Subgroups — C₂×#20243441 #26215939

Order 12032.

1330 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13094032	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093959	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689159	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689141	C₂	1	1	yes	maximal, characteristic
5	C₂×#15689139	C₂	1	1	yes	maximal, characteristic
6	#20243441	C₂	1	8	yes	maximal, direct product factor
7	C₂×#15688895	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#344	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625350	C₂²	1	1	yes	characteristic
10	C₂×#13094032	—	2	1	no	—
11	C₂×#13094032	—	2	1	no	—
12	C₂×#13094032	—	2	2	no	—
13	C₂×#13094032	—	2	2	no	—
14	C₂×#13094032	C₄	1	2	yes	complemented
15	C₂×#13094032	C₄	1	2	yes	complemented
16	C₂×#13094032	C₄	1	4	yes	complemented
17	C₂×#13094032	C₂²	1	4	yes	—
18	C₂²×#10625329	C₂²	1	1	yes	characteristic
19	C₂²×#10625324	—	2	1	no	—
20	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂²×C₈×D₄₇	—	2	1	no	—
22	C₂×#13093983	C₂²	1	1	yes	characteristic
23	C₂×#13093959	—	2	1	no	—
24	C₂×#13093959	—	2	1	no	—
25	C₂×#13093959	—	2	2	no	—
26	C₂×#13093959	C₂²	1	4	yes	complemented
27	#15689159	—	2	2	no	—
28	#15689159	C₂²	1	4	yes	complemented
29	C₂×#13093957	—	2	1	no	—
30	C₂×#13093955	—	2	1	no	—
31	#15689141	—	2	2	no	—
32	#15689141	C₂²	1	4	yes	—
33	#15689139	—	2	2	no	—
34	#15689139	C₂²	1	4	yes	—
35	C₂×#13093952	—	2	2	no	—
36	C₂×#13093950	—	2	2	no	—
37	#15688895	C₂²	1	4	yes	complemented
38	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#344	C₂²	1	4	yes	complemented
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	—	2	1	no	—
47	C₂×#10625350	—	2	1	no	—
48	C₂×#10625350	C₂×C₄	1	2	yes	—
49	C₂×#10625350	C₂×C₄	1	2	yes	—
50	C₂×#10625350	D₄	1	2	yes	—
51	C₂×#10625350	D₄	1	2	yes	—
52	C₂×#10625350	Q₈	1	2	yes	—
53	C₂×#10625350	C₂³	1	2	yes	—
54	C₂²×Dic₉₄	Q₈	1	1	yes	characteristic
55	C₂²×D₁₈₈	Q₈	1	1	yes	characteristic
56	C₂²×C₂²⋊D₄₇	—	2	1	no	—
57	C₂²×C₄×D₄₇	—	2	1	no	—
58	#13094032	—	2	4	no	—
59	#13094032	—	2	4	no	—
60	#13094032	—	2	4	no	—
61	#13094032	—	2	4	no	—
62	#13094032	—	2	4	no	—
63	#13094032	—	2	4	no	—
64	#13094032	C₂×C₄	1	8	yes	complemented
65	#13094032	C₂×C₄	1	8	yes	complemented
66	C₂×#10625329	—	2	1	no	—
67	C₂×#10625329	—	2	1	no	—
68	C₂×#10625329	—	2	1	no	—
69	C₂×#10625329	—	2	1	no	—
70	C₂×#10625329	—	2	1	no	—
71	C₂×#10625329	C₂³	1	2	yes	—
72	C₂×#10625324	—	2	2	no	—
73	C₂×#10625324	—	2	2	no	—
74	C₂×#10625324	—	2	4	no	—
75	C₂×#10625324	—	2	4	no	—
76	C₂²×C₄₇⋊C₈	—	2	1	no	—
77	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
80	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
81	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
