Subgroups — C₂×#20243228 #26214111

Order 12032.

1558 conjugacy classes of subgroups.

The subgroup lattice has 504 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×#13093951	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243228	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688888	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688882	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	C₄	1	8	yes	complemented
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×#13093951	C₄	1	8	yes	complemented
20	C₂×#13093951	C₂²	1	4	yes	—
21	#15689079	—	2	2	no	—
22	#15689079	C₂²	1	4	yes	complemented
23	C₂×#13093935	—	2	1	no	—
24	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
25	C₂×C₈×Dic₄₇	—	2	4	no	—
26	C₂×C₈×Dic₄₇	C₂²	1	4	yes	complemented
27	#15688888	C₂²	1	4	yes	complemented
28	#15688882	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	2	yes	complemented
35	C₂×#102×C₄₇	C₄	1	2	yes	complemented
36	C₂³×Dic₄₇	—	2	1	no	—
37	#13094031	—	2	16	no	—
38	#13094031	—	2	8	no	—
39	#13094031	C₂×C₄	1	16	yes	complemented
40	C₂×#10625329	—	2	1	no	—
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	—	2	1	no	—
43	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	—	2	8	no	—
45	C₂×#10625329	—	2	4	no	—
46	C₂×#10625329	C₂×C₄	1	4	yes	—
47	C₂×#10625329	C₂×C₄	1	4	yes	—
48	C₂×#10625329	C₂³	1	2	yes	—
49	C₂×#10625329	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	—	2	1	no	—
51	C₂²×C₄₇⋊C₈	—	2	1	no	—
52	C₂²×C₄₇⋊C₈	—	2	8	no	—
53	C₂²×C₄₇⋊C₈	—	2	4	no	—
54	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
55	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
56	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
58	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
59	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
60	C₂×C₄×Dic₄₇	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
63	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
64	#13093951	C₂×C₄	1	16	yes	complemented
65	#13093935	—	2	4	no	—
66	C₄×C₄₇⋊C₈	—	2	4	no	—
67	C₈×Dic₄₇	—	2	8	no	—
68	C₂×#41×C₄₇	—	2	2	no	—
69	C₂×#41×C₄₇	—	2	1	no	—
70	C₂×#41×C₄₇	—	2	1	no	—
71	C₂×#41×C₄₇	—	2	2	no	—
72	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
73	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
74	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×#41×C₄₇	C₂³	1	2	yes	—
76	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂²×D₄×C₄₇	—	2	1	no	—
78	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₄₇	—	2	1	no	—
80	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	—	2	2	no	—
82	C₂²×C₈×C₄₇	—	2	2	no	—
83	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
84	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
85	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
86	#117×C₄₇	—	2	1	no	—
87	#117×C₄₇	—	2	1	no	—
88	#117×C₄₇	C₂×C₄	1	2	yes	—
89	#117×C₄₇	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
91	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	—	2	1	no	—
93	#103×C₄₇	C₂×C₄	1	8	yes	complemented
94	#102×C₄₇	C₂×C₄	1	8	yes	complemented
95	C₂⁴×C₄₇	—	2	1	no	—
96	C₂⁴×C₄₇	#41	1	1	yes	characteristic
97	#41×C₄₇	—	2	4	no	—
98	#41×C₄₇	—	2	4	no	—
99	#41×C₄₇	—	2	4	no	—
100	#41×C₄₇	—	2	4	no	—
101	#41×C₄₇	—	2	4	no	—
102	#41×C₄₇	—	2	2	no	—
103	#41×C₄₇	—	2	2	no	—
104	#41×C₄₇	C₄²	1	8	yes	—
105	#41×C₄₇	C₂²×C₄	1	4	yes	—
106	#41×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂×Q₈×C₄₇	—	2	1	no	—
108	C₂×Q₈×C₄₇	—	2	2	no	—
109	C₂×Q₈×C₄₇	C₄²	1	4	yes	—
110	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₄₇	—	2	4	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	4	no	—
114	C₂×D₄×C₄₇	—	2	2	no	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	2	1	no	—
117	C₂×D₄×C₄₇	C₄²	1	4	yes	—
118	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	—	2	4	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	4	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	#41	1	2	yes	—
134	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂²×Dic₄₇	—	2	8	no	—
