Subgroups — #26215017

Order 12032.

1038 conjugacy classes of subgroups.

The subgroup lattice has 534 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×#15689175	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243265	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243263	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243260	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243256	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243254	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243249	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243151	C₂	1	1	yes	maximal, characteristic
12	#20243149	C₂	1	1	yes	maximal, characteristic
13	C₄×(C₂×D₄₇)⋊C₈	C₂	1	1	yes	maximal, characteristic
14	#20243145	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊C₄×D₄₇	C₄	1	2	yes	—
17	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
20	#15689178	C₄	1	8	yes	complemented
21	#15689175	C₄	1	8	yes	complemented
22	C₂×C₄⋊(C₄₇⋊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×(C₂×D₄₇)⋊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×#13093935	C₂²	1	1	yes	characteristic
30	C₂×#13093935	C₂²	1	1	yes	characteristic
31	C₂×#13093934	C₂²	1	1	yes	characteristic
32	C₂×#13093934	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
38	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
39	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
42	#15688974	C₄	1	2	yes	—
43	#95×D₄₇	C₄	1	2	yes	—
44	#15688878	C₂²	1	1	yes	characteristic
45	#15688878	C₂²	1	1	yes	characteristic
46	#15688877	C₂²	1	1	yes	characteristic
47	#15688877	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×#97×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	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
58	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
59	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
62	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
67	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
69	C₄⋊C₄×D₄₇	—	2	8	no	—
70	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
77	C₄²×D₄₇	—	4	1	no	—
78	C₄²×D₄₇	—	4	1	no	—
79	C₄²×D₄₇	—	4	1	no	—
80	C₄²×D₄₇	—	4	1	no	—
81	C₄²×D₄₇	C₂×C₄	1	4	yes	—
82	C₄²×D₄₇	C₂×C₄	1	4	yes	—
83	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
84	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
85	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
86	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
87	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
88	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
89	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
90	#13093935	—	4	1	no	—
91	#13093935	C₂×C₄	1	4	yes	complemented
92	#13093934	—	4	1	no	—
93	#13093934	—	4	1	no	—
94	C₄×C₄₇⋊C₈	—	4	1	no	—
95	C₈×Dic₄₇	—	4	1	no	—
96	C₈×Dic₄₇	—	4	1	no	—
97	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
98	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
99	C₄₇⋊#95	C₂×C₄	1	2	yes	—
100	C₄₇⋊#95	C₂×C₄	1	2	yes	—
101	C₄₇⋊#95	C₂×C₄	1	2	yes	—
102	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
107	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
110	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
