Subgroups — C₂×#20243863 #26218137

Order 12032.

1654 conjugacy classes of subgroups.

The subgroup lattice has 760 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×#15689140	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689132	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13093943	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243863	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688894	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇⋊#338	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#137×C₄₇	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	C₂×#13093983	C₂²	1	1	yes	characteristic
20	#15689140	—	2	2	no	—
21	#15689140	C₂²	1	4	yes	—
22	C₂×#13093951	—	2	2	no	—
23	#15689132	—	2	2	no	—
24	#15689132	C₂²	1	4	yes	complemented
25	C₂×#13093948	—	2	2	no	—
26	C₂×#13093943	—	2	2	no	—
27	C₂×#13093943	—	2	2	no	—
28	C₂×#13093943	C₂²	1	4	yes	complemented
29	#15688894	C₂²	1	4	yes	complemented
30	C₄₇⋊#338	C₂²	1	4	yes	complemented
31	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
32	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#137×C₄₇	—	2	2	no	—
34	C₂×#137×C₄₇	—	2	2	no	—
35	C₂×#137×C₄₇	—	2	2	no	—
36	C₂×#137×C₄₇	—	2	2	no	—
37	C₂×#137×C₄₇	C₄	1	4	yes	complemented
38	C₂×#137×C₄₇	C₂²	1	4	yes	—
39	C₂²×Q₁₆×C₄₇	C₄	1	2	yes	complemented
40	C₂²×SD₁₆×C₄₇	C₄	1	2	yes	complemented
41	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
42	#13094031	—	2	8	no	—
43	#13094031	—	2	8	no	—
44	#13094031	—	2	8	no	—
45	#13094031	—	2	8	no	—
46	C₂×#10625329	—	2	4	no	—
47	C₂×#10625329	—	2	8	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	—	2	1	no	—
57	C₂×#10625329	—	2	1	no	—
58	C₂×#10625329	—	2	1	no	—
59	C₂×#10625329	—	2	1	no	—
60	C₂×#10625329	—	2	1	no	—
61	C₂×#10625329	D₄	1	2	yes	—
62	C₂×#10625329	D₄	1	2	yes	—
63	C₂×#10625329	D₄	1	2	yes	—
64	C₂×#10625329	C₂³	1	2	yes	—
65	C₂×#10625329	C₂³	1	2	yes	—
66	C₂×#10625329	C₂³	1	2	yes	—
67	C₂²×C₄₇⋊C₈	—	2	4	no	—
68	C₂²×C₄₇⋊C₈	—	2	1	no	—
69	C₂²×C₄₇⋊C₈	—	2	1	no	—
70	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
71	#13093983	—	2	1	no	—
72	#13093983	—	2	1	no	—
73	#13093983	—	2	1	no	—
74	#13093983	C₂³	1	2	yes	—
75	C₂×C₄⋊Dic₄₇	—	2	1	no	—
76	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
77	C₂×C₄×Dic₄₇	—	2	1	no	—
78	#13093951	—	2	8	no	—
79	#13093948	—	2	8	no	—
80	#13093943	—	2	8	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	—	2	1	no	—
86	C₂×#41×C₄₇	—	2	1	no	—
87	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
88	C₂×#41×C₄₇	D₄	1	2	yes	—
89	C₂×#41×C₄₇	D₄	1	2	yes	—
90	C₂×#41×C₄₇	D₄	1	2	yes	—
91	C₂×#41×C₄₇	D₄	1	2	yes	—
92	C₂×#41×C₄₇	C₂³	1	2	yes	—
93	C₂²×Q₈×C₄₇	—	2	1	no	—
94	C₂²×Q₈×C₄₇	—	2	1	no	—
95	C₂²×Q₈×C₄₇	—	2	1	no	—
96	C₂²×Q₈×C₄₇	—	2	1	no	—
97	C₂²×Q₈×C₄₇	—	2	1	no	—
98	C₂²×Q₈×C₄₇	—	2	1	no	—
99	C₂²×Q₈×C₄₇	—	2	1	no	—
100	C₂²×Q₈×C₄₇	—	2	1	no	—
101	C₂²×Q₈×C₄₇	—	2	1	no	—
102	C₂²×Q₈×C₄₇	—	2	1	no	—
103	C₂²×Q₈×C₄₇	—	2	1	no	—
