Subgroups — C₂×#20241874 #26183366

Order 12032.

1182 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689176	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15688969	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241874	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688860	C₂	1	2	yes	maximal, complemented
5	C₂×#15688857	C₂	1	2	yes	maximal
6	C₂×C₄₇×#529	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄×Dic₄₇	—	2	1	no	—
8	#15689176	—	2	2	no	—
9	#15689176	C₂²	1	4	yes	complemented
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
11	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
13	#15688969	—	2	2	no	—
14	#15688969	C₂²	1	4	yes	complemented
15	C₂×C₄₇⋊#95	—	2	1	no	—
16	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
17	#15688860	C₂²	1	8	yes	complemented
18	#15688857	C₂²	1	8	yes	—
19	C₄₇×#529	—	2	2	no	—
20	C₄₇×#529	—	2	2	no	—
21	C₄₇×#529	C₄	1	4	yes	complemented
22	C₄₇×#529	C₂²	1	4	yes	—
23	C₂×#126×C₄₇	—	2	1	no	—
24	C₂×#125×C₄₇	C₄	1	1	yes	characteristic, complemented
25	C₂×#124×C₄₇	C₄	1	1	yes	characteristic, complemented
26	C₂×#123×C₄₇	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic, complemented
30	C₂×C₄×D₄×C₄₇	—	2	1	no	—
31	C₂×C₄×D₄×C₄₇	C₄	1	1	yes	characteristic, complemented
32	C₂×#117×C₄₇	—	2	1	no	—
33	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
34	C₂³×Dic₄₇	—	2	2	no	—
35	C₂²×C₄₇⋊C₈	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	2	8	no	—
37	C₂×C₄×Dic₄₇	—	2	4	no	—
38	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
39	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
40	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
41	C₄×C₄₇⋊C₈	—	2	4	no	—
42	C₄₇⋊#95	—	2	4	no	—
43	C₄₇⋊#95	—	2	2	no	—
44	C₄₇⋊#95	C₂³	1	4	yes	—
45	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₄₇	—	2	1	no	—
47	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	—	2	1	no	—
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	#126×C₄₇	—	2	4	no	—
53	#126×C₄₇	—	2	4	no	—
54	#125×C₄₇	—	2	2	no	—
55	#125×C₄₇	C₂×C₄	1	4	yes	complemented
56	#124×C₄₇	—	2	2	no	—
57	#124×C₄₇	C₂×C₄	1	4	yes	complemented
58	#123×C₄₇	—	2	4	no	—
59	#123×C₄₇	—	2	4	no	—
60	C₂²⋊Q₈×C₄₇	—	2	1	no	—
61	C₂²⋊Q₈×C₄₇	—	2	1	no	—
62	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
63	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
64	#121×C₄₇	—	2	1	no	—
65	#121×C₄₇	—	2	1	no	—
66	#121×C₄₇	C₂×C₄	1	2	yes	—
67	#121×C₄₇	C₂³	1	2	yes	—
68	C₄×Q₈×C₄₇	—	2	2	no	—
69	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
70	C₄×D₄×C₄₇	—	2	4	no	—
71	C₄×D₄×C₄₇	—	2	4	no	—
72	C₄×D₄×C₄₇	—	2	2	no	—
73	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
74	#117×C₄₇	—	2	4	no	—
75	#117×C₄₇	—	2	4	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄²×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
91	C₂×C₄²×C₄₇	D₄	1	2	yes	—
92	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	D₄	1	2	yes	—
95	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
96	C₂⁴×C₄₇	—	2	1	no	—
97	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₄₇	—	2	1	no	—
99	C₂×Q₈×C₄₇	—	4	2	no	—
100	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	—	4	2	no	—
105	C₂×D₄×C₄₇	—	4	4	no	—
106	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	—	2	4	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	4	2	no	—
114	C₂²×C₄×C₄₇	—	4	4	no	—
115	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
129	C₂²×Dic₄₇	—	2	8	no	—