111	#97×C₄₇	—	4	1	no	—
112	#97×C₄₇	C₂×C₄	1	4	yes	complemented
113	C₄×C₈×C₄₇	—	4	1	no	—
114	#95×C₄₇	C₂×C₄	1	2	yes	—
115	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
121	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
122	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
125	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₄₇	—	2	4	no	—
127	C₂×C₄×D₄₇	—	2	1	no	—
128	C₂×C₄×D₄₇	—	2	1	no	—
129	C₂×C₄×D₄₇	—	2	1	no	—
130	C₂×C₄×D₄₇	—	2	1	no	—
131	C₂×C₄×D₄₇	—	2	4	no	—
132	C₂×C₄×D₄₇	—	2	4	no	—
133	C₂×C₄×D₄₇	—	2	4	no	—
134	C₂×C₄×D₄₇	—	2	4	no	—
135	C₂×C₄×D₄₇	—	2	4	no	—
136	C₂×C₄×D₄₇	—	4	2	no	—
137	C₂×C₄×D₄₇	—	4	2	no	—
138	C₂×C₄×D₄₇	C₄²	1	4	yes	—
139	C₂×C₄×D₄₇	C₄²	1	4	yes	—
140	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
141	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₄₇	—	2	1	no	—
143	C₂×C₈×C₄₇	—	2	1	no	—
144	C₂×C₈×C₄₇	—	2	1	no	—
145	C₂×C₈×C₄₇	—	2	1	no	—
146	C₂×C₈×C₄₇	—	2	1	no	—
147	C₂×C₈×C₄₇	—	2	1	no	—
148	C₂×C₈×C₄₇	—	2	1	no	—
149	C₂×C₈×C₄₇	—	2	1	no	—
150	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
154	C₄⋊C₄×C₄₇	—	2	4	no	—
155	C₄²×C₄₇	—	2	1	no	—
156	C₄²×C₄₇	—	2	1	no	—
157	C₄²×C₄₇	—	2	1	no	—
158	C₄²×C₄₇	—	2	1	no	—
159	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
160	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
161	C₄⋊Dic₄₇	—	2	4	no	—
162	Dic₄₇⋊C₄	—	2	4	no	—
163	Dic₄₇⋊C₄	M₁₆	1	8	yes	—
164	C₄×Dic₄₇	—	2	1	no	—
165	C₄×Dic₄₇	—	2	1	no	—
166	C₄×Dic₄₇	—	2	1	no	—
167	C₄×Dic₄₇	—	2	1	no	—
168	C₄×Dic₄₇	—	4	2	no	—
169	C₄×Dic₄₇	—	4	2	no	—
170	C₄×Dic₄₇	C₄²	1	4	yes	—
171	C₄×Dic₄₇	C₄²	1	4	yes	—
172	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
173	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
174	C₂×C₄₇⋊C₈	—	2	1	no	—
175	C₂×C₄₇⋊C₈	—	2	1	no	—
176	C₂×C₄₇⋊C₈	—	2	1	no	—
177	C₂×C₄₇⋊C₈	—	2	1	no	—
178	C₂×C₄₇⋊C₈	—	2	1	no	—
179	C₂×C₄₇⋊C₈	—	2	1	no	—
180	C₂×C₄₇⋊C₈	—	2	1	no	—
181	C₂×C₄₇⋊C₈	—	2	1	no	—
182	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
183	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
184	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
185	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
186	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
187	C₂²×D₄₇	—	2	1	no	—
188	C₂²×D₄₇	—	2	1	no	—
189	C₂²×D₄₇	—	2	2	no	—
190	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
191	C₂²×D₄₇	#131	1	4	yes	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
200	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
201	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
202	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
207	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
208	C₂×Dic₄₇	—	2	2	no	—
209	C₂×Dic₄₇	—	2	1	no	—
210	C₂×Dic₄₇	—	2	1	no	—
211	C₂×Dic₄₇	—	2	2	no	—
212	C₂×Dic₄₇	—	2	2	no	—
213	C₂×Dic₄₇	—	2	2	no	—
214	C₂×Dic₄₇	—	2	2	no	—
215	C₂×Dic₄₇	—	2	2	no	—
216	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
217	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
218	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
219	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
220	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
