Subgroups — C₂×#20243187 #26213975

Order 12032.

1474 conjugacy classes of subgroups.

The subgroup lattice has 698 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	C₂×#15689105	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689096	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689081	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15689079	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243187	C₂	1	8	yes	maximal, direct product factor
7	C₂×#15688894	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	1	no	—
13	C₂×#13094032	—	2	1	no	—
14	C₂×#13094032	—	2	2	no	—
15	C₂×#13094032	—	2	2	no	—
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	C₄	1	2	yes	complemented
20	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂²×C₈×D₄₇	C₄	1	2	yes	complemented
22	C₂×#13093983	C₂²	1	1	yes	characteristic
23	#15689105	C₄	1	4	yes	complemented
24	#15689105	C₂²	1	4	yes	—
25	C₂×#13093942	C₄	1	2	yes	complemented
26	C₂×#13093940	C₄	1	2	yes	complemented
27	#15689096	C₄	1	4	yes	—
28	#15689096	C₂²	1	4	yes	—
29	C₂×#13093938	C₄	1	4	yes	—
30	#15689081	—	2	2	no	—
31	#15689081	C₂²	1	4	yes	complemented
32	#15689079	—	2	2	no	—
33	#15689079	C₂²	1	4	yes	complemented
34	C₂×#13093935	—	2	1	no	—
35	C₂×#13093934	—	2	1	no	—
36	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
37	C₂×C₈×Dic₄₇	—	2	1	no	—
38	#15688894	C₂²	1	4	yes	complemented
39	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
40	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#344	C₂²	1	4	yes	complemented
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	—	2	1	no	—
49	C₂×#10625350	—	2	1	no	—
50	C₂×#10625350	—	2	1	no	—
51	C₂×#10625350	C₂×C₄	1	2	yes	—
52	C₂×#10625350	C₂×C₄	1	2	yes	—
53	C₂×#10625350	C₂×C₄	1	2	yes	—
54	C₂×#10625350	C₂³	1	2	yes	—
55	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
56	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
58	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
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	—	2	4	no	—
65	#13094032	—	2	4	no	—
66	#13094032	—	2	4	no	—
67	C₂×#10625329	—	2	1	no	—
68	C₂×#10625329	—	2	1	no	—
69	C₂×#10625329	—	2	1	no	—
70	C₂×#10625329	C₂×C₄	1	2	yes	—
71	C₂×#10625329	C₂×C₄	1	2	yes	—
72	C₂×#10625329	C₂³	1	2	yes	—
73	C₂×#10625324	—	2	4	no	—
74	C₂×#10625324	—	2	2	no	—
75	C₂×#10625324	—	2	2	no	—
76	C₂×#10625324	C₂×C₄	1	8	yes	complemented
77	C₂²×C₄₇⋊C₈	—	2	1	no	—
78	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
79	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
80	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
85	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
86	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
87	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
88	C₂×C₈×D₄₇	—	2	4	no	—
89	C₂×C₈×D₄₇	—	2	2	no	—
90	C₂×C₈×D₄₇	—	2	2	no	—
91	C₂×C₈×D₄₇	C₂×C₄	1	8	yes	complemented
92	#13093983	—	2	1	no	—
93	#13093983	—	2	1	no	—
94	#13093983	C₂×C₄	1	2	yes	—
95	#13093983	C₂³	1	2	yes	—
96	C₂×C₄⋊Dic₄₇	—	2	1	no	—
97	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
98	C₂×C₄×Dic₄₇	—	2	1	no	—
99	#13093942	C₂×C₄	1	8	yes	complemented
100	#13093940	C₂×C₄	1	8	yes	complemented
101	#13093938	C₂×C₄	1	16	yes	—
102	#13093935	—	2	4	no	—
103	#13093934	—	2	4	no	—
104	C₄×C₄₇⋊C₈	—	2	4	no	—
105	C₈×Dic₄₇	—	2	4	no	—
106	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
114	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
