Subgroups — #26221095

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689178	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689075	C₂	1	1	yes	maximal, characteristic
3	C₄×#13093981	C₂	1	1	yes	maximal, characteristic
4	#20244105	C₂	1	2	yes	maximal, complemented
5	#20244103	C₂	1	2	yes	maximal, complemented
6	#20243572	C₂	1	2	yes	maximal
7	#20243569	C₂	1	2	yes	maximal
8	#20243242	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243242	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243241	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	2	yes	—
13	C₂×#13093981	C₄	1	1	yes	characteristic
14	C₂×#13093981	C₄	1	1	yes	characteristic
15	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
16	#15689178	—	2	4	no	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
20	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
22	#15689075	—	2	4	no	—
23	C₂×#13093935	C₂²	1	1	yes	characteristic
24	C₂×#13093935	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
26	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
27	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
28	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
30	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
31	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
32	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
34	#15688969	C₄	1	1	yes	characteristic
35	#15688969	C₄	1	1	yes	characteristic
36	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
37	#15688878	C₂²	1	2	yes	—
38	#15688877	C₂²	1	2	yes	—
39	#15688877	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
41	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
43	C₄³×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#336	C₂²	1	2	yes	—
45	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
48	C₂×#10625324	—	2	4	no	—
49	C₂×#10625324	—	2	4	no	—
50	C₂×#10625324	—	2	4	no	—
51	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
52	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
53	#13093981	—	2	4	no	—
54	#13093981	—	2	4	no	—
55	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	C₄²×D₄₇	D₄	1	4	yes	—
73	C₄²×D₄₇	Q₈	1	4	yes	—
74	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
75	Dic₄₇⋊C₈	—	2	4	no	—
76	Dic₄₇⋊C₈	—	2	4	no	—
77	Dic₄₇⋊C₈	—	2	4	no	—
78	(C₂×D₄₇)⋊C₈	—	2	4	no	—
79	#13093935	—	2	2	no	—
80	#13093935	—	2	2	no	—
81	C₈×Dic₄₇	—	2	4	no	—
82	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
83	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
84	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
85	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
86	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
87	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
88	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
89	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
91	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
