Subgroups — #26234065

Order 12032.

916 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20244105	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244103	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243947	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243946	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243944	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243367	C₂	1	1	yes	maximal, characteristic
8	#20243367	C₂	1	1	yes	maximal, characteristic
9	#20243365	C₂	1	1	yes	maximal, characteristic
10	C₈×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243249	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×(C₂×D₄₇)⋊C₈	C₂	1	1	yes	maximal, characteristic
13	#20243145	C₂	1	1	yes	maximal, characteristic
14	#20243145	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊C₄×D₄₇	C₄	1	1	yes	characteristic
17	C₂×C₄⋊C₄×D₄₇	C₄	1	1	yes	characteristic
18	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
36	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
37	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
40	#15688974	C₄	1	1	yes	characteristic
41	#15688974	C₄	1	1	yes	characteristic
42	#95×D₄₇	C₄	1	1	yes	characteristic
43	#95×D₄₇	C₄	1	1	yes	characteristic
44	#15688878	C₂²	1	1	yes	characteristic
45	#15688878	C₂²	1	1	yes	characteristic
46	#15688878	C₂²	1	1	yes	characteristic
47	#15688878	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
55	C₄₇×#336	C₂²	1	1	yes	characteristic
56	C₄₇×#336	C₂²	1	1	yes	characteristic
57	C₄₇×#336	C₂²	1	1	yes	characteristic
58	C₄₇×#336	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
66	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
76	C₄⋊C₄×D₄₇	—	2	4	no	—
77	C₄⋊C₄×D₄₇	C₈	1	8	yes	complemented
78	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
87	C₄²×D₄₇	—	2	2	no	—
88	C₄²×D₄₇	—	2	2	no	—
89	C₄²×D₄₇	—	4	1	no	—
90	C₄²×D₄₇	—	4	1	no	—
91	C₄²×D₄₇	—	4	1	no	—
92	C₄²×D₄₇	—	4	1	no	—
93	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
94	Dic₄₇⋊C₈	—	2	2	no	—
95	Dic₄₇⋊C₈	—	2	2	no	—
96	Dic₄₇⋊C₈	—	4	1	no	—
97	Dic₄₇⋊C₈	—	4	1	no	—
98	(C₂×D₄₇)⋊C₈	—	2	2	no	—
99	(C₂×D₄₇)⋊C₈	—	2	2	no	—
100	(C₂×D₄₇)⋊C₈	—	2	2	no	—
101	(C₂×D₄₇)⋊C₈	Q₈	1	4	yes	—
102	C₄×C₄₇⋊C₈	—	4	1	no	—
103	C₈×Dic₄₇	—	2	2	no	—
104	C₈×Dic₄₇	—	2	2	no	—
105	C₈×Dic₄₇	—	4	1	no	—
106	C₈×Dic₄₇	—	4	1	no	—
107	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
108	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
109	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
110	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
111	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
112	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
113	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₄₇	—	4	1	no	—
123	C₄×C₈×C₄₇	—	4	1	no	—
124	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
125	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
