Subgroups — #26213733

Order 12032.

1996 conjugacy classes of subgroups.

The subgroup lattice has 686 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×#15689889	C₂	1	1	yes	maximal, characteristic
3	#20256589	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688894	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688893	C₂	1	1	yes	maximal, characteristic, complemented
7	#344×D₄₇	C₂	1	8	yes	maximal, complemented
8	C₂×C₄₇×#344	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	—	2	2	no	—
14	#15689889	—	2	2	no	—
15	#15689889	—	2	2	no	—
16	#15689889	C₄	1	4	yes	complemented
17	#15689889	C₄	1	4	yes	complemented
18	C₂×#13094032	—	2	2	no	—
19	C₂×#13094032	C₄	1	4	yes	complemented
20	C₂×#13094030	—	2	2	no	—
21	C₂×#13094030	C₄	1	4	yes	complemented
22	C₂²×#10625329	C₂²	1	1	yes	characteristic
23	C₂²×#10625329	C₂²	1	1	yes	characteristic
24	C₂×M₁₆×D₄₇	C₂²	1	4	yes	—
25	C₂×M₁₆×D₄₇	C₂²	1	4	yes	—
26	#15689604	—	2	2	no	—
27	#15689603	—	2	2	no	—
28	#15689600	C₄	1	2	yes	—
29	#15689597	C₄	1	2	yes	—
30	#15689596	C₄	1	4	yes	—
31	C₄×#10625350	—	2	2	no	—
32	#15689591	—	2	2	no	—
33	C₂×#13093983	C₂²	1	1	yes	characteristic
34	#117×D₄₇	C₂²	1	4	yes	—
35	#15688895	C₂²	1	4	yes	—
36	#15688894	C₂²	1	4	yes	—
37	#15688893	C₂²	1	4	yes	—
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	—
42	C₂×#10625350	C₂×C₄	1	2	yes	—
43	C₂×#10625350	C₂×C₄	1	2	yes	—
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	D₄	1	2	yes	—
49	C₂×#10625350	D₄	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	Q₈	1	2	yes	—
54	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
57	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
58	#13094032	—	2	8	no	—
59	#13094032	—	2	8	no	—
60	#13094032	—	2	8	no	—
61	#13094032	—	2	8	no	—
62	#13094030	—	2	8	no	—
63	#13094030	—	2	8	no	—
64	#13094030	—	2	8	no	—
65	#13094030	—	2	8	no	—
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	—	2	1	no	—
72	C₂×#10625329	—	2	1	no	—
73	C₂×#10625329	C₂×C₄	1	2	yes	complemented
74	C₂×#10625329	C₂×C₄	1	2	yes	complemented
75	C₂×#10625329	C₂×C₄	1	2	yes	complemented
76	C₂×#10625329	C₂³	1	2	yes	—
77	C₂×#10625329	C₂³	1	2	yes	—
78	C₂×#10625324	—	2	4	no	—
79	C₂×#10625324	C₂×C₄	1	8	yes	complemented
80	M₁₆×D₄₇	—	2	8	no	—
81	M₁₆×D₄₇	—	2	8	no	—
82	M₁₆×D₄₇	—	2	8	no	—
83	M₁₆×D₄₇	C₂×C₄	1	16	yes	complemented
84	C₂²×C₄₇⋊C₈	—	2	1	no	—
85	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	complemented
86	C₂×C₈×D₄₇	—	2	4	no	—
87	C₂×C₈×D₄₇	C₂×C₄	1	8	yes	complemented
88	C₄×Dic₉₄	—	2	4	no	—
89	#13093989	—	2	4	no	—
90	C₄×D₁₈₈	—	2	4	no	—
91	#13093986	—	2	4	no	—
92	C₄×C₂²⋊D₄₇	—	2	8	no	—
93	(C₂²⋊D₄₇)⋊C₄	—	2	8	no	—
94	#13093983	—	2	1	no	—
95	#13093983	—	2	1	no	—
96	#13093983	C₂×C₄	1	2	yes	—
97	#13093983	C₂³	1	2	yes	—
98	#13093982	—	2	4	no	—
99	#13093981	—	2	4	no	—
100	#13093980	C₂×C₄	1	8	yes	—
101	C₂×C₄⋊Dic₄₇	—	2	1	no	—
102	C₄⋊C₄×D₄₇	—	2	4	no	—
103	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
104	C₂²⋊C₄×D₄₇	C₂×C₄	1	8	yes	—
105	C₂×C₄×Dic₄₇	—	2	1	no	—
106	C₄²×D₄₇	—	2	4	no	—
107	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
115	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
116	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
117	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
118	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
119	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
