Subgroups — #26226728

Order 12032.

838 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689174	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20245784	C₂	1	1	yes	maximal, characteristic
4	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244104	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243567	C₂	1	2	yes	maximal
8	#20243564	C₂	1	2	yes	maximal
9	#20243541	C₂	1	2	yes	maximal, complemented
10	#20243506	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
13	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
14	#15689174	—	2	4	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
22	C₄⋊C₈×D₄₇	—	2	4	no	—
23	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	#15688990	C₄	1	2	yes	—
27	#15688988	C₄	1	1	yes	characteristic
28	#15688988	C₄	1	1	yes	characteristic
29	#15688985	C₄	1	2	yes	—
30	#15688980	C₄	1	1	yes	characteristic
31	#15688980	C₄	1	1	yes	characteristic
32	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
33	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
34	#15688969	C₂²	1	2	yes	—
35	#15688878	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	2	yes	—
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×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	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
49	C₂×C₈×D₄₇	—	2	4	no	—
50	C₂×C₈×D₄₇	—	4	2	no	—
51	C₂×C₈×D₄₇	—	4	2	no	—
52	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	C₄²×D₄₇	D₄	1	4	yes	—
61	C₄²×D₄₇	Q₈	1	4	yes	—
62	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
63	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
64	Dic₄₇⋊C₈	—	2	4	no	—
65	Dic₄₇⋊C₈	—	2	2	no	—
66	Dic₄₇⋊C₈	—	2	2	no	—
67	Dic₄₇⋊C₈	—	4	2	no	—
68	Dic₄₇⋊C₈	—	4	2	no	—
69	(C₂×D₄₇)⋊C₈	—	2	2	no	—
70	(C₂×D₄₇)⋊C₈	—	2	2	no	—
71	C₄×C₄₇⋊C₈	—	2	2	no	—
72	C₄₇⋊#95	C₂×C₄	1	2	yes	—
73	C₄₇⋊#95	C₂×C₄	1	2	yes	—
74	C₄₇⋊#95	C₂×C₄	1	2	yes	—
75	C₄₇⋊#95	C₂×C₄	1	2	yes	—
76	C₄₇⋊#95	C₂×C₄	1	2	yes	—
77	C₄₇⋊#95	C₂×C₄	1	2	yes	—
78	C₄₇⋊#95	C₂×C₄	1	2	yes	—
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₇	—	2	2	no	—
87	C₄⋊C₈×C₄₇	—	4	2	no	—
88	C₄×C₈×C₄₇	—	2	2	no	—
89	#95×C₄₇	C₂×C₄	1	2	yes	—
90	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₄₇	—	2	2	no	—
102	C₂×C₄×D₄₇	—	2	2	no	—
103	C₂×C₄×D₄₇	—	2	2	no	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	—	2	1	no	—
106	C₂×C₄×D₄₇	—	2	1	no	—
107	C₂×C₄×D₄₇	—	2	1	no	—
108	C₂×C₄×D₄₇	—	2	1	no	—
109	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
110	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
111	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
112	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	C₂×D₄	1	2	yes	—
127	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
128	(C₂×D₄₇)⋊C₄	—	2	4	no	—
129	(C₂×D₄₇)⋊C₄	—	2	4	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄×Dic₄₇	—	2	2	no	—
133	C₄×Dic₄₇	—	2	2	no	—
134	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
