Subgroups — #26234824

Order 12032.

944 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	C₂×#15689196	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689188	C₂	1	1	yes	maximal, characteristic
3	#20245829	C₂	1	1	yes	maximal, characteristic
4	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243572	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243567	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243564	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243564	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243507	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243369	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243365	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243248	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243083	C₂	1	1	yes	maximal, characteristic, complemented
14	#336×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
21	C₂×#13093981	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
23	#15689196	—	2	4	no	—
24	#15689188	—	2	4	no	—
25	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
35	#15689013	C₄	1	1	yes	characteristic
36	#15689013	C₄	1	1	yes	characteristic
37	#15689006	C₄	1	1	yes	characteristic
38	#15689006	C₄	1	1	yes	characteristic
39	#15689001	C₄	1	1	yes	characteristic
40	#15689001	C₄	1	1	yes	characteristic
41	#15688994	C₄	1	1	yes	characteristic
42	#15688994	C₄	1	1	yes	characteristic
43	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
45	#15688969	C₂²	1	1	yes	characteristic
46	#15688878	C₂²	1	1	yes	characteristic
47	#15688878	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	#15688877	C₂²	1	1	yes	characteristic
53	#15688877	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
59	C₄₇×#336	C₂²	1	1	yes	characteristic
60	C₄₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₁₈₈	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×C₄×D₄₇	C₂³	1	1	yes	characteristic
66	C₂×#10625324	—	2	2	no	—
67	C₂×#10625324	—	2	2	no	—
68	C₂×#10625324	—	4	1	no	—
69	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
73	C₂×C₈×D₄₇	—	2	2	no	—
74	C₂×C₈×D₄₇	—	2	2	no	—
75	C₂×C₈×D₄₇	—	2	2	no	—
76	C₂×C₈×D₄₇	—	2	2	no	—
77	C₂×C₈×D₄₇	—	2	2	no	—
78	C₂×C₈×D₄₇	—	2	2	no	—
79	C₂×C₈×D₄₇	—	4	1	no	—
80	C₂×C₈×D₄₇	—	4	1	no	—
81	C₂×C₈×D₄₇	—	4	1	no	—
82	C₄×D₁₈₈	D₄	1	4	yes	—
83	C₄×D₁₈₈	Q₈	1	4	yes	—
84	#13093981	—	4	1	no	—
85	#13093981	—	4	1	no	—
86	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
100	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
101	C₄²×D₄₇	—	4	1	no	—
102	C₄²×D₄₇	—	4	1	no	—
103	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
104	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
105	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
106	Dic₄₇⋊C₈	—	2	2	no	—
107	Dic₄₇⋊C₈	—	2	2	no	—
108	(C₂×D₄₇)⋊C₈	—	2	2	no	—
109	(C₂×D₄₇)⋊C₈	—	2	2	no	—
110	(C₂×D₄₇)⋊C₈	—	2	2	no	—
111	(C₂×D₄₇)⋊C₈	—	2	2	no	—
112	C₄×C₄₇⋊C₈	—	2	2	no	—
113	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
114	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
115	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
116	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
117	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
118	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
119	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
120	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
