Subgroups — C₄₇×#60310 #26100008

Order 12032.

1914 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3459	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2994	C₂	1	4	yes	maximal, complemented
3	C₄₇×#2992	C₂	1	2	yes	maximal, complemented
4	C₄₇×#2977	C₂	1	4	yes	maximal, complemented
5	C₄₇×#2976	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2973	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#2972	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2968	C₂	1	4	yes	maximal, complemented
9	C₄₇×#2966	C₂	1	2	yes	maximal, complemented
10	C₄₇×#2933	C₂	1	4	yes	maximal, complemented
11	C₄₇×#2929	C₂	1	2	yes	maximal, complemented
12	C₂×C₄₇×#435	C₂	1	2	yes	maximal, complemented
13	C₂×C₈×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#131×C₄₇	C₂²	1	2	yes	complemented
15	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	complemented
16	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
18	C₄₇×#543	C₄	1	1	yes	characteristic
19	C₄₇×#539	C₄	1	2	yes	—
20	C₄₇×#539	C₄	1	4	yes	—
21	C₄₇×#538	C₄	1	2	yes	—
22	C₄₇×#538	C₄	1	4	yes	—
23	C₄₇×#534	C₄	1	1	yes	characteristic
24	C₄₇×#534	C₄	1	2	yes	—
25	C₄₇×#529	C₂²	1	2	yes	—
26	C₄₇×#529	C₂²	1	4	yes	—
27	C₄₇×#525	C₂²	1	2	yes	—
28	C₄₇×#525	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
31	C₄₇×#446	C₂²	1	2	yes	complemented
32	C₄₇×#446	C₂²	1	4	yes	complemented
33	C₈×Q₈×C₄₇	C₂²	1	2	yes	complemented
34	C₄₇×#436	C₂²	1	2	yes	complemented
35	C₄₇×#436	C₂²	1	4	yes	complemented
36	C₄₇×#435	C₂²	1	4	yes	complemented
37	C₄₇×#435	C₂²	1	4	yes	complemented
38	C₄₇×#435	C₂²	1	4	yes	complemented
39	C₄₇×#435	C₂²	1	4	yes	complemented
40	C₄₇×#435	C₂²	1	4	yes	complemented
41	C₄₇×#435	C₂²	1	4	yes	complemented
42	C₄₇×#435	C₂²	1	4	yes	complemented
43	C₄₇×#435	C₂²	1	4	yes	complemented
44	C₄₇×#435	C₂²	1	4	yes	complemented
45	C₈×D₄×C₄₇	C₂²	1	4	yes	complemented
46	C₈×D₄×C₄₇	C₂²	1	4	yes	complemented
47	C₈×D₄×C₄₇	C₂²	1	4	yes	complemented
48	C₈×D₄×C₄₇	C₂²	1	4	yes	complemented
49	C₈×D₄×C₄₇	C₂²	1	4	yes	complemented
50	C₈×D₄×C₄₇	C₂²	1	4	yes	complemented
51	C₈×D₄×C₄₇	C₂²	1	2	yes	complemented
52	C₈×D₄×C₄₇	C₂²	1	4	yes	complemented
53	C₄₇×#433	C₂²	1	4	yes	complemented
54	C₄₇×#433	C₂²	1	4	yes	complemented
55	C₄₇×#433	C₂²	1	4	yes	complemented
56	C₄₇×#432	C₂²	1	2	yes	complemented
57	C₄₇×#431	C₂²	1	4	yes	complemented
58	C₄₇×#424	C₂²	1	2	yes	complemented
59	C₄₇×#424	C₂²	1	4	yes	complemented
60	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	complemented
62	C₄₇×#408	C₂²	1	2	yes	complemented
63	C₄₇×#408	C₂²	1	4	yes	complemented
64	C₄₇×#407	C₂²	1	2	yes	complemented
65	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
67	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	complemented
69	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	complemented
70	C₄₇×#405	C₂²	1	2	yes	complemented
71	C₄₇×#405	C₂²	1	4	yes	complemented
72	C₂×#97×C₄₇	C₂²	1	2	yes	complemented
73	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
74	C₂×#41×C₄₇	C₂³	1	2	yes	—
75	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
77	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
80	#131×C₄₇	—	4	4	no	—
81	C₂×M₁₆×C₄₇	—	4	4	no	—
82	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
83	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
84	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
85	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
86	C₂²×C₈×C₄₇	—	4	2	no	—
87	C₂²×C₈×C₄₇	—	4	2	no	—
88	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
90	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
91	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
92	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
95	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
96	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