82	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
83	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
84	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
85	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
86	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
87	C₂×C₈×D₄₇	—	2	2	no	—
88	C₂×C₈×D₄₇	—	2	2	no	—
89	C₂×C₈×D₄₇	—	2	4	no	—
90	C₂×C₈×D₄₇	—	2	4	no	—
91	#13093983	—	2	1	no	—
92	#13093983	—	2	1	no	—
93	#13093983	—	2	1	no	—
94	#13093983	C₂³	1	2	yes	—
95	C₂×C₄⋊Dic₄₇	—	2	1	no	—
96	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
97	C₂×C₄×Dic₄₇	—	2	1	no	—
98	#13093959	—	2	4	no	—
99	#13093959	—	2	4	no	—
100	#13093957	—	2	4	no	—
101	#13093955	—	2	4	no	—
102	#13093952	—	2	8	no	—
103	#13093950	—	2	8	no	—
104	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
105	C₂×M₁₆×C₄₇	—	2	1	no	—
106	C₂×M₁₆×C₄₇	—	2	1	no	—
107	C₂×M₁₆×C₄₇	—	2	1	no	—
108	C₂×M₁₆×C₄₇	—	2	1	no	—
109	C₂×M₁₆×C₄₇	—	2	1	no	—
110	C₂×M₁₆×C₄₇	—	2	1	no	—
111	C₂×M₁₆×C₄₇	—	2	1	no	—
112	C₂×M₁₆×C₄₇	—	2	1	no	—
113	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
114	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
115	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
116	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
117	C₂²×C₈×C₄₇	—	2	1	no	—
118	C₂²×C₈×C₄₇	—	2	1	no	—
119	#117×C₄₇	—	2	1	no	—
120	#117×C₄₇	—	2	1	no	—
121	#117×C₄₇	—	2	1	no	—
122	#117×C₄₇	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
125	C₂×C₄²×C₄₇	—	2	1	no	—
126	C₂⁴×C₄₇	#41	1	1	yes	characteristic
127	C₂³×D₄₇	—	2	1	no	—
128	C₂²×C₄×C₄₇	—	4	1	no	—
129	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
143	C₂×C₂²⋊D₄₇	—	2	2	no	—
144	C₂×C₂²⋊D₄₇	—	2	2	no	—
145	C₂×C₂²⋊D₄₇	—	2	2	no	—
146	C₂×C₂²⋊D₄₇	—	2	2	no	—
147	C₂×C₂²⋊D₄₇	—	2	2	no	—
148	C₂×C₂²⋊D₄₇	—	2	2	no	—
149	C₂²×Dic₄₇	—	2	1	no	—
150	C₂²×Dic₄₇	—	4	1	no	—
151	#10625350	—	2	2	no	—
152	#10625350	—	2	2	no	—
153	#10625350	—	2	2	no	—
154	#10625350	—	2	2	no	—
155	#10625350	—	2	2	no	—
156	#10625350	—	2	2	no	—
157	#10625350	—	2	2	no	—
158	#10625350	—	2	2	no	—
159	#10625350	—	2	2	no	—
160	#10625350	—	2	2	no	—
161	#10625350	—	2	2	no	—
162	#10625350	—	2	2	no	—
163	#10625350	C₄⋊C₄	1	4	yes	—
164	#10625350	C₄⋊C₄	1	4	yes	—
165	#10625350	C₂²×C₄	1	4	yes	—
166	#10625350	C₂×D₄	1	4	yes	—
167	C₂×D₁₈₈	—	2	1	no	—
168	C₂×D₁₈₈	—	2	1	no	—
169	C₂×D₁₈₈	—	2	1	no	—
170	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
171	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
172	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
173	C₂×C₄×D₄₇	—	2	2	no	—
174	C₂×C₄×D₄₇	—	2	2	no	—
175	C₂×C₄×D₄₇	—	2	2	no	—
176	C₂×C₄×D₄₇	—	2	2	no	—
177	C₂×C₄×D₄₇	—	2	2	no	—
178	C₂×C₄×D₄₇	—	2	2	no	—
179	C₂×Dic₉₄	—	2	1	no	—
180	C₂×Dic₉₄	—	2	1	no	—