130	C₂²×Dic₄₇	—	2	4	no	—
131	C₂²×Dic₄₇	—	4	4	no	—
132	C₂²×Dic₄₇	—	4	4	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	4	no	—
135	C₄⋊C₄×C₄₇	—	2	4	no	—
136	C₄⋊C₄×C₄₇	—	2	4	no	—
137	C₄⋊C₄×C₄₇	—	2	1	no	—
138	C₄⋊C₄×C₄₇	—	2	1	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
141	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₄₇	—	2	2	no	—
143	C₂²⋊C₄×C₄₇	—	2	2	no	—
144	C₂²⋊C₄×C₄₇	—	2	2	no	—
145	C₂²⋊C₄×C₄₇	—	2	4	no	—
146	C₂²⋊C₄×C₄₇	—	2	4	no	—
147	C₂²⋊C₄×C₄₇	—	2	4	no	—
148	C₂²⋊C₄×C₄₇	—	2	2	no	—
149	C₄²×C₄₇	—	2	4	no	—
150	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
151	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
152	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
153	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
154	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
155	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
156	C₄²×C₄₇	C₂×D₄	1	2	yes	—
157	C₄²×C₄₇	C₂×D₄	1	2	yes	—
158	C₄×Dic₄₇	—	2	16	no	—
159	C₂×C₄₇⋊C₈	—	2	4	no	—
160	C₂×C₄₇⋊C₈	—	4	4	no	—
161	C₂³×C₄₇	—	2	2	no	—
162	C₂³×C₄₇	—	2	2	no	—
163	C₂³×C₄₇	—	2	2	no	—
164	C₂³×C₄₇	—	4	2	no	—
165	C₂³×C₄₇	—	4	2	no	—
166	C₂³×C₄₇	—	4	2	no	—
167	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂³×C₄₇	#135	1	4	yes	—
170	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₄₇	—	4	2	no	—
172	Q₈×C₄₇	—	4	2	no	—
173	D₄×C₄₇	—	4	2	no	—
174	D₄×C₄₇	—	4	2	no	—
175	D₄×C₄₇	—	4	4	no	—
176	D₄×C₄₇	—	4	4	no	—
177	C₂×C₄×C₄₇	—	2	4	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	4	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	4	no	—
185	C₂×C₄×C₄₇	—	2	4	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	4	1	no	—
190	C₂×C₄×C₄₇	—	4	1	no	—
191	C₂×C₄×C₄₇	—	4	1	no	—
192	C₂×C₄×C₄₇	—	4	1	no	—
193	C₂×C₄×C₄₇	—	4	2	no	—
194	C₂×C₄×C₄₇	—	4	2	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	—	4	8	no	—
197	C₂×C₄×C₄₇	#104	1	4	yes	—
198	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
204	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
206	C₂×Dic₄₇	—	2	8	no	—
207	C₂×Dic₄₇	—	4	4	no	—
208	C₂×Dic₄₇	—	4	16	no	—
209	C₂×Dic₄₇	—	4	4	no	—
210	C₄₇⋊C₈	—	4	4	no	—
211	C₂×#1500	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	—	2	1	no	—
213	C₂²×C₄₇	—	2	1	no	—
214	C₂²×C₄₇	—	2	1	no	—
215	C₂²×C₄₇	—	2	1	no	—
216	C₂²×C₄₇	—	2	8	no	—
217	C₂²×C₄₇	—	4	2	no	—
218	C₂²×C₄₇	—	4	2	no	—
219	C₂²×C₄₇	—	4	2	no	—
220	C₂²×C₄₇	—	8	4	no	—
221	C₂²×C₄₇	#410	1	2	yes	—
222	C₂²×C₄₇	#416	1	2	yes	—
223	C₂²×C₄₇	#416	1	2	yes	—
224	C₂²×C₄₇	C₂×#104	1	2	yes	—
225	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
226	C₂²×C₄₇	C₂×#135	1	2	yes	—
227	C₄×C₄₇	—	2	1	no	—
228	C₄×C₄₇	—	2	1	no	—
229	C₄×C₄₇	—	2	1	no	—
230	C₄×C₄₇	—	2	1	no	—
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	2	2	no	—
234	C₄×C₄₇	—	4	2	no	—
235	C₄×C₄₇	—	4	2	no	—
236	C₄×C₄₇	—	4	2	no	—
237	C₄×C₄₇	C₂×#104	1	4	yes	—
238	Dic₄₇	—	4	8	no	—
239	C₂×#529	D₄₇	1	1	yes	characteristic
240	C₂×#431	—	47	1	no	—
241	C₂×#376	—	47	1	no	—
242	#1500	—	47	8	no	—
243	C₂×#328	—	47	2	no	—
244	C₂×#327	—	47	2	no	—
245	C₂×C₄₇	—	2	2	no	—
246	C₂×C₄₇	—	2	2	no	—
247	C₂×C₄₇	—	8	2	no	—
248	C₂×C₄₇	#1500	1	4	yes	complemented
249	C₂×C₄₇	C₂×#410	1	1	yes	characteristic
250	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
251	C₂×C₄₇	C₂²×#104	1	1	yes	characteristic
252	#529	—	2	2	no	—
253	#529	—	2	2	no	—
254	#529	Dic₄₇	1	4	yes	complemented
255	#529	C₂×D₄₇	1	4	yes	—
256	C₂×#126	—	2	1	no	—
