Subgroups — #26235062

Order 12032.

790 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₁₆×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20252120	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689198	C₂	1	1	yes	maximal, characteristic
4	#20244162	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244160	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243595	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243594	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243591	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243524	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243428	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243427	C₂	1	1	yes	maximal, characteristic, complemented
12	#108×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243114	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243113	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1855	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625329	C₂²	1	1	yes	characteristic
18	C₂²×#10625324	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
20	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
22	#15689199	—	2	1	no	—
23	#15689198	—	2	1	no	—
24	#15689198	C₄	1	2	yes	—
25	#15689198	C₄	1	2	yes	—
26	#15689198	C₄	1	2	yes	—
27	#15689198	C₄	1	2	yes	—
28	#15689197	—	2	1	no	—
29	#15689194	—	2	1	no	—
30	#15689192	—	2	1	no	—
31	#15689191	—	2	1	no	—
32	C₈×C₂²⋊D₄₇	—	2	1	no	—
33	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
34	C₂×#13093960	C₂²	1	1	yes	characteristic
35	C₂×#13093960	C₂²	1	1	yes	characteristic
36	C₂×#13093959	C₂²	1	1	yes	characteristic
37	C₂×#13093959	C₂²	1	1	yes	characteristic
38	#15689146	C₂²	1	1	yes	characteristic
39	#15689146	C₂²	1	1	yes	characteristic
40	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
41	#15689087	C₂²	1	1	yes	characteristic
42	#15689086	C₂²	1	1	yes	characteristic
43	#15689086	C₂²	1	1	yes	characteristic
44	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
45	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
46	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
47	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
48	#15688888	C₂²	1	1	yes	characteristic
49	#15688888	C₂²	1	1	yes	characteristic
50	#15688887	C₂²	1	1	yes	characteristic
51	#15688887	C₂²	1	1	yes	characteristic
52	#15688887	C₂²	1	1	yes	characteristic
53	#15688887	C₂²	1	1	yes	characteristic
54	#15688887	C₂²	1	1	yes	characteristic
55	#15688887	C₂²	1	1	yes	characteristic
56	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
58	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
59	C₄₇×#407	C₂²	1	1	yes	characteristic
60	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
61	C₄₇×#341	C₂²	1	1	yes	characteristic
62	C₄₇×#341	C₂²	1	1	yes	characteristic
63	C₂²×C₂²⋊D₄₇	Q₈	1	1	yes	characteristic
64	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
65	C₂×#10625329	—	2	1	no	—
66	C₂×#10625329	—	2	2	no	—
67	C₂×#10625329	—	4	1	no	—
68	C₂×#10625329	—	4	1	no	—
69	C₂×#10625329	—	4	1	no	—
70	C₂×#10625329	C₂×C₄	1	2	yes	—
