Subgroups — C₂×#20243717 #26217564

Order 12032.

1754 conjugacy classes of subgroups.

The subgroup lattice has 658 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, complemented
2	C₂²×#13093951	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13093951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689090	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243717	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688888	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688877	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#135×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#13094031	—	2	4	no	—
10	C₂×#13094031	—	2	2	no	—
11	C₂×#13094031	—	2	4	no	—
12	C₂×#13094031	C₂²	1	4	yes	complemented
13	C₂²×#10625329	—	2	1	no	—
14	C₂²×#10625329	C₂²	1	1	yes	characteristic
15	C₂²×#10625329	C₂²	1	1	yes	characteristic
16	C₂³×C₄₇⋊C₈	—	2	1	no	—
17	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
19	C₂×#13093951	—	2	4	no	—
20	C₂×#13093951	—	2	4	no	—
21	C₂×#13093951	C₂²	1	4	yes	complemented
22	C₂×#13093951	C₂²	1	4	yes	complemented
23	#15689090	—	2	2	no	—
24	#15689090	C₂²	1	4	yes	complemented
25	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
26	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
27	#15688888	C₂²	1	4	yes	complemented
28	#15688877	C₂²	1	4	yes	complemented
29	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#135×C₄₇	—	2	4	no	—
32	C₂×#135×C₄₇	—	2	4	no	—
33	C₂×#135×C₄₇	C₄	1	4	yes	complemented
34	C₂×#135×C₄₇	C₂²	1	4	yes	—
35	C₂²×Q₁₆×C₄₇	C₄	1	1	yes	characteristic, complemented
36	C₂²×SD₁₆×C₄₇	C₄	1	1	yes	characteristic, complemented
37	C₂²×SD₁₆×C₄₇	C₄	1	1	yes	characteristic, complemented
38	C₂²×D₈×C₄₇	C₄	1	1	yes	characteristic, complemented
39	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂³×Dic₄₇	—	2	1	no	—
41	#13094031	—	2	16	no	—
42	#13094031	—	2	8	no	—
43	#13094031	—	2	8	no	—
44	C₂×#10625329	—	2	8	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂×#10625329	—	2	1	no	—
47	C₂×#10625329	—	2	1	no	—
48	C₂×#10625329	—	2	4	no	—
49	C₂×#10625329	—	2	2	no	—
50	C₂×#10625329	—	2	2	no	—
51	C₂×#10625329	D₄	1	4	yes	—
52	C₂×#10625329	C₂³	1	2	yes	—
53	C₂×#10625329	C₂³	1	2	yes	—
54	C₂²×C₄₇⋊C₈	—	2	8	no	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	C₂²×C₄₇⋊C₈	—	2	2	no	—
57	C₂²×C₄₇⋊C₈	—	2	2	no	—
58	C₂²×C₄₇⋊C₈	—	2	4	no	—
59	C₂²×C₄₇⋊C₈	—	2	1	no	—
60	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
61	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
62	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
63	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
64	C₂×C₄×Dic₄₇	—	2	2	no	—
65	C₂×C₄×Dic₄₇	—	2	2	no	—
66	C₂×C₄×Dic₄₇	—	2	1	no	—
67	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
68	#13093951	—	2	8	no	—
69	#13093951	—	2	8	no	—
70	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
71	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
72	C₂×#41×C₄₇	—	2	2	no	—
73	C₂×#41×C₄₇	—	2	1	no	—