221	C₄×D₄₇	—	2	8	no	—
222	C₄×D₄₇	—	2	2	no	—
223	C₄×D₄₇	—	2	2	no	—
224	C₄×D₄₇	—	2	2	no	—
225	C₄×D₄₇	—	2	2	no	—
226	C₄×D₄₇	—	2	8	no	—
227	C₄×D₄₇	—	4	8	no	—
228	C₄×D₄₇	—	4	8	no	—
229	C₈×C₄₇	—	2	2	no	—
230	C₈×C₄₇	—	2	2	no	—
231	C₈×C₄₇	—	2	2	no	—
232	C₈×C₄₇	—	2	2	no	—
233	C₄₇⋊C₈	—	2	2	no	—
234	C₄₇⋊C₈	—	2	2	no	—
235	C₄₇⋊C₈	—	2	2	no	—
236	C₄₇⋊C₈	—	2	2	no	—
237	#20535	—	47	1	no	maximal, Sylow
238	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
239	C₂²×C₄₇	#518	1	1	yes	characteristic
240	C₂²×C₄₇	#519	1	1	yes	characteristic
241	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
242	C₂²×C₄₇	C₂×#131	1	2	yes	—
243	C₂×D₄₇	—	2	2	no	—
244	C₂×D₄₇	—	2	4	no	—
245	C₂×D₄₇	—	2	4	no	—
246	C₂×D₄₇	—	2	2	no	—
247	C₂×D₄₇	#405	1	4	yes	—
248	C₄×C₄₇	—	2	2	no	—
249	C₄×C₄₇	—	2	2	no	—
250	C₄×C₄₇	—	2	4	no	—
251	C₄×C₄₇	—	4	2	no	—
252	C₄×C₄₇	#520	1	1	yes	characteristic
253	C₄×C₄₇	#520	1	1	yes	characteristic
254	C₄×C₄₇	#520	1	1	yes	characteristic
255	C₄×C₄₇	#520	1	1	yes	characteristic
256	Dic₄₇	—	2	2	no	—
257	Dic₄₇	—	2	4	no	—
258	Dic₄₇	—	2	2	no	—
259	Dic₄₇	—	4	2	no	—
260	Dic₄₇	C₄×M₁₆	1	4	yes	—
261	C₂×#432	—	47	1	no	—
262	C₂×#431	—	47	1	no	—
263	C₂×C₄×C₄⋊C₄	—	47	1	no	—
264	#1771	—	47	1	no	—
265	#1771	—	47	1	no	—
266	#1771	—	47	1	no	—
267	#1771	D₄₇	1	1	yes	characteristic, complemented
268	#1770	—	47	1	no	—
269	#1770	—	47	1	no	—
270	C₈×C₄⋊C₄	—	47	1	no	—
271	C₈×C₄⋊C₄	—	47	1	no	—
272	#1749	—	47	1	no	—
273	#1749	—	47	1	no	—
274	C₄×C₂²⋊C₈	—	47	1	no	—
275	C₄×C₂²⋊C₈	—	47	1	no	—
276	C₂×C₄₇	#2274	1	1	yes	characteristic
277	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
278	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
279	C₂×C₄₇	#2974	1	2	yes	—
280	C₂×C₄₇	#2984	1	2	yes	—
281	D₄₇	—	2	4	no	—
282	C₂²×C₄⋊C₄	—	47	2	no	—
283	C₂²×C₄²	—	47	1	no	—
284	C₂²×C₄²	—	47	1	no	—
285	C₂²×C₄²	—	47	1	no	—
286	#432	—	47	8	no	—
287	#431	—	47	8	no	—
288	C₂×C₄⋊C₈	—	47	1	no	—
289	C₂×C₄⋊C₈	—	47	1	no	—
290	C₂×C₄⋊C₈	—	47	1	no	—
291	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
292	C₂×C₂²⋊C₈	—	47	1	no	—
293	C₂×C₂²⋊C₈	—	47	1	no	—
294	C₂×C₂²⋊C₈	—	47	1	no	—
295	C₂×C₂²⋊C₈	—	47	1	no	—
296	C₂×#97	—	47	1	no	—
297	C₂×#97	—	47	1	no	—
298	C₂×#97	—	47	1	no	—
299	C₂×#97	—	47	1	no	—
300	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
301	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
302	C₂×C₄×C₈	—	47	1	no	—
303	C₂×C₄×C₈	—	47	1	no	—
304	C₂×C₄×C₈	—	47	1	no	—
305	C₂×C₄×C₈	—	47	1	no	—
306	C₂×C₄×C₈	—	47	1	no	—
307	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
308	C₄×C₄⋊C₄	—	47	2	no	—
309	C₄×C₄⋊C₄	—	47	1	no	—
310	C₄×C₄⋊C₄	—	47	1	no	—
311	C₄×C₄⋊C₄	—	47	1	no	—
312	C₄×C₄⋊C₄	—	47	2	no	—
313	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
314	C₂×#95	—	47	2	no	—
315	#336	—	47	1	no	—
316	#336	—	47	1	no	—
317	#336	—	47	1	no	—
318	#336	—	47	1	no	—
319	#336	—	47	1	no	—
320	#336	—	47	1	no	—
321	#336	C₂×D₄₇	1	1	yes	characteristic
322	#336	C₂×D₄₇	1	1	yes	characteristic
323	C₄₇	#20535	1	1	yes	characteristic, complemented, Sylow
324	C₂³×C₄	—	47	1	no	—
325	C₂³×C₄	—	47	1	no	—
326	C₂³×C₄	—	47	1	no	—
327	C₂³×C₄	—	47	2	no	—
328	C₂³×C₄	—	47	2	no	—
329	C₂²×C₈	—	47	1	no	—
330	C₂²×C₈	—	47	1	no	—
331	C₂²×C₈	—	47	1	no	—
