Subgroups — #26226453

Order 12032.

750 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13093981	C₂	1	1	yes	maximal, characteristic
2	#20244001	C₂	1	2	yes	maximal
3	#20243999	C₂	1	2	yes	maximal
4	#20243952	C₂	1	2	yes	maximal, complemented
5	#20243950	C₂	1	2	yes	maximal, complemented
6	#20243539	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243504	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243365	C₂	1	1	yes	maximal, characteristic
9	#20243365	C₂	1	1	yes	maximal, characteristic
10	#20243241	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13093981	C₄	1	1	yes	characteristic
13	C₂×#13093981	C₄	1	1	yes	characteristic
14	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
21	C₂×#13093935	C₂²	1	2	yes	—
22	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
23	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
24	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
25	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
26	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
27	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
28	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
30	#15688969	C₄	1	1	yes	characteristic
31	#15688969	C₄	1	1	yes	characteristic
32	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
33	#15688878	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#97×C₄₇	C₂²	1	2	yes	—
41	C₄³×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	#13093981	—	2	4	no	—
49	#13093981	—	2	4	no	—
50	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
67	C₄²×D₄₇	—	2	2	no	—
68	C₄²×D₄₇	—	2	2	no	—
69	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
70	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
71	Dic₄₇⋊C₈	—	4	2	no	—
72	Dic₄₇⋊C₈	—	4	2	no	—
73	(C₂×D₄₇)⋊C₈	—	4	2	no	—
74	(C₂×D₄₇)⋊C₈	—	4	2	no	—
75	#13093935	—	4	2	no	—
76	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
77	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
78	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
79	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
80	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
81	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
82	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
83	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
85	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₇	—	2	2	no	—
94	C₄⋊C₈×C₄₇	—	2	2	no	—
95	#97×C₄₇	—	4	2	no	—
96	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₄₇	—	2	2	no	—
112	C₂×C₄×D₄₇	—	2	2	no	—
113	C₂×C₄×D₄₇	—	2	2	no	—
114	C₂×C₄×D₄₇	—	2	1	no	—
115	C₂×C₄×D₄₇	—	2	1	no	—
116	C₂×C₄×D₄₇	—	2	1	no	—
117	C₂×C₄×D₄₇	—	2	1	no	—
118	C₂×C₄×D₄₇	—	2	1	no	—
119	C₂×C₄×D₄₇	—	2	1	no	—
120	C₂×C₄×D₄₇	—	4	1	no	—
121	C₂×C₄×D₄₇	—	4	1	no	—
122	C₂×C₄×D₄₇	M₁₆	1	4	yes	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	2	1	no	—
132	C₄²×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	—	2	1	no	—
