Subgroups — #26223052

Order 12032.

998 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252966	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689237	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252083	C₂	1	1	yes	maximal, characteristic, complemented
4	#20252078	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244273	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244135	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244093	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244089	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243831	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243424	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243266	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243226	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243222	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1896	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13094044	C₂²	1	1	yes	characteristic
17	C₂×#13094032	C₂²	1	1	yes	characteristic
18	C₂×#13094031	C₂²	1	1	yes	characteristic
19	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	#15689634	C₂²	1	1	yes	characteristic
22	#15689362	C₄	1	2	yes	complemented
23	#15689357	C₄	1	2	yes	complemented
24	#15689354	C₄	1	2	yes	complemented
25	#15689350	C₄	1	2	yes	complemented
26	#15689237	—	2	4	no	—
27	#15689195	—	2	2	no	—
28	#15689191	—	2	2	no	—
29	D₄×C₄₇⋊C₈	—	2	2	no	—
30	(C₂²⋊D₄₇)⋊C₈	—	2	2	no	—
31	C₂×#13093959	C₂²	1	1	yes	characteristic
32	C₂×#13093959	C₂²	1	1	yes	characteristic
33	#15689159	C₂²	1	1	yes	characteristic
34	#15689151	C₂²	1	1	yes	characteristic
35	#15689150	C₂²	1	1	yes	characteristic
36	C₂×#13093952	C₂²	1	1	yes	characteristic
37	C₂×#13093952	C₂²	1	1	yes	characteristic
38	#15689119	C₂²	1	1	yes	characteristic
39	#15689117	C₂²	1	1	yes	characteristic
40	#15689091	C₂²	1	1	yes	characteristic
41	#15689090	C₂²	1	1	yes	characteristic
42	#15689087	C₂²	1	1	yes	characteristic
43	#15689081	C₂²	1	1	yes	characteristic
44	#15689079	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₄₇⋊C₈	—	2	4	no	—
46	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
50	#15688887	C₂²	1	1	yes	characteristic
51	#15688887	C₂²	1	1	yes	characteristic
52	#15688883	C₂²	1	1	yes	characteristic
53	#15688883	C₂²	1	1	yes	characteristic
54	C₄₇×#525	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×#104×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×#104×C₄₇	C₂²	1	1	yes	characteristic
58	C₄₇×#407	C₂²	1	1	yes	characteristic
59	C₄₇×#339	C₂²	1	1	yes	characteristic
60	C₄₇×#339	C₂²	1	1	yes	characteristic
61	C₂×#10625350	C₂³	1	1	yes	characteristic
62	#13094044	—	2	2	no	—
63	#13094044	—	2	2	no	—
64	C₂×#10625337	C₂×C₄	1	1	yes	characteristic, complemented
