Subgroups — #26183650

Order 12032.

1338 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689673	C₂	1	1	yes	maximal, characteristic
2	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241957	C₂	1	4	yes	maximal, complemented
4	#20241949	C₂	1	4	yes	maximal, complemented
5	#20241884	C₂	1	4	yes	maximal, complemented
6	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#10625350	—	2	1	no	—
8	#15689673	—	2	1	no	—
9	#15689673	—	2	1	no	—
10	#15689673	—	2	1	no	—
11	#15689673	—	2	1	no	—
12	#15689673	C₄	1	2	yes	complemented
13	#15689673	C₄	1	2	yes	complemented
14	#15689673	C₂²	1	2	yes	—
15	#15689673	C₂²	1	2	yes	—
16	C₂×#13094024	C₄	1	1	yes	characteristic, complemented
17	C₂×#13094021	C₄	1	1	yes	characteristic, complemented
18	C₂×#13094012	—	2	1	no	—
19	C₂×#13093998	—	2	1	no	—
20	C₂×#13093998	C₂²	1	2	yes	—
21	C₂×C₄×D₁₈₈	—	2	1	no	—
22	C₂×C₄×D₁₈₈	C₄	1	2	yes	complemented
23	C₂×#13093983	—	2	1	no	—
24	#15688993	—	2	1	no	—
25	#15688989	C₂²	1	2	yes	complemented
26	#15688983	—	2	1	no	—
27	#15688983	C₂²	1	2	yes	—
28	C₄×C₄⋊Dic₄₇	—	2	1	no	—
29	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
30	#15688858	C₂²	1	16	yes	complemented
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#431	—	2	1	no	—
33	C₄₇×#431	—	2	1	no	—
34	C₄₇×#431	C₂²	1	2	yes	complemented
35	C₄₇×#431	C₂²	1	2	yes	complemented
36	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
37	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₇	—	2	1	no	—
39	C₂×#10625350	—	2	2	no	—
40	C₂×#10625350	—	2	2	no	—
41	C₂×#10625350	—	2	2	no	—
42	C₂×#10625350	—	2	2	no	—
43	C₂×#10625350	—	4	4	no	—
44	C₂×#10625350	—	4	4	no	—
45	C₂²×Dic₉₄	—	2	1	no	—
46	C₂²×D₁₈₈	—	2	1	no	—
47	C₂²×D₁₈₈	—	2	1	no	—
48	C₂²×D₁₈₈	C₂×C₄	1	2	yes	—
49	C₂²×C₂²⋊D₄₇	—	2	2	no	—
50	C₂²×C₄×D₄₇	—	2	2	no	—
51	#13094024	—	2	1	no	—
52	#13094024	—	2	1	no	—
53	#13094024	C₂×C₄	1	2	yes	—
54	#13094024	C₂×C₄	1	2	yes	—
55	#13094021	—	2	1	no	—
56	#13094021	—	2	1	no	—
57	#13094021	C₂×C₄	1	2	yes	—
58	#13094021	C₂×C₄	1	2	yes	—
59	#13094012	—	2	2	no	—
60	#13094012	—	2	2	no	—
61	#13094012	—	2	2	no	—
62	#13094012	—	2	2	no	—
63	#13093998	—	2	2	no	—
64	#13093998	—	2	2	no	—
65	#13093998	—	2	2	no	—
66	#13093998	—	2	2	no	—
67	#13093998	—	2	2	no	—
68	#13093998	—	2	2	no	—
69	#13093998	C₂×C₄	1	4	yes	—
70	#13093998	C₂³	1	4	yes	—
71	C₄×D₁₈₈	—	2	2	no	—
72	C₄×D₁₈₈	—	2	2	no	—
73	C₄×D₁₈₈	—	2	2	no	—
74	C₄×D₁₈₈	—	2	2	no	—
75	C₄×D₁₈₈	—	2	2	no	—
76	C₄×D₁₈₈	—	2	2	no	—
77	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
78	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
79	#13093983	—	4	4	no	—
80	C₂×C₄⋊Dic₄₇	—	2	1	no	—
81	C₂×C₄⋊Dic₄₇	—	2	2	no	—
82	C₂×C₄⋊Dic₄₇	—	2	2	no	—
83	C₂×C₄⋊Dic₄₇	—	2	2	no	—
84	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
85	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
86	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
