Subgroups — C₂×#20243626 #26217173

Order 12032.

1358 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689890	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689171	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689146	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13093951	C₂	1	1	yes	maximal, characteristic
5	#20243626	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688893	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688882	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#421	C₂	1	1	yes	maximal, characteristic
9	#15689890	—	2	2	no	—
10	#15689890	—	2	2	no	—
11	#15689890	—	2	2	no	—
12	#15689890	C₂²	1	4	yes	—
13	C₂×#13094031	—	2	2	no	—
14	C₂×#13094031	—	2	2	no	—
15	C₂²×#10625329	—	2	2	no	—
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625329	C₂²	1	1	yes	characteristic
18	C₂²×#10625329	C₂²	1	1	yes	characteristic
19	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	#15689171	—	2	2	no	—
21	#15689171	C₂²	1	4	yes	complemented
22	C₂×#13093959	—	2	2	no	—
23	#15689146	—	2	2	no	—
24	#15689146	C₂²	1	4	yes	complemented
25	C₂×Dic₄₇⋊C₈	—	2	2	no	—
26	C₂×#13093951	C₄	1	2	yes	complemented
27	C₂×#13093951	C₄	1	2	yes	complemented
28	C₂×#13093951	C₄	1	4	yes	complemented
29	C₂×#13093951	C₂²	1	4	yes	—
30	#15688893	C₂²	1	4	yes	complemented
31	#15688882	C₂²	1	4	yes	complemented
32	C₂²×#41×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×#421	—	2	2	no	—
36	C₄₇×#421	C₂²	1	4	yes	—
37	C₂×#104×C₄₇	—	2	2	no	—
38	C₂³×Dic₄₇	—	2	1	no	—
39	#13094031	—	2	8	no	—
40	#13094031	—	2	8	no	—
41	#13094031	—	2	8	no	—
42	#13094031	—	2	8	no	—
43	C₂×#10625329	—	2	4	no	—
44	C₂×#10625329	—	2	8	no	—
45	C₂×#10625329	—	2	1	no	—
46	C₂×#10625329	—	2	1	no	—
47	C₂×#10625329	—	2	1	no	—
48	C₂×#10625329	—	2	1	no	—
49	C₂×#10625329	—	2	1	no	—
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	—	2	1	no	—
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂×#10625329	—	2	8	no	—
56	C₂×#10625329	C₂×C₄	1	2	yes	—
57	C₂×#10625329	C₂×C₄	1	2	yes	—
58	C₂×#10625329	D₄	1	2	yes	—
59	C₂×#10625329	D₄	1	2	yes	—
60	C₂×#10625329	D₄	1	2	yes	—
61	C₂×#10625329	C₂³	1	2	yes	—
62	C₂×#10625329	C₂³	1	2	yes	—
63	C₂×#10625329	C₂³	1	2	yes	—
64	C₂²×C₄₇⋊C₈	—	2	4	no	—
65	C₂²×C₄₇⋊C₈	—	2	1	no	—
66	C₂²×C₄₇⋊C₈	—	2	1	no	—
67	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
68	C₂×C₄×Dic₄₇	—	2	1	no	—
69	C₂×C₄×Dic₄₇	—	2	1	no	—
70	C₂×C₄×Dic₄₇	—	2	1	no	—
71	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
75	#13093959	—	2	8	no	—
76	Dic₄₇⋊C₈	—	2	8	no	—
77	#13093951	C₂×C₄	1	8	yes	complemented
78	#13093951	C₂×C₄	1	8	yes	complemented
79	C₂×#41×C₄₇	—	2	1	no	—
80	C₂×#41×C₄₇	—	2	1	no	—
81	C₂×#41×C₄₇	—	2	1	no	—
82	C₂×#41×C₄₇	—	2	1	no	—
83	C₂×#41×C₄₇	—	2	1	no	—
84	C₂×#41×C₄₇	—	2	1	no	—
85	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
86	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
87	C₂×#41×C₄₇	D₄	1	2	yes	—
88	C₂×#41×C₄₇	D₄	1	2	yes	—
89	C₂×#41×C₄₇	Q₈	1	2	yes	—
90	C₂×#41×C₄₇	C₂³	1	2	yes	—
91	C₂²×Q₈×C₄₇	Q₈	1	1	yes	characteristic
92	C₂²×D₄×C₄₇	—	2	1	no	—
93	C₂²×D₄×C₄₇	Q₈	1	1	yes	characteristic
94	C₂³×C₄×C₄₇	—	2	1	no	—
95	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₄₇	—	2	1	no	—
97	C₂×M₁₆×C₄₇	—	2	1	no	—
98	C₂×M₁₆×C₄₇	—	2	1	no	—