65	C₂×#10625335	C₂×C₄	1	1	yes	characteristic, complemented
66	C₂×#10625336	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×#10625334	C₂×C₄	1	1	yes	characteristic, complemented
68	#13094032	—	2	2	no	—
69	#13094032	—	2	2	no	—
70	#13094031	—	2	2	no	—
71	#13094031	—	2	2	no	—
72	C₂×#10625329	—	2	1	no	—
73	C₂×#10625329	C₂³	1	1	yes	characteristic
74	C₂×#10625329	C₂³	1	1	yes	characteristic
75	C₂×#10625324	—	2	1	no	—
76	C₂²×C₄₇⋊C₈	—	2	2	no	—
77	C₂²×C₄₇⋊C₈	—	2	2	no	—
78	C₂²×C₄₇⋊C₈	—	2	2	no	—
79	C₂²×C₄₇⋊C₈	—	2	2	no	—
80	C₂²×C₄₇⋊C₈	—	2	1	no	—
81	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
82	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
83	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
84	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
85	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
88	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
89	C₂×C₈×D₄₇	—	2	1	no	—
90	#13094007	—	2	1	no	—
91	#13094003	C₂×C₄	1	2	yes	—
92	#13093998	C₂×C₄	1	2	yes	—
93	#13093993	—	2	1	no	—
94	C₄×C₂²⋊D₄₇	—	2	2	no	—
95	#13093983	C₂³	1	1	yes	characteristic
96	#13093959	—	2	2	no	—
97	#13093959	—	2	2	no	—
98	#13093957	C₂×C₄	1	2	yes	complemented
99	#13093955	C₂×C₄	1	2	yes	complemented
100	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
101	Dic₄₇⋊C₈	—	2	2	no	—
102	#13093952	—	2	2	no	—
103	#13093952	—	2	2	no	—
104	#13093948	C₂×C₄	1	2	yes	complemented
105	#13093947	C₂×C₄	1	2	yes	complemented
106	#13093945	C₂×C₄	1	2	yes	complemented
107	#13093944	C₂×C₄	1	2	yes	complemented
108	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
109	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
110	(C₂×D₄₇)⋊C₈	—	2	2	no	—
111	#13093935	—	2	1	no	—
112	#13093934	—	2	1	no	—
113	C₄×C₄₇⋊C₈	—	2	2	no	—
114	C₄×C₄₇⋊C₈	—	2	2	no	—
115	C₄×C₄₇⋊C₈	—	2	2	no	—
116	C₄×C₄₇⋊C₈	—	2	1	no	—
117	C₄×C₄₇⋊C₈	D₄	1	4	yes	complemented
118	C₈×Dic₄₇	—	2	1	no	—
119	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₄₇	—	2	1	no	—
121	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
122	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
123	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
124	#123×C₄₇	—	2	1	no	—
125	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
126	#121×C₄₇	C₂×C₄	1	2	yes	—
127	#120×C₄₇	—	2	1	no	—
128	C₄×D₄×C₄₇	—	2	2	no	—
129	#117×C₄₇	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₄₇	—	2	1	no	—
131	C₂×C₄²×C₄₇	—	2	2	no	—
132	C₂×C₄²×C₄₇	—	2	2	no	—
133	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
135	#104×C₄₇	—	2	2	no	—
136	#104×C₄₇	—	2	2	no	—
137	C₂²⋊C₈×C₄₇	—	2	2	no	—
138	C₂⁴×C₄₇	#41	1	1	yes	characteristic
139	#41×C₄₇	—	2	1	no	—
140	#41×C₄₇	—	2	1	no	—
141	#41×C₄₇	—	2	1	no	—
142	#41×C₄₇	—	2	1	no	—
