Subgroups — #26215211

Order 12032.

1118 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689195	C₂	1	2	yes	maximal
2	#20243263	C₂	1	2	yes	maximal, complemented
3	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243172	C₂	1	2	yes	maximal, complemented
5	C₂²⋊C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal, complemented
6	#20243150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243137	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243082	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688878	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄²×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
14	#15689195	C₄	1	16	yes	complemented
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×#13093935	C₂²	1	2	yes	—
19	C₂×#13093935	C₂²	1	2	yes	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
22	#15688878	C₂²	1	1	yes	characteristic
23	#15688878	C₂²	1	1	yes	characteristic
24	#15688878	C₂²	1	2	yes	—
25	#15688878	C₂²	1	2	yes	—
26	#15688878	C₂²	1	1	yes	characteristic
27	#15688878	C₂²	1	1	yes	characteristic
28	#15688878	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
30	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
34	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₄×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
36	C₄×C₂²⋊C₄×C₄₇	C₄	1	2	yes	—
37	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₄³×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#10625329	—	4	2	no	—
41	C₂×#10625329	—	4	2	no	—
42	C₂×#10625329	C₂×C₄	1	8	yes	complemented
43	C₂²×C₄₇⋊C₈	—	4	2	no	—
44	C₂²×C₄₇⋊C₈	—	4	2	no	—
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
51	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
52	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
53	#13093935	—	4	2	no	—
54	#13093935	C₂×C₄	1	8	yes	complemented
55	C₄×C₄₇⋊C₈	—	4	2	no	—
56	C₄×C₄₇⋊C₈	—	4	2	no	—
57	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
59	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
60	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₄₇	—	2	8	no	—
63	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
64	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₄₇	—	4	2	no	—
71	C₂×C₄²×C₄₇	—	4	2	no	—
72	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	#95×C₄₇	C₂×C₄	1	2	yes	—
82	#95×C₄₇	C₂×C₄	1	2	yes	—
83	#95×C₄₇	C₂×C₄	1	2	yes	—
84	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
85	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	C₄²	1	4	yes	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	2	1	no	—
92	C₂²×C₄×C₄₇	—	2	1	no	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	4	2	no	—
99	C₂²×C₄×C₄₇	—	4	2	no	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₄⋊C₄×C₄₇	—	2	4	no	—
112	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
113	C₂²⋊C₄×C₄₇	—	2	4	no	—
114	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
115	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
116	C₂²⋊C₄×C₄₇	M₁₆	1	8	yes	complemented
117	C₄²×C₄₇	—	2	4	no	—
118	C₄²×C₄₇	—	2	4	no	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	—	2	1	no	—
123	C₄²×C₄₇	—	2	1	no	—
124	C₄²×C₄₇	—	4	2	no	—
125	C₄²×C₄₇	—	4	2	no	—
126	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
127	#10625329	—	4	8	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	4	8	no	—
137	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
138	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
141	C₂³×C₄₇	—	2	1	no	—
142	C₂³×C₄₇	—	2	1	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	2	1	no	—
145	C₂³×C₄₇	—	2	1	no	—
146	C₂³×C₄₇	—	2	2	no	—
147	C₂³×C₄₇	—	2	2	no	—
148	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
149	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
150	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
151	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	D₄×C₄₇	—	2	8	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	2	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	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	—	2	4	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	—	4	8	no	—
173	C₂×C₄×C₄₇	—	4	8	no	—