87	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
88	C₂×C₄×Dic₄₇	—	2	2	no	—
89	C₄₇⋊#95	—	2	2	no	—
90	C₄₇⋊#95	C₂³	1	4	yes	—
91	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
92	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₄₇	—	2	2	no	—
95	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
107	C₄⋊C₈×C₄₇	—	2	2	no	—
108	C₄⋊C₈×C₄₇	—	2	2	no	—
109	C₂²⋊C₈×C₄₇	—	2	2	no	—
110	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
111	C₄×C₈×C₄₇	—	2	2	no	—
112	C₄×C₈×C₄₇	—	2	2	no	—
113	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂³×D₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	4	2	no	—
116	C₂²×C₄×C₄₇	—	4	2	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	D₈	1	4	yes	—
126	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
127	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
137	C₂×C₂²⋊D₄₇	—	2	4	no	—
138	C₂×C₂²⋊D₄₇	—	2	4	no	—
139	C₂×C₂²⋊D₄₇	—	4	4	no	—
140	C₂×C₂²⋊D₄₇	—	4	4	no	—
141	C₂²×Dic₄₇	—	2	2	no	—
142	C₂²×Dic₄₇	—	2	4	no	—
143	#10625350	—	4	8	no	—
144	#10625350	—	4	8	no	—
145	#10625350	—	4	4	no	—
146	#10625350	—	4	4	no	—
147	#10625350	—	4	4	no	—
148	#10625350	—	4	4	no	—
149	C₂×D₁₈₈	—	2	2	no	—
150	C₂×D₁₈₈	—	2	2	no	—
151	C₂×D₁₈₈	—	2	2	no	—
152	C₂×D₁₈₈	—	2	2	no	—
153	C₂×D₁₈₈	—	2	2	no	—
154	C₂×D₁₈₈	—	4	4	no	—
155	C₂×D₁₈₈	—	4	4	no	—
156	C₂×D₁₈₈	—	4	4	no	—
157	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
158	C₂×C₄×D₄₇	—	2	4	no	—
159	C₂×C₄×D₄₇	—	2	4	no	—
160	C₂×C₄×D₄₇	—	4	8	no	—
161	C₂×Dic₉₄	—	2	2	no	—
162	C₂×Dic₉₄	—	2	2	no	—
163	C₂×Dic₉₄	—	4	4	no	—
164	C₂×C₈×C₄₇	—	2	4	no	—
165	C₂×C₈×C₄₇	—	4	4	no	—
166	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
168	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
182	C₂²⋊Dic₄₇	—	4	4	no	—
183	(C₂×D₄₇)⋊C₄	—	2	4	no	—
184	(C₂×D₄₇)⋊C₄	—	2	4	no	—
185	(C₂×D₄₇)⋊C₄	—	2	4	no	—
186	(C₂×D₄₇)⋊C₄	—	2	4	no	—
187	C₄⋊Dic₄₇	—	2	2	no	—
188	C₄⋊Dic₄₇	—	2	2	no	—
189	C₄⋊Dic₄₇	—	2	2	no	—
190	C₄⋊Dic₄₇	—	4	4	no	—
191	C₄⋊Dic₄₇	—	4	4	no	—
192	C₄⋊Dic₄₇	—	4	4	no	—
193	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
194	C₄×Dic₄₇	—	4	4	no	—
195	C₂³×C₄₇	—	4	1	no	—
196	C₂³×C₄₇	—	4	1	no	—
197	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
198	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂³×C₄₇	C₂×D₈	1	2	yes	—
200	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
201	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
202	C₂²×D₄₇	—	2	4	no	—
203	C₂²×D₄₇	—	4	4	no	—
204	C₂²×D₄₇	—	4	4	no	—
205	C₂²×D₄₇	—	4	4	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	2	2	no	—
212	C₂×C₄×C₄₇	—	4	1	no	—
213	C₂×C₄×C₄₇	—	4	1	no	—
214	C₂×C₄×C₄₇	—	4	1	no	—
215	C₂×C₄×C₄₇	—	4	1	no	—
216	C₂×C₄×C₄₇	—	4	1	no	—
217	C₂×C₄×C₄₇	—	4	1	no	—
218	C₂×C₄×C₄₇	#102	1	4	yes	—
219	C₂×C₄×C₄₇	#102	1	4	yes	—
220	C₂×C₄×C₄₇	#102	1	4	yes	—
221	C₂×C₄×C₄₇	#102	1	4	yes	—
