Subgroups — #26214128

Order 12032.

1474 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094031	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689140	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689081	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689079	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243235	C₂	1	4	yes	maximal, complemented
6	#20243228	C₂	1	4	yes	maximal, complemented
7	#20243115	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243097	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#2896	C₂	1	1	yes	maximal, characteristic
10	C₂×#13094031	—	2	4	no	—
11	C₂×#13094031	—	2	1	no	—
12	C₂×#13094031	—	2	1	no	—
13	C₂×#13094031	C₄	1	8	yes	complemented
14	C₂×#13094031	C₂²	1	2	yes	—
15	C₂×#13094031	C₂²	1	2	yes	—
16	C₂²×#10625329	—	2	1	no	—
17	C₂²×#10625329	C₂²	1	1	yes	characteristic
18	C₂²×#10625329	C₂²	1	1	yes	characteristic
19	C₂³×C₄₇⋊C₈	—	2	1	no	—
20	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×#13093983	C₂²	1	1	yes	characteristic
22	#15689140	C₄	1	8	yes	complemented
23	C₂×#13093951	C₂²	1	4	yes	—
24	#15689081	—	2	4	no	—
25	#15689079	—	2	1	no	—
26	#15689079	—	2	1	no	—
27	#15689079	C₂²	1	2	yes	complemented
28	#15689079	C₂²	1	2	yes	complemented
29	C₂×#13093935	—	2	1	no	—
30	C₂×#13093934	C₂²	1	2	yes	complemented
31	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
32	C₂×C₈×Dic₄₇	C₂²	1	2	yes	complemented
33	#15688888	C₂²	1	4	yes	complemented
34	#15688882	C₂²	1	4	yes	complemented
35	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
36	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#419	C₄	1	2	yes	complemented
39	C₄₇×#418	C₄	1	2	yes	complemented
40	C₄₇×#417	C₄	1	4	yes	complemented
41	C₄₇×#416	C₂²	1	4	yes	—
42	#13094031	—	2	8	no	—
43	#13094031	—	2	8	no	—
44	#13094031	—	2	4	no	—
45	#13094031	—	2	4	no	—
46	#13094031	C₂×C₄	1	8	yes	complemented
47	#13094031	C₂×C₄	1	8	yes	complemented
48	C₂×#10625329	—	2	1	no	—
49	C₂×#10625329	—	2	2	no	—
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	—	2	2	no	—
52	C₂×#10625329	—	2	8	no	—
53	C₂×#10625329	—	2	2	no	—
54	C₂×#10625329	—	2	2	no	—
55	C₂×#10625329	C₂×C₄	1	4	yes	—
56	C₂×#10625329	C₂×C₄	1	4	yes	—
57	C₂×#10625329	C₂³	1	2	yes	—
58	C₂×#10625329	C₂³	1	2	yes	—
59	C₂²×C₄₇⋊C₈	—	2	1	no	—
60	C₂²×C₄₇⋊C₈	—	2	1	no	—
61	C₂²×C₄₇⋊C₈	—	2	8	no	—
62	C₂²×C₄₇⋊C₈	—	2	2	no	—
63	C₂²×C₄₇⋊C₈	—	2	2	no	—
64	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
65	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
66	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
67	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
69	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
70	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
72	#13093983	—	2	2	no	—
73	#13093983	C₂×C₄	1	4	yes	—
74	C₂×C₄⋊Dic₄₇	—	2	1	no	—
75	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
76	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
77	#13093951	C₂×C₄	1	16	yes	complemented
78	#13093935	—	2	2	no	—
79	#13093935	—	2	2	no	—
80	#13093934	—	2	4	no	—
81	C₄×C₄₇⋊C₈	—	2	2	no	—
82	C₄×C₄₇⋊C₈	—	2	2	no	—
83	C₈×Dic₄₇	—	2	4	no	—
84	C₂×#41×C₄₇	—	2	2	no	—
85	C₂×#41×C₄₇	—	2	1	no	—
86	C₂×#41×C₄₇	—	2	1	no	—
87	C₂×#41×C₄₇	—	2	2	no	—
88	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
89	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
90	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
91	C₂×#41×C₄₇	C₂³	1	2	yes	—
92	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂²×D₄×C₄₇	—	2	1	no	—
94	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂³×C₄×C₄₇	—	2	1	no	—
