Subgroups — #26234141

Order 12032.

828 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13093982	C₂	1	1	yes	maximal, characteristic
2	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244104	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243994	C₂	1	2	yes	maximal
5	#20243992	C₂	1	2	yes	maximal
6	#20243503	C₂	1	2	yes	maximal, complemented
7	#20243365	C₂	1	1	yes	maximal, characteristic
8	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×(C₂×D₄₇)⋊C₈	C₂	1	1	yes	maximal, characteristic
10	#20243133	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13093982	C₄	1	1	yes	characteristic
13	C₂×#13093982	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×Dic₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
24	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
25	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
26	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
27	#15688970	C₄	1	2	yes	—
28	#15688968	C₄	1	2	yes	—
29	C₄²×Dic₄₇	C₂²	1	2	yes	—
30	#15688878	C₂²	1	2	yes	—
31	#15688877	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	1	yes	characteristic
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	#13093982	—	2	4	no	—
48	#13093982	C₈	1	8	yes	complemented
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
61	C₄²×D₄₇	—	2	2	no	—
62	C₄²×D₄₇	—	2	2	no	—
63	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
64	Dic₄₇⋊C₈	—	4	2	no	—
65	Dic₄₇⋊C₈	—	4	2	no	—
66	(C₂×D₄₇)⋊C₈	—	2	2	no	—
67	(C₂×D₄₇)⋊C₈	—	2	2	no	—
68	(C₂×D₄₇)⋊C₈	—	4	2	no	—
69	C₄×C₄₇⋊C₈	—	2	2	no	—
70	C₄×C₄₇⋊C₈	—	2	4	no	—
71	C₄₇⋊#95	C₂×C₄	1	2	yes	—
72	C₄₇⋊#95	C₂×C₄	1	2	yes	—
73	C₄₇⋊#95	C₂×C₄	1	2	yes	—
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₇	—	2	2	no	—
82	C₄×C₈×C₄₇	—	2	4	no	—
83	C₄×C₈×C₄₇	—	2	2	no	—
84	#95×C₄₇	C₂×C₄	1	2	yes	—
85	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₄×D₄₇	—	2	2	no	—
97	C₂×C₄×D₄₇	—	2	2	no	—
98	C₂×C₄×D₄₇	—	2	2	no	—
99	C₂×C₄×D₄₇	—	2	1	no	—
100	C₂×C₄×D₄₇	—	2	1	no	—
101	C₂×C₄×D₄₇	—	2	1	no	—
102	C₂×C₄×D₄₇	—	2	1	no	—
103	C₂×C₄×D₄₇	—	2	1	no	—
104	C₂×C₄×D₄₇	—	2	1	no	—
105	C₂×C₄×D₄₇	—	2	2	no	—
106	C₂×C₄×D₄₇	—	4	1	no	—
107	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
108	C₂×C₈×C₄₇	—	2	1	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	#41	1	2	yes	—
117	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	—
118	C₄⋊C₄×C₄₇	M₁₆	1	4	yes	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	#41	1	2	yes	—
122	C₄²×C₄₇	#41	1	2	yes	—
123	(C₂×D₄₇)⋊C₄	—	2	4	no	—
124	(C₂×D₄₇)⋊C₄	C₂×C₈	1	8	yes	—
125	C₄⋊Dic₄₇	—	2	2	no	—
126	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	—
127	C₄×Dic₄₇	—	2	2	no	—
128	C₄×Dic₄₇	—	2	2	no	—
129	C₄×Dic₄₇	—	2	4	no	—
130	C₄×Dic₄₇	—	2	1	no	—
131	C₄×Dic₄₇	—	2	1	no	—
132	C₄×Dic₄₇	—	2	2	no	—
133	C₄×Dic₄₇	—	2	2	no	—
134	C₄×Dic₄₇	—	2	4	no	—
135	C₄×Dic₄₇	—	4	2	no	—
136	C₄×Dic₄₇	C₂×C₈	1	8	yes	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	#41	1	2	yes	—
146	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
147	C₂²×D₄₇	—	2	1	no	—
148	C₂²×D₄₇	—	2	1	no	—
