Subgroups — #26379301

Order 12032.

2190 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246536	C₂	1	4	yes	maximal, complemented
2	#20246488	C₂	1	2	yes	maximal, complemented
3	#20246463	C₂	1	2	yes	maximal, complemented
4	#20246345	C₂	1	1	yes	maximal, characteristic, complemented
5	#20246337	C₂	1	1	yes	maximal, characteristic, complemented
6	#20246337	C₂	1	2	yes	maximal, complemented
7	#20246317	C₂	1	2	yes	maximal, complemented
8	Q₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#20246167	C₂	1	4	yes	maximal, complemented
11	#20246083	C₂	1	2	yes	maximal
12	#20246072	C₂	1	2	yes	maximal, complemented
13	#20246011	C₂	1	2	yes	maximal, complemented
14	#20245997	C₂	1	2	yes	maximal, complemented
15	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
16	#20245795	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄₇×#529	C₂	1	1	yes	maximal, characteristic
18	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
19	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
20	C₂×#13093983	C₂²	1	2	yes	—
21	C₂×#13093983	C₂²	1	2	yes	—
22	C₂×#13093983	C₂²	1	2	yes	—
23	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
24	#15689030	C₂²	1	2	yes	—
25	#15689026	C₂²	1	4	yes	—
26	#15689026	C₂²	1	2	yes	—
27	#15689022	C₂²	1	4	yes	—
28	#15689022	C₂²	1	4	yes	—
29	#15689022	C₂²	1	2	yes	—
30	#15689022	C₂²	1	2	yes	—
31	#15689022	C₂²	1	4	yes	—
32	#15689016	C₂²	1	4	yes	—
33	#15689016	C₂²	1	4	yes	—
34	#15689016	C₂²	1	4	yes	—
35	#15689016	C₂²	1	4	yes	—
36	#15689016	C₂²	1	4	yes	—
37	#15689016	C₂²	1	4	yes	—
38	#15689009	C₂²	1	4	yes	—
39	#15689009	C₂²	1	4	yes	—
40	#15689009	C₂²	1	4	yes	—
41	#15689009	C₂²	1	4	yes	—
42	#15689003	C₂²	1	4	yes	—
43	#15688998	C₂²	1	4	yes	—
44	#15688998	C₂²	1	4	yes	—
45	#15688998	C₂²	1	4	yes	—
46	#15688993	C₂²	1	1	yes	characteristic
47	#15688993	C₂²	1	2	yes	—
48	#15688993	C₂²	1	1	yes	characteristic
49	#15688993	C₂²	1	1	yes	characteristic
50	#15688993	C₂²	1	1	yes	characteristic
51	#15688989	C₂²	1	2	yes	—
52	#15688989	C₂²	1	2	yes	—
53	#15688989	C₂²	1	2	yes	—
54	#15688983	C₂²	1	2	yes	—
55	#15688983	C₂²	1	2	yes	—
56	#15688983	C₂²	1	2	yes	—
57	#15688983	C₂²	1	1	yes	characteristic
58	#15688983	C₂²	1	2	yes	—
59	#15688983	C₂²	1	1	yes	characteristic
60	#15688983	C₂²	1	2	yes	—
61	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
62	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
63	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
64	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
66	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
67	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
68	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
69	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
70	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
71	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
72	C₄₇×#529	C₄	1	16	yes	complemented
73	C₂×#126×C₄₇	C₂²	1	2	yes	—
74	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
75	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
76	C₂×#123×C₄₇	C₂²	1	2	yes	—
77	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
78	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
79	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
80	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