135	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
136	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
137	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₈×D₄₇	—	4	8	no	—
148	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
149	C₂²×D₄₇	—	2	1	no	—
150	C₂²×D₄₇	—	2	1	no	—
151	C₂²×D₄₇	—	2	1	no	—
152	C₂²×D₄₇	—	2	1	no	—
153	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
154	C₂²×D₄₇	#131	1	2	yes	—
155	C₂²×D₄₇	#131	1	2	yes	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	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	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₇	#131	1	2	yes	—
167	C₂×C₄×C₄₇	#131	1	2	yes	—
168	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
174	C₂×Dic₄₇	—	2	1	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	2	no	—
186	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
187	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
188	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
189	C₄×D₄₇	—	2	8	no	—
190	C₄×D₄₇	—	2	2	no	—
191	C₄×D₄₇	—	2	2	no	—
192	C₄×D₄₇	—	2	2	no	—
193	C₄×D₄₇	—	2	2	no	—
194	C₄×D₄₇	—	2	8	no	—
195	C₈×C₄₇	—	4	2	no	—
196	C₈×C₄₇	—	4	1	no	—
197	C₈×C₄₇	—	4	1	no	—
198	C₄₇⋊C₈	—	4	2	no	—
199	C₄₇⋊C₈	—	4	1	no	—
200	C₄₇⋊C₈	—	4	1	no	—
201	#21973	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
203	C₂²×C₄₇	#520	1	1	yes	characteristic
204	C₂²×C₄₇	#520	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
207	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
209	C₂×D₄₇	—	2	2	no	—
210	C₂×D₄₇	—	2	2	no	—
211	C₂×D₄₇	—	2	2	no	—
212	C₂×D₄₇	—	2	2	no	—
213	C₂×D₄₇	—	2	2	no	—
214	C₂×D₄₇	—	2	2	no	—
215	C₂×D₄₇	#424	1	4	yes	—
216	C₄×C₄₇	—	2	2	no	—
217	C₄×C₄₇	—	4	2	no	—
218	C₄×C₄₇	—	4	2	no	—
219	C₄×C₄₇	#424	1	4	yes	—
220	C₄×C₄₇	#535	1	1	yes	characteristic
221	C₄×C₄₇	#536	1	1	yes	characteristic
222	C₄×C₄₇	#544	1	1	yes	characteristic
223	C₄×C₄₇	#544	1	1	yes	characteristic
224	Dic₄₇	—	2	2	no	—
225	Dic₄₇	—	2	2	no	—
226	Dic₄₇	—	2	2	no	—
227	Dic₄₇	—	4	2	no	—
228	Dic₄₇	—	4	2	no	—
229	C₂×#431	—	47	1	no	—
230	C₂²×C₄⋊C₈	—	47	1	no	—
231	#2283	—	47	1	no	—
232	#1939	—	47	1	no	—
233	#1939	—	47	1	no	—
234	#1939	—	47	1	no	—
235	#1939	D₄₇	1	1	yes	characteristic, complemented
236	#1850	—	47	2	no	—
237	#1850	—	47	2	no	—
238	#1843	—	47	2	no	—
239	#1832	—	47	2	no	—
240	C₂×C₄₇	#2317	1	1	yes	characteristic
241	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
242	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
243	C₂×C₄₇	#2994	1	1	yes	characteristic
244	C₂×C₄₇	#2994	1	1	yes	characteristic
245	C₂×C₄₇	#2994	1	1	yes	characteristic
246	C₂×C₄₇	#2994	1	1	yes	characteristic
247	D₄₇	—	2	4	no	—
248	C₂³×C₈	—	47	2	no	—
249	C₂²×C₄²	—	47	1	no	—
250	#431	—	94	4	no	—
251	C₂×C₄⋊C₈	—	47	1	no	—
252	C₂×C₄⋊C₈	—	47	2	no	—
253	C₂×C₄⋊C₈	—	47	1	no	—
254	C₂×C₄⋊C₈	—	47	1	no	—
255	C₂×C₄⋊C₈	—	47	2	no	—
256	C₂×C₄⋊C₈	—	47	2	no	—
257	C₂×C₄⋊C₈	—	47	2	no	—
258	C₂×C₄⋊C₈	—	94	4	no	—
