Subgroups — C₂×#20243627 #26217174

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×#15689889	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689171	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689139	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13093952	C₂	1	1	yes	maximal, characteristic
5	#20243627	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688894	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688883	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#423	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	C₂²	1	4	yes	—
14	C₂×#13094032	—	2	2	no	—
15	C₂×#13094030	—	2	2	no	—
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625329	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×D₄₇	—	2	2	no	—
19	C₂×#13093983	C₂²	1	1	yes	characteristic
20	#15689171	—	2	2	no	—
21	#15689171	C₂²	1	4	yes	complemented
22	C₂×#13093959	—	2	2	no	—
23	#15689139	—	2	2	no	—
24	#15689139	C₂²	1	4	yes	—
25	C₂×#13093952	C₄	1	2	yes	complemented
26	C₂×#13093952	C₄	1	4	yes	complemented
27	C₂×#13093952	C₄	1	2	yes	complemented
28	C₂×#13093952	C₂²	1	4	yes	—
29	C₂×#13093950	—	2	2	no	—
30	#15688894	C₂²	1	4	yes	complemented
31	#15688883	C₂²	1	4	yes	complemented
32	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#423	—	2	2	no	—
36	C₄₇×#423	C₂²	1	4	yes	complemented
37	C₂×C₄⋊C₈×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	C₂×C₄	1	2	yes	—
45	C₂×#10625350	C₂×C₄	1	2	yes	—
46	C₂×#10625350	D₄	1	2	yes	—
47	C₂×#10625350	D₄	1	2	yes	—
48	C₂×#10625350	Q₈	1	2	yes	—
49	C₂×#10625350	C₂³	1	2	yes	—
50	C₂²×Dic₉₄	Q₈	1	1	yes	characteristic
51	C₂²×D₁₈₈	Q₈	1	1	yes	characteristic
52	C₂²×C₂²⋊D₄₇	—	2	1	no	—
53	C₂²×C₄×D₄₇	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
65	C₂×#10625329	C₂×C₄	1	2	yes	—
66	C₂×#10625329	D₄	1	2	yes	—
67	C₂×#10625329	D₄	1	2	yes	—
68	C₂×#10625329	C₂³	1	2	yes	—
69	C₂×#10625329	C₂³	1	2	yes	—
70	C₂×#10625324	—	2	4	no	—
71	M₁₆×D₄₇	—	2	8	no	—
72	M₁₆×D₄₇	—	2	8	no	—
73	C₂²×C₄₇⋊C₈	—	2	1	no	—
74	C₂²×C₄₇⋊C₈	—	2	1	no	—
75	C₂×C₈×D₄₇	—	2	4	no	—
76	#13093983	—	2	1	no	—
77	#13093983	—	2	1	no	—
78	#13093983	—	2	1	no	—
79	#13093983	C₂³	1	2	yes	—
80	C₂×C₄⋊Dic₄₇	—	2	1	no	—
81	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
82	C₂×C₄×Dic₄₇	—	2	1	no	—
83	#13093959	—	2	8	no	—
84	#13093952	C₂×C₄	1	8	yes	complemented
85	#13093952	C₂×C₄	1	8	yes	complemented
86	#13093950	—	2	8	no	—
87	C₂³×C₄×C₄₇	—	2	1	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	—	2	1	no	—
93	C₂×M₁₆×C₄₇	—	2	1	no	—
94	C₂×M₁₆×C₄₇	—	2	1	no	—
95	C₂×M₁₆×C₄₇	—	2	1	no	—
96	C₂×M₁₆×C₄₇	—	2	1	no	—
97	C₂×M₁₆×C₄₇	—	2	1	no	—
98	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
99	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
100	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
101	C₂²×C₈×C₄₇	—	2	1	no	—
102	C₂²×C₈×C₄₇	D₄	1	2	yes	—
103	C₂×C₄²×C₄₇	—	2	1	no	—
104	C₂×C₄²×C₄₇	—	2	1	no	—
105	C₂×C₄²×C₄₇	—	2	1	no	—
106	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
108	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
110	C₄⋊C₈×C₄₇	—	2	8	no	—
111	C₂⁴×C₄₇	#41	1	1	yes	characteristic
112	C₂³×D₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	4	4	no	—
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	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₂×C₂²⋊D₄₇	—	2	2	no	—
