Subgroups — C₂×#20243665 #26217330

Order 12032.

1398 conjugacy classes of subgroups.

The subgroup lattice has 552 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×#13093960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689150	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#13093951	C₂	1	1	yes	maximal, characteristic
5	#20243665	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688882	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688877	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#416	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	—
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×#13093960	—	2	4	no	—
20	C₂×#13093960	C₂²	1	4	yes	complemented
21	#15689150	—	2	2	no	—
22	#15689150	C₂²	1	4	yes	complemented
23	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
24	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
25	C₂×#13093951	—	2	4	no	—
26	C₂×#13093951	C₂²	1	4	yes	—
27	#15688882	C₂²	1	4	yes	complemented
28	#15688877	C₂²	1	4	yes	complemented
29	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#416	C₄	1	4	yes	complemented
33	C₄₇×#416	C₂²	1	4	yes	—
34	C₂×#103×C₄₇	C₄	1	1	yes	characteristic, complemented
35	C₂×#103×C₄₇	C₄	1	1	yes	characteristic, complemented
36	C₂×#102×C₄₇	C₄	1	1	yes	characteristic, complemented
37	C₂×#102×C₄₇	C₄	1	1	yes	characteristic, complemented
38	C₂³×Dic₄₇	—	2	1	no	—
39	#13094031	—	2	16	no	—
40	#13094031	—	2	8	no	—
41	#13094031	—	2	8	no	—
42	C₂×#10625329	—	2	8	no	—
43	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	—	2	1	no	—
45	C₂×#10625329	—	2	1	no	—
46	C₂×#10625329	—	2	4	no	—
47	C₂×#10625329	—	2	2	no	—
48	C₂×#10625329	—	2	2	no	—
49	C₂×#10625329	D₄	1	4	yes	—
50	C₂×#10625329	C₂³	1	2	yes	—
51	C₂×#10625329	C₂³	1	2	yes	—
52	C₂²×C₄₇⋊C₈	—	2	8	no	—
53	C₂²×C₄₇⋊C₈	—	2	1	no	—
54	C₂²×C₄₇⋊C₈	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	—	2	2	no	—
56	C₂²×C₄₇⋊C₈	—	2	4	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
59	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
60	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
61	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
62	C₂×C₄×Dic₄₇	—	2	2	no	—
63	C₂×C₄×Dic₄₇	—	2	2	no	—
64	C₂×C₄×Dic₄₇	—	2	1	no	—
65	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
66	#13093960	—	2	8	no	—
67	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
68	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
69	#13093951	—	2	8	no	—
70	C₂×#41×C₄₇	—	2	2	no	—
71	C₂×#41×C₄₇	—	2	1	no	—
72	C₂×#41×C₄₇	—	2	1	no	—
73	C₂×#41×C₄₇	—	2	2	no	—
74	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×#41×C₄₇	D₄	1	4	yes	—
76	C₂×#41×C₄₇	Q₈	1	4	yes	—
77	C₂×#41×C₄₇	C₂³	1	2	yes	—
78	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂²×D₄×C₄₇	—	2	1	no	—
80	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂³×C₄×C₄₇	—	2	1	no	—
82	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	—	2	2	no	—
84	C₂²×C₈×C₄₇	—	2	2	no	—
85	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
88	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
89	#117×C₄₇	—	2	1	no	—
90	#117×C₄₇	—	2	1	no	—
91	#117×C₄₇	C₂×C₄	1	2	yes	—
92	#117×C₄₇	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
96	C₂×C₄²×C₄₇	—	2	1	no	—
97	#103×C₄₇	C₂×C₄	1	4	yes	complemented
98	#103×C₄₇	C₂×C₄	1	4	yes	complemented
99	#102×C₄₇	C₂×C₄	1	4	yes	complemented
100	#102×C₄₇	C₂×C₄	1	4	yes	complemented
101	C₂⁴×C₄₇	—	2	1	no	—
102	C₂⁴×C₄₇	#41	1	1	yes	characteristic
103	#41×C₄₇	—	2	4	no	—
104	#41×C₄₇	—	2	4	no	—
105	#41×C₄₇	—	2	4	no	—