74	C₂×#41×C₄₇	—	2	1	no	—
75	C₂×#41×C₄₇	—	2	1	no	—
76	C₂×#41×C₄₇	—	2	2	no	—
77	C₂×#41×C₄₇	—	2	1	no	—
78	C₂×#41×C₄₇	—	2	2	no	—
79	C₂×#41×C₄₇	—	2	2	no	—
80	C₂×#41×C₄₇	—	2	2	no	—
81	C₂×#41×C₄₇	—	2	2	no	—
82	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
83	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
84	C₂×#41×C₄₇	D₄	1	4	yes	—
85	C₂×#41×C₄₇	D₄	1	4	yes	—
86	C₂×#41×C₄₇	C₂³	1	2	yes	—
87	C₂×#41×C₄₇	C₂³	1	2	yes	—
88	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂²×D₄×C₄₇	—	2	1	no	—
91	C₂²×D₄×C₄₇	—	2	1	no	—
92	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂³×C₄×C₄₇	—	2	1	no	—
95	C₂³×C₄×C₄₇	—	2	1	no	—
96	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
97	#135×C₄₇	—	2	16	no	—
98	#135×C₄₇	—	2	8	no	—
99	#135×C₄₇	—	2	8	no	—
100	C₂×Q₁₆×C₄₇	—	2	4	no	—
101	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
102	C₂×SD₁₆×C₄₇	—	2	4	no	—
103	C₂×SD₁₆×C₄₇	—	2	4	no	—
104	C₂×SD₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
105	C₂×SD₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
106	C₂×D₈×C₄₇	—	2	4	no	—
107	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
108	C₂²×C₈×C₄₇	—	2	2	no	—
109	C₂²×C₈×C₄₇	—	2	2	no	—
110	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
111	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
112	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
113	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
114	C₂⁴×C₄₇	—	2	1	no	—
115	C₂⁴×C₄₇	—	2	1	no	—
116	C₂⁴×C₄₇	#41	1	1	yes	characteristic
117	#41×C₄₇	—	2	4	no	—
118	#41×C₄₇	—	2	4	no	—
119	#41×C₄₇	—	2	4	no	—
120	#41×C₄₇	—	2	4	no	—
121	#41×C₄₇	—	2	4	no	—
122	#41×C₄₇	—	2	2	no	—
123	#41×C₄₇	—	2	2	no	—
124	#41×C₄₇	—	2	4	no	—
125	#41×C₄₇	—	2	4	no	—
126	#41×C₄₇	—	2	2	no	—
127	#41×C₄₇	—	2	2	no	—
128	#41×C₄₇	—	2	2	no	—
129	#41×C₄₇	—	2	2	no	—
130	#41×C₄₇	—	4	2	no	—
131	#41×C₄₇	—	4	2	no	—
132	#41×C₄₇	—	4	2	no	—
133	#41×C₄₇	—	4	2	no	—
134	#41×C₄₇	C₂²⋊C₄	1	8	yes	—
135	#41×C₄₇	C₂×D₄	1	4	yes	—
136	#41×C₄₇	C₂×D₄	1	4	yes	—
137	C₂×Q₈×C₄₇	—	2	1	no	—
138	C₂×Q₈×C₄₇	—	2	2	no	—
139	C₂×Q₈×C₄₇	—	2	1	no	—
140	C₂×Q₈×C₄₇	—	2	2	no	—
141	C₂×Q₈×C₄₇	—	2	2	no	—
142	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
143	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
145	C₂×D₄×C₄₇	—	2	2	no	—
146	C₂×D₄×C₄₇	—	2	4	no	—
147	C₂×D₄×C₄₇	—	2	4	no	—
148	C₂×D₄×C₄₇	—	2	2	no	—
149	C₂×D₄×C₄₇	—	2	2	no	—
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	1	no	—
154	C₂×D₄×C₄₇	—	2	2	no	—
155	C₂×D₄×C₄₇	—	2	1	no	—
156	C₂×D₄×C₄₇	—	4	2	no	—
157	C₂×D₄×C₄₇	—	4	2	no	—
158	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	—
159	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
160	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₄₇	—	2	1	no	—
162	C₂²×C₄×C₄₇	—	2	2	no	—
163	C₂²×C₄×C₄₇	—	2	4	no	—
164	C₂²×C₄×C₄₇	—	2	4	no	—
165	C₂²×C₄×C₄₇	—	2	2	no	—
166	C₂²×C₄×C₄₇	—	2	1	no	—
167	C₂²×C₄×C₄₇	—	2	2	no	—
168	C₂²×C₄×C₄₇	—	2	2	no	—
169	C₂²×C₄×C₄₇	—	4	2	no	—
170	C₂²×C₄×C₄₇	—	4	2	no	—
