Subgroups — #26235761

Order 12032.

960 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×(C₂²⋊D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic
2	#20243996	C₂	1	1	yes	maximal, characteristic, complemented
3	#20243948	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243942	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243677	C₂	1	1	yes	maximal, characteristic
6	#20243677	C₂	1	1	yes	maximal, characteristic
7	#20243530	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243454	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243365	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243158	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243133	C₂	1	1	yes	maximal, characteristic, complemented
14	#336×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1923	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
19	C₂×(C₂²⋊D₄₇)⋊C₄	C₄	1	1	yes	characteristic
20	C₂×(C₂²⋊D₄₇)⋊C₄	C₄	1	1	yes	characteristic
21	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
31	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
32	#15688974	C₄	1	1	yes	characteristic
33	#15688974	C₄	1	1	yes	characteristic
34	C₂²⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
35	C₂²⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
36	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
37	#15688970	C₄	1	1	yes	characteristic
38	#15688970	C₄	1	1	yes	characteristic
39	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
40	#15688878	C₂²	1	1	yes	characteristic
41	#15688878	C₂²	1	1	yes	characteristic
42	#15688877	C₂²	1	1	yes	characteristic
43	#15688877	C₂²	1	1	yes	characteristic
44	#15688877	C₂²	1	1	yes	characteristic
45	#15688877	C₂²	1	1	yes	characteristic
46	#15688877	C₂²	1	1	yes	characteristic
47	#15688877	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
57	C₄₇×#336	C₂²	1	1	yes	characteristic
58	C₄₇×#336	C₂²	1	1	yes	characteristic
59	C₂²×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
65	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₂×C₈×D₄₇	—	2	2	no	—
70	C₂×C₈×D₄₇	—	2	2	no	—
71	C₂×C₈×D₄₇	—	2	2	no	—
72	C₂×C₈×D₄₇	—	2	2	no	—
73	C₂×C₈×D₄₇	—	4	1	no	—
74	C₂×C₈×D₄₇	—	4	1	no	—
75	C₄×C₂²⋊D₄₇	—	2	2	no	—
76	C₄×C₂²⋊D₄₇	—	2	2	no	—
77	(C₂²⋊D₄₇)⋊C₄	—	2	4	no	—
78	(C₂²⋊D₄₇)⋊C₄	C₈	1	8	yes	complemented
79	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₄₇	—	4	1	no	—
87	C₂×C₄×Dic₄₇	—	4	1	no	—
88	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
97	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
99	C₄²×D₄₇	—	4	1	no	—
100	C₄²×D₄₇	—	4	1	no	—
101	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
102	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
