Subgroups — C₂×#20243440 #26215938

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×#13094031	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×#15689140	C₂	1	1	yes	maximal, characteristic
5	#20243440	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688894	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688893	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#421	C₂	1	1	yes	maximal, characteristic
9	C₂×#13094031	—	2	1	no	—
10	C₂×#13094031	—	2	1	no	—
11	C₂×#13094031	—	2	2	no	—
12	C₂×#13094031	—	2	2	no	—
13	C₂×#13094031	C₄	1	2	yes	complemented
14	C₂×#13094031	C₄	1	2	yes	complemented
15	C₂×#13094031	C₄	1	4	yes	complemented
16	C₂×#13094031	C₂²	1	4	yes	—
17	C₂²×#10625329	—	2	1	no	—
18	C₂²×#10625329	C₂²	1	1	yes	characteristic
19	C₂²×#10625329	C₂²	1	1	yes	characteristic
20	C₂³×C₄₇⋊C₈	—	2	1	no	—
21	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
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	#15689140	—	2	2	no	—
32	#15689140	C₂²	1	4	yes	—
33	C₂×#13093951	—	2	2	no	—
34	#15688894	C₂²	1	4	yes	complemented
35	#15688893	C₂²	1	4	yes	complemented
36	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
37	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#421	—	2	2	no	—
40	C₄₇×#421	C₂²	1	4	yes	—
41	C₂×#104×C₄₇	—	2	2	no	—
42	#13094031	—	2	4	no	—
43	#13094031	—	2	4	no	—
44	#13094031	—	2	4	no	—
45	#13094031	—	2	4	no	—
46	#13094031	—	2	4	no	—
47	#13094031	—	2	4	no	—
48	#13094031	C₂×C₄	1	8	yes	complemented
49	#13094031	C₂×C₄	1	8	yes	complemented
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	2	no	—
55	C₂×#10625329	—	2	2	no	—
56	C₂×#10625329	—	2	4	no	—
57	C₂×#10625329	—	2	4	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	C₂×C₄	1	2	yes	—
63	C₂×#10625329	C₂×C₄	1	2	yes	—
64	C₂×#10625329	C₂³	1	2	yes	—
65	C₂×#10625329	C₂³	1	2	yes	—
66	C₂²×C₄₇⋊C₈	—	2	1	no	—
67	C₂²×C₄₇⋊C₈	—	2	2	no	—
68	C₂²×C₄₇⋊C₈	—	2	2	no	—
69	C₂²×C₄₇⋊C₈	—	2	4	no	—
70	C₂²×C₄₇⋊C₈	—	2	4	no	—
71	C₂²×C₄₇⋊C₈	—	2	1	no	—
72	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
75	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
76	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
77	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
78	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
79	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
80	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
81	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
82	#13093983	—	2	1	no	—
83	#13093983	—	2	1	no	—
84	#13093983	—	2	1	no	—
85	#13093983	C₂³	1	2	yes	—
86	C₂×C₄⋊Dic₄₇	—	2	1	no	—
87	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
88	C₂×C₄×Dic₄₇	—	2	1	no	—
89	#13093959	—	2	4	no	—
90	#13093959	—	2	4	no	—
91	#13093957	—	2	4	no	—
92	#13093955	—	2	4	no	—
93	#13093951	—	2	8	no	—
94	C₂×#41×C₄₇	—	2	1	no	—
95	C₂×#41×C₄₇	—	2	1	no	—
96	C₂×#41×C₄₇	—	2	1	no	—
97	C₂×#41×C₄₇	—	2	1	no	—
98	C₂×#41×C₄₇	—	2	1	no	—
99	C₂×#41×C₄₇	—	2	1	no	—
100	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
101	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
102	C₂×#41×C₄₇	D₄	1	2	yes	—
103	C₂×#41×C₄₇	D₄	1	2	yes	—
104	C₂×#41×C₄₇	Q₈	1	2	yes	—
105	C₂×#41×C₄₇	C₂³	1	2	yes	—
106	C₂²×Q₈×C₄₇	Q₈	1	1	yes	characteristic
107	C₂²×D₄×C₄₇	—	2	1	no	—
108	C₂²×D₄×C₄₇	Q₈	1	1	yes	characteristic
109	C₂³×C₄×C₄₇	—	2	1	no	—
110	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
116	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
117	C₂²×C₈×C₄₇	—	2	1	no	—
118	#117×C₄₇	—	2	1	no	—
119	#117×C₄₇	—	2	1	no	—