121	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
127	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
130	C₄⋊C₈×C₄₇	—	2	2	no	—
131	C₄⋊C₈×C₄₇	—	4	1	no	—
132	C₄⋊C₈×C₄₇	—	4	1	no	—
133	#97×C₄₇	—	2	2	no	—
134	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
135	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
136	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂³×D₄₇	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	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₂×D₁₈₈	—	2	2	no	—
152	C₂×D₁₈₈	—	2	2	no	—
153	C₂×D₁₈₈	C₄⋊C₄	1	4	yes	—
154	C₂×C₄×D₄₇	—	2	1	no	—
155	C₂×C₄×D₄₇	—	2	1	no	—
156	C₂×C₄×D₄₇	—	2	1	no	—
157	C₂×C₄×D₄₇	—	2	1	no	—
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	—	2	2	no	—
165	C₂×C₄×D₄₇	—	4	1	no	—
166	C₂×C₄×D₄₇	—	4	1	no	—
167	C₂×C₄×D₄₇	—	4	1	no	—
168	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
169	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
170	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
171	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
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	—	2	1	no	—
182	C₂×C₈×C₄₇	—	2	1	no	—
183	C₂×C₈×C₄₇	#41	1	2	yes	—
184	C₄⋊C₄×C₄₇	—	2	2	no	—
185	C₄⋊C₄×C₄₇	—	4	1	no	—
186	C₄²×C₄₇	—	2	1	no	—
187	C₄²×C₄₇	—	2	1	no	—
188	C₄²×C₄₇	—	2	1	no	—
189	C₄²×C₄₇	—	2	1	no	—
190	C₄²×C₄₇	C₂×D₄	1	2	yes	—
191	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
192	(C₂×D₄₇)⋊C₄	—	2	2	no	—
193	(C₂×D₄₇)⋊C₄	—	2	2	no	—
194	(C₂×D₄₇)⋊C₄	—	2	2	no	—
195	(C₂×D₄₇)⋊C₄	—	4	1	no	—
196	(C₂×D₄₇)⋊C₄	—	4	1	no	—
197	(C₂×D₄₇)⋊C₄	—	4	1	no	—
198	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
199	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
200	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
201	Dic₄₇⋊C₄	—	4	1	no	—
202	Dic₄₇⋊C₄	—	4	1	no	—
203	C₄×Dic₄₇	—	2	1	no	—
204	C₄×Dic₄₇	—	2	1	no	—
205	C₄×Dic₄₇	—	2	1	no	—
206	C₄×Dic₄₇	—	2	1	no	—
207	C₄×Dic₄₇	—	4	1	no	—
208	C₄×Dic₄₇	—	4	1	no	—
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	#10625324	—	4	4	no	—
222	C₈×D₄₇	—	4	4	no	—
223	C₈×D₄₇	—	4	4	no	—
224	C₈×D₄₇	—	4	4	no	—
225	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
226	C₂²×D₄₇	—	2	1	no	—
227	C₂²×D₄₇	—	2	1	no	—
228	C₂²×D₄₇	—	2	1	no	—
229	C₂²×D₄₇	—	2	1	no	—
230	C₂²×D₄₇	—	2	1	no	—
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	—	2	1	no	—
236	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
237	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
238	C₂²×D₄₇	#131	1	2	yes	—
239	C₂²×D₄₇	#131	1	2	yes	—
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	—	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	C₂×C₄⋊C₄	1	2	yes	—
256	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
257	C₂×C₄×C₄₇	#131	1	2	yes	—
258	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
260	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
263	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
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	—	2	1	no	—
280	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
281	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
282	D₁₈₈	—	2	8	no	—
283	C₄×D₄₇	—	2	2	no	—
284	C₄×D₄₇	—	2	2	no	—
285	C₄×D₄₇	—	2	2	no	—
286	C₄×D₄₇	—	2	2	no	—
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	#22697	—	47	1	no	maximal, Sylow
302	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
303	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