181	C₂×Dic₉₄	—	2	1	no	—
182	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
183	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
184	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
185	M₁₆×C₄₇	—	2	2	no	—
186	M₁₆×C₄₇	—	2	2	no	—
187	M₁₆×C₄₇	—	2	2	no	—
188	M₁₆×C₄₇	—	2	2	no	—
189	M₁₆×C₄₇	—	2	2	no	—
190	M₁₆×C₄₇	—	4	1	no	—
191	M₁₆×C₄₇	—	4	1	no	—
192	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
193	C₂×C₈×C₄₇	—	2	2	no	—
194	C₂×C₈×C₄₇	—	2	2	no	—
195	C₂×C₈×C₄₇	—	2	2	no	—
196	C₂×C₈×C₄₇	—	2	2	no	—
197	C₂×C₈×C₄₇	—	4	1	no	—
198	C₂×C₈×C₄₇	—	4	1	no	—
199	C₄⋊C₄×C₄₇	—	2	2	no	—
200	C₄⋊C₄×C₄₇	—	4	1	no	—
201	C₂²⋊C₄×C₄₇	—	2	2	no	—
202	C₂²⋊C₄×C₄₇	—	4	1	no	—
203	C₄²×C₄₇	—	2	2	no	—
204	C₄²×C₄₇	—	4	1	no	—
205	C₂²⋊Dic₄₇	—	2	2	no	—
206	C₂²⋊Dic₄₇	—	4	1	no	—
207	C₄⋊Dic₄₇	—	2	2	no	—
208	C₄⋊Dic₄₇	—	4	1	no	—
209	C₄×Dic₄₇	—	2	2	no	—
210	C₄×Dic₄₇	—	4	1	no	—
211	#10625329	—	2	2	no	—
212	#10625329	—	2	2	no	—
213	#10625329	—	4	1	no	—
214	#10625329	—	4	1	no	—
215	C₂×C₄₇⋊C₈	—	2	2	no	—
216	C₂×C₄₇⋊C₈	—	4	1	no	—
217	C₂×C₄₇⋊C₈	—	4	1	no	—
218	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
221	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
224	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
225	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
226	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
227	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
228	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
229	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
230	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
231	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
232	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
233	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
234	#10625324	—	2	8	no	—
235	#10625324	—	2	8	no	—
236	C₈×D₄₇	—	2	8	no	—
237	C₈×D₄₇	—	2	8	no	—
238	C₂³×C₄₇	—	4	2	no	—
239	C₂³×C₄₇	#117	1	1	yes	characteristic
240	C₂³×C₄₇	#117	1	1	yes	characteristic
241	C₂³×C₄₇	#121	1	1	yes	characteristic
242	C₂³×C₄₇	#121	1	1	yes	characteristic
243	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
244	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
246	C₂²×D₄₇	—	2	2	no	—
247	C₂²×D₄₇	—	2	2	no	—
248	C₂²×D₄₇	—	2	2	no	—
249	C₂²×D₄₇	—	4	4	no	—
250	C₂×C₄×C₄₇	—	4	2	no	—
251	C₂×C₄×C₄₇	—	8	2	no	—
252	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
261	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
262	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
263	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
264	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
265	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
266	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