97	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
99	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
100	#126×C₄₇	C₂×C₄	1	4	yes	—
101	#126×C₄₇	C₂×C₄	1	4	yes	—
102	#126×C₄₇	C₂×C₄	1	4	yes	—
103	#125×C₄₇	C₂×C₄	1	2	yes	—
104	#125×C₄₇	C₂×C₄	1	4	yes	—
105	#124×C₄₇	C₂×C₄	1	2	yes	—
106	#124×C₄₇	C₂×C₄	1	4	yes	—
107	#123×C₄₇	C₂×C₄	1	4	yes	—
108	#123×C₄₇	C₂×C₄	1	4	yes	—
109	#123×C₄₇	C₂×C₄	1	4	yes	—
110	#123×C₄₇	C₂×C₄	1	4	yes	—
111	#123×C₄₇	C₂×C₄	1	4	yes	—
112	#123×C₄₇	C₂×C₄	1	4	yes	—
113	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
114	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
115	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
116	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
117	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
118	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
119	#121×C₄₇	C₂×C₄	1	2	yes	—
120	#121×C₄₇	C₂×C₄	1	4	yes	—
121	#121×C₄₇	C₂×C₄	1	2	yes	—
122	#121×C₄₇	C₂×C₄	1	4	yes	—
123	#121×C₄₇	C₂×C₄	1	2	yes	—
124	#121×C₄₇	C₂×C₄	1	4	yes	—
125	#120×C₄₇	C₂×C₄	1	4	yes	—
126	#120×C₄₇	C₂×C₄	1	4	yes	—
127	#120×C₄₇	C₂×C₄	1	4	yes	—
128	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
129	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
130	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
131	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
132	C₄×D₄×C₄₇	C₂³	1	4	yes	—
133	C₄×D₄×C₄₇	C₂³	1	4	yes	—
134	C₄×D₄×C₄₇	C₂³	1	4	yes	—
135	C₄×D₄×C₄₇	C₂³	1	4	yes	—
136	C₄×D₄×C₄₇	C₂³	1	2	yes	—
137	#117×C₄₇	C₂³	1	2	yes	—
138	#117×C₄₇	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
141	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
142	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
143	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
144	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
145	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
147	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
148	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
149	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
150	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
151	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
152	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
153	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
154	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
155	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
156	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
157	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
158	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
159	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
160	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
161	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
162	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
163	#97×C₄₇	C₂³	1	4	yes	—
164	#97×C₄₇	C₂³	1	4	yes	—
165	#97×C₄₇	C₂³	1	4	yes	—
166	C₄×C₈×C₄₇	C₂³	1	2	yes	—
167	C₄×C₈×C₄₇	C₂³	1	2	yes	—
168	C₄×C₈×C₄₇	C₂³	1	4	yes	—
169	C₄×C₈×C₄₇	C₂³	1	4	yes	—
170	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
171	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
172	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
173	#41×C₄₇	—	4	2	no	—
174	#41×C₄₇	—	4	2	no	—
175	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
176	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
177	C₂×D₄×C₄₇	—	2	4	no	—
178	C₂×D₄×C₄₇	—	2	8	no	—
179	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
180	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
181	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
182	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
183	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
184	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