222	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	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×D₈	1	2	yes	—
233	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
234	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
235	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
236	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
238	C₂²⋊D₄₇	—	4	4	no	—
239	C₂²⋊D₄₇	—	4	4	no	—
240	C₂²⋊D₄₇	—	4	8	no	—
241	C₂×Dic₄₇	—	2	4	no	—
242	C₂×Dic₄₇	—	4	4	no	—
243	C₂×Dic₄₇	—	4	4	no	—
244	C₂×Dic₄₇	—	4	4	no	—
245	C₂×Dic₄₇	—	4	4	no	—
246	D₁₈₈	—	4	4	no	—
247	D₁₈₈	—	4	4	no	—
248	D₁₈₈	—	4	4	no	—
249	D₁₈₈	—	4	4	no	—
250	D₁₈₈	—	4	4	no	—
251	D₁₈₈	—	4	4	no	—
252	C₄×D₄₇	—	4	8	no	—
253	C₄×D₄₇	—	4	8	no	—
254	Dic₉₄	—	4	4	no	—
255	Dic₉₄	—	4	4	no	—
256	C₈×C₄₇	—	4	4	no	—
257	#17574	—	47	1	no	maximal, Sylow
258	C₂²×C₄₇	—	2	1	no	—
259	C₂²×C₄₇	—	2	1	no	—
260	C₂²×C₄₇	—	2	1	no	—
261	C₂²×C₄₇	—	2	1	no	—
262	C₂²×C₄₇	—	2	1	no	—
263	C₂²×C₄₇	—	2	1	no	—
264	C₂²×C₄₇	—	4	2	no	—
265	C₂²×C₄₇	—	4	2	no	—
266	C₂²×C₄₇	C₂×#102	1	2	yes	—
267	C₂²×C₄₇	C₂×#102	1	2	yes	—
268	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
269	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
270	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
271	C₂×D₄₇	—	4	4	no	—
272	C₂×D₄₇	—	4	4	no	—
273	C₂×D₄₇	—	4	4	no	—
274	C₂×D₄₇	—	8	8	no	—
275	C₄×C₄₇	—	2	1	no	—
276	C₄×C₄₇	—	2	1	no	—
277	C₄×C₄₇	—	2	1	no	—
278	C₄×C₄₇	—	2	1	no	—
279	C₄×C₄₇	—	2	1	no	—
280	C₄×C₄₇	—	2	1	no	—
281	C₄×C₄₇	#410	1	2	yes	—
282	C₄×C₄₇	C₂×#102	1	2	yes	—
283	C₄×C₄₇	C₂×#102	1	2	yes	—
284	C₄×C₄₇	C₂×#102	1	2	yes	—
285	C₄×C₄₇	C₂×#102	1	2	yes	—
286	C₄×C₄₇	#421	1	2	yes	—
287	Dic₄₇	—	4	4	no	—
288	Dic₄₇	—	8	4	no	—
289	C₂×#532	—	47	1	no	—
290	C₂×#431	D₄₇	1	1	yes	characteristic, complemented
291	#2285	—	47	1	no	—
292	#1519	—	47	4	no	—
293	#1517	—	47	4	no	—
294	#1502	—	47	4	no	—
295	C₂×C₄₇	—	2	1	no	—
296	C₂×C₄₇	—	2	2	no	—
297	C₂×C₄₇	—	2	1	no	—
298	C₂×C₄₇	—	2	2	no	—
299	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
300	C₂×C₄₇	C₂²×#102	1	1	yes	characteristic
301	C₂×C₄₇	C₂×#421	1	1	yes	characteristic
302	D₄₇	—	8	4	no	—
303	C₂²×#41	—	94	1	no	—
304	#532	—	47	2	no	—
305	#532	—	47	2	no	—
306	#532	—	47	2	no	—
307	#532	—	47	2	no	—
308	#532	—	94	1	no	—
309	#532	—	94	1	no	—
310	#532	—	94	1	no	—
311	#532	—	94	1	no	—
312	C₂×C₄⋊Q₈	—	47	1	no	—
313	C₂×#127	—	47	1	no	—
314	C₂×#124	—	94	1	no	—
315	C₂×#121	—	47	2	no	—
316	C₂×#121	—	94	1	no	—
317	C₂×C₄×D₄	—	47	2	no	—
318	C₂×C₄×D₄	—	94	1	no	—
319	C₂×#117	—	94	1	no	—
320	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
321	#431	—	2	1	no	—
322	#431	—	2	1	no	—
323	#431	C₂×D₄₇	1	2	yes	complemented
324	#431	C₂×D₄₇	1	2	yes	complemented
325	C₂×C₄⋊C₈	—	2	1	no	—
326	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
327	C₂×C₄×C₈	—	2	1	no	—
328	#384	—	94	1	no	—
329	#382	—	47	2	no	—