171	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
179	C₂²×C₄×C₄₇	#41	1	2	yes	—
180	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
181	C₂²×Dic₄₇	—	2	4	no	—
182	C₂²×Dic₄₇	—	2	2	no	—
183	C₂²×Dic₄₇	—	4	2	no	—
184	C₂²×Dic₄₇	—	4	2	no	—
185	Q₁₆×C₄₇	—	2	8	no	—
186	SD₁₆×C₄₇	—	2	8	no	—
187	SD₁₆×C₄₇	—	2	8	no	—
188	D₈×C₄₇	—	2	8	no	—
189	C₂×C₈×C₄₇	—	2	2	no	—
190	C₂×C₈×C₄₇	—	2	2	no	—
191	C₂×C₈×C₄₇	—	2	4	no	—
192	C₂×C₈×C₄₇	—	2	2	no	—
193	C₂×C₈×C₄₇	—	2	2	no	—
194	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
195	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
196	C₄×Dic₄₇	—	2	2	no	—
197	C₄×Dic₄₇	—	2	2	no	—
198	C₄×Dic₄₇	—	4	2	no	—
199	#10625329	—	2	16	no	—
200	#10625329	—	2	4	no	—
201	#10625329	—	2	2	no	—
202	#10625329	—	2	2	no	—
203	#10625329	—	2	2	no	—
204	#10625329	—	4	2	no	—
205	#10625329	C₂×D₄	1	4	yes	—
206	C₂×C₄₇⋊C₈	—	2	16	no	—
207	C₂×C₄₇⋊C₈	—	2	2	no	—
208	C₂×C₄₇⋊C₈	—	2	4	no	—
209	C₂×C₄₇⋊C₈	—	2	2	no	—
210	C₂×C₄₇⋊C₈	—	2	4	no	—
211	C₂×C₄₇⋊C₈	—	2	2	no	—
212	C₂×C₄₇⋊C₈	—	2	2	no	—
213	C₂×C₄₇⋊C₈	—	2	2	no	—
214	C₂×C₄₇⋊C₈	—	2	2	no	—
215	C₂×C₄₇⋊C₈	—	4	2	no	—
216	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
217	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
218	C₂³×C₄₇	—	2	2	no	—
219	C₂³×C₄₇	—	2	2	no	—
220	C₂³×C₄₇	—	2	2	no	—
221	C₂³×C₄₇	—	2	4	no	—
222	C₂³×C₄₇	—	2	2	no	—
223	C₂³×C₄₇	—	4	2	no	—
224	C₂³×C₄₇	—	4	2	no	—
225	C₂³×C₄₇	—	4	2	no	—
226	C₂³×C₄₇	—	4	2	no	—
227	C₂³×C₄₇	—	4	2	no	—
228	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
229	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
230	C₂³×C₄₇	#121	1	2	yes	—
231	C₂³×C₄₇	#123	1	2	yes	—
232	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
233	Q₈×C₄₇	—	2	2	no	—
234	Q₈×C₄₇	—	2	4	no	—
235	Q₈×C₄₇	—	2	2	no	—
236	Q₈×C₄₇	—	2	2	no	—
237	Q₈×C₄₇	—	4	2	no	—
238	Q₈×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
239	D₄×C₄₇	—	2	4	no	—
240	D₄×C₄₇	—	2	4	no	—
241	D₄×C₄₇	—	2	8	no	—
242	D₄×C₄₇	—	2	2	no	—
243	D₄×C₄₇	—	2	2	no	—
244	D₄×C₄₇	—	2	2	no	—
245	D₄×C₄₇	—	2	4	no	—
246	D₄×C₄₇	—	4	2	no	—
247	D₄×C₄₇	—	4	2	no	—
248	D₄×C₄₇	—	4	4	no	—
249	D₄×C₄₇	—	4	2	no	—
250	D₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
251	C₂×C₄×C₄₇	—	2	2	no	—
252	C₂×C₄×C₄₇	—	2	4	no	—
253	C₂×C₄×C₄₇	—	2	4	no	—
254	C₂×C₄×C₄₇	—	2	4	no	—
255	C₂×C₄×C₄₇	—	2	8	no	—
256	C₂×C₄×C₄₇	—	2	2	no	—
257	C₂×C₄×C₄₇	—	4	2	no	—
258	C₂×C₄×C₄₇	—	4	2	no	—
259	C₂×C₄×C₄₇	—	4	2	no	—
260	C₂×C₄×C₄₇	—	4	4	no	—
261	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
264	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
265	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
267	C₂×C₄×C₄₇	#120	1	2	yes	—
268	C₂×C₄×C₄₇	#120	1	2	yes	—
269	C₂×C₄×C₄₇	#121	1	2	yes	—
270	C₂×C₄×C₄₇	#121	1	2	yes	—
271	C₂×C₄×C₄₇	#121	1	2	yes	—
272	C₂×C₄×C₄₇	#123	1	2	yes	—
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×D₄	1	1	yes	characteristic
278	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
279	C₂×Dic₄₇	—	2	4	no	—
280	C₂×Dic₄₇	—	4	8	no	—