267	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
269	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
270	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
272	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
273	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
274	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
275	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
279	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
280	C₂²⋊D₄₇	—	2	4	no	—
281	C₂²⋊D₄₇	—	2	4	no	—
282	C₂²⋊D₄₇	—	2	4	no	—
283	C₂²⋊D₄₇	—	2	4	no	—
284	C₂×Dic₄₇	—	2	2	no	—
285	C₂×Dic₄₇	—	2	2	no	—
286	C₂×Dic₄₇	—	2	2	no	—
287	C₂×Dic₄₇	—	4	2	no	—
288	C₂×Dic₄₇	—	8	2	no	—
289	D₁₈₈	—	2	2	no	—
290	D₁₈₈	—	2	2	no	—
291	D₁₈₈	—	2	2	no	—
292	D₁₈₈	C₂×C₄⋊C₄	1	4	yes	—
293	C₄×D₄₇	—	2	4	no	—
294	C₄×D₄₇	—	2	4	no	—
295	C₄×D₄₇	—	2	4	no	—
296	C₄×D₄₇	—	2	4	no	—
297	Dic₉₄	—	2	2	no	—
298	Dic₉₄	—	2	2	no	—
299	Dic₉₄	—	2	2	no	—
300	Dic₉₄	C₂×C₄⋊C₄	1	4	yes	—
301	C₈×C₄₇	—	2	4	no	—
302	C₈×C₄₇	—	4	2	no	—
303	C₄₇⋊C₈	—	4	2	no	—
304	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
305	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
306	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
307	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
308	C₂×#1814	—	47	1	no	maximal, Sylow
309	C₂²×C₄₇	—	2	2	no	—
310	C₂²×C₄₇	—	2	2	no	—
311	C₂²×C₄₇	—	2	2	no	—
312	C₂²×C₄₇	—	4	1	no	—
313	C₂²×C₄₇	—	4	1	no	—
314	C₂²×C₄₇	—	4	1	no	—
315	C₂²×C₄₇	—	4	1	no	—
316	C₂²×C₄₇	#380	1	1	yes	characteristic
317	C₂²×C₄₇	#380	1	1	yes	characteristic
318	C₂²×C₄₇	#380	1	1	yes	characteristic
319	C₂²×C₄₇	#380	1	1	yes	characteristic
320	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
321	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
322	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
323	C₂×D₄₇	—	2	4	no	—
324	C₂×D₄₇	—	4	4	no	—
325	C₂×D₄₇	—	4	4	no	—
326	C₂×D₄₇	—	4	4	no	—
327	C₄×C₄₇	—	8	2	no	—
328	C₄×C₄₇	#380	1	1	yes	characteristic
329	C₄×C₄₇	#380	1	1	yes	characteristic
330	C₄×C₄₇	#380	1	1	yes	characteristic
331	C₄×C₄₇	#380	1	1	yes	characteristic
332	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
333	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
334	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
335	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
336	Dic₄₇	—	2	4	no	—
337	Dic₄₇	—	8	2	no	—
338	C₂²×#131	—	47	1	no	—
339	C₂²×#108	—	47	1	no	—
340	C₂×#427	—	47	1	no	—
341	C₂×#421	—	47	1	no	—
342	C₂×#421	—	47	1	no	—
343	#1814	—	47	8	no	—
344	C₂×#344	—	47	1	no	—
345	C₂×#344	D₄₇	1	1	yes	characteristic, complemented
346	C₂×C₄₇	—	2	1	no	—
347	C₂×C₄₇	—	2	1	no	—
348	C₂×C₄₇	—	2	1	no	—
349	C₂×C₄₇	—	2	1	no	—
350	C₂×C₄₇	—	2	1	no	—
