Subgroups — #26216778

Order 12032.

854 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689183	C₂	1	2	yes	maximal
2	C₄×#13093981	C₂	1	1	yes	maximal, characteristic
3	#20243540	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243507	C₂	1	2	yes	maximal, complemented
5	#20243369	C₂	1	2	yes	maximal
6	#20243365	C₂	1	1	yes	maximal, characteristic
7	#20243365	C₂	1	1	yes	maximal, characteristic
8	#20243247	C₂	1	2	yes	maximal, complemented
9	#20243243	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13093981	C₂²	1	1	yes	characteristic
13	C₂×#13093981	C₂²	1	1	yes	characteristic
14	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
15	#15689183	—	2	8	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
21	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
22	C₂×#13093934	C₂²	1	2	yes	—
23	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
24	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
25	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
26	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
27	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
28	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
29	C₄×(C₂×D₄₇)⋊C₄	C₄	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	#15688969	C₂²	1	1	yes	characteristic
33	#15688969	C₂²	1	1	yes	characteristic
34	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	#15688877	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
43	C₄³×C₄₇	C₂²	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
49	#13093981	—	2	2	no	—
50	#13093981	—	2	2	no	—
51	#13093981	D₄	1	4	yes	—
52	#13093981	Q₈	1	4	yes	—
53	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×(C₂×D₄₇)⋊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×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	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	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
70	C₄²×D₄₇	—	2	2	no	—
71	C₄²×D₄₇	—	2	2	no	—
72	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
73	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
74	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
75	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
76	(C₂×D₄₇)⋊C₈	—	2	4	no	—
77	(C₂×D₄₇)⋊C₈	—	2	4	no	—
78	#13093934	—	2	4	no	—
79	C₈×Dic₄₇	—	2	4	no	—
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	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	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
89	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
90	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₄₇	—	2	4	no	—
98	C₄⋊C₈×C₄₇	—	2	2	no	—
99	C₄⋊C₈×C₄₇	—	2	2	no	—
100	C₄⋊C₈×C₄₇	—	2	4	no	—
101	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	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	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₇	C₂²×C₄	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	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	—	2	2	no	—
121	C₂×C₄×D₄₇	—	2	2	no	—