185	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
186	C₂²×C₄×C₄₇	—	4	1	no	—
187	C₂²×C₄×C₄₇	—	4	1	no	—
188	C₂²×C₄×C₄₇	—	4	2	no	—
189	C₂²×C₄×C₄₇	—	4	1	no	—
190	C₂²×C₄×C₄₇	—	4	2	no	—
191	C₂²×C₄×C₄₇	—	4	1	no	—
192	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
194	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
196	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
198	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
200	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
202	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
203	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
206	M₁₆×C₄₇	—	2	8	no	—
207	M₁₆×C₄₇	—	4	4	no	—
208	M₁₆×C₄₇	—	4	2	no	—
209	M₁₆×C₄₇	—	4	2	no	—
210	C₂×C₈×C₄₇	—	2	2	no	—
211	C₂×C₈×C₄₇	—	2	4	no	—
212	C₂×C₈×C₄₇	—	2	4	no	—
213	C₂×C₈×C₄₇	—	4	1	no	—
214	C₂×C₈×C₄₇	—	4	2	no	—
215	C₂×C₈×C₄₇	—	4	2	no	—
216	C₂×C₈×C₄₇	—	4	1	no	—
217	C₂×C₈×C₄₇	—	4	1	no	—
218	C₂×C₈×C₄₇	—	4	4	no	—
219	C₂×C₈×C₄₇	—	4	2	no	—
220	C₂×C₈×C₄₇	—	4	2	no	—
221	C₂×C₈×C₄₇	—	4	4	no	—
222	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
223	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
224	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
225	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
226	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
227	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
228	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
229	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
230	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
231	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
232	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
233	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
234	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
235	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
236	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
237	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
238	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
239	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
240	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
241	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
242	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
243	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
244	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
245	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
246	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
247	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
248	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
249	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
250	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
251	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
252	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
253	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
254	C₄²×C₄₇	C₂⁴	1	2	yes	—
255	C₄²×C₄₇	C₂⁴	1	4	yes	—
256	C₂³×C₄₇	—	2	2	no	—
257	C₂³×C₄₇	—	2	4	no	—
258	C₂³×C₄₇	—	4	1	no	—
259	C₂³×C₄₇	—	4	1	no	—
260	C₂³×C₄₇	—	4	1	no	—
261	C₂³×C₄₇	—	4	1	no	—
262	C₂³×C₄₇	—	4	2	no	—
263	C₂³×C₄₇	—	4	2	no	—
264	C₂³×C₄₇	#131	1	4	yes	complemented
265	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
266	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
267	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
268	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
269	Q₈×C₄₇	—	4	2	no	—
270	Q₈×C₄₇	—	4	2	no	—
271	D₄×C₄₇	—	2	8	no	—
272	D₄×C₄₇	—	2	8	no	—
273	D₄×C₄₇	—	2	8	no	—
274	D₄×C₄₇	—	4	4	no	—
275	D₄×C₄₇	—	4	2	no	—
276	D₄×C₄₇	—	4	2	no	—
277	D₄×C₄₇	—	4	4	no	—
278	C₂×C₄×C₄₇	—	2	2	no	—
279	C₂×C₄×C₄₇	—	2	4	no	—
280	C₂×C₄×C₄₇	—	2	1	no	—
281	C₂×C₄×C₄₇	—	2	2	no	—