120	C₂²×C₈×C₄₇	—	2	1	no	—
121	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	complemented
122	#117×C₄₇	—	2	1	no	—
123	#117×C₄₇	—	2	1	no	—
124	#117×C₄₇	C₂×C₄	1	2	yes	—
125	#117×C₄₇	C₂³	1	2	yes	—
126	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
128	C₂×C₄²×C₄₇	—	2	1	no	—
129	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂³×D₄₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₄₇	—	2	2	no	—
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	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂×C₂²⋊D₄₇	C₄²	1	4	yes	—
147	C₂×C₂²⋊D₄₇	C₄²	1	4	yes	—
148	C₂×C₂²⋊D₄₇	C₂²⋊C₄	1	4	yes	—
149	C₂×C₂²⋊D₄₇	C₂²⋊C₄	1	4	yes	—
150	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	4	yes	—
151	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	4	yes	—
152	C₂²×Dic₄₇	—	2	2	no	—
153	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
154	#10625350	C₂²⋊C₄	1	4	yes	—
155	#10625350	C₂²⋊C₄	1	4	yes	—
156	#10625350	C₂²⋊C₄	1	4	yes	—
157	#10625350	C₂²⋊C₄	1	4	yes	—
158	#10625350	C₂²⋊C₄	1	4	yes	—
159	#10625350	C₂²⋊C₄	1	4	yes	—
160	#10625350	C₂²⋊C₄	1	4	yes	—
161	#10625350	C₂²⋊C₄	1	4	yes	—
162	#10625350	C₄⋊C₄	1	4	yes	—
163	#10625350	C₄⋊C₄	1	4	yes	—
164	#10625350	C₄⋊C₄	1	4	yes	—
165	#10625350	C₄⋊C₄	1	4	yes	—
166	#10625350	C₄⋊C₄	1	4	yes	—
167	#10625350	C₄⋊C₄	1	4	yes	—
168	#10625350	C₄⋊C₄	1	4	yes	—
169	#10625350	C₄⋊C₄	1	4	yes	—
170	C₂×D₁₈₈	C₄²	1	2	yes	—
171	C₂×D₁₈₈	C₄²	1	2	yes	—
172	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
173	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
174	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
175	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
176	C₂×C₄×D₄₇	—	2	8	no	—
177	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
178	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
179	C₂×C₄×D₄₇	C₂×D₄	1	4	yes	—
180	C₂×C₄×D₄₇	C₂×D₄	1	4	yes	—
181	C₂×C₄×D₄₇	C₂×D₄	1	4	yes	—
182	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
183	C₂×Dic₉₄	C₄²	1	2	yes	—
184	C₂×Dic₉₄	C₄²	1	2	yes	—
185	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
186	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
187	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
188	C₂×Dic₉₄	C₄⋊C₄	1	2	yes	—
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	—	2	2	no	—
195	M₁₆×C₄₇	—	2	2	no	—
196	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
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	—	2	2	no	—
201	C₂×C₈×C₄₇	—	2	2	no	—
202	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
203	C₄⋊C₄×C₄₇	—	2	2	no	—
204	C₄⋊C₄×C₄₇	—	2	2	no	—
205	C₂²⋊C₄×C₄₇	—	2	2	no	—
206	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
207	C₄²×C₄₇	—	2	2	no	—
208	C₄²×C₄₇	—	2	2	no	—
209	C₂²⋊Dic₄₇	—	2	2	no	—
210	C₂²⋊Dic₄₇	C₂²×C₄	1	4	yes	—
211	(C₂×D₄₇)⋊C₄	—	2	8	no	—
212	C₄⋊Dic₄₇	—	2	2	no	—
213	C₄⋊Dic₄₇	—	2	2	no	—
214	Dic₄₇⋊C₄	—	2	8	no	—
215	C₄×Dic₄₇	—	2	2	no	—
216	C₄×Dic₄₇	—	2	2	no	—
217	C₄×Dic₄₇	—	2	8	no	—
218	#10625329	—	2	2	no	—
219	#10625329	—	2	2	no	—
220	#10625329	—	2	2	no	—
221	#10625329	—	2	2	no	—
222	#10625329	—	2	2	no	—
223	#10625329	—	2	2	no	—
224	#10625329	—	2	2	no	—
225	#10625329	C₂²×C₄	1	4	yes	—
226	C₂×C₄₇⋊C₈	—	2	2	no	—
227	C₂×C₄₇⋊C₈	—	2	2	no	—
228	C₂×C₄₇⋊C₈	—	2	2	no	—
229	C₂×C₄₇⋊C₈	—	2	2	no	—
230	C₂×C₄₇⋊C₈	—	2	2	no	—
231	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