133	C₂×C₂²⋊D₄₇	—	2	2	no	—
134	C₂×C₂²⋊D₄₇	—	2	2	no	—
135	C₂×C₂²⋊D₄₇	—	2	2	no	—
136	C₂×C₂²⋊D₄₇	—	2	2	no	—
137	C₂×C₂²⋊D₄₇	—	2	2	no	—
138	C₂²×Dic₄₇	—	2	1	no	—
139	C₂²×Dic₄₇	—	4	1	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	C₄⋊C₄	1	4	yes	—
153	#10625350	C₄⋊C₄	1	4	yes	—
154	#10625350	C₂²×C₄	1	4	yes	—
155	#10625350	C₂×D₄	1	4	yes	—
156	C₂×D₁₈₈	—	2	1	no	—
157	C₂×D₁₈₈	—	2	1	no	—
158	C₂×D₁₈₈	—	2	1	no	—
159	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
160	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
161	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
162	C₂×C₄×D₄₇	—	2	2	no	—
163	C₂×C₄×D₄₇	—	2	2	no	—
164	C₂×C₄×D₄₇	—	2	2	no	—
165	C₂×C₄×D₄₇	—	2	2	no	—
166	C₂×C₄×D₄₇	—	2	2	no	—
167	C₂×C₄×D₄₇	—	2	2	no	—
168	C₂×Dic₉₄	—	2	1	no	—
169	C₂×Dic₉₄	—	2	1	no	—
170	C₂×Dic₉₄	—	2	1	no	—
171	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
172	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
173	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
174	M₁₆×C₄₇	—	2	2	no	—
175	M₁₆×C₄₇	—	2	2	no	—
176	M₁₆×C₄₇	—	2	2	no	—
177	M₁₆×C₄₇	—	2	2	no	—
178	M₁₆×C₄₇	—	2	2	no	—
179	M₁₆×C₄₇	—	2	2	no	—
180	M₁₆×C₄₇	—	4	1	no	—
181	M₁₆×C₄₇	—	4	1	no	—
182	C₂×C₈×C₄₇	—	2	2	no	—
183	C₂×C₈×C₄₇	—	2	2	no	—
184	C₂×C₈×C₄₇	—	2	2	no	—
185	C₂×C₈×C₄₇	—	4	1	no	—
186	C₂×C₈×C₄₇	—	4	1	no	—
187	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
188	C₄²×C₄₇	—	2	1	no	—
189	C₄²×C₄₇	—	2	2	no	—
190	C₄²×C₄₇	—	2	1	no	—
191	C₄²×C₄₇	—	2	2	no	—
192	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
193	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
194	C₂²⋊Dic₄₇	—	2	2	no	—
195	C₂²⋊Dic₄₇	—	4	1	no	—
196	C₄⋊Dic₄₇	—	2	2	no	—
197	C₄⋊Dic₄₇	—	4	1	no	—
198	C₄×Dic₄₇	—	2	2	no	—
199	C₄×Dic₄₇	—	4	1	no	—
200	#10625329	—	2	2	no	—
201	#10625329	—	2	2	no	—
202	#10625329	—	2	2	no	—
203	#10625329	—	2	2	no	—
204	#10625329	—	2	2	no	—
205	#10625329	—	2	2	no	—
206	#10625329	C₂²×C₄	1	4	yes	—
207	#10625329	C₂×D₄	1	4	yes	—
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	#10625324	—	2	16	no	—
215	C₈×D₄₇	—	2	16	no	—
216	C₂³×C₄₇	—	4	2	no	—
217	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
218	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
219	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
220	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
221	C₂³×C₄₇	#123	1	1	yes	characteristic
222	C₂³×C₄₇	#123	1	1	yes	characteristic
223	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
224	C₂²×D₄₇	—	2	2	no	—
225	C₂²×D₄₇	—	2	2	no	—
226	C₂²×D₄₇	—	2	2	no	—
227	C₂²×D₄₇	—	8	2	no	—
228	C₂×C₄×C₄₇	—	2	4	no	—
229	C₂×C₄×C₄₇	—	2	2	no	—
230	C₂×C₄×C₄₇	—	2	2	no	—
231	C₂×C₄×C₄₇	—	4	4	no	—
232	C₂×C₄×C₄₇	—	4	4	no	—
233	C₂×C₄×C₄₇	—	4	2	no	—
234	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂×C₄⋊C₄	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	#120	1	1	yes	characteristic
245	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
246	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
247	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
255	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
257	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
262	C₂²⋊D₄₇	—	2	4	no	—
263	C₂²⋊D₄₇	—	2	4	no	—
264	C₂²⋊D₄₇	—	2	4	no	—