96	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₄₇	—	2	2	no	—
98	C₂×M₁₆×C₄₇	—	2	2	no	—
99	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
100	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
101	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
102	#117×C₄₇	—	2	1	no	—
103	#117×C₄₇	—	2	1	no	—
104	#117×C₄₇	C₂×C₄	1	2	yes	—
105	#117×C₄₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
107	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
108	C₂×C₄²×C₄₇	—	2	1	no	—
109	#103×C₄₇	C₂×C₄	1	8	yes	—
110	#102×C₄₇	C₂×C₄	1	8	yes	—
111	C₂⁴×C₄₇	—	2	1	no	—
112	C₂⁴×C₄₇	#41	1	1	yes	characteristic
113	#41×C₄₇	—	2	4	no	—
114	#41×C₄₇	—	2	4	no	—
115	#41×C₄₇	—	2	4	no	—
116	#41×C₄₇	—	2	4	no	—
117	#41×C₄₇	—	2	4	no	—
118	#41×C₄₇	—	2	2	no	—
119	#41×C₄₇	—	2	2	no	—
120	#41×C₄₇	C₄²	1	8	yes	—
121	#41×C₄₇	C₂²×C₄	1	4	yes	—
122	#41×C₄₇	C₂²×C₄	1	4	yes	—
123	C₂×Q₈×C₄₇	—	2	1	no	—
124	C₂×Q₈×C₄₇	—	2	2	no	—
125	C₂×Q₈×C₄₇	C₄²	1	4	yes	—
126	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂×D₄×C₄₇	—	2	4	no	—
128	C₂×D₄×C₄₇	—	2	2	no	—
129	C₂×D₄×C₄₇	—	2	4	no	—
130	C₂×D₄×C₄₇	—	2	2	no	—
131	C₂×D₄×C₄₇	—	2	2	no	—
132	C₂×D₄×C₄₇	—	2	1	no	—
133	C₂×D₄×C₄₇	C₄²	1	4	yes	—
134	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	—	2	4	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	4	no	—
139	C₂²×C₄×C₄₇	—	2	2	no	—
140	C₂²×C₄×C₄₇	—	2	2	no	—
141	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	#41	1	2	yes	—
150	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
151	C₂²×Dic₄₇	—	2	2	no	—
152	M₁₆×C₄₇	—	2	4	no	—
153	M₁₆×C₄₇	—	2	4	no	—
154	C₂×C₈×C₄₇	—	2	2	no	—
155	C₂×C₈×C₄₇	—	2	2	no	—
156	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
157	C₄⋊C₄×C₄₇	—	2	2	no	—
158	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
159	C₂²⋊C₄×C₄₇	—	2	2	no	—
160	C₂²⋊C₄×C₄₇	—	2	2	no	—
161	C₄²×C₄₇	—	2	2	no	—
162	C₄²×C₄₇	—	2	2	no	—
163	C₂²⋊Dic₄₇	—	2	4	no	—
164	C₄⋊Dic₄₇	—	2	4	no	—
165	C₄×Dic₄₇	—	2	2	no	—
166	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
167	#10625329	—	2	4	no	—
168	#10625329	—	2	4	no	—
169	#10625329	—	2	2	no	—
170	#10625329	—	2	2	no	—
171	#10625329	—	2	8	no	—
172	#10625329	—	2	8	no	—
173	#10625329	C₂²×C₄	1	4	yes	—
174	#10625329	C₂²×C₄	1	4	yes	—
175	C₂×C₄₇⋊C₈	—	2	4	no	—
176	C₂×C₄₇⋊C₈	—	2	4	no	—
177	C₂×C₄₇⋊C₈	—	2	2	no	—
178	C₂×C₄₇⋊C₈	—	2	2	no	—
179	C₂×C₄₇⋊C₈	—	2	8	no	—
180	C₂×C₄₇⋊C₈	—	2	8	no	—
181	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
182	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
183	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
184	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
185	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
186	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
187	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
188	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
189	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
190	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
191	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
192	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
193	C₂³×C₄₇	—	2	2	no	—
194	C₂³×C₄₇	—	2	4	no	—
195	C₂³×C₄₇	—	4	2	no	—
196	C₂³×C₄₇	—	4	4	no	—
197	C₂³×C₄₇	#117	1	2	yes	—
198	C₂³×C₄₇	C₄×D₄	1	2	yes	—
199	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
200	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
201	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
202	Q₈×C₄₇	—	2	2	no	—
203	Q₈×C₄₇	—	2	4	no	—
204	Q₈×C₄₇	C₂×C₄²	1	4	yes	—
205	D₄×C₄₇	—	2	4	no	—
206	D₄×C₄₇	—	2	4	no	—
207	D₄×C₄₇	—	2	8	no	—
208	D₄×C₄₇	—	2	2	no	—
209	D₄×C₄₇	—	2	4	no	—