120	#117×C₄₇	—	2	1	no	—
121	#117×C₄₇	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
123	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
124	C₂×C₄²×C₄₇	—	2	1	no	—
125	#104×C₄₇	—	2	8	no	—
126	C₂⁴×C₄₇	—	2	1	no	—
127	C₂⁴×C₄₇	#41	1	1	yes	characteristic
128	#41×C₄₇	—	2	2	no	—
129	#41×C₄₇	—	2	2	no	—
130	#41×C₄₇	—	2	2	no	—
131	#41×C₄₇	—	2	2	no	—
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	C₄⋊C₄	1	4	yes	—
141	#41×C₄₇	C₄⋊C₄	1	4	yes	—
142	#41×C₄₇	C₂²×C₄	1	4	yes	—
143	#41×C₄₇	C₂×D₄	1	4	yes	—
144	C₂×Q₈×C₄₇	—	2	1	no	—
145	C₂×Q₈×C₄₇	—	2	1	no	—
146	C₂×Q₈×C₄₇	—	2	1	no	—
147	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
148	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
149	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	—
150	C₂×D₄×C₄₇	—	2	2	no	—
151	C₂×D₄×C₄₇	—	2	2	no	—
152	C₂×D₄×C₄₇	—	2	2	no	—
153	C₂×D₄×C₄₇	—	2	2	no	—
154	C₂×D₄×C₄₇	—	2	2	no	—
155	C₂×D₄×C₄₇	—	2	2	no	—
156	C₂×D₄×C₄₇	—	2	1	no	—
157	C₂×D₄×C₄₇	—	2	1	no	—
158	C₂×D₄×C₄₇	—	2	1	no	—
159	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
160	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
161	C₂×D₄×C₄₇	C₂×Q₈	1	2	yes	—
162	C₂²×C₄×C₄₇	—	2	1	no	—
163	C₂²×C₄×C₄₇	—	2	2	no	—
164	C₂²×C₄×C₄₇	—	2	2	no	—
165	C₂²×C₄×C₄₇	—	2	2	no	—
166	C₂²×C₄×C₄₇	—	2	2	no	—
167	C₂²×C₄×C₄₇	—	2	2	no	—
168	C₂²×C₄×C₄₇	—	2	2	no	—
169	C₂²×C₄×C₄₇	—	4	1	no	—
170	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
179	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
180	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
181	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
182	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
183	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
184	C₂²×Dic₄₇	—	4	1	no	—
185	M₁₆×C₄₇	—	2	2	no	—
186	M₁₆×C₄₇	—	2	2	no	—
187	M₁₆×C₄₇	—	4	1	no	—
188	M₁₆×C₄₇	—	4	1	no	—
189	C₂×C₈×C₄₇	—	2	2	no	—
190	C₂×C₈×C₄₇	—	4	1	no	—
191	C₂×C₈×C₄₇	—	4	1	no	—
192	C₄⋊C₄×C₄₇	—	2	2	no	—
193	C₄⋊C₄×C₄₇	—	4	1	no	—
194	C₂²⋊C₄×C₄₇	—	2	2	no	—
195	C₂²⋊C₄×C₄₇	—	4	1	no	—
196	C₄²×C₄₇	—	2	2	no	—
197	C₄²×C₄₇	—	4	1	no	—
198	C₂²⋊Dic₄₇	—	2	2	no	—
199	C₂²⋊Dic₄₇	—	4	1	no	—
200	C₄⋊Dic₄₇	—	2	2	no	—
201	C₄⋊Dic₄₇	—	4	1	no	—
202	C₄×Dic₄₇	—	2	2	no	—
203	C₄×Dic₄₇	—	4	1	no	—
204	#10625329	—	2	2	no	—
205	#10625329	—	2	2	no	—
206	#10625329	—	2	2	no	—
207	#10625329	—	2	8	no	—
208	#10625329	—	2	8	no	—
209	#10625329	—	2	2	no	—
210	#10625329	—	2	2	no	—
211	#10625329	—	4	1	no	—
212	#10625329	—	4	1	no	—
213	#10625329	C₂²×C₄	1	4	yes	—
214	C₂×C₄₇⋊C₈	—	2	2	no	—
215	C₂×C₄₇⋊C₈	—	2	2	no	—
216	C₂×C₄₇⋊C₈	—	2	2	no	—
217	C₂×C₄₇⋊C₈	—	2	8	no	—
218	C₂×C₄₇⋊C₈	—	2	8	no	—
219	C₂×C₄₇⋊C₈	—	2	2	no	—
220	C₂×C₄₇⋊C₈	—	4	1	no	—
221	C₂×C₄₇⋊C₈	—	4	1	no	—
222	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	2	yes	—
225	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	2	yes	—
233	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
234	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
235	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
236	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
237	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
238	C₂³×C₄₇	—	2	2	no	—
239	C₂³×C₄₇	—	2	2	no	—
240	C₂³×C₄₇	—	2	2	no	—
241	C₂³×C₄₇	—	4	2	no	—
242	C₂³×C₄₇	—	4	4	no	—
243	C₂³×C₄₇	#117	1	1	yes	characteristic
244	C₂³×C₄₇	#117	1	1	yes	characteristic
245	C₂³×C₄₇	#121	1	1	yes	characteristic
246	C₂³×C₄₇	#121	1	1	yes	characteristic
247	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
250	Q₈×C₄₇	—	2	2	no	—
251	Q₈×C₄₇	—	2	2	no	—