104	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
105	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
106	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
107	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
108	C₂²×D₄×C₄₇	—	2	1	no	—
109	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
110	C₂³×C₄×C₄₇	—	2	1	no	—
111	C₂³×C₄×C₄₇	—	2	1	no	—
112	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
113	#137×C₄₇	—	2	8	no	—
114	#137×C₄₇	—	2	8	no	—
115	#137×C₄₇	—	2	8	no	—
116	#137×C₄₇	—	2	8	no	—
117	C₂×Q₁₆×C₄₇	—	2	4	no	—
118	C₂×Q₁₆×C₄₇	—	2	4	no	—
119	C₂×Q₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
120	C₂×SD₁₆×C₄₇	—	2	4	no	—
121	C₂×SD₁₆×C₄₇	—	2	4	no	—
122	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
123	C₂×M₁₆×C₄₇	—	2	1	no	—
124	C₂×M₁₆×C₄₇	—	2	1	no	—
125	C₂×M₁₆×C₄₇	—	2	1	no	—
126	C₂×M₁₆×C₄₇	—	2	1	no	—
127	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
128	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
129	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
130	C₂⁴×C₄₇	—	2	1	no	—
131	C₂⁴×C₄₇	#41	1	1	yes	characteristic
132	#41×C₄₇	—	2	2	no	—
133	#41×C₄₇	—	2	2	no	—
134	#41×C₄₇	—	2	2	no	—
135	#41×C₄₇	—	2	2	no	—
136	#41×C₄₇	—	2	2	no	—
137	#41×C₄₇	—	2	2	no	—
138	#41×C₄₇	—	2	2	no	—
139	#41×C₄₇	—	2	2	no	—
140	#41×C₄₇	—	2	2	no	—
141	#41×C₄₇	—	2	2	no	—
142	#41×C₄₇	—	2	2	no	—
143	#41×C₄₇	—	2	2	no	—
144	#41×C₄₇	C₂²⋊C₄	1	4	yes	—
145	#41×C₄₇	C₂²⋊C₄	1	4	yes	—
146	#41×C₄₇	C₂×D₄	1	4	yes	—
147	#41×C₄₇	C₂×D₄	1	4	yes	—
148	C₂×Q₈×C₄₇	—	2	1	no	—
149	C₂×Q₈×C₄₇	—	2	1	no	—
150	C₂×Q₈×C₄₇	—	2	1	no	—
151	C₂×Q₈×C₄₇	—	2	2	no	—
152	C₂×Q₈×C₄₇	—	2	2	no	—
153	C₂×Q₈×C₄₇	—	2	2	no	—
154	C₂×Q₈×C₄₇	—	2	2	no	—
155	C₂×Q₈×C₄₇	—	2	2	no	—
156	C₂×Q₈×C₄₇	—	2	2	no	—
157	C₂×Q₈×C₄₇	—	2	2	no	—
158	C₂×Q₈×C₄₇	—	2	2	no	—
159	C₂×Q₈×C₄₇	—	2	2	no	—
160	C₂×Q₈×C₄₇	—	2	2	no	—
161	C₂×Q₈×C₄₇	—	2	2	no	—
162	C₂×Q₈×C₄₇	—	2	2	no	—
163	C₂×Q₈×C₄₇	—	2	2	no	—
164	C₂×Q₈×C₄₇	—	2	2	no	—
165	C₂×Q₈×C₄₇	—	2	2	no	—
166	C₂×Q₈×C₄₇	—	4	1	no	—
167	C₂×Q₈×C₄₇	—	4	1	no	—
168	C₂×Q₈×C₄₇	—	4	1	no	—
169	C₂×Q₈×C₄₇	—	4	1	no	—
170	C₂×Q₈×C₄₇	—	4	1	no	—
171	C₂×Q₈×C₄₇	—	4	1	no	—
172	C₂×Q₈×C₄₇	—	4	1	no	—
173	C₂×Q₈×C₄₇	—	4	1	no	—
174	C₂×Q₈×C₄₇	—	4	1	no	—
175	C₂×Q₈×C₄₇	—	4	1	no	—
176	C₂×Q₈×C₄₇	—	4	1	no	—
177	C₂×Q₈×C₄₇	—	4	1	no	—
178	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
179	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
180	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
181	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
182	C₂×D₄×C₄₇	—	2	2	no	—
183	C₂×D₄×C₄₇	—	2	2	no	—
184	C₂×D₄×C₄₇	—	2	2	no	—
185	C₂×D₄×C₄₇	—	2	2	no	—
186	C₂×D₄×C₄₇	—	2	2	no	—
187	C₂×D₄×C₄₇	—	2	2	no	—
188	C₂×D₄×C₄₇	—	2	1	no	—
189	C₂×D₄×C₄₇	—	2	1	no	—
190	C₂×D₄×C₄₇	—	2	1	no	—
191	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
192	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
193	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