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	C₂²×C₈	1	2	yes	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	#117	1	2	yes	—
161	C₂×C₄×C₄₇	#117	1	2	yes	—
162	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
163	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
165	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×Dic₄₇	—	2	1	no	—
173	C₂×Dic₄₇	—	2	1	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	2	2	no	—
178	C₂×Dic₄₇	—	2	1	no	—
179	C₂×Dic₄₇	—	2	1	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	1	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	2	2	no	—
184	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
185	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
186	C₂×Dic₄₇	#131	1	2	yes	—
187	C₄×D₄₇	—	2	8	no	—
188	C₄×D₄₇	—	4	4	no	—
189	C₄×D₄₇	—	4	1	no	—
190	C₄×D₄₇	—	4	1	no	—
191	C₄×D₄₇	—	4	1	no	—
192	C₄×D₄₇	—	4	1	no	—
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	—	4	1	no	—
195	C₈×C₄₇	—	4	2	no	—
196	C₄₇⋊C₈	—	2	2	no	—
197	C₄₇⋊C₈	—	4	2	no	—
198	C₄₇⋊C₈	—	4	1	no	—
199	#22632	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
201	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
202	C₂²×C₄₇	#520	1	1	yes	characteristic
203	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
204	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
206	C₂²×C₄₇	#568	1	1	yes	characteristic
207	C₂×D₄₇	—	2	2	no	—
208	C₂×D₄₇	—	2	2	no	—
209	C₂×D₄₇	—	2	2	no	—
210	C₂×D₄₇	—	4	1	no	—
211	C₂×D₄₇	—	4	1	no	—
212	C₂×D₄₇	—	4	1	no	—
213	C₂×D₄₇	—	4	1	no	—
214	C₄×C₄₇	—	2	2	no	—
215	C₄×C₄₇	—	2	4	no	—
216	C₄×C₄₇	—	2	4	no	—
217	C₄×C₄₇	#431	1	4	yes	—
218	C₄×C₄₇	#552	1	1	yes	characteristic
219	C₄×C₄₇	#552	1	1	yes	characteristic
220	C₄×C₄₇	#555	1	1	yes	characteristic
221	C₄×C₄₇	#555	1	1	yes	characteristic
222	Dic₄₇	—	2	2	no	—
223	Dic₄₇	—	2	2	no	—
224	Dic₄₇	—	2	4	no	—
225	Dic₄₇	—	4	1	no	—
226	Dic₄₇	—	4	2	no	—
227	C₄×#117	—	47	1	no	—
228	#1939	—	47	1	no	—
229	#1939	—	47	1	no	—
230	#1923	—	47	2	no	—
231	#1923	—	47	2	no	—
232	#1831	—	47	2	no	—
233	#1797	—	47	1	no	—
234	C₈×C₄⋊C₄	—	47	1	no	—
235	C₈×C₄⋊C₄	D₄₇	1	1	yes	characteristic, complemented
236	C₄×C₂²⋊C₈	—	47	1	no	—
237	#1744	—	47	2	no	—
238	C₂×C₄₇	#2346	1	1	yes	characteristic
239	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
240	C₂×C₄₇	#2924	1	1	yes	characteristic
241	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
242	C₂×C₄₇	#2970	1	1	yes	characteristic
243	C₂×C₄₇	#2988	1	1	yes	characteristic
244	C₂×C₄₇	#2991	1	1	yes	characteristic
245	D₄₇	—	4	2	no	—
246	C₂×#117	—	47	1	no	—
247	C₂×#117	—	47	1	no	—
248	C₂²×C₄²	—	47	1	no	—
249	C₂×C₄⋊C₈	—	47	1	no	—
250	C₂×C₄⋊C₈	—	47	2	no	—
251	C₂×C₄⋊C₈	—	47	2	no	—
252	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
253	C₂×C₂²⋊C₈	—	47	1	no	—
254	C₂×C₂²⋊C₈	—	47	1	no	—
255	C₂×C₂²⋊C₈	—	47	2	no	—
256	C₂×C₄×C₈	—	47	2	no	—
257	C₂×C₄×C₈	—	47	1	no	—
258	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
259	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
260	C₄×C₄⋊C₄	—	47	1	no	—