174	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
175	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
176	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
177	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
178	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
179	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
180	C₂×C₄×C₄₇	#131	1	4	yes	—
181	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
182	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
183	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
185	C₄₇⋊C₈	—	2	4	no	—
186	C₄₇⋊C₈	—	2	4	no	—
187	C₄₇⋊C₈	—	2	4	no	—
188	C₄₇⋊C₈	—	2	4	no	—
189	#20559	—	47	1	no	maximal, Sylow
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	2	4	no	—
192	C₂²×C₄₇	—	2	4	no	—
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	4	2	no	—
198	C₂²×C₄₇	—	4	2	no	—
199	C₂²×C₄₇	C₄×M₁₆	1	4	yes	—
200	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
201	C₂²×C₄₇	#518	1	1	yes	characteristic
202	C₂²×C₄₇	#520	1	1	yes	characteristic
203	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
204	C₂²×C₄₇	C₂×#131	1	2	yes	—
205	C₄×C₄₇	—	2	2	no	—
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	2	4	no	—
208	C₄×C₄₇	—	2	4	no	—
209	C₄×C₄₇	—	2	4	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	4	2	no	—
213	C₄×C₄₇	#518	1	2	yes	—
214	C₄×C₄₇	#520	1	2	yes	—
215	C₂×#435	—	47	2	no	—
216	C₄²×D₄	D₄₇	1	1	yes	characteristic
217	#1771	—	47	2	no	—
218	C₄×C₄⋊C₈	—	47	1	no	—
219	#1753	—	47	2	no	—
220	C₈×C₂²⋊C₄	—	47	2	no	—
221	#1749	—	47	1	no	—
222	C₄×C₂²⋊C₈	—	47	1	no	—
223	#1745	—	47	1	no	—
224	#1728	—	47	1	no	—
225	C₂×#336	—	47	1	no	—
226	C₂×C₄₇	—	2	4	no	—
227	C₂×C₄₇	—	4	2	no	—
228	C₂×C₄₇	#2275	1	1	yes	characteristic
229	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
230	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
231	C₂×C₄₇	#2974	1	2	yes	—
232	C₂×C₄₇	#2990	1	2	yes	—
233	C₂²×M₁₆	—	47	2	no	—
234	C₂³×C₈	—	47	2	no	—
235	C₂×C₄×D₄	Dic₄₇	1	2	yes	—
236	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
237	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
238	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
239	#435	—	47	16	no	—
240	C₂×C₄⋊C₈	—	47	2	no	—
241	C₂×C₂²⋊C₈	—	47	2	no	—
242	C₂×C₂²⋊C₈	—	47	2	no	—
243	C₂×#97	—	47	2	no	—
244	C₂×#97	—	47	2	no	—
245	C₂×C₄×C₈	—	47	2	no	—
246	C₂×C₄×C₈	—	47	2	no	—
247	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	—
248	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
249	C₄×C₂²⋊C₄	Dic₄₇	1	2	yes	—
250	C₄×C₂²⋊C₄	Dic₄₇	1	2	yes	—
251	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
252	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
253	C₄³	C₂×D₄₇	1	1	yes	characteristic
254	#336	—	47	1	no	—
255	#336	—	47	1	no	—
256	#336	—	47	2	no	—
257	#336	—	47	1	no	—
258	#336	—	47	2	no	—
259	#336	—	47	1	no	—
260	#336	—	47	2	no	—
261	C₄₇	#20559	1	1	yes	characteristic, complemented, Sylow
262	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
263	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
264	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
265	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
266	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
267	C₂×M₁₆	—	47	8	no	—
268	C₂×M₁₆	—	188	2	no	—
269	C₂×M₁₆	—	188	2	no	—
270	C₂²×C₈	—	47	2	no	—
271	C₂²×C₈	—	47	2	no	—
272	C₂²×C₈	—	47	2	no	—
273	C₂²×C₈	—	47	2	no	—
274	C₂²×C₈	—	47	8	no	—
275	C₂²×C₈	—	188	2	no	—
276	C₂²×C₈	—	188	2	no	—
277	C₄×D₄	—	2	8	no	—
278	C₄×D₄	C₄×D₄₇	1	8	yes	—
279	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
280	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
285	C₂×C₄²	—	4	2	no	—
286	C₂×C₄²	—	4	2	no	—
287	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
288	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
289	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
290	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
291	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
292	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
293	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
296	C₄⋊C₈	—	47	8	no	—
297	C₂²⋊C₈	—	47	8	no	—
298	C₂²⋊C₈	—	47	8	no	—
299	#97	—	47	8	no	—