232	#10625324	—	2	16	no	—
233	#10625324	—	2	16	no	—
234	C₈×D₄₇	—	2	16	no	—
235	C₈×D₄₇	—	2	16	no	—
236	C₂³×C₄₇	—	8	1	no	—
237	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
238	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
239	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
244	C₂²×D₄₇	—	8	2	no	—
245	C₂²×D₄₇	C₂×C₄²	1	4	yes	—
246	C₂²×D₄₇	C₂×C₂²⋊C₄	1	4	yes	—
247	C₂²×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
248	C₂×C₄×C₄₇	—	2	4	no	—
249	C₂×C₄×C₄₇	—	8	2	no	—
250	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
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×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	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
273	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₄₇	C₂²×D₄	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×Q₈	1	1	yes	characteristic
278	C₂²⋊D₄₇	#95	1	8	yes	—
279	C₂²⋊D₄₇	#95	1	8	yes	—
280	C₂²⋊D₄₇	#95	1	8	yes	—
281	C₂²⋊D₄₇	#95	1	8	yes	—
282	C₂×Dic₄₇	—	2	4	no	—
283	C₂×Dic₄₇	—	8	2	no	—
284	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
285	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	4	yes	—
286	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
287	D₁₈₈	#95	1	4	yes	—
288	D₁₈₈	#95	1	4	yes	—
289	D₁₈₈	#95	1	4	yes	—
290	D₁₈₈	#95	1	4	yes	—
291	C₄×D₄₇	—	8	8	no	—
292	C₄×D₄₇	C₂×C₂²⋊C₄	1	8	yes	—
293	C₄×D₄₇	C₂×C₂²⋊C₄	1	8	yes	—
294	C₄×D₄₇	C₂×C₄⋊C₄	1	8	yes	—
295	C₄×D₄₇	C₂×C₄⋊C₄	1	8	yes	—
296	Dic₉₄	#95	1	4	yes	—
297	Dic₉₄	#95	1	4	yes	—
298	Dic₉₄	#95	1	4	yes	—
299	Dic₉₄	#95	1	4	yes	—
300	C₈×C₄₇	—	2	4	no	—
301	C₈×C₄₇	—	2	4	no	—
302	C₄₇⋊C₈	—	2	4	no	—
303	C₄₇⋊C₈	—	2	4	no	—
304	#20360	—	47	1	no	maximal, Sylow
305	C₂²×C₄₇	—	4	1	no	—
306	C₂²×C₄₇	—	4	1	no	—
307	C₂²×C₄₇	—	4	1	no	—
308	C₂²×C₄₇	—	4	1	no	—
309	C₂²×C₄₇	—	4	1	no	—
310	C₂²×C₄₇	—	4	1	no	—
311	C₂²×C₄₇	—	4	1	no	—
312	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
313	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
314	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
315	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
316	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
317	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
319	C₂×D₄₇	—	4	4	no	—
320	C₂×D₄₇	—	4	4	no	—
321	C₂×D₄₇	—	4	4	no	—
322	C₂×D₄₇	C₂×#95	1	8	yes	—
323	C₄×C₄₇	—	4	4	no	—
324	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
325	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
326	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
327	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
328	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
329	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
330	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
331	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
332	Dic₄₇	—	4	4	no	—
333	Dic₄₇	C₂×#95	1	8	yes	—
334	C₂×#568	—	47	1	no	—
335	C₂×#568	—	47	1	no	—
336	#3428	—	47	1	no	—
337	C₂×#344	—	47	8	no	—
338	C₂×#344	—	47	1	no	—
339	C₂×#344	—	47	1	no	—
340	C₂×#344	—	47	1	no	—
341	C₂×#344	D₄₇	1	1	yes	characteristic, complemented
342	C₂×C₄₇	—	2	1	no	—
343	C₂×C₄₇	—	2	1	no	—
344	C₂×C₄₇	—	2	1	no	—
345	C₂×C₄₇	—	2	1	no	—
346	C₂×C₄₇	—	2	1	no	—
347	C₂×C₄₇	—	2	1	no	—
348	C₂×C₄₇	—	2	1	no	—
349	C₂×C₄₇	C₂²×#95	1	1	yes	characteristic
350	D₄₇	—	2	8	no	—
351	C₂²×#41	—	47	1	no	—
352	#568	—	47	4	no	—