71	C₂×#10625329	C₂×C₄	1	2	yes	—
72	C₂×#10625329	C₂³	1	1	yes	characteristic
73	C₂×#10625329	C₂³	1	1	yes	characteristic
74	C₂×#10625329	C₂³	1	1	yes	characteristic
75	C₂×#10625329	C₂³	1	1	yes	characteristic
76	C₂×#10625324	—	2	1	no	—
77	C₂×#10625324	—	2	1	no	—
78	C₂×#10625324	—	4	1	no	—
79	C₂×#10625324	—	4	1	no	—
80	C₂×#10625324	C₂×C₄	1	2	yes	—
81	C₂×#10625324	C₂×C₄	1	2	yes	—
82	M₁₆×D₄₇	—	2	2	no	—
83	M₁₆×D₄₇	—	2	2	no	—
84	M₁₆×D₄₇	—	4	1	no	—
85	M₁₆×D₄₇	—	4	1	no	—
86	C₂²×C₄₇⋊C₈	—	2	1	no	—
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	C₂×C₈×D₄₇	—	2	1	no	—
91	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
92	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
93	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
94	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
95	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
96	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
97	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
98	C₄×C₂²⋊D₄₇	D₄	1	1	yes	characteristic
99	C₂×Dic₄₇⋊C₄	Q₈	1	1	yes	characteristic
100	C₂×C₂²⋊Dic₄₇	Q₈	1	1	yes	characteristic
101	C₂×(C₂×D₄₇)⋊C₄	Q₈	1	1	yes	characteristic
102	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
103	#13093960	—	2	2	no	—
104	#13093960	—	4	1	no	—
105	#13093959	—	4	1	no	—
106	#13093959	—	4	1	no	—
107	Dic₄₇⋊C₈	—	2	1	no	—
108	Dic₄₇⋊C₈	—	2	1	no	—
109	Dic₄₇⋊C₈	—	2	1	no	—
110	Dic₄₇⋊C₈	—	2	1	no	—
111	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
112	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
113	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
114	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
115	(C₂×D₄₇)⋊C₈	—	2	1	no	—
116	(C₂×D₄₇)⋊C₈	—	2	1	no	—
117	(C₂×D₄₇)⋊C₈	—	2	1	no	—
118	(C₂×D₄₇)⋊C₈	—	2	1	no	—
119	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
120	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
121	#13093934	—	2	1	no	—
122	#13093934	—	2	1	no	—
123	C₈×Dic₄₇	—	2	1	no	—
124	C₈×Dic₄₇	—	2	1	no	—
125	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
126	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
127	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×M₁₆×C₄₇	—	2	1	no	—
129	C₂×M₁₆×C₄₇	—	2	2	no	—
130	C₂×M₁₆×C₄₇	—	4	1	no	—
131	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
133	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
134	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₄₇	—	2	1	no	—
136	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
138	#108×C₄₇	—	2	2	no	—
139	#108×C₄₇	—	4	1	no	—
140	C₂²⋊C₈×C₄₇	—	2	1	no	—
141	C₂²⋊C₈×C₄₇	—	2	1	no	—
142	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
143	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
144	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
145	C₂³×D₄₇	C₂×Q₈	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	—	2	1	no	—
147	C₂²×C₄×C₄₇	—	2	1	no	—
148	C₂²×C₄×C₄₇	—	2	1	no	—
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
156	C₂×C₂²⋊D₄₇	—	4	2	no	—
157	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	1	yes	characteristic