351	C₂×C₄₇	—	2	1	no	—
352	C₂×C₄₇	#1814	1	2	yes	complemented
353	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
354	D₄₇	—	4	4	no	—
355	C₂²×#41	—	47	1	no	—
356	C₂×#131	—	47	2	no	—
357	C₂×#131	—	47	2	no	—
358	C₂×#131	—	47	4	no	—
359	C₂×#131	—	47	4	no	—
360	C₂×#131	—	94	1	no	—
361	C₂×#131	—	94	1	no	—
362	C₂×#131	—	94	2	no	—
363	C₂×#131	—	94	2	no	—
364	C₂²×M₁₆	—	47	1	no	—
365	C₂²×M₁₆	—	94	1	no	—
366	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
367	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
368	C₂³×C₈	—	47	1	no	—
369	C₂³×C₈	—	94	1	no	—
370	C₂×#117	—	47	1	no	—
371	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
372	C₂×#108	—	47	4	no	—
373	C₂×#108	—	94	1	no	—
374	C₂×#108	—	94	1	no	—
375	C₂×#108	—	94	2	no	—
376	#427	—	47	4	no	—
377	#427	—	94	2	no	—
378	C₂×#107	—	94	1	no	—
379	C₂×#106	—	94	1	no	—
380	#421	—	47	4	no	—
381	#421	—	47	4	no	—
382	#421	—	94	2	no	—
383	#421	—	94	2	no	—
384	C₂×#104	—	94	2	no	—
385	C₂×#104	—	94	2	no	—
386	#344	—	47	4	no	—
387	#344	C₂×D₄₇	1	4	yes	complemented
388	C₄₇	C₂×#1814	1	1	yes	characteristic, complemented, Sylow
389	C₂×#41	—	47	2	no	—
390	C₂×#41	—	47	2	no	—
391	C₂×#41	—	47	2	no	—
392	C₂×#41	—	47	2	no	—
393	C₂×#41	—	47	2	no	—
394	C₂×#41	—	47	2	no	—
395	C₂×#41	—	94	1	no	—
396	C₂×#41	—	94	1	no	—
397	C₂×#41	—	94	1	no	—
398	C₂×#41	—	94	1	no	—
399	C₂×#41	—	94	1	no	—
400	C₂×#41	—	94	1	no	—
401	C₂²×Q₈	—	47	1	no	—
402	C₂²×D₄	—	47	1	no	—
403	C₂²×D₄	—	94	1	no	—
404	C₂³×C₄	—	94	1	no	—
405	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
406	#131	—	47	8	no	—
407	#131	—	47	8	no	—
408	#131	—	94	4	no	—
409	#131	—	94	4	no	—
410	#131	—	94	4	no	—
411	#131	—	94	4	no	—
412	#131	—	94	4	no	—
413	#131	—	94	4	no	—
414	C₂×M₁₆	—	2	1	no	—
415	C₂×M₁₆	—	2	1	no	—
416	C₂×M₁₆	—	2	1	no	—
417	C₂×M₁₆	—	2	1	no	—
418	C₂×M₁₆	—	2	1	no	—
419	C₂×M₁₆	—	2	1	no	—
420	C₂×M₁₆	—	2	1	no	—
421	C₂×M₁₆	—	2	1	no	—
422	C₂×M₁₆	—	47	2	no	—
423	C₂×M₁₆	—	94	2	no	—
424	C₂×M₁₆	—	94	2	no	—
425	C₂×M₁₆	—	94	4	no	—
426	C₂×M₁₆	—	94	4	no	—
427	C₂×M₁₆	—	94	1	no	—
428	C₂×M₁₆	—	94	1	no	—
429	C₂×M₁₆	—	94	1	no	—
430	C₂×M₁₆	—	94	1	no	—
431	C₂×M₁₆	—	94	1	no	—
432	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
433	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
434	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
435	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
436	C₂²×C₈	—	2	1	no	—
437	C₂²×C₈	—	2	1	no	—
438	C₂²×C₈	—	47	1	no	—
439	C₂²×C₈	—	47	1	no	—
440	C₂²×C₈	—	47	2	no	—
441	C₂²×C₈	—	47	1	no	—
442	C₂²×C₈	—	47	1	no	—
443	C₂²×C₈	—	47	1	no	—
444	C₂²×C₈	—	47	1	no	—
445	C₂²×C₈	—	47	2	no	—
446	C₂²×C₈	—	47	2	no	—
447	C₂²×C₈	—	47	2	no	—
448	C₂²×C₈	—	94	2	no	—
449	C₂²×C₈	—	94	2	no	—
450	C₂²×C₈	—	94	4	no	—
