Subgroups — #26124106

Order 12032.

886 conjugacy classes of subgroups.

The subgroup lattice has 620 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×#15689120	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689089	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688888	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688883	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243084	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625350	C₂²	1	1	yes	characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂×#13093983	C₂²	1	1	yes	characteristic
12	C₂×#13093952	—	2	2	no	—
13	C₂×#13093952	—	2	2	no	—
14	C₂×#13093952	—	2	2	no	—
15	#15689120	—	2	2	no	—
16	#15689120	—	2	2	no	—
17	C₂×#13093949	C₄	1	2	yes	complemented
18	C₂×#13093946	C₄	1	2	yes	complemented
19	#15689089	—	2	2	no	—
20	#15689089	—	2	2	no	—
21	C₂×(C₂×D₄₇)⋊C₈	—	2	2	no	—
22	#15688888	—	2	2	no	—
23	#15688883	—	2	2	no	—
24	#15688877	—	2	2	no	—
25	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#336	—	2	2	no	—
29	C₂×#10625350	—	2	1	no	—
30	C₂×#10625350	—	2	1	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	D₄	1	2	yes	—
40	C₂×#10625350	D₄	1	2	yes	—
41	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
42	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₂²⋊D₄₇	—	2	1	no	—
44	C₂²×C₄×D₄₇	—	2	1	no	—
45	C₂×#10625329	—	2	1	no	—
46	C₂×#10625329	—	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	—	2	1	no	—
53	C₂×#10625329	—	2	1	no	—
54	C₂×#10625329	—	2	1	no	—
55	C₂×#10625329	D₄	1	2	yes	—
56	C₂×#10625329	D₄	1	2	yes	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	—	2	1	no	—
59	#13093983	—	2	1	no	—
60	#13093983	—	2	1	no	—
61	#13093983	—	2	1	no	—
62	#13093983	—	2	1	no	—
63	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
65	C₂×C₄×Dic₄₇	—	2	1	no	—
66	#13093952	—	2	8	no	—
67	#13093949	—	2	4	no	—
68	#13093946	—	2	4	no	—
69	(C₂×D₄₇)⋊C₈	—	2	8	no	—
70	C₂³×C₄×C₄₇	—	2	1	no	—
71	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	—	2	1	no	—
73	C₂²×C₈×C₄₇	—	2	1	no	—
74	C₂²×C₈×C₄₇	—	2	1	no	—
75	C₂²×C₈×C₄₇	—	2	1	no	—
76	C₂²×C₈×C₄₇	—	2	1	no	—
77	C₂²×C₈×C₄₇	—	2	1	no	—
78	C₂²×C₈×C₄₇	—	2	1	no	—
79	C₂²×C₈×C₄₇	—	2	1	no	—
80	C₂²×C₈×C₄₇	—	2	1	no	—
81	C₂²×C₈×C₄₇	—	2	1	no	—
82	C₂²×C₈×C₄₇	—	2	1	no	—
83	C₂²×C₈×C₄₇	—	2	1	no	—
84	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
85	C₂²×C₈×C₄₇	D₄	1	2	yes	—
86	C₂×C₄²×C₄₇	—	2	1	no	—
87	C₂×C₄²×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	D₄	1	2	yes	—
92	C₂⁴×C₄₇	#41	1	1	yes	characteristic
93	C₂³×D₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	4	2	no	—
97	C₂²×C₄×C₄₇	—	4	1	no	—
98	C₂²×C₄×C₄₇	—	4	1	no	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₄₇	—	2	2	no	—
114	C₂×C₂²⋊D₄₇	—	2	2	no	—
115	C₂×C₂²⋊D₄₇	—	4	1	no	—
116	C₂×C₂²⋊D₄₇	—	4	1	no	—
117	C₂×C₂²⋊D₄₇	—	4	1	no	—
