Subgroups — #26213983

Order 12032.

1444 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689889	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689105	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689096	C₂	1	1	yes	maximal, characteristic
4	#20251806	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243189	C₂	1	8	yes	maximal, complemented
6	C₂×#15688895	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#2873	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625350	C₂²	1	1	yes	characteristic
10	#15689889	—	2	2	no	—
11	#15689889	—	2	2	no	—
12	#15689889	—	2	2	no	—
13	#15689889	—	2	2	no	—
14	C₂×#13094032	C₄	1	4	yes	complemented
15	C₂×#13094030	C₂²	1	4	yes	—
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625329	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×D₄₇	C₄	1	4	yes	complemented
19	C₂×#13093983	C₂²	1	1	yes	characteristic
20	#15689105	C₄	1	4	yes	complemented
21	#15689105	C₂²	1	4	yes	—
22	C₂×#13093942	C₄	1	2	yes	complemented
23	C₂×#13093940	C₄	1	2	yes	complemented
24	#15689096	C₄	1	4	yes	—
25	#15689096	C₂²	1	4	yes	—
26	C₂×#13093938	C₄	1	4	yes	—
27	#15689081	—	2	2	no	—
28	#15689078	C₂²	1	4	yes	complemented
29	M₁₆×Dic₄₇	—	2	2	no	—
30	#15688895	C₂²	1	4	yes	complemented
31	#15688893	C₂²	1	4	yes	complemented
32	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#405	—	2	2	no	—
36	C₄₇×#405	C₂²	1	4	yes	complemented
37	C₄×M₁₆×C₄₇	—	2	2	no	—
38	C₂×#10625350	—	2	1	no	—
39	C₂×#10625350	—	2	1	no	—
40	C₂×#10625350	—	2	1	no	—
41	C₂×#10625350	—	2	1	no	—
42	C₂×#10625350	—	2	1	no	—
43	C₂×#10625350	—	2	1	no	—
44	C₂×#10625350	—	2	1	no	—
45	C₂×#10625350	—	2	1	no	—
46	C₂×#10625350	C₂×C₄	1	2	yes	—
47	C₂×#10625350	C₂×C₄	1	2	yes	—
48	C₂×#10625350	C₂×C₄	1	2	yes	—
49	C₂×#10625350	C₂³	1	2	yes	—
50	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
53	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
54	#13094032	—	2	8	no	—
55	#13094032	—	2	8	no	—
56	#13094030	—	2	8	no	—
57	#13094030	—	2	8	no	—
58	C₂×#10625329	—	2	1	no	—
59	C₂×#10625329	—	2	1	no	—
60	C₂×#10625329	—	2	1	no	—
61	C₂×#10625329	—	2	1	no	—
62	C₂×#10625329	—	2	1	no	—
63	C₂×#10625329	—	2	1	no	—
64	C₂×#10625329	—	2	1	no	—
65	C₂×#10625329	C₂×C₄	1	2	yes	—
66	C₂×#10625329	C₂×C₄	1	2	yes	—
67	C₂×#10625329	C₂×C₄	1	2	yes	—
68	C₂×#10625329	C₂³	1	2	yes	—
69	C₂×#10625329	C₂³	1	2	yes	—
70	C₂×#10625324	C₂×C₄	1	8	yes	complemented
71	M₁₆×D₄₇	—	2	8	no	—
72	M₁₆×D₄₇	—	2	8	no	—
73	C₂²×C₄₇⋊C₈	—	2	1	no	—
74	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
75	C₂×C₈×D₄₇	C₂×C₄	1	8	yes	complemented
76	#13093983	—	2	1	no	—
77	#13093983	—	2	1	no	—
78	#13093983	C₂×C₄	1	2	yes	—
79	#13093983	C₂³	1	2	yes	—
80	C₂×C₄⋊Dic₄₇	—	2	1	no	—
81	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
82	C₂×C₄×Dic₄₇	—	2	1	no	—
83	#13093942	C₂×C₄	1	8	yes	complemented
84	#13093940	C₂×C₄	1	8	yes	complemented
85	#13093938	C₂×C₄	1	16	yes	—
86	#13093934	—	2	4	no	—
87	C₈×Dic₄₇	—	2	4	no	—
88	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×M₁₆×C₄₇	—	2	1	no	—
90	C₂×M₁₆×C₄₇	—	2	1	no	—
91	C₂×M₁₆×C₄₇	—	2	1	no	—
92	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
93	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
94	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
95	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