353	#568	—	47	4	no	—
354	#568	—	94	2	no	—
355	#568	—	94	2	no	—
356	#568	—	94	2	no	—
357	#568	—	94	2	no	—
358	#568	—	94	2	no	—
359	#568	—	94	2	no	—
360	C₂×#131	—	47	4	no	—
361	C₂×#131	—	47	4	no	—
362	C₂×#131	—	94	2	no	—
363	C₂×#131	—	94	2	no	—
364	C₂²×M₁₆	—	47	1	no	—
365	C₂²×M₁₆	—	47	4	no	—
366	C₂²×M₁₆	—	47	1	no	—
367	C₂²×M₁₆	—	47	4	no	—
368	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
369	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
370	#520	—	94	2	no	—
371	#520	—	94	2	no	—
372	#519	—	47	2	no	—
373	#518	—	47	2	no	—
374	#518	—	47	4	no	—
375	C₄×#41	—	94	2	no	—
376	C₄×#41	—	94	2	no	—
377	C₂×#117	—	47	1	no	—
378	C₂×#117	—	47	4	no	—
379	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
380	#344	—	47	4	no	—
381	#344	—	47	4	no	—
382	#344	—	47	4	no	—
383	#344	C₂×D₄₇	1	4	yes	—
384	C₄₇	#20360	1	1	yes	characteristic, complemented, Sylow
385	C₂×#41	—	47	2	no	—
386	C₂×#41	—	47	2	no	—
387	C₂×#41	—	47	2	no	—
388	C₂×#41	—	47	2	no	—
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	—	47	2	no	—
396	C₂×#41	—	47	2	no	—
397	C₂²×Q₈	—	47	1	no	—
398	C₂²×D₄	—	47	2	no	—
399	C₂²×D₄	—	47	1	no	—
400	C₂³×C₄	—	47	2	no	—
401	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
402	#131	—	94	8	no	—
403	#131	—	94	8	no	—
404	#131	—	94	8	no	—
405	#131	—	94	8	no	—
406	#131	—	94	8	no	—
407	#131	—	94	8	no	—
408	#131	—	94	8	no	—
409	#131	—	94	8	no	—
410	C₂×M₁₆	—	2	1	no	—
411	C₂×M₁₆	—	2	1	no	—
412	C₂×M₁₆	—	2	1	no	—
413	C₂×M₁₆	—	2	1	no	—
414	C₂×M₁₆	—	2	1	no	—
415	C₂×M₁₆	—	2	1	no	—
416	C₂×M₁₆	—	2	1	no	—
417	C₂×M₁₆	—	47	2	no	—
418	C₂×M₁₆	—	47	2	no	—
419	C₂×M₁₆	—	47	8	no	—
420	C₂×M₁₆	—	47	2	no	—
421	C₂×M₁₆	—	47	2	no	—
422	C₂×M₁₆	—	47	2	no	—
423	C₂×M₁₆	—	47	16	no	—
424	C₂×M₁₆	—	94	4	no	—
425	C₂×M₁₆	—	94	8	no	—
426	C₂×M₁₆	—	94	8	no	—
427	C₂×M₁₆	—	94	8	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	—	94	1	no	—
433	C₂×M₁₆	—	94	1	no	—
434	C₂×M₁₆	—	94	1	no	—
435	C₂×M₁₆	C₄×D₄₇	1	2	yes	complemented
436	C₂×M₁₆	C₄×D₄₇	1	2	yes	complemented
437	C₂×M₁₆	C₄×D₄₇	1	2	yes	complemented
438	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
439	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
440	C₂²×C₈	—	2	1	no	—
441	C₂²×C₈	—	47	2	no	—
442	C₂²×C₈	—	47	8	no	—
443	C₂²×C₈	—	94	4	no	—
444	C₂²×C₈	—	94	1	no	—
445	C₂²×C₈	C₄×D₄₇	1	2	yes	complemented
446	C₄×Q₈	—	94	4	no	—
447	C₄×Q₈	—	94	4	no	—
448	C₄×D₄	—	94	4	no	—
449	C₄×D₄	—	94	8	no	—
450	C₄×D₄	—	94	4	no	—
451	C₄×D₄	—	94	8	no	—
452	#117	—	2	1	no	—
453	#117	—	2	1	no	—
454	#117	—	47	2	no	—
455	#117	—	47	2	no	—
456	#117	—	47	8	no	—
457	#117	—	94	4	no	—
458	#117	—	94	4	no	—
459	#117	—	94	1	no	—
460	#117	—	94	1	no	—
461	#117	C₄×D₄₇	1	2	yes	—
462	#117	C₂²×D₄₇	1	2	yes	—
463	C₂×C₄⋊C₄	—	2	1	no	—
464	C₂×C₄⋊C₄	—	94	4	no	—
465	C₂×C₄⋊C₄	—	94	1	no	—
466	C₂×C₂²⋊C₄	—	47	2	no	—
467	C₂×C₂²⋊C₄	—	47	8	no	—
468	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
469	C₂×C₄²	—	2	1	no	—
470	C₂×C₄²	—	94	4	no	—
471	C₂×C₄²	—	94	1	no	—
472	C₂⁴	—	47	2	no	—
473	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
474	#41	—	47	4	no	—
475	#41	—	47	4	no	—
476	#41	—	47	4	no	—
477	#41	—	47	4	no	—
478	#41	—	47	4	no	—
479	#41	—	47	4	no	—
480	#41	—	47	4	no	—
481	#41	—	47	4	no	—
482	#41	—	47	4	no	—
483	#41	—	47	4	no	—
484	#41	—	47	4	no	—
485	#41	—	47	4	no	—
486	#41	—	47	4	no	—
487	#41	—	47	4	no	—
488	#41	—	47	4	no	—