92	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₇	—	2	4	no	—
100	#97×C₄₇	—	2	2	no	—
101	#97×C₄₇	—	2	2	no	—
102	C₂³×D₄₇	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	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
110	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₄₇	—	2	2	no	—
118	C₂×C₄×D₄₇	—	2	2	no	—
119	C₂×C₄×D₄₇	—	2	2	no	—
120	C₂×C₄×D₄₇	—	2	2	no	—
121	C₂×C₄×D₄₇	—	4	1	no	—
122	C₂×C₄×D₄₇	—	4	1	no	—
123	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
124	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
125	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
126	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	—	2	2	no	—
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	#41	1	4	yes	—
133	C₄²×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	—	4	1	no	—
138	C₄²×C₄₇	—	4	1	no	—
139	C₄²×C₄₇	C₂×D₄	1	2	yes	—
140	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
141	(C₂×D₄₇)⋊C₄	—	2	2	no	—
142	(C₂×D₄₇)⋊C₄	—	2	2	no	—
143	(C₂×D₄₇)⋊C₄	—	2	2	no	—
144	(C₂×D₄₇)⋊C₄	—	2	2	no	—
145	Dic₄₇⋊C₄	—	2	2	no	—
146	Dic₄₇⋊C₄	—	2	2	no	—
147	Dic₄₇⋊C₄	M₁₆	1	4	yes	complemented
148	Dic₄₇⋊C₄	M₁₆	1	4	yes	complemented
149	C₄×Dic₄₇	—	2	2	no	—
150	C₄×Dic₄₇	—	2	2	no	—
151	C₄×Dic₄₇	—	2	2	no	—
152	C₄×Dic₄₇	—	2	2	no	—
153	C₄×Dic₄₇	—	4	1	no	—
154	C₄×Dic₄₇	—	4	1	no	—
155	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
156	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
157	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
158	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂×C₄₇⋊C₈	—	2	2	no	—
161	C₂×C₄₇⋊C₈	—	2	2	no	—
162	C₂×C₄₇⋊C₈	—	2	2	no	—
163	C₂×C₄₇⋊C₈	—	2	2	no	—
164	C₂×C₄₇⋊C₈	#41	1	4	yes	—
165	#10625324	—	2	16	no	—
166	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
167	C₂²×D₄₇	—	2	1	no	—
168	C₂²×D₄₇	—	2	1	no	—
169	C₂²×D₄₇	—	2	1	no	—
170	C₂²×D₄₇	—	2	1	no	—
171	C₂²×D₄₇	—	2	1	no	—
172	C₂²×D₄₇	—	2	1	no	—
173	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	1	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	2	1	no	—
188	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
189	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
192	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
195	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	1	no	—
198	C₂×Dic₄₇	—	2	1	no	—
199	C₂×Dic₄₇	—	2	1	no	—
200	C₂×Dic₄₇	—	2	1	no	—
201	C₂×Dic₄₇	—	2	1	no	—
202	C₂×Dic₄₇	—	2	1	no	—
203	C₂×Dic₄₇	—	2	1	no	—
204	C₂×Dic₄₇	—	2	1	no	—
205	C₂×Dic₄₇	—	2	1	no	—
206	C₂×Dic₄₇	—	2	1	no	—
207	C₂×Dic₄₇	—	2	1	no	—
208	C₂×Dic₄₇	—	2	1	no	—
209	C₂×Dic₄₇	—	2	1	no	—
210	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
211	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
212	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
213	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
214	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
215	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