118	C₂×C₂²⋊D₄₇	—	4	1	no	—
119	C₂²×Dic₄₇	—	2	1	no	—
120	C₂²×Dic₄₇	—	2	2	no	—
121	#10625350	—	2	2	no	—
122	#10625350	—	2	2	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	—	4	1	no	—
130	#10625350	—	4	1	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	C₂×D₁₈₈	—	2	1	no	—
138	C₂×D₁₈₈	—	2	1	no	—
139	C₂×D₁₈₈	—	2	1	no	—
140	C₂×D₁₈₈	—	2	1	no	—
141	C₂×D₁₈₈	—	2	1	no	—
142	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×D₄₇	—	2	2	no	—
144	C₂×C₄×D₄₇	—	2	2	no	—
145	C₂×C₄×D₄₇	—	4	1	no	—
146	C₂×C₄×D₄₇	—	4	1	no	—
147	C₂×C₄×D₄₇	—	4	1	no	—
148	C₂×C₄×D₄₇	—	4	1	no	—
149	C₂×Dic₉₄	—	2	1	no	—
150	C₂×Dic₉₄	—	2	1	no	—
151	C₂×Dic₉₄	—	2	1	no	—
152	C₂×Dic₉₄	—	2	1	no	—
153	C₂×Dic₉₄	—	2	1	no	—
154	C₂×Dic₉₄	C₂²⋊C₄	1	2	yes	—
155	C₂×C₈×C₄₇	—	2	2	no	—
156	C₂×C₈×C₄₇	—	2	2	no	—
157	C₂×C₈×C₄₇	—	2	2	no	—
158	C₂×C₈×C₄₇	—	2	2	no	—
159	C₂×C₈×C₄₇	—	2	2	no	—
160	C₂×C₈×C₄₇	—	2	2	no	—
161	C₂×C₈×C₄₇	—	4	1	no	—
162	C₂×C₈×C₄₇	—	4	1	no	—
163	C₂×C₈×C₄₇	—	4	1	no	—
164	C₂×C₈×C₄₇	—	4	1	no	—
165	C₂×C₈×C₄₇	—	4	1	no	—
166	C₂×C₈×C₄₇	—	4	1	no	—
167	C₂×C₈×C₄₇	—	4	1	no	—
168	C₂×C₈×C₄₇	—	4	1	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	C₂²⋊Dic₄₇	—	4	1	no	—
174	C₂²⋊Dic₄₇	—	4	1	no	—
175	C₄⋊Dic₄₇	—	2	2	no	—
176	C₄⋊Dic₄₇	—	2	2	no	—
177	C₄×Dic₄₇	—	4	1	no	—
178	C₄×Dic₄₇	—	4	1	no	—
179	#10625329	—	2	2	no	—
180	#10625329	—	2	2	no	—
181	#10625329	—	2	2	no	—
182	#10625329	—	2	2	no	—
183	#10625329	—	4	1	no	—
184	#10625329	—	4	1	no	—
185	#10625329	—	4	1	no	—
186	#10625329	—	4	1	no	—
187	C₂×C₄₇⋊C₈	—	2	2	no	—
188	C₂×C₄₇⋊C₈	—	2	2	no	—
189	C₂×C₄₇⋊C₈	—	4	1	no	—
190	C₂×C₄₇⋊C₈	—	4	1	no	—
191	C₂×C₄₇⋊C₈	—	4	1	no	—
192	C₂×C₄₇⋊C₈	—	4	1	no	—
193	C₂³×C₄₇	—	2	2	no	—
194	C₂³×C₄₇	—	2	2	no	—
195	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
196	C₂³×C₄₇	#121	1	1	yes	characteristic
197	C₂³×C₄₇	#123	1	1	yes	characteristic
198	C₂³×C₄₇	#123	1	1	yes	characteristic
199	C₂³×C₄₇	#124	1	1	yes	characteristic
200	C₂³×C₄₇	#126	1	1	yes	characteristic
201	C₂³×C₄₇	#126	1	1	yes	characteristic
202	C₂²×D₄₇	—	2	2	no	—
203	C₂²×D₄₇	—	4	1	no	—
204	C₂²×D₄₇	—	4	1	no	—
205	C₂²×D₄₇	—	4	2	no	—
206	C₂²×D₄₇	—	4	2	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	4	4	no	—
209	C₂×C₄×C₄₇	—	4	4	no	—
210	C₂×C₄×C₄₇	—	4	2	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
214	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
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	1	yes	characteristic
219	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
220	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
221	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
222	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
223	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
224	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
225	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