194	C₂²×C₄×C₄₇	—	2	1	no	—
195	C₂²×C₄×C₄₇	—	2	2	no	—
196	C₂²×C₄×C₄₇	—	2	2	no	—
197	C₂²×C₄×C₄₇	—	2	2	no	—
198	C₂²×C₄×C₄₇	—	2	2	no	—
199	C₂²×C₄×C₄₇	—	2	2	no	—
200	C₂²×C₄×C₄₇	—	2	2	no	—
201	C₂²×C₄×C₄₇	—	2	2	no	—
202	C₂²×C₄×C₄₇	—	2	2	no	—
203	C₂²×C₄×C₄₇	—	2	2	no	—
204	C₂²×C₄×C₄₇	—	4	1	no	—
205	C₂²×C₄×C₄₇	—	4	1	no	—
206	C₂²×C₄×C₄₇	—	4	1	no	—
207	C₂²×C₄×C₄₇	—	4	1	no	—
208	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
209	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
219	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
220	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
221	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
222	C₂²×Dic₄₇	—	4	1	no	—
223	Q₁₆×C₄₇	—	2	16	no	—
224	SD₁₆×C₄₇	—	2	16	no	—
225	M₁₆×C₄₇	—	2	2	no	—
226	M₁₆×C₄₇	—	2	2	no	—
227	M₁₆×C₄₇	—	2	2	no	—
228	M₁₆×C₄₇	—	2	2	no	—
229	C₂×C₈×C₄₇	—	2	2	no	—
230	C₂×C₈×C₄₇	—	2	2	no	—
231	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
232	C₂²⋊Dic₄₇	—	2	2	no	—
233	C₂²⋊Dic₄₇	—	4	1	no	—
234	C₄⋊Dic₄₇	—	2	2	no	—
235	C₄⋊Dic₄₇	—	4	1	no	—
236	C₄×Dic₄₇	—	2	2	no	—
237	C₄×Dic₄₇	—	4	1	no	—
238	#10625329	—	2	16	no	—
239	#10625329	—	2	2	no	—
240	#10625329	—	2	2	no	—
241	#10625329	—	2	2	no	—
242	#10625329	—	2	2	no	—
243	#10625329	—	2	2	no	—
244	#10625329	—	2	2	no	—
245	#10625329	—	2	2	no	—
246	#10625329	—	2	2	no	—
247	#10625329	—	2	2	no	—
248	#10625329	—	4	1	no	—
249	#10625329	—	4	1	no	—
250	#10625329	C₂×D₄	1	4	yes	—
251	C₂×C₄₇⋊C₈	—	2	16	no	—
252	C₂×C₄₇⋊C₈	—	2	2	no	—
253	C₂×C₄₇⋊C₈	—	2	2	no	—
254	C₂×C₄₇⋊C₈	—	2	2	no	—
255	C₂×C₄₇⋊C₈	—	2	2	no	—
256	C₂×C₄₇⋊C₈	—	2	2	no	—
257	C₂×C₄₇⋊C₈	—	2	2	no	—
258	C₂×C₄₇⋊C₈	—	4	1	no	—
259	C₂×C₄₇⋊C₈	—	4	1	no	—
260	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
261	C₂³×C₄₇	—	2	2	no	—
262	C₂³×C₄₇	—	2	2	no	—
263	C₂³×C₄₇	—	2	2	no	—
264	C₂³×C₄₇	—	4	2	no	—
265	C₂³×C₄₇	—	8	2	no	—
266	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
267	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
268	C₂³×C₄₇	#121	1	1	yes	characteristic
269	C₂³×C₄₇	#121	1	1	yes	characteristic
270	C₂³×C₄₇	#123	1	1	yes	characteristic
271	C₂³×C₄₇	#123	1	1	yes	characteristic
272	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
273	Q₈×C₄₇	—	2	2	no	—
274	Q₈×C₄₇	—	2	2	no	—
275	Q₈×C₄₇	—	2	2	no	—
276	Q₈×C₄₇	—	2	4	no	—
277	Q₈×C₄₇	—	2	4	no	—
278	Q₈×C₄₇	—	4	2	no	—
279	Q₈×C₄₇	—	4	2	no	—
280	Q₈×C₄₇	—	4	2	no	—
281	Q₈×C₄₇	—	4	2	no	—
282	Q₈×C₄₇	—	4	2	no	—
283	Q₈×C₄₇	—	4	2	no	—
284	Q₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
285	D₄×C₄₇	—	2	4	no	—
286	D₄×C₄₇	—	2	4	no	—
287	D₄×C₄₇	—	2	4	no	—
288	D₄×C₄₇	—	2	4	no	—
289	D₄×C₄₇	—	2	2	no	—
290	D₄×C₄₇	—	2	2	no	—
291	D₄×C₄₇	—	2	2	no	—
292	D₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
293	C₂×C₄×C₄₇	—	2	2	no	—
294	C₂×C₄×C₄₇	—	2	2	no	—
295	C₂×C₄×C₄₇	—	2	2	no	—
296	C₂×C₄×C₄₇	—	2	4	no	—
297	C₂×C₄×C₄₇	—	2	4	no	—
298	C₂×C₄×C₄₇	—	2	4	no	—
299	C₂×C₄×C₄₇	—	2	4	no	—
300	C₂×C₄×C₄₇	—	2	4	no	—
301	C₂×C₄×C₄₇	—	4	2	no	—