265	C₂²⋊D₄₇	—	2	4	no	—
266	C₂×Dic₄₇	—	2	2	no	—
267	C₂×Dic₄₇	—	2	2	no	—
268	C₂×Dic₄₇	—	2	2	no	—
269	C₂×Dic₄₇	—	4	2	no	—
270	C₂×Dic₄₇	—	8	2	no	—
271	D₁₈₈	—	2	2	no	—
272	D₁₈₈	—	2	2	no	—
273	D₁₈₈	—	2	2	no	—
274	D₁₈₈	C₂×C₄⋊C₄	1	4	yes	—
275	C₄×D₄₇	—	2	4	no	—
276	C₄×D₄₇	—	2	4	no	—
277	C₄×D₄₇	—	2	4	no	—
278	C₄×D₄₇	—	2	4	no	—
279	Dic₉₄	—	2	2	no	—
280	Dic₉₄	—	2	2	no	—
281	Dic₉₄	—	2	2	no	—
282	Dic₉₄	C₂×C₄⋊C₄	1	4	yes	—
283	C₈×C₄₇	—	2	4	no	—
284	C₈×C₄₇	—	4	2	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	—	4	1	no	—
292	C₂²×C₄₇	—	4	1	no	—
293	C₂²×C₄₇	—	4	1	no	—
294	C₂²×C₄₇	—	4	1	no	—
295	C₂²×C₄₇	#385	1	1	yes	characteristic
296	C₂²×C₄₇	#385	1	1	yes	characteristic
297	C₂²×C₄₇	#385	1	1	yes	characteristic
298	C₂²×C₄₇	#385	1	1	yes	characteristic
299	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
301	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
302	C₂×D₄₇	—	2	4	no	—
303	C₂×D₄₇	—	4	4	no	—
304	C₂×D₄₇	—	8	2	no	—
305	C₂×D₄₇	—	8	2	no	—
306	C₄×C₄₇	—	2	4	no	—
307	C₄×C₄₇	—	4	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	—	8	2	no	—
318	C₂×#568	—	47	1	no	—
319	C₂×#430	—	47	1	no	—
320	C₂×#423	D₄₇	1	1	yes	characteristic, complemented
321	C₂×#421	—	47	1	no	—
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	#1861	1	2	yes	complemented
333	C₂×C₄₇	C₂×#385	1	1	yes	characteristic
334	D₄₇	—	4	4	no	—
335	C₂²×#41	—	47	1	no	—
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	—	94	2	no	—
345	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
346	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
347	C₂×#117	—	47	1	no	—
348	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
349	#430	—	47	4	no	—
350	#430	—	94	2	no	—
351	C₂×#108	—	94	2	no	—
352	#423	—	2	2	no	—
353	#423	C₂×D₄₇	1	4	yes	complemented
354	C₂×C₄⋊C₈	—	2	2	no	—
355	#421	—	47	4	no	—
356	#421	—	94	2	no	—
357	C₂×#104	—	47	2	no	—
358	C₂×#104	—	47	4	no	—
359	C₂×#104	—	47	2	no	—
360	C₂×#104	—	47	4	no	—
361	C₂×#104	—	94	2	no	—
362	#344	—	47	4	no	—
363	#339	—	47	4	no	—
364	C₄₇	C₂×#1861	1	1	yes	characteristic, complemented, Sylow
365	C₂×#41	—	47	2	no	—
366	C₂×#41	—	47	2	no	—
367	C₂×#41	—	47	2	no	—
368	C₂×#41	—	47	2	no	—
369	C₂×#41	—	47	2	no	—
370	C₂×#41	—	47	2	no	—
371	C₂×#41	—	94	1	no	—
372	C₂×#41	—	94	1	no	—
373	C₂×#41	—	94	1	no	—
374	C₂×#41	—	94	1	no	—
375	C₂×#41	—	94	1	no	—
376	C₂×#41	—	94	1	no	—
377	C₂²×Q₈	—	47	1	no	—
378	C₂²×D₄	—	47	1	no	—
379	C₂²×D₄	—	94	1	no	—
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	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	1	no	—
395	C₂×M₁₆	—	2	1	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	—	47	2	no	—
401	C₂×M₁₆	—	47	2	no	—
402	C₂×M₁₆	—	94	4	no	—
403	C₂×M₁₆	—	94	8	no	—
404	C₂×M₁₆	—	94	8	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	C₂²⋊D₄₇	1	2	yes	—
412	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
413	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
414	C₂²×C₈	—	2	1	no	—
415	C₂²×C₈	—	94	4	no	—
416	C₂²×C₈	—	94	1	no	—
417	C₂²×C₈	—	94	1	no	—
418	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
419	#117	—	47	2	no	—
420	#117	—	94	1	no	—
421	#117	—	94	1	no	—
422	#117	—	94	1	no	—
423	C₂×C₄⋊C₄	—	94	1	no	—
424	C₂×C₂²⋊C₄	—	94	1	no	—
425	C₂×C₄²	—	2	1	no	—
426	C₂×C₄²	—	2	1	no	—
427	C₂×C₄²	—	2	1	no	—
