Subgroups — C₄₇×#22702 #26062400

Order 12032.

888 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#435	C₂	1	2	yes	maximal
2	C₄₇×#2293	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#1940	C₂	1	2	yes	maximal, complemented
4	C₄₇×#1851	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1850	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1798	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1729	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
11	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
12	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₄₇	C₂²	1	2	yes	—
14	C₄₇×#435	—	2	8	no	—
15	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
20	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
21	C₂×#97×C₄₇	C₂²	1	2	yes	—
22	C₄₇×#390	C₄	1	1	yes	characteristic
23	C₄₇×#390	C₄	1	1	yes	characteristic
24	C₄₇×#389	C₄	1	1	yes	characteristic
25	C₄₇×#389	C₄	1	1	yes	characteristic
26	C₄₇×#388	C₄	1	2	yes	—
27	C₄₇×#388	C₄	1	2	yes	—
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
30	C₄³×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#336	C₂²	1	1	yes	characteristic
32	C₄₇×#336	C₂²	1	1	yes	characteristic
33	C₄₇×#336	C₂²	1	2	yes	—
34	C₄₇×#336	C₂²	1	1	yes	characteristic
35	C₄₇×#336	C₂²	1	1	yes	characteristic
36	C₄₇×#336	C₂²	1	2	yes	—
37	C₄₇×#336	C₂²	1	2	yes	—
38	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
40	C₂×M₁₆×C₄₇	—	2	4	no	—
41	C₂×M₁₆×C₄₇	—	2	4	no	—
42	C₂×M₁₆×C₄₇	—	4	2	no	—
43	C₂²×C₈×C₄₇	—	2	4	no	—
44	C₂²×C₈×C₄₇	—	2	4	no	—
45	C₂²×C₈×C₄₇	—	4	2	no	—
46	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
50	C₄×D₄×C₄₇	D₄	1	4	yes	—
51	C₄×D₄×C₄₇	Q₈	1	4	yes	—
52	#117×C₄₇	—	4	2	no	—
53	#117×C₄₇	—	4	2	no	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₄₇	—	2	4	no	—
73	C₄⋊C₈×C₄₇	—	2	4	no	—
74	C₄⋊C₈×C₄₇	—	4	2	no	—
75	C₄⋊C₈×C₄₇	—	4	2	no	—
76	C₂²⋊C₈×C₄₇	—	2	4	no	—
77	C₂²⋊C₈×C₄₇	—	2	4	no	—
78	#97×C₄₇	—	2	4	no	—
79	#95×C₄₇	C₂×C₄	1	2	yes	—
80	#95×C₄₇	C₂×C₄	1	2	yes	—
81	#95×C₄₇	C₂×C₄	1	2	yes	—
82	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
83	C₂×D₄×C₄₇	—	4	1	no	—
84	C₂×D₄×C₄₇	—	4	1	no	—
85	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	M₁₆×C₄₇	—	4	8	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	4	8	no	—
115	C₂×C₈×C₄₇	#41	1	4	yes	—
116	C₄⋊C₄×C₄₇	—	4	1	no	—
117	C₄⋊C₄×C₄₇	—	4	1	no	—
118	C₄⋊C₄×C₄₇	—	4	2	no	—
119	C₄⋊C₄×C₄₇	—	4	2	no	—
120	C₄⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	—
121	C₂²⋊C₄×C₄₇	—	2	4	no	—
122	C₂²⋊C₄×C₄₇	—	4	2	no	—
123	C₂²⋊C₄×C₄₇	—	4	2	no	—
124	C₂²⋊C₄×C₄₇	—	4	2	no	—
125	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	4	1	no	—
132	C₄²×C₄₇	—	4	1	no	—
133	C₄²×C₄₇	—	4	1	no	—
134	C₄²×C₄₇	C₂×D₄	1	2	yes	—
135	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	—	2	2	no	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
143	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
144	D₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
175	C₂×C₄×C₄₇	#131	1	2	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
179	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
180	C₈×C₄₇	—	2	4	no	—
181	C₈×C₄₇	—	4	2	no	—
182	C₈×C₄₇	—	4	2	no	—
183	C₈×C₄₇	—	4	2	no	—
184	#22702	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	—	2	4	no	—
187	C₂²×C₄₇	—	2	4	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	4	2	no	—
192	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