210	D₄×C₄₇	C₂×C₄²	1	4	yes	—
211	C₂×C₄×C₄₇	—	2	2	no	—
212	C₂×C₄×C₄₇	—	2	4	no	—
213	C₂×C₄×C₄₇	—	2	4	no	—
214	C₂×C₄×C₄₇	—	2	4	no	—
215	C₂×C₄×C₄₇	—	2	8	no	—
216	C₂×C₄×C₄₇	—	2	4	no	—
217	C₂×C₄×C₄₇	—	4	4	no	—
218	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
219	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
220	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
221	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
222	C₂×C₄×C₄₇	#117	1	2	yes	—
223	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
224	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
236	C₂×Dic₄₇	—	2	4	no	—
237	C₂×Dic₄₇	—	4	4	no	—
238	C₈×C₄₇	—	2	4	no	—
239	C₄₇⋊C₈	—	2	4	no	—
240	C₄₇⋊C₈	—	2	4	no	—
241	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
242	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
243	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
244	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
245	#20420	—	47	1	no	maximal, Sylow
246	C₂²×C₄₇	—	2	2	no	—
247	C₂²×C₄₇	—	2	2	no	—
248	C₂²×C₄₇	—	2	2	no	—
249	C₂²×C₄₇	—	2	4	no	—
250	C₂²×C₄₇	—	4	2	no	—
251	C₂²×C₄₇	—	4	2	no	—
252	C₂²×C₄₇	—	4	8	no	—
253	C₂²×C₄₇	—	4	4	no	—
254	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
255	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
256	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
257	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
258	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
259	C₄×C₄₇	—	2	4	no	—
260	C₄×C₄₇	—	4	4	no	—
261	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
262	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
263	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
264	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
265	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
266	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
267	Dic₄₇	—	4	4	no	—
268	C₂²×#131	—	47	1	no	—
269	C₂×#421	—	47	1	no	—
270	#2896	D₄₇	1	1	yes	characteristic
271	C₂×#405	—	47	1	no	—
272	C₂×#405	—	47	1	no	—
273	#1765	—	47	4	no	—
274	#1764	—	47	4	no	—
275	#1738	—	47	1	no	—
276	#1733	—	47	1	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	2	2	no	—
279	C₂×C₄₇	—	2	1	no	—
280	C₂×C₄₇	—	2	2	no	—
281	C₂×C₄₇	—	4	4	no	—
282	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
283	C₂×C₄₇	#2955	1	2	yes	—
284	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
285	C₂×#131	—	47	8	no	—
286	C₂×#131	—	47	2	no	—
287	C₂×#131	—	47	2	no	—
288	C₂×#131	—	94	1	no	—
289	C₂×#131	—	94	1	no	—
290	C₂×#131	—	94	4	no	—
291	C₂²×M₁₆	—	47	1	no	—
292	C₂²×M₁₆	—	47	1	no	—
293	C₂²×M₁₆	—	94	1	no	—
294	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
295	C₂³×C₈	—	47	1	no	—
296	C₂³×C₈	—	94	1	no	—
297	C₂×#117	—	47	1	no	—
298	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
299	#421	—	47	8	no	—
300	C₂×#104	—	47	4	no	—
301	#419	Dic₄₇	1	2	yes	complemented
302	#418	Dic₄₇	1	2	yes	complemented
303	#417	Dic₄₇	1	4	yes	complemented
304	#416	C₂×D₄₇	1	4	yes	—
305	#405	—	47	2	no	—
306	#405	—	47	2	no	—
307	#405	—	94	1	no	—
308	#405	—	94	1	no	—
309	#405	—	94	4	no	—
310	C₂×#97	—	47	2	no	—
311	C₂×#97	—	94	1	no	—
312	C₂×C₄×C₈	—	47	2	no	—
313	C₂×C₄×C₈	—	94	1	no	—
314	#341	—	47	4	no	—
315	#339	—	47	4	no	—
316	C₄₇	#20420	1	1	yes	characteristic, complemented, Sylow
317	C₂×#41	—	2	2	no	—
318	C₂×#41	—	2	1	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	1	no	—
321	C₂×#41	C₄×D₄₇	1	4	yes	—
322	C₂×#41	C₄×D₄₇	1	4	yes	—
323	C₂×#41	C₂×Dic₄₇	1	2	yes	—
324	C₂×#41	C₂²×D₄₇	1	2	yes	—
325	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