96	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
97	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
98	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
99	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
100	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
101	C₂²×C₈×C₄₇	—	2	1	no	—
102	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
103	#117×C₄₇	—	2	1	no	—
104	#117×C₄₇	—	2	1	no	—
105	#117×C₄₇	C₂×C₄	1	2	yes	—
106	#117×C₄₇	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
109	C₂×C₄²×C₄₇	—	2	1	no	—
110	#97×C₄₇	—	2	4	no	—
111	C₄×C₈×C₄₇	—	2	4	no	—
112	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂³×D₄₇	C₄²	1	2	yes	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
129	C₂×C₂²⋊D₄₇	—	2	2	no	—
130	C₂×C₂²⋊D₄₇	—	2	2	no	—
131	C₂×C₂²⋊D₄₇	—	2	2	no	—
132	C₂×C₂²⋊D₄₇	—	2	2	no	—
133	C₂×C₂²⋊D₄₇	C₄²	1	4	yes	—
134	C₂×C₂²⋊D₄₇	C₂²×C₄	1	4	yes	—
135	C₂²×Dic₄₇	—	2	2	no	—
136	C₂²×Dic₄₇	C₄²	1	2	yes	—
137	#10625350	—	2	2	no	—
138	#10625350	—	2	2	no	—
139	#10625350	—	2	2	no	—
140	#10625350	—	2	2	no	—
141	#10625350	—	2	2	no	—
142	#10625350	—	2	2	no	—
143	#10625350	—	2	2	no	—
144	#10625350	—	2	2	no	—
145	#10625350	—	2	2	no	—
146	#10625350	—	2	2	no	—
147	#10625350	—	2	2	no	—
148	#10625350	—	2	2	no	—
149	#10625350	—	2	2	no	—
150	#10625350	—	2	2	no	—
151	#10625350	—	2	2	no	—
152	#10625350	—	2	2	no	—
153	C₂×D₁₈₈	—	2	1	no	—
154	C₂×D₁₈₈	—	2	1	no	—
155	C₂×D₁₈₈	—	2	1	no	—
156	C₂×D₁₈₈	—	2	1	no	—
157	C₂×D₁₈₈	C₄²	1	2	yes	—
158	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
159	C₂×C₄×D₄₇	—	2	2	no	—
160	C₂×C₄×D₄₇	—	2	2	no	—
161	C₂×C₄×D₄₇	—	2	2	no	—
162	C₂×C₄×D₄₇	—	2	2	no	—
163	C₂×C₄×D₄₇	C₄²	1	4	yes	—
164	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
165	C₂×Dic₉₄	—	2	1	no	—
166	C₂×Dic₉₄	—	2	1	no	—
167	C₂×Dic₉₄	—	2	1	no	—
168	C₂×Dic₉₄	—	2	1	no	—
169	C₂×Dic₉₄	C₄²	1	2	yes	—
170	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
171	M₁₆×C₄₇	—	2	2	no	—
172	M₁₆×C₄₇	—	2	2	no	—
173	M₁₆×C₄₇	—	2	2	no	—
174	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
175	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
176	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
177	M₁₆×C₄₇	C₂²⋊C₄	1	4	yes	—
178	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
179	C₂×C₈×C₄₇	—	2	2	no	—
180	C₂×C₈×C₄₇	—	2	2	no	—
181	C₂×C₈×C₄₇	—	2	2	no	—
182	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
183	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
184	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
185	C₄⋊C₄×C₄₇	—	2	2	no	—
186	C₄⋊C₄×C₄₇	—	2	2	no	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
189	C₄²×C₄₇	—	2	2	no	—
190	C₄²×C₄₇	—	2	2	no	—
191	C₂²⋊Dic₄₇	—	2	2	no	—
192	C₂²⋊Dic₄₇	C₂²×C₄	1	4	yes	—
193	C₄⋊Dic₄₇	—	2	2	no	—
194	C₄⋊Dic₄₇	—	2	2	no	—
195	C₄×Dic₄₇	—	2	2	no	—
196	C₄×Dic₄₇	—	2	2	no	—
197	#10625329	—	2	2	no	—
198	#10625329	—	2	2	no	—
199	#10625329	—	2	2	no	—
200	#10625329	—	2	2	no	—
201	#10625329	—	2	2	no	—
202	#10625329	—	2	2	no	—
203	#10625329	—	2	2	no	—
204	#10625329	C₂²×C₄	1	4	yes	—
205	C₂×C₄₇⋊C₈	—	2	2	no	—
206	C₂×C₄₇⋊C₈	—	2	2	no	—
207	C₂×C₄₇⋊C₈	—	2	2	no	—
208	C₂×C₄₇⋊C₈	—	2	2	no	—
209	C₂×C₄₇⋊C₈	—	2	2	no	—
210	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
211	#10625324	—	2	16	no	—
212	C₈×D₄₇	—	2	16	no	—
213	C₂³×C₄₇	—	8	1	no	—