99	C₂×M₁₆×C₄₇	—	2	1	no	—
100	C₂×M₁₆×C₄₇	—	2	1	no	—
101	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
102	C₂²×C₈×C₄₇	—	2	1	no	—
103	#117×C₄₇	—	2	1	no	—
104	#117×C₄₇	—	2	1	no	—
105	#117×C₄₇	—	2	1	no	—
106	#117×C₄₇	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
109	C₂×C₄²×C₄₇	—	2	1	no	—
110	#104×C₄₇	—	2	8	no	—
111	C₂⁴×C₄₇	—	2	1	no	—
112	C₂⁴×C₄₇	#41	1	1	yes	characteristic
113	#41×C₄₇	—	2	2	no	—
114	#41×C₄₇	—	2	2	no	—
115	#41×C₄₇	—	2	2	no	—
116	#41×C₄₇	—	2	2	no	—
117	#41×C₄₇	—	2	2	no	—
118	#41×C₄₇	—	2	2	no	—
119	#41×C₄₇	—	2	2	no	—
120	#41×C₄₇	—	2	2	no	—
121	#41×C₄₇	—	2	2	no	—
122	#41×C₄₇	—	2	2	no	—
123	#41×C₄₇	—	2	2	no	—
124	#41×C₄₇	—	2	2	no	—
125	#41×C₄₇	C₄⋊C₄	1	4	yes	—
126	#41×C₄₇	C₄⋊C₄	1	4	yes	—
127	#41×C₄₇	C₂²×C₄	1	4	yes	—
128	#41×C₄₇	C₂×D₄	1	4	yes	—
129	C₂×Q₈×C₄₇	—	2	1	no	—
130	C₂×Q₈×C₄₇	—	2	1	no	—
131	C₂×Q₈×C₄₇	—	2	1	no	—
132	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
133	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
134	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	—
135	C₂×D₄×C₄₇	—	2	2	no	—
136	C₂×D₄×C₄₇	—	2	2	no	—
137	C₂×D₄×C₄₇	—	2	2	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	2	2	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	2	1	no	—
142	C₂×D₄×C₄₇	—	2	1	no	—
143	C₂×D₄×C₄₇	—	2	1	no	—
144	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
145	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
146	C₂×D₄×C₄₇	C₂×Q₈	1	2	yes	—
147	C₂²×C₄×C₄₇	—	2	1	no	—
148	C₂²×C₄×C₄₇	—	2	2	no	—
149	C₂²×C₄×C₄₇	—	2	2	no	—
150	C₂²×C₄×C₄₇	—	2	2	no	—
151	C₂²×C₄×C₄₇	—	2	2	no	—
152	C₂²×C₄×C₄₇	—	2	2	no	—
153	C₂²×C₄×C₄₇	—	2	2	no	—
154	C₂²×C₄×C₄₇	—	4	1	no	—
155	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
164	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
165	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
166	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
167	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
168	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂²×Dic₄₇	—	2	1	no	—
170	C₂²×Dic₄₇	—	2	2	no	—
171	C₂²×Dic₄₇	—	2	1	no	—
172	C₂²×Dic₄₇	—	2	2	no	—
173	C₂²×Dic₄₇	—	4	4	no	—
174	M₁₆×C₄₇	—	2	2	no	—
175	M₁₆×C₄₇	—	2	2	no	—
176	M₁₆×C₄₇	—	4	1	no	—
177	M₁₆×C₄₇	—	4	1	no	—
178	C₂×C₈×C₄₇	—	2	2	no	—
179	C₂×C₈×C₄₇	—	4	1	no	—
180	C₂×C₈×C₄₇	—	4	1	no	—
181	C₄⋊C₄×C₄₇	—	2	2	no	—
182	C₄⋊C₄×C₄₇	—	4	1	no	—
183	C₂²⋊C₄×C₄₇	—	2	2	no	—
184	C₂²⋊C₄×C₄₇	—	4	1	no	—
185	C₄²×C₄₇	—	2	2	no	—
186	C₄²×C₄₇	—	4	1	no	—
187	C₄×Dic₄₇	—	2	1	no	—
188	C₄×Dic₄₇	—	2	2	no	—
189	C₄×Dic₄₇	—	2	1	no	—
190	C₄×Dic₄₇	—	2	2	no	—
191	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
192	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
193	#10625329	—	2	16	no	—
194	#10625329	—	2	2	no	—
195	#10625329	—	2	2	no	—
196	#10625329	—	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	#10625329	C₂×D₄	1	4	yes	—
206	C₂×C₄₇⋊C₈	—	2	16	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	—	2	2	no	—
211	C₂×C₄₇⋊C₈	—	2	2	no	—
212	C₂×C₄₇⋊C₈	—	2	2	no	—
213	C₂×C₄₇⋊C₈	—	2	2	no	—
214	C₂×C₄₇⋊C₈	—	2	2	no	—
215	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
216	C₂³×C₄₇	—	2	2	no	—
217	C₂³×C₄₇	—	2	2	no	—
218	C₂³×C₄₇	—	2	2	no	—
219	C₂³×C₄₇	—	4	2	no	—
220	C₂³×C₄₇	—	8	2	no	—