330	#131	—	47	8	no	—
331	#131	—	47	8	no	—
332	#131	—	94	8	no	—
333	#131	—	94	8	no	—
334	#131	—	94	4	no	—
335	#131	—	94	4	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂×M₁₆	—	47	4	no	—
339	C₂×M₁₆	—	47	4	no	—
340	C₂×M₁₆	—	47	2	no	—
341	C₂×M₁₆	—	47	2	no	—
342	C₂×M₁₆	—	94	8	no	—
343	C₂×M₁₆	—	94	2	no	—
344	C₂×M₁₆	—	94	2	no	—
345	C₂×M₁₆	—	94	2	no	—
346	C₂×M₁₆	—	94	1	no	—
347	C₂×M₁₆	—	94	1	no	—
348	C₂×M₁₆	—	94	2	no	—
349	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
350	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
351	C₂²×C₈	—	47	4	no	—
352	C₂²×C₈	—	47	1	no	—
353	C₂²×C₈	—	47	1	no	—
354	C₂²×C₈	—	47	1	no	—
355	C₂²×C₈	—	47	1	no	—
356	C₂²×C₈	—	47	4	no	—
357	C₂²×C₈	—	47	1	no	—
358	C₂²×C₈	—	47	1	no	—
359	C₂²×C₈	—	94	8	no	—
360	C₂²×C₈	—	94	2	no	—
361	C₂²×C₈	—	94	2	no	—
362	C₂²×C₈	—	94	1	no	—
363	C₂²×C₈	—	94	1	no	—
364	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
365	#117	—	2	1	no	—
366	#117	—	2	1	no	—
367	#117	—	47	4	no	—
368	#117	—	94	2	no	—
369	#117	C₂×Dic₄₇	1	2	yes	—
370	#117	C₂²×D₄₇	1	2	yes	—
371	C₂×C₄⋊C₄	—	94	1	no	—
372	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	94	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	—	47	2	no	—
377	#104	—	47	16	no	—
378	#103	C₂×Dic₄₇	1	8	yes	—
379	#102	C₂×Dic₄₇	1	8	yes	—
380	#97	—	94	2	no	—
381	#97	—	94	2	no	—
382	#97	—	94	4	no	—
383	C₄×C₈	—	94	2	no	—
384	C₄×C₈	—	94	2	no	—
385	C₄×C₈	—	94	4	no	—
386	C₂⁴	—	2	1	no	—
387	C₂⁴	#10625352	1	1	yes	characteristic
388	#41	—	2	4	no	—
389	#41	—	2	4	no	—
390	#41	—	2	4	no	—
391	#41	—	2	4	no	—
392	#41	—	2	4	no	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	C₄×Dic₄₇	1	8	yes	—
396	#41	C₂×C₄×D₄₇	1	4	yes	—
397	#41	C₂×C₄×D₄₇	1	4	yes	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	C₄×Dic₄₇	1	4	yes	—
401	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
409	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	94	2	no	—
417	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
418	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
419	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
420	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
421	C₂²×C₄	D₄×D₄₇	1	2	yes	—
422	C₂²×C₄	#10625352	1	1	yes	characteristic
423	C₂²×C₄	#10625352	1	2	yes	—
424	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
425	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
426	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
427	M₁₆	—	2	4	no	—
428	M₁₆	—	2	4	no	—
429	M₁₆	—	47	4	no	—
430	M₁₆	—	47	4	no	—
431	M₁₆	—	94	8	no	—
432	M₁₆	—	94	8	no	—
433	M₁₆	—	94	4	no	—
434	M₁₆	—	94	4	no	—
435	M₁₆	—	94	2	no	—
436	M₁₆	—	94	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	47	4	no	—
440	C₂×C₈	—	47	4	no	—
441	C₂×C₈	—	47	4	no	—
442	C₂×C₈	—	47	4	no	—
443	C₂×C₈	—	47	2	no	—
444	C₂×C₈	—	47	2	no	—
445	C₂×C₈	—	47	2	no	—
446	C₂×C₈	—	47	2	no	—
447	C₂×C₈	—	47	1	no	—
448	C₂×C₈	—	47	1	no	—
449	C₂×C₈	—	47	1	no	—
450	C₂×C₈	—	47	1	no	—
451	C₂×C₈	—	94	8	no	—
452	C₂×C₈	—	94	8	no	—
453	C₂×C₈	—	94	4	no	—
454	C₂×C₈	—	94	4	no	—
455	C₂×C₈	—	94	2	no	—
456	C₂×C₈	—	94	2	no	—
457	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	94	4	no	—
460	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	94	4	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	47	4	no	—
467	C₄²	—	94	2	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	4	no	—
472	C₂³	#13093980	1	2	yes	—
473	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
474	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
475	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
476	C₂³	C₂×#10625352	1	1	yes	characteristic
