	C₄₇×#433	C₄	1	4	yes	—
20	C₄₇×#431	C₂²	1	2	yes	—
21	C₄₇×#431	C₂²	1	2	yes	—
22	C₄₇×#431	C₂²	1	1	yes	characteristic
23	C₄₇×#431	C₂²	1	2	yes	—
24	C₄₇×#431	C₂²	1	1	yes	characteristic
25	C₄₇×#431	C₂²	1	2	yes	—
26	C₄₇×#424	C₄	1	2	yes	—
27	C₄₇×#408	C₄	1	2	yes	—
28	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
29	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
34	C₄₇×#322	C₂²	1	2	yes	—
35	C₄₇×#322	C₂²	1	2	yes	—
36	C₄₇×#322	C₂²	1	2	yes	—
37	C₄₇×#322	C₂²	1	2	yes	—
38	C₄₇×#322	C₂²	1	2	yes	—
39	C₈²×C₄₇	C₂²	1	1	yes	characteristic
40	C₈²×C₄₇	C₂²	1	1	yes	characteristic
41	C₈²×C₄₇	C₂²	1	1	yes	characteristic
42	C₈²×C₄₇	C₂²	1	1	yes	characteristic
43	C₈²×C₄₇	C₂²	1	2	yes	—
44	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
46	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
48	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
51	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
54	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
56	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
57	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
58	#117×C₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
61	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
62	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
63	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
64	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
65	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
66	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
67	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
68	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
69	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
70	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
71	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
72	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
73	#97×C₄₇	C₂×C₄	1	2	yes	—
74	#97×C₄₇	C₂×C₄	1	4	yes	—
75	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
76	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
78	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
79	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₄₇	C₂³	1	2	yes	—
85	C₄×C₈×C₄₇	C₂³	1	2	yes	—
86	C₄×C₈×C₄₇	C₂³	1	2	yes	—
87	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	#41×C₄₇	—	2	4	no	—
89	C₂×Q₈×C₄₇	C₄²	1	1	yes	characteristic
90	C₂×D₄×C₄₇	C₄²	1	2	yes	—
91	C₂×D₄×C₄₇	C₄²	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	M₁₆×C₄₇	—	2	4	no	—
99	M₁₆×C₄₇	—	2	8	no	—
100	C₂×C₈×C₄₇	—	2	4	no	—
101	C₂×C₈×C₄₇	—	2	4	no	—
102	C₂×C₈×C₄₇	—	2	8	no	—
103	C₂×C₈×C₄₇	—	2	4	no	—
104	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
110	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
111	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
113	C₄⋊C₄×C₄₇	C₄²	1	2	yes	—
114	C₄⋊C₄×C₄₇	C₄²	1	2	yes	—
115	C₄⋊C₄×C₄₇	C₄²	1	1	yes	characteristic
116	C₄⋊C₄×C₄₇	C₄²	1	1	yes	characteristic
117	C₂²⋊C₄×C₄₇	C₄²	1	2	yes	—
118	C₂²⋊C₄×C₄₇	C₄²	1	2	yes	—
119	C₂²⋊C₄×C₄₇	C₄²	1	2	yes	—
120	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
121	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
122	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
125	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
128	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
129	Q₈×C₄₇	—	2	2	no	—
130	D₄×C₄₇	—	2	4	no	—
131	D₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
138	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
142	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₄₇	#131	1	4	yes	—
144	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₈×C₄₇	—	2	2	no	—
148	C₈×C₄₇	—	2	2	no	—
149	C₈×C₄₇	—	2	2	no	—
150	C₈×C₄₇	—	2	4	no	—
151	C₈×C₄₇	—	2	2	no	—
152	C₈×C₄₇	—	2	4	no	—
153	C₈×C₄₇	—	2	4	no	—
154	C₈×C₄₇	#131	1	4	yes	—
155	C₈×C₄₇	#131	1	4	yes	—
156	#17328	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂²×C₄₇	—	2	1	no	—
158	C₂²×C₄₇	—	2	1	no	—
159	C₂²×C₄₇	—	2	2	no	—
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	#405	1	2	yes	—