221	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
222	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
223	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
225	C₂³×C₄₇	#123	1	1	yes	characteristic
226	C₂³×C₄₇	#123	1	1	yes	characteristic
227	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
228	Q₈×C₄₇	—	2	2	no	—
229	Q₈×C₄₇	—	2	2	no	—
230	Q₈×C₄₇	—	2	2	no	—
231	Q₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
232	D₄×C₄₇	—	2	4	no	—
233	D₄×C₄₇	—	2	4	no	—
234	D₄×C₄₇	—	2	4	no	—
235	D₄×C₄₇	—	2	4	no	—
236	D₄×C₄₇	—	2	2	no	—
237	D₄×C₄₇	—	2	2	no	—
238	D₄×C₄₇	—	2	2	no	—
239	D₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
240	C₂×C₄×C₄₇	—	2	2	no	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	2	4	no	—
244	C₂×C₄×C₄₇	—	2	4	no	—
245	C₂×C₄×C₄₇	—	2	4	no	—
246	C₂×C₄×C₄₇	—	2	4	no	—
247	C₂×C₄×C₄₇	—	4	2	no	—
248	C₂×C₄×C₄₇	—	8	2	no	—
249	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
259	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
260	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
261	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
262	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
263	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
267	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
269	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
270	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
271	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
276	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
277	C₂×Dic₄₇	—	2	4	no	—
278	C₂×Dic₄₇	—	2	2	no	—
279	C₂×Dic₄₇	—	2	2	no	—
280	C₂×Dic₄₇	—	4	4	no	—
281	C₂×Dic₄₇	—	4	4	no	—
282	C₂×Dic₄₇	—	4	2	no	—
283	C₈×C₄₇	—	4	2	no	—
284	C₄₇⋊C₈	—	2	4	no	—
285	C₄₇⋊C₈	—	2	4	no	—
286	C₄₇⋊C₈	—	2	4	no	—
287	C₂×#1861	—	47	1	no	maximal, Sylow
288	C₂²×C₄₇	—	2	2	no	—
289	C₂²×C₄₇	—	2	2	no	—
290	C₂²×C₄₇	—	2	2	no	—
291	C₂²×C₄₇	—	2	4	no	—
292	C₂²×C₄₇	—	4	1	no	—
293	C₂²×C₄₇	—	4	1	no	—
294	C₂²×C₄₇	—	4	1	no	—
295	C₂²×C₄₇	—	4	1	no	—
296	C₂²×C₄₇	—	4	4	no	—
297	C₂²×C₄₇	—	8	2	no	—
298	C₂²×C₄₇	—	8	2	no	—
299	C₂²×C₄₇	#385	1	1	yes	characteristic
300	C₂²×C₄₇	#385	1	1	yes	characteristic
301	C₂²×C₄₇	#385	1	1	yes	characteristic
302	C₂²×C₄₇	#385	1	1	yes	characteristic
303	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
304	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
305	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
306	C₄×C₄₇	—	2	4	no	—
307	C₄×C₄₇	—	8	2	no	—
308	C₄×C₄₇	#385	1	1	yes	characteristic
309	C₄×C₄₇	#385	1	1	yes	characteristic
310	C₄×C₄₇	#385	1	1	yes	characteristic
311	C₄×C₄₇	#385	1	1	yes	characteristic
312	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
313	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
314	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
315	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
316	Dic₄₇	—	2	4	no	—
317	Dic₄₇	—	4	2	no	—
318	C₂×#568	—	47	1	no	—
319	C₂×#430	—	47	1	no	—
320	C₂×#423	—	47	1	no	—
321	C₂×#421	D₄₇	1	1	yes	characteristic
322	C₂²×#104	—	47	1	no	—
323	#1861	—	47	8	no	—
324	C₂×#344	—	47	1	no	—
325	C₂×#339	—	47	1	no	—
326	C₂×C₄₇	—	2	1	no	—
327	C₂×C₄₇	—	2	1	no	—
328	C₂×C₄₇	—	2	1	no	—
329	C₂×C₄₇	—	2	1	no	—
330	C₂×C₄₇	—	2	1	no	—
331	C₂×C₄₇	—	2	1	no	—