281	C₂×Dic₄₇	—	4	2	no	—
282	C₂×Dic₄₇	—	4	2	no	—
283	C₈×C₄₇	—	2	2	no	—
284	C₈×C₄₇	—	2	2	no	—
285	C₄₇⋊C₈	—	2	2	no	—
286	C₄₇⋊C₈	—	2	4	no	—
287	C₄₇⋊C₈	—	2	2	no	—
288	C₄₇⋊C₈	—	4	2	no	—
289	C₂×#1876	—	47	1	no	maximal, Sylow
290	C₂²×C₄₇	—	2	4	no	—
291	C₂²×C₄₇	—	2	4	no	—
292	C₂²×C₄₇	—	2	1	no	—
293	C₂²×C₄₇	—	2	1	no	—
294	C₂²×C₄₇	—	2	1	no	—
295	C₂²×C₄₇	—	2	1	no	—
296	C₂²×C₄₇	—	2	4	no	—
297	C₂²×C₄₇	—	4	8	no	—
298	C₂²×C₄₇	—	4	2	no	—
299	C₂²×C₄₇	—	4	2	no	—
300	C₂²×C₄₇	—	4	2	no	—
301	C₂²×C₄₇	—	4	2	no	—
302	C₂²×C₄₇	—	4	2	no	—
303	C₂²×C₄₇	—	8	4	no	—
304	C₂²×C₄₇	#386	1	2	yes	—
305	C₂²×C₄₇	#386	1	2	yes	—
306	C₂²×C₄₇	#443	1	2	yes	—
307	C₂²×C₄₇	#444	1	2	yes	—
308	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
309	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
310	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
311	C₄×C₄₇	—	2	4	no	—
312	C₄×C₄₇	—	4	2	no	—
313	C₄×C₄₇	#386	1	2	yes	—
314	C₄×C₄₇	#386	1	2	yes	—
315	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
316	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
317	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
318	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
319	Dic₄₇	—	4	4	no	—
320	C₂²×#135	D₄₇	1	1	yes	characteristic
321	C₂²×#131	—	47	1	no	—
322	C₂²×#104	—	47	1	no	—
323	C₂²×#104	—	47	1	no	—
324	C₂×#408	—	47	1	no	—
325	#1876	—	47	8	no	—
326	C₂×#341	—	47	1	no	—
327	C₂×#336	—	47	1	no	—
328	C₂×C₄₇	—	2	1	no	—
329	C₂×C₄₇	—	2	1	no	—
330	C₂×C₄₇	—	2	2	no	—
331	C₂×C₄₇	—	4	4	no	—
332	C₂×C₄₇	—	8	2	no	—
333	C₂×C₄₇	#1876	1	4	yes	complemented
334	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
335	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
336	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
337	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
338	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
339	C₂×#135	—	2	4	no	—
340	C₂×#135	—	2	4	no	—
341	C₂×#135	Dic₄₇	1	4	yes	complemented
342	C₂×#135	C₂×D₄₇	1	4	yes	—
343	C₂²×Q₁₆	Dic₄₇	1	1	yes	characteristic, complemented
344	C₂²×SD₁₆	Dic₄₇	1	1	yes	characteristic, complemented
345	C₂²×SD₁₆	Dic₄₇	1	1	yes	characteristic, complemented
346	C₂²×D₈	Dic₄₇	1	1	yes	characteristic, complemented
347	C₂×#131	—	47	4	no	—
348	C₂×#131	—	94	2	no	—
349	C₂×#131	—	94	4	no	—
350	C₂×#131	—	94	4	no	—
351	C₂²×M₁₆	—	47	1	no	—
352	C₂²×M₁₆	—	47	1	no	—
353	C₂²×M₁₆	—	94	1	no	—
354	C₂³×C₈	—	47	1	no	—
355	C₂³×C₈	—	94	1	no	—
356	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
357	C₂²×C₄²	—	47	1	no	—
358	C₂×#104	—	47	4	no	—
359	C₂×#104	—	47	4	no	—
360	C₂×#104	—	94	4	no	—
361	C₂×#104	—	94	4	no	—
362	#408	—	47	4	no	—
363	#408	—	94	2	no	—
364	C₂×C₂²⋊C₈	—	94	1	no	—
365	C₂×C₂²⋊C₈	—	94	1	no	—
366	#341	—	47	4	no	—
367	#336	—	47	4	no	—
368	C₄₇	C₂×#1876	1	1	yes	characteristic, complemented, Sylow
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	—	2	1	no	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	2	2	no	—
374	C₂×#41	—	2	1	no	—
375	C₂×#41	—	2	2	no	—