257	C₂×#125	Dic₄₇	1	1	yes	characteristic, complemented
258	C₂×#124	Dic₄₇	1	1	yes	characteristic, complemented
259	C₂×#123	—	2	1	no	—
260	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
261	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
262	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic, complemented
263	C₂×C₄×D₄	—	2	1	no	—
264	C₂×C₄×D₄	Dic₄₇	1	1	yes	characteristic, complemented
265	C₂×#117	—	2	1	no	—
266	C₂²×C₄²	—	94	1	no	—
267	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
268	#431	—	47	4	no	—
269	#431	—	94	2	no	—
270	C₂×C₄⋊C₈	—	94	1	no	—
271	C₂×C₂²⋊C₈	—	47	2	no	—
272	C₂×C₄×C₈	—	94	1	no	—
273	#376	—	47	4	no	—
274	#376	—	94	2	no	—
275	C₂×#95	—	47	2	no	—
276	C₂×#95	—	94	1	no	—
277	#328	—	47	8	no	—
278	#327	—	47	8	no	—
279	C₄₇	C₂×#1500	1	1	yes	characteristic, complemented, Sylow
280	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	—	94	2	no	—
285	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
286	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
287	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
288	C₂²×C₈	—	94	2	no	—
289	#126	—	2	4	no	—
290	#126	—	2	4	no	—
291	#125	—	2	2	no	—
292	#125	C₂×Dic₄₇	1	4	yes	complemented
293	#124	—	2	2	no	—
294	#124	C₂×Dic₄₇	1	4	yes	complemented
295	#123	—	2	4	no	—
296	#123	—	2	4	no	—
297	C₂²⋊Q₈	—	2	1	no	—
298	C₂²⋊Q₈	—	2	1	no	—
299	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
300	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
301	#121	—	2	1	no	—
302	#121	—	2	1	no	—
303	#121	C₂×Dic₄₇	1	2	yes	—
304	#121	C₂²×D₄₇	1	2	yes	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	C₂×Dic₄₇	1	4	yes	complemented
311	#117	—	2	4	no	—
312	#117	—	2	4	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	94	8	no	—
326	C₂×C₄²	—	94	4	no	—
327	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
328	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
329	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
330	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
331	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
332	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
333	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
334	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
335	C₄⋊C₈	—	94	4	no	—
336	C₂²⋊C₈	—	47	4	no	—
337	C₂²⋊C₈	—	94	2	no	—
338	C₄×C₈	—	94	4	no	—
339	#95	—	47	4	no	—
340	#95	—	94	2	no	—
341	#95	—	94	4	no	—
342	C₂⁴	—	2	1	no	—
343	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
344	C₂×Q₈	—	2	1	no	—
345	C₂×Q₈	—	4	2	no	—
346	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	4	no	—
361	C₂²×C₄	—	94	8	no	—
362	C₂²×C₄	—	94	4	no	—
363	C₂²×C₄	—	188	4	no	—
364	C₂²×C₄	—	188	4	no	—
365	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
367	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
369	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
370	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
371	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
372	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
374	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
375	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
378	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
379	C₂×C₈	—	94	4	no	—
380	C₂×C₈	—	188	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
389	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
390	C₂²⋊C₄	—	2	2	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₄²	—	2	4	no	—