216	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
217	C₄×D₄₇	—	2	4	no	—
218	C₄×D₄₇	—	2	4	no	—
219	C₄×D₄₇	—	2	8	no	—
220	C₄×D₄₇	—	4	4	no	—
221	C₈×C₄₇	—	2	4	no	—
222	C₈×C₄₇	—	4	2	no	—
223	C₄₇⋊C₈	—	2	4	no	—
224	C₄₇⋊C₈	—	4	2	no	—
225	#21356	—	47	1	no	maximal, Sylow
226	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
227	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
228	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
229	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
230	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
231	C₂²×C₄₇	#568	1	1	yes	characteristic
232	C₂²×C₄₇	#568	1	1	yes	characteristic
233	C₂×D₄₇	—	2	2	no	—
234	C₂×D₄₇	—	2	2	no	—
235	C₂×D₄₇	—	2	2	no	—
236	C₂×D₄₇	—	4	1	no	—
237	C₂×D₄₇	—	4	1	no	—
238	C₂×D₄₇	—	4	1	no	—
239	C₂×D₄₇	—	4	1	no	—
240	C₄×C₄₇	—	2	2	no	—
241	C₄×C₄₇	—	2	2	no	—
242	C₄×C₄₇	—	2	2	no	—
243	C₄×C₄₇	—	2	2	no	—
244	C₄×C₄₇	—	4	1	no	—
245	C₄×C₄₇	—	4	1	no	—
246	C₄×C₄₇	#525	1	2	yes	—
247	C₄×C₄₇	#533	1	2	yes	—
248	Dic₄₇	—	2	2	no	—
249	Dic₄₇	—	2	2	no	—
250	Dic₄₇	—	2	2	no	—
251	Dic₄₇	—	2	2	no	—
252	Dic₄₇	—	4	1	no	—
253	Dic₄₇	—	4	1	no	—
254	Dic₄₇	#423	1	4	yes	—
255	C₂×#432	—	47	1	no	—
256	C₂×C₄×M₁₆	—	47	1	no	—
257	C₄×#117	—	47	1	no	—
258	#1939	—	47	2	no	—
259	#1939	—	47	2	no	—
260	#1851	—	47	2	no	—
261	#1851	—	47	2	no	—
262	#1767	—	47	1	no	—
263	#1767	—	47	1	no	—
264	#1767	—	47	1	no	—
265	#1767	D₄₇	1	1	yes	characteristic, complemented
266	C₂×C₄₇	#2296	1	1	yes	characteristic
267	C₂×C₄₇	C₂×#423	1	1	yes	characteristic
268	C₂×C₄₇	#2905	1	1	yes	characteristic
269	C₂×C₄₇	#2970	1	1	yes	characteristic
270	C₂×C₄₇	#2970	1	1	yes	characteristic
271	C₂×C₄₇	#2971	1	1	yes	characteristic
272	C₂×C₄₇	#2971	1	1	yes	characteristic
273	D₄₇	—	4	2	no	—
274	C₂²×M₁₆	—	47	2	no	—
275	C₂×#117	—	47	1	no	—
276	C₂×#117	—	47	1	no	—
277	C₂²×C₄²	—	47	1	no	—
278	#432	—	94	4	no	—
279	C₂×C₄⋊C₈	—	47	2	no	—
280	C₂×C₄⋊C₈	—	47	2	no	—
281	C₂×C₄⋊C₈	—	47	2	no	—
282	C₂×C₄⋊C₈	—	47	2	no	—
283	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
284	C₂×C₂²⋊C₈	—	47	2	no	—
285	C₄×M₁₆	—	94	4	no	—
286	C₂×#97	—	47	1	no	—
287	C₂×#97	—	47	1	no	—
288	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
289	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
290	C₂×C₄×C₈	—	47	2	no	—
291	C₄×C₄⋊C₄	—	47	1	no	—
292	C₄×C₄⋊C₄	—	47	1	no	—
293	C₄×C₄⋊C₄	—	47	1	no	—
294	C₄×C₄⋊C₄	—	47	1	no	—
295	C₄×C₂²⋊C₄	—	47	1	no	—
296	C₄×C₂²⋊C₄	—	47	1	no	—
297	C₄×C₂²⋊C₄	—	47	1	no	—
298	C₄×C₂²⋊C₄	—	47	1	no	—
299	#376	—	47	1	no	—
300	#376	—	47	1	no	—
301	C₄³	—	47	1	no	—
302	C₄³	C₂×D₄₇	1	1	yes	characteristic
303	#336	—	47	2	no	—
304	#336	—	47	2	no	—
305	#336	—	47	2	no	—
306	#336	C₂×D₄₇	1	2	yes	—
307	C₄₇	#21356	1	1	yes	characteristic, complemented, Sylow
308	C₂³×C₄	—	47	1	no	—
309	C₂³×C₄	—	47	1	no	—
310	C₂³×C₄	—	47	1	no	—
311	C₂×M₁₆	—	94	4	no	—
312	C₂×M₁₆	—	94	4	no	—
313	C₂×M₁₆	—	94	4	no	—
314	C₂²×C₈	—	47	2	no	—