428	C₂×C₄²	—	94	1	no	—
429	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
430	C₂×C₄²	C₄×D₄₇	1	2	yes	—
431	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
432	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
433	#108	—	94	8	no	—
434	C₄⋊C₈	—	2	8	no	—
435	#104	—	47	8	no	—
436	#104	—	47	8	no	—
437	#104	—	94	8	no	—
438	C₂⁴	—	94	1	no	—
439	C₂⁴	#10625350	1	1	yes	characteristic
440	#41	—	47	4	no	—
441	#41	—	47	4	no	—
442	#41	—	47	4	no	—
443	#41	—	47	4	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	#41	—	94	2	no	—
450	#41	—	94	2	no	—
451	#41	—	94	2	no	—
452	#41	—	94	2	no	—
453	#41	—	94	2	no	—
454	#41	—	94	2	no	—
455	#41	—	94	2	no	—
456	C₂×Q₈	—	47	2	no	—
457	C₂×Q₈	—	47	2	no	—
458	C₂×Q₈	—	47	2	no	—
459	C₂×Q₈	—	94	1	no	—
460	C₂×Q₈	—	94	1	no	—
461	C₂×Q₈	—	94	1	no	—
462	C₂×D₄	—	47	2	no	—
463	C₂×D₄	—	47	2	no	—
464	C₂×D₄	—	47	2	no	—
465	C₂×D₄	—	94	2	no	—
466	C₂×D₄	—	94	2	no	—
467	C₂×D₄	—	94	2	no	—
468	C₂×D₄	—	94	2	no	—
469	C₂×D₄	—	94	2	no	—
470	C₂×D₄	—	94	2	no	—
471	C₂×D₄	—	94	1	no	—
472	C₂×D₄	—	94	1	no	—
473	C₂×D₄	—	94	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	—	94	1	no	—
480	C₂²×C₄	—	94	2	no	—
481	C₂²×C₄	—	94	2	no	—
482	C₂²×C₄	—	94	2	no	—
483	C₂²×C₄	—	94	2	no	—
484	C₂²×C₄	—	94	2	no	—
485	C₂²×C₄	—	94	2	no	—
486	C₂²×C₄	—	188	1	no	—
487	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
489	C₂²×C₄	#10625350	1	1	yes	characteristic
490	C₂²×C₄	D₄×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	Q₈×D₄₇	1	1	yes	characteristic
495	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
496	C₂²×C₄	#10625354	1	1	yes	characteristic
497	C₂²×C₄	#10625354	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	—	2	2	no	—
504	M₁₆	—	2	2	no	—
505	M₁₆	—	2	2	no	—
506	M₁₆	—	2	2	no	—
507	M₁₆	—	4	1	no	—
508	M₁₆	—	4	1	no	—
509	M₁₆	—	47	4	no	—
510	M₁₆	—	47	4	no	—
511	M₁₆	—	94	16	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	—	2	2	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	4	1	no	—
522	C₂×C₈	—	4	1	no	—
523	C₂×C₈	—	94	16	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	C₂×C₂²⋊D₄₇	1	4	yes	—
531	C₄⋊C₄	—	94	2	no	—
532	C₄⋊C₄	—	188	1	no	—
533	C₂²⋊C₄	—	94	2	no	—
534	C₂²⋊C₄	—	188	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	94	2	no	—
540	C₄²	—	188	1	no	—
541	C₄²	C₂×C₄×D₄₇	1	2	yes	—
542	C₄²	C₂×C₄×D₄₇	1	2	yes	—
543	C₂³	—	4	2	no	—
544	C₂³	—	94	2	no	—
545	C₂³	—	94	2	no	—
546	C₂³	—	94	2	no	—
547	C₂³	—	376	2	no	—
548	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
549	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
550	C₂³	#13094002	1	1	yes	characteristic
551	C₂³	#13094002	1	1	yes	characteristic
552	C₂³	#13094009	1	1	yes	characteristic
553	C₂³	#13094009	1	1	yes	characteristic
554	C₂³	C₂×#10625350	1	1	yes	characteristic
555	Q₈	—	47	4	no	—
556	Q₈	—	94	2	no	—
557	Q₈	—	94	2	no	—
558	Q₈	—	94	2	no	—
559	D₄	—	47	4	no	—
560	D₄	—	94	4	no	—
561	D₄	—	94	4	no	—
562	D₄	—	94	4	no	—
563	D₄	—	94	4	no	—
564	D₄	—	94	2	no	—
565	D₄	—	94	2	no	—
566	D₄	—	94	2	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	4	4	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	94	2	no	—
574	C₂×C₄	—	94	2	no	—
575	C₂×C₄	—	94	2	no	—
576	C₂×C₄	—	94	4	no	—
577	C₂×C₄	—	94	4	no	—
578	C₂×C₄	—	94	4	no	—
579	C₂×C₄	—	94	4	no	—