330	#380	—	47	2	no	—
331	#380	—	94	1	no	—
332	C₄×C₄⋊C₄	—	47	2	no	—
333	C₄×C₄⋊C₄	—	94	1	no	—
334	#327	—	47	16	no	—
335	C₄₇	#17574	1	1	yes	characteristic, complemented, Sylow
336	C₂×#41	—	94	2	no	—
337	C₂×#41	—	94	2	no	—
338	C₂×#41	—	94	2	no	—
339	C₂×#41	—	94	2	no	—
340	C₂×#41	—	188	4	no	—
341	C₂×#41	—	188	4	no	—
342	C₂²×Q₈	—	94	1	no	—
343	C₂²×D₄	—	47	2	no	—
344	C₂²×D₄	—	94	2	no	—
345	C₂²×D₄	—	94	1	no	—
346	C₂²×D₄	—	94	1	no	—
347	C₂³×C₄	—	94	2	no	—
348	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
349	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
350	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
351	C₂²×C₈	—	2	2	no	—
352	C₄⋊Q₈	—	47	2	no	—
353	C₄⋊Q₈	—	47	2	no	—
354	C₄⋊Q₈	—	94	1	no	—
355	C₄⋊Q₈	—	94	1	no	—
356	#127	—	47	2	no	—
357	#127	—	47	2	no	—
358	#127	—	94	1	no	—
359	#127	—	94	1	no	—
360	#124	—	94	2	no	—
361	#124	—	94	2	no	—
362	#124	—	94	2	no	—
363	#124	—	94	2	no	—
364	#121	—	47	4	no	—
365	#121	—	47	4	no	—
366	#121	—	94	2	no	—
367	#121	—	94	2	no	—
368	#121	—	94	2	no	—
369	#121	—	94	2	no	—
370	#121	—	94	2	no	—
371	#121	—	94	2	no	—
372	C₄×D₄	—	47	4	no	—
373	C₄×D₄	—	47	4	no	—
374	C₄×D₄	—	94	2	no	—
375	C₄×D₄	—	94	2	no	—
376	C₄×D₄	—	94	2	no	—
377	C₄×D₄	—	94	2	no	—
378	C₄×D₄	—	94	2	no	—
379	C₄×D₄	—	94	2	no	—
380	#117	—	188	4	no	—
381	C₂×C₄⋊C₄	—	47	2	no	—
382	C₂×C₄⋊C₄	—	94	1	no	—
383	C₂×C₄⋊C₄	—	94	2	no	—
384	C₂×C₄⋊C₄	—	94	2	no	—
385	C₂×C₄⋊C₄	—	94	2	no	—
386	C₂×C₂²⋊C₄	—	94	2	no	—
387	C₂×C₂²⋊C₄	—	94	2	no	—
388	C₂×C₂²⋊C₄	—	94	2	no	—
389	C₂×C₄²	—	94	2	no	—
390	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
391	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
392	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
394	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
395	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
396	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
397	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
398	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
399	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
400	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
401	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
402	C₄⋊C₈	—	2	2	no	—
403	C₄⋊C₈	—	2	2	no	—
404	C₂²⋊C₈	—	2	2	no	—
405	C₂²⋊C₈	C₂²×D₄₇	1	4	yes	—
406	C₄×C₈	—	2	2	no	—
407	C₄×C₈	—	2	2	no	—
408	#95	—	47	4	no	—
409	#95	—	94	2	no	—
410	C₂⁴	—	94	2	no	—
411	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
412	#41	—	188	8	no	—
413	#41	—	188	8	no	—
414	#41	—	188	4	no	—
415	#41	—	188	4	no	—
416	#41	—	188	4	no	—
417	#41	—	188	4	no	—
418	C₂×Q₈	—	94	2	no	—
419	C₂×Q₈	—	94	2	no	—
420	C₂×Q₈	—	188	4	no	—
421	C₂×D₄	—	47	4	no	—
422	C₂×D₄	—	94	4	no	—
423	C₂×D₄	—	94	4	no	—
424	C₂×D₄	—	94	2	no	—
425	C₂×D₄	—	94	2	no	—
426	C₂×D₄	—	94	2	no	—
427	C₂×D₄	—	94	2	no	—
428	C₂×D₄	—	94	2	no	—
429	C₂×D₄	—	188	4	no	—