115	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
116	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
117	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
118	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
119	C₂²×C₈×C₄₇	—	2	1	no	—
120	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
121	#117×C₄₇	—	2	1	no	—
122	#117×C₄₇	—	2	1	no	—
123	#117×C₄₇	C₂×C₄	1	2	yes	—
124	#117×C₄₇	C₂³	1	2	yes	—
125	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
127	C₂×C₄²×C₄₇	—	2	1	no	—
128	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂³×D₄₇	C₄²	1	2	yes	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂×D₄	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	#41	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	C₂×C₂²⋊D₄₇	C₄²	1	4	yes	—
150	C₂×C₂²⋊D₄₇	C₂²×C₄	1	4	yes	—
151	C₂²×Dic₄₇	—	2	2	no	—
152	C₂²×Dic₄₇	C₄²	1	2	yes	—
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	—	2	2	no	—
164	#10625350	—	2	2	no	—
165	#10625350	—	2	2	no	—
166	#10625350	—	2	2	no	—
167	#10625350	—	2	2	no	—
168	#10625350	—	2	2	no	—
169	C₂×D₁₈₈	—	2	1	no	—
170	C₂×D₁₈₈	—	2	1	no	—
171	C₂×D₁₈₈	—	2	1	no	—
172	C₂×D₁₈₈	—	2	1	no	—
173	C₂×D₁₈₈	C₄²	1	2	yes	—
174	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
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×C₄×D₄₇	C₄²	1	4	yes	—
180	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
181	C₂×Dic₉₄	—	2	1	no	—
182	C₂×Dic₉₄	—	2	1	no	—
183	C₂×Dic₉₄	—	2	1	no	—
184	C₂×Dic₉₄	—	2	1	no	—
185	C₂×Dic₉₄	C₄²	1	2	yes	—
186	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
187	M₁₆×C₄₇	—	2	2	no	—
188	M₁₆×C₄₇	—	2	2	no	—
189	M₁₆×C₄₇	—	2	2	no	—
190	M₁₆×C₄₇	—	2	2	no	—
191	M₁₆×C₄₇	—	2	2	no	—
192	M₁₆×C₄₇	—	2	2	no	—
193	M₁₆×C₄₇	—	2	2	no	—
194	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
195	C₂×C₈×C₄₇	—	2	2	no	—
196	C₂×C₈×C₄₇	—	2	2	no	—
197	C₂×C₈×C₄₇	—	2	2	no	—
198	C₂×C₈×C₄₇	—	2	2	no	—
199	C₂×C₈×C₄₇	—	2	2	no	—
200	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
201	C₄⋊C₄×C₄₇	—	2	2	no	—
202	C₄⋊C₄×C₄₇	—	2	2	no	—
203	C₂²⋊C₄×C₄₇	—	2	2	no	—
204	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
205	C₄²×C₄₇	—	2	2	no	—
206	C₄²×C₄₇	—	2	2	no	—
207	C₂²⋊Dic₄₇	—	2	2	no	—
208	C₂²⋊Dic₄₇	C₂²×C₄	1	4	yes	—
209	C₄⋊Dic₄₇	—	2	2	no	—
210	C₄⋊Dic₄₇	—	2	2	no	—
211	C₄×Dic₄₇	—	2	2	no	—
212	C₄×Dic₄₇	—	2	2	no	—
213	#10625329	—	2	2	no	—
214	#10625329	—	2	2	no	—
215	#10625329	—	2	2	no	—
216	#10625329	C₂²×C₄	1	4	yes	—
217	C₂×C₄₇⋊C₈	—	2	2	no	—
218	C₂×C₄₇⋊C₈	—	2	2	no	—
219	C₂×C₄₇⋊C₈	—	2	2	no	—
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	1	yes	characteristic
225	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	2	yes	—
231	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
232	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
233	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
234	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
235	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
236	#10625324	—	2	8	no	—
237	#10625324	—	2	8	no	—
238	C₈×D₄₇	—	2	8	no	—
239	C₈×D₄₇	—	2	8	no	—
240	C₂³×C₄₇	—	4	2	no	—
241	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
242	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
243	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
244	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
245	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
246	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
247	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