126	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
134	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄×D₄₇	—	2	1	no	—
142	C₂×C₄×D₄₇	—	2	1	no	—
143	C₂×C₄×D₄₇	—	2	1	no	—
144	C₂×C₄×D₄₇	—	2	1	no	—
145	C₂×C₄×D₄₇	—	2	2	no	—
146	C₂×C₄×D₄₇	—	2	2	no	—
147	C₂×C₄×D₄₇	—	2	2	no	—
148	C₂×C₄×D₄₇	—	2	2	no	—
149	C₂×C₄×D₄₇	—	2	2	no	—
150	C₂×C₄×D₄₇	—	2	2	no	—
151	C₂×C₄×D₄₇	—	2	2	no	—
152	C₂×C₄×D₄₇	—	2	2	no	—
153	C₂×C₄×D₄₇	—	4	1	no	—
154	C₂×C₄×D₄₇	—	4	1	no	—
155	C₂×C₄×D₄₇	—	4	1	no	—
156	C₂×C₄×D₄₇	—	4	1	no	—
157	C₂×C₄×D₄₇	—	4	1	no	—
158	C₂×C₄×D₄₇	—	4	1	no	—
159	C₂×C₄×D₄₇	—	4	1	no	—
160	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
161	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
162	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
163	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
164	C₂×C₄×D₄₇	#41	1	2	yes	—
165	C₂×C₈×C₄₇	—	2	1	no	—
166	C₂×C₈×C₄₇	—	2	1	no	—
167	C₂×C₈×C₄₇	—	2	1	no	—
168	C₂×C₈×C₄₇	—	2	1	no	—
169	C₂×C₈×C₄₇	—	2	1	no	—
170	C₂×C₈×C₄₇	—	2	1	no	—
171	C₂×C₈×C₄₇	—	2	1	no	—
172	C₂×C₈×C₄₇	—	2	1	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	—	2	1	no	—
176	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
177	C₄⋊C₄×C₄₇	—	2	2	no	—
178	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	—
179	C₄²×C₄₇	—	2	1	no	—
180	C₄²×C₄₇	—	2	1	no	—
181	C₄²×C₄₇	—	2	1	no	—
182	C₄²×C₄₇	—	2	1	no	—
183	C₄²×C₄₇	—	2	1	no	—
184	C₄²×C₄₇	—	2	1	no	—
185	C₄⋊Dic₄₇	—	2	2	no	—
186	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	—
187	Dic₄₇⋊C₄	—	2	2	no	—
188	Dic₄₇⋊C₄	C₂×C₈	1	4	yes	—
189	Dic₄₇⋊C₄	C₂×C₈	1	4	yes	—
190	Dic₄₇⋊C₄	M₁₆	1	4	yes	—
191	C₄×Dic₄₇	—	2	1	no	—
192	C₄×Dic₄₇	—	2	1	no	—
193	C₄×Dic₄₇	—	2	1	no	—
194	C₄×Dic₄₇	—	2	1	no	—
195	C₄×Dic₄₇	—	2	2	no	—
196	C₄×Dic₄₇	—	2	2	no	—
197	C₄×Dic₄₇	—	4	1	no	—
198	C₄×Dic₄₇	—	4	1	no	—
199	C₄×Dic₄₇	—	4	1	no	—
200	C₄×Dic₄₇	—	4	1	no	—
201	C₄×Dic₄₇	#41	1	2	yes	—
202	C₄×Dic₄₇	#41	1	2	yes	—
203	C₂×C₄₇⋊C₈	—	2	1	no	—
204	C₂×C₄₇⋊C₈	—	2	1	no	—
205	C₂×C₄₇⋊C₈	—	2	1	no	—
206	C₂×C₄₇⋊C₈	—	2	1	no	—
207	C₂×C₄₇⋊C₈	—	2	1	no	—
208	C₂×C₄₇⋊C₈	—	2	1	no	—
209	C₂×C₄₇⋊C₈	—	2	1	no	—
210	C₂×C₄₇⋊C₈	—	2	1	no	—
211	C₂×C₄₇⋊C₈	—	2	1	no	—
212	C₂×C₄₇⋊C₈	—	2	1	no	—
213	C₂×C₄₇⋊C₈	—	2	1	no	—
214	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
215	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
216	C₂²×D₄₇	—	2	1	no	—
217	C₂²×D₄₇	—	2	1	no	—
218	C₂²×D₄₇	—	2	1	no	—
219	C₂²×D₄₇	—	2	1	no	—
220	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
221	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
222	C₂²×D₄₇	#131	1	2	yes	—
223	C₂×C₄×C₄₇	—	2	1	no	—
224	C₂×C₄×C₄₇	—	2	1	no	—
225	C₂×C₄×C₄₇	—	2	1	no	—
226	C₂×C₄×C₄₇	—	2	1	no	—
227	C₂×C₄×C₄₇	—	2	1	no	—
228	C₂×C₄×C₄₇	—	2	1	no	—
229	C₂×C₄×C₄₇	—	2	1	no	—
230	C₂×C₄×C₄₇	—	2	1	no	—
231	C₂×C₄×C₄₇	—	2	1	no	—
232	C₂×C₄×C₄₇	—	2	1	no	—
233	C₂×C₄×C₄₇	—	2	1	no	—
234	C₂×C₄×C₄₇	—	2	1	no	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