161	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
162	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
163	C₂²×Dic₄₇	C₂×Q₈	1	1	yes	characteristic
164	C₂×C₄×D₄₇	—	2	1	no	—
165	C₂×C₄×D₄₇	—	2	1	no	—
166	C₂×C₄×D₄₇	—	2	1	no	—
167	C₂×C₄×D₄₇	—	2	1	no	—
168	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
172	M₁₆×C₄₇	—	2	1	no	—
173	M₁₆×C₄₇	—	2	1	no	—
174	M₁₆×C₄₇	—	2	1	no	—
175	M₁₆×C₄₇	—	2	1	no	—
176	M₁₆×C₄₇	—	2	1	no	—
177	M₁₆×C₄₇	—	2	1	no	—
178	M₁₆×C₄₇	—	2	1	no	—
179	M₁₆×C₄₇	—	4	2	no	—
180	M₁₆×C₄₇	#41	1	2	yes	—
181	C₂×C₈×C₄₇	—	2	1	no	—
182	C₂×C₈×C₄₇	—	2	1	no	—
183	C₂×C₈×C₄₇	—	2	1	no	—
184	C₂×C₈×C₄₇	—	2	1	no	—
185	C₂×C₈×C₄₇	—	2	1	no	—
186	C₂×C₈×C₄₇	—	2	1	no	—
187	C₂×C₈×C₄₇	—	2	1	no	—
188	C₂×C₈×C₄₇	—	2	1	no	—
189	C₂×C₈×C₄₇	—	4	2	no	—
190	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
191	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
192	C₂²⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
193	C₂²⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
194	C₂²⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
195	C₂²⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
196	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
197	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
198	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
199	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
200	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
201	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
202	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
203	Dic₄₇⋊C₄	C₄⋊C₄	1	1	yes	characteristic
204	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
205	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
206	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
207	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
208	#10625329	—	2	1	no	—
209	#10625329	—	2	1	no	—
210	#10625329	—	2	1	no	—
211	#10625329	—	2	1	no	—
212	#10625329	—	2	1	no	—
213	#10625329	—	2	1	no	—
214	#10625329	—	2	1	no	—
215	#10625329	—	4	2	no	—
216	#10625329	—	4	2	no	—
217	#10625329	—	4	2	no	—
218	#10625329	#41	1	2	yes	—
219	C₂×C₄₇⋊C₈	—	2	1	no	—
220	C₂×C₄₇⋊C₈	—	2	1	no	—
221	C₂×C₄₇⋊C₈	—	2	1	no	—
222	C₂×C₄₇⋊C₈	—	2	1	no	—
223	C₂×C₄₇⋊C₈	—	2	1	no	—
224	C₂×C₄₇⋊C₈	—	2	1	no	—
225	C₂×C₄₇⋊C₈	—	2	1	no	—
226	C₂×C₄₇⋊C₈	—	2	1	no	—
227	C₂×C₄₇⋊C₈	—	4	2	no	—
228	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
229	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
230	#10625324	—	4	2	no	—
231	#10625324	—	4	2	no	—
232	#10625324	—	4	2	no	—
233	#10625324	—	4	2	no	—
234	C₈×D₄₇	—	4	2	no	—
235	C₈×D₄₇	—	4	2	no	—
236	C₂³×C₄₇	—	2	1	no	—
237	C₂³×C₄₇	—	2	1	no	—
238	C₂³×C₄₇	—	4	1	no	—
239	C₂³×C₄₇	—	4	1	no	—
240	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
241	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
243	C₂²×D₄₇	—	2	1	no	—
244	C₂²×D₄₇	—	2	1	no	—
245	C₂²×D₄₇	—	4	1	no	—
246	C₂²×D₄₇	—	4	1	no	—
247	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
248	C₂²×D₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	—	2	1	no	—