248	C₂²×D₄₇	—	2	2	no	—
249	C₂²×D₄₇	—	2	2	no	—
250	C₂²×D₄₇	—	4	4	no	—
251	C₂²×D₄₇	C₂×C₄²	1	4	yes	—
252	C₂×C₄×C₄₇	—	2	4	no	—
253	C₂×C₄×C₄₇	—	4	4	no	—
254	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₄₇	C₂×C₂²⋊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	#117	1	1	yes	characteristic
263	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
265	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
267	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
270	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
271	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
272	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
273	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
274	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
275	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
276	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
277	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
278	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
282	C₂²⋊D₄₇	—	2	4	no	—
283	C₂²⋊D₄₇	—	2	4	no	—
284	C₂²⋊D₄₇	—	2	4	no	—
285	C₂²⋊D₄₇	—	2	4	no	—
286	C₂×Dic₄₇	—	2	2	no	—
287	C₂×Dic₄₇	—	2	2	no	—
288	C₂×Dic₄₇	—	2	4	no	—
289	C₂×Dic₄₇	—	4	4	no	—
290	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
291	D₁₈₈	—	2	2	no	—
292	D₁₈₈	—	2	2	no	—
293	D₁₈₈	—	2	2	no	—
294	D₁₈₈	—	2	2	no	—
295	C₄×D₄₇	—	2	4	no	—
296	C₄×D₄₇	—	2	4	no	—
297	C₄×D₄₇	—	2	4	no	—
298	C₄×D₄₇	—	2	4	no	—
299	Dic₉₄	—	2	2	no	—
300	Dic₉₄	—	2	2	no	—
301	Dic₉₄	—	2	2	no	—
302	Dic₉₄	—	2	2	no	—
303	C₈×C₄₇	—	2	4	no	—
304	C₈×C₄₇	—	2	4	no	—
305	C₄₇⋊C₈	—	2	4	no	—
306	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
307	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
308	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
309	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	2	yes	—
310	C₂×#1757	—	47	1	no	maximal, Sylow
311	C₂²×C₄₇	—	2	2	no	—
312	C₂²×C₄₇	—	2	2	no	—
313	C₂²×C₄₇	—	2	2	no	—
314	C₂²×C₄₇	—	4	1	no	—
315	C₂²×C₄₇	—	4	1	no	—
316	C₂²×C₄₇	—	4	1	no	—
317	C₂²×C₄₇	—	4	1	no	—
318	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
319	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
320	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
321	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
323	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
324	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
325	C₂×D₄₇	—	2	4	no	—
326	C₂×D₄₇	—	4	4	no	—
327	C₂×D₄₇	—	4	4	no	—
328	C₂×D₄₇	—	4	4	no	—
329	C₄×C₄₇	—	4	4	no	—
330	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
331	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
332	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
333	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
334	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
335	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
336	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
337	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
338	Dic₄₇	—	2	4	no	—
339	Dic₄₇	—	4	4	no	—
340	C₂²×#131	—	47	1	no	—
341	C₂×#413	—	47	1	no	—
342	C₂×#410	—	47	1	no	—
343	C₂×#405	—	47	1	no	—
344	C₂×#405	—	47	1	no	—
345	#1757	—	47	8	no	—
346	C₂×#344	—	47	1	no	—
347	C₂×#344	D₄₇	1	1	yes	characteristic, complemented
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	—	2	1	no	—
353	C₂×C₄₇	—	2	1	no	—
354	C₂×C₄₇	#1757	1	2	yes	complemented
355	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