226	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
227	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
228	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
229	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
230	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
231	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
232	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
233	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
234	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
235	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
238	C₂×C₄×C₄₇	#126	1	1	yes	characteristic
239	C₂×C₄×C₄₇	#126	1	1	yes	characteristic
240	C₂²⋊D₄₇	—	4	2	no	—
241	C₂²⋊D₄₇	—	4	2	no	—
242	C₂²⋊D₄₇	—	4	2	no	—
243	C₂²⋊D₄₇	—	4	2	no	—
244	C₂×Dic₄₇	—	2	2	no	—
245	C₂×Dic₄₇	—	4	1	no	—
246	C₂×Dic₄₇	—	4	1	no	—
247	C₂×Dic₄₇	—	4	2	no	—
248	C₂×Dic₄₇	—	4	2	no	—
249	C₂×Dic₄₇	—	4	2	no	—
250	D₁₈₈	—	2	2	no	—
251	D₁₈₈	—	2	2	no	—
252	D₁₈₈	—	4	1	no	—
253	D₁₈₈	—	4	1	no	—
254	C₄×D₄₇	—	4	2	no	—
255	C₄×D₄₇	—	4	2	no	—
256	C₄×D₄₇	—	4	2	no	—
257	C₄×D₄₇	—	4	2	no	—
258	Dic₉₄	—	2	2	no	—
259	Dic₉₄	—	2	2	no	—
260	Dic₉₄	—	4	1	no	—
261	Dic₉₄	—	4	1	no	—
262	C₈×C₄₇	—	4	2	no	—
263	C₈×C₄₇	—	4	2	no	—
264	C₄₇⋊C₈	—	4	2	no	—
265	C₄₇⋊C₈	—	4	2	no	—
266	#11191	—	47	1	no	maximal, Sylow
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	—	2	1	no	—
272	C₂²×C₄₇	—	2	1	no	—
273	C₂²×C₄₇	—	2	1	no	—
274	C₂²×C₄₇	—	2	1	no	—
275	C₂²×C₄₇	#386	1	1	yes	characteristic
276	C₂²×C₄₇	#388	1	1	yes	characteristic
277	C₂²×C₄₇	#388	1	1	yes	characteristic
278	C₂²×C₄₇	#394	1	1	yes	characteristic
279	C₂²×C₄₇	#397	1	1	yes	characteristic
280	C₂²×C₄₇	#397	1	1	yes	characteristic
281	C₂²×C₄₇	#397	1	1	yes	characteristic
282	C₂²×C₄₇	#443	1	2	yes	—
283	C₂²×C₄₇	#444	1	2	yes	—
284	C₂×D₄₇	—	4	4	no	—
285	C₂×D₄₇	—	4	2	no	—
286	C₂×D₄₇	—	8	2	no	—
287	C₂×D₄₇	—	8	1	no	—
288	C₂×D₄₇	—	8	1	no	—
289	C₄×C₄₇	—	4	4	no	—
290	C₄×C₄₇	#381	1	1	yes	characteristic
291	C₄×C₄₇	#386	1	1	yes	characteristic
292	C₄×C₄₇	#388	1	1	yes	characteristic
293	C₄×C₄₇	#388	1	1	yes	characteristic
294	C₄×C₄₇	#394	1	1	yes	characteristic
295	C₄×C₄₇	#394	1	1	yes	characteristic
296	C₄×C₄₇	#394	1	1	yes	characteristic
297	C₄×C₄₇	#397	1	1	yes	characteristic
298	Dic₄₇	—	4	2	no	—
299	Dic₄₇	—	8	2	no	—
300	C₂²×#104	—	47	1	no	—
301	C₂×#416	—	47	1	no	—
302	C₂×#408	—	47	1	no	—
303	C₂×#341	—	47	1	no	—
304	C₂×#339	—	47	1	no	—
305	#1729	—	47	1	no	—
306	C₂×#336	D₄₇	1	1	yes	characteristic, complemented
307	C₂×C₄₇	—	2	1	no	—
308	C₂×C₄₇	—	2	1	no	—
309	C₂×C₄₇	—	2	1	no	—
310	C₂×C₄₇	—	2	1	no	—
311	C₂×C₄₇	#1440	1	1	yes	characteristic
312	C₂×C₄₇	#1876	1	2	yes	—
313	C₂×C₄₇	#1929	1	2	yes	—
314	C₂×C₄₇	#1937	1	1	yes	characteristic
315	C₂×C₄₇	#1938	1	1	yes	characteristic
316	D₄₇	—	8	2	no	—
317	C₂²×#41	—	47	1	no	—