376	C₂×#41	—	2	2	no	—
377	C₂×#41	—	2	2	no	—
378	C₂×#41	—	2	2	no	—
379	C₂×#41	C₂×Dic₄₇	1	2	yes	—
380	C₂×#41	C₂×Dic₄₇	1	2	yes	—
381	C₂×#41	C₂²⋊D₄₇	1	4	yes	—
382	C₂×#41	C₂²⋊D₄₇	1	4	yes	—
383	C₂×#41	C₂²×D₄₇	1	2	yes	—
384	C₂×#41	C₂²×D₄₇	1	2	yes	—
385	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
386	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	1	no	—
389	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
390	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
391	C₂³×C₄	—	2	1	no	—
392	C₂³×C₄	—	2	1	no	—
393	C₂³×C₄	—	94	1	no	—
394	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
395	#135	—	2	16	no	—
396	#135	—	2	8	no	—
397	#135	—	2	8	no	—
398	C₂×Q₁₆	—	2	4	no	—
399	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	complemented
400	C₂×SD₁₆	—	2	4	no	—
401	C₂×SD₁₆	—	2	4	no	—
402	C₂×SD₁₆	C₂×Dic₄₇	1	4	yes	complemented
403	C₂×SD₁₆	C₂×Dic₄₇	1	4	yes	complemented
404	C₂×D₈	—	2	4	no	—
405	C₂×D₈	C₂×Dic₄₇	1	4	yes	complemented
406	#131	—	94	8	no	—
407	#131	—	94	16	no	—
408	#131	—	94	8	no	—
409	C₂×M₁₆	—	47	4	no	—
410	C₂×M₁₆	—	47	2	no	—
411	C₂×M₁₆	—	47	2	no	—
412	C₂×M₁₆	—	94	4	no	—
413	C₂×M₁₆	—	94	8	no	—
414	C₂×M₁₆	—	94	1	no	—
415	C₂×M₁₆	—	94	2	no	—
416	C₂×M₁₆	—	94	1	no	—
417	C₂×M₁₆	—	94	2	no	—
418	C₂×M₁₆	—	94	2	no	—
419	C₂²×C₈	—	2	2	no	—
420	C₂²×C₈	—	2	2	no	—
421	C₂²×C₈	—	47	2	no	—
422	C₂²×C₈	—	47	1	no	—
423	C₂²×C₈	—	47	1	no	—
424	C₂²×C₈	—	47	2	no	—
425	C₂²×C₈	—	94	4	no	—
426	C₂²×C₈	—	94	8	no	—
427	C₂²×C₈	—	94	2	no	—
428	C₂²×C₈	—	94	1	no	—
429	C₂²×C₈	—	94	2	no	—
430	C₂²×C₈	—	94	1	no	—
431	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
432	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
433	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
434	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
435	C₂×C₄²	—	47	2	no	—
436	C₂×C₄²	—	94	2	no	—
437	C₂×C₄²	—	94	2	no	—
438	C₂×C₄²	—	94	1	no	—
439	#104	—	94	8	no	—
440	#104	—	94	8	no	—
441	C₂²⋊C₈	—	94	4	no	—
442	C₂²⋊C₈	—	94	4	no	—
443	C₂⁴	—	2	1	no	—
444	C₂⁴	—	2	1	no	—
445	C₂⁴	#10625352	1	1	yes	characteristic
446	#41	—	2	4	no	—
447	#41	—	2	4	no	—
448	#41	—	2	4	no	—
449	#41	—	2	4	no	—
450	#41	—	2	4	no	—
451	#41	—	2	2	no	—
452	#41	—	2	2	no	—
453	#41	—	2	4	no	—
454	#41	—	2	4	no	—
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	—	4	2	no	—
460	#41	—	4	2	no	—
461	#41	—	4	2	no	—
462	#41	—	4	2	no	—
463	#41	C₂²⋊Dic₄₇	1	8	yes	—
464	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
465	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	2	1	no	—
468	C₂×Q₈	—	2	1	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	2	no	—
471	C₂×Q₈	C₂²⋊Dic₄₇	1	4	yes	—
472	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
473	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	2	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	C₂²⋊Dic₄₇	1	4	yes	—
488	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
489	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	94	4	no	—