282	C₂×C₄×C₄₇	—	2	2	no	—
283	C₂×C₄×C₄₇	—	2	4	no	—
284	C₂×C₄×C₄₇	—	2	1	no	—
285	C₂×C₄×C₄₇	—	2	2	no	—
286	C₂×C₄×C₄₇	—	2	4	no	—
287	C₂×C₄×C₄₇	—	2	2	no	—
288	C₂×C₄×C₄₇	—	4	1	no	—
289	C₂×C₄×C₄₇	—	4	2	no	—
290	C₂×C₄×C₄₇	—	4	2	no	—
291	C₂×C₄×C₄₇	—	4	4	no	—
292	C₂×C₄×C₄₇	—	4	1	no	—
293	C₂×C₄×C₄₇	—	4	2	no	—
294	C₂×C₄×C₄₇	—	4	1	no	—
295	C₂×C₄×C₄₇	—	4	2	no	—
296	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
297	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
299	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
300	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
301	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
302	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
303	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
304	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
305	C₈×C₄₇	—	2	1	no	—
306	C₈×C₄₇	—	2	2	no	—
307	C₈×C₄₇	—	2	2	no	—
308	C₈×C₄₇	—	2	4	no	—
309	C₈×C₄₇	—	2	2	no	—
310	C₈×C₄₇	—	2	4	no	—
311	C₈×C₄₇	H(5,𝔽₂)	1	2	yes	—
312	#60310	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂²×C₄₇	—	2	1	no	—
314	C₂²×C₄₇	—	2	2	no	—
315	C₂²×C₄₇	—	2	1	no	—
316	C₂²×C₄₇	—	2	2	no	—
317	C₂²×C₄₇	—	2	2	no	—
318	C₂²×C₄₇	—	2	4	no	—
319	C₂²×C₄₇	—	2	2	no	—
320	C₂²×C₄₇	—	2	4	no	—
321	C₂²×C₄₇	—	2	2	no	—
322	C₂²×C₄₇	—	2	4	no	—
323	C₂²×C₄₇	—	4	4	no	—
324	C₂²×C₄₇	—	4	4	no	—
325	C₂²×C₄₇	—	8	4	no	—
326	C₂²×C₄₇	C₂×#131	1	2	yes	—
327	C₂²×C₄₇	C₂×#131	1	4	yes	—
328	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
329	C₄×C₄₇	—	2	1	no	—
330	C₄×C₄₇	—	2	2	no	—
331	C₄×C₄₇	—	2	2	no	—
332	C₄×C₄₇	—	2	4	no	—
333	C₄×C₄₇	—	2	2	no	—
334	C₄×C₄₇	—	2	4	no	—
335	C₄×C₄₇	—	2	2	no	—
336	C₄×C₄₇	—	2	4	no	—
337	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₄×C₄₇	#585	1	1	yes	characteristic
339	#3459	C₂×C₄₇	1	1	yes	characteristic
340	#2994	C₂×C₄₇	1	4	yes	complemented
341	#2992	C₂×C₄₇	1	2	yes	complemented
342	#2977	C₂×C₄₇	1	4	yes	complemented
343	#2976	C₂×C₄₇	1	2	yes	complemented
344	#2973	C₂×C₄₇	1	1	yes	characteristic, complemented
345	#2972	C₂×C₄₇	1	2	yes	complemented
346	#2968	C₂×C₄₇	1	4	yes	complemented
347	#2966	C₂×C₄₇	1	2	yes	complemented
348	#2933	C₂×C₄₇	1	4	yes	complemented
349	#2929	C₂×C₄₇	1	2	yes	complemented
350	C₂×#435	C₂×C₄₇	1	2	yes	complemented
351	C₂×C₈×D₄	C₂×C₄₇	1	1	yes	characteristic, complemented
352	C₂×C₄₇	—	2	2	no	—
353	C₂×C₄₇	—	2	4	no	—
354	C₂×C₄₇	—	4	2	no	—
355	C₂×C₄₇	—	4	4	no	—
356	C₂×C₄₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
357	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
358	C₂×C₄₇	#3573	1	1	yes	characteristic
359	C₂×#131	C₂²×C₄₇	1	2	yes	complemented
360	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	complemented
361	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
362	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
363	#543	C₄×C₄₇	1	1	yes	characteristic
364	#539	C₄×C₄₇	1	2	yes	—
365	#539	C₄×C₄₇	1	4	yes	—
366	#538	C₄×C₄₇	1	2	yes	—
367	#538	C₄×C₄₇	1	4	yes	—
368	#534	C₄×C₄₇	1	1	yes	characteristic
369	#534	C₄×C₄₇	1	2	yes	—
370	#529	C₂²×C₄₇	1	2	yes	—
371	#529	C₂²×C₄₇	1	4	yes	—
372	#525	C₂²×C₄₇	1	2	yes	—
373	#525	C₂²×C₄₇	1	4	yes	—
374	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
375	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
376	#446	C₂²×C₄₇	1	2	yes	complemented
377	#446	C₂²×C₄₇	1	4	yes	complemented
378	C₈×Q₈	C₂²×C₄₇	1	2	yes	complemented
379	#436	C₂²×C₄₇	1	2	yes	complemented
380	#436	C₂²×C₄₇	1	4	yes	complemented
381	#435	C₂²×C₄₇	1	4	yes	complemented
382	#435	C₂²×C₄₇	1	4	yes	complemented
383	#435	C₂²×C₄₇	1	4	yes	complemented
384	#435	C₂²×C₄₇	1	4	yes	complemented
385	#435	C₂²×C₄₇	1	4	yes	complemented
386	#435	C₂²×C₄₇	1	4	yes	complemented
387	#435	C₂²×C₄₇	1	4	yes	complemented
388	#435	C₂²×C₄₇	1	4	yes	complemented
389	#435	C₂²×C₄₇	1	4	yes	complemented