259	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
261	C₂×C₂²⋊C₈	—	47	1	no	—
262	C₂×C₂²⋊C₈	—	47	1	no	—
263	C₂×C₄×C₈	—	47	1	no	—
264	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
265	#383	—	47	2	no	—
266	#382	—	47	1	no	—
267	#382	—	47	1	no	—
268	#381	—	47	2	no	—
269	#380	—	47	1	no	—
270	#380	—	47	1	no	—
271	C₄×C₄⋊C₄	—	47	1	no	—
272	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
273	C₄×C₂²⋊C₄	—	47	2	no	—
274	#376	—	47	2	no	—
275	#336	—	47	2	no	—
276	#336	—	47	2	no	—
277	#336	—	47	2	no	—
278	#336	C₂×D₄₇	1	2	yes	—
279	C₄₇	#21973	1	1	yes	characteristic, complemented, Sylow
280	C₂³×C₄	—	47	1	no	—
281	C₂³×C₄	—	47	1	no	—
282	C₂³×C₄	—	47	1	no	—
283	C₂²×C₈	—	47	2	no	—
284	C₂²×C₈	—	47	1	no	—
285	C₂²×C₈	—	47	1	no	—
286	C₂²×C₈	—	94	4	no	—
287	C₂²×C₈	—	188	2	no	—
288	C₂²×C₈	—	188	2	no	—
289	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
290	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	—	47	1	no	—
293	C₂×C₄⋊C₄	—	47	1	no	—
294	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
296	C₂×C₂²⋊C₄	—	47	2	no	—
297	C₂×C₂²⋊C₄	—	47	2	no	—
298	C₂×C₄²	—	47	1	no	—
299	C₂×C₄²	—	47	1	no	—
300	C₂×C₄²	—	47	1	no	—
301	C₂×C₄²	—	47	4	no	—
302	C₂×C₄²	—	47	4	no	—
303	C₂×C₄²	—	47	2	no	—
304	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
305	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	4	2	no	—
308	C₄⋊C₈	—	94	4	no	—
309	C₄⋊C₈	—	94	2	no	—
310	C₄⋊C₈	—	94	2	no	—
311	C₄⋊C₈	—	94	2	no	—
312	C₄⋊C₈	—	188	2	no	—
313	C₄⋊C₈	—	188	2	no	—
314	C₄⋊C₈	—	188	2	no	—
315	C₂²⋊C₈	—	94	2	no	—
316	C₂²⋊C₈	—	94	2	no	—
317	C₄×C₈	—	2	2	no	—
318	C₄×C₈	—	94	2	no	—
319	#95	—	47	2	no	—
320	#95	—	47	2	no	—
321	#95	—	47	2	no	—
322	#95	—	47	2	no	—
323	#95	—	47	2	no	—
324	#95	—	47	2	no	—
325	#95	—	47	2	no	—
326	#95	C₄×D₄₇	1	2	yes	—
327	C₂⁴	—	47	1	no	—
328	C₂²×C₄	—	47	1	no	—
329	C₂²×C₄	—	47	1	no	—
330	C₂²×C₄	—	47	1	no	—
331	C₂²×C₄	—	47	4	no	—
332	C₂²×C₄	—	47	4	no	—
333	C₂²×C₄	—	47	2	no	—
334	C₂²×C₄	—	47	2	no	—
335	C₂²×C₄	—	47	2	no	—
336	C₂²×C₄	—	47	2	no	—
337	C₂²×C₄	—	94	2	no	—
338	C₂²×C₄	—	94	2	no	—
339	C₂²×C₄	—	94	2	no	—
340	C₂²×C₄	—	94	2	no	—
341	C₂²×C₄	—	94	1	no	—
342	C₂²×C₄	—	94	1	no	—
343	C₂²×C₄	—	94	1	no	—
344	C₂²×C₄	—	94	1	no	—
345	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
346	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
347	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	94	1	no	—
360	C₂×C₈	—	94	1	no	—
361	C₂×C₈	—	94	2	no	—
362	C₂×C₈	—	94	1	no	—
363	C₂×C₈	—	94	2	no	—
364	C₂×C₈	—	94	1	no	—
365	C₂×C₈	—	94	2	no	—
366	C₂×C₈	—	94	1	no	—
367	C₂×C₈	—	94	1	no	—
368	C₂×C₈	—	188	8	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	94	2	no	—
372	C₄⋊C₄	—	94	2	no	—
373	C₂²⋊C₄	—	94	4	no	—
374	C₂²⋊C₄	—	94	4	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	47	4	no	—
378	C₄²	—	47	4	no	—
379	C₄²	—	47	2	no	—
380	C₄²	—	47	2	no	—
381	C₄²	—	94	2	no	—
382	C₄²	—	94	2	no	—
383	C₄²	D₄×D₄₇	1	2	yes	—
384	C₄²	Q₈×D₄₇	1	2	yes	—