136	C₂²×Dic₄₇	—	2	4	no	—
137	C₂²×Dic₄₇	—	2	2	no	—
138	C₂×C₈×C₄₇	—	2	4	no	—
139	C₂×C₈×C₄₇	—	2	4	no	—
140	C₂×C₈×C₄₇	—	2	2	no	—
141	C₂×C₈×C₄₇	—	2	2	no	—
142	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
143	C₄⋊C₄×C₄₇	—	2	2	no	—
144	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
145	C₂²⋊C₄×C₄₇	—	2	2	no	—
146	C₂²⋊C₄×C₄₇	—	2	2	no	—
147	C₄²×C₄₇	—	2	2	no	—
148	C₄²×C₄₇	—	2	2	no	—
149	C₄×Dic₄₇	—	2	4	no	—
150	C₄×Dic₄₇	—	2	2	no	—
151	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
152	#10625329	—	2	4	no	—
153	#10625329	—	2	4	no	—
154	#10625329	—	2	2	no	—
155	#10625329	—	2	2	no	—
156	#10625329	—	2	16	no	—
157	#10625329	C₂²×C₄	1	4	yes	—
158	#10625329	C₂²×C₄	1	4	yes	—
159	C₂×C₄₇⋊C₈	—	2	4	no	—
160	C₂×C₄₇⋊C₈	—	2	4	no	—
161	C₂×C₄₇⋊C₈	—	2	2	no	—
162	C₂×C₄₇⋊C₈	—	2	2	no	—
163	C₂×C₄₇⋊C₈	—	2	16	no	—
164	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
165	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
166	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	8	yes	—
167	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
168	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
169	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
170	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
171	C₂³×C₄₇	—	2	4	no	—
172	C₂³×C₄₇	—	2	2	no	—
173	C₂³×C₄₇	—	2	4	no	—
174	C₂³×C₄₇	—	4	4	no	—
175	C₂³×C₄₇	#117	1	2	yes	—
176	C₂³×C₄₇	C₄×D₄	1	2	yes	—
177	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
178	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
179	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
180	Q₈×C₄₇	—	2	2	no	—
181	Q₈×C₄₇	—	2	4	no	—
182	Q₈×C₄₇	C₂×C₄²	1	4	yes	—
183	D₄×C₄₇	—	2	4	no	—
184	D₄×C₄₇	—	2	4	no	—
185	D₄×C₄₇	—	2	8	no	—
186	D₄×C₄₇	—	2	2	no	—
187	D₄×C₄₇	—	2	4	no	—
188	D₄×C₄₇	C₂×C₄²	1	4	yes	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	4	no	—
191	C₂×C₄×C₄₇	—	2	4	no	—
192	C₂×C₄×C₄₇	—	2	4	no	—
193	C₂×C₄×C₄₇	—	2	8	no	—
194	C₂×C₄×C₄₇	—	2	4	no	—
195	C₂×C₄×C₄₇	—	4	4	no	—
196	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
197	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
198	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂×C₄×C₄₇	#117	1	2	yes	—
201	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
214	C₂×Dic₄₇	—	2	8	no	—
215	C₂×Dic₄₇	—	2	16	no	—
216	C₂×Dic₄₇	—	2	4	no	—
217	C₈×C₄₇	—	2	4	no	—
218	C₄₇⋊C₈	—	2	4	no	—
219	C₄₇⋊C₈	—	2	4	no	—
220	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	4	yes	—
221	C₄₇⋊C₈	C₂×C₂²⋊C₄	1	4	yes	—
222	C₂×#1764	—	47	1	no	maximal, Sylow
223	C₂²×C₄₇	—	2	2	no	—
224	C₂²×C₄₇	—	2	2	no	—
225	C₂²×C₄₇	—	2	4	no	—
226	C₂²×C₄₇	—	2	4	no	—
227	C₂²×C₄₇	—	2	4	no	—
228	C₂²×C₄₇	—	4	4	no	—
229	C₂²×C₄₇	—	4	8	no	—
230	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
231	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
232	C₂²×C₄₇	#443	1	4	yes	—
233	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
234	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
235	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
236	C₄×C₄₇	—	2	4	no	—
237	C₄×C₄₇	—	4	4	no	—
238	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
239	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
240	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
241	C₄×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
242	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
243	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
244	Dic₄₇	—	2	8	no	—
245	C₂²×#131	—	47	1	no	—
246	C₂²×#104	—	47	1	no	—
247	C₂×#416	D₄₇	1	1	yes	characteristic
248	C₂×#405	—	47	1	no	—
249	C₂²×C₄×C₈	—	47	1	no	—
250	#1764	—	47	8	no	—
251	C₂×#341	—	47	1	no	—
252	C₂×#339	—	47	1	no	—
253	C₂×C₄₇	—	2	1	no	—
254	C₂×C₄₇	—	2	1	no	—
255	C₂×C₄₇	—	2	2	no	—
256	C₂×C₄₇	—	4	4	no	—
257	C₂×C₄₇	#1764	1	4	yes	complemented
258	C₂×C₄₇	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄₇	C₂×#443	1	2	yes	—
260	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
261	C₂×#131	—	47	8	no	—
262	C₂×#131	—	47	4	no	—