356	D₄₇	—	4	4	no	—
357	C₂²×#41	—	47	1	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	1	no	—
363	C₂×#131	—	94	1	no	—
364	C₂×#131	—	94	2	no	—
365	C₂×#131	—	94	2	no	—
366	C₂²×M₁₆	—	47	2	no	—
367	C₂²×M₁₆	—	47	1	no	—
368	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
369	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
370	C₂³×C₈	—	47	1	no	—
371	C₂³×C₈	—	47	2	no	—
372	C₂×#117	—	47	1	no	—
373	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
374	#413	—	47	4	no	—
375	#413	—	47	4	no	—
376	C₂×#101	—	47	2	no	—
377	C₂×#100	—	47	2	no	—
378	#410	—	47	4	no	—
379	#410	—	47	4	no	—
380	C₂×#99	—	47	4	no	—
381	#405	—	47	4	no	—
382	#405	—	47	4	no	—
383	#405	—	94	2	no	—
384	#405	—	94	2	no	—
385	C₂×#97	—	94	1	no	—
386	C₂×#97	—	94	1	no	—
387	C₂×C₄×C₈	—	94	1	no	—
388	C₂×C₄×C₈	—	94	1	no	—
389	#344	—	47	4	no	—
390	#344	C₂×D₄₇	1	4	yes	complemented
391	C₄₇	C₂×#1757	1	1	yes	characteristic, complemented, Sylow
392	C₂×#41	—	47	2	no	—
393	C₂×#41	—	47	2	no	—
394	C₂×#41	—	47	2	no	—
395	C₂×#41	—	47	2	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	C₂×#41	—	94	1	no	—
402	C₂×#41	—	94	1	no	—
403	C₂×#41	—	94	1	no	—
404	C₂²×Q₈	—	47	1	no	—
405	C₂²×D₄	—	47	2	no	—
406	C₂²×D₄	—	47	1	no	—
407	C₂³×C₄	—	47	2	no	—
408	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
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	#131	—	94	4	no	—
415	#131	—	94	4	no	—
416	#131	—	94	4	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	—	2	1	no	—
423	C₂×M₁₆	—	2	1	no	—
424	C₂×M₁₆	—	47	8	no	—
425	C₂×M₁₆	—	47	2	no	—
426	C₂×M₁₆	—	47	2	no	—
427	C₂×M₁₆	—	47	2	no	—
428	C₂×M₁₆	—	94	4	no	—
429	C₂×M₁₆	—	94	2	no	—
430	C₂×M₁₆	—	94	2	no	—
431	C₂×M₁₆	—	94	1	no	—
432	C₂×M₁₆	—	94	1	no	—
433	C₂×M₁₆	—	94	1	no	—
434	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
435	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
436	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
437	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
438	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
439	C₂²×C₈	—	2	1	no	—
440	C₂²×C₈	—	47	1	no	—
441	C₂²×C₈	—	47	1	no	—
442	C₂²×C₈	—	47	2	no	—
443	C₂²×C₈	—	47	1	no	—
444	C₂²×C₈	—	47	1	no	—
445	C₂²×C₈	—	47	1	no	—
446	C₂²×C₈	—	47	1	no	—
447	C₂²×C₈	—	47	2	no	—
448	C₂²×C₈	—	47	2	no	—
449	C₂²×C₈	—	47	2	no	—
450	C₂²×C₈	—	47	8	no	—
451	C₂²×C₈	—	94	4	no	—
452	C₂²×C₈	—	94	2	no	—
453	C₂²×C₈	—	94	2	no	—
454	C₂²×C₈	—	94	1	no	—
455	C₂²×C₈	C₄×D₄₇	1	2	yes	—
456	#117	—	2	1	no	—
457	#117	—	2	1	no	—
458	#117	—	47	2	no	—
459	#117	—	47	2	no	—
460	#117	—	94	1	no	—
461	#117	—	94	1	no	—
462	#117	C₄×D₄₇	1	2	yes	—
463	#117	C₂²×D₄₇	1	2	yes	—
464	C₂×C₄⋊C₄	—	2	1	no	—
465	C₂×C₄⋊C₄	—	94	1	no	—
466	C₂×C₂²⋊C₄	—	47	2	no	—
467	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
468	C₂×C₄²	—	2	1	no	—
469	C₂×C₄²	—	94	1	no	—
470	#101	—	47	8	no	—
471	#100	—	47	8	no	—
472	#99	—	47	16	no	—
473	#97	—	94	4	no	—
474	#97	—	94	4	no	—
475	C₄×C₈	—	94	4	no	—
476	C₄×C₈	—	94	4	no	—
477	C₂⁴	—	47	2	no	—
478	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
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	#41	—	94	2	no	—
492	#41	—	94	2	no	—
493	#41	—	94	2	no	—
494	#41	—	94	2	no	—
495	C₂×Q₈	—	47	2	no	—
496	C₂×Q₈	—	47	2	no	—
497	C₂×Q₈	—	94	1	no	—
498	C₂×Q₈	—	94	1	no	—
499	C₂×Q₈	—	94	1	no	—
500	C₂×Q₈	—	94	1	no	—
501	C₂×D₄	—	47	4	no	—
502	C₂×D₄	—	47	4	no	—
503	C₂×D₄	—	47	2	no	—
504	C₂×D₄	—	47	2	no	—
505	C₂×D₄	—	94	2	no	—