135	C₄²×C₄₇	—	4	1	no	—
136	C₄²×C₄₇	—	4	1	no	—
137	C₄²×C₄₇	#41	1	2	yes	—
138	C₄²×C₄₇	#41	1	2	yes	—
139	(C₂×D₄₇)⋊C₄	—	2	2	no	—
140	(C₂×D₄₇)⋊C₄	—	2	2	no	—
141	(C₂×D₄₇)⋊C₄	—	2	2	no	—
142	(C₂×D₄₇)⋊C₄	—	2	2	no	—
143	Dic₄₇⋊C₄	—	2	2	no	—
144	Dic₄₇⋊C₄	—	2	2	no	—
145	Dic₄₇⋊C₄	—	2	2	no	—
146	Dic₄₇⋊C₄	—	2	2	no	—
147	C₄×Dic₄₇	—	2	2	no	—
148	C₄×Dic₄₇	—	2	2	no	—
149	C₄×Dic₄₇	—	2	2	no	—
150	C₄×Dic₄₇	—	2	1	no	—
151	C₄×Dic₄₇	—	2	1	no	—
152	C₄×Dic₄₇	—	2	1	no	—
153	C₄×Dic₄₇	—	2	1	no	—
154	C₄×Dic₄₇	—	2	1	no	—
155	C₄×Dic₄₇	—	2	1	no	—
156	C₄×Dic₄₇	—	4	1	no	—
157	C₄×Dic₄₇	—	4	1	no	—
158	C₄×Dic₄₇	M₁₆	1	4	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	—	2	2	no	—
165	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂²×D₄₇	—	2	1	no	—
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	C₂×M₁₆	1	2	yes	—
173	C₂×C₄×C₄₇	—	2	1	no	—
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	#117	1	2	yes	—
188	C₂×C₄×C₄₇	#117	1	2	yes	—
189	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
190	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
196	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
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	—	2	1	no	—
211	C₂×Dic₄₇	—	2	1	no	—
212	C₂×Dic₄₇	—	2	1	no	—
213	C₂×Dic₄₇	—	2	1	no	—
214	C₂×Dic₄₇	—	2	1	no	—
215	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
216	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
217	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
218	C₄×D₄₇	—	2	8	no	—
219	C₄×D₄₇	—	4	4	no	—
220	C₄×D₄₇	—	4	1	no	—
221	C₄×D₄₇	—	4	1	no	—
222	C₄×D₄₇	—	4	1	no	—
223	C₄×D₄₇	—	4	1	no	—
224	C₈×C₄₇	—	4	2	no	—
225	C₈×C₄₇	—	4	2	no	—
226	C₄₇⋊C₈	—	4	2	no	—
227	C₄₇⋊C₈	—	4	2	no	—
228	#21926	—	47	1	no	maximal, Sylow
229	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
230	C₂²×C₄₇	#520	1	1	yes	characteristic
231	C₂²×C₄₇	#520	1	1	yes	characteristic
232	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
233	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
234	C₂²×C₄₇	#568	1	1	yes	characteristic
235	C₂²×C₄₇	#568	1	1	yes	characteristic
236	C₂×D₄₇	—	2	2	no	—
237	C₂×D₄₇	—	2	2	no	—
238	C₂×D₄₇	—	2	2	no	—
239	C₂×D₄₇	—	4	1	no	—
240	C₂×D₄₇	—	4	1	no	—
241	C₂×D₄₇	—	4	1	no	—
242	C₂×D₄₇	—	4	1	no	—
243	C₄×C₄₇	—	2	2	no	—
244	C₄×C₄₇	—	4	1	no	—
245	C₄×C₄₇	—	4	1	no	—
246	C₄×C₄₇	—	4	1	no	—
247	C₄×C₄₇	—	4	1	no	—
248	C₄×C₄₇	#432	1	4	yes	—
249	C₄×C₄₇	#540	1	1	yes	characteristic
250	C₄×C₄₇	#541	1	1	yes	characteristic
251	C₄×C₄₇	#542	1	1	yes	characteristic
252	C₄×C₄₇	#542	1	1	yes	characteristic
253	Dic₄₇	—	2	2	no	—
254	Dic₄₇	—	2	2	no	—
255	Dic₄₇	—	2	2	no	—
256	Dic₄₇	—	4	1	no	—
257	Dic₄₇	—	4	1	no	—
258	Dic₄₇	—	4	1	no	—
259	Dic₄₇	—	4	1	no	—
260	C₄×#117	—	47	1	no	—
261	#1924	—	47	2	no	—
262	#1924	—	47	2	no	—
263	#1917	—	47	2	no	—
264	#1917	—	47	2	no	—
265	#1842	—	47	1	no	—
266	#1831	—	47	1	no	—
267	#1797	—	47	1	no	—
268	#1797	—	47	1	no	—
269	#1767	—	47	1	no	—