332	C₂×C₄₇	—	4	4	no	—
333	C₂×C₄₇	#1861	1	2	yes	complemented
334	C₂×C₄₇	C₂×#385	1	1	yes	characteristic
335	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
336	#568	—	47	4	no	—
337	#568	—	94	2	no	—
338	#568	—	94	2	no	—
339	#568	—	94	2	no	—
340	C₂×#131	—	94	2	no	—
341	C₂×#131	—	94	2	no	—
342	C₂²×M₁₆	—	47	1	no	—
343	C₂²×M₁₆	—	47	1	no	—
344	C₂²×M₁₆	—	47	1	no	—
345	C₂²×M₁₆	—	94	2	no	—
346	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
347	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
348	C₂²×C₄²	—	47	1	no	—
349	#430	—	47	4	no	—
350	#430	—	94	2	no	—
351	C₂×#108	—	94	2	no	—
352	#423	—	47	4	no	—
353	#423	—	94	2	no	—
354	C₂×C₄⋊C₈	—	94	2	no	—
355	#421	—	2	2	no	—
356	#421	C₂×D₄₇	1	4	yes	—
357	C₂×#104	—	2	2	no	—
358	C₂×#104	—	47	2	no	—
359	C₂×#104	—	47	4	no	—
360	C₂×#104	—	47	2	no	—
361	C₂×#104	—	47	4	no	—
362	#344	—	47	4	no	—
363	#339	—	47	4	no	—
364	C₄₇	C₂×#1861	1	1	yes	characteristic, complemented, Sylow
365	C₂×#41	—	2	1	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	Dic₉₄	1	2	yes	—
372	C₂×#41	C₄×D₄₇	1	2	yes	—
373	C₂×#41	C₄×D₄₇	1	2	yes	—
374	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
375	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
376	C₂×#41	C₂²×D₄₇	1	2	yes	—
377	C₂²×Q₈	Dic₉₄	1	1	yes	characteristic
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
380	C₂³×C₄	—	2	1	no	—
381	C₂³×C₄	—	94	1	no	—
382	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
383	#131	—	94	8	no	—
384	#131	—	94	8	no	—
385	#131	—	94	8	no	—
386	#131	—	94	8	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂×M₁₆	—	2	1	no	—
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	47	2	no	—
393	C₂×M₁₆	—	47	2	no	—
394	C₂×M₁₆	—	47	2	no	—
395	C₂×M₁₆	—	47	2	no	—
396	C₂×M₁₆	—	47	2	no	—
397	C₂×M₁₆	—	47	2	no	—
398	C₂×M₁₆	—	47	2	no	—
399	C₂×M₁₆	—	47	2	no	—
400	C₂×M₁₆	—	94	8	no	—
401	C₂×M₁₆	—	94	4	no	—
402	C₂×M₁₆	—	94	8	no	—
403	C₂×M₁₆	—	94	1	no	—
404	C₂×M₁₆	—	94	1	no	—
405	C₂×M₁₆	—	94	1	no	—
406	C₂×M₁₆	—	94	1	no	—
407	C₂×M₁₆	—	94	1	no	—
408	C₂×M₁₆	—	94	1	no	—
409	C₂×M₁₆	—	94	1	no	—
410	C₂×M₁₆	—	94	1	no	—
411	C₂×M₁₆	—	94	1	no	—
412	C₂×M₁₆	—	94	1	no	—
413	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
414	C₂²×C₈	—	2	1	no	—
415	C₂²×C₈	—	47	2	no	—
416	C₂²×C₈	—	94	4	no	—
417	C₂²×C₈	—	94	1	no	—
418	C₂²×C₈	—	94	1	no	—
419	#117	—	2	1	no	—
420	#117	—	2	1	no	—
421	#117	—	2	1	no	—
422	#117	C₂²×D₄₇	1	2	yes	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	47	1	no	—
427	C₂×C₄²	—	47	2	no	—
428	C₂×C₄²	—	47	1	no	—
429	C₂×C₄²	—	47	2	no	—
430	C₂×C₄²	—	94	1	no	—
431	C₂×C₄²	—	94	1	no	—
432	C₂×C₄²	—	94	1	no	—
433	#108	—	94	8	no	—
434	C₄⋊C₈	—	94	8	no	—
435	#104	—	2	8	no	—
436	#104	—	47	8	no	—
437	#104	—	47	8	no	—
438	C₂⁴	—	2	1	no	—
439	C₂⁴	#10625352	1	1	yes	characteristic
440	#41	—	2	2	no	—
441	#41	—	2	2	no	—
442	#41	—	2	2	no	—
443	#41	—	2	2	no	—
444	#41	—	2	2	no	—
445	#41	—	2	2	no	—
446	#41	—	2	2	no	—
447	#41	—	2	2	no	—
448	#41	—	2	2	no	—
449	#41	—	2	2	no	—
450	#41	—	2	2	no	—
451	#41	—	2	2	no	—
452	#41	Dic₄₇⋊C₄	1	4	yes	—
453	#41	Dic₄₇⋊C₄	1	4	yes	—
454	#41	C₂×C₄×D₄₇	1	4	yes	—
455	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	Dic₄₇⋊C₄	1	2	yes	—
460	C₂×Q₈	Dic₄₇⋊C₄	1	2	yes	—