506	C₂×D₄	—	94	2	no	—
507	C₂×D₄	—	94	2	no	—
508	C₂×D₄	—	94	2	no	—
509	C₂×D₄	—	94	1	no	—
510	C₂×D₄	—	94	1	no	—
511	C₂×D₄	—	94	1	no	—
512	C₂×D₄	—	94	1	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	47	2	no	—
515	C₂²×C₄	—	47	4	no	—
516	C₂²×C₄	—	47	4	no	—
517	C₂²×C₄	—	94	2	no	—
518	C₂²×C₄	—	94	2	no	—
519	C₂²×C₄	—	94	2	no	—
520	C₂²×C₄	—	94	2	no	—
521	C₂²×C₄	—	94	2	no	—
522	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
526	C₂²×C₄	C₂×C₄×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	D₄×D₄₇	1	1	yes	characteristic
530	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
531	C₂²×C₄	#10625352	1	1	yes	characteristic
532	C₂²×C₄	#10625352	1	1	yes	characteristic
533	C₂²×C₄	#10625354	1	1	yes	characteristic
534	C₂²×C₄	#10625354	1	1	yes	characteristic
535	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
536	M₁₆	—	2	2	no	—
537	M₁₆	—	2	2	no	—
538	M₁₆	—	2	2	no	—
539	M₁₆	—	2	2	no	—
540	M₁₆	—	2	2	no	—
541	M₁₆	—	2	2	no	—
542	M₁₆	—	2	2	no	—
543	M₁₆	—	47	4	no	—
544	M₁₆	—	94	8	no	—
545	M₁₆	—	94	8	no	—
546	M₁₆	—	94	2	no	—
547	M₁₆	—	94	2	no	—
548	M₁₆	—	94	2	no	—
549	M₁₆	C₂×C₄×D₄₇	1	4	yes	—
550	C₂×C₈	—	2	2	no	—
551	C₂×C₈	—	2	2	no	—
552	C₂×C₈	—	2	2	no	—
553	C₂×C₈	—	2	2	no	—
554	C₂×C₈	—	2	2	no	—
555	C₂×C₈	—	47	2	no	—
556	C₂×C₈	—	47	2	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	1	no	—
562	C₂×C₈	—	47	1	no	—
563	C₂×C₈	—	47	1	no	—
564	C₂×C₈	—	47	1	no	—
565	C₂×C₈	—	47	2	no	—
566	C₂×C₈	—	47	2	no	—
567	C₂×C₈	—	47	2	no	—
568	C₂×C₈	—	47	2	no	—
569	C₂×C₈	—	47	2	no	—
570	C₂×C₈	—	47	2	no	—
571	C₂×C₈	—	94	8	no	—
572	C₂×C₈	—	94	8	no	—
573	C₂×C₈	—	94	2	no	—
574	C₂×C₈	—	94	2	no	—
575	C₂×C₈	—	94	2	no	—
576	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	94	2	no	—
580	C₄⋊C₄	—	94	2	no	—
581	C₂²⋊C₄	—	2	2	no	—
582	C₂²⋊C₄	—	47	4	no	—
583	C₂²⋊C₄	—	94	2	no	—
584	C₂²⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
585	C₄²	—	2	2	no	—
586	C₄²	—	2	2	no	—
587	C₄²	—	94	2	no	—
588	C₄²	—	94	2	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	47	4	no	—
591	C₂³	—	94	2	no	—
592	C₂³	—	94	2	no	—
593	C₂³	—	188	4	no	—
594	C₂³	C₄²×D₄₇	1	1	yes	characteristic
595	C₂³	C₄²×D₄₇	1	1	yes	characteristic
596	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
597	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
598	C₂³	#13093986	1	1	yes	characteristic
599	C₂³	#13093986	1	1	yes	characteristic
600	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
601	Q₈	—	94	2	no	—
602	Q₈	—	94	2	no	—
603	Q₈	—	94	2	no	—
604	Q₈	—	94	2	no	—
605	D₄	—	94	4	no	—
606	D₄	—	94	4	no	—
607	D₄	—	94	4	no	—
608	D₄	—	94	4	no	—
609	D₄	—	94	2	no	—
610	D₄	—	94	2	no	—
611	D₄	—	94	2	no	—
612	D₄	—	94	2	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	47	4	no	—
616	C₂×C₄	—	94	2	no	—
617	C₂×C₄	—	94	2	no	—
618	C₂×C₄	—	94	4	no	—
619	C₂×C₄	—	94	4	no	—
620	C₂×C₄	—	94	4	no	—
621	C₂×C₄	—	94	4	no	—
622	C₂×C₄	—	94	4	no	—
623	C₂×C₄	—	188	4	no	—
624	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
625	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
626	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
627	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
628	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
629	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
630	C₂×C₄	#13093982	1	1	yes	characteristic
631	C₂×C₄	#13093982	1	1	yes	characteristic
632	C₂×C₄	#13093982	1	1	yes	characteristic
633	C₂×C₄	#13093982	1	1	yes	characteristic