304	C₂²×C₄₇	#518	1	1	yes	characteristic
305	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
306	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
307	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
308	C₂²×C₄₇	#568	1	1	yes	characteristic
309	C₂×D₄₇	—	2	2	no	—
310	C₂×D₄₇	—	2	2	no	—
311	C₂×D₄₇	—	2	2	no	—
312	C₂×D₄₇	—	2	2	no	—
313	C₂×D₄₇	—	2	2	no	—
314	C₂×D₄₇	—	2	2	no	—
315	C₂×D₄₇	—	2	2	no	—
316	C₂×D₄₇	—	2	2	no	—
317	C₂×D₄₇	—	2	2	no	—
318	C₂×D₄₇	—	4	1	no	—
319	C₂×D₄₇	—	4	1	no	—
320	C₂×D₄₇	—	4	1	no	—
321	C₂×D₄₇	—	4	1	no	—
322	C₂×D₄₇	#424	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	—	4	1	no	—
329	C₄×C₄₇	#546	1	1	yes	characteristic
330	C₄×C₄₇	#546	1	1	yes	characteristic
331	C₄×C₄₇	#554	1	1	yes	characteristic
332	C₄×C₄₇	#554	1	1	yes	characteristic
333	Dic₄₇	—	2	2	no	—
334	Dic₄₇	—	2	2	no	—
335	Dic₄₇	—	4	1	no	—
336	Dic₄₇	—	4	1	no	—
337	Dic₄₇	—	4	1	no	—
338	Dic₄₇	—	4	1	no	—
339	C₂×#435	—	47	1	no	—
340	C₂×C₈×D₄	—	47	1	no	—
341	#2290	—	47	1	no	—
342	#1940	D₄₇	1	1	yes	characteristic, complemented
343	#1939	—	47	1	no	—
344	#1851	—	47	1	no	—
345	#1850	—	47	1	no	—
346	#1850	—	47	1	no	—
347	#1850	—	47	1	no	—
348	#1832	—	47	1	no	—
349	#1798	—	47	1	no	—
350	#1797	—	47	1	no	—
351	#1768	—	47	1	no	—
352	#1729	—	47	1	no	—
353	C₂×#336	—	47	1	no	—
354	C₂×C₄₇	#2349	1	1	yes	characteristic
355	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
356	C₂×C₄₇	#2906	1	1	yes	characteristic
357	C₂×C₄₇	#2966	1	1	yes	characteristic
358	C₂×C₄₇	#2968	1	1	yes	characteristic
359	C₂×C₄₇	#2976	1	1	yes	characteristic
360	C₂×C₄₇	#2977	1	1	yes	characteristic
361	D₄₇	—	2	4	no	—
362	D₄₇	—	4	2	no	—
363	C₂²×M₁₆	—	47	1	no	—
364	C₂³×C₈	—	47	1	no	—
365	C₂³×C₈	—	47	1	no	—
366	C₂³×C₈	—	47	1	no	—
367	C₂×C₄×D₄	—	47	1	no	—
368	C₂×#117	—	47	1	no	—
369	C₂²×C₄²	—	47	1	no	—
370	#435	—	94	4	no	—
371	C₈×D₄	—	94	4	no	—
372	C₂×C₄⋊C₈	—	47	1	no	—
373	C₂×C₄⋊C₈	—	47	1	no	—
374	C₂×C₄⋊C₈	—	47	1	no	—
375	C₂×C₄⋊C₈	—	47	1	no	—
376	C₂×C₄⋊C₈	—	47	1	no	—
377	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
378	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
379	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
380	C₂×C₂²⋊C₈	—	47	1	no	—
381	C₂×C₂²⋊C₈	—	47	1	no	—
382	C₂×C₂²⋊C₈	—	47	1	no	—
383	C₂×C₂²⋊C₈	—	47	1	no	—
384	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
385	C₂×C₄×C₈	—	47	1	no	—
386	#388	—	47	1	no	—
387	#388	—	47	1	no	—
388	#387	—	47	1	no	—
389	#387	—	47	1	no	—
390	#386	—	47	1	no	—
391	#386	—	47	1	no	—
392	#385	—	47	1	no	—
393	#385	—	47	1	no	—
394	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
395	C₄×C₂²⋊C₄	—	47	1	no	—
396	C₄×C₂²⋊C₄	—	47	1	no	—
397	#376	—	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	—	47	1	no	—
405	#336	—	47	1	no	—
406	#336	C₂×D₄₇	1	1	yes	characteristic
407	#336	C₂×D₄₇	1	1	yes	characteristic
408	C₄₇	#22697	1	1	yes	characteristic, complemented, Sylow
409	C₂²×D₄	—	47	1	no	—
410	C₂³×C₄	—	47	1	no	—
411	C₂³×C₄	—	47	1	no	—
412	C₂³×C₄	—	47	1	no	—
413	C₂³×C₄	—	47	1	no	—
414	C₂×M₁₆	—	94	2	no	—
415	C₂×M₁₆	—	94	2	no	—
416	C₂×M₁₆	—	188	1	no	—
417	C₂²×C₈	—	47	1	no	—
418	C₂²×C₈	—	47	1	no	—
419	C₂²×C₈	—	47	1	no	—
420	C₂²×C₈	—	47	1	no	—
421	C₂²×C₈	—	94	2	no	—
422	C₂²×C₈	—	94	2	no	—
423	C₂²×C₈	—	94	2	no	—
424	C₂²×C₈	—	94	2	no	—
425	C₂²×C₈	—	94	2	no	—
426	C₂²×C₈	—	94	2	no	—
427	C₂²×C₈	—	188	1	no	—
428	C₂²×C₈	—	188	1	no	—
429	C₂²×C₈	—	188	1	no	—