318	C₂²×M₁₆	—	47	1	no	—
319	C₂²×M₁₆	—	47	1	no	—
320	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
321	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
322	C₂×#117	—	47	1	no	—
323	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
324	C₂×#104	—	94	2	no	—
325	C₂×#104	—	94	2	no	—
326	C₂×#104	—	94	2	no	—
327	#416	—	94	2	no	—
328	#416	—	94	2	no	—
329	C₂×#103	—	47	2	no	—
330	C₂×#102	—	47	2	no	—
331	#408	—	94	2	no	—
332	#408	—	94	2	no	—
333	C₂×C₂²⋊C₈	—	94	2	no	—
334	#341	—	94	2	no	—
335	#339	—	94	2	no	—
336	#336	—	2	2	no	—
337	#336	—	94	2	no	—
338	C₄₇	#11191	1	1	yes	characteristic, complemented, Sylow
339	C₂×#41	—	47	2	no	—
340	C₂×#41	—	47	2	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	C₂×#41	—	94	1	no	—
347	C₂×#41	—	94	1	no	—
348	C₂×#41	—	94	1	no	—
349	C₂×#41	—	94	1	no	—
350	C₂×#41	—	94	1	no	—
351	C₂²×Q₈	—	47	1	no	—
352	C₂²×D₄	—	47	1	no	—
353	C₂²×D₄	—	94	1	no	—
354	C₂³×C₄	—	2	1	no	—
355	C₂³×C₄	—	94	1	no	—
356	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
357	C₂×M₁₆	—	47	2	no	—
358	C₂×M₁₆	—	47	2	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	—	94	1	no	—
364	C₂×M₁₆	—	94	1	no	—
365	C₂×M₁₆	—	94	1	no	—
366	C₂×M₁₆	—	94	1	no	—
367	C₂×M₁₆	—	94	1	no	—
368	C₂×M₁₆	—	94	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₂²×C₈	—	2	1	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	—	2	1	no	—
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	94	1	no	—
382	C₂²×C₈	—	94	1	no	—
383	C₂²×C₈	C₄×D₄₇	1	2	yes	—
384	C₂²×C₈	D₁₈₈	1	2	yes	—
385	#117	—	94	1	no	—
386	#117	—	94	1	no	—
387	#117	—	94	1	no	—
388	#117	—	94	1	no	—
389	C₂×C₄⋊C₄	—	47	2	no	—
390	C₂×C₂²⋊C₄	—	94	1	no	—
391	C₂×C₄²	—	2	1	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	94	1	no	—
397	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
398	#104	—	94	8	no	—
399	#103	—	94	4	no	—
400	#102	—	94	4	no	—
401	C₂²⋊C₈	—	94	8	no	—
402	C₂⁴	—	94	1	no	—
403	C₂⁴	#10625350	1	1	yes	characteristic
404	#41	—	94	2	no	—
405	#41	—	94	2	no	—
406	#41	—	94	2	no	—
407	#41	—	94	2	no	—
408	#41	—	94	2	no	—
409	#41	—	94	2	no	—
410	#41	—	94	2	no	—
411	#41	—	94	2	no	—
412	#41	—	188	1	no	—
413	#41	—	188	1	no	—
414	#41	—	188	1	no	—
415	#41	—	188	1	no	—
416	#41	—	188	1	no	—
417	#41	—	188	1	no	—
418	#41	—	188	1	no	—
419	#41	—	188	1	no	—
420	C₂×Q₈	—	47	2	no	—
421	C₂×Q₈	—	94	1	no	—
422	C₂×Q₈	—	94	1	no	—
423	C₂×Q₈	—	94	1	no	—
424	C₂×Q₈	—	94	1	no	—
425	C₂×Q₈	—	94	1	no	—
426	C₂×D₄	—	47	2	no	—
427	C₂×D₄	—	94	2	no	—
428	C₂×D₄	—	94	2	no	—
429	C₂×D₄	—	94	1	no	—
430	C₂×D₄	—	94	1	no	—
431	C₂×D₄	—	94	1	no	—
432	C₂×D₄	—	94	1	no	—
433	C₂×D₄	—	94	1	no	—
434	C₂×D₄	—	188	1	no	—
435	C₂×D₄	—	188	1	no	—
436	C₂×D₄	—	188	1	no	—
437	C₂×D₄	—	188	1	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	4	2	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	94	1	no	—