81	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
82	C₂×#117×C₄₇	C₂²	1	2	yes	—
83	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
84	C₂³×Dic₄₇	C₂³	1	4	yes	—
85	Q₈×Dic₄₇	—	4	4	no	—
86	D₄×Dic₄₇	—	4	4	no	—
87	#13093983	—	4	4	no	—
88	#13093983	—	4	4	no	—
89	#13093983	—	4	4	no	—
90	C₂×C₄⋊Dic₄₇	—	4	4	no	—
91	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
94	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
96	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
97	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
99	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
100	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
101	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
102	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
103	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
104	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
105	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
106	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
107	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
108	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
109	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
110	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
111	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
112	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
113	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
114	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
115	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
116	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
117	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
118	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
119	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
120	C₄₇⋊#95	C₂³	1	2	yes	—
121	C₄₇⋊#95	C₂³	1	4	yes	—
122	C₄₇⋊#95	C₂³	1	2	yes	—
123	C₄₇⋊#95	C₂³	1	2	yes	—
124	C₄₇⋊#95	C₂³	1	4	yes	—
125	C₄₇⋊#95	C₂³	1	4	yes	—
126	C₄₇⋊#95	C₂³	1	2	yes	—
127	C₄₇⋊#95	C₂³	1	4	yes	—
128	C₄₇⋊#95	C₂³	1	4	yes	—
129	C₄₇⋊#95	C₂³	1	4	yes	—
130	C₄₇⋊#95	C₂³	1	4	yes	—
131	C₄₇⋊#95	C₂³	1	4	yes	—
132	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
138	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
139	#126×C₄₇	C₂×C₄	1	16	yes	complemented
140	#125×C₄₇	C₂×C₄	1	8	yes	complemented
141	#124×C₄₇	C₂×C₄	1	8	yes	—
142	#123×C₄₇	C₂×C₄	1	16	yes	complemented
143	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
144	#121×C₄₇	C₂×C₄	1	8	yes	—
145	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
146	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
147	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
148	#117×C₄₇	C₂×C₄	1	16	yes	complemented
149	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
160	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
161	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
164	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
166	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
167	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
168	C₂×Q₈×C₄₇	—	2	2	no	—
169	C₂×Q₈×C₄₇	—	2	2	no	—
170	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
171	C₂×D₄×C₄₇	—	2	2	no	—
172	C₂×D₄×C₄₇	—	2	2	no	—
173	C₂×D₄×C₄₇	—	4	2	no	—
174	C₂×D₄×C₄₇	—	4	2	no	—