194	C₂²×C₄₇	#518	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
196	C₂²×C₄₇	#568	1	1	yes	characteristic
197	C₂²×C₄₇	#568	1	1	yes	characteristic
198	C₂²×C₄₇	#568	1	1	yes	characteristic
199	C₄×C₄₇	—	2	4	no	—
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	2	2	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	4	1	no	—
204	C₄×C₄₇	—	4	1	no	—
205	C₄×C₄₇	—	4	2	no	—
206	C₄×C₄₇	—	4	1	no	—
207	C₄×C₄₇	—	4	2	no	—
208	C₄×C₄₇	#546	1	2	yes	—
209	C₄×C₄₇	#554	1	2	yes	—
210	C₂×#435	C₂×C₄₇	1	2	yes	—
211	#2293	C₂×C₄₇	1	1	yes	characteristic
212	#1940	C₂×C₄₇	1	2	yes	complemented
213	#1851	C₂×C₄₇	1	2	yes	complemented
214	#1850	C₂×C₄₇	1	2	yes	complemented
215	#1831	C₂×C₄₇	1	1	yes	characteristic, complemented
216	#1798	C₂×C₄₇	1	2	yes	complemented
217	#1767	C₂×C₄₇	1	1	yes	characteristic, complemented
218	#1729	C₂×C₄₇	1	2	yes	complemented
219	C₂×C₄₇	—	4	4	no	—
220	C₂×C₄₇	#2349	1	1	yes	characteristic
221	C₂×C₄₇	#2905	1	1	yes	characteristic
222	C₂×C₄₇	#2906	1	1	yes	characteristic
223	C₂×C₄₇	#2967	1	1	yes	characteristic
224	C₂×C₄₇	#2968	1	1	yes	characteristic
225	C₂×C₄₇	#2980	1	1	yes	characteristic
226	C₂×C₄₇	#2981	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
228	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
229	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
230	C₂×#117	C₂²×C₄₇	1	2	yes	—
231	#435	—	2	8	no	—
232	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
233	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
234	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
235	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
236	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
237	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
238	C₂×#97	C₂²×C₄₇	1	2	yes	—
239	#390	C₄×C₄₇	1	1	yes	characteristic
240	#390	C₄×C₄₇	1	1	yes	characteristic
241	#389	C₄×C₄₇	1	1	yes	characteristic
242	#389	C₄×C₄₇	1	1	yes	characteristic
243	#388	C₄×C₄₇	1	2	yes	—
244	#388	C₄×C₄₇	1	2	yes	—
245	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
246	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
247	C₄³	C₂²×C₄₇	1	1	yes	characteristic
248	#336	C₂²×C₄₇	1	1	yes	characteristic
249	#336	C₂²×C₄₇	1	2	yes	—
250	#336	C₂²×C₄₇	1	1	yes	characteristic
251	#336	C₂²×C₄₇	1	1	yes	characteristic
252	#336	C₂²×C₄₇	1	2	yes	—
253	#336	C₂²×C₄₇	1	2	yes	—
254	#336	C₂²×C₄₇	1	1	yes	characteristic
255	C₄₇	#22702	1	1	yes	characteristic, direct product factor, Sylow
256	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
258	C₂×M₁₆	—	2	4	no	—
259	C₂×M₁₆	—	2	4	no	—
260	C₂×M₁₆	—	4	2	no	—
261	C₂²×C₈	—	2	4	no	—
262	C₂²×C₈	—	2	4	no	—
263	C₂²×C₈	—	4	2	no	—
264	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
265	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
266	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
267	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
268	C₄×D₄	D₄×C₄₇	1	4	yes	—
269	C₄×D₄	Q₈×C₄₇	1	4	yes	—
270	#117	—	4	2	no	—
271	#117	—	4	2	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
273	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
274	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
278	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
280	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
282	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
283	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