103	C₂²⋊(C₄₇⋊C₈)	—	4	1	no	—
104	(C₂×D₄₇)⋊C₈	—	2	2	no	—
105	(C₂×D₄₇)⋊C₈	—	2	2	no	—
106	C₄×C₄₇⋊C₈	—	2	2	no	—
107	C₈×Dic₄₇	—	4	1	no	—
108	C₈×Dic₄₇	—	4	1	no	—
109	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
110	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
111	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
112	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
113	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₄₇	—	4	1	no	—
123	C₂²⋊C₈×C₄₇	—	2	2	no	—
124	C₂²⋊C₈×C₄₇	—	4	1	no	—
125	C₄×C₈×C₄₇	—	2	2	no	—
126	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
127	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
128	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	1	no	—
133	C₂²×C₄×C₄₇	—	2	1	no	—
134	C₂²×C₄×C₄₇	—	2	1	no	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂×C₂²⋊D₄₇	—	2	2	no	—
143	C₂×C₂²⋊D₄₇	—	2	2	no	—
144	C₂×C₂²⋊D₄₇	C₂×C₈	1	4	yes	—
145	C₂²×Dic₄₇	—	2	2	no	—
146	C₂²×Dic₄₇	—	2	2	no	—
147	C₂²×Dic₄₇	—	4	1	no	—
148	C₂²×Dic₄₇	—	4	1	no	—
149	C₂²×Dic₄₇	—	4	1	no	—
150	C₂²×Dic₄₇	C₂×C₈	1	4	yes	complemented
151	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₄₇	—	2	1	no	—
159	C₂×C₄×D₄₇	—	2	1	no	—
160	C₂×C₄×D₄₇	—	2	1	no	—
161	C₂×C₄×D₄₇	—	2	1	no	—
162	C₂×C₄×D₄₇	—	2	2	no	—
163	C₂×C₄×D₄₇	—	2	2	no	—
164	C₂×C₄×D₄₇	—	4	1	no	—
165	C₂×C₄×D₄₇	—	4	1	no	—
166	C₂×C₄×D₄₇	—	4	1	no	—
167	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
168	C₂×C₄×D₄₇	#41	1	2	yes	—
169	C₂×C₄×D₄₇	#41	1	2	yes	—
170	C₂×C₈×C₄₇	—	2	1	no	—
171	C₂×C₈×C₄₇	—	2	1	no	—
172	C₂×C₈×C₄₇	—	2	1	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	—	2	1	no	—
176	C₂×C₈×C₄₇	—	2	1	no	—
177	C₂×C₈×C₄₇	—	2	1	no	—
178	C₂×C₈×C₄₇	—	2	1	no	—
179	C₂×C₈×C₄₇	—	2	1	no	—
180	C₂×C₈×C₄₇	—	2	1	no	—
181	C₂×C₈×C₄₇	#41	1	2	yes	—
182	C₂²⋊C₄×C₄₇	—	2	2	no	—
183	C₂²⋊C₄×C₄₇	C₂×C₈	1	4	yes	complemented
184	C₄²×C₄₇	—	2	1	no	—
185	C₄²×C₄₇	—	2	1	no	—
186	C₄²×C₄₇	—	2	1	no	—
187	C₄²×C₄₇	—	2	1	no	—
188	C₂²⋊Dic₄₇	—	2	2	no	—
189	(C₂×D₄₇)⋊C₄	—	2	2	no	—
190	(C₂×D₄₇)⋊C₄	C₂×C₈	1	4	yes	—
191	(C₂×D₄₇)⋊C₄	M₁₆	1	4	yes	—
192	Dic₄₇⋊C₄	—	2	2	no	—
193	Dic₄₇⋊C₄	—	2	2	no	—
194	Dic₄₇⋊C₄	C₂×C₈	1	4	yes	complemented
195	C₄×Dic₄₇	—	2	2	no	—
196	C₄×Dic₄₇	—	2	1	no	—
197	C₄×Dic₄₇	—	2	1	no	—
198	C₄×Dic₄₇	—	2	1	no	—
199	C₄×Dic₄₇	—	2	1	no	—
200	C₄×Dic₄₇	—	2	1	no	—
201	C₄×Dic₄₇	—	2	1	no	—
202	C₄×Dic₄₇	—	2	2	no	—
203	C₄×Dic₄₇	—	4	1	no	—
204	C₄×Dic₄₇	—	4	1	no	—
205	C₄×Dic₄₇	—	4	1	no	—
206	C₄×Dic₄₇	—	4	1	no	—
207	C₄×Dic₄₇	—	4	1	no	—
208	C₄×Dic₄₇	C₂×C₈	1	4	yes	complemented
209	C₂×C₄₇⋊C₈	—	2	1	no	—
210	C₂×C₄₇⋊C₈	—	2	1	no	—
211	C₂×C₄₇⋊C₈	—	2	1	no	—
212	C₂×C₄₇⋊C₈	—	2	1	no	—
213	C₂×C₄₇⋊C₈	—	2	1	no	—
214	C₂×C₄₇⋊C₈	—	2	1	no	—
215	C₂×C₄₇⋊C₈	—	2	1	no	—
216	C₂×C₄₇⋊C₈	—	2	1	no	—