175	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
176	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
177	C₂²×C₄×C₄₇	—	2	4	no	—
178	C₂²×C₄×C₄₇	—	2	2	no	—
179	C₂²×C₄×C₄₇	—	2	2	no	—
180	C₂²×C₄×C₄₇	—	2	2	no	—
181	C₂²×C₄×C₄₇	—	2	4	no	—
182	C₂²×C₄×C₄₇	—	2	2	no	—
183	C₂²×C₄×C₄₇	—	4	1	no	—
184	C₂²×C₄×C₄₇	—	4	1	no	—
185	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
186	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
187	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
188	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
189	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
198	C₂²×Dic₄₇	—	4	4	no	—
199	C₂²×Dic₄₇	—	4	4	no	—
200	C₂²×Dic₄₇	—	4	4	no	—
201	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
202	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
203	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
204	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
205	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
206	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
207	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
208	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
209	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
210	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
211	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
212	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
213	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
214	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
215	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
216	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
217	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
218	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
219	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
220	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
221	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
222	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
223	C₂²⋊Dic₄₇	—	4	4	no	—
224	C₂²⋊Dic₄₇	—	4	2	no	—
225	C₂²⋊Dic₄₇	—	4	2	no	—
226	C₂²⋊Dic₄₇	—	4	4	no	—
227	C₂²⋊Dic₄₇	—	4	4	no	—
228	C₂²⋊Dic₄₇	—	4	4	no	—
229	C₄⋊Dic₄₇	—	2	2	no	—
230	C₄⋊Dic₄₇	—	2	4	no	—
231	C₄⋊Dic₄₇	—	2	4	no	—
232	C₄⋊Dic₄₇	—	2	2	no	—
233	C₄⋊Dic₄₇	—	2	4	no	—
234	C₄⋊Dic₄₇	—	2	2	no	—
235	C₄⋊Dic₄₇	—	2	2	no	—
236	C₄⋊Dic₄₇	—	2	4	no	—
237	C₄⋊Dic₄₇	—	4	4	no	—
238	C₄⋊Dic₄₇	—	4	2	no	—
239	C₄⋊Dic₄₇	—	4	2	no	—
240	C₄⋊Dic₄₇	—	4	4	no	—
241	C₄⋊Dic₄₇	—	4	2	no	—
242	C₄⋊Dic₄₇	—	4	2	no	—
243	C₄⋊Dic₄₇	—	4	2	no	—
244	C₄⋊Dic₄₇	—	4	2	no	—
245	C₄⋊Dic₄₇	—	4	4	no	—
246	C₄×Dic₄₇	—	2	4	no	—
247	C₄×Dic₄₇	—	2	4	no	—
248	C₄×Dic₄₇	—	4	4	no	—
249	C₄×Dic₄₇	—	4	4	no	—
250	C₄×Dic₄₇	—	4	4	no	—
251	C₄×Dic₄₇	—	4	4	no	—
252	C₂³×C₄₇	—	2	1	no	—
253	C₂³×C₄₇	—	2	1	no	—
254	C₂³×C₄₇	—	2	2	no	—
255	C₂³×C₄₇	—	2	2	no	—
256	C₂³×C₄₇	—	2	2	no	—
257	C₂³×C₄₇	—	2	1	no	—
258	C₂³×C₄₇	—	2	1	no	—
259	C₂³×C₄₇	—	2	2	no	—
260	C₂³×C₄₇	—	2	2	no	—
261	C₂³×C₄₇	—	2	2	no	—
262	C₂³×C₄₇	—	2	1	no	—
263	C₂³×C₄₇	—	2	1	no	—
264	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
265	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
266	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
267	Q₈×C₄₇	—	2	8	no	—
268	D₄×C₄₇	—	2	8	no	—
269	D₄×C₄₇	—	4	8	no	—
270	C₂×C₄×C₄₇	—	2	1	no	—
271	C₂×C₄×C₄₇	—	2	2	no	—