238	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
239	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
240	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
241	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×Dic₄₇	—	2	1	no	—
248	C₂×Dic₄₇	—	2	1	no	—
249	C₂×Dic₄₇	—	2	1	no	—
250	C₂×Dic₄₇	—	2	1	no	—
251	C₂×Dic₄₇	—	2	1	no	—
252	C₂×Dic₄₇	—	2	1	no	—
253	C₂×Dic₄₇	—	2	1	no	—
254	C₂×Dic₄₇	—	2	1	no	—
255	C₂×Dic₄₇	—	2	1	no	—
256	C₂×Dic₄₇	—	2	1	no	—
257	C₂×Dic₄₇	—	2	1	no	—
258	C₂×Dic₄₇	—	2	1	no	—
259	C₂×Dic₄₇	—	2	1	no	—
260	C₂×Dic₄₇	#117	1	2	yes	—
261	C₂×Dic₄₇	#117	1	2	yes	—
262	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
263	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
264	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
265	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
266	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
267	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
268	C₄×D₄₇	—	2	2	no	—
269	C₄×D₄₇	—	2	2	no	—
270	C₄×D₄₇	—	2	2	no	—
271	C₄×D₄₇	—	2	2	no	—
272	C₄×D₄₇	—	2	8	no	—
273	C₄×D₄₇	—	4	4	no	—
274	C₄×D₄₇	—	4	4	no	—
275	C₄×D₄₇	—	4	4	no	—
276	C₄×D₄₇	—	4	4	no	—
277	C₄×D₄₇	—	4	4	no	—
278	C₈×C₄₇	—	2	2	no	—
279	C₈×C₄₇	—	4	1	no	—
280	C₈×C₄₇	—	4	1	no	—
281	C₈×C₄₇	—	4	1	no	—
282	C₄₇⋊C₈	—	2	2	no	—
283	C₄₇⋊C₈	—	4	1	no	—
284	C₄₇⋊C₈	—	4	1	no	—
285	C₄₇⋊C₈	—	4	1	no	—
286	#22625	—	47	1	no	maximal, Sylow
287	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
288	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
289	C₂²×C₄₇	#518	1	1	yes	characteristic
290	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
291	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
292	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
293	C₂²×C₄₇	#568	1	1	yes	characteristic
294	C₂×D₄₇	—	2	2	no	—
295	C₂×D₄₇	—	2	2	no	—
296	C₂×D₄₇	—	2	2	no	—
297	C₂×D₄₇	—	2	2	no	—
298	C₂×D₄₇	—	2	2	no	—
299	C₂×D₄₇	—	2	2	no	—
300	C₂×D₄₇	C₈×Q₈	1	4	yes	—
301	C₄×C₄₇	—	2	2	no	—
302	C₄×C₄₇	—	2	2	no	—
303	C₄×C₄₇	—	2	2	no	—
304	C₄×C₄₇	—	2	2	no	—
305	C₄×C₄₇	—	4	1	no	—
306	C₄×C₄₇	—	4	1	no	—
307	C₄×C₄₇	#553	1	1	yes	characteristic
308	C₄×C₄₇	#553	1	1	yes	characteristic
309	C₄×C₄₇	#554	1	1	yes	characteristic
310	C₄×C₄₇	#554	1	1	yes	characteristic
311	Dic₄₇	—	2	2	no	—
312	Dic₄₇	—	2	2	no	—
313	Dic₄₇	—	2	2	no	—
314	Dic₄₇	—	2	2	no	—
315	Dic₄₇	—	2	2	no	—
316	Dic₄₇	—	4	1	no	—
317	Dic₄₇	#431	1	4	yes	—
318	C₂×C₄×C₄⋊C₄	—	47	1	no	—
319	#1939	—	47	1	no	—
320	#1939	—	47	1	no	—
321	#1916	—	47	1	no	—
322	#1916	—	47	1	no	—
323	#1916	—	47	1	no	—
324	#1916	D₄₇	1	1	yes	characteristic, complemented
325	#1797	—	47	1	no	—
326	#1797	—	47	1	no	—
327	#1797	—	47	1	no	—
328	C₈×C₄⋊C₄	—	47	1	no	—
329	C₈×C₄⋊C₄	—	47	1	no	—
330	C₄×C₂²⋊C₈	—	47	1	no	—
331	C₄×C₂²⋊C₈	—	47	1	no	—
332	C₄×C₂²⋊C₈	—	47	1	no	—
333	C₂×C₄₇	#2345	1	1	yes	characteristic
334	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
335	C₂×C₄₇	#2924	1	1	yes	characteristic
