Subgroups — #26122559

Order 12032.

1010 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093952	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689117	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689091	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688887	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243085	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#339	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625350	C₂²	1	1	yes	characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×#13093952	—	2	2	no	—
13	C₂×#13093952	—	2	2	no	—
14	C₂×#13093952	C₄	1	4	yes	complemented
15	#15689117	—	2	2	no	—
16	#15689117	—	2	2	no	—
17	C₂×#13093947	C₄	1	2	yes	complemented
18	C₂×#13093944	C₄	1	2	yes	complemented
19	#15689091	—	2	2	no	—
20	#15689091	C₄	1	4	yes	complemented
21	C₂×(C₂×D₄₇)⋊C₈	—	2	2	no	—
22	C₂×C₄×C₄₇⋊C₈	—	2	2	no	—
23	C₂×C₄×C₄₇⋊C₈	—	2	2	no	—
24	C₂×C₄×C₄₇⋊C₈	—	2	2	no	—
25	#15688887	—	2	2	no	—
26	#15688878	—	2	2	no	—
27	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#339	—	2	2	no	—
31	C₂×#10625350	—	2	1	no	—
32	C₂×#10625350	—	2	1	no	—
33	C₂×#10625350	—	2	1	no	—
34	C₂×#10625350	—	2	1	no	—
35	C₂×#10625350	—	2	1	no	—
36	C₂×#10625350	—	2	1	no	—
37	C₂×#10625350	—	2	1	no	—
38	C₂×#10625350	—	2	1	no	—
39	C₂×#10625350	—	2	1	no	—
40	C₂×#10625350	—	2	1	no	—
41	C₂×#10625350	C₂×C₄	1	2	yes	—
42	C₂×#10625350	C₂×C₄	1	2	yes	—
43	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₂²⋊D₄₇	—	2	1	no	—
46	C₂²×C₄×D₄₇	—	2	1	no	—
47	C₂×#10625329	—	2	1	no	—
48	C₂×#10625329	—	2	1	no	—
49	C₂×#10625329	—	2	1	no	—
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	C₂×C₄	1	2	yes	—
53	C₂²×C₄₇⋊C₈	—	2	1	no	—
54	C₂²×C₄₇⋊C₈	—	2	1	no	—
55	C₂²×C₄₇⋊C₈	—	2	1	no	—
56	C₂²×C₄₇⋊C₈	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	—	2	1	no	—
59	C₂²×C₄₇⋊C₈	—	2	1	no	—
60	C₂²×C₄₇⋊C₈	—	2	1	no	—
61	C₂²×C₄₇⋊C₈	—	2	1	no	—
62	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
63	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
64	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
65	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
66	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
67	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
68	#13093952	—	2	8	no	—
69	#13093947	—	2	4	no	—
70	#13093944	—	2	4	no	—
71	(C₂×D₄₇)⋊C₈	—	2	8	no	—
72	C₄×C₄₇⋊C₈	—	2	8	no	—
73	C₂³×C₄×C₄₇	—	2	1	no	—
74	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₄₇	—	2	1	no	—
76	C₂×M₁₆×C₄₇	—	2	1	no	—
77	C₂×M₁₆×C₄₇	—	2	1	no	—
78	C₂×M₁₆×C₄₇	—	2	1	no	—
79	C₂×M₁₆×C₄₇	—	2	1	no	—
80	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
81	C₂²×C₈×C₄₇	—	2	1	no	—
82	#117×C₄₇	—	2	1	no	—
83	#117×C₄₇	—	2	1	no	—
84	#117×C₄₇	—	2	1	no	—
85	#117×C₄₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	—	2	1	no	—