261	C₄×C₄⋊C₄	—	47	1	no	—
262	C₄×C₄⋊C₄	—	47	1	no	—
263	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
264	C₄×C₂²⋊C₄	—	47	2	no	—
265	C₄×C₂²⋊C₄	—	47	2	no	—
266	#376	—	47	2	no	—
267	C₄³	—	47	2	no	—
268	#336	—	47	2	no	—
269	#336	—	47	1	no	—
270	#336	—	47	2	no	—
271	#336	—	47	2	no	—
272	#336	—	47	1	no	—
273	#336	—	47	2	no	—
274	#336	C₂×D₄₇	1	2	yes	—
275	C₄₇	#22632	1	1	yes	characteristic, complemented, Sylow
276	C₂³×C₄	—	47	1	no	—
277	C₂³×C₄	—	47	1	no	—
278	C₂³×C₄	—	47	1	no	—
279	C₂²×C₈	—	47	1	no	—
280	C₂²×C₈	—	47	2	no	—
281	C₂²×C₈	—	47	1	no	—
282	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
283	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
284	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
285	#117	—	47	8	no	—
286	#117	—	94	4	no	—
287	C₂×C₄⋊C₄	—	47	1	no	—
288	C₂×C₄⋊C₄	—	47	1	no	—
289	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
291	C₂×C₂²⋊C₄	—	47	2	no	—
292	C₂×C₂²⋊C₄	—	47	2	no	—
293	C₂×C₄²	—	47	2	no	—
294	C₂×C₄²	—	47	2	no	—
295	C₂×C₄²	—	47	2	no	—
296	C₂×C₄²	—	47	1	no	—
297	C₂×C₄²	—	47	1	no	—
298	C₂×C₄²	—	47	1	no	—
299	C₂×C₄²	—	47	2	no	—
300	C₂×C₄²	—	47	2	no	—
301	C₂×C₄²	—	94	2	no	—
302	C₂×C₄²	—	94	2	no	—
303	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
304	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	94	2	no	—
307	C₄⋊C₈	—	188	2	no	—
308	C₄⋊C₈	—	188	2	no	—
309	C₂²⋊C₈	—	94	2	no	—
310	C₂²⋊C₈	—	94	2	no	—
311	C₂²⋊C₈	—	188	2	no	—
312	C₄×C₈	—	2	4	no	—
313	C₄×C₈	—	2	2	no	—
314	C₄×C₈	—	94	4	no	—
315	C₄×C₈	—	94	2	no	—
316	#95	—	47	2	no	—
317	#95	—	47	2	no	—
318	#95	—	47	2	no	—
319	#95	C₄×D₄₇	1	2	yes	—
320	C₂⁴	—	47	1	no	—
321	C₂²×C₄	—	47	2	no	—
322	C₂²×C₄	—	47	1	no	—
323	C₂²×C₄	—	47	1	no	—
324	C₂²×C₄	—	47	4	no	—
325	C₂²×C₄	—	47	1	no	—
326	C₂²×C₄	—	47	2	no	—
327	C₂²×C₄	—	94	2	no	—
328	C₂²×C₄	—	94	2	no	—
329	C₂²×C₄	—	94	2	no	—
330	C₂²×C₄	—	94	2	no	—
331	C₂²×C₄	—	94	1	no	—
332	C₂²×C₄	—	94	1	no	—
333	C₂²×C₄	—	94	1	no	—
334	C₂²×C₄	—	94	1	no	—
335	C₂²×C₄	—	94	1	no	—
336	C₂²×C₄	—	94	1	no	—
337	C₂²×C₄	—	188	1	no	—
338	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
340	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
341	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
342	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	47	2	no	—
352	C₂×C₈	—	94	1	no	—
353	C₂×C₈	—	94	1	no	—
354	C₂×C₈	—	94	2	no	—
355	C₂×C₈	—	94	1	no	—
356	C₂×C₈	—	94	1	no	—
357	C₂×C₈	—	94	2	no	—
358	C₂×C₈	—	94	2	no	—
359	C₂×C₈	—	94	1	no	—
360	C₂×C₈	#10625352	1	2	yes	—
361	C₄⋊C₄	—	47	4	no	—
362	C₄⋊C₄	—	94	2	no	—
363	C₄⋊C₄	C₈×D₄₇	1	4	yes	—
364	C₄⋊C₄	#10625324	1	4	yes	—
365	C₂²⋊C₄	—	47	8	no	—
366	C₂²⋊C₄	—	94	4	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	47	8	no	—
370	C₄²	—	94	4	no	—
371	C₄²	—	94	2	no	—
372	C₄²	—	94	2	no	—
373	C₄²	—	94	4	no	—
374	C₄²	—	94	1	no	—
375	C₄²	—	94	1	no	—
376	C₄²	—	94	2	no	—
377	C₄²	—	94	2	no	—
378	C₄²	—	188	2	no	—
379	C₄²	#10625350	1	2	yes	—
380	C₄²	#10625350	1	2	yes	—
381	C₂³	—	47	2	no	—
382	C₂³	—	94	1	no	—
383	C₂³	—	94	1	no	—
384	C₂³	—	94	1	no	—