300	#97	—	188	2	no	—
301	C₄×C₈	—	188	2	no	—
302	C₄×C₈	—	188	2	no	—
303	#95	C₂×Dic₄₇	1	2	yes	—
304	#95	C₂×Dic₄₇	1	2	yes	—
305	#95	C₂×Dic₄₇	1	2	yes	—
306	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
307	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
323	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
324	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
325	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
328	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
329	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
330	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
331	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	M₁₆	—	188	8	no	—
334	C₂×C₈	—	47	4	no	—
335	C₂×C₈	—	47	4	no	—
336	C₂×C₈	—	47	4	no	—
337	C₂×C₈	—	47	4	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	—	94	2	no	—
343	C₂×C₈	—	94	2	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	94	2	no	—
346	C₂×C₈	—	188	8	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	#10625329	1	8	yes	complemented
351	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
352	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
353	C₄²	—	2	4	no	—
354	C₄²	—	2	4	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	4	2	no	—
361	C₄²	—	4	2	no	—
362	C₄²	C₂×C₄×D₄₇	1	4	yes	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	2	no	—
370	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
371	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
372	C₂³	C₂×#10625329	1	4	yes	—
373	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
374	D₄	—	2	8	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	8	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
397	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
398	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
399	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
400	C₂×C₄	C₂×#10625329	1	4	yes	—
401	C₂×C₄	C₂×#10625329	1	4	yes	—
402	C₂×C₄	#13094031	1	4	yes	—
403	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
404	C₂×C₄	#13094069	1	2	yes	—
405	C₂×C₄	#13094070	1	1	yes	characteristic
406	C₂×C₄	#13094071	1	1	yes	characteristic
407	C₈	—	94	4	no	—
408	C₈	—	94	4	no	—
409	C₈	—	94	4	no	—
410	C₈	—	94	4	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	C₄×#10625329	1	4	yes	—
421	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
422	C₂²	#15689598	1	1	yes	characteristic
423	C₂²	#15689606	1	1	yes	characteristic
424	C₂²	C₂²×#10625329	1	2	yes	—
425	C₂²	C₂×#13094031	1	2	yes	—
426	C₄	—	2	4	no	—
427	C₄	—	2	4	no	—
428	C₄	—	2	4	no	—
429	C₄	—	2	2	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	2	no	—
433	C₄	—	4	2	no	—
434	C₄	#15689595	1	2	yes	—
435	C₄	#15689602	1	2	yes	—
436	C₂	—	2	4	no	—
437	C₂	—	4	2	no	—
438	C₂	#20245749	1	1	yes	characteristic
439	C₂	C₂×C₄×#10625329	1	1	yes	characteristic
440	C₂	C₄×#13094031	1	1	yes	characteristic
441	C₂	#20252423	1	2	yes	—
442	C₂	#20252513	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄²×D₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄²×D₄	D₄₇
hypocenter	C₄₇	#20559
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄²×D₄

Complements

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

N	H ≅ G/N	type
2. #20243263	C₂	semidirect
3. C₄×C₄⋊(C₄₇⋊C₈)	C₂	semidirect
4. #20243172	C₂	semidirect
5. C₂²⋊C₄×C₄₇⋊C₈	C₂	semidirect
6. #20243150	C₂	semidirect
7. C₄×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
8. #20243137	C₂	semidirect
9. #20243082	C₂	semidirect
10. C₂×#15688878	C₂	semidirect
14. #15689195	C₄	semidirect
42. C₂×#10625329	C₂×C₄	semidirect
45. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
50. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
51. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
52. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
54. #13093935	C₂×C₄	semidirect
116. C₂²⋊C₄×C₄₇	M₁₆	semidirect
261. C₄₇	#20559	semidirect
350. C₂²⋊C₄	#10625329	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689195	2
#20243263	2
C₄×C₄⋊(C₄₇⋊C₈)	2
#20243172	2
C₂²⋊C₄×C₄₇⋊C₈	2
#20243150	2
C₄×C₂²⋊(C₄₇⋊C₈)	2
#20243137	2
#20243082	2
C₂×#15688878	2
C₄²×D₄×C₄₇	2
#20559	47