385	C₂³	—	47	2	no	—
386	C₂³	—	47	2	no	—
387	C₂³	—	47	2	no	—
388	C₂³	—	94	1	no	—
389	C₂³	—	94	1	no	—
390	C₂³	—	94	1	no	—
391	C₂³	—	94	1	no	—
392	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	47	2	no	—
402	C₂×C₄	—	47	2	no	—
403	C₂×C₄	—	47	2	no	—
404	C₂×C₄	—	94	8	no	—
405	C₂×C₄	—	94	1	no	—
406	C₂×C₄	—	94	1	no	—
407	C₂×C₄	—	94	1	no	—
408	C₂×C₄	—	94	1	no	—
409	C₂×C₄	—	94	1	no	—
410	C₂×C₄	—	94	1	no	—
411	C₂×C₄	—	94	2	no	—
412	C₂×C₄	—	94	2	no	—
413	C₂×C₄	—	94	8	no	—
414	C₂×C₄	—	94	2	no	—
415	C₂×C₄	—	94	2	no	—
416	C₂×C₄	—	94	2	no	—
417	C₂×C₄	—	94	2	no	—
418	C₂×C₄	—	94	2	no	—
419	C₂×C₄	—	94	2	no	—
420	C₂×C₄	—	94	2	no	—
421	C₂×C₄	—	94	2	no	—
422	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
423	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
424	C₂×C₄	#13094030	1	2	yes	—
425	C₂×C₄	#13094032	1	2	yes	—
426	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
427	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
428	C₂×C₄	#13094069	1	1	yes	characteristic
429	C₂×C₄	#13094070	1	1	yes	characteristic
430	C₂×C₄	#13094071	1	1	yes	characteristic
431	C₂×C₄	#13094072	1	1	yes	characteristic
432	C₈	—	4	1	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	188	1	no	—
436	C₈	—	188	2	no	—
437	C₈	—	188	1	no	—
438	C₂²	—	47	4	no	—
439	C₂²	—	94	2	no	—
440	C₂²	—	94	2	no	—
441	C₂²	—	94	2	no	—
442	C₂²	—	94	2	no	—
443	C₂²	—	94	2	no	—
444	C₂²	—	94	2	no	—
445	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
446	C₂²	#15689602	1	1	yes	characteristic
447	C₂²	#15689605	1	1	yes	characteristic
448	C₂²	#131×D₄₇	1	1	yes	characteristic
449	C₂²	#131×D₄₇	1	1	yes	characteristic
450	C₂²	C₂×#13094030	1	1	yes	characteristic
451	C₂²	C₂×#13094032	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	94	2	no	—
456	C₄	—	94	2	no	—
457	C₄	—	94	2	no	—
458	C₄	—	188	2	no	—
459	C₄	—	188	2	no	—
460	C₄	#15689148	1	4	yes	—
461	C₄	#15689689	1	1	yes	characteristic
462	C₄	#15689696	1	1	yes	characteristic
463	C₄	#15689750	1	1	yes	characteristic
464	C₄	#15689753	1	1	yes	characteristic
465	C₂	—	94	4	no	—
466	C₂	#20246010	1	1	yes	characteristic
467	C₂	#424×D₄₇	1	1	yes	characteristic
468	C₂	C₂×#15689148	1	1	yes	characteristic
469	C₂	#20252543	1	1	yes	characteristic
470	C₂	#20252547	1	1	yes	characteristic
471	C₂	#20252549	1	1	yes	characteristic
472	C₂	#20252551	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1939	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1939	D₄₇
hypocenter	C₄₇	#21973
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
4. #20244107	C₂	semidirect
5. #20244106	C₂	semidirect
6. #20244104	C₂	semidirect
9. #20243541	C₂	semidirect
10. #20243506	C₂	semidirect
11. C₄₇×#1939	C₂	semidirect
235. #1939	D₄₇	semidirect
279. C₄₇	#21973	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689174	2
C₂×C₄⋊C₈×D₄₇	2
#20245784	2
#20244107	2
#20244106	2
#20244104	2
#20243567	2
#20243564	2
#20243541	2
#20243506	2
C₄₇×#1939	2
#21973	47