143	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂×D₄×C₄₇	—	2	2	no	—
145	C₂×D₄×C₄₇	—	2	1	no	—
146	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	—	2	4	no	—
148	C₂²×C₄×C₄₇	—	2	8	no	—
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂²×C₄×C₄₇	—	2	1	no	—
152	C₂²×C₄×C₄₇	—	2	1	no	—
153	C₂²×C₄×C₄₇	—	2	1	no	—
154	C₂²×C₄×C₄₇	—	2	1	no	—
155	C₂²×C₄×C₄₇	—	2	1	no	—
156	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
160	C₂×C₂²⋊D₄₇	—	2	2	no	—
161	C₂×C₂²⋊D₄₇	—	2	1	no	—
162	#10625350	—	2	1	no	—
163	#10625350	—	2	1	no	—
164	#10625350	—	2	1	no	—
165	#10625350	—	2	1	no	—
166	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₄₇	—	2	1	no	—
168	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
169	M₁₆×C₄₇	—	2	1	no	—
170	M₁₆×C₄₇	—	2	1	no	—
171	M₁₆×C₄₇	—	2	1	no	—
172	M₁₆×C₄₇	—	2	1	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₄⋊C₄×C₄₇	—	2	2	no	—
176	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
177	C₂²⋊C₄×C₄₇	—	2	2	no	—
178	C₂²⋊C₄×C₄₇	—	2	1	no	—
179	C₂²⋊C₄×C₄₇	—	2	2	no	—
180	C₄²×C₄₇	—	2	4	no	—
181	C₄²×C₄₇	—	2	1	no	—
182	C₄²×C₄₇	—	2	1	no	—
183	C₄²×C₄₇	—	2	1	no	—
184	C₄²×C₄₇	C₂×D₄	1	2	yes	—
185	C₄²×C₄₇	#41	1	2	yes	—
186	C₂²⋊Dic₄₇	—	2	2	no	—
187	C₂²⋊Dic₄₇	—	2	1	no	—
188	#10625337	—	2	2	no	—
189	#10625336	—	2	2	no	—
190	#10625335	—	2	2	no	—
191	#10625334	—	2	2	no	—
192	(C₂×D₄₇)⋊C₄	—	2	2	no	—
193	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
194	Dic₄₇⋊C₄	—	2	2	no	—
195	C₄×Dic₄₇	—	2	1	no	—
196	#10625329	—	2	1	no	—
197	#10625329	—	2	1	no	—
198	#10625329	—	2	1	no	—
199	#10625329	—	2	1	no	—
200	#10625329	—	4	2	no	—
201	C₂×C₄₇⋊C₈	—	2	1	no	—
202	C₂×C₄₇⋊C₈	—	2	1	no	—
203	C₂×C₄₇⋊C₈	—	2	1	no	—
204	C₂×C₄₇⋊C₈	—	2	1	no	—
205	C₂×C₄₇⋊C₈	—	2	4	no	—
206	C₂×C₄₇⋊C₈	—	2	4	no	—
207	C₂×C₄₇⋊C₈	—	2	4	no	—
208	C₂×C₄₇⋊C₈	—	2	4	no	—
209	C₂×C₄₇⋊C₈	—	2	1	no	—
210	C₂×C₄₇⋊C₈	—	2	1	no	—
211	C₂×C₄₇⋊C₈	—	4	2	no	—
212	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
213	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
214	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
215	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
216	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
217	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
218	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
219	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
220	C₂×C₄₇⋊C₈	#41	1	2	yes	—
221	C₂×C₄₇⋊C₈	#41	1	2	yes	—
222	#10625324	—	4	2	no	—
223	C₈×D₄₇	—	4	2	no	—
224	C₂³×C₄₇	—	2	1	no	—
225	C₂³×C₄₇	—	2	1	no	—
226	C₂³×C₄₇	—	2	4	no	—
227	C₂³×C₄₇	—	2	1	no	—
228	C₂³×C₄₇	C₄×D₄	1	2	yes	—
229	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
230	C₂²×D₄₇	—	2	1	no	—
231	Q₈×C₄₇	—	2	1	no	—
232	Q₈×C₄₇	—	2	1	no	—
233	D₄×C₄₇	—	2	1	no	—
234	D₄×C₄₇	—	2	1	no	—
235	D₄×C₄₇	—	4	1	no	—