214	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
215	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
216	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
217	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
218	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
219	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
220	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
221	C₂²×D₄₇	—	2	2	no	—
222	C₂²×D₄₇	—	2	2	no	—
223	C₂²×D₄₇	—	8	2	no	—
224	C₂²×D₄₇	C₂×C₄²	1	4	yes	—
225	C₂×C₄×C₄₇	—	2	4	no	—
226	C₂×C₄×C₄₇	—	8	2	no	—
227	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
255	C₂²⋊D₄₇	—	2	4	no	—
256	C₂²⋊D₄₇	—	2	4	no	—
257	C₂²⋊D₄₇	—	2	4	no	—
258	C₂²⋊D₄₇	—	2	4	no	—
259	C₂×Dic₄₇	—	2	2	no	—
260	C₂×Dic₄₇	—	2	2	no	—
261	C₂×Dic₄₇	—	2	4	no	—
262	C₂×Dic₄₇	—	8	2	no	—
263	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
264	D₁₈₈	—	2	2	no	—
265	D₁₈₈	—	2	2	no	—
266	D₁₈₈	—	2	2	no	—
267	D₁₈₈	—	2	2	no	—
268	C₄×D₄₇	—	2	4	no	—
269	C₄×D₄₇	—	2	4	no	—
270	C₄×D₄₇	—	2	4	no	—
271	C₄×D₄₇	—	2	4	no	—
272	Dic₉₄	—	2	2	no	—
273	Dic₉₄	—	2	2	no	—
274	Dic₉₄	—	2	2	no	—
275	Dic₉₄	—	2	2	no	—
276	C₈×C₄₇	—	2	4	no	—
277	C₈×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
278	C₄₇⋊C₈	—	2	4	no	—
279	C₄₇⋊C₈	—	2	4	no	—
280	#20401	—	47	1	no	maximal, Sylow
281	C₂²×C₄₇	—	4	1	no	—
282	C₂²×C₄₇	—	4	1	no	—
283	C₂²×C₄₇	—	4	1	no	—
284	C₂²×C₄₇	—	4	1	no	—
285	C₂²×C₄₇	—	4	1	no	—
286	C₂²×C₄₇	—	4	1	no	—
287	C₂²×C₄₇	—	4	1	no	—
288	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
290	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
291	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
292	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
293	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
294	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
295	C₂×D₄₇	—	2	4	no	—
296	C₂×D₄₇	—	4	4	no	—
297	C₂×D₄₇	—	8	2	no	—
298	C₂×D₄₇	—	8	2	no	—
299	C₄×C₄₇	—	4	4	no	—
300	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
301	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
302	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
303	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
304	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
305	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
306	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
307	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
308	Dic₄₇	—	2	4	no	—
309	Dic₄₇	—	4	4	no	—
310	C₂×#568	—	47	1	no	—
311	C₂×#413	—	47	1	no	—
312	C₂×#410	—	47	1	no	—
313	#2873	—	47	1	no	—
314	#2873	D₄₇	1	1	yes	characteristic, complemented
315	#1757	—	47	8	no	—
316	C₂×#344	—	47	1	no	—
317	C₂×#344	—	47	1	no	—
318	C₂×C₄₇	—	2	1	no	—
319	C₂×C₄₇	—	2	1	no	—
320	C₂×C₄₇	—	2	1	no	—
321	C₂×C₄₇	—	2	1	no	—
322	C₂×C₄₇	—	2	1	no	—
323	C₂×C₄₇	—	2	1	no	—
324	C₂×C₄₇	—	2	1	no	—
325	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
326	D₄₇	—	4	4	no	—
327	C₂²×#41	—	47	1	no	—
328	#568	—	94	2	no	—
329	#568	—	94	2	no	—
330	#568	—	94	2	no	—
331	#568	—	94	2	no	—
332	C₂×#131	—	47	4	no	—
333	C₂×#131	—	47	4	no	—
334	C₂²×M₁₆	—	47	1	no	—
335	C₂²×M₁₆	—	47	4	no	—
336	C₂²×M₁₆	—	47	1	no	—
337	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
338	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
339	C₂×#117	—	47	1	no	—