501	C₂²×C₄	—	94	2	no	—
502	C₂²×C₄	—	188	2	no	—
503	C₂²×C₄	—	188	2	no	—
504	C₂²×C₄	D₄×D₄₇	1	2	yes	—
505	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
506	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
507	C₂²×C₄	#10625352	1	1	yes	characteristic
508	C₂²×C₄	#10625352	1	2	yes	—
509	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
510	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
511	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
512	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
513	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
514	Q₁₆	—	2	8	no	—
515	SD₁₆	—	2	8	no	—
516	SD₁₆	—	2	8	no	—
517	D₈	—	2	8	no	—
518	M₁₆	—	47	4	no	—
519	M₁₆	—	94	16	no	—
520	M₁₆	—	94	4	no	—
521	M₁₆	—	94	2	no	—
522	M₁₆	—	94	2	no	—
523	M₁₆	—	94	2	no	—
524	M₁₆	—	188	2	no	—
525	C₂×C₈	—	2	2	no	—
526	C₂×C₈	—	2	2	no	—
527	C₂×C₈	—	2	4	no	—
528	C₂×C₈	—	2	2	no	—
529	C₂×C₈	—	2	2	no	—
530	C₂×C₈	—	47	2	no	—
531	C₂×C₈	—	47	2	no	—
532	C₂×C₈	—	94	16	no	—
533	C₂×C₈	—	94	2	no	—
534	C₂×C₈	—	94	2	no	—
535	C₂×C₈	—	94	4	no	—
536	C₂×C₈	—	94	4	no	—
537	C₂×C₈	—	94	2	no	—
538	C₂×C₈	—	94	2	no	—
539	C₂×C₈	—	94	2	no	—
540	C₂×C₈	—	94	2	no	—
541	C₂×C₈	—	188	2	no	—
542	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
543	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
544	C₄²	—	94	2	no	—
545	C₄²	—	94	2	no	—
546	C₄²	—	188	2	no	—
547	C₂³	—	2	2	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	4	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	2	no	—
557	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
558	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
559	C₂³	#13093996	1	2	yes	—
560	C₂³	#13094005	1	2	yes	—
561	C₂³	C₂×#10625352	1	1	yes	characteristic
562	Q₈	—	2	4	no	—
563	Q₈	—	2	2	no	—
564	Q₈	—	2	2	no	—
565	Q₈	—	2	2	no	—
566	Q₈	—	4	2	no	—
567	Q₈	C₂×C₂²⋊Dic₄₇	1	4	yes	—
568	D₄	—	2	8	no	—
569	D₄	—	2	4	no	—
570	D₄	—	2	4	no	—
571	D₄	—	2	4	no	—
572	D₄	—	2	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	4	4	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	8	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	4	2	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	94	4	no	—
591	C₂×C₄	—	188	8	no	—
592	C₂×C₄	—	188	2	no	—
593	C₂×C₄	—	188	2	no	—
594	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
595	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
596	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
597	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
598	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
599	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
600	C₂×C₄	#13093992	1	2	yes	—
601	C₂×C₄	#13093992	1	2	yes	—
602	C₂×C₄	#13093996	1	2	yes	—
603	C₂×C₄	#13093996	1	2	yes	—
604	C₂×C₄	#13093996	1	2	yes	—
605	C₂×C₄	#13094005	1	2	yes	—
606	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
607	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
608	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