430	C₂×D₄	—	188	4	no	—
431	C₂×D₄	—	188	4	no	—
432	C₂×D₄	—	188	4	no	—
433	C₂×D₄	—	188	4	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	4	2	no	—
436	C₂²×C₄	—	94	2	no	—
437	C₂²×C₄	—	94	4	no	—
438	C₂²×C₄	—	94	4	no	—
439	C₂²×C₄	—	94	4	no	—
440	C₂²×C₄	—	188	8	no	—
441	C₂²×C₄	#10625325	1	4	yes	—
442	C₂²×C₄	D₃₇₆	1	4	yes	—
443	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
444	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
445	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
446	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
447	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
448	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
449	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
450	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
452	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
460	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
461	C₂×C₈	—	2	4	no	—
462	C₂×C₈	—	4	4	no	—
463	C₄⋊C₄	—	47	4	no	—
464	C₄⋊C₄	—	94	2	no	—
465	C₄⋊C₄	—	94	2	no	—
466	C₄⋊C₄	—	94	2	no	—
467	C₄⋊C₄	—	188	4	no	—
468	C₄⋊C₄	—	188	4	no	—
469	C₄⋊C₄	—	188	4	no	—
470	C₂²⋊C₄	—	94	4	no	—
471	C₂²⋊C₄	—	94	4	no	—
472	C₂²⋊C₄	—	94	4	no	—
473	C₂²⋊C₄	—	94	4	no	—
474	C₂²⋊C₄	—	188	4	no	—
475	C₄²	—	188	4	no	—
476	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
477	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
478	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
479	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
480	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
481	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
482	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
483	C₄²	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
484	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
485	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
486	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
487	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
488	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
489	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
490	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
491	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	94	4	no	—
495	C₂³	—	188	4	no	—
496	C₂³	—	188	4	no	—
497	C₂³	—	188	4	no	—
498	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
499	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
500	C₂³	C₂×D₃₇₆	1	2	yes	—
501	C₂³	C₂×#10625325	1	2	yes	—
502	C₂³	C₂²×D₁₈₈	1	1	yes	characteristic
503	Q₈	—	188	4	no	—
504	Q₈	—	188	4	no	—
505	D₄	—	188	4	no	—
506	D₄	—	188	4	no	—
507	D₄	—	188	8	no	—
508	D₄	—	188	4	no	—
509	D₄	—	188	4	no	—
510	D₄	—	188	4	no	—
511	D₄	—	188	4	no	—
512	D₄	—	188	4	no	—
513	D₄	—	188	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	94	4	no	—
527	C₂×C₄	—	188	4	no	—
528	C₂×C₄	—	188	4	no	—