252	Q₈×C₄₇	—	2	2	no	—
253	Q₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
254	D₄×C₄₇	—	2	4	no	—
255	D₄×C₄₇	—	2	4	no	—
256	D₄×C₄₇	—	2	4	no	—
257	D₄×C₄₇	—	2	4	no	—
258	D₄×C₄₇	—	2	2	no	—
259	D₄×C₄₇	—	2	2	no	—
260	D₄×C₄₇	—	2	2	no	—
261	D₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
262	C₂×C₄×C₄₇	—	2	2	no	—
263	C₂×C₄×C₄₇	—	2	2	no	—
264	C₂×C₄×C₄₇	—	2	2	no	—
265	C₂×C₄×C₄₇	—	2	4	no	—
266	C₂×C₄×C₄₇	—	2	4	no	—
267	C₂×C₄×C₄₇	—	2	4	no	—
268	C₂×C₄×C₄₇	—	2	4	no	—
269	C₂×C₄×C₄₇	—	4	2	no	—
270	C₂×C₄×C₄₇	—	8	2	no	—
271	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
280	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
281	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
282	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
283	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
284	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
285	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
286	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
287	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
288	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
289	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
290	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
291	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
292	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
293	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
298	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
299	C₂×Dic₄₇	—	4	2	no	—
300	C₂×Dic₄₇	—	8	2	no	—
301	C₈×C₄₇	—	4	2	no	—
302	C₄₇⋊C₈	—	2	4	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	—	2	4	no	—
313	C₂²×C₄₇	—	4	1	no	—
314	C₂²×C₄₇	—	4	1	no	—
315	C₂²×C₄₇	—	4	1	no	—
316	C₂²×C₄₇	—	4	1	no	—
317	C₂²×C₄₇	—	4	4	no	—
318	C₂²×C₄₇	—	4	4	no	—
319	C₂²×C₄₇	—	4	4	no	—
320	C₂²×C₄₇	#380	1	1	yes	characteristic
321	C₂²×C₄₇	#380	1	1	yes	characteristic
322	C₂²×C₄₇	#380	1	1	yes	characteristic
323	C₂²×C₄₇	#380	1	1	yes	characteristic
324	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
325	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
326	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
327	C₄×C₄₇	—	2	4	no	—
328	C₄×C₄₇	—	8	2	no	—
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	#380	1	1	yes	characteristic
333	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
334	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
335	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
336	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
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	D₄₇	1	1	yes	characteristic
343	#1814	—	47	8	no	—
344	C₂×#344	—	47	1	no	—
345	C₂×#344	—	47	1	no	—
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	—	4	4	no	—
353	C₂×C₄₇	#1814	1	2	yes	complemented
354	C₂×C₄₇	C₂×#380	1	1	yes	characteristic
355	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
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	—	47	1	no	—
366	C₂²×M₁₆	—	94	1	no	—
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	—	2	2	no	—
381	#421	—	47	4	no	—
382	#421	—	94	2	no	—
383	#421	C₂×D₄₇	1	4	yes	—
384	C₂×#104	—	2	2	no	—
385	C₂×#104	—	94	2	no	—
386	#344	—	47	4	no	—
387	#344	—	47	4	no	—
388	C₄₇	C₂×#1814	1	1	yes	characteristic, complemented, Sylow
389	C₂×#41	—	2	1	no	—
390	C₂×#41	—	2	1	no	—
391	C₂×#41	—	2	1	no	—
392	C₂×#41	—	2	1	no	—
393	C₂×#41	—	2	1	no	—
394	C₂×#41	—	2	1	no	—
395	C₂×#41	Dic₉₄	1	2	yes	—
396	C₂×#41	C₄×D₄₇	1	2	yes	—
397	C₂×#41	C₄×D₄₇	1	2	yes	—