302	C₂×C₄×C₄₇	—	4	2	no	—
303	C₂×C₄×C₄₇	—	4	2	no	—
304	C₂×C₄×C₄₇	—	4	2	no	—
305	C₂×C₄×C₄₇	—	4	2	no	—
306	C₂×C₄×C₄₇	—	4	2	no	—
307	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
312	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
313	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
314	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
315	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
316	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
317	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
318	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
319	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
320	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
321	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
322	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
323	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
324	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
325	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
326	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
327	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
328	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
329	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
330	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
335	C₂×Dic₄₇	—	4	2	no	—
336	C₂×Dic₄₇	—	8	2	no	—
337	C₈×C₄₇	—	2	4	no	—
338	C₄₇⋊C₈	—	2	4	no	—
339	C₄₇⋊C₈	—	2	4	no	—
340	C₄₇⋊C₈	—	4	2	no	—
341	C₂×#1902	—	47	1	no	maximal, Sylow
342	C₂²×C₄₇	—	2	2	no	—
343	C₂²×C₄₇	—	2	2	no	—
344	C₂²×C₄₇	—	2	2	no	—
345	C₂²×C₄₇	—	2	4	no	—
346	C₂²×C₄₇	—	4	1	no	—
347	C₂²×C₄₇	—	4	1	no	—
348	C₂²×C₄₇	—	4	1	no	—
349	C₂²×C₄₇	—	4	1	no	—
350	C₂²×C₄₇	—	4	4	no	—
351	C₂²×C₄₇	—	8	2	no	—
352	C₂²×C₄₇	—	8	2	no	—
353	C₂²×C₄₇	#386	1	1	yes	characteristic
354	C₂²×C₄₇	#386	1	1	yes	characteristic
355	C₂²×C₄₇	#386	1	1	yes	characteristic
356	C₂²×C₄₇	#386	1	1	yes	characteristic
357	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
358	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
359	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
360	C₄×C₄₇	—	2	4	no	—
361	C₄×C₄₇	—	4	4	no	—
362	C₄×C₄₇	#386	1	1	yes	characteristic
363	C₄×C₄₇	#386	1	1	yes	characteristic
364	C₄×C₄₇	#386	1	1	yes	characteristic
365	C₄×C₄₇	#386	1	1	yes	characteristic
366	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
367	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
368	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
369	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
370	Dic₄₇	—	8	2	no	—
371	C₂²×#137	D₄₇	1	1	yes	characteristic
372	C₂×#568	—	47	1	no	—
373	C₂×#421	—	47	1	no	—
374	C₂×#419	—	47	1	no	—
375	C₂²×#101	—	47	1	no	—
376	#1902	—	47	8	no	—
377	C₂×#344	—	47	1	no	—
378	C₂×#338	—	47	1	no	—
379	C₂×C₄₇	—	2	1	no	—
380	C₂×C₄₇	—	2	1	no	—
381	C₂×C₄₇	—	2	1	no	—
382	C₂×C₄₇	—	2	1	no	—
383	C₂×C₄₇	—	2	1	no	—
384	C₂×C₄₇	—	2	1	no	—
385	C₂×C₄₇	—	4	4	no	—