385	C₂³	—	94	1	no	—
386	C₂³	—	94	1	no	—
387	C₂³	—	94	1	no	—
388	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	47	2	no	—
396	C₂×C₄	—	47	4	no	—
397	C₂×C₄	—	47	2	no	—
398	C₂×C₄	—	94	1	no	—
399	C₂×C₄	—	94	1	no	—
400	C₂×C₄	—	94	2	no	—
401	C₂×C₄	—	94	1	no	—
402	C₂×C₄	—	94	1	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	94	8	no	—
405	C₂×C₄	—	94	1	no	—
406	C₂×C₄	—	94	1	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	1	no	—
409	C₂×C₄	—	94	2	no	—
410	C₂×C₄	—	94	2	no	—
411	C₂×C₄	—	188	4	no	—
412	C₂×C₄	—	188	1	no	—
413	C₂×C₄	—	188	1	no	—
414	C₂×C₄	—	188	1	no	—
415	C₂×C₄	—	188	1	no	—
416	C₂×C₄	#13093981	1	2	yes	—
417	C₂×C₄	#13093981	1	2	yes	—
418	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
419	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
420	C₂×C₄	C₂×#10625324	1	4	yes	—
421	C₂×C₄	C₂×#10625324	1	2	yes	—
422	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
424	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
425	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
426	C₂×C₄	#13094070	1	1	yes	characteristic
427	C₂×C₄	#13094072	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	4	1	no	—
430	C₈	—	4	2	no	—
431	C₈	—	94	2	no	—
432	C₈	—	188	2	no	—
433	C₈	—	188	1	no	—
434	C₂²	—	94	2	no	—
435	C₂²	—	94	2	no	—
436	C₂²	—	94	2	no	—
437	C₂²	—	188	1	no	—
438	C₂²	—	188	1	no	—
439	C₂²	—	188	1	no	—
440	C₂²	—	188	1	no	—
441	C₂²	C₂×#13093981	1	1	yes	characteristic
442	C₂²	C₄×#10625352	1	1	yes	characteristic
443	C₂²	#15689605	1	1	yes	characteristic
444	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
445	C₂²	C₂²×#10625324	1	1	yes	characteristic
446	C₂²	#131×D₄₇	1	1	yes	characteristic
447	C₂²	#15689888	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	4	no	—
450	C₄	—	2	4	no	—
451	C₄	—	94	4	no	—
452	C₄	—	94	2	no	—
453	C₄	—	94	2	no	—
454	C₄	—	188	2	no	—
455	C₄	—	188	1	no	—
456	C₄	#15689174	1	4	yes	—
457	C₄	#15689808	1	1	yes	characteristic
458	C₄	#15689814	1	1	yes	characteristic
459	C₄	#15689836	1	1	yes	characteristic
460	C₄	#15689838	1	1	yes	characteristic
461	C₂	—	188	2	no	—
462	C₂	#20246269	1	1	yes	characteristic
463	C₂	C₂×#15689174	1	1	yes	characteristic
464	C₂	#20252043	1	1	yes	characteristic
465	C₂	C₈×#10625352	1	1	yes	characteristic
466	C₂	#20252396	1	1	yes	characteristic
467	C₂	#20252498	1	1	yes	characteristic
468	C₂	#20252519	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₈×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#22632
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #20244106	C₂	semidirect
3. #20244104	C₂	semidirect
6. #20243503	C₂	semidirect
8. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
10. #20243133	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₇	C₂	semidirect
48. #13093982	C₈	semidirect
235. C₈×C₄⋊C₄	D₄₇	semidirect
275. C₄₇	#22632	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13093982	2
#20244106	2
#20244104	2
#20243994	2
#20243992	2
#20243503	2
#20243365	2
C₄⋊C₄×C₄₇⋊C₈	2
C₄×(C₂×D₄₇)⋊C₈	2
#20243133	2
C₈×C₄⋊C₄×C₄₇	2
#22632	47