122	C₂×C₄×D₄₇	—	2	2	no	—
123	C₂×C₄×D₄₇	—	2	2	no	—
124	C₂×C₄×D₄₇	—	4	1	no	—
125	C₂×C₄×D₄₇	—	4	1	no	—
126	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
127	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
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	—	2	2	no	—
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	—	4	1	no	—
137	C₄²×C₄₇	—	4	1	no	—
138	C₄²×C₄₇	C₂×D₄	1	2	yes	—
139	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
140	C₄²×C₄₇	#41	1	2	yes	—
141	C₄²×C₄₇	#41	1	2	yes	—
142	C₄²×C₄₇	#41	1	2	yes	—
143	C₄²×C₄₇	#41	1	2	yes	—
144	(C₂×D₄₇)⋊C₄	—	2	2	no	—
145	(C₂×D₄₇)⋊C₄	—	2	2	no	—
146	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
147	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
148	Dic₄₇⋊C₄	—	2	2	no	—
149	Dic₄₇⋊C₄	—	2	2	no	—
150	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
151	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
152	C₄×Dic₄₇	—	2	2	no	—
153	C₄×Dic₄₇	—	2	2	no	—
154	C₄×Dic₄₇	—	2	2	no	—
155	C₄×Dic₄₇	—	2	2	no	—
156	C₄×Dic₄₇	—	2	1	no	—
157	C₄×Dic₄₇	—	2	1	no	—
158	C₄×Dic₄₇	—	2	1	no	—
159	C₄×Dic₄₇	—	2	1	no	—
160	C₄×Dic₄₇	—	4	1	no	—
161	C₄×Dic₄₇	—	4	1	no	—
162	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
163	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
164	C₂×C₄₇⋊C₈	—	2	2	no	—
165	C₂×C₄₇⋊C₈	—	2	2	no	—
166	C₂×C₄₇⋊C₈	—	2	2	no	—
167	C₂×C₄₇⋊C₈	—	2	2	no	—
168	C₂×C₄₇⋊C₈	—	2	2	no	—
169	C₂×C₄₇⋊C₈	—	2	2	no	—
170	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
171	C₂²×D₄₇	—	2	1	no	—
172	C₂²×D₄₇	—	2	1	no	—
173	C₂²×D₄₇	—	2	1	no	—
174	C₂²×D₄₇	—	2	1	no	—
175	C₂²×D₄₇	—	2	1	no	—
176	C₂²×D₄₇	—	2	1	no	—
177	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
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	#117	1	2	yes	—
191	C₂×C₄×C₄₇	#117	1	2	yes	—
192	C₂×C₄×C₄₇	#117	1	2	yes	—
193	C₂×C₄×C₄₇	#117	1	2	yes	—
194	C₂×C₄×C₄₇	#131	1	2	yes	—
195	C₂×C₄×C₄₇	#131	1	2	yes	—
196	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
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	—	2	1	no	—
216	C₂×Dic₄₇	—	2	1	no	—
217	C₂×Dic₄₇	—	2	1	no	—
218	C₂×Dic₄₇	—	2	1	no	—
219	C₂×Dic₄₇	—	2	1	no	—
220	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
221	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
222	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
223	C₄×D₄₇	—	2	2	no	—
224	C₄×D₄₇	—	2	2	no	—
225	C₄×D₄₇	—	2	2	no	—
226	C₄×D₄₇	—	2	2	no	—
227	C₄×D₄₇	—	4	4	no	—
228	C₄×D₄₇	—	4	4	no	—
229	C₈×C₄₇	—	4	2	no	—
230	C₈×C₄₇	—	4	2	no	—
231	C₄₇⋊C₈	—	4	2	no	—
232	C₄₇⋊C₈	—	4	2	no	—
233	#20812	—	47	1	no	maximal, Sylow
234	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
235	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
236	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
237	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
238	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
239	C₂²×C₄₇	#568	1	1	yes	characteristic
240	C₂²×C₄₇	#568	1	1	yes	characteristic
241	C₂×D₄₇	—	2	2	no	—