386	C₂×C₄₇	#1902	1	2	yes	complemented
387	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
388	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
389	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
390	C₂×#137	—	2	2	no	—
391	C₂×#137	—	2	2	no	—
392	C₂×#137	—	2	2	no	—
393	C₂×#137	—	2	2	no	—
394	C₂×#137	Dic₄₇	1	4	yes	complemented
395	C₂×#137	C₂×D₄₇	1	4	yes	—
396	C₂²×Q₁₆	Dic₄₇	1	2	yes	complemented
397	C₂²×SD₁₆	Dic₄₇	1	2	yes	complemented
398	#568	—	47	4	no	—
399	#568	—	94	2	no	—
400	#568	—	94	2	no	—
401	#568	—	94	2	no	—
402	C₂×#131	—	94	2	no	—
403	C₂×#131	—	94	2	no	—
404	C₂²×M₁₆	—	47	1	no	—
405	C₂²×M₁₆	—	47	1	no	—
406	C₂²×M₁₆	—	47	1	no	—
407	C₂²×M₁₆	—	94	2	no	—
408	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
409	C₂×#117	—	47	1	no	—
410	#421	—	47	4	no	—
411	#421	—	94	2	no	—
412	C₂×#104	—	94	2	no	—
413	#419	—	47	4	no	—
414	#419	—	94	2	no	—
415	C₂×#103	—	94	2	no	—
416	C₂×#101	—	47	4	no	—
417	C₂×#101	—	94	2	no	—
418	C₂×#101	—	94	2	no	—
419	#344	—	47	4	no	—
420	#338	—	47	4	no	—
421	C₄₇	C₂×#1902	1	1	yes	characteristic, complemented, Sylow
422	C₂×#41	—	2	1	no	—
423	C₂×#41	—	2	1	no	—
424	C₂×#41	—	2	1	no	—
425	C₂×#41	—	2	1	no	—
426	C₂×#41	—	2	1	no	—
427	C₂×#41	—	2	1	no	—
428	C₂×#41	C₂×Dic₄₇	1	2	yes	—
429	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
430	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
431	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
432	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
433	C₂×#41	C₂²×D₄₇	1	2	yes	—
434	C₂²×Q₈	—	2	1	no	—
435	C₂²×Q₈	—	2	1	no	—
436	C₂²×Q₈	—	2	1	no	—
437	C₂²×Q₈	—	2	1	no	—
438	C₂²×Q₈	—	2	1	no	—
439	C₂²×Q₈	—	2	1	no	—
440	C₂²×Q₈	—	2	1	no	—
441	C₂²×Q₈	—	2	1	no	—
442	C₂²×Q₈	—	2	1	no	—
443	C₂²×Q₈	—	2	1	no	—
444	C₂²×Q₈	—	2	1	no	—
445	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
446	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
447	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
448	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
449	C₂²×D₄	—	2	1	no	—
450	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
451	C₂³×C₄	—	2	1	no	—
452	C₂³×C₄	—	2	1	no	—
453	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
454	#137	—	2	8	no	—
455	#137	—	2	8	no	—
456	#137	—	2	8	no	—
457	#137	—	2	8	no	—
458	C₂×Q₁₆	—	2	4	no	—
459	C₂×Q₁₆	—	2	4	no	—
460	C₂×Q₁₆	C₂×Dic₄₇	1	8	yes	complemented
461	C₂×SD₁₆	—	2	4	no	—
462	C₂×SD₁₆	—	2	4	no	—
463	C₂×SD₁₆	C₂×Dic₄₇	1	8	yes	complemented
464	#131	—	94	8	no	—
465	#131	—	94	8	no	—
466	#131	—	94	8	no	—
467	#131	—	94	8	no	—
468	C₂×M₁₆	—	2	1	no	—
469	C₂×M₁₆	—	2	1	no	—
470	C₂×M₁₆	—	2	1	no	—
471	C₂×M₁₆	—	2	1	no	—
472	C₂×M₁₆	—	47	2	no	—
473	C₂×M₁₆	—	47	2	no	—
474	C₂×M₁₆	—	47	2	no	—
475	C₂×M₁₆	—	47	2	no	—
476	C₂×M₁₆	—	47	2	no	—
477	C₂×M₁₆	—	47	2	no	—
478	C₂×M₁₆	—	94	8	no	—
479	C₂×M₁₆	—	94	4	no	—
480	C₂×M₁₆	—	94	8	no	—
481	C₂×M₁₆	—	94	1	no	—
482	C₂×M₁₆	—	94	1	no	—
483	C₂×M₁₆	—	94	1	no	—
484	C₂×M₁₆	—	94	1	no	—