284	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
285	C₂×C₄²	C₂×C₄×C₄₇	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
288	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
290	C₄⋊C₈	—	2	4	no	—
291	C₄⋊C₈	—	2	4	no	—
292	C₄⋊C₈	—	4	2	no	—
293	C₄⋊C₈	—	4	2	no	—
294	C₂²⋊C₈	—	2	4	no	—
295	C₂²⋊C₈	—	2	4	no	—
296	#97	—	2	4	no	—
297	#95	C₂×C₄×C₄₇	1	2	yes	—
298	#95	C₂×C₄×C₄₇	1	2	yes	—
299	#95	C₂×C₄×C₄₇	1	2	yes	—
300	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	C₄⋊C₄×C₄₇	1	4	yes	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
311	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
312	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
318	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
319	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
320	M₁₆	—	4	8	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	8	no	—
333	C₂×C₈	#41×C₄₇	1	4	yes	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	C₄⋊C₄×C₄₇	1	4	yes	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	4	2	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	C₄⋊C₄×C₄₇	1	8	yes	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	4	1	no	—
350	C₄²	—	4	1	no	—
351	C₄²	—	4	1	no	—
352	C₄²	C₂×D₄×C₄₇	1	2	yes	—
353	C₄²	C₂×Q₈×C₄₇	1	2	yes	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
361	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
362	D₄	—	4	4	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
391	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	2	yes	—
392	C₂×C₄	C₂×C₄⋊C₄×C₄₇	1	4	yes	—
393	C₂×C₄	#131×C₄₇	1	2	yes	—
394	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
395	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
397	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
398	C₈	—	2	4	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	C₂²×C₄⋊C₄×C₄₇	1	1	yes	characteristic
410	C₂²	C₄×#41×C₄₇	1	1	yes	characteristic
411	C₂²	C₄₇×#518	1	1	yes	characteristic
412	C₂²	C₂×#131×C₄₇	1	1	yes	characteristic
413	C₂²	C₄₇×#568	1	1	yes	characteristic
414	C₂²	C₄₇×#568	1	1	yes	characteristic
415	C₂²	C₄₇×#568	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	4	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	1	no	—
424	C₄	—	4	2	no	—
425	C₄	C₄₇×#546	1	2	yes	—
426	C₄	C₄₇×#554	1	2	yes	—
427	C₂	—	4	4	no	—
428	C₂	C₄₇×#2349	1	1	yes	characteristic
429	C₂	C₄₇×#2905	1	1	yes	characteristic
430	C₂	C₄₇×#2906	1	1	yes	characteristic
431	C₂	C₄₇×#2967	1	1	yes	characteristic
432	C₂	C₄₇×#2968	1	1	yes	characteristic
433	C₂	C₄₇×#2980	1	1	yes	characteristic
434	C₂	C₄₇×#2981	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₄₇×#1940	C₂	semidirect
4. C₄₇×#1851	C₂	semidirect
5. C₄₇×#1850	C₂	semidirect
6. C₄₇×#1831	C₂	semidirect
7. C₄₇×#1798	C₂	semidirect
8. C₄₇×#1767	C₂	semidirect
9. C₄₇×#1729	C₂	semidirect
184. #22702	C₄₇	direct (N × H)
212. #1940	C₂×C₄₇	semidirect
213. #1851	C₂×C₄₇	semidirect
214. #1850	C₂×C₄₇	semidirect
215. #1831	C₂×C₄₇	semidirect
216. #1798	C₂×C₄₇	semidirect
217. #1767	C₂×C₄₇	semidirect
218. #1729	C₂×C₄₇	semidirect
255. C₄₇	#22702	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×#435	2
C₄₇×#2293	2
C₄₇×#1940	2
C₄₇×#1851	2
C₄₇×#1850	2
C₄₇×#1831	2
C₄₇×#1798	2
C₄₇×#1767	2
C₄₇×#1729	2
#22702	47

Subgroups — C47×#22702 #26062400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#22702 #26062400