272	C₂×C₄×C₄₇	—	2	2	no	—
273	C₂×C₄×C₄₇	—	2	1	no	—
274	C₂×C₄×C₄₇	—	2	1	no	—
275	C₂×C₄×C₄₇	—	2	2	no	—
276	C₂×C₄×C₄₇	—	2	1	no	—
277	C₂×C₄×C₄₇	—	2	2	no	—
278	C₂×C₄×C₄₇	—	2	2	no	—
279	C₂×C₄×C₄₇	—	2	1	no	—
280	C₂×C₄×C₄₇	—	2	1	no	—
281	C₂×C₄×C₄₇	—	2	1	no	—
282	C₂×C₄×C₄₇	—	2	1	no	—
283	C₂×C₄×C₄₇	—	2	2	no	—
284	C₂×C₄×C₄₇	—	2	16	no	—
285	C₂×C₄×C₄₇	—	2	8	no	—
286	C₂×C₄×C₄₇	—	2	8	no	—
287	C₂×C₄×C₄₇	—	4	4	no	—
288	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
289	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
293	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
294	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
296	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
297	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
298	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
299	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
300	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
301	C₂×Dic₄₇	—	2	2	no	—
302	C₂×Dic₄₇	—	2	2	no	—
303	C₂×Dic₄₇	—	2	2	no	—
304	C₂×Dic₄₇	—	2	2	no	—
305	C₂×Dic₄₇	—	2	2	no	—
306	C₂×Dic₄₇	—	2	4	no	—
307	C₂×Dic₄₇	—	2	4	no	—
308	C₂×Dic₄₇	—	2	4	no	—
309	C₂×Dic₄₇	—	2	2	no	—
310	C₂×Dic₄₇	—	2	2	no	—
311	C₂×Dic₄₇	—	2	2	no	—
312	C₂×Dic₄₇	—	2	4	no	—
313	C₂×Dic₄₇	—	2	2	no	—
314	C₂×Dic₄₇	—	2	4	no	—
315	C₂×Dic₄₇	—	2	2	no	—
316	C₂×Dic₄₇	—	2	4	no	—
317	C₂×Dic₄₇	—	2	2	no	—
318	C₂×Dic₄₇	—	2	2	no	—
319	C₂×Dic₄₇	—	8	8	no	—
320	#34383	—	47	1	no	maximal, Sylow
321	C₂²×C₄₇	—	2	2	no	—
322	C₂²×C₄₇	—	2	2	no	—
323	C₂²×C₄₇	—	2	4	no	—
324	C₂²×C₄₇	—	2	4	no	—
325	C₂²×C₄₇	—	2	2	no	—
326	C₂²×C₄₇	—	2	4	no	—
327	C₂²×C₄₇	—	4	2	no	—
328	C₂²×C₄₇	—	4	1	no	—
329	C₂²×C₄₇	—	4	1	no	—
330	C₂²×C₄₇	—	4	2	no	—
331	C₂²×C₄₇	—	4	1	no	—
332	C₂²×C₄₇	—	4	2	no	—
333	C₂²×C₄₇	—	4	1	no	—
334	C₂²×C₄₇	—	4	2	no	—
335	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
336	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
337	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
338	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
339	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
340	C₂²×C₄₇	#585	1	1	yes	characteristic
341	C₂²×C₄₇	#585	1	1	yes	characteristic
342	C₄×C₄₇	—	2	2	no	—
343	C₄×C₄₇	—	2	4	no	—
344	C₄×C₄₇	—	2	2	no	—
345	C₄×C₄₇	—	2	4	no	—
346	C₄×C₄₇	—	2	2	no	—
347	C₄×C₄₇	—	2	2	no	—
348	C₄×C₄₇	—	2	4	no	—
349	C₄×C₄₇	#520	1	4	yes	—
350	C₄×C₄₇	#520	1	4	yes	—
351	Dic₄₇	—	4	2	no	—
352	Dic₄₇	—	4	4	no	—
353	Dic₄₇	—	4	2	no	—
354	Dic₄₇	—	4	2	no	—
355	Dic₄₇	—	4	2	no	—
356	Dic₄₇	—	4	4	no	—
357	C₂×#529	D₄₇	1	1	yes	characteristic
358	#2376	—	47	4	no	—
359	#2370	—	47	2	no	—
360	#2367	—	47	2	no	—
361	#2355	—	47	1	no	—
362	#2354	—	47	1	no	—
363	#2354	—	47	2	no	—
364	#2352	—	47	2	no	—
365	Q₈×C₄⋊C₄	—	47	1	no	—
366	D₄×C₄⋊C₄	—	47	1	no	—
367	#2334	—	47	4	no	—
368	#2324	—	47	2	no	—
369	#2323	—	47	2	no	—
370	#2317	—	47	2	no	—
371	#2314	—	47	2	no	—
372	#2285	—	47	1	no	—
373	#2285	—	47	1	no	—
374	C₂×C₄₇	—	4	2	no	—
375	C₂×C₄₇	—	4	4	no	—
376	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
377	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
378	C₂×C₄₇	#3428	1	1	yes	characteristic
379	C₂×C₄₇	#3546	1	1	yes	characteristic
380	C₂×C₄₇	#3547	1	1	yes	characteristic
381	C₂×C₄₇	#3554	1	1	yes	characteristic
382	C₂×C₄₇	#3555	1	1	yes	characteristic