485	C₂×M₁₆	—	94	1	no	—
486	C₂×M₁₆	—	94	1	no	—
487	C₂×M₁₆	—	94	1	no	—
488	C₂×M₁₆	—	94	1	no	—
489	C₂×M₁₆	—	94	1	no	—
490	C₂×M₁₆	—	94	1	no	—
491	C₂×M₁₆	—	94	1	no	—
492	C₂×M₁₆	—	94	1	no	—
493	C₂×M₁₆	C₂×Dic₄₇	1	2	yes	—
494	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
495	C₂²×C₈	—	47	2	no	—
496	C₂²×C₈	—	94	4	no	—
497	C₂²×C₈	—	94	1	no	—
498	C₂²×C₈	—	94	1	no	—
499	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
500	#117	—	47	2	no	—
501	#117	—	94	1	no	—
502	#117	—	94	1	no	—
503	#117	—	94	1	no	—
504	C₂×C₄⋊C₄	—	94	1	no	—
505	C₂×C₂²⋊C₄	—	94	1	no	—
506	C₂×C₄²	—	94	1	no	—
507	#104	—	94	8	no	—
508	#103	—	94	8	no	—
509	#101	—	94	8	no	—
510	C₂⁴	—	2	1	no	—
511	C₂⁴	#10625352	1	1	yes	characteristic
512	#41	—	2	2	no	—
513	#41	—	2	2	no	—
514	#41	—	2	2	no	—
515	#41	—	2	2	no	—
516	#41	—	2	2	no	—
517	#41	—	2	2	no	—
518	#41	—	2	2	no	—
519	#41	—	2	2	no	—
520	#41	—	2	2	no	—
521	#41	—	2	2	no	—
522	#41	—	2	2	no	—
523	#41	—	2	2	no	—
524	#41	C₂²⋊Dic₄₇	1	4	yes	—
525	#41	C₂²⋊Dic₄₇	1	4	yes	—
526	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
527	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
528	C₂×Q₈	—	2	1	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	2	no	—
537	C₂×Q₈	—	2	2	no	—
538	C₂×Q₈	—	2	2	no	—
539	C₂×Q₈	—	2	2	no	—
540	C₂×Q₈	—	2	2	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	2	no	—
543	C₂×Q₈	—	2	2	no	—
544	C₂×Q₈	—	2	2	no	—
545	C₂×Q₈	—	2	2	no	—
546	C₂×Q₈	—	4	1	no	—
547	C₂×Q₈	—	4	1	no	—
548	C₂×Q₈	—	4	1	no	—
549	C₂×Q₈	—	4	1	no	—
550	C₂×Q₈	—	4	1	no	—
551	C₂×Q₈	—	4	1	no	—
552	C₂×Q₈	—	4	1	no	—
553	C₂×Q₈	—	4	1	no	—
554	C₂×Q₈	—	4	1	no	—
555	C₂×Q₈	—	4	1	no	—
556	C₂×Q₈	—	4	1	no	—
557	C₂×Q₈	—	4	1	no	—
558	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
559	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
560	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
561	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	2	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
572	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
573	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	4	1	no	—
585	C₂²×C₄	—	4	1	no	—
586	C₂²×C₄	—	4	1	no	—
587	C₂²×C₄	—	4	1	no	—
588	C₂²×C₄	—	188	1	no	—
589	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
590	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
591	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
592	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
593	C₂²×C₄	#10625352	1	1	yes	characteristic
594	C₂²×C₄	#10625352	1	1	yes	characteristic
595	C₂²×C₄	#10625352	1	1	yes	characteristic
596	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
597	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
598	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
599	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
600	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
601	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