250	C₂×C₄×C₄₇	—	2	1	no	—
251	C₂×C₄×C₄₇	—	2	1	no	—
252	C₂×C₄×C₄₇	—	2	1	no	—
253	C₂×C₄×C₄₇	—	2	1	no	—
254	C₂×C₄×C₄₇	—	2	1	no	—
255	C₂×C₄×C₄₇	—	2	1	no	—
256	C₂×C₄×C₄₇	—	2	1	no	—
257	C₂×C₄×C₄₇	—	2	1	no	—
258	C₂×C₄×C₄₇	—	2	1	no	—
259	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
265	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
266	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
267	C₂²⋊D₄₇	—	2	2	no	—
268	C₂²⋊D₄₇	—	2	2	no	—
269	C₂²⋊D₄₇	—	4	1	no	—
270	C₂²⋊D₄₇	—	4	1	no	—
271	C₂×Dic₄₇	—	2	1	no	—
272	C₂×Dic₄₇	—	2	1	no	—
273	C₂×Dic₄₇	—	2	2	no	—
274	C₂×Dic₄₇	—	4	1	no	—
275	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
276	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
277	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
278	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
279	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
280	C₂×Dic₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
281	C₄×D₄₇	—	2	1	no	—
282	C₄×D₄₇	—	2	1	no	—
283	C₄×D₄₇	—	2	1	no	—
284	C₄×D₄₇	—	2	1	no	—
285	C₄×D₄₇	—	2	1	no	—
286	C₄×D₄₇	—	2	1	no	—
287	C₄×D₄₇	—	2	1	no	—
288	C₄×D₄₇	—	2	1	no	—
289	C₈×C₄₇	—	2	2	no	—
290	C₈×C₄₇	—	2	2	no	—
291	C₈×C₄₇	—	2	2	no	—
292	C₈×C₄₇	—	4	1	no	—
293	C₈×C₄₇	—	4	1	no	—
294	C₈×C₄₇	—	4	1	no	—
295	C₄₇⋊C₈	—	2	2	no	—
296	C₄₇⋊C₈	—	2	2	no	—
297	C₄₇⋊C₈	—	2	2	no	—
298	C₄₇⋊C₈	—	4	1	no	—
299	C₄₇⋊C₈	—	4	1	no	—
300	C₄₇⋊C₈	—	4	1	no	—
301	#22719	—	47	1	no	maximal, Sylow
302	C₂²×C₄₇	—	2	1	no	—
303	C₂²×C₄₇	—	2	1	no	—
304	C₂²×C₄₇	—	2	1	no	—
305	C₂²×C₄₇	—	2	1	no	—
306	C₂²×C₄₇	—	2	1	no	—
307	C₂²×C₄₇	—	2	1	no	—
308	C₂²×C₄₇	—	2	1	no	—
309	C₂²×C₄₇	—	2	1	no	—
310	C₂²×C₄₇	—	8	1	no	—
311	C₂²×C₄₇	—	8	1	no	—
312	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
313	C₂²×C₄₇	#554	1	1	yes	characteristic
314	C₂²×C₄₇	#554	1	1	yes	characteristic
315	C₂×D₄₇	—	2	1	no	—
316	C₂×D₄₇	—	2	1	no	—
317	C₂×D₄₇	—	2	1	no	—
318	C₂×D₄₇	—	2	1	no	—
319	C₂×D₄₇	—	2	1	no	—
320	C₂×D₄₇	—	2	1	no	—
321	C₂×D₄₇	—	8	1	no	—
322	C₂×D₄₇	—	8	1	no	—
323	C₄×C₄₇	—	2	1	no	—
324	C₄×C₄₇	—	2	1	no	—
325	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
326	C₄×C₄₇	#518	1	1	yes	characteristic
327	C₄×C₄₇	#546	1	1	yes	characteristic
328	C₄×C₄₇	#546	1	1	yes	characteristic
329	Dic₄₇	—	2	1	no	—
330	Dic₄₇	—	2	1	no	—
331	Dic₄₇	—	2	1	no	—
332	Dic₄₇	—	2	1	no	—
333	Dic₄₇	—	2	1	no	—
334	Dic₄₇	#430	1	2	yes	—
335	D₄×M₁₆	—	47	1	no	—
336	D₄×M₁₆	—	47	1	no	—
337	C₂×#436	—	47	1	no	—
338	#1950	—	47	1	no	—
339	#1950	—	47	1	no	—
340	#1855	—	47	1	no	—
341	#1855	—	47	1	no	—
342	#1855	—	47	1	no	—
343	#1855	D₄₇	1	1	yes	characteristic, complemented
344	#1837	—	47	1	no	—
345	#1811	—	47	1	no	—
346	#1811	—	47	1	no	—
347	C₄×#108	—	47	1	no	—
348	#1738	—	47	1	no	—
349	#1738	—	47	1	no	—
350	C₂×C₄₇	—	2	1	no	—
351	C₂×C₄₇	—	2	1	no	—
352	C₂×C₄₇	—	4	1	no	—
353	C₂×C₄₇	—	4	1	no	—
354	C₂×C₄₇	#2349	1	1	yes	characteristic
355	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
356	C₂×C₄₇	#2916	1	1	yes	characteristic
357	D₄₇	—	4	1	no	—
358	D₄₇	—	4	1	no	—
359	C₂²×M₁₆	—	47	1	no	—