217	C₂×C₄₇⋊C₈	—	2	1	no	—
218	C₂×C₄₇⋊C₈	—	2	1	no	—
219	C₂×C₄₇⋊C₈	—	2	1	no	—
220	C₂×C₄₇⋊C₈	#41	1	2	yes	—
221	C₈×D₄₇	—	4	4	no	—
222	C₈×D₄₇	—	4	4	no	—
223	C₂³×C₄₇	—	2	1	no	—
224	C₂³×C₄₇	—	2	1	no	—
225	C₂³×C₄₇	—	2	1	no	—
226	C₂³×C₄₇	—	2	1	no	—
227	C₂³×C₄₇	—	2	1	no	—
228	C₂³×C₄₇	—	2	1	no	—
229	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
230	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
231	C₂²×D₄₇	—	2	1	no	—
232	C₂²×D₄₇	—	2	1	no	—
233	C₂²×D₄₇	—	2	1	no	—
234	C₂²×D₄₇	—	2	1	no	—
235	C₂²×D₄₇	#117	1	2	yes	—
236	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
237	C₂²×D₄₇	C₂×M₁₆	1	2	yes	—
238	C₂×C₄×C₄₇	—	2	1	no	—
239	C₂×C₄×C₄₇	—	2	1	no	—
240	C₂×C₄×C₄₇	—	2	1	no	—
241	C₂×C₄×C₄₇	—	2	1	no	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	1	no	—
244	C₂×C₄×C₄₇	—	2	1	no	—
245	C₂×C₄×C₄₇	—	2	1	no	—
246	C₂×C₄×C₄₇	—	2	1	no	—
247	C₂×C₄×C₄₇	—	2	1	no	—
248	C₂×C₄×C₄₇	—	2	1	no	—
249	C₂×C₄×C₄₇	—	2	1	no	—
250	C₂×C₄×C₄₇	—	4	1	no	—
251	C₂×C₄×C₄₇	—	4	1	no	—
252	C₂×C₄×C₄₇	—	4	1	no	—
253	C₂×C₄×C₄₇	—	4	1	no	—
254	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
255	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
256	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
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	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
262	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂²⋊D₄₇	—	2	8	no	—
264	C₂×Dic₄₇	—	2	1	no	—
265	C₂×Dic₄₇	—	2	1	no	—
266	C₂×Dic₄₇	—	2	1	no	—
267	C₂×Dic₄₇	—	2	1	no	—
268	C₂×Dic₄₇	—	2	1	no	—
269	C₂×Dic₄₇	—	2	1	no	—
270	C₂×Dic₄₇	—	2	1	no	—
271	C₂×Dic₄₇	—	2	1	no	—
272	C₂×Dic₄₇	—	2	1	no	—
273	C₂×Dic₄₇	—	2	1	no	—
274	C₂×Dic₄₇	—	2	1	no	—
275	C₂×Dic₄₇	—	2	1	no	—
276	C₂×Dic₄₇	—	2	1	no	—
277	C₂×Dic₄₇	—	2	1	no	—
278	C₂×Dic₄₇	—	2	1	no	—
279	C₂×Dic₄₇	—	4	4	no	—
280	C₂×Dic₄₇	—	4	4	no	—
281	C₂×Dic₄₇	#117	1	2	yes	—
282	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
283	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
284	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
285	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
286	C₂×Dic₄₇	#131	1	2	yes	—
287	C₄×D₄₇	—	2	2	no	—
288	C₄×D₄₇	—	2	2	no	—
289	C₄×D₄₇	—	2	2	no	—
290	C₄×D₄₇	—	2	2	no	—
291	C₄×D₄₇	—	4	4	no	—
292	C₄×D₄₇	—	4	4	no	—
293	C₈×C₄₇	—	2	2	no	—
294	C₈×C₄₇	—	4	1	no	—
295	C₈×C₄₇	—	4	1	no	—
296	C₈×C₄₇	—	4	1	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	#22785	—	47	1	no	maximal, Sylow
302	C₂²×C₄₇	—	2	2	no	—
303	C₂²×C₄₇	—	2	2	no	—
304	C₂²×C₄₇	—	2	2	no	—
305	C₂²×C₄₇	—	4	1	no	—
306	C₂²×C₄₇	—	4	1	no	—
307	C₂²×C₄₇	—	4	1	no	—
308	C₂²×C₄₇	—	4	1	no	—
309	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
310	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