390	C₈×D₄	C₂²×C₄₇	1	4	yes	complemented
391	C₈×D₄	C₂²×C₄₇	1	4	yes	complemented
392	C₈×D₄	C₂²×C₄₇	1	4	yes	complemented
393	C₈×D₄	C₂²×C₄₇	1	4	yes	complemented
394	C₈×D₄	C₂²×C₄₇	1	4	yes	complemented
395	C₈×D₄	C₂²×C₄₇	1	4	yes	complemented
396	C₈×D₄	C₂²×C₄₇	1	2	yes	complemented
397	C₈×D₄	C₂²×C₄₇	1	4	yes	complemented
398	#433	C₂²×C₄₇	1	4	yes	complemented
399	#433	C₂²×C₄₇	1	4	yes	complemented
400	#433	C₂²×C₄₇	1	4	yes	complemented
401	#432	C₂²×C₄₇	1	2	yes	complemented
402	#431	C₂²×C₄₇	1	4	yes	complemented
403	#424	C₂²×C₄₇	1	2	yes	complemented
404	#424	C₂²×C₄₇	1	4	yes	complemented
405	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
406	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
407	#408	C₂²×C₄₇	1	2	yes	complemented
408	#408	C₂²×C₄₇	1	4	yes	complemented
409	#407	C₂²×C₄₇	1	2	yes	complemented
410	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
411	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
412	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
413	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	complemented
414	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	complemented
415	#405	C₂²×C₄₇	1	2	yes	complemented
416	#405	C₂²×C₄₇	1	4	yes	complemented
417	C₂×#97	C₂²×C₄₇	1	2	yes	complemented
418	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
419	C₄₇	#60310	1	1	yes	characteristic, direct product factor, Sylow
420	C₂×#41	C₂³×C₄₇	1	2	yes	—
421	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
422	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
423	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
426	#131	—	4	4	no	—
427	C₂×M₁₆	—	4	4	no	—
428	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
429	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
430	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
431	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
432	C₂²×C₈	—	4	2	no	—
433	C₂²×C₈	—	4	2	no	—
434	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
436	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
437	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
438	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
441	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
442	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
443	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
444	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
445	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
446	#126	C₂×C₄×C₄₇	1	4	yes	—
447	#126	C₂×C₄×C₄₇	1	4	yes	—
448	#126	C₂×C₄×C₄₇	1	4	yes	—
449	#125	C₂×C₄×C₄₇	1	2	yes	—
450	#125	C₂×C₄×C₄₇	1	4	yes	—
451	#124	C₂×C₄×C₄₇	1	2	yes	—
452	#124	C₂×C₄×C₄₇	1	4	yes	—
453	#123	C₂×C₄×C₄₇	1	4	yes	—
454	#123	C₂×C₄×C₄₇	1	4	yes	—
455	#123	C₂×C₄×C₄₇	1	4	yes	—
456	#123	C₂×C₄×C₄₇	1	4	yes	—
457	#123	C₂×C₄×C₄₇	1	4	yes	—
458	#123	C₂×C₄×C₄₇	1	4	yes	—
459	C₂²⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
460	C₂²⋊Q₈	C₂×C₄×C₄₇	1	4	yes	—
461	C₂²⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
462	C₂²⋊Q₈	C₂×C₄×C₄₇	1	4	yes	—
463	C₂²⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
464	C₂²⋊Q₈	C₂×C₄×C₄₇	1	4	yes	—
465	#121	C₂×C₄×C₄₇	1	2	yes	—
466	#121	C₂×C₄×C₄₇	1	4	yes	—
467	#121	C₂×C₄×C₄₇	1	2	yes	—
468	#121	C₂×C₄×C₄₇	1	4	yes	—
469	#121	C₂×C₄×C₄₇	1	2	yes	—
470	#121	C₂×C₄×C₄₇	1	4	yes	—
471	#120	C₂×C₄×C₄₇	1	4	yes	—
472	#120	C₂×C₄×C₄₇	1	4	yes	—
473	#120	C₂×C₄×C₄₇	1	4	yes	—
474	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
475	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	—
476	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	—
477	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	—
478	C₄×D₄	C₂³×C₄₇	1	4	yes	—
479	C₄×D₄	C₂³×C₄₇	1	4	yes	—
480	C₄×D₄	C₂³×C₄₇	1	4	yes	—
481	C₄×D₄	C₂³×C₄₇	1	4	yes	—
482	C₄×D₄	C₂³×C₄₇	1	2	yes	—