263	C₂×#131	—	94	4	no	—
264	C₂×#131	—	94	2	no	—
265	C₂²×M₁₆	—	47	1	no	—
266	C₂²×M₁₆	—	47	1	no	—
267	C₂²×M₁₆	—	94	1	no	—
268	C₂³×C₈	—	47	1	no	—
269	C₂³×C₈	—	94	1	no	—
270	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
271	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
272	C₂²×C₄²	—	47	1	no	—
273	C₂×#104	—	47	8	no	—
274	C₂×#104	—	47	4	no	—
275	#416	Dic₄₇	1	4	yes	complemented
276	#416	C₂×D₄₇	1	4	yes	—
277	C₂×#103	Dic₄₇	1	2	yes	complemented
278	C₂×#102	Dic₄₇	1	2	yes	complemented
279	#405	—	47	4	no	—
280	#405	—	94	2	no	—
281	C₂×#97	—	94	1	no	—
282	C₂×C₄×C₈	—	47	4	no	—
283	C₂×C₄×C₈	—	94	1	no	—
284	C₂×C₄×C₈	—	94	4	no	—
285	#341	—	47	4	no	—
286	#339	—	47	4	no	—
287	C₄₇	C₂×#1764	1	1	yes	characteristic, complemented, Sylow
288	C₂×#41	—	2	2	no	—
289	C₂×#41	—	2	1	no	—
290	C₂×#41	—	2	2	no	—
291	C₂×#41	—	2	1	no	—
292	C₂×#41	C₄×D₄₇	1	4	yes	—
293	C₂×#41	C₄×D₄₇	1	4	yes	—
294	C₂×#41	C₂×Dic₄₇	1	2	yes	—
295	C₂×#41	C₂²×D₄₇	1	2	yes	—
296	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
299	C₂³×C₄	—	2	1	no	—
300	C₂³×C₄	—	94	1	no	—
301	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
302	#131	—	47	16	no	—
303	#131	—	94	16	no	—
304	#131	—	94	8	no	—
305	C₂×M₁₆	—	47	4	no	—
306	C₂×M₁₆	—	47	4	no	—
307	C₂×M₁₆	—	47	2	no	—
308	C₂×M₁₆	—	47	2	no	—
309	C₂×M₁₆	—	94	8	no	—
310	C₂×M₁₆	—	94	4	no	—
311	C₂×M₁₆	—	94	2	no	—
312	C₂×M₁₆	—	94	1	no	—
313	C₂×M₁₆	—	94	1	no	—
314	C₂×M₁₆	—	94	2	no	—
315	C₂²×C₈	—	2	2	no	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	—	47	4	no	—
318	C₂²×C₈	—	47	4	no	—
319	C₂²×C₈	—	47	2	no	—
320	C₂²×C₈	—	47	1	no	—
321	C₂²×C₈	—	47	1	no	—
322	C₂²×C₈	—	47	2	no	—
323	C₂²×C₈	—	94	8	no	—
324	C₂²×C₈	—	94	4	no	—
325	C₂²×C₈	—	94	1	no	—
326	C₂²×C₈	—	94	1	no	—
327	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
328	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
329	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
330	#117	—	2	1	no	—
331	#117	—	2	1	no	—
332	#117	C₂×Dic₄₇	1	2	yes	—
333	#117	C₂²×D₄₇	1	2	yes	—
334	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	47	4	no	—
338	C₂×C₄²	—	47	2	no	—
339	C₂×C₄²	—	94	2	no	—
340	C₂×C₄²	—	94	1	no	—
341	#104	—	47	16	no	—
342	#103	C₂×Dic₄₇	1	8	yes	complemented
343	#102	C₂×Dic₄₇	1	8	yes	complemented
344	#97	—	94	4	no	—
345	C₄×C₈	—	94	4	no	—
346	C₄×C₈	—	94	8	no	—
347	C₂⁴	—	2	1	no	—
348	C₂⁴	#10625352	1	1	yes	characteristic
349	#41	—	2	4	no	—
350	#41	—	2	4	no	—
351	#41	—	2	4	no	—
352	#41	—	2	4	no	—
353	#41	—	2	4	no	—
354	#41	—	2	2	no	—
355	#41	—	2	2	no	—
356	#41	C₄×Dic₄₇	1	8	yes	—
357	#41	C₂×C₄×D₄₇	1	4	yes	—
358	#41	C₂×C₄×D₄₇	1	4	yes	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	C₄×Dic₄₇	1	4	yes	—
362	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
370	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	94	8	no	—
378	C₂²×C₄	—	94	4	no	—
379	C₂²×C₄	—	94	2	no	—
380	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
381	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
382	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
383	C₂²×C₄	D₄×D₄₇	1	2	yes	—
384	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
385	C₂²×C₄	#10625352	1	1	yes	characteristic
386	C₂²×C₄	#10625352	1	2	yes	—
387	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
388	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
389	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
390	M₁₆	—	47	4	no	—
391	M₁₆	—	47	4	no	—
392	M₁₆	—	94	16	no	—
393	M₁₆	—	94	4	no	—
394	M₁₆	—	94	4	no	—
395	M₁₆	—	94	2	no	—
396	M₁₆	—	94	2	no	—
397	C₂×C₈	—	2	4	no	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	47	4	no	—
402	C₂×C₈	—	47	4	no	—
403	C₂×C₈	—	47	8	no	—
404	C₂×C₈	—	47	4	no	—
405	C₂×C₈	—	47	2	no	—
406	C₂×C₈	—	47	4	no	—
407	C₂×C₈	—	47	2	no	—
408	C₂×C₈	—	94	16	no	—
409	C₂×C₈	—	94	4	no	—
410	C₂×C₈	—	94	4	no	—
411	C₂×C₈	—	94	2	no	—
412	C₂×C₈	—	94	2	no	—
413	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	47	4	no	—
421	C₄²	—	94	4	no	—