311	C₂²×C₄₇	#518	1	1	yes	characteristic
312	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
313	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
314	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
315	C₂²×C₄₇	#568	1	1	yes	characteristic
316	C₂×D₄₇	—	2	2	no	—
317	C₂×D₄₇	—	2	2	no	—
318	C₂×D₄₇	—	2	2	no	—
319	C₂×D₄₇	—	2	2	no	—
320	C₂×D₄₇	—	2	2	no	—
321	C₂×D₄₇	—	2	2	no	—
322	C₂×D₄₇	#431	1	4	yes	—
323	C₄×C₄₇	—	2	2	no	—
324	C₄×C₄₇	—	2	2	no	—
325	C₄×C₄₇	—	2	2	no	—
326	C₄×C₄₇	—	4	1	no	—
327	C₄×C₄₇	—	4	1	no	—
328	C₄×C₄₇	#551	1	1	yes	characteristic
329	C₄×C₄₇	#551	1	1	yes	characteristic
330	C₄×C₄₇	#553	1	1	yes	characteristic
331	C₄×C₄₇	#553	1	1	yes	characteristic
332	Dic₄₇	—	2	2	no	—
333	Dic₄₇	—	2	2	no	—
334	Dic₄₇	—	2	2	no	—
335	Dic₄₇	—	2	2	no	—
336	Dic₄₇	—	2	2	no	—
337	Dic₄₇	—	2	2	no	—
338	Dic₄₇	—	4	1	no	—
339	C₄²×D₄	—	47	1	no	—
340	#1923	—	47	1	no	—
341	#1923	D₄₇	1	1	yes	characteristic, complemented
342	#1916	—	47	1	no	—
343	#1916	—	47	1	no	—
344	#1869	—	47	1	no	—
345	#1869	—	47	1	no	—
346	#1839	—	47	1	no	—
347	#1817	—	47	1	no	—
348	#1797	—	47	1	no	—
349	C₈×C₂²⋊C₄	—	47	1	no	—
350	C₈×C₂²⋊C₄	—	47	1	no	—
351	C₄×C₂²⋊C₈	—	47	1	no	—
352	#1744	—	47	1	no	—
353	C₂×#336	—	47	1	no	—
354	C₂×C₄₇	—	4	2	no	—
355	C₂×C₄₇	#2353	1	1	yes	characteristic
356	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
357	C₂×C₄₇	#2925	1	1	yes	characteristic
358	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
359	C₂×C₄₇	#2970	1	1	yes	characteristic
360	C₂×C₄₇	#2972	1	1	yes	characteristic
361	C₂×C₄₇	#2974	1	1	yes	characteristic
362	D₄₇	—	2	4	no	—
363	C₂³×C₈	—	47	1	no	—
364	C₂³×C₈	—	47	1	no	—
365	C₂×C₄×D₄	—	47	1	no	—
366	C₂×C₄×D₄	—	47	1	no	—
367	C₂×C₄×D₄	—	47	1	no	—
368	C₂²×C₄²	—	47	1	no	—
369	C₂²×C₄²	—	47	1	no	—
370	C₂×C₄⋊C₈	—	47	1	no	—
371	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
372	C₂×C₂²⋊C₈	—	47	1	no	—
373	C₂×C₂²⋊C₈	—	47	1	no	—
374	C₂×C₂²⋊C₈	—	47	1	no	—
375	C₂×C₂²⋊C₈	—	47	1	no	—
376	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
377	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
378	C₂×C₄×C₈	—	47	1	no	—
379	C₂×C₄×C₈	—	47	1	no	—
380	C₂×C₄×C₈	—	47	1	no	—
381	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
382	C₄×C₄⋊C₄	—	47	1	no	—
383	C₄×C₄⋊C₄	—	47	1	no	—
384	C₄×C₄⋊C₄	—	47	1	no	—
385	C₄×C₂²⋊C₄	—	47	1	no	—
386	C₄×C₂²⋊C₄	—	47	1	no	—
387	C₄×C₂²⋊C₄	—	47	1	no	—
388	C₄×C₂²⋊C₄	—	47	1	no	—
389	C₄×C₂²⋊C₄	—	47	1	no	—
390	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
391	C₄³	—	47	1	no	—
392	#336	—	47	1	no	—
393	#336	—	47	1	no	—
394	#336	—	47	1	no	—
395	#336	—	47	1	no	—
396	#336	—	47	1	no	—
397	#336	—	47	1	no	—
398	#336	—	47	1	no	—
399	#336	—	47	1	no	—