483	#117	C₂³×C₄₇	1	2	yes	—
484	#117	C₂³×C₄₇	1	4	yes	—
485	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
486	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
487	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
488	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
489	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
491	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
493	C₄⋊C₈	C₂³×C₄₇	1	4	yes	—
494	C₄⋊C₈	C₂³×C₄₇	1	4	yes	—
495	C₄⋊C₈	C₂³×C₄₇	1	4	yes	—
496	C₄⋊C₈	C₂³×C₄₇	1	4	yes	—
497	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
498	C₄⋊C₈	C₂³×C₄₇	1	4	yes	—
499	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
500	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
501	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
502	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
503	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
504	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
505	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
506	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
507	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
508	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
509	#97	C₂³×C₄₇	1	4	yes	—
510	#97	C₂³×C₄₇	1	4	yes	—
511	#97	C₂³×C₄₇	1	4	yes	—
512	C₄×C₈	C₂³×C₄₇	1	2	yes	—
513	C₄×C₈	C₂³×C₄₇	1	2	yes	—
514	C₄×C₈	C₂³×C₄₇	1	4	yes	—
515	C₄×C₈	C₂³×C₄₇	1	4	yes	—
516	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
517	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
518	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
519	#41	—	4	2	no	—
520	#41	—	4	2	no	—
521	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
522	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
523	C₂×D₄	—	2	4	no	—
524	C₂×D₄	—	2	8	no	—
525	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
526	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
527	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
528	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
529	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
530	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
531	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	—	4	1	no	—
534	C₂²×C₄	—	4	2	no	—
535	C₂²×C₄	—	4	1	no	—
536	C₂²×C₄	—	4	2	no	—
537	C₂²×C₄	—	4	1	no	—
538	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
539	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
540	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
541	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
542	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
543	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
544	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
545	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
546	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
547	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
548	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
549	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
551	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
552	M₁₆	—	2	8	no	—
553	M₁₆	—	4	4	no	—
554	M₁₆	—	4	2	no	—
555	M₁₆	—	4	2	no	—
556	C₂×C₈	—	2	2	no	—
557	C₂×C₈	—	2	4	no	—
558	C₂×C₈	—	2	4	no	—
559	C₂×C₈	—	4	1	no	—
560	C₂×C₈	—	4	2	no	—
561	C₂×C₈	—	4	2	no	—
562	C₂×C₈	—	4	1	no	—
563	C₂×C₈	—	4	1	no	—
564	C₂×C₈	—	4	4	no	—
565	C₂×C₈	—	4	2	no	—
566	C₂×C₈	—	4	2	no	—
567	C₂×C₈	—	4	4	no	—
568	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
569	C₂×C₈	C₂⁴×C₄₇	1	1	yes	characteristic
570	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
571	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
572	C₂×C₈	C₂⁴×C₄₇	1	4	yes	—
573	C₂×C₈	C₂⁴×C₄₇	1	2	yes	—
574	C₂×C₈	C₂⁴×C₄₇	1	1	yes	characteristic
575	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