602	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
603	Q₁₆	—	2	16	no	—
604	SD₁₆	—	2	16	no	—
605	M₁₆	—	2	2	no	—
606	M₁₆	—	2	2	no	—
607	M₁₆	—	2	2	no	—
608	M₁₆	—	2	2	no	—
609	M₁₆	—	47	4	no	—
610	M₁₆	—	94	16	no	—
611	M₁₆	—	94	2	no	—
612	M₁₆	—	94	2	no	—
613	M₁₆	—	94	2	no	—
614	M₁₆	—	94	2	no	—
615	M₁₆	—	94	2	no	—
616	M₁₆	—	94	2	no	—
617	M₁₆	—	94	2	no	—
618	M₁₆	—	94	2	no	—
619	M₁₆	—	94	2	no	—
620	M₁₆	—	188	1	no	—
621	M₁₆	—	188	1	no	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	2	no	—
624	C₂×C₈	—	47	4	no	—
625	C₂×C₈	—	94	16	no	—
626	C₂×C₈	—	94	2	no	—
627	C₂×C₈	—	94	2	no	—
628	C₂×C₈	—	94	2	no	—
629	C₂×C₈	—	94	2	no	—
630	C₂×C₈	—	94	2	no	—
631	C₂×C₈	—	94	2	no	—
632	C₂×C₈	—	188	1	no	—
633	C₂×C₈	—	188	1	no	—
634	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
635	C₄⋊C₄	—	94	2	no	—
636	C₄⋊C₄	—	188	1	no	—
637	C₂²⋊C₄	—	94	2	no	—
638	C₂²⋊C₄	—	188	1	no	—
639	C₄²	—	94	2	no	—
640	C₄²	—	188	1	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	4	2	no	—
645	C₂³	—	8	2	no	—
646	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
647	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
648	C₂³	#13093996	1	1	yes	characteristic
649	C₂³	#13093996	1	1	yes	characteristic
650	C₂³	#13094005	1	1	yes	characteristic
651	C₂³	#13094005	1	1	yes	characteristic
652	C₂³	C₂×#10625352	1	1	yes	characteristic
653	Q₈	—	2	2	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	2	4	no	—
657	Q₈	—	2	4	no	—
658	Q₈	—	4	2	no	—
659	Q₈	—	4	2	no	—
660	Q₈	—	4	2	no	—
661	Q₈	—	4	2	no	—
662	Q₈	—	4	2	no	—
663	Q₈	—	4	2	no	—
664	Q₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
665	D₄	—	2	4	no	—
666	D₄	—	2	4	no	—
667	D₄	—	2	4	no	—
668	D₄	—	2	4	no	—
669	D₄	—	2	2	no	—
670	D₄	—	2	2	no	—
671	D₄	—	2	2	no	—
672	D₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	4	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	4	2	no	—
687	C₂×C₄	—	376	2	no	—
688	C₂×C₄	—	188	2	no	—
689	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
690	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
691	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
692	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
693	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
694	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
695	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
696	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
697	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
698	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
699	C₂×C₄	#13093992	1	1	yes	characteristic
700	C₂×C₄	#13093992	1	1	yes	characteristic
701	C₂×C₄	#13093992	1	1	yes	characteristic
702	C₂×C₄	#13093992	1	1	yes	characteristic
703	C₂×C₄	#13093996	1	1	yes	characteristic
704	C₂×C₄	#13093996	1	1	yes	characteristic
705	C₂×C₄	#13093996	1	1	yes	characteristic
706	C₂×C₄	#13093996	1	1	yes	characteristic
707	C₂×C₄	#13093996	1	1	yes	characteristic
708	C₂×C₄	#13093996	1	1	yes	characteristic