461	C₂×Q₈	C₂×Dic₉₄	1	2	yes	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
472	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
473	C₂×D₄	C₂×Dic₉₄	1	2	yes	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	—	94	1	no	—
483	C₂²×C₄	—	94	2	no	—
484	C₂²×C₄	—	94	1	no	—
485	C₂²×C₄	—	94	2	no	—
486	C₂²×C₄	—	188	4	no	—
487	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
488	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
489	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
490	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
491	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
492	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
493	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
494	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
495	C₂²×C₄	#10625352	1	1	yes	characteristic
496	C₂²×C₄	#10625352	1	1	yes	characteristic
497	C₂²×C₄	#10625352	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
499	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
500	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
501	M₁₆	—	2	2	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	4	1	no	—
504	M₁₆	—	4	1	no	—
505	M₁₆	—	47	4	no	—
506	M₁₆	—	47	4	no	—
507	M₁₆	—	94	16	no	—
508	M₁₆	—	94	2	no	—
509	M₁₆	—	94	2	no	—
510	M₁₆	—	94	2	no	—
511	M₁₆	—	94	2	no	—
512	M₁₆	—	94	2	no	—
513	M₁₆	—	94	2	no	—
514	M₁₆	—	94	2	no	—
515	M₁₆	—	94	2	no	—
516	M₁₆	—	94	2	no	—
517	M₁₆	—	94	2	no	—
518	C₂×C₈	—	2	2	no	—
519	C₂×C₈	—	4	1	no	—
520	C₂×C₈	—	4	1	no	—
521	C₂×C₈	—	47	4	no	—
522	C₂×C₈	—	94	16	no	—
523	C₂×C₈	—	94	2	no	—
524	C₂×C₈	—	94	2	no	—
525	C₂×C₈	—	94	2	no	—
526	C₂×C₈	—	94	2	no	—
527	C₂×C₈	—	94	2	no	—
528	C₂×C₈	—	94	2	no	—
529	C₂×C₈	—	94	2	no	—
530	C₂×C₈	—	94	2	no	—
531	C₄⋊C₄	—	2	2	no	—
532	C₄⋊C₄	—	4	1	no	—
533	C₂²⋊C₄	—	2	2	no	—
534	C₂²⋊C₄	—	4	1	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	4	1	no	—
537	C₄²	—	47	2	no	—
538	C₄²	—	47	2	no	—
539	C₄²	—	94	1	no	—
540	C₄²	—	94	2	no	—
541	C₄²	—	94	1	no	—
542	C₄²	—	94	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	8	2	no	—
548	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
549	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
550	C₂³	#13094001	1	1	yes	characteristic
551	C₂³	#13094001	1	1	yes	characteristic
552	C₂³	#13094005	1	1	yes	characteristic
553	C₂³	#13094005	1	1	yes	characteristic
554	C₂³	C₂×#10625352	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	—	2	2	no	—
558	Q₈	C₂×Dic₄₇⋊C₄	1	4	yes	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	—	2	2	no	—
566	D₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	8	2	no	—
576	C₂×C₄	—	94	4	no	—
577	C₂×C₄	—	94	2	no	—
578	C₂×C₄	—	94	2	no	—
579	C₂×C₄	—	188	4	no	—
580	C₂×C₄	—	188	4	no	—
581	C₂×C₄	—	188	2	no	—
582	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
583	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
584	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
585	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
586	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
587	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
588	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
589	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