576	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
577	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
578	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
579	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
580	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
581	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
582	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
583	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
584	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
585	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
586	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
587	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
588	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
589	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
590	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
591	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
592	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
593	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
594	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
595	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
596	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
597	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
598	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
599	C₄²	C₂²×C₄×C₄₇	1	4	yes	—
600	C₄²	C₂⁴×C₄₇	1	2	yes	—
601	C₄²	C₂⁴×C₄₇	1	4	yes	—
602	C₂³	—	2	2	no	—
603	C₂³	—	2	4	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	2	no	—
609	C₂³	—	4	2	no	—
610	C₂³	#131×C₄₇	1	4	yes	complemented
611	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
612	C₂³	C₂³×C₄×C₄₇	1	4	yes	—
613	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
614	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
615	Q₈	—	4	2	no	—
616	Q₈	—	4	2	no	—
617	D₄	—	2	8	no	—
618	D₄	—	2	8	no	—
619	D₄	—	2	8	no	—
620	D₄	—	4	4	no	—
621	D₄	—	4	2	no	—
622	D₄	—	4	2	no	—
623	D₄	—	4	4	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	2	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	4	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	2	no	—
642	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
643	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
644	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
645	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
646	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
647	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
648	C₂×C₄	C₂³×C₄×C₄₇	1	2	yes	—
649	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
650	C₂×C₄	C₂⁵×C₄₇	1	1	yes	characteristic
651	C₈	—	2	1	no	—
652	C₈	—	2	2	no	—
653	C₈	—	2	2	no	—
654	C₈	—	2	4	no	—
655	C₈	—	2	2	no	—
656	C₈	—	2	4	no	—
657	C₈	H(5,𝔽₂)×C₄₇	1	2	yes	—
658	C₂²	—	2	1	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	2	4	no	—
668	C₂²	—	4	4	no	—
669	C₂²	—	4	4	no	—
670	C₂²	—	8	4	no	—
671	C₂²	C₂×#131×C₄₇	1	2	yes	—
672	C₂²	C₂×#131×C₄₇	1	4	yes	—
673	C₂²	C₂⁴×C₄×C₄₇	1	1	yes	characteristic
674	C₄	—	2	2	no	—
675	C₄	—	2	4	no	—
676	C₄	—	2	2	no	—
677	C₄	—	2	4	no	—
678	C₄	—	2	1	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	4	no	—
682	C₄	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
683	C₄	C₄₇×#585	1	1	yes	characteristic
684	C₂	—	2	2	no	—
685	C₂	—	2	4	no	—
686	C₂	—	4	2	no	—
687	C₂	—	4	4	no	—
688	C₂	C₄×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
689	C₂	C₂²×#131×C₄₇	1	1	yes	characteristic
690	C₂	C₄₇×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₄₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₄₇
socle	C₂²×C₄₇	C₂⁴×C₄
prime radical	C₄₇×#3459	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2994	C₂	semidirect
3. C₄₇×#2992	C₂	semidirect
4. C₄₇×#2977	C₂	semidirect
5. C₄₇×#2976	C₂	semidirect