242	C₂×D₄₇	—	2	2	no	—
243	C₂×D₄₇	—	2	2	no	—
244	C₂×D₄₇	—	4	1	no	—
245	C₂×D₄₇	—	4	1	no	—
246	C₂×D₄₇	—	4	1	no	—
247	C₂×D₄₇	—	4	1	no	—
248	C₄×C₄₇	—	2	2	no	—
249	C₄×C₄₇	—	2	2	no	—
250	C₄×C₄₇	—	2	2	no	—
251	C₄×C₄₇	—	2	2	no	—
252	C₄×C₄₇	—	2	2	no	—
253	C₄×C₄₇	#433	1	4	yes	complemented
254	C₄×C₄₇	#532	1	1	yes	characteristic
255	C₄×C₄₇	#532	1	1	yes	characteristic
256	C₄×C₄₇	#533	1	1	yes	characteristic
257	C₄×C₄₇	#533	1	1	yes	characteristic
258	Dic₄₇	—	2	2	no	—
259	Dic₄₇	—	2	2	no	—
260	Dic₄₇	—	2	2	no	—
261	Dic₄₇	—	4	1	no	—
262	Dic₄₇	—	4	1	no	—
263	Dic₄₇	—	4	1	no	—
264	Dic₄₇	—	4	1	no	—
265	C₂×#433	—	47	2	no	—
266	C₄×#117	—	47	1	no	—
267	#1842	—	47	1	no	—
268	#1842	D₄₇	1	1	yes	characteristic, complemented
269	#1832	—	47	2	no	—
270	#1798	—	47	2	no	—
271	#1797	—	47	1	no	—
272	#1797	—	47	1	no	—
273	#1768	—	47	2	no	—
274	#1767	—	47	1	no	—
275	C₄×C₄⋊C₈	—	47	1	no	—
276	C₂×C₄₇	#2285	1	1	yes	characteristic
277	C₂×C₄₇	#2906	1	1	yes	characteristic
278	C₂×C₄₇	#2906	1	1	yes	characteristic
279	C₂×C₄₇	C₂×#433	1	1	yes	characteristic
280	C₂×C₄₇	#2921	1	1	yes	characteristic
281	C₂×C₄₇	#2925	1	1	yes	characteristic
282	C₂×C₄₇	#2925	1	1	yes	characteristic
283	D₄₇	—	4	2	no	—
284	C₂×#117	—	47	1	no	—
285	C₂×#117	—	47	1	no	—
286	C₂²×C₄²	—	47	1	no	—
287	#433	—	94	8	no	—
288	C₂×C₄⋊C₈	—	47	1	no	—
289	C₂×C₄⋊C₈	—	47	1	no	—
290	C₂×C₄⋊C₈	—	47	2	no	—
291	C₂×C₄⋊C₈	—	47	2	no	—
292	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
293	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
294	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
295	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
296	C₂×C₂²⋊C₈	—	47	2	no	—
297	C₂×C₂²⋊C₈	—	47	2	no	—
298	C₂×#97	—	47	2	no	—
299	C₂×C₄×C₈	—	47	2	no	—
300	C₄×C₄⋊C₄	—	47	1	no	—
301	C₄×C₄⋊C₄	—	47	1	no	—
302	C₄×C₄⋊C₄	—	47	1	no	—
303	C₄×C₄⋊C₄	—	47	1	no	—
304	C₄×C₂²⋊C₄	—	47	1	no	—
305	C₄×C₂²⋊C₄	—	47	1	no	—
306	C₄×C₂²⋊C₄	—	47	1	no	—
307	C₄×C₂²⋊C₄	—	47	1	no	—
308	#376	—	47	1	no	—
309	#376	—	47	1	no	—
310	C₄³	—	47	1	no	—
311	C₄³	C₂×D₄₇	1	1	yes	characteristic
312	#336	—	47	2	no	—
313	#336	—	47	2	no	—
314	#336	—	47	2	no	—
315	#336	—	47	2	no	—
316	C₄₇	#20812	1	1	yes	characteristic, complemented, Sylow
317	C₂³×C₄	—	47	1	no	—
318	C₂³×C₄	—	47	1	no	—
319	C₂³×C₄	—	47	1	no	—
320	C₂²×C₈	—	47	2	no	—
321	C₂²×C₈	—	47	2	no	—
322	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
323	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
324	#117	—	47	4	no	—
325	#117	—	47	4	no	—
326	#117	—	94	2	no	—
327	#117	—	94	2	no	—
328	C₂×C₄⋊C₄	—	47	1	no	—
329	C₂×C₄⋊C₄	—	47	1	no	—
330	C₂×C₄⋊C₄	—	47	1	no	—
331	C₂×C₄⋊C₄	—	47	1	no	—
332	C₂×C₂²⋊C₄	—	47	1	no	—
333	C₂×C₂²⋊C₄	—	47	1	no	—
334	C₂×C₂²⋊C₄	—	47	1	no	—
335	C₂×C₂²⋊C₄	—	47	1	no	—
336	C₂×C₄²	—	47	1	no	—
337	C₂×C₄²	—	47	1	no	—
338	C₂×C₄²	—	47	1	no	—
339	C₂×C₄²	—	47	1	no	—
340	C₂×C₄²	—	47	1	no	—
341	C₂×C₄²	—	47	1	no	—
342	C₂×C₄²	—	47	1	no	—
343	C₂×C₄²	—	47	1	no	—
344	C₂×C₄²	—	47	1	no	—
345	C₂×C₄²	—	94	2	no	—
346	C₂×C₄²	—	94	2	no	—