340	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
341	#413	—	47	4	no	—
342	#413	—	47	4	no	—
343	C₂×#101	—	47	2	no	—
344	C₂×#100	—	47	2	no	—
345	#410	—	47	4	no	—
346	#410	—	47	4	no	—
347	C₂×#99	—	47	4	no	—
348	#405	—	2	2	no	—
349	#405	—	47	4	no	—
350	#405	—	94	2	no	—
351	#405	C₂×D₄₇	1	4	yes	complemented
352	C₄×M₁₆	—	2	2	no	—
353	C₄×M₁₆	—	94	2	no	—
354	#344	—	47	4	no	—
355	#344	—	47	4	no	—
356	C₄₇	#20401	1	1	yes	characteristic, complemented, Sylow
357	C₂×#41	—	47	2	no	—
358	C₂×#41	—	47	2	no	—
359	C₂×#41	—	47	2	no	—
360	C₂×#41	—	47	2	no	—
361	C₂×#41	—	94	1	no	—
362	C₂×#41	—	94	1	no	—
363	C₂×#41	—	94	1	no	—
364	C₂×#41	—	94	1	no	—
365	C₂×#41	—	94	1	no	—
366	C₂×#41	—	94	1	no	—
367	C₂×#41	—	94	1	no	—
368	C₂×#41	—	94	1	no	—
369	C₂²×Q₈	—	47	1	no	—
370	C₂²×D₄	—	47	2	no	—
371	C₂²×D₄	—	47	1	no	—
372	C₂³×C₄	—	47	2	no	—
373	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
374	#131	—	94	8	no	—
375	#131	—	94	8	no	—
376	#131	—	94	8	no	—
377	#131	—	94	8	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	47	2	no	—
382	C₂×M₁₆	—	47	2	no	—
383	C₂×M₁₆	—	47	8	no	—
384	C₂×M₁₆	—	47	2	no	—
385	C₂×M₁₆	—	47	2	no	—
386	C₂×M₁₆	—	47	2	no	—
387	C₂×M₁₆	—	94	1	no	—
388	C₂×M₁₆	—	94	1	no	—
389	C₂×M₁₆	—	94	1	no	—
390	C₂×M₁₆	—	94	1	no	—
391	C₂×M₁₆	—	94	1	no	—
392	C₂×M₁₆	—	94	1	no	—
393	C₂×M₁₆	—	94	1	no	—
394	C₂×M₁₆	—	94	8	no	—
395	C₂×M₁₆	—	94	8	no	—
396	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
397	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
398	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
399	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
400	C₂×M₁₆	D₁₈₈	1	2	yes	—
401	C₂×M₁₆	D₁₈₈	1	2	yes	—
402	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
403	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
404	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
405	C₂²×C₈	—	2	1	no	—
406	C₂²×C₈	—	47	2	no	—
407	C₂²×C₈	—	47	8	no	—
408	C₂²×C₈	—	94	1	no	—
409	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	#117	—	47	2	no	—
413	#117	—	47	2	no	—
414	#117	—	94	1	no	—
415	#117	—	94	1	no	—
416	#117	C₄×D₄₇	1	2	yes	—
417	#117	C₂²×D₄₇	1	2	yes	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	94	1	no	—
420	C₂×C₂²⋊C₄	—	47	2	no	—
421	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	94	1	no	—
424	#101	—	47	8	no	—
425	#100	—	47	8	no	—
426	#99	—	47	16	no	—
427	#97	—	2	4	no	—
428	#97	—	94	4	no	—
429	C₄×C₈	—	2	4	no	—
430	C₄×C₈	—	94	4	no	—
431	C₂⁴	—	47	2	no	—
432	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
433	#41	—	94	2	no	—
434	#41	—	94	2	no	—
435	#41	—	94	2	no	—
436	#41	—	94	2	no	—
437	#41	—	94	2	no	—
438	#41	—	94	2	no	—
439	#41	—	94	2	no	—
440	#41	—	94	2	no	—
441	#41	—	94	2	no	—
442	#41	—	94	2	no	—
443	#41	—	94	2	no	—
444	#41	—	94	2	no	—
445	#41	—	94	2	no	—
446	#41	—	94	2	no	—
447	#41	—	94	2	no	—
448	#41	—	94	2	no	—
449	C₂×Q₈	—	47	2	no	—
450	C₂×Q₈	—	47	2	no	—
451	C₂×Q₈	—	94	1	no	—
452	C₂×Q₈	—	94	1	no	—
453	C₂×Q₈	—	94	1	no	—
454	C₂×Q₈	—	94	1	no	—
455	C₂×D₄	—	47	4	no	—
456	C₂×D₄	—	47	4	no	—
457	C₂×D₄	—	47	2	no	—
458	C₂×D₄	—	47	2	no	—
459	C₂×D₄	—	94	2	no	—
460	C₂×D₄	—	94	2	no	—
461	C₂×D₄	—	94	2	no	—
462	C₂×D₄	—	94	2	no	—
463	C₂×D₄	—	94	1	no	—
464	C₂×D₄	—	94	1	no	—
465	C₂×D₄	—	94	1	no	—
466	C₂×D₄	—	94	1	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	47	2	no	—