360	C₂²×M₁₆	—	47	1	no	—
361	C₂²×M₁₆	—	47	1	no	—
362	C₂²×M₁₆	—	47	1	no	—
363	C₂²×M₁₆	—	47	1	no	—
364	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
365	C₂×C₄×D₄	—	47	1	no	—
366	#436	—	47	2	no	—
367	#436	—	47	2	no	—
368	#436	—	47	2	no	—
369	#436	—	47	2	no	—
370	#436	—	94	1	no	—
371	#436	—	94	1	no	—
372	#435	—	94	1	no	—
373	#435	—	94	1	no	—
374	#435	—	94	1	no	—
375	#435	—	94	1	no	—
376	C₈×D₄	—	94	1	no	—
377	C₈×D₄	—	94	1	no	—
378	C₂×#108	—	47	1	no	—
379	C₂×#108	—	47	1	no	—
380	C₂×#108	—	47	1	no	—
381	C₂×#108	—	47	1	no	—
382	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
383	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
384	#423	—	47	1	no	—
385	#423	—	47	1	no	—
386	C₂×C₄⋊C₈	—	47	1	no	—
387	#407	—	47	1	no	—
388	#407	—	47	1	no	—
389	#407	—	47	1	no	—
390	#407	C₂×D₄₇	1	1	yes	characteristic
391	C₂×C₂²⋊C₈	—	47	1	no	—
392	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
393	C₄×M₁₆	—	47	1	no	—
394	C₄×M₁₆	—	47	1	no	—
395	C₂×C₄×C₈	—	47	1	no	—
396	#341	—	47	1	no	—
397	#341	—	47	1	no	—
398	#341	—	47	1	no	—
399	#341	—	47	1	no	—
400	#341	—	47	1	no	—
401	#341	—	47	1	no	—
402	#341	—	47	1	no	—
403	#341	—	47	1	no	—
404	#341	C₂×D₄₇	1	1	yes	characteristic
405	#341	C₂×D₄₇	1	1	yes	characteristic
406	C₄₇	#22719	1	1	yes	characteristic, complemented, Sylow
407	C₂²×D₄	—	47	1	no	—
408	C₂³×C₄	—	47	1	no	—
409	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
410	C₂×M₁₆	—	2	1	no	—
411	C₂×M₁₆	—	2	2	no	—
412	C₂×M₁₆	—	4	1	no	—
413	C₂×M₁₆	—	47	2	no	—
414	C₂×M₁₆	—	47	2	no	—
415	C₂×M₁₆	—	47	2	no	—
416	C₂×M₁₆	—	47	2	no	—
417	C₂×M₁₆	—	47	1	no	—
418	C₂×M₁₆	—	47	1	no	—
419	C₂×M₁₆	—	47	1	no	—
420	C₂×M₁₆	—	47	1	no	—
421	C₂×M₁₆	—	94	1	no	—
422	C₂×M₁₆	—	94	1	no	—
423	C₂×M₁₆	—	94	1	no	—
424	C₂×M₁₆	—	94	2	no	—
425	C₂×M₁₆	—	94	2	no	—
426	C₂×M₁₆	—	94	2	no	—
427	C₂×M₁₆	—	188	1	no	—
428	C₂×M₁₆	—	188	1	no	—
429	C₂×M₁₆	—	188	1	no	—
430	C₂×M₁₆	—	188	1	no	—
431	C₂×M₁₆	—	188	1	no	—
432	C₂×M₁₆	—	188	1	no	—
433	C₂×M₁₆	—	188	1	no	—
434	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
435	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
436	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
437	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
438	C₂²×C₈	—	2	1	no	—
439	C₂²×C₈	—	47	1	no	—
440	C₂²×C₈	—	47	1	no	—
441	C₂²×C₈	—	94	1	no	—
442	C₂²×C₈	—	94	1	no	—
443	C₂²×C₈	—	94	1	no	—
444	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
445	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
446	C₄×D₄	—	47	1	no	—
447	C₄×D₄	—	47	1	no	—
448	C₄×D₄	—	47	1	no	—
449	C₄×D₄	—	47	1	no	—
450	C₄×D₄	—	47	1	no	—
451	C₄×D₄	—	47	1	no	—
452	C₄×D₄	—	47	1	no	—
453	C₄×D₄	—	47	1	no	—
454	C₂×C₄⋊C₄	—	47	1	no	—
455	C₂×C₂²⋊C₄	—	47	1	no	—
456	C₂×C₂²⋊C₄	—	47	1	no	—
457	C₂×C₄²	—	47	1	no	—
458	#108	—	2	2	no	—
459	#108	—	4	1	no	—
460	#108	—	94	2	no	—
461	#108	—	188	1	no	—
462	#108	—	188	1	no	—
463	#108	—	188	1	no	—
464	C₄⋊C₈	—	47	2	no	—
465	C₄⋊C₈	—	47	2	no	—
466	C₄⋊C₈	—	94	1	no	—
467	C₄⋊C₈	—	94	1	no	—
468	C₄⋊C₈	—	94	1	no	—
469	C₄⋊C₈	—	94	1	no	—
470	C₂²⋊C₈	—	2	1	no	—
471	C₂²⋊C₈	—	2	1	no	—