400	#336	—	47	1	no	—
401	#336	—	47	1	no	—
402	#336	—	47	1	no	—
403	#336	—	47	1	no	—
404	#336	C₂×D₄₇	1	1	yes	characteristic
405	#336	C₂×D₄₇	1	1	yes	characteristic
406	C₄₇	#22785	1	1	yes	characteristic, complemented, Sylow
407	C₂²×D₄	—	47	1	no	—
408	C₂³×C₄	—	47	1	no	—
409	C₂³×C₄	—	47	1	no	—
410	C₂³×C₄	—	47	1	no	—
411	C₂³×C₄	—	47	1	no	—
412	C₂³×C₄	—	47	1	no	—
413	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
414	C₂²×C₈	—	47	1	no	—
415	C₂²×C₈	—	47	1	no	—
416	C₂²×C₈	—	47	1	no	—
417	C₂²×C₈	—	47	1	no	—
418	C₂²×C₈	—	94	2	no	—
419	C₂²×C₈	—	94	2	no	—
420	C₂²×C₈	—	94	2	no	—
421	C₂²×C₈	—	94	2	no	—
422	C₂²×C₈	—	188	1	no	—
423	C₂²×C₈	—	188	1	no	—
424	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
425	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
426	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
427	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
428	C₄×D₄	—	47	8	no	—
429	C₄×D₄	—	94	4	no	—
430	C₄×D₄	—	94	2	no	—
431	C₄×D₄	—	94	2	no	—
432	C₂×C₄⋊C₄	—	47	1	no	—
433	C₂×C₄⋊C₄	—	47	1	no	—
434	C₂×C₄⋊C₄	—	47	1	no	—
435	C₂×C₂²⋊C₄	—	47	1	no	—
436	C₂×C₂²⋊C₄	—	47	1	no	—
437	C₂×C₂²⋊C₄	—	47	1	no	—
438	C₂×C₂²⋊C₄	—	47	1	no	—
439	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
441	C₂×C₄²	—	47	1	no	—
442	C₂×C₄²	—	47	1	no	—
443	C₂×C₄²	—	47	1	no	—
444	C₂×C₄²	—	47	1	no	—
445	C₂×C₄²	—	47	1	no	—
446	C₂×C₄²	—	47	1	no	—
447	C₂×C₄²	—	47	1	no	—
448	C₂×C₄²	—	47	1	no	—
449	C₂×C₄²	—	47	1	no	—
450	C₂×C₄²	—	47	1	no	—
451	C₂×C₄²	—	47	1	no	—
452	C₂×C₄²	—	188	1	no	—
453	C₂×C₄²	—	188	1	no	—
454	C₂×C₄²	—	188	1	no	—
455	C₂×C₄²	—	188	1	no	—
456	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
457	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
458	C₄⋊C₈	—	4	1	no	—
459	C₄⋊C₈	—	188	1	no	—
460	C₂²⋊C₈	—	2	2	no	—
461	C₂²⋊C₈	—	4	1	no	—
462	C₂²⋊C₈	—	94	2	no	—
463	C₂²⋊C₈	—	94	2	no	—
464	C₂²⋊C₈	—	94	2	no	—
465	C₂²⋊C₈	—	188	1	no	—
466	C₄×C₈	—	2	2	no	—
467	C₄×C₈	—	94	2	no	—
468	C₄×C₈	—	188	1	no	—
469	C₄×C₈	—	188	1	no	—
470	#95	—	47	1	no	—
471	#95	—	47	1	no	—
472	#95	—	47	1	no	—
473	#95	—	47	1	no	—
474	#95	C₄×D₄₇	1	1	yes	characteristic
475	#95	C₄×D₄₇	1	1	yes	characteristic
476	C₂⁴	—	47	1	no	—
477	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
478	C₂×D₄	—	47	4	no	—
479	C₂×D₄	—	94	2	no	—
480	C₂×D₄	—	94	2	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	47	1	no	—
488	C₂²×C₄	—	47	1	no	—
489	C₂²×C₄	—	47	1	no	—
490	C₂²×C₄	—	47	1	no	—
491	C₂²×C₄	—	47	1	no	—
492	C₂²×C₄	—	47	1	no	—
493	C₂²×C₄	—	47	4	no	—
494	C₂²×C₄	—	47	2	no	—
495	C₂²×C₄	—	47	2	no	—
496	C₂²×C₄	—	47	4	no	—
497	C₂²×C₄	—	47	1	no	—
498	C₂²×C₄	—	94	2	no	—
499	C₂²×C₄	—	94	2	no	—
500	C₂²×C₄	—	94	2	no	—
501	C₂²×C₄	—	94	2	no	—
502	C₂²×C₄	—	94	1	no	—