236	D₄×C₄₇	—	4	1	no	—
237	D₄×C₄₇	—	4	4	no	—
238	C₂×C₄×C₄₇	—	2	16	no	—
239	C₂×C₄×C₄₇	—	2	4	no	—
240	C₂×C₄×C₄₇	—	2	4	no	—
241	C₂×C₄×C₄₇	—	2	1	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	2	2	no	—
244	C₂×C₄×C₄₇	—	2	1	no	—
245	C₂×C₄×C₄₇	—	2	2	no	—
246	C₂×C₄×C₄₇	—	2	2	no	—
247	C₂×C₄×C₄₇	—	2	2	no	—
248	C₂×C₄×C₄₇	—	2	2	no	—
249	C₂×C₄×C₄₇	—	2	2	no	—
250	C₂×C₄×C₄₇	—	2	1	no	—
251	C₂×C₄×C₄₇	—	4	1	no	—
252	C₂×C₄×C₄₇	—	4	1	no	—
253	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
254	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
260	C₂²⋊D₄₇	—	4	1	no	—
261	C₂²⋊D₄₇	—	4	1	no	—
262	C₂²⋊D₄₇	—	4	4	no	—
263	C₂×Dic₄₇	—	2	2	no	—
264	C₂×Dic₄₇	—	2	1	no	—
265	D₁₈₈	—	2	1	no	—
266	D₁₈₈	—	2	1	no	—
267	C₄×D₄₇	—	4	1	no	—
268	C₄×D₄₇	—	4	1	no	—
269	Dic₉₄	—	2	1	no	—
270	Dic₉₄	—	2	1	no	—
271	C₈×C₄₇	—	4	1	no	—
272	C₈×C₄₇	—	4	1	no	—
273	C₄₇⋊C₈	—	2	2	no	—
274	C₄₇⋊C₈	—	2	2	no	—
275	C₄₇⋊C₈	—	4	1	no	—
276	C₄₇⋊C₈	—	4	1	no	—
277	C₄₇⋊C₈	C₄×D₄	1	2	yes	—
278	C₄₇⋊C₈	C₄×D₄	1	2	yes	—
279	C₄₇⋊C₈	#121	1	2	yes	—
280	C₄₇⋊C₈	#121	1	2	yes	—
281	#21544	—	47	1	no	maximal, Sylow
282	C₂²×C₄₇	—	2	4	no	—
283	C₂²×C₄₇	—	2	4	no	—
284	C₂²×C₄₇	—	2	2	no	—
285	C₂²×C₄₇	—	2	2	no	—
286	C₂²×C₄₇	—	2	2	no	—
287	C₂²×C₄₇	—	4	2	no	—
288	C₂²×C₄₇	—	4	1	no	—
289	C₂²×C₄₇	#443	1	4	yes	complemented
290	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂²×C₄₇	#525	1	1	yes	characteristic
292	C₂²×C₄₇	#529	1	1	yes	characteristic
293	C₂×D₄₇	—	4	2	no	—
294	C₂×D₄₇	—	4	1	no	—
295	C₄×C₄₇	—	2	4	no	—
296	C₄×C₄₇	—	2	4	no	—
297	C₄×C₄₇	—	2	2	no	—
298	C₄×C₄₇	—	4	2	no	—
299	C₄×C₄₇	—	4	1	no	—
300	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
301	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
302	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
303	C₄×C₄₇	#532	1	1	yes	characteristic
304	Dic₄₇	—	4	2	no	—
305	Dic₄₇	—	4	1	no	—
306	#3050	—	47	1	no	—
307	C₂×#443	—	47	1	no	—
308	#2929	—	47	1	no	—
309	#2929	—	47	1	no	—
310	C₂²×C₄×C₈	—	47	1	no	—
311	#1974	—	47	1	no	—
312	#1945	—	47	1	no	—
313	#1937	—	47	1	no	—
314	#1937	—	47	1	no	—
315	#1896	—	47	1	no	—
316	#1896	D₄₇	1	1	yes	characteristic, complemented
317	#1810	—	47	1	no	—
318	#1772	—	47	1	no	—
319	#1764	—	47	1	no	—
320	#1764	—	47	1	no	—
321	C₂×C₄₇	—	2	1	no	—
322	C₂×C₄₇	—	2	1	no	—
323	C₂×C₄₇	—	2	4	no	—
324	C₂×C₄₇	—	8	1	no	—
325	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
326	C₂×C₄₇	C₂×#443	1	2	yes	—
327	D₄₇	—	8	1	no	—
328	C₂×#135	—	47	1	no	—
329	C₂×#131	—	47	1	no	—
330	C₂×#131	—	47	1	no	—
331	C₂³×C₈	—	47	1	no	—
332	C₂³×C₈	—	47	1	no	—
333	#525	—	47	1	no	—
334	#525	C₂×D₄₇	1	1	yes	characteristic
335	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
336	#467	—	47	2	no	—
337	#466	—	47	2	no	—
338	#465	—	47	2	no	—
339	#465	—	47	2	no	—
340	#443	—	94	4	no	—