90	C₂×C₄²×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
93	C₂×C₄²×C₄₇	D₄	1	2	yes	—
94	C₂×C₄²×C₄₇	D₄	1	2	yes	—
95	C₂⁴×C₄₇	#41	1	1	yes	characteristic
96	C₂³×D₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	8	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
116	C₂×C₂²⋊D₄₇	—	2	2	no	—
117	C₂×C₂²⋊D₄₇	—	2	2	no	—
118	C₂×C₂²⋊D₄₇	—	4	1	no	—
119	C₂×C₂²⋊D₄₇	—	4	1	no	—
120	C₂×C₂²⋊D₄₇	—	4	1	no	—
121	C₂×C₂²⋊D₄₇	—	4	1	no	—
122	C₂²×Dic₄₇	—	2	1	no	—
123	#10625350	—	2	2	no	—
124	#10625350	—	2	2	no	—
125	#10625350	—	2	2	no	—
126	#10625350	—	2	2	no	—
127	#10625350	—	2	2	no	—
128	#10625350	—	2	2	no	—
129	#10625350	—	2	2	no	—
130	#10625350	—	2	2	no	—
131	#10625350	—	4	1	no	—
132	#10625350	—	4	1	no	—
133	#10625350	—	4	1	no	—
134	#10625350	—	4	1	no	—
135	#10625350	—	4	1	no	—
136	#10625350	—	4	1	no	—
137	#10625350	—	4	1	no	—
138	#10625350	—	4	1	no	—
139	C₂×D₁₈₈	—	2	1	no	—
140	C₂×D₁₈₈	—	2	1	no	—
141	C₂×D₁₈₈	—	2	1	no	—
142	C₂×D₁₈₈	—	2	1	no	—
143	C₂×D₁₈₈	—	2	1	no	—
144	C₂×D₁₈₈	C₄²	1	2	yes	—
145	C₂×C₄×D₄₇	—	2	2	no	—
146	C₂×C₄×D₄₇	—	2	2	no	—
147	C₂×C₄×D₄₇	—	4	1	no	—
148	C₂×C₄×D₄₇	—	4	1	no	—
149	C₂×C₄×D₄₇	—	4	1	no	—
150	C₂×C₄×D₄₇	—	4	1	no	—
151	C₂×Dic₉₄	—	2	1	no	—
152	C₂×Dic₉₄	—	2	1	no	—
153	C₂×Dic₉₄	—	2	1	no	—
154	C₂×Dic₉₄	—	2	1	no	—
155	C₂×Dic₉₄	—	2	1	no	—
156	C₂×Dic₉₄	C₄²	1	2	yes	—
157	M₁₆×C₄₇	—	2	2	no	—
158	M₁₆×C₄₇	—	2	2	no	—
159	M₁₆×C₄₇	—	4	1	no	—
160	M₁₆×C₄₇	—	4	1	no	—
161	C₂×C₈×C₄₇	—	2	2	no	—
162	C₂×C₈×C₄₇	—	4	1	no	—
163	C₂×C₈×C₄₇	—	4	1	no	—
164	C₄⋊C₄×C₄₇	—	2	2	no	—
165	C₄⋊C₄×C₄₇	—	2	2	no	—
166	C₂²⋊C₄×C₄₇	—	4	1	no	—
167	C₂²⋊C₄×C₄₇	—	4	1	no	—
168	C₄²×C₄₇	—	2	2	no	—
169	C₄²×C₄₇	—	2	2	no	—
170	C₄²×C₄₇	—	2	2	no	—
171	C₄²×C₄₇	—	4	1	no	—
172	C₄²×C₄₇	—	4	1	no	—
173	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
174	#10625329	—	2	2	no	—
175	#10625329	—	2	2	no	—
176	#10625329	—	4	1	no	—
177	#10625329	—	4	1	no	—
178	C₂×C₄₇⋊C₈	—	2	2	no	—
179	C₂×C₄₇⋊C₈	—	2	2	no	—
180	C₂×C₄₇⋊C₈	—	2	2	no	—
181	C₂×C₄₇⋊C₈	—	2	2	no	—
182	C₂×C₄₇⋊C₈	—	2	2	no	—
183	C₂×C₄₇⋊C₈	—	2	2	no	—
184	C₂×C₄₇⋊C₈	—	2	2	no	—
185	C₂×C₄₇⋊C₈	—	2	2	no	—
186	C₂×C₄₇⋊C₈	—	2	2	no	—
187	C₂×C₄₇⋊C₈	—	2	2	no	—
188	C₂×C₄₇⋊C₈	—	2	2	no	—
189	C₂×C₄₇⋊C₈	—	2	2	no	—
190	C₂×C₄₇⋊C₈	—	2	2	no	—
191	C₂×C₄₇⋊C₈	—	4	1	no	—
192	C₂×C₄₇⋊C₈	—	4	1	no	—
193	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
194	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	4	yes	—
195	C₂³×C₄₇	—	2	4	no	—
196	C₂³×C₄₇	#117	1	1	yes	characteristic
197	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
198	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₄₇	#121	1	1	yes	characteristic
200	C₂³×C₄₇	#123	1	1	yes	characteristic
201	C₂³×C₄₇	#124	1	1	yes	characteristic
202	C₂³×C₄₇	#126	1	1	yes	characteristic
203	C₂²×D₄₇	—	2	2	no	—
204	C₂²×D₄₇	—	4	1	no	—