398	C₄²	—	94	16	no	—
399	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
400	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
401	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
402	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
403	C₄²	C₂²×Dic₄₇	1	2	yes	—
404	C₄²	C₂²×Dic₄₇	1	2	yes	—
405	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
406	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	—	4	2	no	—
413	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
414	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
415	C₂³	#13094044	1	4	yes	—
416	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	4	no	—
422	D₄	—	4	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	8	no	—
443	C₂×C₄	—	94	8	no	—
444	C₂×C₄	—	188	4	no	—
445	C₂×C₄	—	188	16	no	—
446	C₂×C₄	—	188	4	no	—
447	C₂×C₄	#13093951	1	4	yes	—
448	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
449	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
451	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
452	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
453	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
454	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
455	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
456	C₈	—	188	4	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	8	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	8	4	no	—
466	C₂²	#15689097	1	2	yes	—
467	C₂²	#15689119	1	2	yes	—
468	C₂²	#15689119	1	2	yes	—
469	C₂²	C₂×#13093951	1	2	yes	—
470	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
471	C₂²	C₂×#13094044	1	2	yes	—
472	C₄	—	2	2	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	2	no	—
478	C₄	—	2	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	188	8	no	—
483	C₄	C₂×#13093951	1	4	yes	—
484	C₂	—	2	2	no	—
485	C₂	—	2	2	no	—
486	C₂	—	8	2	no	—
487	C₂	#20241874	1	4	yes	direct product factor
488	C₂	C₂×#15689097	1	1	yes	characteristic
489	C₂	C₂×#15689119	1	1	yes	characteristic
490	C₂	C₂²×#13093951	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#529	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂×#121×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#529	D₄₇
hypocenter	C₄₇	C₂×#1500
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. C₂×#15689176	C₂	semidirect
2. C₂×#15688969	C₂	semidirect
3. #20241874	C₂	direct (N × H)
4. C₂×#15688860	C₂	semidirect
9. #15689176	C₂²	semidirect
14. #15688969	C₂²	semidirect
17. #15688860	C₂²	semidirect
21. C₄₇×#529	C₄	semidirect
24. C₂×#125×C₄₇	C₄	semidirect
25. C₂×#124×C₄₇	C₄	semidirect
29. C₂×C₄×Q₈×C₄₇	C₄	semidirect
31. C₂×C₄×D₄×C₄₇	C₄	semidirect
55. #125×C₄₇	C₂×C₄	semidirect
57. #124×C₄₇	C₂×C₄	semidirect
69. C₄×Q₈×C₄₇	C₂×C₄	semidirect
73. C₄×D₄×C₄₇	C₂×C₄	semidirect
248. C₂×C₄₇	#1500	semidirect
254. #529	Dic₄₇	semidirect
257. C₂×#125	Dic₄₇	semidirect
258. C₂×#124	Dic₄₇	semidirect
262. C₂×C₄×Q₈	Dic₄₇	semidirect
264. C₂×C₄×D₄	Dic₄₇	semidirect
279. C₄₇	C₂×#1500	semidirect
292. #125	C₂×Dic₄₇	semidirect
294. #124	C₂×Dic₄₇	semidirect
306. C₄×Q₈	C₂×Dic₄₇	semidirect
310. C₄×D₄	C₂×Dic₄₇	semidirect
487. C₂	#20241874	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×#15689176	2
C₂×#15688969	2
#20241874	2
C₂×#15688860	2
C₂×#15688857	2
C₂×C₄₇×#529	2
C₂×#1500	47

Subgroups — C2×#20241874 #26183366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20241874 #26183366