341	#435	—	94	2	no	—
342	#435	—	94	2	no	—
343	C₈×D₄	—	94	2	no	—
344	C₈×D₄	—	94	2	no	—
345	C₂×#108	—	47	1	no	—
346	C₂×#108	—	47	1	no	—
347	#427	—	47	1	no	—
348	#424	—	47	1	no	—
349	#424	—	47	1	no	—
350	C₂×#104	—	47	1	no	—
351	C₂×#104	—	47	1	no	—
352	C₂×#104	C₂×D₄₇	1	1	yes	characteristic
353	C₂×#104	C₂×D₄₇	1	1	yes	characteristic
354	#416	—	47	1	no	—
355	#416	—	47	1	no	—
356	#408	—	47	1	no	—
357	#408	—	47	1	no	—
358	#407	—	47	1	no	—
359	#407	C₂×D₄₇	1	1	yes	characteristic
360	#405	—	47	1	no	—
361	#405	—	47	1	no	—
362	C₂×C₄×C₈	—	47	1	no	—
363	C₂×C₄×C₈	—	47	1	no	—
364	C₂×C₄×C₈	—	47	1	no	—
365	C₂×C₄×C₈	—	47	1	no	—
366	C₂×C₄×C₈	—	94	4	no	—
367	#341	—	47	1	no	—
368	#341	—	47	1	no	—
369	#339	—	47	1	no	—
370	#339	—	47	1	no	—
371	#339	C₂×D₄₇	1	1	yes	characteristic
372	#339	C₂×D₄₇	1	1	yes	characteristic
373	C₄₇	#21544	1	1	yes	characteristic, complemented, Sylow
374	C₂×#41	—	47	1	no	—
375	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
376	C₂³×C₄	—	2	1	no	—
377	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
378	#135	—	94	2	no	—
379	#135	—	94	2	no	—
380	C₂×Q₁₆	—	47	1	no	—
381	C₂×SD₁₆	—	47	1	no	—
382	C₂×SD₁₆	—	47	1	no	—
383	C₂×D₈	—	47	1	no	—
384	#131	—	94	2	no	—
385	#131	—	94	2	no	—
386	#131	—	94	2	no	—
387	#131	—	94	2	no	—
388	C₂×M₁₆	—	47	1	no	—
389	C₂×M₁₆	—	47	1	no	—
390	C₂×M₁₆	—	94	1	no	—
391	C₂×M₁₆	—	94	1	no	—
392	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
393	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
394	C₂²×C₈	—	47	1	no	—
395	C₂²×C₈	—	47	1	no	—
396	C₂²×C₈	—	47	2	no	—
397	C₂²×C₈	—	47	2	no	—
398	C₂²×C₈	—	47	2	no	—
399	C₂²×C₈	—	47	2	no	—
400	C₂²×C₈	—	47	1	no	—
401	C₂²×C₈	—	47	1	no	—
402	C₂²×C₈	—	94	1	no	—
403	C₂²×C₈	—	94	2	no	—
404	C₂²×C₈	—	94	2	no	—
405	C₂²×C₈	—	94	2	no	—
406	C₂²×C₈	—	94	2	no	—
407	C₂²×C₈	—	94	1	no	—
408	#123	—	2	1	no	—
409	#123	—	94	1	no	—
410	C₂²⋊Q₈	—	47	2	no	—
411	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
412	#121	—	47	2	no	—
413	#121	C₄×D₄₇	1	2	yes	—
414	#120	—	2	1	no	—
415	#120	—	94	1	no	—
416	C₄×D₄	—	2	2	no	—
417	C₄×D₄	—	94	2	no	—
418	#117	—	47	1	no	—
419	#117	C₂²×D₄₇	1	1	yes	characteristic
420	C₂×C₄²	—	2	1	no	—
421	C₂×C₄²	—	2	2	no	—
422	C₂×C₄²	—	2	2	no	—
423	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
424	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
425	#108	—	94	2	no	—
426	#108	—	94	2	no	—
427	#107	—	47	2	no	—
428	#106	—	47	2	no	—
429	C₄⋊C₈	—	94	2	no	—
430	C₄⋊C₈	—	94	2	no	—
431	#104	—	2	2	no	—
432	#104	—	2	2	no	—
433	#104	—	94	2	no	—
434	#104	—	94	2	no	—
435	#103	—	47	2	no	—
436	#103	—	47	2	no	—
437	#102	—	47	2	no	—
438	#102	—	47	2	no	—
439	C₂²⋊C₈	—	2	2	no	—
440	C₂²⋊C₈	—	94	2	no	—
441	C₂²⋊C₈	—	94	2	no	—
442	C₂²⋊C₈	—	94	2	no	—
443	#97	—	94	1	no	—
444	#97	—	94	1	no	—