106	#41×C₄₇	—	2	4	no	—
107	#41×C₄₇	—	2	4	no	—
108	#41×C₄₇	—	2	2	no	—
109	#41×C₄₇	—	2	2	no	—
110	#41×C₄₇	C₄⋊C₄	1	8	yes	—
111	#41×C₄₇	C₂×D₄	1	4	yes	—
112	#41×C₄₇	C₂×Q₈	1	4	yes	—
113	C₂×Q₈×C₄₇	—	2	1	no	—
114	C₂×Q₈×C₄₇	—	2	2	no	—
115	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
116	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×D₄×C₄₇	—	2	2	no	—
118	C₂×D₄×C₄₇	—	2	4	no	—
119	C₂×D₄×C₄₇	—	2	4	no	—
120	C₂×D₄×C₄₇	—	2	2	no	—
121	C₂×D₄×C₄₇	—	2	2	no	—
122	C₂×D₄×C₄₇	—	2	1	no	—
123	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
124	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂²×C₄×C₄₇	—	2	1	no	—
126	C₂²×C₄×C₄₇	—	2	2	no	—
127	C₂²×C₄×C₄₇	—	2	4	no	—
128	C₂²×C₄×C₄₇	—	2	4	no	—
129	C₂²×C₄×C₄₇	—	2	2	no	—
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	1	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	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
139	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	#41	1	2	yes	—
141	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂²×Dic₄₇	—	2	4	no	—
143	C₂²×Dic₄₇	—	2	2	no	—
144	C₂²×Dic₄₇	—	4	2	no	—
145	C₂²×Dic₄₇	—	4	2	no	—
146	C₂×C₈×C₄₇	—	2	2	no	—
147	C₂×C₈×C₄₇	—	2	2	no	—
148	C₂×C₈×C₄₇	—	2	4	no	—
149	C₂×C₈×C₄₇	—	2	2	no	—
150	C₂×C₈×C₄₇	—	2	2	no	—
151	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
153	C₄⋊C₄×C₄₇	—	2	1	no	—
154	C₄⋊C₄×C₄₇	—	2	1	no	—
155	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
156	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
157	C₂²⋊C₄×C₄₇	—	2	2	no	—
158	C₂²⋊C₄×C₄₇	—	2	2	no	—
159	C₄²×C₄₇	—	2	2	no	—
160	C₄²×C₄₇	—	2	2	no	—
161	C₄×Dic₄₇	—	2	2	no	—
162	C₄×Dic₄₇	—	2	2	no	—
163	C₄×Dic₄₇	—	4	2	no	—
164	#10625329	—	2	16	no	—
165	#10625329	—	2	4	no	—
166	#10625329	—	2	2	no	—
167	#10625329	—	2	2	no	—
168	#10625329	—	2	2	no	—
169	#10625329	—	4	2	no	—
170	#10625329	C₂×D₄	1	4	yes	—
171	C₂×C₄₇⋊C₈	—	2	16	no	—
172	C₂×C₄₇⋊C₈	—	2	2	no	—
173	C₂×C₄₇⋊C₈	—	2	4	no	—
174	C₂×C₄₇⋊C₈	—	2	2	no	—
175	C₂×C₄₇⋊C₈	—	2	4	no	—
176	C₂×C₄₇⋊C₈	—	2	2	no	—
177	C₂×C₄₇⋊C₈	—	2	2	no	—
178	C₂×C₄₇⋊C₈	—	2	2	no	—
179	C₂×C₄₇⋊C₈	—	2	2	no	—
180	C₂×C₄₇⋊C₈	—	4	2	no	—
181	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
182	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
183	C₂³×C₄₇	—	2	2	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	2	2	no	—
186	C₂³×C₄₇	—	2	4	no	—
187	C₂³×C₄₇	—	4	2	no	—
188	C₂³×C₄₇	—	4	2	no	—
189	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
190	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
191	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
192	C₂³×C₄₇	#123	1	2	yes	—
193	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
194	Q₈×C₄₇	—	2	2	no	—
195	Q₈×C₄₇	—	2	4	no	—
196	Q₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
197	D₄×C₄₇	—	2	4	no	—
198	D₄×C₄₇	—	2	4	no	—
199	D₄×C₄₇	—	2	8	no	—
200	D₄×C₄₇	—	2	2	no	—
201	D₄×C₄₇	—	2	4	no	—
202	D₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	4	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	8	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	4	2	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
213	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
214	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
215	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
216	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₇	#120	1	2	yes	—
219	C₂×C₄×C₄₇	#120	1	2	yes	—
220	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
221	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