529	C₂×C₄	—	188	4	no	—
530	C₂×C₄	—	188	4	no	—
531	C₂×C₄	—	188	8	no	—
532	C₂×C₄	—	188	8	no	—
533	C₂×C₄	#13093946	1	4	yes	—
534	C₂×C₄	#13093946	1	4	yes	—
535	C₂×C₄	#13093946	1	4	yes	—
536	C₂×C₄	#13093946	1	4	yes	—
537	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
538	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
539	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
540	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
541	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
542	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
543	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
544	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
545	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
546	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
547	C₂×C₄	C₂×D₃₇₆	1	2	yes	—
548	C₂×C₄	C₂×D₃₇₆	1	2	yes	—
549	C₂×C₄	C₂×#10625325	1	2	yes	—
550	C₂×C₄	C₂×#10625325	1	2	yes	—
551	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
552	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
553	C₈	—	4	4	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	2	no	—
562	C₂²	—	376	8	no	—
563	C₂²	—	188	4	no	—
564	C₂²	—	188	4	no	—
565	C₂²	—	188	4	no	—
566	C₂²	C₂×#13093946	1	2	yes	—
567	C₂²	C₂×#13093946	1	2	yes	—
568	C₂²	C₂²×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
569	C₂²	C₂²×D₃₇₆	1	1	yes	characteristic
570	C₂²	C₂²×#10625325	1	1	yes	characteristic
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	376	4	no	—
578	C₄	—	188	4	no	—
579	C₄	#15689096	1	2	yes	—
580	C₄	C₂×#13093946	1	2	yes	—
581	C₄	C₂×#13093946	1	2	yes	—
582	C₄	C₂×#13093946	1	2	yes	—
583	C₄	C₂×#13093946	1	2	yes	—
584	C₄	#15689139	1	2	yes	—
585	C₂	—	2	1	no	—
586	C₂	—	2	2	no	—
587	C₂	—	2	2	no	—
588	C₂	—	2	1	no	—
589	C₂	—	376	4	no	—
590	C₂	C₂×#15689096	1	1	yes	characteristic
591	C₂	C₂²×#13093946	1	1	yes	characteristic
592	C₂	C₂×#15689139	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#431	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂×#15689673	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#431	D₄₇
hypocenter	C₄₇	#17574
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
2. #20245795	C₂	semidirect
3. #20241957	C₂	semidirect
4. #20241949	C₂	semidirect
5. #20241884	C₂	semidirect
6. C₂×C₄₇×#431	C₂	semidirect
12. #15689673	C₄	semidirect
13. #15689673	C₄	semidirect
16. C₂×#13094024	C₄	semidirect
17. C₂×#13094021	C₄	semidirect
22. C₂×C₄×D₁₈₈	C₄	semidirect
25. #15688989	C₂²	semidirect
29. C₄×C₄⋊Dic₄₇	C₂²	semidirect
30. #15688858	C₂²	semidirect
34. C₄₇×#431	C₂²	semidirect
35. C₄₇×#431	C₂²	semidirect
290. C₂×#431	D₄₇	semidirect
323. #431	C₂×D₄₇	semidirect
324. #431	C₂×D₄₇	semidirect
335. C₄₇	#17574	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689673	2
#20245795	2
#20241957	2
#20241949	2
#20241884	2
C₂×C₄₇×#431	2
#17574	47