445	C₄×C₈	—	47	4	no	—
446	C₄×C₈	—	94	2	no	—
447	C₄×C₈	—	94	2	no	—
448	C₄×C₈	—	94	1	no	—
449	C₄×C₈	—	94	1	no	—
450	C₄×C₈	—	94	2	no	—
451	C₂⁴	#10625352	1	1	yes	characteristic
452	#41	—	2	1	no	—
453	#41	—	2	1	no	—
454	#41	—	2	1	no	—
455	#41	—	2	1	no	—
456	#41	—	94	1	no	—
457	#41	—	94	1	no	—
458	#41	—	94	1	no	—
459	#41	—	94	1	no	—
460	C₂×Q₈	—	47	1	no	—
461	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	47	1	no	—
465	C₂×D₄	—	94	2	no	—
466	C₂×D₄	—	94	1	no	—
467	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	94	1	no	—
478	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
479	C₂²×C₄	D₄×D₄₇	1	2	yes	—
480	C₂²×C₄	#10625352	1	1	yes	characteristic
481	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
482	Q₁₆	—	94	2	no	—
483	SD₁₆	—	94	2	no	—
484	SD₁₆	—	94	2	no	—
485	D₈	—	94	2	no	—
486	M₁₆	—	2	1	no	—
487	M₁₆	—	2	1	no	—
488	M₁₆	—	2	1	no	—
489	M₁₆	—	2	1	no	—
490	M₁₆	—	94	1	no	—
491	M₁₆	—	94	1	no	—
492	M₁₆	—	94	1	no	—
493	M₁₆	—	94	1	no	—
494	M₁₆	—	188	2	no	—
495	M₁₆	—	188	2	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	47	1	no	—
499	C₂×C₈	—	47	1	no	—
500	C₂×C₈	—	47	2	no	—
501	C₂×C₈	—	47	2	no	—
502	C₂×C₈	—	47	1	no	—
503	C₂×C₈	—	47	1	no	—
504	C₂×C₈	—	47	2	no	—
505	C₂×C₈	—	47	2	no	—
506	C₂×C₈	—	47	2	no	—
507	C₂×C₈	—	47	2	no	—
508	C₂×C₈	—	94	4	no	—
509	C₂×C₈	—	94	4	no	—
510	C₂×C₈	—	94	4	no	—
511	C₂×C₈	—	94	4	no	—
512	C₂×C₈	—	94	1	no	—
513	C₂×C₈	—	94	1	no	—
514	C₂×C₈	—	94	1	no	—
515	C₂×C₈	—	94	1	no	—
516	C₂×C₈	—	94	1	no	—
517	C₂×C₈	—	94	1	no	—
518	C₂×C₈	—	188	2	no	—
519	C₂×C₈	—	188	2	no	—
520	C₄⋊C₄	—	2	2	no	—
521	C₄⋊C₄	—	47	2	no	—
522	C₄⋊C₄	—	94	2	no	—
523	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	94	2	no	—
528	C₂²⋊C₄	—	94	1	no	—
529	C₂²⋊C₄	—	94	2	no	—
530	C₄²	—	2	4	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	94	1	no	—
535	C₄²	D₄×D₄₇	1	2	yes	—
536	C₄²	#10625352	1	2	yes	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	94	1	no	—
542	C₂³	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
543	C₂³	C₂×#10625352	1	1	yes	characteristic
544	Q₈	—	2	1	no	—
545	Q₈	—	2	1	no	—
546	Q₈	—	94	1	no	—
547	Q₈	—	94	1	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	1	no	—
550	D₄	—	4	4	no	—
551	D₄	—	4	1	no	—
552	D₄	—	4	1	no	—
553	D₄	—	94	1	no	—
554	D₄	—	94	1	no	—
555	D₄	—	188	4	no	—
556	D₄	—	188	1	no	—
557	D₄	—	188	1	no	—
558	C₂×C₄	—	2	16	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	94	2	no	—
574	C₂×C₄	—	94	1	no	—
575	C₂×C₄	—	188	1	no	—
576	C₂×C₄	—	188	1	no	—
577	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
578	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
579	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
580	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