451	C₂²×C₈	—	94	4	no	—
452	C₂²×C₈	—	94	1	no	—
453	#117	—	2	1	no	—
454	#117	—	2	1	no	—
455	#117	—	2	1	no	—
456	#117	—	47	2	no	—
457	#117	—	94	1	no	—
458	#117	—	94	1	no	—
459	#117	—	94	1	no	—
460	#117	C₂²×D₄₇	1	2	yes	—
461	C₂×C₄⋊C₄	—	2	1	no	—
462	C₂×C₄⋊C₄	—	94	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	94	1	no	—
465	C₂×C₄²	—	2	1	no	—
466	C₂×C₄²	—	94	1	no	—
467	#108	—	94	4	no	—
468	#108	—	94	4	no	—
469	#107	—	94	4	no	—
470	#106	—	94	4	no	—
471	#104	—	94	8	no	—
472	#104	—	94	8	no	—
473	C₂⁴	—	94	1	no	—
474	C₂⁴	#10625350	1	1	yes	characteristic
475	#41	—	47	4	no	—
476	#41	—	47	4	no	—
477	#41	—	47	4	no	—
478	#41	—	47	4	no	—
479	#41	—	94	2	no	—
480	#41	—	94	2	no	—
481	#41	—	94	2	no	—
482	#41	—	94	2	no	—
483	#41	—	94	2	no	—
484	#41	—	94	2	no	—
485	#41	—	94	2	no	—
486	#41	—	94	2	no	—
487	#41	—	94	2	no	—
488	#41	—	94	2	no	—
489	#41	—	94	2	no	—
490	#41	—	94	2	no	—
491	C₂×Q₈	—	47	2	no	—
492	C₂×Q₈	—	47	2	no	—
493	C₂×Q₈	—	47	2	no	—
494	C₂×Q₈	—	94	1	no	—
495	C₂×Q₈	—	94	1	no	—
496	C₂×Q₈	—	94	1	no	—
497	C₂×D₄	—	47	2	no	—
498	C₂×D₄	—	47	2	no	—
499	C₂×D₄	—	47	2	no	—
500	C₂×D₄	—	94	2	no	—
501	C₂×D₄	—	94	2	no	—
502	C₂×D₄	—	94	2	no	—
503	C₂×D₄	—	94	2	no	—
504	C₂×D₄	—	94	2	no	—
505	C₂×D₄	—	94	2	no	—
506	C₂×D₄	—	94	1	no	—
507	C₂×D₄	—	94	1	no	—
508	C₂×D₄	—	94	1	no	—
509	C₂²×C₄	—	4	1	no	—
510	C₂²×C₄	—	94	1	no	—
511	C₂²×C₄	—	94	2	no	—
512	C₂²×C₄	—	94	2	no	—
513	C₂²×C₄	—	94	2	no	—
514	C₂²×C₄	—	94	2	no	—
515	C₂²×C₄	—	94	2	no	—
516	C₂²×C₄	—	94	2	no	—
517	C₂²×C₄	—	188	1	no	—
518	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
519	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
520	C₂²×C₄	#10625350	1	1	yes	characteristic
521	C₂²×C₄	#10625350	1	1	yes	characteristic
522	C₂²×C₄	#10625350	1	1	yes	characteristic
523	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
524	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
525	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
526	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
527	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
528	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
529	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
530	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
531	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
532	M₁₆	—	2	2	no	—
533	M₁₆	—	2	2	no	—
534	M₁₆	—	2	2	no	—
535	M₁₆	—	2	2	no	—
536	M₁₆	—	2	2	no	—
537	M₁₆	—	4	1	no	—
538	M₁₆	—	4	1	no	—
539	M₁₆	—	94	8	no	—
540	M₁₆	—	94	8	no	—
541	M₁₆	—	94	2	no	—
542	M₁₆	—	94	2	no	—
543	M₁₆	—	188	1	no	—
544	M₁₆	—	188	1	no	—
545	M₁₆	C₂×C₄×D₄₇	1	4	yes	—
546	C₂×C₈	—	2	2	no	—
547	C₂×C₈	—	2	2	no	—
548	C₂×C₈	—	2	2	no	—
549	C₂×C₈	—	2	2	no	—
550	C₂×C₈	—	4	1	no	—
551	C₂×C₈	—	4	1	no	—
552	C₂×C₈	—	47	1	no	—