580	C₂×C₄	—	376	2	no	—
581	C₂×C₄	—	188	2	no	—
582	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
583	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
584	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
585	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
586	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
587	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
588	C₂×C₄	#13093986	1	1	yes	characteristic
589	C₂×C₄	#13093986	1	1	yes	characteristic
590	C₂×C₄	#13093986	1	1	yes	characteristic
591	C₂×C₄	#13093986	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	#13094000	1	1	yes	characteristic
597	C₂×C₄	#13094000	1	1	yes	characteristic
598	C₂×C₄	#13094000	1	1	yes	characteristic
599	C₂×C₄	#13094000	1	1	yes	characteristic
600	C₂×C₄	#13094002	1	1	yes	characteristic
601	C₂×C₄	#13094002	1	1	yes	characteristic
602	C₂×C₄	#13094009	1	1	yes	characteristic
603	C₂×C₄	#13094009	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	C₂×Q₈×D₄₇	1	1	yes	characteristic
609	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
610	C₈	—	2	4	no	—
611	C₈	—	4	2	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	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	94	4	no	—
622	C₂²	—	376	2	no	—
623	C₂²	—	376	2	no	—
624	C₂²	—	188	4	no	—
625	C₂²	#15688994	1	1	yes	characteristic
626	C₂²	#15688994	1	1	yes	characteristic
627	C₂²	#15688994	1	1	yes	characteristic
628	C₂²	#15688994	1	1	yes	characteristic
629	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
630	C₂²	C₂×#13094002	1	1	yes	characteristic
631	C₂²	C₂×#13094009	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	4	2	no	—
634	C₄	—	94	4	no	—
635	C₄	—	376	2	no	—
636	C₄	#15688994	1	1	yes	characteristic
637	C₄	#15688994	1	1	yes	characteristic
638	C₄	#15688994	1	1	yes	characteristic
639	C₄	#15688994	1	1	yes	characteristic
640	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
641	C₄	C₂×#13093986	1	1	yes	characteristic
642	C₄	C₂×#13093992	1	1	yes	characteristic
643	C₄	C₂×#13094000	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	—	188	4	no	—
651	C₂	#20243627	1	2	yes	direct product factor
652	C₂	C₂×#15688994	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×#423	C₂
socle	C₂²×C₄₇	#385
prime radical	C₂²×#10625350	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#423	D₄₇
hypocenter	C₄₇	C₂×#1861
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
2. C₂×#15689171	C₂	semidirect
5. #20243627	C₂	direct (N × H)
6. C₂×#15688894	C₂	semidirect
7. C₂×#15688883	C₂	semidirect
8. C₂×C₄₇×#423	C₂	semidirect
21. #15689171	C₂²	semidirect
25. C₂×#13093952	C₄	semidirect
26. C₂×#13093952	C₄	semidirect
27. C₂×#13093952	C₄	semidirect
30. #15688894	C₂²	semidirect
31. #15688883	C₂²	semidirect
36. C₄₇×#423	C₂²	semidirect
84. #13093952	C₂×C₄	semidirect
85. #13093952	C₂×C₄	semidirect
320. C₂×#423	D₄₇	semidirect
332. C₂×C₄₇	#1861	semidirect
353. #423	C₂×D₄₇	semidirect
364. C₄₇	C₂×#1861	semidirect
651. C₂	#20243627	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×#15689889	2
C₂×#15689171	2
C₂×#15689139	2
C₂²×#13093952	2
#20243627	2
C₂×#15688894	2
C₂×#15688883	2
C₂×C₄₇×#423	2
C₂×#1861	47

Subgroups — C2×#20243627 #26217174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243627 #26217174