444	C₂²×C₄	—	94	2	no	—
445	C₂²×C₄	—	94	2	no	—
446	C₂²×C₄	—	94	2	no	—
447	C₂²×C₄	—	188	1	no	—
448	C₂²×C₄	—	188	1	no	—
449	C₂²×C₄	—	188	1	no	—
450	C₂²×C₄	—	188	1	no	—
451	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
453	C₂²×C₄	#10625350	1	1	yes	characteristic
454	C₂²×C₄	#10625350	1	1	yes	characteristic
455	C₂²×C₄	#10625350	1	1	yes	characteristic
456	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
457	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
458	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
459	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
460	C₂²×C₄	#10625352	1	1	yes	characteristic
461	C₂²×C₄	#10625352	1	1	yes	characteristic
462	C₂²×C₄	#10625354	1	1	yes	characteristic
463	C₂²×C₄	#10625354	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
465	M₁₆	—	94	2	no	—
466	M₁₆	—	94	2	no	—
467	M₁₆	—	94	2	no	—
468	M₁₆	—	94	2	no	—
469	M₁₆	—	188	1	no	—
470	M₁₆	—	188	1	no	—
471	M₁₆	—	188	1	no	—
472	M₁₆	—	188	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	4	1	no	—
484	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	4	1	no	—
486	C₂×C₈	—	4	1	no	—
487	C₂×C₈	—	94	2	no	—
488	C₂×C₈	—	94	2	no	—
489	C₂×C₈	—	188	1	no	—
490	C₂×C₈	—	188	1	no	—
491	C₂×C₈	—	188	1	no	—
492	C₂×C₈	—	188	1	no	—
493	C₄⋊C₄	—	94	2	no	—
494	C₄⋊C₄	—	94	2	no	—
495	C₂²⋊C₄	—	188	1	no	—
496	C₂²⋊C₄	—	188	1	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	4	1	no	—
500	C₄²	—	4	1	no	—
501	C₄²	—	188	1	no	—
502	C₄²	—	188	1	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	94	2	no	—
506	C₂³	—	188	2	no	—
507	C₂³	—	188	2	no	—
508	C₂³	—	188	1	no	—
509	C₂³	—	188	1	no	—
510	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
511	C₂³	#13093997	1	1	yes	characteristic
512	C₂³	#13094007	1	1	yes	characteristic
513	C₂³	#13094009	1	1	yes	characteristic
514	C₂³	#13094010	1	1	yes	characteristic
515	C₂³	#13094018	1	1	yes	characteristic
516	C₂³	#13094019	1	1	yes	characteristic
517	Q₈	—	94	2	no	—
518	Q₈	—	94	2	no	—
519	Q₈	—	188	1	no	—
520	Q₈	—	188	1	no	—
521	D₄	—	94	2	no	—
522	D₄	—	94	2	no	—
523	D₄	—	188	2	no	—
524	D₄	—	188	2	no	—
525	D₄	—	188	2	no	—
526	D₄	—	188	2	no	—
527	D₄	—	188	1	no	—
528	D₄	—	188	1	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	4	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	94	2	no	—
535	C₂×C₄	—	188	2	no	—
536	C₂×C₄	—	188	2	no	—
537	C₂×C₄	—	188	2	no	—
538	C₂×C₄	—	188	1	no	—
539	C₂×C₄	—	188	1	no	—
540	C₂×C₄	—	188	2	no	—
541	C₂×C₄	—	188	2	no	—
542	C₂×C₄	—	188	2	no	—
543	C₂×C₄	—	188	2	no	—
544	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
545	C₂×C₄	#13093981	1	1	yes	characteristic
546	C₂×C₄	#13093982	1	1	yes	characteristic
547	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
548	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
549	C₂×C₄	#13093986	1	1	yes	characteristic