422	C₄²	—	94	2	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	4	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	4	no	—
427	C₂³	#13093980	1	2	yes	—
428	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
429	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
430	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
431	C₂³	C₂×#10625352	1	1	yes	characteristic
432	Q₈	—	2	4	no	—
433	Q₈	—	2	2	no	—
434	Q₈	C₂×C₄×Dic₄₇	1	4	yes	—
435	D₄	—	2	8	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	4	no	—
439	D₄	—	2	2	no	—
440	D₄	C₂×C₄×Dic₄₇	1	4	yes	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	94	16	no	—
449	C₂×C₄	—	94	8	no	—
450	C₂×C₄	—	94	4	no	—
451	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
452	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
453	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
454	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
455	C₂×C₄	#13093980	1	2	yes	—
456	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
457	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
458	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
459	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
460	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
461	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
462	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
463	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
464	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
465	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
466	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
467	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
468	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
469	C₈	—	2	4	no	—
470	C₈	—	47	4	no	—
471	C₈	—	47	4	no	—
472	C₈	—	94	4	no	—
473	C₈	—	94	4	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	4	8	no	—
480	C₂²	—	4	4	no	—
481	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
482	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
483	C₂²	#15689240	1	4	yes	—
484	C₂²	C₂×#13093980	1	1	yes	characteristic
485	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
486	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
487	C₄	—	2	4	no	—
488	C₄	—	4	4	no	—
489	C₄	—	94	8	no	—
490	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
491	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
492	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
493	C₄	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
494	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
495	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
496	C₂	—	2	1	no	—
497	C₂	—	2	2	no	—
498	C₂	—	2	1	no	—
499	C₂	—	4	4	no	—
500	C₂	#20243228	1	4	yes	direct product factor
501	C₂	C₂×C₂²⋊C₄×Dic₄₇	1	1	yes	characteristic
502	C₂	C₂×#15689240	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
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×#1764
LCS	G ▷ 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
3. C₂×#15689079	C₂	semidirect
4. C₂²×C₈×Dic₄₇	C₂	semidirect
5. #20243228	C₂	direct (N × H)
6. C₂×#15688888	C₂	semidirect
7. C₂×#15688882	C₂	semidirect
11. C₂×#13094031	C₄	semidirect
19. C₂×#13093951	C₄	semidirect
22. #15689079	C₂²	semidirect
26. C₂×C₈×Dic₄₇	C₂²	semidirect
27. #15688888	C₂²	semidirect
28. #15688882	C₂²	semidirect
32. C₄₇×#416	C₄	semidirect
34. C₂×#103×C₄₇	C₄	semidirect
35. C₂×#102×C₄₇	C₄	semidirect
39. #13094031	C₂×C₄	semidirect
64. #13093951	C₂×C₄	semidirect
93. #103×C₄₇	C₂×C₄	semidirect
94. #102×C₄₇	C₂×C₄	semidirect
257. C₂×C₄₇	#1764	semidirect
275. #416	Dic₄₇	semidirect
277. C₂×#103	Dic₄₇	semidirect
278. C₂×#102	Dic₄₇	semidirect
287. C₄₇	C₂×#1764	semidirect
342. #103	C₂×Dic₄₇	semidirect
343. #102	C₂×Dic₄₇	semidirect
500. C₂	#20243228	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×#15689079	2
C₂²×C₈×Dic₄₇	2
#20243228	2
C₂×#15688888	2
C₂×#15688882	2
C₂×C₄₇×#416	2
C₂×#1764	47

Subgroups — C2×#20243228 #26214111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243228 #26214111