332	C₂²×C₈	—	47	1	no	—
333	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
334	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
335	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
336	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
337	C₂×C₄⋊C₄	—	47	2	no	—
338	C₂×C₄⋊C₄	—	47	2	no	—
339	C₂×C₄⋊C₄	—	47	2	no	—
340	C₂×C₄⋊C₄	—	94	8	no	—
341	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
342	C₂×C₄²	—	47	1	no	—
343	C₂×C₄²	—	47	1	no	—
344	C₂×C₄²	—	47	1	no	—
345	C₂×C₄²	—	47	4	no	—
346	C₂×C₄²	—	47	4	no	—
347	C₂×C₄²	—	47	1	no	—
348	C₂×C₄²	—	47	1	no	—
349	C₂×C₄²	—	47	2	no	—
350	C₂×C₄²	—	47	2	no	—
351	C₂×C₄²	—	188	1	no	—
352	C₂×C₄²	—	188	1	no	—
353	C₂×C₄²	—	188	1	no	—
354	C₂×C₄²	—	188	1	no	—
355	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
356	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
357	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
358	C₄⋊C₈	—	47	4	no	—
359	C₄⋊C₈	—	47	4	no	—
360	C₄⋊C₈	—	47	4	no	—
361	C₄⋊C₈	C₄×D₄₇	1	4	yes	complemented
362	C₂²⋊C₈	—	47	4	no	—
363	C₂²⋊C₈	—	47	4	no	—
364	C₂²⋊C₈	—	47	4	no	—
365	C₂²⋊C₈	—	47	4	no	—
366	#97	—	4	1	no	—
367	#97	—	47	4	no	—
368	#97	—	188	1	no	—
369	#97	—	188	1	no	—
370	#97	—	188	1	no	—
371	#97	C₄×D₄₇	1	4	yes	complemented
372	C₄×C₈	—	4	1	no	—
373	C₄×C₈	—	47	4	no	—
374	C₄×C₈	—	47	4	no	—
375	C₄×C₈	—	188	1	no	—
376	C₄×C₈	—	188	1	no	—
377	C₄×C₈	—	188	1	no	—
378	#95	—	47	2	no	—
379	#95	—	47	2	no	—
380	#95	—	47	2	no	—
381	#95	C₄×D₄₇	1	2	yes	—
382	C₂⁴	—	47	1	no	—
383	C₂²×C₄	—	47	1	no	—
384	C₂²×C₄	—	47	1	no	—
385	C₂²×C₄	—	47	2	no	—
386	C₂²×C₄	—	47	1	no	—
387	C₂²×C₄	—	47	4	no	—
388	C₂²×C₄	—	47	4	no	—
389	C₂²×C₄	—	47	2	no	—
390	C₂²×C₄	—	47	2	no	—
391	C₂²×C₄	—	47	2	no	—
392	C₂²×C₄	—	94	4	no	—
393	C₂²×C₄	—	94	4	no	—
394	C₂²×C₄	—	94	4	no	—
395	C₂²×C₄	—	94	4	no	—
396	C₂²×C₄	—	94	4	no	—
397	C₂²×C₄	—	94	1	no	—
398	C₂²×C₄	—	94	1	no	—
399	C₂²×C₄	—	94	1	no	—
400	C₂²×C₄	—	94	1	no	—
401	C₂²×C₄	—	94	4	no	—
402	C₂²×C₄	—	188	2	no	—
403	C₂²×C₄	—	188	2	no	—
404	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
405	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
406	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
407	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
408	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
409	C₂×C₈	—	2	1	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	47	2	no	—
418	C₂×C₈	—	47	2	no	—
419	C₂×C₈	—	47	2	no	—
420	C₂×C₈	—	47	2	no	—
421	C₂×C₈	—	94	1	no	—
422	C₂×C₈	—	94	1	no	—
423	C₂×C₈	—	94	1	no	—
424	C₂×C₈	—	94	1	no	—
425	C₂×C₈	—	94	1	no	—
426	C₂×C₈	—	94	1	no	—
427	C₂×C₈	—	94	1	no	—
428	C₂×C₈	—	94	1	no	—
429	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
430	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
431	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
432	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	47	8	no	—
435	C₄⋊C₄	—	94	4	no	—
436	C₄⋊C₄	—	94	4	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	2	1	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	47	4	no	—
442	C₄²	—	47	4	no	—
443	C₄²	—	47	2	no	—
444	C₄²	—	47	2	no	—
445	C₄²	—	94	1	no	—
446	C₄²	—	94	1	no	—
447	C₄²	—	94	1	no	—
448	C₄²	—	94	1	no	—
449	C₄²	—	188	2	no	—