205	C₂²×D₄₇	—	4	1	no	—
206	C₂²×D₄₇	—	4	4	no	—
207	C₂×C₄×C₄₇	—	2	8	no	—
208	C₂×C₄×C₄₇	—	2	8	no	—
209	C₂×C₄×C₄₇	—	2	8	no	—
210	C₂×C₄×C₄₇	—	2	4	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	4	no	—
213	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
218	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
230	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
232	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#126	1	1	yes	characteristic
240	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
241	C₂²⋊D₄₇	—	4	2	no	—
242	C₂²⋊D₄₇	—	4	2	no	—
243	C₂²⋊D₄₇	—	4	2	no	—
244	C₂²⋊D₄₇	—	4	2	no	—
245	C₂×Dic₄₇	—	2	2	no	—
246	C₂×Dic₄₇	—	4	1	no	—
247	C₂×Dic₄₇	—	4	1	no	—
248	D₁₈₈	—	2	2	no	—
249	D₁₈₈	—	2	2	no	—
250	D₁₈₈	—	4	1	no	—
251	D₁₈₈	—	4	1	no	—
252	C₄×D₄₇	—	4	2	no	—
253	C₄×D₄₇	—	4	2	no	—
254	C₄×D₄₇	—	4	2	no	—
255	C₄×D₄₇	—	4	2	no	—
256	Dic₉₄	—	2	2	no	—
257	Dic₉₄	—	2	2	no	—
258	Dic₉₄	—	4	1	no	—
259	Dic₉₄	—	4	1	no	—
260	C₈×C₄₇	—	4	2	no	—
261	C₄₇⋊C₈	—	2	4	no	—
262	C₄₇⋊C₈	—	2	4	no	—
263	C₄₇⋊C₈	—	4	2	no	—
264	#10929	—	47	1	no	maximal, Sylow
265	C₂²×C₄₇	—	2	2	no	—
266	C₂²×C₄₇	—	2	2	no	—
267	C₂²×C₄₇	—	2	2	no	—
268	C₂²×C₄₇	—	2	2	no	—
269	C₂²×C₄₇	—	2	2	no	—
270	C₂²×C₄₇	—	2	2	no	—
271	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₄₇	#386	1	1	yes	characteristic
273	C₂²×C₄₇	#388	1	1	yes	characteristic
274	C₂²×C₄₇	#388	1	1	yes	characteristic
275	C₂²×C₄₇	#388	1	1	yes	characteristic
276	C₂²×C₄₇	#388	1	1	yes	characteristic
277	C₂²×C₄₇	#390	1	1	yes	characteristic
278	C₂²×C₄₇	#443	1	4	yes	—
279	C₂×D₄₇	—	4	2	no	—
280	C₂×D₄₇	—	4	4	no	—
281	C₂×D₄₇	—	8	2	no	—
282	C₂×D₄₇	—	8	2	no	—
283	C₄×C₄₇	—	2	8	no	—
284	C₄×C₄₇	—	8	2	no	—
285	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
286	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
287	C₄×C₄₇	#386	1	1	yes	characteristic
288	C₄×C₄₇	#386	1	1	yes	characteristic
289	C₄×C₄₇	#388	1	1	yes	characteristic
290	C₄×C₄₇	#388	1	1	yes	characteristic
291	C₄×C₄₇	#390	1	1	yes	characteristic
292	C₄×C₄₇	#390	1	1	yes	characteristic
293	Dic₄₇	—	4	2	no	—
294	C₂²×#104	—	47	1	no	—
295	C₂×#416	—	47	1	no	—
296	C₂×#408	—	47	1	no	—
297	C₂²×C₄×C₈	—	47	1	no	—
298	C₂×#341	—	47	1	no	—
299	C₂×#339	D₄₇	1	1	yes	characteristic, complemented
300	#1729	—	47	1	no	—
301	C₂×C₄₇	—	2	1	no	—
302	C₂×C₄₇	—	2	1	no	—
303	C₂×C₄₇	—	2	1	no	—
304	C₂×C₄₇	—	2	1	no	—
305	C₂×C₄₇	#1437	1	1	yes	characteristic
306	C₂×C₄₇	#1764	1	2	yes	—
307	C₂×C₄₇	#1937	1	2	yes	—
308	C₂×C₄₇	#1974	1	2	yes	—
309	D₄₇	—	8	2	no	—
310	C₂²×#41	—	47	1	no	—
311	C₂²×M₁₆	—	47	1	no	—
312	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
313	C₂³×C₈	—	47	1	no	—
314	C₂³×C₈	—	47	1	no	—
315	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
316	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
317	C₂×#104	—	47	4	no	—