503	C₂²×C₄	—	94	1	no	—
504	C₂²×C₄	—	94	1	no	—
505	C₂²×C₄	—	94	1	no	—
506	C₂²×C₄	—	188	1	no	—
507	C₂²×C₄	—	188	1	no	—
508	C₂²×C₄	—	188	1	no	—
509	C₂²×C₄	—	188	1	no	—
510	C₂²×C₄	—	188	1	no	—
511	C₂²×C₄	—	188	1	no	—
512	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
513	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
514	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
515	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
516	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
517	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	47	2	no	—
530	C₂×C₈	—	94	1	no	—
531	C₂×C₈	—	94	1	no	—
532	C₂×C₈	—	94	1	no	—
533	C₂×C₈	—	94	1	no	—
534	C₂×C₈	—	94	1	no	—
535	C₂×C₈	—	94	1	no	—
536	C₂×C₈	—	94	1	no	—
537	C₂×C₈	—	94	1	no	—
538	C₂×C₈	—	94	1	no	—
539	C₂×C₈	—	94	1	no	—
540	C₂×C₈	—	94	1	no	—
541	C₂×C₈	—	188	4	no	—
542	C₂×C₈	—	188	4	no	—
543	C₂×C₈	#10625352	1	2	yes	—
544	C₄⋊C₄	—	47	4	no	—
545	C₄⋊C₄	—	94	2	no	—
546	C₄⋊C₄	—	94	2	no	—
547	C₂²⋊C₄	—	2	2	no	—
548	C₂²⋊C₄	—	47	4	no	—
549	C₂²⋊C₄	—	47	4	no	—
550	C₂²⋊C₄	—	94	2	no	—
551	C₂²⋊C₄	—	94	2	no	—
552	C₂²⋊C₄	C₈×D₄₇	1	4	yes	complemented
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	47	4	no	—
558	C₄²	—	94	2	no	—
559	C₄²	—	94	2	no	—
560	C₄²	—	94	1	no	—
561	C₄²	—	94	1	no	—
562	C₄²	—	94	1	no	—
563	C₄²	—	94	1	no	—
564	C₄²	—	94	1	no	—
565	C₄²	—	94	1	no	—
566	C₄²	—	188	1	no	—
567	C₄²	—	188	1	no	—
568	C₄²	—	188	1	no	—
569	C₄²	—	188	1	no	—
570	C₄²	—	188	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	47	2	no	—
578	C₂³	—	47	2	no	—
579	C₂³	—	47	2	no	—
580	C₂³	—	94	1	no	—
581	C₂³	—	94	1	no	—
582	C₂³	—	94	1	no	—
583	C₂³	—	94	1	no	—
584	C₂³	C₂×C₈×D₄₇	1	2	yes	—
585	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
586	D₄	—	94	8	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	47	2	no	—
604	C₂×C₄	—	47	2	no	—
605	C₂×C₄	—	47	2	no	—
606	C₂×C₄	—	47	2	no	—
607	C₂×C₄	—	47	2	no	—
608	C₂×C₄	—	47	2	no	—
609	C₂×C₄	—	94	1	no	—
610	C₂×C₄	—	94	1	no	—
611	C₂×C₄	—	94	1	no	—
612	C₂×C₄	—	94	1	no	—
613	C₂×C₄	—	94	1	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	2	no	—
622	C₂×C₄	—	94	2	no	—
623	C₂×C₄	—	94	2	no	—
624	C₂×C₄	—	94	2	no	—
625	C₂×C₄	—	94	1	no	—
626	C₂×C₄	—	94	1	no	—
627	C₂×C₄	—	94	1	no	—
628	C₂×C₄	—	188	4	no	—
629	C₂×C₄	—	188	4	no	—
630	C₂×C₄	—	188	4	no	—
631	C₂×C₄	—	188	4	no	—
632	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
633	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
634	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
635	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
636	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
637	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