450	C₄²	—	188	2	no	—
451	C₄²	C₂×C₄×D₄₇	1	2	yes	—
452	C₄²	C₂×C₄×D₄₇	1	2	yes	—
453	C₂³	—	47	2	no	—
454	C₂³	—	47	4	no	—
455	C₂³	—	94	1	no	—
456	C₂³	—	94	1	no	—
457	C₂³	—	94	2	no	—
458	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	47	2	no	—
467	C₂×C₄	—	47	4	no	—
468	C₂×C₄	—	47	2	no	—
469	C₂×C₄	—	47	2	no	—
470	C₂×C₄	—	47	4	no	—
471	C₂×C₄	—	94	8	no	—
472	C₂×C₄	—	94	8	no	—
473	C₂×C₄	—	94	2	no	—
474	C₂×C₄	—	94	1	no	—
475	C₂×C₄	—	94	1	no	—
476	C₂×C₄	—	94	2	no	—
477	C₂×C₄	—	94	2	no	—
478	C₂×C₄	—	94	2	no	—
479	C₂×C₄	—	94	2	no	—
480	C₂×C₄	—	94	2	no	—
481	C₂×C₄	—	94	2	no	—
482	C₂×C₄	—	94	2	no	—
483	C₂×C₄	—	94	2	no	—
484	C₂×C₄	—	94	2	no	—
485	C₂×C₄	—	188	8	no	—
486	C₂×C₄	—	188	8	no	—
487	C₂×C₄	C₄²×D₄₇	1	2	yes	—
488	C₂×C₄	C₄²×D₄₇	1	2	yes	—
489	C₂×C₄	M₁₆×D₄₇	1	4	yes	—
490	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
491	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
492	C₂×C₄	#13094069	1	1	yes	characteristic
493	C₂×C₄	#13094070	1	1	yes	characteristic
494	C₂×C₄	#13094071	1	1	yes	characteristic
495	C₂×C₄	#13094072	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	2	2	no	—
498	C₈	—	2	2	no	—
499	C₈	—	2	2	no	—
500	C₈	—	94	2	no	—
501	C₈	—	94	2	no	—
502	C₈	—	94	2	no	—
503	C₈	—	94	2	no	—
504	C₂²	—	47	4	no	—
505	C₂²	—	94	4	no	—
506	C₂²	—	94	4	no	—
507	C₂²	—	94	2	no	—
508	C₂²	—	94	2	no	—
509	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
510	C₂²	#15689595	1	1	yes	characteristic
511	C₂²	#15689599	1	1	yes	characteristic
512	C₂²	C₂×M₁₆×D₄₇	1	2	yes	—
513	C₂²	#131×D₄₇	1	2	yes	—
514	C₄	—	2	4	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	47	4	no	—
519	C₄	—	94	4	no	—
520	C₄	—	94	2	no	—
521	C₄	—	94	2	no	—
522	C₄	—	188	2	no	—
523	C₄	#15689602	1	1	yes	characteristic
524	C₄	#15689603	1	1	yes	characteristic
525	C₄	#15689604	1	1	yes	characteristic
526	C₄	#15689605	1	1	yes	characteristic
527	C₂	—	94	4	no	—
528	C₂	#20245742	1	1	yes	characteristic
529	C₂	C₄×M₁₆×D₄₇	1	1	yes	characteristic
530	C₂	#405×D₄₇	1	1	yes	characteristic
531	C₂	#20252418	1	2	yes	—
532	C₂	#20252474	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1771	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1771	D₄₇
hypocenter	C₄₇	#20535
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
4. #20243265	C₂	semidirect
5. #20243263	C₂	semidirect
6. #20243260	C₂	semidirect
7. #20243256	C₂	semidirect
8. #20243254	C₂	semidirect
9. C₈×Dic₄₇⋊C₄	C₂	semidirect
10. #20243249	C₂	semidirect
15. C₄₇×#1771	C₂	semidirect
20. #15689178	C₄	semidirect
21. #15689175	C₄	semidirect
83. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
84. Dic₄₇⋊C₈	C₂×C₄	semidirect
85. Dic₄₇⋊C₈	C₂×C₄	semidirect
91. #13093935	C₂×C₄	semidirect
97. C₈×Dic₄₇	C₂×C₄	semidirect
98. C₈×Dic₄₇	C₂×C₄	semidirect
110. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
112. #97×C₄₇	C₂×C₄	semidirect
267. #1771	D₄₇	semidirect
323. C₄₇	#20535	semidirect
361. C₄⋊C₈	C₄×D₄₇	semidirect
371. #97	C₄×D₄₇	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×#15689175	2
C₄×C₄⋊C₄×D₄₇	2
#20243265	2
#20243263	2
#20243260	2
#20243256	2
#20243254	2
C₈×Dic₄₇⋊C₄	2
#20243249	2
#20243151	2
#20243149	2
C₄×(C₂×D₄₇)⋊C₈	2
#20243145	2
C₄₇×#1771	2
#20535	47