709	C₂×C₄	#13094005	1	1	yes	characteristic
710	C₂×C₄	#13094005	1	1	yes	characteristic
711	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
712	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
713	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
714	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
715	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
716	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
717	C₈	—	2	4	no	—
718	C₈	—	94	4	no	—
719	C₈	—	94	4	no	—
720	C₈	—	188	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	4	no	—
730	C₂²	—	8	2	no	—
731	C₂²	—	8	2	no	—
732	C₂²	#15689003	1	1	yes	characteristic
733	C₂²	#15689003	1	1	yes	characteristic
734	C₂²	#15689003	1	1	yes	characteristic
735	C₂²	#15689003	1	1	yes	characteristic
736	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
737	C₂²	C₂×#13093996	1	1	yes	characteristic
738	C₂²	C₂×#13094005	1	1	yes	characteristic
739	C₄	—	2	4	no	—
740	C₄	—	4	4	no	—
741	C₄	—	376	2	no	—
742	C₄	#15689003	1	1	yes	characteristic
743	C₄	#15689003	1	1	yes	characteristic
744	C₄	#15689003	1	1	yes	characteristic
745	C₄	#15689003	1	1	yes	characteristic
746	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
747	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
748	C₄	C₂×#13093992	1	1	yes	characteristic
749	C₄	C₂×#13093996	1	1	yes	characteristic
750	C₂	—	2	1	no	—
751	C₂	—	2	1	no	—
752	C₂	—	2	1	no	—
753	C₂	—	2	1	no	—
754	C₂	—	2	1	no	—
755	C₂	—	2	1	no	—
756	C₂	—	4	4	no	—
757	C₂	#20243863	1	2	yes	direct product factor
758	C₂	C₂×#15689003	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#15689003
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#137×C₄₇	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#137	D₄₇
hypocenter	C₄₇	C₂×#1902
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂²×#137

Complements

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

N	H ≅ G/N	type
3. C₂×#15689132	C₂	semidirect
4. C₂²×#13093943	C₂	semidirect
5. #20243863	C₂	direct (N × H)
6. C₂×#15688894	C₂	semidirect
7. C₂×C₄₇⋊#338	C₂	semidirect
24. #15689132	C₂²	semidirect
28. C₂×#13093943	C₂²	semidirect
29. #15688894	C₂²	semidirect
30. C₄₇⋊#338	C₂²	semidirect
37. C₂×#137×C₄₇	C₄	semidirect
39. C₂²×Q₁₆×C₄₇	C₄	semidirect
40. C₂²×SD₁₆×C₄₇	C₄	semidirect
119. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
122. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
386. C₂×C₄₇	#1902	semidirect
394. C₂×#137	Dic₄₇	semidirect
396. C₂²×Q₁₆	Dic₄₇	semidirect
397. C₂²×SD₁₆	Dic₄₇	semidirect
421. C₄₇	C₂×#1902	semidirect
460. C₂×Q₁₆	C₂×Dic₄₇	semidirect
463. C₂×SD₁₆	C₂×Dic₄₇	semidirect
757. C₂	#20243863	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×#15689140	2
C₂×#15689132	2
C₂²×#13093943	2
#20243863	2
C₂×#15688894	2
C₂×C₄₇⋊#338	2
C₂²×#137×C₄₇	2
C₂×#1902	47

Subgroups — C2×#20243863 #26218137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243863 #26218137