472	C₂²⋊C₈	—	47	2	no	—
473	C₂²⋊C₈	—	47	2	no	—
474	C₂²⋊C₈	—	94	1	no	—
475	C₂²⋊C₈	—	94	1	no	—
476	C₂²⋊C₈	—	94	1	no	—
477	C₂²⋊C₈	—	94	1	no	—
478	C₂²⋊C₈	—	94	1	no	—
479	C₂²⋊C₈	—	94	1	no	—
480	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
481	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
482	#97	—	94	1	no	—
483	#97	—	94	1	no	—
484	C₄×C₈	—	47	2	no	—
485	C₄×C₈	—	47	2	no	—
486	C₄×C₈	—	94	1	no	—
487	C₄×C₈	—	94	1	no	—
488	C₂⁴	—	47	1	no	—
489	C₂⁴	Q₈×D₄₇	1	1	yes	characteristic
490	C₂×D₄	—	47	1	no	—
491	C₂×D₄	—	47	1	no	—
492	C₂×D₄	—	47	1	no	—
493	C₂×D₄	—	47	1	no	—
494	C₂×D₄	—	188	2	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	47	1	no	—
500	C₂²×C₄	—	47	1	no	—
501	C₂²×C₄	—	47	1	no	—
502	C₂²×C₄	—	47	1	no	—
503	C₂²×C₄	—	47	1	no	—
504	C₂²×C₄	—	47	1	no	—
505	C₂²×C₄	—	47	1	no	—
506	C₂²×C₄	—	94	1	no	—
507	C₂²×C₄	—	94	1	no	—
508	C₂²×C₄	—	94	1	no	—
509	C₂²×C₄	—	94	1	no	—
510	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
511	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
512	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
513	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
514	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
515	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	1	no	—
518	M₁₆	—	2	1	no	—
519	M₁₆	—	2	1	no	—
520	M₁₆	—	2	1	no	—
521	M₁₆	—	2	1	no	—
522	M₁₆	—	2	1	no	—
523	M₁₆	—	4	2	no	—
524	M₁₆	—	47	2	no	—
525	M₁₆	—	94	1	no	—
526	M₁₆	—	94	1	no	—
527	M₁₆	—	94	1	no	—
528	M₁₆	—	94	1	no	—
529	M₁₆	—	94	1	no	—
530	M₁₆	—	94	1	no	—
531	M₁₆	—	94	1	no	—
532	M₁₆	—	188	2	no	—
533	M₁₆	—	188	2	no	—
534	M₁₆	—	188	2	no	—
535	M₁₆	—	188	2	no	—
536	M₁₆	—	188	2	no	—
537	M₁₆	—	188	2	no	—
538	M₁₆	—	188	2	no	—
539	M₁₆	#10625352	1	2	yes	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	4	2	no	—
549	C₂×C₈	—	47	2	no	—
550	C₂×C₈	—	47	2	no	—
551	C₂×C₈	—	94	1	no	—
552	C₂×C₈	—	94	1	no	—
553	C₂×C₈	—	94	1	no	—
554	C₂×C₈	—	94	1	no	—
555	C₂×C₈	—	94	1	no	—
556	C₂×C₈	—	94	1	no	—
557	C₂×C₈	—	94	1	no	—
558	C₂×C₈	—	94	1	no	—
559	C₂×C₈	—	188	2	no	—
560	C₂×C₈	—	188	2	no	—
561	C₂×C₈	—	188	2	no	—
562	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
563	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
564	C₄⋊C₄	—	47	1	no	—
565	C₄⋊C₄	—	47	1	no	—
566	C₄⋊C₄	—	47	1	no	—
567	C₄⋊C₄	—	47	1	no	—
568	C₂²⋊C₄	—	47	1	no	—
569	C₂²⋊C₄	—	47	1	no	—
570	C₂²⋊C₄	—	47	1	no	—
571	C₂²⋊C₄	—	47	1	no	—
572	C₂²⋊C₄	—	47	1	no	—
573	C₂²⋊C₄	—	47	1	no	—
574	C₂²⋊C₄	—	47	1	no	—
575	C₂²⋊C₄	—	47	1	no	—
576	C₄²	—	47	1	no	—
577	C₄²	—	47	1	no	—
578	C₄²	—	47	1	no	—
579	C₄²	—	47	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	4	1	no	—
583	C₂³	—	4	1	no	—
584	C₂³	—	47	1	no	—
585	C₂³	—	47	1	no	—
586	C₂³	—	94	1	no	—
587	C₂³	—	94	1	no	—
588	C₂³	—	188	1	no	—
589	C₂³	—	188	1	no	—
590	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
591	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
592	C₂³	C₂×Q₈×D₄₇	1	1	yes	characteristic
593	D₄	—	94	2	no	—
594	D₄	—	94	2	no	—
595	D₄	—	188	1	no	—
596	D₄	—	188	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	47	1	no	—