270	#1767	D₄₇	1	1	yes	characteristic, complemented
271	C₂×C₄₇	#2314	1	1	yes	characteristic
272	C₂×C₄₇	C₂×#432	1	1	yes	characteristic
273	C₂×C₄₇	#2921	1	1	yes	characteristic
274	C₂×C₄₇	#2989	1	1	yes	characteristic
275	C₂×C₄₇	#2989	1	1	yes	characteristic
276	C₂×C₄₇	#2989	1	1	yes	characteristic
277	C₂×C₄₇	#2989	1	1	yes	characteristic
278	D₄₇	—	4	2	no	—
279	C₂×#117	—	47	1	no	—
280	C₂×#117	—	47	1	no	—
281	C₂²×C₄²	—	47	1	no	—
282	C₂×C₄⋊C₈	—	47	1	no	—
283	C₂×C₄⋊C₈	—	47	1	no	—
284	C₂×C₄⋊C₈	—	47	2	no	—
285	C₂×C₄⋊C₈	—	47	2	no	—
286	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	—	47	2	no	—
289	C₂×C₂²⋊C₈	—	47	2	no	—
290	C₂×#97	—	47	2	no	—
291	C₂×#97	C₂×D₄₇	1	2	yes	—
292	C₄×C₄⋊C₄	—	47	1	no	—
293	C₄×C₄⋊C₄	—	47	1	no	—
294	C₄×C₄⋊C₄	—	47	1	no	—
295	C₄×C₄⋊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	C₄×C₂²⋊C₄	—	47	1	no	—
300	#376	—	47	1	no	—
301	#376	—	47	1	no	—
302	C₄³	—	47	1	no	—
303	C₄³	C₂×D₄₇	1	1	yes	characteristic
304	#336	—	47	2	no	—
305	#336	—	47	2	no	—
306	#336	—	47	2	no	—
307	#336	—	47	2	no	—
308	#336	—	47	2	no	—
309	#336	C₂×D₄₇	1	2	yes	—
310	C₄₇	#21926	1	1	yes	characteristic, complemented, Sylow
311	C₂³×C₄	—	47	1	no	—
312	C₂³×C₄	—	47	1	no	—
313	C₂³×C₄	—	47	1	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	1	no	—
332	C₂×C₄²	—	47	1	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	—	94	2	no	—
338	C₂×C₄²	—	94	2	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	2	no	—
347	C₄⋊C₈	—	2	2	no	—
348	C₄⋊C₈	—	94	2	no	—
349	C₄⋊C₈	—	94	2	no	—
350	C₄⋊C₈	—	188	2	no	—
351	C₄⋊C₈	—	188	2	no	—
352	C₂²⋊C₈	—	188	2	no	—
353	C₂²⋊C₈	—	188	2	no	—
354	#97	—	4	2	no	—
355	#97	—	188	2	no	—
356	#95	—	47	1	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	C₂⁴	—	47	1	no	—
365	C₂²×C₄	—	47	1	no	—
366	C₂²×C₄	—	47	1	no	—
367	C₂²×C₄	—	47	1	no	—
368	C₂²×C₄	—	47	4	no	—
369	C₂²×C₄	—	47	1	no	—
370	C₂²×C₄	—	47	1	no	—
371	C₂²×C₄	—	47	1	no	—
372	C₂²×C₄	—	47	1	no	—
373	C₂²×C₄	—	94	2	no	—
374	C₂²×C₄	—	94	2	no	—
375	C₂²×C₄	—	94	2	no	—
376	C₂²×C₄	—	94	1	no	—
377	C₂²×C₄	—	94	1	no	—
378	C₂²×C₄	—	94	1	no	—
379	C₂²×C₄	—	94	1	no	—
380	C₂²×C₄	—	94	1	no	—
381	C₂²×C₄	—	94	1	no	—
382	C₂²×C₄	—	188	1	no	—
383	C₂²×C₄	—	188	1	no	—
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	C₂×C₄×D₄₇	1	1	yes	characteristic
390	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
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	—	2	2	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	—	94	2	no	—
403	C₄⋊C₄	—	94	2	no	—
404	C₄⋊C₄	—	94	2	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	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	4	1	no	—
418	C₄²	—	4	1	no	—
419	C₄²	—	47	4	no	—
420	C₄²	—	94	2	no	—
421	C₄²	—	94	2	no	—
422	C₄²	—	94	2	no	—
423	C₄²	—	94	1	no	—
424	C₄²	—	94	1	no	—
425	C₄²	—	94	1	no	—
426	C₄²	—	94	1	no	—
427	C₄²	—	94	1	no	—
428	C₄²	—	94	1	no	—
429	C₄²	—	188	1	no	—
430	C₄²	—	188	1	no	—
431	C₄²	#10625350	1	2	yes	—
432	C₄²	#10625350	1	2	yes	—