222	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
223	C₂×C₄×C₄₇	#123	1	2	yes	—
224	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
230	C₂×Dic₄₇	—	2	4	no	—
231	C₂×Dic₄₇	—	4	8	no	—
232	C₂×Dic₄₇	—	4	2	no	—
233	C₂×Dic₄₇	—	4	2	no	—
234	C₈×C₄₇	—	2	2	no	—
235	C₈×C₄₇	—	2	2	no	—
236	C₄₇⋊C₈	—	2	2	no	—
237	C₄₇⋊C₈	—	2	4	no	—
238	C₄₇⋊C₈	—	2	2	no	—
239	C₄₇⋊C₈	—	4	2	no	—
240	C₂×#1866	—	47	1	no	maximal, Sylow
241	C₂²×C₄₇	—	2	4	no	—
242	C₂²×C₄₇	—	2	4	no	—
243	C₂²×C₄₇	—	2	1	no	—
244	C₂²×C₄₇	—	2	1	no	—
245	C₂²×C₄₇	—	2	1	no	—
246	C₂²×C₄₇	—	2	1	no	—
247	C₂²×C₄₇	—	2	4	no	—
248	C₂²×C₄₇	—	4	8	no	—
249	C₂²×C₄₇	—	4	2	no	—
250	C₂²×C₄₇	—	4	2	no	—
251	C₂²×C₄₇	#385	1	2	yes	—
252	C₂²×C₄₇	#385	1	2	yes	—
253	C₂²×C₄₇	#443	1	2	yes	—
254	C₂²×C₄₇	#444	1	2	yes	—
255	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
256	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
257	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
258	C₄×C₄₇	—	2	4	no	—
259	C₄×C₄₇	—	4	2	no	—
260	C₄×C₄₇	—	4	2	no	—
261	C₄×C₄₇	#385	1	2	yes	—
262	C₄×C₄₇	#385	1	2	yes	—
263	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
264	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
265	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
266	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
267	Dic₄₇	—	4	4	no	—
268	C₂²×#131	—	47	1	no	—
269	C₂²×#108	—	47	1	no	—
270	C₂×#424	—	47	1	no	—
271	C₂²×#104	—	47	1	no	—
272	C₂×#416	D₄₇	1	1	yes	characteristic
273	#1866	—	47	8	no	—
274	C₂×#339	—	47	1	no	—
275	C₂×#336	—	47	1	no	—
276	C₂×C₄₇	—	2	1	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	2	2	no	—
279	C₂×C₄₇	—	4	4	no	—
280	C₂×C₄₇	#1866	1	4	yes	complemented
281	C₂×C₄₇	C₂×#385	1	1	yes	characteristic
282	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
283	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
284	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
285	C₂×#131	—	47	4	no	—
286	C₂×#131	—	94	2	no	—
287	C₂×#131	—	94	4	no	—
288	C₂×#131	—	94	4	no	—
289	C₂²×M₁₆	—	47	1	no	—
290	C₂²×M₁₆	—	47	1	no	—
291	C₂²×M₁₆	—	94	1	no	—
292	C₂³×C₈	—	47	1	no	—
293	C₂³×C₈	—	94	1	no	—
294	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
295	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
296	C₂²×C₄²	—	47	1	no	—
297	C₂×#108	—	47	4	no	—
298	C₂×#108	—	94	4	no	—
299	#424	—	47	4	no	—
300	#424	—	94	2	no	—
301	C₂×C₄⋊C₈	—	94	1	no	—
302	C₂×C₄⋊C₈	—	94	1	no	—
303	C₂×#104	—	47	4	no	—
304	C₂×#104	—	94	4	no	—
305	#416	Dic₄₇	1	4	yes	complemented
306	#416	C₂×D₄₇	1	4	yes	—
307	C₂×#103	Dic₄₇	1	1	yes	characteristic, complemented
308	C₂×#103	Dic₄₇	1	1	yes	characteristic, complemented
309	C₂×#102	Dic₄₇	1	1	yes	characteristic, complemented
310	C₂×#102	Dic₄₇	1	1	yes	characteristic, complemented
311	#339	—	47	4	no	—
312	#336	—	47	4	no	—
313	C₄₇	C₂×#1866	1	1	yes	characteristic, complemented, Sylow
314	C₂×#41	—	2	2	no	—
315	C₂×#41	—	2	1	no	—
316	C₂×#41	—	2	1	no	—
317	C₂×#41	—	2	2	no	—
318	C₂×#41	Dic₉₄	1	4	yes	—
319	C₂×#41	D₁₈₈	1	4	yes	—
320	C₂×#41	C₂×Dic₄₇	1	2	yes	—
321	C₂×#41	C₂²×D₄₇	1	2	yes	—
322	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
323	C₂²×D₄	—	2	1	no	—
324	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
325	C₂³×C₄	—	2	1	no	—
326	C₂³×C₄	—	94	1	no	—
327	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
328	#131	—	94	8	no	—
329	#131	—	94	16	no	—
330	#131	—	94	8	no	—
331	C₂×M₁₆	—	47	4	no	—
332	C₂×M₁₆	—	47	2	no	—
333	C₂×M₁₆	—	47	2	no	—
334	C₂×M₁₆	—	94	4	no	—
335	C₂×M₁₆	—	94	8	no	—
336	C₂×M₁₆	—	94	2	no	—
337	C₂×M₁₆	—	94	1	no	—