336	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
337	C₂×C₄₇	Q₈×M₁₆	1	1	yes	characteristic
338	C₂×C₄₇	#2972	1	1	yes	characteristic
339	C₂×C₄₇	#2974	1	1	yes	characteristic
340	D₄₇	—	2	4	no	—
341	C₂²×C₄⋊C₄	—	47	1	no	—
342	C₂²×C₄⋊C₄	—	47	1	no	—
343	C₂²×C₄²	—	47	1	no	—
344	C₂²×C₄²	—	47	1	no	—
345	C₂²×C₄²	—	47	1	no	—
346	C₂×C₄⋊C₈	—	47	1	no	—
347	C₂×C₄⋊C₈	—	47	1	no	—
348	C₂×C₄⋊C₈	—	47	1	no	—
349	C₂×C₄⋊C₈	—	47	1	no	—
350	C₂×C₄⋊C₈	—	47	1	no	—
351	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
352	C₂×C₂²⋊C₈	—	47	1	no	—
353	C₂×C₂²⋊C₈	—	47	1	no	—
354	C₂×C₂²⋊C₈	—	47	1	no	—
355	C₂×C₂²⋊C₈	—	47	1	no	—
356	C₂×C₄×C₈	—	47	1	no	—
357	C₂×C₄×C₈	—	47	1	no	—
358	C₂×C₄×C₈	—	47	1	no	—
359	C₂×C₄×C₈	—	47	1	no	—
360	C₂×C₄×C₈	—	47	1	no	—
361	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
362	C₄×C₄⋊C₄	—	47	1	no	—
363	C₄×C₄⋊C₄	—	47	1	no	—
364	C₄×C₄⋊C₄	—	47	1	no	—
365	C₄×C₄⋊C₄	—	47	1	no	—
366	C₄×C₄⋊C₄	—	47	1	no	—
367	C₄×C₄⋊C₄	—	47	1	no	—
368	C₄×C₄⋊C₄	—	47	1	no	—
369	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
370	C₂×#95	—	47	1	no	—
371	C₂×#95	—	47	1	no	—
372	#336	—	47	1	no	—
373	#336	—	47	1	no	—
374	#336	—	47	1	no	—
375	#336	—	47	1	no	—
376	#336	—	47	1	no	—
377	#336	—	47	1	no	—
378	#336	—	47	1	no	—
379	#336	—	47	1	no	—
380	#336	C₂×D₄₇	1	1	yes	characteristic
381	#336	C₂×D₄₇	1	1	yes	characteristic
382	#336	C₂×D₄₇	1	1	yes	characteristic
383	#336	C₂×D₄₇	1	1	yes	characteristic
384	C₄₇	#22625	1	1	yes	characteristic, complemented, Sylow
385	C₂³×C₄	—	47	1	no	—
386	C₂³×C₄	—	47	1	no	—
387	C₂³×C₄	—	47	1	no	—
388	C₂³×C₄	—	47	1	no	—
389	C₂³×C₄	—	47	1	no	—
390	C₂³×C₄	—	47	1	no	—
391	C₂³×C₄	—	47	1	no	—
392	C₂²×C₈	—	47	1	no	—
393	C₂²×C₈	—	47	1	no	—
394	C₂²×C₈	—	47	1	no	—
395	C₂²×C₈	—	47	1	no	—
396	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
397	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
398	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
399	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
400	C₂×C₄⋊C₄	—	47	1	no	—
401	C₂×C₄⋊C₄	—	47	1	no	—
402	C₂×C₄⋊C₄	—	47	1	no	—
403	C₂×C₄⋊C₄	—	47	1	no	—
404	C₂×C₄⋊C₄	—	47	8	no	—
405	C₂×C₄⋊C₄	—	47	1	no	—
406	C₂×C₄⋊C₄	—	47	1	no	—
407	C₂×C₄⋊C₄	—	94	4	no	—
408	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
410	C₂×C₄²	—	47	1	no	—
411	C₂×C₄²	—	47	1	no	—
412	C₂×C₄²	—	47	1	no	—
413	C₂×C₄²	—	47	1	no	—
414	C₂×C₄²	—	47	1	no	—
415	C₂×C₄²	—	47	1	no	—
416	C₂×C₄²	—	47	1	no	—
417	C₂×C₄²	—	47	1	no	—
418	C₂×C₄²	—	47	1	no	—
419	C₂×C₄²	—	94	2	no	—
420	C₂×C₄²	—	94	2	no	—
421	C₂×C₄²	—	188	1	no	—
422	C₂×C₄²	—	188	1	no	—
423	C₂×C₄²	—	188	1	no	—
424	C₂×C₄²	—	188	1	no	—
425	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
426	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
427	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
428	C₄⋊C₈	—	4	1	no	—
429	C₄⋊C₈	—	94	2	no	—
430	C₄⋊C₈	—	94	2	no	—
431	C₄⋊C₈	—	188	1	no	—
432	C₄⋊C₈	—	188	1	no	—
433	C₄⋊C₈	—	188	1	no	—