477	Q₈	—	2	4	no	—
478	Q₈	—	2	2	no	—
479	Q₈	C₂×C₄×Dic₄₇	1	4	yes	—
480	D₄	—	2	8	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	4	no	—
483	D₄	—	2	4	no	—
484	D₄	—	2	2	no	—
485	D₄	C₂×C₄×Dic₄₇	1	4	yes	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	94	4	no	—
494	C₂×C₄	—	188	4	no	—
495	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
496	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
497	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
498	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
499	C₂×C₄	#13093980	1	2	yes	—
500	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
501	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
502	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
503	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
504	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
505	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
506	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
507	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
508	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
509	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
510	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
511	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
512	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
513	C₈	—	2	4	no	—
514	C₈	—	47	2	no	—
515	C₈	—	47	2	no	—
516	C₈	—	47	2	no	—
517	C₈	—	47	2	no	—
518	C₈	—	94	4	no	—
519	C₈	—	94	4	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	8	no	—
527	C₂²	—	4	4	no	—
528	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
529	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
530	C₂²	C₂×#13093980	1	1	yes	characteristic
531	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
532	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
533	C₄	—	2	4	no	—
534	C₄	—	4	4	no	—
535	C₄	—	188	4	no	—
536	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
537	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
538	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
539	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
540	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
541	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
542	C₂	—	2	1	no	—
543	C₂	—	2	2	no	—
544	C₂	—	2	2	no	—
545	C₂	—	2	1	no	—
546	C₂	—	4	4	no	—
547	C₂	C₂×C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
548	C₂	#20252291	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2896	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2896	D₄₇
hypocenter	C₄₇	#20420
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #2896

Complements

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

N	H ≅ G/N	type
3. C₂×#15689081	C₂	semidirect
4. C₂×#15689079	C₂	semidirect
5. #20243235	C₂	semidirect
6. #20243228	C₂	semidirect
7. #20243115	C₂	semidirect
8. #20243097	C₂	semidirect
13. C₂×#13094031	C₄	semidirect
22. #15689140	C₄	semidirect
27. #15689079	C₂²	semidirect
28. #15689079	C₂²	semidirect
30. C₂×#13093934	C₂²	semidirect
32. C₂×C₈×Dic₄₇	C₂²	semidirect
33. #15688888	C₂²	semidirect
34. #15688882	C₂²	semidirect
38. C₄₇×#419	C₄	semidirect
39. C₄₇×#418	C₄	semidirect
40. C₄₇×#417	C₄	semidirect
46. #13094031	C₂×C₄	semidirect
47. #13094031	C₂×C₄	semidirect
77. #13093951	C₂×C₄	semidirect
301. #419	Dic₄₇	semidirect
302. #418	Dic₄₇	semidirect
303. #417	Dic₄₇	semidirect
316. C₄₇	#20420	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13094031	2
C₂×#15689140	2
C₂×#15689081	2
C₂×#15689079	2
#20243235	2
#20243228	2
#20243115	2
#20243097	2
C₄₇×#2896	2
#20420	47