163	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
164	C₄×C₄₇	—	2	2	no	—
165	C₄×C₄₇	—	2	1	no	—
166	C₄×C₄₇	—	2	1	no	—
167	C₄×C₄₇	—	2	2	no	—
168	C₄×C₄₇	—	2	2	no	—
169	C₄×C₄₇	#405	1	2	yes	—
170	C₄×C₄₇	C₂×#131	1	2	yes	—
171	C₄×C₄₇	C₂×#131	1	2	yes	—
172	C₄×C₄₇	C₂×#131	1	2	yes	—
173	#2965	C₂×C₄₇	1	1	yes	characteristic
174	C₈×#41	C₂×C₄₇	1	1	yes	characteristic
175	#2922	C₂×C₄₇	1	1	yes	characteristic
176	#1454	C₂×C₄₇	1	2	yes	complemented
177	#1453	C₂×C₄₇	1	2	yes	complemented
178	#1452	C₂×C₄₇	1	1	yes	characteristic, complemented
179	#1451	C₂×C₄₇	1	1	yes	characteristic, complemented
180	#1450	C₂×C₄₇	1	2	yes	complemented
181	C₈×M₁₆	C₂×C₄₇	1	2	yes	complemented
182	C₈×M₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
183	C₂×C₈²	C₂×C₄₇	1	1	yes	characteristic, complemented
184	C₂×C₄₇	—	2	2	no	—
185	C₂×C₄₇	—	4	2	no	—
186	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
187	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
188	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
189	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
190	#446	C₄×C₄₇	1	2	yes	—
191	C₈×Q₈	C₄×C₄₇	1	2	yes	—
192	#436	C₄×C₄₇	1	2	yes	—
193	#435	C₄×C₄₇	1	4	yes	—
194	C₈×D₄	C₄×C₄₇	1	2	yes	—
195	C₈×D₄	C₄×C₄₇	1	4	yes	—
196	#433	C₄×C₄₇	1	4	yes	—
197	#431	C₂²×C₄₇	1	2	yes	—
198	#431	C₂²×C₄₇	1	2	yes	—
199	#431	C₂²×C₄₇	1	1	yes	characteristic
200	#431	C₂²×C₄₇	1	2	yes	—
201	#431	C₂²×C₄₇	1	1	yes	characteristic
202	#431	C₂²×C₄₇	1	2	yes	—
203	#424	C₄×C₄₇	1	2	yes	—
204	#408	C₄×C₄₇	1	2	yes	—
205	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
206	C₄×M₁₆	C₂²×C₄₇	1	2	yes	—
207	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
208	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
209	C₂×C₄×C₈	C₂²×C₄₇	1	2	yes	—
210	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
211	#322	C₂²×C₄₇	1	2	yes	—
212	#322	C₂²×C₄₇	1	2	yes	—
213	#322	C₂²×C₄₇	1	2	yes	—
214	#322	C₂²×C₄₇	1	2	yes	—
215	#322	C₂²×C₄₇	1	2	yes	—
216	C₈²	C₂²×C₄₇	1	1	yes	characteristic
217	C₈²	C₂²×C₄₇	1	1	yes	characteristic
218	C₈²	C₂²×C₄₇	1	1	yes	characteristic
219	C₈²	C₂²×C₄₇	1	1	yes	characteristic
220	C₈²	C₂²×C₄₇	1	2	yes	—
221	C₄₇	#17328	1	1	yes	characteristic, direct product factor, Sylow
222	C₂×#41	C₂×C₄×C₄₇	1	1	yes	characteristic
223	C₂×M₁₆	C₂×C₄×C₄₇	1	2	yes	—
224	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
225	C₂²×C₈	C₂×C₄×C₄₇	1	2	yes	—
226	C₂²×C₈	C₂×C₄×C₄₇	1	2	yes	—
227	C₂²×C₈	C₂×C₄×C₄₇	1	4	yes	—
228	C₂²×C₈	C₂×C₄×C₄₇	1	2	yes	—
229	C₄×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
230	C₄×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
231	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
232	C₄×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
233	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
234	C₄×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
235	#117	C₂×C₄×C₄₇	1	1	yes	characteristic
236	#117	C₂×C₄×C₄₇	1	2	yes	—
237	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
238	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
239	C₄⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
240	C₄⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
241	C₄⋊C₈	C₂×C₄×C₄₇	1	2	yes	—
242	C₄⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
243	C₄⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
244	C₄⋊C₈	C₂×C₄×C₄₇	1	2	yes	—
245	C₂²⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
246	C₂²⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
247	C₂²⋊C₈	C₂×C₄×C₄₇	1	2	yes	—
248	C₂²⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
249	C₂²⋊C₈	C₂×C₄×C₄₇	1	2	yes	—
250	C₂²⋊C₈	C₂×C₄×C₄₇	1	4	yes	—
251	#97	C₂×C₄×C₄₇	1	2	yes	—
252	#97	C₂×C₄×C₄₇	1	4	yes	—
253	C₄×C₈	C₂×C₄×C₄₇	1	2	yes	—
254	C₄×C₈	C₂×C₄×C₄₇	1	2	yes	—
255	C₄×C₈	C₂×C₄×C₄₇	1	4	yes	—
256	C₄×C₈	C₂×C₄×C₄₇	1	2	yes	—
257	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
258	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