347	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
348	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
349	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
350	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
351	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
352	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
353	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
354	C₄⋊C₈	—	2	4	no	—
355	C₄⋊C₈	—	2	2	no	—
356	C₄⋊C₈	—	2	2	no	—
357	C₄⋊C₈	—	2	4	no	—
358	C₄⋊C₈	—	94	4	no	—
359	C₄⋊C₈	—	94	2	no	—
360	C₄⋊C₈	—	94	2	no	—
361	C₄⋊C₈	—	94	4	no	—
362	C₂²⋊C₈	—	94	4	no	—
363	C₂²⋊C₈	—	94	4	no	—
364	#97	—	94	4	no	—
365	C₄×C₈	—	94	4	no	—
366	#95	—	47	1	no	—
367	#95	—	47	1	no	—
368	#95	—	47	1	no	—
369	#95	—	47	1	no	—
370	#95	—	47	1	no	—
371	#95	—	47	1	no	—
372	#95	—	47	1	no	—
373	#95	—	47	1	no	—
374	C₂⁴	—	47	1	no	—
375	C₂²×C₄	—	47	1	no	—
376	C₂²×C₄	—	47	1	no	—
377	C₂²×C₄	—	47	1	no	—
378	C₂²×C₄	—	47	2	no	—
379	C₂²×C₄	—	47	2	no	—
380	C₂²×C₄	—	47	1	no	—
381	C₂²×C₄	—	47	1	no	—
382	C₂²×C₄	—	47	1	no	—
383	C₂²×C₄	—	47	1	no	—
384	C₂²×C₄	—	94	1	no	—
385	C₂²×C₄	—	94	1	no	—
386	C₂²×C₄	—	94	1	no	—
387	C₂²×C₄	—	94	1	no	—
388	C₂²×C₄	—	94	2	no	—
389	C₂²×C₄	—	94	2	no	—
390	C₂²×C₄	—	94	2	no	—
391	C₂²×C₄	—	94	2	no	—
392	C₂²×C₄	—	188	1	no	—
393	C₂²×C₄	—	188	1	no	—
394	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
395	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
396	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
397	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
398	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
399	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
400	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	94	2	no	—
408	C₂×C₈	—	94	2	no	—
409	C₂×C₈	—	94	2	no	—
410	C₂×C₈	—	94	2	no	—
411	C₂×C₈	—	94	2	no	—
412	C₂×C₈	—	94	2	no	—
413	C₄⋊C₄	—	47	4	no	—
414	C₄⋊C₄	—	47	4	no	—
415	C₄⋊C₄	—	94	2	no	—
416	C₄⋊C₄	—	94	2	no	—
417	C₂²⋊C₄	—	47	4	no	—
418	C₂²⋊C₄	—	47	4	no	—
419	C₂²⋊C₄	—	94	2	no	—
420	C₂²⋊C₄	—	94	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	4	1	no	—
424	C₄²	—	4	1	no	—
425	C₄²	—	47	2	no	—
426	C₄²	—	47	2	no	—
427	C₄²	—	94	2	no	—
428	C₄²	—	94	2	no	—
429	C₄²	—	94	2	no	—
430	C₄²	—	94	2	no	—
431	C₄²	—	94	1	no	—
432	C₄²	—	94	1	no	—
433	C₄²	—	94	1	no	—
434	C₄²	—	94	1	no	—
435	C₄²	—	188	1	no	—
436	C₄²	—	188	1	no	—
437	C₄²	D₄×D₄₇	1	2	yes	—
438	C₄²	#10625352	1	2	yes	—
439	C₄²	#10625352	1	2	yes	—
440	C₄²	Q₈×D₄₇	1	2	yes	—
441	C₄²	#10625354	1	2	yes	—
442	C₄²	#10625354	1	2	yes	—
443	C₂³	—	47	2	no	—
444	C₂³	—	94	1	no	—
445	C₂³	—	94	1	no	—
446	C₂³	—	94	1	no	—
447	C₂³	—	94	1	no	—
448	C₂³	—	94	1	no	—
449	C₂³	—	94	1	no	—
450	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
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	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	47	2	no	—
462	C₂×C₄	—	47	2	no	—
463	C₂×C₄	—	47	2	no	—
464	C₂×C₄	—	94	1	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	2	no	—
471	C₂×C₄	—	94	2	no	—