608	C₂×C₄	—	47	1	no	—
609	C₂×C₄	—	47	1	no	—
610	C₂×C₄	—	47	1	no	—
611	C₂×C₄	—	47	1	no	—
612	C₂×C₄	—	47	1	no	—
613	C₂×C₄	—	94	2	no	—
614	C₂×C₄	—	94	1	no	—
615	C₂×C₄	—	94	1	no	—
616	C₂×C₄	—	94	1	no	—
617	C₂×C₄	—	94	1	no	—
618	C₂×C₄	—	94	1	no	—
619	C₂×C₄	—	94	1	no	—
620	C₂×C₄	—	94	1	no	—
621	C₂×C₄	—	94	1	no	—
622	C₂×C₄	—	94	1	no	—
623	C₂×C₄	—	94	1	no	—
624	C₂×C₄	—	188	1	no	—
625	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
626	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
627	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
628	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
629	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
630	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
631	C₂×C₄	#13094069	1	1	yes	characteristic
632	C₂×C₄	#13094070	1	1	yes	characteristic
633	C₈	—	2	2	no	—
634	C₈	—	2	2	no	—
635	C₈	—	2	2	no	—
636	C₈	—	4	1	no	—
637	C₈	—	4	1	no	—
638	C₈	—	4	1	no	—
639	C₈	—	94	2	no	—
640	C₈	—	94	2	no	—
641	C₈	—	94	2	no	—
642	C₈	—	188	1	no	—
643	C₈	—	188	1	no	—
644	C₈	—	188	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	1	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	94	1	no	—
656	C₂²	—	94	1	no	—
657	C₂²	—	94	1	no	—
658	C₂²	—	94	1	no	—
659	C₂²	—	94	1	no	—
660	C₂²	—	94	1	no	—
661	C₂²	—	376	1	no	—
662	C₂²	—	376	1	no	—
663	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
664	C₂²	#15689827	1	1	yes	characteristic
665	C₂²	#15689831	1	1	yes	characteristic
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	47	2	no	—
669	C₄	—	94	1	no	—
670	C₄	—	94	1	no	—
671	C₄	—	94	1	no	—
672	C₄	—	94	1	no	—
673	C₄	—	94	1	no	—
674	C₄	C₄×#10625352	1	1	yes	characteristic
675	C₄	#15689595	1	1	yes	characteristic
676	C₄	#15689760	1	1	yes	characteristic
677	C₄	#15689765	1	1	yes	characteristic
678	C₂	—	2	1	no	—
679	C₂	—	2	1	no	—
680	C₂	—	4	1	no	—
681	C₂	—	4	1	no	—
682	C₂	—	188	1	no	—
683	C₂	—	188	1	no	—
684	C₂	#20246294	1	1	yes	characteristic
685	C₂	#430×D₄₇	1	1	yes	characteristic
686	C₂	#20251996	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1855	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂²×C₂²⋊D₄₇	Q₈
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1855	D₄₇
hypocenter	C₄₇	#22719
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1855

Complements

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

N	H ≅ G/N	type
4. #20244162	C₂	semidirect
5. #20244160	C₂	semidirect
6. #20243595	C₂	semidirect
7. #20243594	C₂	semidirect
8. #20243591	C₂	semidirect
9. #20243524	C₂	semidirect
10. #20243428	C₂	semidirect
11. #20243427	C₂	semidirect
12. #108×Dic₄₇	C₂	semidirect
13. #20243114	C₂	semidirect
14. #20243113	C₂	semidirect
15. C₄₇×#1855	C₂	semidirect
343. #1855	D₄₇	semidirect
406. C₄₇	#22719	semidirect

Maximal subgroups

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

subgroup	index
M₁₆×C₂²⋊D₄₇	2
#20252120	2
C₂×#15689198	2
#20244162	2
#20244160	2
#20243595	2
#20243594	2
#20243591	2
#20243524	2
#20243428	2
#20243427	2
#108×Dic₄₇	2
#20243114	2
#20243113	2
C₄₇×#1855	2
#22719	47