430	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
431	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
432	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
433	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
434	C₄×D₄	—	47	4	no	—
435	C₄×D₄	—	47	4	no	—
436	#117	—	188	1	no	—
437	#117	—	188	1	no	—
438	C₂×C₄⋊C₄	—	47	1	no	—
439	C₂×C₄⋊C₄	—	47	1	no	—
440	C₂×C₄⋊C₄	—	47	1	no	—
441	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	—	47	1	no	—
444	C₂×C₂²⋊C₄	—	47	1	no	—
445	C₂×C₂²⋊C₄	—	47	1	no	—
446	C₂×C₂²⋊C₄	—	47	1	no	—
447	C₂×C₂²⋊C₄	—	47	1	no	—
448	C₂×C₂²⋊C₄	—	47	1	no	—
449	C₂×C₂²⋊C₄	—	47	1	no	—
450	C₂×C₂²⋊C₄	—	47	1	no	—
451	C₂×C₄²	—	47	1	no	—
452	C₂×C₄²	—	47	1	no	—
453	C₂×C₄²	—	47	1	no	—
454	C₂×C₄²	—	47	1	no	—
455	C₂×C₄²	—	188	1	no	—
456	C₂×C₄²	—	188	1	no	—
457	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
458	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
459	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
460	C₄⋊C₈	—	2	2	no	—
461	C₄⋊C₈	—	4	1	no	—
462	C₄⋊C₈	—	4	1	no	—
463	C₄⋊C₈	—	94	2	no	—
464	C₄⋊C₈	—	94	2	no	—
465	C₄⋊C₈	—	94	2	no	—
466	C₄⋊C₈	—	188	1	no	—
467	C₄⋊C₈	—	188	1	no	—
468	C₂²⋊C₈	—	94	2	no	—
469	C₂²⋊C₈	—	94	2	no	—
470	C₂²⋊C₈	—	94	2	no	—
471	C₂²⋊C₈	—	94	2	no	—
472	#97	—	2	2	no	—
473	C₄×C₈	—	94	2	no	—
474	#95	—	47	1	no	—
475	#95	—	47	1	no	—
476	#95	—	47	1	no	—
477	#95	—	47	1	no	—
478	#95	—	47	1	no	—
479	#95	—	47	1	no	—
480	#95	—	47	1	no	—
481	#95	—	47	1	no	—
482	#95	C₄×D₄₇	1	1	yes	characteristic
483	#95	C₄×D₄₇	1	1	yes	characteristic
484	C₂⁴	—	47	1	no	—
485	C₂⁴	—	47	1	no	—
486	C₂×D₄	—	47	4	no	—
487	C₂×D₄	—	94	2	no	—
488	C₂×D₄	—	94	2	no	—
489	C₂²×C₄	—	47	1	no	—
490	C₂²×C₄	—	47	1	no	—
491	C₂²×C₄	—	47	2	no	—
492	C₂²×C₄	—	47	2	no	—
493	C₂²×C₄	—	47	2	no	—
494	C₂²×C₄	—	47	2	no	—
495	C₂²×C₄	—	47	1	no	—
496	C₂²×C₄	—	47	1	no	—
497	C₂²×C₄	—	47	1	no	—
498	C₂²×C₄	—	47	1	no	—
499	C₂²×C₄	—	94	2	no	—
500	C₂²×C₄	—	94	2	no	—
501	C₂²×C₄	—	94	1	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	—	94	1	no	—
507	C₂²×C₄	—	94	1	no	—
508	C₂²×C₄	—	94	1	no	—
509	C₂²×C₄	—	94	2	no	—
510	C₂²×C₄	—	188	1	no	—
511	C₂²×C₄	—	188	1	no	—
512	C₂²×C₄	—	188	1	no	—
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	C₂×C₄×D₄₇	1	1	yes	characteristic
518	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
519	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
520	M₁₆	—	188	4	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	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	47	2	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	—	94	1	no	—
542	C₂×C₈	—	94	1	no	—
543	C₂×C₈	—	94	1	no	—
544	C₂×C₈	—	188	4	no	—
545	C₂×C₈	—	188	4	no	—
546	C₂×C₈	—	188	4	no	—
547	C₂×C₈	#10625354	1	2	yes	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	4	1	no	—
550	C₄⋊C₄	—	47	4	no	—
551	C₄⋊C₄	—	188	1	no	—
552	C₄⋊C₄	—	188	1	no	—
553	C₂²⋊C₄	—	47	4	no	—
554	C₂²⋊C₄	—	47	4	no	—
555	C₂²⋊C₄	—	94	2	no	—
556	C₂²⋊C₄	—	94	2	no	—
557	C₂²⋊C₄	—	94	2	no	—
558	C₂²⋊C₄	—	188	1	no	—
559	C₂²⋊C₄	—	188	1	no	—
560	C₂²⋊C₄	—	188	1	no	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	94	1	no	—
566	C₄²	—	94	1	no	—
567	C₄²	—	94	1	no	—
568	C₄²	—	94	1	no	—
569	C₄²	—	188	1	no	—
570	C₄²	—	188	1	no	—
571	C₄²	D₄×D₄₇	1	2	yes	—
572	C₄²	Q₈×D₄₇	1	2	yes	—
573	C₂³	—	47	2	no	—
574	C₂³	—	47	2	no	—
575	C₂³	—	47	2	no	—
576	C₂³	—	47	2	no	—
577	C₂³	—	94	1	no	—
578	C₂³	—	94	1	no	—
579	C₂³	—	94	1	no	—