469	C₂²×C₄	—	47	4	no	—
470	C₂²×C₄	—	47	4	no	—
471	C₂²×C₄	—	94	2	no	—
472	C₂²×C₄	—	94	2	no	—
473	C₂²×C₄	—	94	2	no	—
474	C₂²×C₄	—	94	2	no	—
475	C₂²×C₄	—	94	2	no	—
476	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
482	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
483	C₂²×C₄	#10625350	1	1	yes	characteristic
484	C₂²×C₄	#10625350	1	1	yes	characteristic
485	C₂²×C₄	#10625350	1	1	yes	characteristic
486	C₂²×C₄	#10625350	1	1	yes	characteristic
487	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
489	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
490	M₁₆	—	2	2	no	—
491	M₁₆	—	2	2	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	—	47	4	no	—
494	M₁₆	—	94	2	no	—
495	M₁₆	—	94	2	no	—
496	M₁₆	—	94	2	no	—
497	M₁₆	—	94	2	no	—
498	M₁₆	—	94	2	no	—
499	M₁₆	—	94	2	no	—
500	M₁₆	—	94	2	no	—
501	M₁₆	—	94	16	no	—
502	M₁₆	(C₂×D₄₇)⋊C₄	1	4	yes	—
503	M₁₆	(C₂×D₄₇)⋊C₄	1	4	yes	—
504	M₁₆	(C₂×D₄₇)⋊C₄	1	4	yes	—
505	M₁₆	(C₂×D₄₇)⋊C₄	1	4	yes	—
506	M₁₆	C₂×C₄×D₄₇	1	4	yes	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	47	4	no	—
511	C₂×C₈	—	94	2	no	—
512	C₂×C₈	—	94	2	no	—
513	C₂×C₈	—	94	2	no	—
514	C₂×C₈	—	94	2	no	—
515	C₂×C₈	—	94	2	no	—
516	C₂×C₈	—	94	16	no	—
517	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
518	C₂×C₈	C₂×D₁₈₈	1	4	yes	—
519	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	94	2	no	—
523	C₄⋊C₄	—	94	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	47	4	no	—
526	C₂²⋊C₄	—	94	2	no	—
527	C₂²⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	94	2	no	—
531	C₄²	—	94	2	no	—
532	C₂³	—	8	1	no	—
533	C₂³	—	47	4	no	—
534	C₂³	—	94	2	no	—
535	C₂³	—	94	2	no	—
536	C₂³	—	376	2	no	—
537	C₂³	C₄²×D₄₇	1	1	yes	characteristic
538	C₂³	C₄²×D₄₇	1	1	yes	characteristic
539	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
540	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
541	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
542	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
543	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
544	Q₈	—	94	2	no	—
545	Q₈	—	94	2	no	—
546	Q₈	—	94	2	no	—
547	Q₈	—	94	2	no	—
548	D₄	—	94	4	no	—
549	D₄	—	94	4	no	—
550	D₄	—	94	4	no	—
551	D₄	—	94	4	no	—
552	D₄	—	94	2	no	—
553	D₄	—	94	2	no	—
554	D₄	—	94	2	no	—
555	D₄	—	94	2	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	—	47	4	no	—
559	C₂×C₄	—	94	2	no	—
560	C₂×C₄	—	94	2	no	—
561	C₂×C₄	—	94	4	no	—
562	C₂×C₄	—	94	4	no	—
563	C₂×C₄	—	94	4	no	—
564	C₂×C₄	—	94	4	no	—
565	C₂×C₄	—	94	4	no	—
566	C₂×C₄	—	376	2	no	—
567	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
568	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
569	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
570	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
571	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
572	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
573	C₂×C₄	#13093981	1	1	yes	characteristic
574	C₂×C₄	#13093981	1	1	yes	characteristic
575	C₂×C₄	#13093981	1	1	yes	characteristic
576	C₂×C₄	#13093981	1	1	yes	characteristic
577	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
578	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
579	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
580	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