318	C₂×#104	—	94	2	no	—
319	C₂×#104	—	94	2	no	—
320	#416	—	94	2	no	—
321	#416	—	94	2	no	—
322	C₂×#103	—	47	2	no	—
323	C₂×#102	—	47	2	no	—
324	#408	—	47	4	no	—
325	#408	—	94	2	no	—
326	C₂×C₂²⋊C₈	—	94	2	no	—
327	C₂×C₄×C₈	—	94	2	no	—
328	C₂×C₄×C₈	—	94	2	no	—
329	C₂×C₄×C₈	—	94	2	no	—
330	#341	—	94	2	no	—
331	#339	—	2	2	no	—
332	#336	—	94	2	no	—
333	C₄₇	#10929	1	1	yes	characteristic, complemented, Sylow
334	C₂×#41	—	47	2	no	—
335	C₂×#41	—	47	2	no	—
336	C₂×#41	—	94	1	no	—
337	C₂×#41	—	94	1	no	—
338	C₂×#41	—	94	1	no	—
339	C₂×#41	—	94	1	no	—
340	C₂×#41	—	94	1	no	—
341	C₂×#41	—	94	1	no	—
342	C₂×#41	—	94	1	no	—
343	C₂×#41	—	94	1	no	—
344	C₂×#41	—	94	1	no	—
345	C₂×#41	—	94	1	no	—
346	C₂²×Q₈	—	47	1	no	—
347	C₂²×D₄	—	47	1	no	—
348	C₂²×D₄	—	94	1	no	—
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	—	94	1	no	—
351	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	47	2	no	—
358	C₂×M₁₆	—	94	1	no	—
359	C₂×M₁₆	—	94	1	no	—
360	C₂×M₁₆	—	94	1	no	—
361	C₂×M₁₆	—	94	1	no	—
362	C₂×M₁₆	—	94	1	no	—
363	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	—	47	2	no	—
366	C₂²×C₈	—	47	2	no	—
367	C₂²×C₈	—	47	2	no	—
368	C₂²×C₈	—	47	2	no	—
369	C₂²×C₈	—	47	2	no	—
370	C₂²×C₈	—	47	2	no	—
371	C₂²×C₈	—	94	1	no	—
372	C₂²×C₈	—	94	1	no	—
373	C₂²×C₈	—	94	1	no	—
374	C₂²×C₈	—	94	1	no	—
375	C₂²×C₈	—	94	1	no	—
376	C₂²×C₈	—	94	1	no	—
377	C₂²×C₈	—	94	1	no	—
378	C₂²×C₈	—	94	1	no	—
379	C₂²×C₈	—	94	1	no	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	2	1	no	—
384	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	C₄×D₄₇	1	2	yes	—
391	C₂×C₄²	D₁₈₈	1	2	yes	—
392	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
393	#104	—	94	8	no	—
394	#103	—	94	4	no	—
395	#102	—	94	4	no	—
396	C₂²⋊C₈	—	94	8	no	—
397	C₄×C₈	—	94	8	no	—
398	C₂⁴	—	94	1	no	—
399	C₂⁴	#10625352	1	1	yes	characteristic
400	#41	—	94	2	no	—
401	#41	—	94	2	no	—
402	#41	—	94	2	no	—
403	#41	—	94	2	no	—
404	#41	—	94	2	no	—
405	#41	—	94	2	no	—
406	#41	—	94	2	no	—
407	#41	—	94	2	no	—
408	#41	—	188	1	no	—
409	#41	—	188	1	no	—
410	#41	—	188	1	no	—
411	#41	—	188	1	no	—
412	#41	—	188	1	no	—
413	#41	—	188	1	no	—
414	#41	—	188	1	no	—
415	#41	—	188	1	no	—
416	C₂×Q₈	—	47	2	no	—
417	C₂×Q₈	—	94	1	no	—
418	C₂×Q₈	—	94	1	no	—
419	C₂×Q₈	—	94	1	no	—
420	C₂×Q₈	—	94	1	no	—
421	C₂×Q₈	—	94	1	no	—
422	C₂×D₄	—	47	2	no	—
423	C₂×D₄	—	94	2	no	—
424	C₂×D₄	—	94	2	no	—
425	C₂×D₄	—	94	1	no	—
426	C₂×D₄	—	94	1	no	—
427	C₂×D₄	—	94	1	no	—
428	C₂×D₄	—	94	1	no	—
429	C₂×D₄	—	94	1	no	—
430	C₂×D₄	—	188	1	no	—
431	C₂×D₄	—	188	1	no	—
432	C₂×D₄	—	188	1	no	—
433	C₂×D₄	—	188	1	no	—
434	C₂²×C₄	—	2	8	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	94	1	no	—
440	C₂²×C₄	—	94	2	no	—
441	C₂²×C₄	—	94	2	no	—
442	C₂²×C₄	—	188	1	no	—
443	C₂²×C₄	—	188	1	no	—
444	C₂²×C₄	—	188	1	no	—
445	C₂²×C₄	—	188	1	no	—