581	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
582	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
583	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
584	C₈	—	4	1	no	—
585	C₈	—	4	1	no	—
586	C₈	—	47	2	no	—
587	C₈	—	47	2	no	—
588	C₈	—	47	2	no	—
589	C₈	—	47	2	no	—
590	C₈	—	94	2	no	—
591	C₈	—	94	2	no	—
592	C₈	—	188	1	no	—
593	C₈	—	188	1	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	188	2	no	—
602	C₂²	—	188	1	no	—
603	C₂²	#15689237	1	4	yes	complemented
604	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
605	C₂²	#15689629	1	1	yes	characteristic
606	C₂²	#15689650	1	1	yes	characteristic
607	C₄	—	2	4	no	—
608	C₄	—	2	4	no	—
609	C₄	—	2	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	1	no	—
612	C₄	—	188	2	no	—
613	C₄	—	188	1	no	—
614	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
615	C₄	C₄×#10625352	1	1	yes	characteristic
616	C₄	#121×D₄₇	1	1	yes	characteristic
617	C₄	#15689668	1	1	yes	characteristic
618	C₂	—	2	1	no	—
619	C₂	—	2	4	no	—
620	C₂	—	2	1	no	—
621	C₂	—	8	1	no	—
622	C₂	—	376	1	no	—
623	C₂	#20245898	1	1	yes	characteristic
624	C₂	C₂×#15689237	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1896	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20252966	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1896	D₄₇
hypocenter	C₄₇	#21544
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1896

Complements

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

N	H ≅ G/N	type
2. C₂×#15689237	C₂	semidirect
3. #20252083	C₂	semidirect
4. #20252078	C₂	semidirect
5. C₂²×C₄×C₄₇⋊C₈	C₂	semidirect
6. #20244273	C₂	semidirect
7. #20244135	C₂	semidirect
8. #20244093	C₂	semidirect
9. #20244089	C₂	semidirect
10. #20243831	C₂	semidirect
11. #20243424	C₂	semidirect
12. #20243266	C₂	semidirect
13. #20243226	C₂	semidirect
14. #20243222	C₂	semidirect
15. C₄₇×#1896	C₂	semidirect
22. #15689362	C₄	semidirect
23. #15689357	C₄	semidirect
24. #15689354	C₄	semidirect
25. #15689350	C₄	semidirect
64. C₂×#10625337	C₂×C₄	semidirect
65. C₂×#10625335	C₂×C₄	semidirect
66. C₂×#10625336	C₂×C₄	semidirect
67. C₂×#10625334	C₂×C₄	semidirect
98. #13093957	C₂×C₄	semidirect
99. #13093955	C₂×C₄	semidirect
104. #13093948	C₂×C₄	semidirect
105. #13093947	C₂×C₄	semidirect
106. #13093945	C₂×C₄	semidirect
107. #13093944	C₂×C₄	semidirect
117. C₄×C₄₇⋊C₈	D₄	semidirect
289. C₂²×C₄₇	#443	semidirect
316. #1896	D₄₇	semidirect
373. C₄₇	#21544	semidirect
603. C₂²	#15689237	semidirect

Maximal subgroups

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

subgroup	index
#20252966	2
C₂×#15689237	2
#20252083	2
#20252078	2
C₂²×C₄×C₄₇⋊C₈	2
#20244273	2
#20244135	2
#20244093	2
#20244089	2
#20243831	2
#20243424	2
#20243266	2
#20243226	2
#20243222	2
C₄₇×#1896	2
#21544	47