638	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
639	C₂×C₄	#13094069	1	1	yes	characteristic
640	C₂×C₄	#13094070	1	1	yes	characteristic
641	C₈	—	2	2	no	—
642	C₈	—	4	1	no	—
643	C₈	—	4	1	no	—
644	C₈	—	4	1	no	—
645	C₈	—	94	2	no	—
646	C₈	—	188	1	no	—
647	C₈	—	188	1	no	—
648	C₈	—	188	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	47	4	no	—
657	C₂²	—	94	2	no	—
658	C₂²	—	94	2	no	—
659	C₂²	—	94	2	no	—
660	C₂²	—	94	2	no	—
661	C₂²	—	94	2	no	—
662	C₂²	—	94	2	no	—
663	C₂²	#117×D₄₇	1	1	yes	characteristic
664	C₂²	C₄×#10625352	1	1	yes	characteristic
665	C₂²	#15689595	1	1	yes	characteristic
666	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
667	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
668	C₂²	#131×D₄₇	1	1	yes	characteristic
669	C₂²	#15689888	1	1	yes	characteristic
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	2	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	94	2	no	—
676	C₄	—	94	2	no	—
677	C₄	—	94	2	no	—
678	C₄	—	94	2	no	—
679	C₄	—	94	2	no	—
680	C₄	—	94	2	no	—
681	C₄	—	188	1	no	—
682	C₄	#15689796	1	1	yes	characteristic
683	C₄	#15689803	1	1	yes	characteristic
684	C₄	#15689820	1	1	yes	characteristic
685	C₄	#15689824	1	1	yes	characteristic
686	C₂	—	4	2	no	—
687	C₂	—	94	4	no	—
688	C₂	#20246323	1	1	yes	characteristic
689	C₂	#431×D₄₇	1	1	yes	characteristic
690	C₂	#20252051	1	1	yes	characteristic
691	C₂	C₈×#10625352	1	1	yes	characteristic
692	C₂	#20252398	1	1	yes	characteristic
693	C₂	#20252409	1	1	yes	characteristic
694	C₂	#20252420	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1923	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×C₂²⋊D₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1923	D₄₇
hypocenter	C₄₇	#22785
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1923

Complements

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

N	H ≅ G/N	type
2. #20243996	C₂	semidirect
3. #20243948	C₂	semidirect
4. #20243942	C₂	semidirect
7. #20243530	C₂	semidirect
8. #20243454	C₂	semidirect
9. #20243365	C₂	semidirect
10. C₈×(C₂×D₄₇)⋊C₄	C₂	semidirect
11. #20243158	C₂	semidirect
12. C₂²⋊C₈×Dic₄₇	C₂	semidirect
13. #20243133	C₂	semidirect
14. #336×D₄₇	C₂	semidirect
15. C₄₇×#1923	C₂	semidirect
78. (C₂²⋊D₄₇)⋊C₄	C₈	semidirect
150. C₂²×Dic₄₇	C₂×C₈	semidirect
183. C₂²⋊C₄×C₄₇	C₂×C₈	semidirect
194. Dic₄₇⋊C₄	C₂×C₈	semidirect
208. C₄×Dic₄₇	C₂×C₈	semidirect
341. #1923	D₄₇	semidirect
406. C₄₇	#22785	semidirect
552. C₂²⋊C₄	C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×(C₂²⋊D₄₇)⋊C₄	2
#20243996	2
#20243948	2
#20243942	2
#20243677	2
#20243530	2
#20243454	2
#20243365	2
C₈×(C₂×D₄₇)⋊C₄	2
#20243158	2
C₂²⋊C₈×Dic₄₇	2
#20243133	2
#336×D₄₇	2
C₄₇×#1923	2
#22785	47