489	#41	—	47	4	no	—
490	C₂×Q₈	—	47	2	no	—
491	C₂×Q₈	—	47	2	no	—
492	C₂×Q₈	—	47	2	no	—
493	C₂×Q₈	—	47	2	no	—
494	C₂×Q₈	—	47	2	no	—
495	C₂×Q₈	—	47	2	no	—
496	C₂×D₄	—	47	4	no	—
497	C₂×D₄	—	47	4	no	—
498	C₂×D₄	—	47	4	no	—
499	C₂×D₄	—	47	4	no	—
500	C₂×D₄	—	47	4	no	—
501	C₂×D₄	—	47	4	no	—
502	C₂×D₄	—	47	2	no	—
503	C₂×D₄	—	47	2	no	—
504	C₂×D₄	—	47	2	no	—
505	C₂×D₄	—	47	2	no	—
506	C₂×D₄	—	47	2	no	—
507	C₂×D₄	—	47	2	no	—
508	C₂²×C₄	—	2	2	no	—
509	C₂²×C₄	—	47	2	no	—
510	C₂²×C₄	—	47	4	no	—
511	C₂²×C₄	—	47	4	no	—
512	C₂²×C₄	—	47	4	no	—
513	C₂²×C₄	—	47	4	no	—
514	C₂²×C₄	—	47	4	no	—
515	C₂²×C₄	—	47	4	no	—
516	C₂²×C₄	—	94	8	no	—
517	C₂²×C₄	—	94	2	no	—
518	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
519	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
520	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
522	C₂²×C₄	C₂×C₄×D₄₇	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	—	2	2	no	—
538	M₁₆	—	2	2	no	—
539	M₁₆	—	47	4	no	—
540	M₁₆	—	94	16	no	—
541	M₁₆	—	94	16	no	—
542	M₁₆	—	94	2	no	—
543	M₁₆	—	94	2	no	—
544	M₁₆	—	94	2	no	—
545	M₁₆	—	94	2	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	4	no	—
556	C₂×C₈	—	94	16	no	—
557	C₂×C₈	—	94	16	no	—
558	C₂×C₈	—	94	2	no	—
559	C₂×C₈	—	94	2	no	—
560	C₂×C₈	—	94	2	no	—
561	C₂×C₈	—	94	2	no	—
562	C₂×C₈	—	94	2	no	—
563	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	94	8	no	—
567	C₄⋊C₄	—	94	2	no	—
568	C₄⋊C₄	—	94	2	no	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	47	4	no	—
571	C₂²⋊C₄	—	94	8	no	—
572	C₂²⋊C₄	—	94	2	no	—
573	C₂²⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
574	C₄²	—	2	2	no	—
575	C₄²	—	2	2	no	—
576	C₄²	—	94	8	no	—
577	C₄²	—	94	2	no	—
578	C₄²	—	94	2	no	—
579	C₂³	—	8	1	no	—
580	C₂³	—	47	4	no	—
581	C₂³	—	47	4	no	—
582	C₂³	—	47	4	no	—
583	C₂³	—	376	2	no	—
584	C₂³	C₄²×D₄₇	1	1	yes	characteristic
585	C₂³	C₄²×D₄₇	1	1	yes	characteristic
586	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
587	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
588	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
589	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
590	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
591	Q₈	—	47	4	no	—
592	Q₈	—	47	4	no	—
593	Q₈	—	47	4	no	—
594	Q₈	—	47	4	no	—
595	D₄	—	47	8	no	—
596	D₄	—	47	8	no	—
597	D₄	—	47	8	no	—
598	D₄	—	47	8	no	—
599	D₄	—	47	4	no	—
600	D₄	—	47	4	no	—
601	D₄	—	47	4	no	—
602	D₄	—	47	4	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	8	2	no	—
605	C₂×C₄	—	47	4	no	—
606	C₂×C₄	—	47	4	no	—
607	C₂×C₄	—	47	4	no	—
608	C₂×C₄	—	47	8	no	—
609	C₂×C₄	—	47	8	no	—
610	C₂×C₄	—	47	8	no	—
611	C₂×C₄	—	47	8	no	—
612	C₂×C₄	—	94	4	no	—
613	C₂×C₄	—	376	8	no	—
614	C₂×C₄	—	376	2	no	—
615	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
616	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
617	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
618	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
619	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
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	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
625	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
626	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
627	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
628	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