434	C₂²⋊C₈	—	47	4	no	—
435	C₂²⋊C₈	—	94	2	no	—
436	C₂²⋊C₈	—	94	2	no	—
437	C₂²⋊C₈	—	94	2	no	—
438	C₄×C₈	—	4	1	no	—
439	C₄×C₈	—	94	2	no	—
440	C₄×C₈	—	94	2	no	—
441	C₄×C₈	—	188	1	no	—
442	C₄×C₈	—	188	1	no	—
443	C₄×C₈	—	188	1	no	—
444	#95	—	47	1	no	—
445	#95	—	47	1	no	—
446	#95	—	47	1	no	—
447	#95	—	47	1	no	—
448	#95	—	47	1	no	—
449	#95	—	47	1	no	—
450	#95	C₄×D₄₇	1	1	yes	characteristic
451	#95	C₄×D₄₇	1	1	yes	characteristic
452	C₂⁴	—	47	1	no	—
453	C₂²×C₄	—	47	1	no	—
454	C₂²×C₄	—	47	1	no	—
455	C₂²×C₄	—	47	1	no	—
456	C₂²×C₄	—	47	1	no	—
457	C₂²×C₄	—	47	1	no	—
458	C₂²×C₄	—	47	1	no	—
459	C₂²×C₄	—	47	4	no	—
460	C₂²×C₄	—	47	2	no	—
461	C₂²×C₄	—	47	2	no	—
462	C₂²×C₄	—	47	4	no	—
463	C₂²×C₄	—	47	4	no	—
464	C₂²×C₄	—	47	1	no	—
465	C₂²×C₄	—	94	2	no	—
466	C₂²×C₄	—	94	2	no	—
467	C₂²×C₄	—	94	2	no	—
468	C₂²×C₄	—	94	2	no	—
469	C₂²×C₄	—	94	2	no	—
470	C₂²×C₄	—	94	2	no	—
471	C₂²×C₄	—	94	2	no	—
472	C₂²×C₄	—	94	1	no	—
473	C₂²×C₄	—	94	1	no	—
474	C₂²×C₄	—	94	1	no	—
475	C₂²×C₄	—	94	1	no	—
476	C₂²×C₄	—	94	2	no	—
477	C₂²×C₄	—	188	1	no	—
478	C₂²×C₄	—	188	1	no	—
479	C₂²×C₄	—	188	1	no	—
480	C₂²×C₄	—	188	1	no	—
481	C₂²×C₄	—	188	1	no	—
482	C₂²×C₄	—	188	1	no	—
483	C₂²×C₄	—	188	1	no	—
484	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
486	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
487	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
489	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
490	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	47	2	no	—
503	C₂×C₈	—	94	1	no	—
504	C₂×C₈	—	94	1	no	—
505	C₂×C₈	—	94	1	no	—
506	C₂×C₈	—	94	1	no	—
507	C₂×C₈	—	94	1	no	—
508	C₂×C₈	—	94	1	no	—
509	C₂×C₈	—	94	1	no	—
510	C₂×C₈	—	94	1	no	—
511	C₂×C₈	—	94	1	no	—
512	C₂×C₈	—	94	1	no	—
513	C₂×C₈	—	94	1	no	—
514	C₂×C₈	Q₈×D₄₇	1	2	yes	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	47	4	no	—
517	C₄⋊C₄	—	47	4	no	—
518	C₄⋊C₄	—	47	4	no	—
519	C₄⋊C₄	—	47	4	no	—
520	C₄⋊C₄	—	94	2	no	—
521	C₄⋊C₄	—	94	2	no	—
522	C₄⋊C₄	C₈×D₄₇	1	4	yes	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	47	2	no	—
530	C₄²	—	47	2	no	—
531	C₄²	—	94	2	no	—
532	C₄²	—	94	2	no	—
533	C₄²	—	94	1	no	—
534	C₄²	—	94	1	no	—
535	C₄²	—	94	1	no	—
536	C₄²	—	94	1	no	—
537	C₄²	—	188	1	no	—
538	C₄²	—	188	1	no	—
539	C₄²	—	188	1	no	—
540	C₄²	—	188	1	no	—
541	C₂³	—	47	2	no	—
542	C₂³	—	47	2	no	—
543	C₂³	—	47	2	no	—
544	C₂³	—	94	1	no	—
545	C₂³	—	94	1	no	—
546	C₂³	—	94	1	no	—
547	C₂³	—	94	1	no	—
548	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	47	2	no	—
564	C₂×C₄	—	47	2	no	—
565	C₂×C₄	—	47	2	no	—
566	C₂×C₄	—	47	2	no	—
567	C₂×C₄	—	47	2	no	—
568	C₂×C₄	—	47	2	no	—
569	C₂×C₄	—	47	2	no	—
570	C₂×C₄	—	47	2	no	—
571	C₂×C₄	—	94	8	no	—
572	C₂×C₄	—	94	1	no	—
573	C₂×C₄	—	94	1	no	—
574	C₂×C₄	—	94	1	no	—
575	C₂×C₄	—	94	1	no	—
576	C₂×C₄	—	94	1	no	—
577	C₂×C₄	—	94	1	no	—
578	C₂×C₄	—	94	1	no	—
579	C₂×C₄	—	94	1	no	—
580	C₂×C₄	—	94	1	no	—
581	C₂×C₄	—	94	1	no	—
582	C₂×C₄	—	94	2	no	—