553	C₂×C₈	—	47	1	no	—
554	C₂×C₈	—	47	2	no	—
555	C₂×C₈	—	47	1	no	—
556	C₂×C₈	—	47	1	no	—
557	C₂×C₈	—	47	2	no	—
558	C₂×C₈	—	47	2	no	—
559	C₂×C₈	—	47	2	no	—
560	C₂×C₈	—	47	2	no	—
561	C₂×C₈	—	47	2	no	—
562	C₂×C₈	—	47	2	no	—
563	C₂×C₈	—	47	2	no	—
564	C₂×C₈	—	47	2	no	—
565	C₂×C₈	—	47	2	no	—
566	C₂×C₈	—	47	2	no	—
567	C₂×C₈	—	47	2	no	—
568	C₂×C₈	—	94	8	no	—
569	C₂×C₈	—	94	8	no	—
570	C₂×C₈	—	94	2	no	—
571	C₂×C₈	—	188	1	no	—
572	C₂×C₈	—	188	1	no	—
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	4	1	no	—
575	C₄⋊C₄	—	94	2	no	—
576	C₄⋊C₄	—	188	1	no	—
577	C₂²⋊C₄	—	2	2	no	—
578	C₂²⋊C₄	—	4	1	no	—
579	C₂²⋊C₄	—	94	2	no	—
580	C₂²⋊C₄	—	188	1	no	—
581	C₄²	—	2	2	no	—
582	C₄²	—	4	1	no	—
583	C₄²	—	94	2	no	—
584	C₄²	—	188	1	no	—
585	C₂³	—	4	2	no	—
586	C₂³	—	94	2	no	—
587	C₂³	—	94	2	no	—
588	C₂³	—	94	2	no	—
589	C₂³	—	188	4	no	—
590	C₂³	#13093981	1	1	yes	characteristic
591	C₂³	#13093981	1	1	yes	characteristic
592	C₂³	#13093997	1	1	yes	characteristic
593	C₂³	#13093997	1	1	yes	characteristic
594	C₂³	#13094002	1	1	yes	characteristic
595	C₂³	#13094002	1	1	yes	characteristic
596	C₂³	C₂×#10625350	1	1	yes	characteristic
597	Q₈	—	47	4	no	—
598	Q₈	—	94	2	no	—
599	Q₈	—	94	2	no	—
600	Q₈	—	94	2	no	—
601	D₄	—	47	4	no	—
602	D₄	—	94	4	no	—
603	D₄	—	94	4	no	—
604	D₄	—	94	4	no	—
605	D₄	—	94	4	no	—
606	D₄	—	94	2	no	—
607	D₄	—	94	2	no	—
608	D₄	—	94	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	8	2	no	—
611	C₂×C₄	—	94	2	no	—
612	C₂×C₄	—	94	2	no	—
613	C₂×C₄	—	94	2	no	—
614	C₂×C₄	—	94	4	no	—
615	C₂×C₄	—	94	4	no	—
616	C₂×C₄	—	94	4	no	—
617	C₂×C₄	—	94	4	no	—
618	C₂×C₄	—	376	2	no	—
619	C₂×C₄	—	188	2	no	—
620	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
621	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
622	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
623	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
624	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
625	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
626	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
627	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
628	C₂×C₄	#13093981	1	1	yes	characteristic
629	C₂×C₄	#13093981	1	1	yes	characteristic
630	C₂×C₄	#13093997	1	1	yes	characteristic
631	C₂×C₄	#13093997	1	1	yes	characteristic
632	C₂×C₄	#13093997	1	1	yes	characteristic
633	C₂×C₄	#13093997	1	1	yes	characteristic
634	C₂×C₄	#13093997	1	1	yes	characteristic
635	C₂×C₄	#13093997	1	1	yes	characteristic
636	C₂×C₄	#13094002	1	1	yes	characteristic
637	C₂×C₄	#13094002	1	1	yes	characteristic
638	C₂×C₄	#13094002	1	1	yes	characteristic
639	C₂×C₄	#13094002	1	1	yes	characteristic
640	C₂×C₄	#13094002	1	1	yes	characteristic
641	C₂×C₄	#13094002	1	1	yes	characteristic