634	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
635	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
636	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
637	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
638	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
639	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
640	C₂×C₄	#13093986	1	1	yes	characteristic
641	C₂×C₄	#13093986	1	1	yes	characteristic
642	C₂×C₄	#13093986	1	1	yes	characteristic
643	C₂×C₄	#13093986	1	1	yes	characteristic
644	C₂×C₄	#13093986	1	1	yes	characteristic
645	C₂×C₄	#13093986	1	1	yes	characteristic
646	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
647	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
648	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
649	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
650	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
651	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
652	C₈	—	2	4	no	—
653	C₈	—	2	4	no	—
654	C₈	—	47	2	no	—
655	C₈	—	47	2	no	—
656	C₈	—	47	2	no	—
657	C₈	—	47	2	no	—
658	C₈	—	94	4	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	94	4	no	—
667	C₂²	—	188	4	no	—
668	C₂²	—	188	4	no	—
669	C₂²	—	188	4	no	—
670	C₂²	#15688970	1	1	yes	characteristic
671	C₂²	#15688970	1	1	yes	characteristic
672	C₂²	#15688970	1	1	yes	characteristic
673	C₂²	#15688970	1	1	yes	characteristic
674	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
675	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
676	C₂²	C₂×#13093986	1	1	yes	characteristic
677	C₄	—	4	4	no	—
678	C₄	—	94	4	no	—
679	C₄	—	188	4	no	—
680	C₄	#15688970	1	1	yes	characteristic
681	C₄	#15688970	1	1	yes	characteristic
682	C₄	#15688970	1	1	yes	characteristic
683	C₄	#15688970	1	1	yes	characteristic
684	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
685	C₄	C₂×#13093982	1	1	yes	characteristic
686	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
687	C₄	C₂×#13093986	1	1	yes	characteristic
688	C₂	—	2	1	no	—
689	C₂	—	2	1	no	—
690	C₂	—	2	1	no	—
691	C₂	—	2	1	no	—
692	C₂	—	2	1	no	—
693	C₂	—	2	1	no	—
694	C₂	—	188	4	no	—
695	C₂	#20243187	1	2	yes	direct product factor
696	C₂	C₂×#15688970	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#344	C₂
socle	C₂²×C₄₇	C₄×C₂²⋊C₄
prime radical	C₂²×#10625350	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#344	D₄₇
hypocenter	C₄₇	C₂×#1757
LCS	G ▷ C₂²×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
4. C₂×#15689081	C₂	semidirect
5. C₂×#15689079	C₂	semidirect
6. #20243187	C₂	direct (N × H)
7. C₂×#15688894	C₂	semidirect
8. C₂×C₄₇×#344	C₂	semidirect
16. C₂×#13094032	C₄	semidirect
19. C₂²×#10625324	C₄	semidirect
21. C₂²×C₈×D₄₇	C₄	semidirect
23. #15689105	C₄	semidirect
25. C₂×#13093942	C₄	semidirect
26. C₂×#13093940	C₄	semidirect
31. #15689081	C₂²	semidirect
33. #15689079	C₂²	semidirect
38. #15688894	C₂²	semidirect
42. C₄₇×#344	C₂²	semidirect
76. C₂×#10625324	C₂×C₄	semidirect
91. C₂×C₈×D₄₇	C₂×C₄	semidirect
99. #13093942	C₂×C₄	semidirect
100. #13093940	C₂×C₄	semidirect
347. C₂×#344	D₄₇	semidirect
354. C₂×C₄₇	#1757	semidirect
390. #344	C₂×D₄₇	semidirect
391. C₄₇	C₂×#1757	semidirect
695. C₂	#20243187	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
C₂×#15689105	2
C₂×#15689096	2
C₂×#15689081	2
C₂×#15689079	2
#20243187	2
C₂×#15688894	2
C₂×C₄₇×#344	2
C₂×#1757	47

Subgroups — C2×#20243187 #26213975

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243187 #26213975