583	C₂×C₄	—	94	2	no	—
584	C₂×C₄	—	94	2	no	—
585	C₂×C₄	—	94	2	no	—
586	C₂×C₄	—	94	1	no	—
587	C₂×C₄	—	94	1	no	—
588	C₂×C₄	—	94	1	no	—
589	C₂×C₄	—	188	4	no	—
590	C₂×C₄	—	188	4	no	—
591	C₂×C₄	—	188	4	no	—
592	C₂×C₄	—	188	4	no	—
593	C₂×C₄	—	188	4	no	—
594	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
595	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
596	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
597	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
598	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
599	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
600	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
601	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
602	C₂×C₄	#13094069	1	1	yes	characteristic
603	C₂×C₄	#13094070	1	1	yes	characteristic
604	C₈	—	2	2	no	—
605	C₈	—	4	1	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₈	—	94	2	no	—
609	C₈	—	188	1	no	—
610	C₈	—	188	1	no	—
611	C₈	—	188	1	no	—
612	C₂²	—	47	4	no	—
613	C₂²	—	94	2	no	—
614	C₂²	—	94	2	no	—
615	C₂²	—	94	2	no	—
616	C₂²	—	94	2	no	—
617	C₂²	—	94	2	no	—
618	C₂²	—	94	2	no	—
619	C₂²	#117×D₄₇	1	1	yes	characteristic
620	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
621	C₂²	#15689595	1	1	yes	characteristic
622	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
623	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
624	C₂²	#131×D₄₇	1	1	yes	characteristic
625	C₂²	#15689888	1	1	yes	characteristic
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	47	4	no	—
633	C₄	—	94	2	no	—
634	C₄	—	94	2	no	—
635	C₄	—	94	2	no	—
636	C₄	—	94	2	no	—
637	C₄	—	94	2	no	—
638	C₄	—	188	1	no	—
639	C₄	#15689818	1	1	yes	characteristic
640	C₄	#15689824	1	1	yes	characteristic
641	C₄	#15689827	1	1	yes	characteristic
642	C₄	#15689829	1	1	yes	characteristic
643	C₂	—	94	4	no	—
644	C₂	#20246262	1	1	yes	characteristic
645	C₂	#431×D₄₇	1	1	yes	characteristic
646	C₂	#20252044	1	1	yes	characteristic
647	C₂	C₈×Q₈×D₄₇	1	1	yes	characteristic
648	C₂	#20252340	1	1	yes	characteristic
649	C₂	#20252409	1	1	yes	characteristic
650	C₂	#20252418	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1916	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1916	D₄₇
hypocenter	C₄₇	#22625
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1916

Complements

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

N	H ≅ G/N	type
2. #20244105	C₂	semidirect
3. #20244103	C₂	semidirect
4. #20243947	C₂	semidirect
5. #20243946	C₂	semidirect
6. #20243944	C₂	semidirect
10. C₈×Dic₄₇⋊C₄	C₂	semidirect
11. #20243249	C₂	semidirect
15. C₄₇×#1916	C₂	semidirect
77. C₄⋊C₄×D₄₇	C₈	semidirect
324. #1916	D₄₇	semidirect
384. C₄₇	#22625	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊C₄×D₄₇	2
#20244105	2
#20244103	2
#20243947	2
#20243946	2
#20243944	2
#20243367	2
#20243365	2
C₈×Dic₄₇⋊C₄	2
#20243249	2
C₄×(C₂×D₄₇)⋊C₈	2
#20243145	2
C₄₇×#1916	2
#22625	47