580	C₂³	—	94	1	no	—
581	C₂³	—	94	1	no	—
582	C₂³	—	94	1	no	—
583	C₂³	—	94	1	no	—
584	C₂³	—	94	1	no	—
585	C₂³	—	94	1	no	—
586	C₂³	—	94	1	no	—
587	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
588	D₄	—	94	8	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	—	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	—	47	2	no	—
605	C₂×C₄	—	47	2	no	—
606	C₂×C₄	—	94	1	no	—
607	C₂×C₄	—	94	1	no	—
608	C₂×C₄	—	94	1	no	—
609	C₂×C₄	—	94	1	no	—
610	C₂×C₄	—	94	2	no	—
611	C₂×C₄	—	94	2	no	—
612	C₂×C₄	—	94	2	no	—
613	C₂×C₄	—	94	2	no	—
614	C₂×C₄	—	94	2	no	—
615	C₂×C₄	—	94	2	no	—
616	C₂×C₄	—	94	2	no	—
617	C₂×C₄	—	94	2	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	—	94	1	no	—
625	C₂×C₄	—	94	1	no	—
626	C₂×C₄	—	94	1	no	—
627	C₂×C₄	—	94	1	no	—
628	C₂×C₄	—	94	1	no	—
629	C₂×C₄	—	94	1	no	—
630	C₂×C₄	—	188	4	no	—
631	C₂×C₄	—	188	4	no	—
632	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
633	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
634	C₂×C₄	#13094032	1	2	yes	—
635	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
636	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
637	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
638	C₂×C₄	C₂×#10625354	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	—	47	4	no	—
650	C₂²	—	94	2	no	—
651	C₂²	—	94	2	no	—
652	C₂²	—	94	2	no	—
653	C₂²	—	94	2	no	—
654	C₂²	—	94	2	no	—
655	C₂²	—	94	2	no	—
656	C₂²	—	94	2	no	—
657	C₂²	—	94	2	no	—
658	C₂²	—	94	2	no	—
659	C₂²	—	188	1	no	—
660	C₂²	—	188	1	no	—
661	C₂²	—	188	1	no	—
662	C₂²	—	188	1	no	—
663	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
664	C₂²	C₄×#10625354	1	1	yes	characteristic
665	C₂²	#15689595	1	1	yes	characteristic
666	C₂²	#131×D₄₇	1	1	yes	characteristic
667	C₂²	#131×D₄₇	1	1	yes	characteristic
668	C₂²	C₂×#13094032	1	1	yes	characteristic
669	C₂²	#15689889	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	—	4	1	no	—
676	C₄	—	94	2	no	—
677	C₄	—	94	2	no	—
678	C₄	—	188	1	no	—
679	C₄	—	188	1	no	—
680	C₄	—	188	1	no	—
681	C₄	—	188	1	no	—
682	C₄	#15689764	1	1	yes	characteristic
683	C₄	#15689770	1	1	yes	characteristic
684	C₄	#15689829	1	1	yes	characteristic
685	C₄	#15689834	1	1	yes	characteristic
686	C₂	—	94	4	no	—
687	C₂	—	188	2	no	—
688	C₂	#20246297	1	1	yes	characteristic
689	C₂	#424×D₄₇	1	1	yes	characteristic
690	C₂	#20251957	1	1	yes	characteristic
691	C₂	#20252362	1	1	yes	characteristic
692	C₂	#20252381	1	1	yes	characteristic
693	C₂	#20252435	1	1	yes	characteristic
694	C₂	#20252439	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1940	C₂
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1940	D₄₇
hypocenter	C₄₇	#22697
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1940

Complements

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

N	H ≅ G/N	type
4. #20244107	C₂	semidirect
5. #20243572	C₂	semidirect
6. #20243567	C₂	semidirect
7. #20243564	C₂	semidirect
8. #20243564	C₂	semidirect
9. #20243507	C₂	semidirect
10. #20243369	C₂	semidirect
11. #20243365	C₂	semidirect
12. #20243248	C₂	semidirect
13. #20243083	C₂	semidirect
14. #336×D₄₇	C₂	semidirect
15. C₄₇×#1940	C₂	semidirect
342. #1940	D₄₇	semidirect
408. C₄₇	#22697	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689196	2
C₂×#15689188	2
#20245829	2
#20244107	2
#20243572	2
#20243567	2
#20243564	2
#20243507	2
#20243369	2
#20243365	2
#20243248	2
#20243083	2
#336×D₄₇	2
C₄₇×#1940	2
#22697	47