629	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
630	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
631	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
632	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
633	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
634	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
635	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
636	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
637	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
638	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
639	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
640	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
641	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
642	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
643	C₈	—	2	4	no	—
644	C₈	—	2	4	no	—
645	C₈	—	94	4	no	—
646	C₈	—	94	4	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	47	8	no	—
655	C₂²	—	188	4	no	—
656	C₂²	—	188	4	no	—
657	C₂²	—	188	4	no	—
658	C₂²	#95×D₄₇	1	1	yes	characteristic
659	C₂²	#95×D₄₇	1	1	yes	characteristic
660	C₂²	#95×D₄₇	1	1	yes	characteristic
661	C₂²	#95×D₄₇	1	1	yes	characteristic
662	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
663	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
664	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
665	C₄	—	4	4	no	—
666	C₄	—	47	8	no	—
667	C₄	—	188	4	no	—
668	C₄	#95×D₄₇	1	1	yes	characteristic
669	C₄	#95×D₄₇	1	1	yes	characteristic
670	C₄	#95×D₄₇	1	1	yes	characteristic
671	C₄	#95×D₄₇	1	1	yes	characteristic
672	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
673	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
674	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
675	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
676	C₂	—	2	1	no	—
677	C₂	—	2	1	no	—
678	C₂	—	2	1	no	—
679	C₂	—	2	1	no	—
680	C₂	—	2	1	no	—
681	C₂	—	2	1	no	—
682	C₂	—	2	1	no	—
683	C₂	—	94	8	no	—
684	C₂	C₂×#95×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×C₂²⋊C₄×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#344	C₂
socle	C₂×C₄₇	C₂²×#95
prime radical	C₂²×#10625350	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#344	D₄₇
hypocenter	C₄₇	#20360
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
4. C₂×#15688895	C₂	semidirect
5. C₂×#15688894	C₂	semidirect
6. C₂×#15688893	C₂	semidirect
7. #344×D₄₇	C₂	semidirect
8. C₂×C₄₇×#344	C₂	semidirect
16. #15689889	C₄	semidirect
17. #15689889	C₄	semidirect
19. C₂×#13094032	C₄	semidirect
21. C₂×#13094030	C₄	semidirect
73. C₂×#10625329	C₂×C₄	semidirect
74. C₂×#10625329	C₂×C₄	semidirect
75. C₂×#10625329	C₂×C₄	semidirect
79. C₂×#10625324	C₂×C₄	semidirect
83. M₁₆×D₄₇	C₂×C₄	semidirect
85. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
87. C₂×C₈×D₄₇	C₂×C₄	semidirect
115. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
116. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
117. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
121. C₂²×C₈×C₄₇	C₂×C₄	semidirect
341. C₂×#344	D₄₇	semidirect
384. C₄₇	#20360	semidirect
435. C₂×M₁₆	C₄×D₄₇	semidirect
436. C₂×M₁₆	C₄×D₄₇	semidirect
437. C₂×M₁₆	C₄×D₄₇	semidirect
445. C₂²×C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689889	2
#20256589	2
C₂×#15688895	2
C₂×#15688894	2
C₂×#15688893	2
#344×D₄₇	2
C₂×C₄₇×#344	2
#20360	47