590	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
591	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
592	C₂×C₄	#13093992	1	1	yes	characteristic
593	C₂×C₄	#13093992	1	1	yes	characteristic
594	C₂×C₄	#13093992	1	1	yes	characteristic
595	C₂×C₄	#13093992	1	1	yes	characteristic
596	C₂×C₄	#13094001	1	1	yes	characteristic
597	C₂×C₄	#13094001	1	1	yes	characteristic
598	C₂×C₄	#13094001	1	1	yes	characteristic
599	C₂×C₄	#13094001	1	1	yes	characteristic
600	C₂×C₄	#13094001	1	1	yes	characteristic
601	C₂×C₄	#13094001	1	1	yes	characteristic
602	C₂×C₄	#13094005	1	1	yes	characteristic
603	C₂×C₄	#13094005	1	1	yes	characteristic
604	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
605	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
606	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
607	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
608	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
609	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
610	C₈	—	4	2	no	—
611	C₈	—	94	4	no	—
612	C₈	—	94	4	no	—
613	C₈	—	94	4	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	8	2	no	—
624	C₂²	—	8	2	no	—
625	C₂²	#15688995	1	1	yes	characteristic
626	C₂²	#15688995	1	1	yes	characteristic
627	C₂²	#15688995	1	1	yes	characteristic
628	C₂²	#15688995	1	1	yes	characteristic
629	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
630	C₂²	C₂×#13094001	1	1	yes	characteristic
631	C₂²	C₂×#13094005	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	8	2	no	—
634	C₄	—	94	4	no	—
635	C₄	—	188	2	no	—
636	C₄	#15688995	1	1	yes	characteristic
637	C₄	#15688995	1	1	yes	characteristic
638	C₄	#15688995	1	1	yes	characteristic
639	C₄	#15688995	1	1	yes	characteristic
640	C₄	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
641	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
642	C₄	C₂×#13093992	1	1	yes	characteristic
643	C₄	C₂×#13094001	1	1	yes	characteristic
644	C₂	—	2	1	no	—
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	4	4	no	—
651	C₂	#20243626	1	2	yes	direct product factor
652	C₂	C₂×#15688995	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093992
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#421	C₂
socle	C₂²×C₄₇	#385
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#421	D₄₇
hypocenter	C₄₇	C₂×#1861
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#421

Complements

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

N	H ≅ G/N	type
2. C₂×#15689171	C₂	semidirect
3. C₂×#15689146	C₂	semidirect
5. #20243626	C₂	direct (N × H)
6. C₂×#15688893	C₂	semidirect
7. C₂×#15688882	C₂	semidirect
21. #15689171	C₂²	semidirect
24. #15689146	C₂²	semidirect
26. C₂×#13093951	C₄	semidirect
27. C₂×#13093951	C₄	semidirect
28. C₂×#13093951	C₄	semidirect
30. #15688893	C₂²	semidirect
31. #15688882	C₂²	semidirect
77. #13093951	C₂×C₄	semidirect
78. #13093951	C₂×C₄	semidirect
333. C₂×C₄₇	#1861	semidirect
364. C₄₇	C₂×#1861	semidirect
651. C₂	#20243626	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689890	2
C₂×#15689171	2
C₂×#15689146	2
C₂²×#13093951	2
#20243626	2
C₂×#15688893	2
C₂×#15688882	2
C₂×C₄₇×#421	2
C₂×#1861	47

Subgroups — C2×#20243626 #26217173

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243626 #26217173