446	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
450	C₂²×C₄	#10625350	1	1	yes	characteristic
451	C₂²×C₄	#10625350	1	1	yes	characteristic
452	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
453	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
454	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
455	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
456	C₂²×C₄	#10625352	1	1	yes	characteristic
457	C₂²×C₄	#10625354	1	1	yes	characteristic
458	C₂²×C₄	#10625354	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	4	1	no	—
463	M₁₆	—	4	1	no	—
464	M₁₆	—	94	2	no	—
465	M₁₆	—	94	2	no	—
466	M₁₆	—	188	1	no	—
467	M₁₆	—	188	1	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	4	1	no	—
470	C₂×C₈	—	4	1	no	—
471	C₂×C₈	—	47	4	no	—
472	C₂×C₈	—	47	4	no	—
473	C₂×C₈	—	94	2	no	—
474	C₂×C₈	—	94	2	no	—
475	C₂×C₈	—	94	2	no	—
476	C₂×C₈	—	94	2	no	—
477	C₂×C₈	—	94	2	no	—
478	C₂×C₈	—	94	2	no	—
479	C₂×C₈	—	94	2	no	—
480	C₂×C₈	—	94	2	no	—
481	C₂×C₈	—	94	2	no	—
482	C₂×C₈	—	94	2	no	—
483	C₂×C₈	—	94	2	no	—
484	C₂×C₈	—	94	2	no	—
485	C₂×C₈	—	94	2	no	—
486	C₂×C₈	—	188	1	no	—
487	C₂×C₈	—	188	1	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	4	1	no	—
496	C₄²	—	4	1	no	—
497	C₄²	(C₂×D₄₇)⋊C₄	1	4	yes	—
498	C₂³	—	2	4	no	—
499	C₂³	—	94	2	no	—
500	C₂³	—	188	4	no	—
501	C₂³	—	188	1	no	—
502	C₂³	—	188	1	no	—
503	C₂³	#13093982	1	1	yes	characteristic
504	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
505	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
506	C₂³	#13093996	1	1	yes	characteristic
507	C₂³	#13094008	1	1	yes	characteristic
508	C₂³	#13094010	1	1	yes	characteristic
509	C₂³	#13094019	1	1	yes	characteristic
510	Q₈	—	94	2	no	—
511	Q₈	—	94	2	no	—
512	Q₈	—	188	1	no	—
513	Q₈	—	188	1	no	—
514	D₄	—	94	2	no	—
515	D₄	—	94	2	no	—
516	D₄	—	188	2	no	—
517	D₄	—	188	2	no	—
518	D₄	—	188	2	no	—
519	D₄	—	188	2	no	—
520	D₄	—	188	1	no	—
521	D₄	—	188	1	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	8	no	—
524	C₂×C₄	—	2	8	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	4	4	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	94	2	no	—
529	C₂×C₄	—	188	1	no	—
530	C₂×C₄	—	188	1	no	—
531	C₂×C₄	—	188	2	no	—
532	C₂×C₄	—	188	2	no	—
533	C₂×C₄	—	188	2	no	—
534	C₂×C₄	—	188	2	no	—
535	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
536	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
537	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
538	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
539	C₂×C₄	#13093981	1	1	yes	characteristic
540	C₂×C₄	#13093982	1	1	yes	characteristic
541	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
542	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
543	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