315	C₂²×C₈	—	47	2	no	—
316	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
317	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
318	#117	—	94	4	no	—
319	#117	—	94	4	no	—
320	C₂×C₄⋊C₄	—	47	1	no	—
321	C₂×C₄⋊C₄	—	47	1	no	—
322	C₂×C₄⋊C₄	—	47	1	no	—
323	C₂×C₄⋊C₄	—	47	1	no	—
324	C₂×C₂²⋊C₄	—	47	1	no	—
325	C₂×C₂²⋊C₄	—	47	1	no	—
326	C₂×C₂²⋊C₄	—	47	1	no	—
327	C₂×C₂²⋊C₄	—	47	1	no	—
328	C₂×C₄²	—	47	1	no	—
329	C₂×C₄²	—	47	1	no	—
330	C₂×C₄²	—	47	1	no	—
331	C₂×C₄²	—	47	4	no	—
332	C₂×C₄²	—	47	4	no	—
333	C₂×C₄²	—	47	1	no	—
334	C₂×C₄²	—	47	1	no	—
335	C₂×C₄²	—	47	1	no	—
336	C₂×C₄²	—	47	1	no	—
337	C₂×C₄²	—	47	1	no	—
338	C₂×C₄²	—	47	1	no	—
339	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
340	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
341	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
342	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
343	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
344	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
345	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
346	C₄⋊C₈	—	2	4	no	—
347	C₄⋊C₈	—	94	4	no	—
348	C₄⋊C₈	—	94	4	no	—
349	C₄⋊C₈	—	94	4	no	—
350	C₄⋊C₈	—	94	4	no	—
351	C₂²⋊C₈	—	94	4	no	—
352	#97	—	2	2	no	—
353	#97	—	2	2	no	—
354	#97	—	94	2	no	—
355	#97	—	94	2	no	—
356	C₄×C₈	—	94	4	no	—
357	#95	—	47	1	no	—
358	#95	—	47	1	no	—
359	#95	—	47	1	no	—
360	#95	—	47	1	no	—
361	#95	—	47	1	no	—
362	#95	—	47	1	no	—
363	#95	—	47	1	no	—
364	#95	—	47	1	no	—
365	C₂⁴	—	47	1	no	—
366	C₂²×C₄	—	47	1	no	—
367	C₂²×C₄	—	47	1	no	—
368	C₂²×C₄	—	47	1	no	—
369	C₂²×C₄	—	47	1	no	—
370	C₂²×C₄	—	47	1	no	—
371	C₂²×C₄	—	47	4	no	—
372	C₂²×C₄	—	47	2	no	—
373	C₂²×C₄	—	47	2	no	—
374	C₂²×C₄	—	47	4	no	—
375	C₂²×C₄	—	47	1	no	—
376	C₂²×C₄	—	47	1	no	—
377	C₂²×C₄	—	94	2	no	—
378	C₂²×C₄	—	94	2	no	—
379	C₂²×C₄	—	94	2	no	—
380	C₂²×C₄	—	94	2	no	—
381	C₂²×C₄	—	188	1	no	—
382	C₂²×C₄	—	188	1	no	—
383	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
389	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
390	M₁₆	—	94	16	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	47	4	no	—
397	C₂×C₈	—	94	2	no	—
398	C₂×C₈	—	94	2	no	—
399	C₂×C₈	—	94	2	no	—
400	C₂×C₈	—	94	2	no	—
401	C₂×C₈	—	94	2	no	—
402	C₂×C₈	#10625350	1	4	yes	—
403	C₄⋊C₄	—	47	4	no	—
404	C₄⋊C₄	—	47	4	no	—
405	C₄⋊C₄	—	94	2	no	—
406	C₄⋊C₄	—	94	2	no	—
407	C₂²⋊C₄	—	94	2	no	—
408	C₂²⋊C₄	—	94	2	no	—
409	C₂²⋊C₄	—	94	2	no	—
410	C₂²⋊C₄	—	94	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	4	1	no	—
416	C₄²	—	4	1	no	—
417	C₄²	—	47	4	no	—
418	C₄²	—	47	4	no	—
419	C₄²	—	47	2	no	—
420	C₄²	—	47	2	no	—
421	C₄²	—	94	2	no	—
422	C₄²	—	94	2	no	—
423	C₄²	—	94	2	no	—
424	C₄²	—	94	2	no	—
425	C₄²	—	188	1	no	—
426	C₄²	—	188	1	no	—
427	C₄²	D₄×D₄₇	1	2	yes	—
428	C₄²	Q₈×D₄₇	1	2	yes	—
429	C₂³	—	47	2	no	—
430	C₂³	—	94	1	no	—
431	C₂³	—	94	1	no	—
432	C₂³	—	94	1	no	—
433	C₂³	—	94	1	no	—
434	C₂³	—	94	1	no	—
435	C₂³	—	94	1	no	—