642	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
643	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
644	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
645	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
646	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
647	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
648	C₈	—	2	4	no	—
649	C₈	—	4	2	no	—
650	C₈	—	47	2	no	—
651	C₈	—	47	2	no	—
652	C₈	—	47	2	no	—
653	C₈	—	47	2	no	—
654	C₈	—	188	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	94	4	no	—
663	C₂²	—	188	4	no	—
664	C₂²	—	188	4	no	—
665	C₂²	—	188	4	no	—
666	C₂²	#15688982	1	1	yes	characteristic
667	C₂²	#15688982	1	1	yes	characteristic
668	C₂²	#15688982	1	1	yes	characteristic
669	C₂²	#15688982	1	1	yes	characteristic
670	C₂²	C₂×#13093981	1	1	yes	characteristic
671	C₂²	C₂×#13093997	1	1	yes	characteristic
672	C₂²	C₂×#13094002	1	1	yes	characteristic
673	C₄	—	8	2	no	—
674	C₄	—	94	4	no	—
675	C₄	—	376	2	no	—
676	C₄	#15688982	1	1	yes	characteristic
677	C₄	#15688982	1	1	yes	characteristic
678	C₄	#15688982	1	1	yes	characteristic
679	C₄	#15688982	1	1	yes	characteristic
680	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
681	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
682	C₄	C₂×#13093997	1	1	yes	characteristic
683	C₄	C₂×#13094002	1	1	yes	characteristic
684	C₂	—	2	1	no	—
685	C₂	—	2	1	no	—
686	C₂	—	2	1	no	—
687	C₂	—	2	1	no	—
688	C₂	—	2	1	no	—
689	C₂	—	2	1	no	—
690	C₂	—	188	4	no	—
691	C₂	#20243441	1	2	yes	direct product factor
692	C₂	C₂×#15688982	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093997
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#344	C₂
socle	C₂²×C₄₇	#380
prime radical	C₂²×#10625350	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#344	D₄₇
hypocenter	C₄₇	C₂×#1814
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
2. C₂²×#13093959	C₂	semidirect
3. C₂×#15689159	C₂	semidirect
6. #20243441	C₂	direct (N × H)
7. C₂×#15688895	C₂	semidirect
8. C₂×C₄₇×#344	C₂	semidirect
14. C₂×#13094032	C₄	semidirect
15. C₂×#13094032	C₄	semidirect
16. C₂×#13094032	C₄	semidirect
26. C₂×#13093959	C₂²	semidirect
28. #15689159	C₂²	semidirect
37. #15688895	C₂²	semidirect
41. C₄₇×#344	C₂²	semidirect
64. #13094032	C₂×C₄	semidirect
65. #13094032	C₂×C₄	semidirect
345. C₂×#344	D₄₇	semidirect
352. C₂×C₄₇	#1814	semidirect
387. #344	C₂×D₄₇	semidirect
388. C₄₇	C₂×#1814	semidirect
691. C₂	#20243441	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13094032	2
C₂²×#13093959	2
C₂×#15689159	2
C₂×#15689141	2
C₂×#15689139	2
#20243441	2
C₂×#15688895	2
C₂×C₄₇×#344	2
C₂×#1814	47

Subgroups — C2×#20243441 #26215939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243441 #26215939