338	C₂×M₁₆	—	94	1	no	—
339	C₂×M₁₆	—	94	2	no	—
340	C₂×M₁₆	—	94	2	no	—
341	C₂²×C₈	—	2	2	no	—
342	C₂²×C₈	—	2	2	no	—
343	C₂²×C₈	—	47	2	no	—
344	C₂²×C₈	—	47	1	no	—
345	C₂²×C₈	—	47	1	no	—
346	C₂²×C₈	—	47	2	no	—
347	C₂²×C₈	—	94	4	no	—
348	C₂²×C₈	—	94	8	no	—
349	C₂²×C₈	—	94	2	no	—
350	C₂²×C₈	—	94	2	no	—
351	C₂²×C₈	—	94	1	no	—
352	C₂²×C₈	—	94	1	no	—
353	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
354	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
355	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
356	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
357	#117	—	2	1	no	—
358	#117	—	2	1	no	—
359	#117	C₂×Dic₄₇	1	2	yes	—
360	#117	C₂²×D₄₇	1	2	yes	—
361	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
362	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	47	2	no	—
366	C₂×C₄²	—	94	2	no	—
367	C₂×C₄²	—	94	2	no	—
368	C₂×C₄²	—	94	1	no	—
369	#108	—	94	8	no	—
370	C₄⋊C₈	—	94	4	no	—
371	C₄⋊C₈	—	94	4	no	—
372	#104	—	94	8	no	—
373	#103	C₂×Dic₄₇	1	4	yes	complemented
374	#103	C₂×Dic₄₇	1	4	yes	complemented
375	#102	C₂×Dic₄₇	1	4	yes	complemented
376	#102	C₂×Dic₄₇	1	4	yes	complemented
377	C₂⁴	—	2	1	no	—
378	C₂⁴	#10625352	1	1	yes	characteristic
379	#41	—	2	4	no	—
380	#41	—	2	4	no	—
381	#41	—	2	4	no	—
382	#41	—	2	4	no	—
383	#41	—	2	4	no	—
384	#41	—	2	2	no	—
385	#41	—	2	2	no	—
386	#41	C₄⋊Dic₄₇	1	8	yes	—
387	#41	C₂×Dic₉₄	1	4	yes	—
388	#41	C₂×D₁₈₈	1	4	yes	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	C₄⋊Dic₄₇	1	4	yes	—
392	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	C₄⋊Dic₄₇	1	4	yes	—
400	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	94	4	no	—
409	C₂²×C₄	—	94	2	no	—
410	C₂²×C₄	—	188	2	no	—
411	C₂²×C₄	—	188	2	no	—
412	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
413	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
414	C₂²×C₄	D₄×D₄₇	1	2	yes	—
415	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
416	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
417	C₂²×C₄	#10625352	1	1	yes	characteristic
418	C₂²×C₄	#10625352	1	2	yes	—
419	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
420	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
421	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
422	M₁₆	—	47	4	no	—
423	M₁₆	—	94	16	no	—
424	M₁₆	—	94	4	no	—
425	M₁₆	—	94	2	no	—
426	M₁₆	—	94	2	no	—
427	M₁₆	—	94	2	no	—
428	M₁₆	—	188	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	4	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	47	2	no	—
435	C₂×C₈	—	47	2	no	—
436	C₂×C₈	—	94	16	no	—
437	C₂×C₈	—	94	2	no	—
438	C₂×C₈	—	94	2	no	—
439	C₂×C₈	—	94	4	no	—
440	C₂×C₈	—	94	4	no	—
441	C₂×C₈	—	94	2	no	—
442	C₂×C₈	—	94	2	no	—
443	C₂×C₈	—	94	2	no	—
444	C₂×C₈	—	94	2	no	—
445	C₂×C₈	—	188	2	no	—
446	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
447	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
451	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₄²	—	2	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	94	2	no	—
457	C₄²	—	94	2	no	—
458	C₄²	—	188	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
466	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
467	C₂³	#13094001	1	2	yes	—
468	C₂³	#13094008	1	2	yes	—
469	C₂³	C₂×#10625352	1	1	yes	characteristic
470	Q₈	—	2	4	no	—
471	Q₈	—	2	2	no	—
472	Q₈	C₂×C₄⋊Dic₄₇	1	4	yes	—
473	D₄	—	2	8	no	—
474	D₄	—	2	4	no	—
475	D₄	—	2	4	no	—
476	D₄	—	2	4	no	—
477	D₄	—	2	2	no	—
478	D₄	C₂×C₄⋊Dic₄₇	1	4	yes	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	94	4	no	—
489	C₂×C₄	—	188	2	no	—