398	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
399	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
400	C₂×#41	C₂²×D₄₇	1	2	yes	—
401	C₂²×Q₈	Dic₉₄	1	1	yes	characteristic
402	C₂²×D₄	—	2	1	no	—
403	C₂²×D₄	Dic₉₄	1	1	yes	characteristic
404	C₂³×C₄	—	2	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	—	47	2	no	—
420	C₂×M₁₆	—	47	2	no	—
421	C₂×M₁₆	—	47	2	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	—	94	1	no	—
433	C₂×M₁₆	—	94	1	no	—
434	C₂×M₁₆	—	94	1	no	—
435	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
436	C₂²×C₈	—	2	1	no	—
437	C₂²×C₈	—	47	1	no	—
438	C₂²×C₈	—	47	1	no	—
439	C₂²×C₈	—	47	2	no	—
440	C₂²×C₈	—	47	1	no	—
441	C₂²×C₈	—	47	1	no	—
442	C₂²×C₈	—	47	1	no	—
443	C₂²×C₈	—	47	1	no	—
444	C₂²×C₈	—	47	2	no	—
445	C₂²×C₈	—	47	2	no	—
446	C₂²×C₈	—	47	2	no	—
447	C₂²×C₈	—	94	2	no	—
448	C₂²×C₈	—	94	2	no	—
449	C₂²×C₈	—	94	4	no	—
450	C₂²×C₈	—	94	4	no	—
451	C₂²×C₈	—	94	1	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	—	2	8	no	—
472	#104	—	94	8	no	—
473	C₂⁴	—	2	1	no	—
474	C₂⁴	#10625352	1	1	yes	characteristic
475	#41	—	2	2	no	—
476	#41	—	2	2	no	—
477	#41	—	2	2	no	—
478	#41	—	2	2	no	—
479	#41	—	2	2	no	—
480	#41	—	2	2	no	—
481	#41	—	2	2	no	—
482	#41	—	2	2	no	—
483	#41	—	2	2	no	—
484	#41	—	2	2	no	—
485	#41	—	2	2	no	—
486	#41	—	2	2	no	—
487	#41	Dic₄₇⋊C₄	1	4	yes	—
488	#41	Dic₄₇⋊C₄	1	4	yes	—
489	#41	C₂×C₄×D₄₇	1	4	yes	—
490	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	2	1	no	—
494	C₂×Q₈	Dic₄₇⋊C₄	1	2	yes	—
495	C₂×Q₈	Dic₄₇⋊C₄	1	2	yes	—
496	C₂×Q₈	C₂×Dic₉₄	1	2	yes	—
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	2	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
507	C₂×D₄	Dic₄₇⋊C₄	1	2	yes	—
508	C₂×D₄	C₂×Dic₉₄	1	2	yes	—
509	C₂²×C₄	—	2	1	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	4	1	no	—
517	C₂²×C₄	—	188	1	no	—
518	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
519	C₂²×C₄	C₂×Dic₉₄	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	D₄×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	#10625352	1	1	yes	characteristic
527	C₂²×C₄	#10625352	1	1	yes	characteristic
528	C₂²×C₄	#10625352	1	1	yes	characteristic
529	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
530	C₂²×C₄	C₂×C₂²⋊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	—	4	1	no	—
535	M₁₆	—	4	1	no	—
536	M₁₆	—	47	4	no	—
537	M₁₆	—	94	8	no	—
538	M₁₆	—	94	8	no	—
539	M₁₆	—	94	2	no	—
540	M₁₆	—	94	2	no	—
541	M₁₆	—	94	2	no	—
542	M₁₆	—	94	2	no	—
543	M₁₆	—	94	2	no	—
544	M₁₆	—	188	1	no	—
545	M₁₆	—	188	1	no	—
546	C₂×C₈	—	2	2	no	—
547	C₂×C₈	—	4	1	no	—
548	C₂×C₈	—	4	1	no	—
549	C₂×C₈	—	47	1	no	—
550	C₂×C₈	—	47	1	no	—
551	C₂×C₈	—	47	2	no	—
552	C₂×C₈	—	47	1	no	—
553	C₂×C₈	—	47	1	no	—
554	C₂×C₈	—	47	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	2	no	—
562	C₂×C₈	—	47	2	no	—
563	C₂×C₈	—	47	2	no	—
564	C₂×C₈	—	47	2	no	—
565	C₂×C₈	—	94	8	no	—
566	C₂×C₈	—	94	8	no	—
567	C₂×C₈	—	94	2	no	—
568	C₂×C₈	—	94	2	no	—
569	C₂×C₈	—	94	2	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	—	2	2	no	—
586	C₂³	—	2	2	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	4	2	no	—
589	C₂³	—	4	4	no	—
590	C₂³	#13093980	1	1	yes	characteristic
591	C₂³	#13093980	1	1	yes	characteristic
592	C₂³	#13093996	1	1	yes	characteristic
593	C₂³	#13093996	1	1	yes	characteristic
594	C₂³	#13094001	1	1	yes	characteristic
595	C₂³	#13094001	1	1	yes	characteristic
596	C₂³	C₂×#10625352	1	1	yes	characteristic
597	Q₈	—	2	2	no	—
598	Q₈	—	2	2	no	—
599	Q₈	—	2	2	no	—
600	Q₈	C₂×Dic₄₇⋊C₄	1	4	yes	—
601	D₄	—	2	4	no	—
602	D₄	—	2	4	no	—