581	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
582	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
583	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
584	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
585	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
586	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
587	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
588	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
589	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
590	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
591	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
592	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
593	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
594	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
595	C₈	—	2	4	no	—
596	C₈	—	94	4	no	—
597	C₈	—	94	4	no	—
598	C₈	C₂×(C₂×D₄₇)⋊C₄	1	8	yes	—
599	C₂²	—	4	1	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	94	4	no	—
607	C₂²	—	376	2	no	—
608	C₂²	—	376	2	no	—
609	C₂²	—	188	4	no	—
610	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
611	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
612	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
613	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
614	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
615	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
616	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
617	C₄	—	4	4	no	—
618	C₄	—	94	4	no	—
619	C₄	—	188	4	no	—
620	C₄	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
621	C₄	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
622	C₄	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
623	C₄	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
624	C₄	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
625	C₄	C₂×#13093981	1	1	yes	characteristic
626	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
627	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	2	1	no	—
634	C₂	—	2	1	no	—
635	C₂	—	188	4	no	—
636	C₂	C₂×C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×(C₂×D₄₇)⋊C₄
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2873	C₂
socle	C₂×C₄₇	C₂×C₄×C₂²⋊C₄
prime radical	C₂²×#10625350	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2873	D₄₇
hypocenter	C₄₇	#20401
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×M₁₆ ◁ #2873

Complements

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

N	H ≅ G/N	type
4. #20251806	C₂	semidirect
5. #20243189	C₂	semidirect
6. C₂×#15688895	C₂	semidirect
7. C₂×#15688893	C₂	semidirect
8. C₄₇×#2873	C₂	semidirect
14. C₂×#13094032	C₄	semidirect
18. C₂×M₁₆×D₄₇	C₄	semidirect
20. #15689105	C₄	semidirect
22. C₂×#13093942	C₄	semidirect
23. C₂×#13093940	C₄	semidirect
28. #15689078	C₂²	semidirect
30. #15688895	C₂²	semidirect
31. #15688893	C₂²	semidirect
36. C₄₇×#405	C₂²	semidirect
70. C₂×#10625324	C₂×C₄	semidirect
75. C₂×C₈×D₄₇	C₂×C₄	semidirect
83. #13093942	C₂×C₄	semidirect
84. #13093940	C₂×C₄	semidirect
314. #2873	D₄₇	semidirect
351. #405	C₂×D₄₇	semidirect
356. C₄₇	#20401	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689889	2
C₂×#15689105	2
C₂×#15689096	2
#20251806	2
#20243189	2
C₂×#15688895	2
C₂×#15688893	2
C₄₇×#2873	2
#20401	47