6. C₄₇×#2973	C₂	semidirect
7. C₄₇×#2972	C₂	semidirect
8. C₄₇×#2968	C₂	semidirect
9. C₄₇×#2966	C₂	semidirect
10. C₄₇×#2933	C₂	semidirect
11. C₄₇×#2929	C₂	semidirect
12. C₂×C₄₇×#435	C₂	semidirect
13. C₂×C₈×D₄×C₄₇	C₂	semidirect
14. C₂×#131×C₄₇	C₂²	semidirect
15. C₂²×M₁₆×C₄₇	C₂²	semidirect
17. C₂³×C₈×C₄₇	C₂²	semidirect
31. C₄₇×#446	C₂²	semidirect
32. C₄₇×#446	C₂²	semidirect
33. C₈×Q₈×C₄₇	C₂²	semidirect
34. C₄₇×#436	C₂²	semidirect
35. C₄₇×#436	C₂²	semidirect
36. C₄₇×#435	C₂²	semidirect
37. C₄₇×#435	C₂²	semidirect
38. C₄₇×#435	C₂²	semidirect
39. C₄₇×#435	C₂²	semidirect
40. C₄₇×#435	C₂²	semidirect
41. C₄₇×#435	C₂²	semidirect
42. C₄₇×#435	C₂²	semidirect
43. C₄₇×#435	C₂²	semidirect
44. C₄₇×#435	C₂²	semidirect
45. C₈×D₄×C₄₇	C₂²	semidirect
46. C₈×D₄×C₄₇	C₂²	semidirect
47. C₈×D₄×C₄₇	C₂²	semidirect
48. C₈×D₄×C₄₇	C₂²	semidirect
49. C₈×D₄×C₄₇	C₂²	semidirect
50. C₈×D₄×C₄₇	C₂²	semidirect
51. C₈×D₄×C₄₇	C₂²	semidirect
52. C₈×D₄×C₄₇	C₂²	semidirect
53. C₄₇×#433	C₂²	semidirect
54. C₄₇×#433	C₂²	semidirect
55. C₄₇×#433	C₂²	semidirect
56. C₄₇×#432	C₂²	semidirect
57. C₄₇×#431	C₂²	semidirect
58. C₄₇×#424	C₂²	semidirect
59. C₄₇×#424	C₂²	semidirect
60. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
61. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
62. C₄₇×#408	C₂²	semidirect
63. C₄₇×#408	C₂²	semidirect
64. C₄₇×#407	C₂²	semidirect
67. C₂×C₂²⋊C₈×C₄₇	C₂²	semidirect
68. C₂×C₂²⋊C₈×C₄₇	C₂²	semidirect
69. C₂×C₂²⋊C₈×C₄₇	C₂²	semidirect
70. C₄₇×#405	C₂²	semidirect
71. C₄₇×#405	C₂²	semidirect
72. C₂×#97×C₄₇	C₂²	semidirect
73. C₂×C₄×C₈×C₄₇	C₂²	semidirect
264. C₂³×C₄₇	#131	semidirect
312. #60310	C₄₇	direct (N × H)
340. #2994	C₂×C₄₇	semidirect
341. #2992	C₂×C₄₇	semidirect
342. #2977	C₂×C₄₇	semidirect
343. #2976	C₂×C₄₇	semidirect
344. #2973	C₂×C₄₇	semidirect
345. #2972	C₂×C₄₇	semidirect
346. #2968	C₂×C₄₇	semidirect
347. #2966	C₂×C₄₇	semidirect
348. #2933	C₂×C₄₇	semidirect
349. #2929	C₂×C₄₇	semidirect
350. C₂×#435	C₂×C₄₇	semidirect
351. C₂×C₈×D₄	C₂×C₄₇	semidirect
359. C₂×#131	C₂²×C₄₇	semidirect
360. C₂²×M₁₆	C₂²×C₄₇	semidirect
362. C₂³×C₈	C₂²×C₄₇	semidirect
376. #446	C₂²×C₄₇	semidirect
377. #446	C₂²×C₄₇	semidirect
378. C₈×Q₈	C₂²×C₄₇	semidirect
379. #436	C₂²×C₄₇	semidirect
380. #436	C₂²×C₄₇	semidirect
381. #435	C₂²×C₄₇	semidirect
382. #435	C₂²×C₄₇	semidirect
383. #435	C₂²×C₄₇	semidirect
384. #435	C₂²×C₄₇	semidirect
385. #435	C₂²×C₄₇	semidirect
386. #435	C₂²×C₄₇	semidirect
387. #435	C₂²×C₄₇	semidirect
388. #435	C₂²×C₄₇	semidirect
389. #435	C₂²×C₄₇	semidirect
390. C₈×D₄	C₂²×C₄₇	semidirect
391. C₈×D₄	C₂²×C₄₇	semidirect
392. C₈×D₄	C₂²×C₄₇	semidirect
393. C₈×D₄	C₂²×C₄₇	semidirect
394. C₈×D₄	C₂²×C₄₇	semidirect
395. C₈×D₄	C₂²×C₄₇	semidirect
396. C₈×D₄	C₂²×C₄₇	semidirect
397. C₈×D₄	C₂²×C₄₇	semidirect
398. #433	C₂²×C₄₇	semidirect
399. #433	C₂²×C₄₇	semidirect
400. #433	C₂²×C₄₇	semidirect
401. #432	C₂²×C₄₇	semidirect
402. #431	C₂²×C₄₇	semidirect
403. #424	C₂²×C₄₇	semidirect
404. #424	C₂²×C₄₇	semidirect
405. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
406. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
407. #408	C₂²×C₄₇	semidirect
408. #408	C₂²×C₄₇	semidirect
409. #407	C₂²×C₄₇	semidirect
412. C₂×C₂²⋊C₈	C₂²×C₄₇	semidirect
413. C₂×C₂²⋊C₈	C₂²×C₄₇	semidirect
414. C₂×C₂²⋊C₈	C₂²×C₄₇	semidirect
415. #405	C₂²×C₄₇	semidirect
416. #405	C₂²×C₄₇	semidirect
417. C₂×#97	C₂²×C₄₇	semidirect
418. C₂×C₄×C₈	C₂²×C₄₇	semidirect
419. C₄₇	#60310	direct (N × H)
610. C₂³	#131×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3459	2
C₄₇×#2994	2
C₄₇×#2992	2
C₄₇×#2977	2
C₄₇×#2976	2
C₄₇×#2973	2
C₄₇×#2972	2
C₄₇×#2968	2
C₄₇×#2966	2
C₄₇×#2933	2
C₄₇×#2929	2
C₂×C₄₇×#435	2
C₂×C₈×D₄×C₄₇	2
#60310	47

Subgroups — C47×#60310 #26100008

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#60310 #26100008