609	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
610	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
611	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
612	C₈	—	2	2	no	—
613	C₈	—	2	2	no	—
614	C₈	—	94	2	no	—
615	C₈	—	94	2	no	—
616	C₈	—	94	4	no	—
617	C₈	—	188	2	no	—
618	C₂²	—	2	4	no	—
619	C₂²	—	2	4	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	4	no	—
625	C₂²	—	4	8	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	2	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	8	4	no	—
632	C₂²	#15689003	1	2	yes	—
633	C₂²	#15689003	1	2	yes	—
634	C₂²	#15689240	1	2	yes	—
635	C₂²	#15689245	1	2	yes	—
636	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
637	C₂²	C₂×#13093996	1	1	yes	characteristic
638	C₂²	C₂×#13094005	1	1	yes	characteristic
639	C₄	—	2	4	no	—
640	C₄	—	4	2	no	—
641	C₄	—	188	4	no	—
642	C₄	#15689003	1	2	yes	—
643	C₄	#15689003	1	2	yes	—
644	C₄	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
645	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
646	C₄	C₂×#13093992	1	1	yes	characteristic
647	C₄	C₂×#13093996	1	1	yes	characteristic
648	C₂	—	2	1	no	—
649	C₂	—	2	2	no	—
650	C₂	—	2	1	no	—
651	C₂	—	4	4	no	—
652	C₂	—	8	2	no	—
653	C₂	#20243717	1	4	yes	direct product factor
654	C₂	C₂×#15689003	1	1	yes	characteristic
655	C₂	C₂×#15689240	1	1	yes	characteristic
656	C₂	C₂×#15689245	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂²×#135×C₄₇	C₂
socle	C₂³×C₄₇	C₄×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#135	D₄₇
hypocenter	C₄₇	C₂×#1876
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂²×#13094031	C₂	semidirect
2. C₂²×#13093951	C₂	semidirect
3. C₂²×#13093951	C₂	semidirect
4. C₂×#15689090	C₂	semidirect
5. #20243717	C₂	direct (N × H)
6. C₂×#15688888	C₂	semidirect
7. C₂×#15688877	C₂	semidirect
12. C₂×#13094031	C₂²	semidirect
21. C₂×#13093951	C₂²	semidirect
22. C₂×#13093951	C₂²	semidirect
24. #15689090	C₂²	semidirect
27. #15688888	C₂²	semidirect
28. #15688877	C₂²	semidirect
33. C₂×#135×C₄₇	C₄	semidirect
35. C₂²×Q₁₆×C₄₇	C₄	semidirect
36. C₂²×SD₁₆×C₄₇	C₄	semidirect
37. C₂²×SD₁₆×C₄₇	C₄	semidirect
38. C₂²×D₈×C₄₇	C₄	semidirect
101. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
104. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
105. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
107. C₂×D₈×C₄₇	C₂×C₄	semidirect
333. C₂×C₄₇	#1876	semidirect
341. C₂×#135	Dic₄₇	semidirect
343. C₂²×Q₁₆	Dic₄₇	semidirect
344. C₂²×SD₁₆	Dic₄₇	semidirect
345. C₂²×SD₁₆	Dic₄₇	semidirect
346. C₂²×D₈	Dic₄₇	semidirect
368. C₄₇	C₂×#1876	semidirect
399. C₂×Q₁₆	C₂×Dic₄₇	semidirect
402. C₂×SD₁₆	C₂×Dic₄₇	semidirect
403. C₂×SD₁₆	C₂×Dic₄₇	semidirect
405. C₂×D₈	C₂×Dic₄₇	semidirect
653. C₂	#20243717	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×#13093951	2
C₂×#15689090	2
#20243717	2
C₂×#15688888	2
C₂×#15688877	2
C₂²×#135×C₄₇	2
C₂×#1876	47

Subgroups — C2×#20243717 #26217564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243717 #26217564