603	D₄	—	2	4	no	—
604	D₄	—	2	4	no	—
605	D₄	—	2	2	no	—
606	D₄	—	2	2	no	—
607	D₄	—	2	2	no	—
608	D₄	C₂×Dic₄₇⋊C₄	1	4	yes	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	8	2	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	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
625	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
626	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
627	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
628	C₂×C₄	#13093980	1	1	yes	characteristic
629	C₂×C₄	#13093980	1	1	yes	characteristic
630	C₂×C₄	#13093996	1	1	yes	characteristic
631	C₂×C₄	#13093996	1	1	yes	characteristic
632	C₂×C₄	#13093996	1	1	yes	characteristic
633	C₂×C₄	#13093996	1	1	yes	characteristic
634	C₂×C₄	#13093996	1	1	yes	characteristic
635	C₂×C₄	#13093996	1	1	yes	characteristic
636	C₂×C₄	#13094001	1	1	yes	characteristic
637	C₂×C₄	#13094001	1	1	yes	characteristic
638	C₂×C₄	#13094001	1	1	yes	characteristic
639	C₂×C₄	#13094001	1	1	yes	characteristic
640	C₂×C₄	#13094001	1	1	yes	characteristic
641	C₂×C₄	#13094001	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	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
646	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
647	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
648	C₈	—	4	2	no	—
649	C₈	—	47	2	no	—
650	C₈	—	47	2	no	—
651	C₈	—	47	2	no	—
652	C₈	—	47	2	no	—
653	C₈	—	94	4	no	—
654	C₈	—	188	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	4	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	4	no	—
664	C₂²	—	4	4	no	—
665	C₂²	—	4	4	no	—
666	C₂²	#15688981	1	1	yes	characteristic
667	C₂²	#15688981	1	1	yes	characteristic
668	C₂²	#15688981	1	1	yes	characteristic
669	C₂²	#15688981	1	1	yes	characteristic
670	C₂²	C₂×#13093980	1	1	yes	characteristic
671	C₂²	C₂×#13093996	1	1	yes	characteristic
672	C₂²	C₂×#13094001	1	1	yes	characteristic
673	C₄	—	2	4	no	—
674	C₄	—	8	2	no	—
675	C₄	—	376	2	no	—
676	C₄	#15688981	1	1	yes	characteristic
677	C₄	#15688981	1	1	yes	characteristic
678	C₄	#15688981	1	1	yes	characteristic
679	C₄	#15688981	1	1	yes	characteristic
680	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
681	C₄	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
682	C₄	C₂×#13093996	1	1	yes	characteristic
683	C₄	C₂×#13094001	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	—	4	4	no	—
691	C₂	#20243440	1	2	yes	direct product factor
692	C₂	C₂×#15688981	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13093996
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#421	C₂
socle	C₂²×C₄₇	#380
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#421	D₄₇
hypocenter	C₄₇	C₂×#1814
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#421

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
5. #20243440	C₂	direct (N × H)
6. C₂×#15688894	C₂	semidirect
7. C₂×#15688893	C₂	semidirect
13. C₂×#13094031	C₄	semidirect
14. C₂×#13094031	C₄	semidirect
15. C₂×#13094031	C₄	semidirect
26. C₂×#13093959	C₂²	semidirect
28. #15689159	C₂²	semidirect
34. #15688894	C₂²	semidirect
35. #15688893	C₂²	semidirect
48. #13094031	C₂×C₄	semidirect
49. #13094031	C₂×C₄	semidirect
353. C₂×C₄₇	#1814	semidirect
388. C₄₇	C₂×#1814	semidirect
691. C₂	#20243440	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×#13094031	2
C₂²×#13093959	2
C₂×#15689159	2
C₂×#15689140	2
#20243440	2
C₂×#15688894	2
C₂×#15688893	2
C₂×C₄₇×#421	2
C₂×#1814	47

Subgroups — C2×#20243440 #26215938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243440 #26215938