259	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
260	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
261	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₄₇	1	2	yes	—
264	C₄×C₈	C₂³×C₄₇	1	2	yes	—
265	C₄×C₈	C₂³×C₄₇	1	2	yes	—
266	#41	—	2	4	no	—
267	C₂×Q₈	C₄²×C₄₇	1	1	yes	characteristic
268	C₂×D₄	C₄²×C₄₇	1	2	yes	—
269	C₂×D₄	C₄²×C₄₇	1	1	yes	characteristic
270	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
272	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
276	M₁₆	—	2	4	no	—
277	M₁₆	—	2	8	no	—
278	C₂×C₈	—	2	4	no	—
279	C₂×C₈	—	2	4	no	—
280	C₂×C₈	—	2	8	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
283	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
284	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
285	C₂×C₈	C₂²×C₄×C₄₇	1	4	yes	—
286	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
287	C₂×C₈	C₂²×C₄×C₄₇	1	4	yes	—
288	C₂×C₈	C₂²×C₄×C₄₇	1	4	yes	—
289	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
290	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
291	C₄⋊C₄	C₄²×C₄₇	1	2	yes	—
292	C₄⋊C₄	C₄²×C₄₇	1	2	yes	—
293	C₄⋊C₄	C₄²×C₄₇	1	1	yes	characteristic
294	C₄⋊C₄	C₄²×C₄₇	1	1	yes	characteristic
295	C₂²⋊C₄	C₄²×C₄₇	1	2	yes	—
296	C₂²⋊C₄	C₄²×C₄₇	1	2	yes	—
297	C₂²⋊C₄	C₄²×C₄₇	1	2	yes	—
298	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
299	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
300	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
301	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
302	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
303	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
304	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
305	C₂³	C₂×C₄²×C₄₇	1	2	yes	—
306	C₂³	C₂×C₄²×C₄₇	1	1	yes	characteristic
307	Q₈	—	2	2	no	—
308	D₄	—	2	4	no	—
309	D₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	C₂×C₄²×C₄₇	1	1	yes	characteristic
316	C₂×C₄	C₂×C₄²×C₄₇	1	1	yes	characteristic
317	C₂×C₄	C₂×C₄²×C₄₇	1	2	yes	—
318	C₂×C₄	C₂×C₄²×C₄₇	1	2	yes	—
319	C₂×C₄	C₂×C₄²×C₄₇	1	2	yes	—
320	C₂×C₄	C₂×C₄²×C₄₇	1	1	yes	characteristic
321	C₂×C₄	#131×C₄₇	1	4	yes	—
322	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
323	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
324	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
325	C₈	—	2	2	no	—
326	C₈	—	2	2	no	—
327	C₈	—	2	2	no	—
328	C₈	—	2	4	no	—
329	C₈	—	2	2	no	—
330	C₈	—	2	4	no	—
331	C₈	—	2	4	no	—
332	C₈	#131×C₄₇	1	4	yes	—
333	C₈	#131×C₄₇	1	4	yes	—
334	C₂²	—	2	1	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	2	no	—
339	C₂²	C₄₇×#405	1	2	yes	—
340	C₂²	C₂²×C₄²×C₄₇	1	1	yes	characteristic
341	C₄	—	2	2	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	2	no	—
346	C₄	C₄₇×#405	1	2	yes	—
347	C₄	C₂×#131×C₄₇	1	2	yes	—
348	C₄	C₂×#131×C₄₇	1	2	yes	—
349	C₄	C₂×#131×C₄₇	1	2	yes	—
350	C₂	—	2	2	no	—
351	C₂	—	4	2	no	—
352	C₂	C₂×C₄₇×#405	1	1	yes	characteristic
353	C₂	C₄×#131×C₄₇	1	1	yes	characteristic
354	C₂	C₄×#131×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈×C₄₇	C₂³
commutator	C₂²	C₂²×C₄²×C₄₇
Frattini, cosocle	C₄²	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂²×C₄²
prime radical	C₂×#41×C₄₇	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₇×#1454	C₂	semidirect
5. C₄₇×#1453	C₂	semidirect
6. C₄₇×#1452	C₂	semidirect
7. C₄₇×#1451	C₂	semidirect
8. C₄₇×#1450	C₂	semidirect
9. C₈×M₁₆×C₄₇	C₂	semidirect
10. C₈×M₁₆×C₄₇	C₂	semidirect
11. C₂×C₈²×C₄₇	C₂	semidirect
156. #17328	C₄₇	direct (N × H)
176. #1454	C₂×C₄₇	semidirect
177. #1453	C₂×C₄₇	semidirect
178. #1452	C₂×C₄₇	semidirect
179. #1451	C₂×C₄₇	semidirect
180. #1450	C₂×C₄₇	semidirect
181. C₈×M₁₆	C₂×C₄₇	semidirect
182. C₈×M₁₆	C₂×C₄₇	semidirect
183. C₂×C₈²	C₂×C₄₇	semidirect
221. C₄₇	#17328	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#2965	2
C₈×#41×C₄₇	2
C₄₇×#2922	2
C₄₇×#1454	2
C₄₇×#1453	2
C₄₇×#1452	2
C₄₇×#1451	2
C₄₇×#1450	2
C₈×M₁₆×C₄₇	2
C₂×C₈²×C₄₇	2
#17328	47

Subgroups — C47×#17328 #26057026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17328 #26057026