472	C₂×C₄	—	94	2	no	—
473	C₂×C₄	—	94	2	no	—
474	C₂×C₄	—	94	1	no	—
475	C₂×C₄	—	94	1	no	—
476	C₂×C₄	—	94	1	no	—
477	C₂×C₄	—	94	1	no	—
478	C₂×C₄	—	94	1	no	—
479	C₂×C₄	—	94	1	no	—
480	C₂×C₄	—	94	1	no	—
481	C₂×C₄	—	94	1	no	—
482	C₂×C₄	—	94	1	no	—
483	C₂×C₄	—	94	1	no	—
484	C₂×C₄	—	94	1	no	—
485	C₂×C₄	—	94	1	no	—
486	C₂×C₄	—	188	4	no	—
487	C₂×C₄	—	188	4	no	—
488	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
489	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
490	C₂×C₄	#13093982	1	2	yes	—
491	C₂×C₄	#13093982	1	2	yes	—
492	C₂×C₄	#13093982	1	2	yes	—
493	C₂×C₄	#13093982	1	2	yes	—
494	C₂×C₄	#13094030	1	2	yes	—
495	C₂×C₄	#13094032	1	2	yes	—
496	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
497	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
498	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
499	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
500	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
501	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
502	C₈	—	4	2	no	—
503	C₈	—	4	2	no	—
504	C₈	—	188	2	no	—
505	C₈	—	188	2	no	—
506	C₂²	—	94	2	no	—
507	C₂²	—	94	2	no	—
508	C₂²	—	94	2	no	—
509	C₂²	—	188	1	no	—
510	C₂²	—	188	1	no	—
511	C₂²	—	188	1	no	—
512	C₂²	—	188	1	no	—
513	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
514	C₂²	C₂×#13093982	1	1	yes	characteristic
515	C₂²	C₂×#13093982	1	1	yes	characteristic
516	C₂²	C₂×#13094030	1	1	yes	characteristic
517	C₂²	C₂×#13094032	1	1	yes	characteristic
518	C₂²	#15689889	1	1	yes	characteristic
519	C₂²	#15689889	1	1	yes	characteristic
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	94	2	no	—
526	C₄	—	94	2	no	—
527	C₄	—	94	2	no	—
528	C₄	—	188	1	no	—
529	C₄	—	188	1	no	—
530	C₄	—	188	1	no	—
531	C₄	—	188	1	no	—
532	C₄	#15689183	1	4	yes	complemented
533	C₄	#15689671	1	1	yes	characteristic
534	C₄	#15689674	1	1	yes	characteristic
535	C₄	#15689678	1	1	yes	characteristic
536	C₄	#15689678	1	1	yes	characteristic
537	C₂	—	188	2	no	—
538	C₂	#20245793	1	1	yes	characteristic
539	C₂	#20251953	1	1	yes	characteristic
540	C₂	#20251957	1	1	yes	characteristic
541	C₂	C₂×#15689183	1	1	yes	characteristic
542	C₂	#20252025	1	1	yes	characteristic
543	C₂	#20252053	1	1	yes	characteristic
544	C₂	#20252056	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1842	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1842	D₄₇
hypocenter	C₄₇	#20812
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1842

Complements

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

N	H ≅ G/N	type
3. #20243540	C₂	semidirect
4. #20243507	C₂	semidirect
8. #20243247	C₂	semidirect
9. #20243243	C₂	semidirect
10. C₄⋊C₈×Dic₄₇	C₂	semidirect
11. C₄₇×#1842	C₂	semidirect
253. C₄×C₄₇	#433	semidirect
268. #1842	D₄₇	semidirect
316. C₄₇	#20812	semidirect
532. C₄	#15689183	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689183	2
C₄×#13093981	2
#20243540	2
#20243507	2
#20243369	2
#20243365	2
#20243247	2
#20243243	2
C₄⋊C₈×Dic₄₇	2
C₄₇×#1842	2
#20812	47