490	C₂×C₄	—	188	8	no	—
491	C₂×C₄	—	188	2	no	—
492	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
493	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
494	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
495	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
496	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
497	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
498	C₂×C₄	#13093994	1	2	yes	—
499	C₂×C₄	#13093994	1	2	yes	—
500	C₂×C₄	#13094001	1	2	yes	—
501	C₂×C₄	#13094001	1	2	yes	—
502	C₂×C₄	#13094001	1	2	yes	—
503	C₂×C₄	#13094008	1	2	yes	—
504	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
505	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
506	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
507	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
508	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
509	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
510	C₈	—	2	2	no	—
511	C₈	—	2	2	no	—
512	C₈	—	94	2	no	—
513	C₈	—	94	2	no	—
514	C₈	—	94	4	no	—
515	C₈	—	188	2	no	—
516	C₂²	—	2	1	no	—
517	C₂²	—	2	1	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	4	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	8	no	—
526	C₂²	#15688998	1	2	yes	—
527	C₂²	#15688998	1	2	yes	—
528	C₂²	#15689240	1	2	yes	—
529	C₂²	#15689245	1	2	yes	—
530	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
531	C₂²	C₂×#13094001	1	1	yes	characteristic
532	C₂²	C₂×#13094008	1	1	yes	characteristic
533	C₄	—	2	4	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	188	4	no	—
537	C₄	#15688998	1	2	yes	—
538	C₄	#15688998	1	2	yes	—
539	C₄	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
540	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
541	C₄	C₂×#13093994	1	1	yes	characteristic
542	C₄	C₂×#13094001	1	1	yes	characteristic
543	C₂	—	2	1	no	—
544	C₂	—	2	2	no	—
545	C₂	—	2	1	no	—
546	C₂	—	4	4	no	—
547	C₂	#20243665	1	4	yes	direct product factor
548	C₂	C₂×#15688998	1	1	yes	characteristic
549	C₂	C₂×#15689240	1	1	yes	characteristic
550	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	C₂×C₄₇×#416	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#416	D₄₇
hypocenter	C₄₇	C₂×#1866
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#416

Complements

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

N	H ≅ G/N	type
2. C₂²×#13093960	C₂	semidirect
3. C₂×#15689150	C₂	semidirect
5. #20243665	C₂	direct (N × H)
6. C₂×#15688882	C₂	semidirect
7. C₂×#15688877	C₂	semidirect
20. C₂×#13093960	C₂²	semidirect
22. #15689150	C₂²	semidirect
27. #15688882	C₂²	semidirect
28. #15688877	C₂²	semidirect
32. C₄₇×#416	C₄	semidirect
34. C₂×#103×C₄₇	C₄	semidirect
35. C₂×#103×C₄₇	C₄	semidirect
36. C₂×#102×C₄₇	C₄	semidirect
37. C₂×#102×C₄₇	C₄	semidirect
97. #103×C₄₇	C₂×C₄	semidirect
98. #103×C₄₇	C₂×C₄	semidirect
99. #102×C₄₇	C₂×C₄	semidirect
100. #102×C₄₇	C₂×C₄	semidirect
280. C₂×C₄₇	#1866	semidirect
305. #416	Dic₄₇	semidirect
307. C₂×#103	Dic₄₇	semidirect
308. C₂×#103	Dic₄₇	semidirect
309. C₂×#102	Dic₄₇	semidirect
310. C₂×#102	Dic₄₇	semidirect
313. C₄₇	C₂×#1866	semidirect
373. #103	C₂×Dic₄₇	semidirect
374. #103	C₂×Dic₄₇	semidirect
375. #102	C₂×Dic₄₇	semidirect
376. #102	C₂×Dic₄₇	semidirect
547. C₂	#20243665	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×#13093960	2
C₂×#15689150	2
C₂²×#13093951	2
#20243665	2
C₂×#15688882	2
C₂×#15688877	2
C₂×C₄₇×#416	2
C₂×#1866	47

Subgroups — C2×#20243665 #26217330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243665 #26217330