550	C₂×C₄	#13093992	1	1	yes	characteristic
551	C₂×C₄	#13093994	1	1	yes	characteristic
552	C₂×C₄	#13093995	1	1	yes	characteristic
553	C₂×C₄	#13093996	1	1	yes	characteristic
554	C₂×C₄	#13093997	1	1	yes	characteristic
555	C₂×C₄	#13093997	1	1	yes	characteristic
556	C₂×C₄	#13093998	1	1	yes	characteristic
557	C₂×C₄	#13093999	1	1	yes	characteristic
558	C₂×C₄	#13093999	1	1	yes	characteristic
559	C₂×C₄	#13094006	1	1	yes	characteristic
560	C₂×C₄	#13094006	1	1	yes	characteristic
561	C₂×C₄	#13094006	1	1	yes	characteristic
562	C₂×C₄	#13094008	1	1	yes	characteristic
563	C₂×C₄	#13094009	1	1	yes	characteristic
564	C₂×C₄	#13094009	1	1	yes	characteristic
565	C₂×C₄	#13094009	1	1	yes	characteristic
566	C₂×C₄	#13094009	1	1	yes	characteristic
567	C₂×C₄	#13094010	1	1	yes	characteristic
568	C₂×C₄	#13094012	1	1	yes	characteristic
569	C₂×C₄	#13094013	1	1	yes	characteristic
570	C₂×C₄	#13094019	1	1	yes	characteristic
571	C₂×C₄	#13094019	1	1	yes	characteristic
572	C₈	—	4	2	no	—
573	C₈	—	4	2	no	—
574	C₈	—	188	2	no	—
575	C₈	—	188	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	376	2	no	—
585	C₂²	—	376	1	no	—
586	C₂²	—	376	1	no	—
587	C₂²	—	188	4	no	—
588	C₂²	—	188	2	no	—
589	C₂²	#15689001	1	1	yes	characteristic
590	C₂²	#15689014	1	1	yes	characteristic
591	C₂²	#15689015	1	1	yes	characteristic
592	C₂²	#15689038	1	1	yes	characteristic
593	C₂²	#15689049	1	1	yes	characteristic
594	C₂²	#15689052	1	1	yes	characteristic
595	C₂²	#15689052	1	1	yes	characteristic
596	C₂²	#15689241	1	2	yes	—
597	C₂²	#15689246	1	2	yes	—
598	C₄	—	4	4	no	—
599	C₄	—	376	2	no	—
600	C₄	—	188	2	no	—
601	C₄	#15688985	1	1	yes	characteristic
602	C₄	#15688999	1	1	yes	characteristic
603	C₄	#15689012	1	1	yes	characteristic
604	C₄	#15689013	1	1	yes	characteristic
605	C₄	#15689039	1	1	yes	characteristic
606	C₄	#15689040	1	1	yes	characteristic
607	C₄	#15689041	1	1	yes	characteristic
608	C₄	#15689050	1	1	yes	characteristic
609	C₂	—	2	1	no	—
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	376	2	no	—
614	C₂	#20241636	1	1	yes	characteristic
615	C₂	#20243714	1	2	yes	—
616	C₂	#20244037	1	2	yes	—
617	C₂	#20244092	1	1	yes	characteristic
618	C₂	#20244099	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#336	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×#10625350	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#336	D₄₇
hypocenter	C₄₇	#11191
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
4. C₂×#15688888	C₂	semidirect
5. C₂×#15688883	C₂	semidirect
6. #20243084	C₂	semidirect
7. C₂×C₄₇×#336	C₂	semidirect
17. C₂×#13093949	C₄	semidirect
18. C₂×#13093946	C₄	semidirect
306. C₂×#336	D₄₇	semidirect
338. C₄₇	#11191	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×#15689120	2
C₂×#15689089	2
C₂×#15688888	2
C₂×#15688883	2
#20243084	2
C₂×C₄₇×#336	2
#11191	47