433	C₂³	—	47	2	no	—
434	C₂³	—	94	1	no	—
435	C₂³	—	94	1	no	—
436	C₂³	—	94	1	no	—
437	C₂³	—	94	1	no	—
438	C₂³	—	94	1	no	—
439	C₂³	—	94	1	no	—
440	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
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	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	47	2	no	—
456	C₂×C₄	—	47	2	no	—
457	C₂×C₄	—	47	2	no	—
458	C₂×C₄	—	94	1	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	8	no	—
465	C₂×C₄	—	94	1	no	—
466	C₂×C₄	—	94	1	no	—
467	C₂×C₄	—	94	1	no	—
468	C₂×C₄	—	94	1	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	—	94	1	no	—
476	C₂×C₄	—	94	1	no	—
477	C₂×C₄	—	188	4	no	—
478	C₂×C₄	—	188	1	no	—
479	C₂×C₄	—	188	1	no	—
480	C₂×C₄	—	188	1	no	—
481	C₂×C₄	—	188	1	no	—
482	C₂×C₄	#13093981	1	2	yes	—
483	C₂×C₄	#13093981	1	2	yes	—
484	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
485	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
486	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
487	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
488	C₂×C₄	#13094069	1	1	yes	characteristic
489	C₂×C₄	#13094070	1	1	yes	characteristic
490	C₂×C₄	#13094071	1	1	yes	characteristic
491	C₂×C₄	#13094072	1	1	yes	characteristic
492	C₈	—	4	2	no	—
493	C₈	—	4	2	no	—
494	C₈	—	188	2	no	—
495	C₈	—	188	2	no	—
496	C₂²	—	94	2	no	—
497	C₂²	—	94	2	no	—
498	C₂²	—	94	2	no	—
499	C₂²	—	188	1	no	—
500	C₂²	—	188	1	no	—
501	C₂²	—	188	1	no	—
502	C₂²	—	188	1	no	—
503	C₂²	C₂×#13093981	1	1	yes	characteristic
504	C₂²	#15689603	1	1	yes	characteristic
505	C₂²	#15689604	1	1	yes	characteristic
506	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
507	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
508	C₂²	#15689889	1	1	yes	characteristic
509	C₂²	#15689889	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	94	2	no	—
516	C₄	—	94	2	no	—
517	C₄	—	94	2	no	—
518	C₄	—	188	1	no	—
519	C₄	—	188	1	no	—
520	C₄	—	188	1	no	—
521	C₄	—	188	1	no	—
522	C₄	#15689178	1	4	yes	—
523	C₄	#15689724	1	1	yes	characteristic
524	C₄	#15689731	1	1	yes	characteristic
525	C₄	#15689738	1	1	yes	characteristic
526	C₄	#15689745	1	1	yes	characteristic
527	C₂	—	188	2	no	—
528	C₂	#20245993	1	1	yes	characteristic
529	C₂	C₂×#15689178	1	1	yes	characteristic
530	C₂	#20252024	1	1	yes	characteristic
531	C₂	#20252502	1	1	yes	characteristic
532	C₂	#20252502	1	1	yes	characteristic
533	C₂	#20252507	1	1	yes	characteristic
534	C₂	#20252507	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	#21926
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. #20243952	C₂	semidirect
5. #20243950	C₂	semidirect
6. #20243539	C₂	semidirect
7. #20243504	C₂	semidirect
10. #20243241	C₂	semidirect
11. C₄₇×#1767	C₂	semidirect
270. #1767	D₄₇	semidirect
310. C₄₇	#21926	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13093981	2
#20244001	2
#20243999	2
#20243952	2
#20243950	2
#20243539	2
#20243504	2
#20243365	2
#20243241	2
C₄₇×#1767	2
#21926	47