544	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
545	C₂×C₄	#13093986	1	1	yes	characteristic
546	C₂×C₄	#13093986	1	1	yes	characteristic
547	C₂×C₄	#13093986	1	1	yes	characteristic
548	C₂×C₄	#13093986	1	1	yes	characteristic
549	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
550	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
551	C₂×C₄	#13093994	1	1	yes	characteristic
552	C₂×C₄	#13093996	1	1	yes	characteristic
553	C₂×C₄	#13093997	1	1	yes	characteristic
554	C₂×C₄	#13093997	1	1	yes	characteristic
555	C₂×C₄	#13093999	1	1	yes	characteristic
556	C₂×C₄	#13093999	1	1	yes	characteristic
557	C₂×C₄	#13094009	1	1	yes	characteristic
558	C₂×C₄	#13094009	1	1	yes	characteristic
559	C₂×C₄	#13094010	1	1	yes	characteristic
560	C₂×C₄	#13094013	1	1	yes	characteristic
561	C₂×C₄	#13094019	1	1	yes	characteristic
562	C₂×C₄	#13094020	1	1	yes	characteristic
563	C₈	—	4	2	no	—
564	C₈	—	94	4	no	—
565	C₈	—	94	4	no	—
566	C₈	—	188	2	no	—
567	C₂²	—	2	2	no	—
568	C₂²	—	2	2	no	—
569	C₂²	—	2	2	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	376	2	no	—
574	C₂²	—	376	2	no	—
575	C₂²	—	188	4	no	—
576	C₂²	—	188	2	no	—
577	C₂²	#15688970	1	1	yes	characteristic
578	C₂²	#15689000	1	1	yes	characteristic
579	C₂²	#15689012	1	1	yes	characteristic
580	C₂²	#15689013	1	1	yes	characteristic
581	C₂²	#15689015	1	1	yes	characteristic
582	C₂²	#15689015	1	1	yes	characteristic
583	C₂²	#15689023	1	1	yes	characteristic
584	C₂²	#15689237	1	4	yes	—
585	C₄	—	2	8	no	—
586	C₄	—	8	2	no	—
587	C₄	—	188	2	no	—
588	C₄	#15688970	1	1	yes	characteristic
589	C₄	C₄×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
590	C₄	#15689001	1	1	yes	characteristic
591	C₄	#15689001	1	1	yes	characteristic
592	C₄	#15689012	1	1	yes	characteristic
593	C₄	#15689013	1	1	yes	characteristic
594	C₄	#15689023	1	1	yes	characteristic
595	C₄	#15689024	1	1	yes	characteristic
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	—	2	1	no	—
599	C₂	—	2	1	no	—
600	C₂	—	376	2	no	—
601	C₂	#20241624	1	1	yes	characteristic
602	C₂	#20243222	1	2	yes	—
603	C₂	#20244093	1	2	yes	—
604	C₂	#20244273	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#339	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×#10625350	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#339	D₄₇
hypocenter	C₄₇	#10929
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
4. C₂²×C₄×C₄₇⋊C₈	C₂	semidirect
5. C₂×#15688887	C₂	semidirect
6. #20243085	C₂	semidirect
7. C₂×C₄₇×#339	C₂	semidirect
14. C₂×#13093952	C₄	semidirect
17. C₂×#13093947	C₄	semidirect
18. C₂×#13093944	C₄	semidirect
20. #15689091	C₄	semidirect
299. C₂×#339	D₄₇	semidirect
333. C₄₇	#10929	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#13093952	2
C₂×#15689117	2
C₂×#15689091	2
C₂²×C₄×C₄₇⋊C₈	2
C₂×#15688887	2
#20243085	2
C₂×C₄₇×#339	2
#10929	47