436	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	47	2	no	—
452	C₂×C₄	—	47	2	no	—
453	C₂×C₄	—	47	2	no	—
454	C₂×C₄	—	47	2	no	—
455	C₂×C₄	—	47	2	no	—
456	C₂×C₄	—	47	2	no	—
457	C₂×C₄	—	47	2	no	—
458	C₂×C₄	—	94	8	no	—
459	C₂×C₄	—	94	1	no	—
460	C₂×C₄	—	94	1	no	—
461	C₂×C₄	—	94	1	no	—
462	C₂×C₄	—	94	1	no	—
463	C₂×C₄	—	94	1	no	—
464	C₂×C₄	—	94	1	no	—
465	C₂×C₄	—	94	1	no	—
466	C₂×C₄	—	94	1	no	—
467	C₂×C₄	—	94	4	no	—
468	C₂×C₄	—	94	4	no	—
469	C₂×C₄	—	94	1	no	—
470	C₂×C₄	—	94	1	no	—
471	C₂×C₄	—	94	1	no	—
472	C₂×C₄	—	94	1	no	—
473	C₂×C₄	—	94	1	no	—
474	C₂×C₄	—	94	1	no	—
475	C₂×C₄	—	188	4	no	—
476	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
477	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
478	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
479	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
480	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
481	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
482	C₂×C₄	#41×D₄₇	1	2	yes	—
483	C₂×C₄	C₂×#10625350	1	2	yes	—
484	C₈	—	2	4	no	—
485	C₈	—	4	2	no	—
486	C₈	—	94	4	no	—
487	C₈	—	188	2	no	—
488	C₂²	—	94	2	no	—
489	C₂²	—	94	2	no	—
490	C₂²	—	94	2	no	—
491	C₂²	—	188	1	no	—
492	C₂²	—	188	1	no	—
493	C₂²	—	188	1	no	—
494	C₂²	—	188	1	no	—
495	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
496	C₂²	#15689591	1	1	yes	characteristic
497	C₂²	C₄×#10625350	1	1	yes	characteristic
498	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
499	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
500	C₂²	#15689889	1	1	yes	characteristic
501	C₂²	#15689889	1	1	yes	characteristic
502	C₄	—	2	2	no	—
503	C₄	—	2	2	no	—
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	1	no	—
508	C₄	—	47	4	no	—
509	C₄	—	94	2	no	—
510	C₄	—	94	2	no	—
511	C₄	—	94	2	no	—
512	C₄	—	94	2	no	—
513	C₄	—	188	1	no	—
514	C₄	—	188	1	no	—
515	C₄	#15689632	1	2	yes	—
516	C₄	#15689677	1	2	yes	—
517	C₂	—	188	2	no	—
518	C₂	#20245868	1	1	yes	characteristic
519	C₂	#423×D₄₇	1	1	yes	characteristic
520	C₂	#20251950	1	1	yes	characteristic
521	C₂	#20252397	1	1	yes	characteristic
522	C₂	#20252399	1	1	yes	characteristic
523	C₂	#20252405	1	1	yes	characteristic
524	C₂	#20252406	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1767	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1767	D₄₇
hypocenter	C₄₇	#21356
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1767

Complements

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

N	H ≅ G/N	type
4. #20244105	C₂	semidirect
5. #20244103	C₂	semidirect
8. #20243242	C₂	semidirect
9. #20243242	C₂	semidirect
10. #20243241	C₂	semidirect
11. C₄₇×#1767	C₂	semidirect
147. Dic₄₇⋊C₄	M₁₆	semidirect
148. Dic₄₇⋊C₄	M₁₆	semidirect
265. #1767	D₄₇	semidirect
307. C₄₇	#21356	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689178	2
C₂×#15689075	2
C₄×#13093981	2
#20244105	2
#20244103	2
#20243572	2
#20243569	2
#20243242	2
#20243241	2
C₄₇×#1767	2
#21356	47