383	#529	Dic₄₇	1	16	yes	complemented
384	C₂×#126	C₂×D₄₇	1	2	yes	—
385	C₂×#125	C₂×D₄₇	1	1	yes	characteristic
386	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
387	C₂×#123	C₂×D₄₇	1	2	yes	—
388	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
389	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
390	C₂×C₄×Q₈	—	47	2	no	—
391	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
392	C₂×C₄×D₄	—	47	2	no	—
393	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
394	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
395	C₂×#117	—	47	2	no	—
396	C₂×#117	—	47	2	no	—
397	C₂×#117	—	47	2	no	—
398	C₂×#117	C₂×D₄₇	1	2	yes	—
399	C₂²×C₄⋊C₄	—	47	2	no	—
400	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
401	#391	—	47	2	no	—
402	#390	—	47	2	no	—
403	#390	—	47	4	no	—
404	#389	—	47	4	no	—
405	#389	—	47	4	no	—
406	#389	—	47	2	no	—
407	#389	—	47	2	no	—
408	#389	—	47	4	no	—
409	#388	—	47	4	no	—
410	#388	—	47	4	no	—
411	#388	—	47	4	no	—
412	#388	—	47	4	no	—
413	#388	—	47	4	no	—
414	#388	—	47	4	no	—
415	#387	—	47	4	no	—
416	#387	—	47	4	no	—
417	#387	—	47	4	no	—
418	#387	—	47	4	no	—
419	#386	—	47	4	no	—
420	#385	—	47	4	no	—
421	#385	—	47	4	no	—
422	#385	—	47	4	no	—
423	#384	—	47	1	no	—
424	#384	—	47	1	no	—
425	#384	—	47	2	no	—
426	#384	—	47	1	no	—
427	#384	—	47	1	no	—
428	#382	—	47	2	no	—
429	#382	—	47	2	no	—
430	#382	—	47	2	no	—
431	#380	—	47	2	no	—
432	#380	—	47	2	no	—
433	#380	—	47	2	no	—
434	#380	—	47	1	no	—
435	#380	—	47	1	no	—
436	#380	—	47	2	no	—
437	#380	—	47	2	no	—
438	C₄×C₄⋊C₄	—	47	2	no	—
439	C₄×C₄⋊C₄	—	47	2	no	—
440	C₄×C₄⋊C₄	—	47	4	no	—
441	C₄×C₄⋊C₄	—	47	2	no	—
442	C₄×C₄⋊C₄	—	47	2	no	—
443	C₄×C₄⋊C₄	—	47	2	no	—
444	C₄×C₄⋊C₄	—	47	1	no	—
445	C₄×C₄⋊C₄	—	47	1	no	—
446	C₄×C₄⋊C₄	—	47	2	no	—
447	C₄×C₄⋊C₄	—	47	2	no	—
448	C₄×C₂²⋊C₄	—	47	4	no	—
449	C₄₇	#34383	1	1	yes	characteristic, complemented, Sylow
450	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
451	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
452	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
453	C₂³×C₄	—	47	4	no	—
454	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
455	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
456	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
457	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
458	#126	C₂×Dic₄₇	1	16	yes	complemented
459	#125	C₂×Dic₄₇	1	8	yes	complemented
460	#124	C₂×Dic₄₇	1	8	yes	—
461	#123	C₂×Dic₄₇	1	16	yes	complemented
462	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
463	#121	C₂×Dic₄₇	1	8	yes	—
464	C₄×Q₈	—	188	4	no	—
465	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
466	C₄×D₄	—	188	4	no	—
467	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
468	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
469	#117	—	188	4	no	—
470	#117	—	188	4	no	—
471	#117	—	188	4	no	—
472	#117	C₂×Dic₄₇	1	16	yes	complemented
473	C₂×C₄⋊C₄	—	47	1	no	—
474	C₂×C₄⋊C₄	—	47	2	no	—
475	C₂×C₄⋊C₄	—	47	2	no	—
476	C₂×C₄⋊C₄	—	47	1	no	—
477	C₂×C₄⋊C₄	—	47	2	no	—
478	C₂×C₄⋊C₄	—	47	1	no	—
479	C₂×C₄⋊C₄	—	47	1	no	—
480	C₂×C₄⋊C₄	—	47	2	no	—
481	C₂×C₄⋊C₄	—	47	4	no	—
482	C₂×C₄⋊C₄	—	47	2	no	—
483	C₂×C₄⋊C₄	—	47	2	no	—
484	C₂×C₄⋊C₄	—	47	4	no	—
485	C₂×C₄⋊C₄	—	47	2	no	—
486	C₂×C₄⋊C₄	—	47	2	no	—
487	C₂×C₄⋊C₄	—	47	2	no	—
488	C₂×C₄⋊C₄	—	47	2	no	—
489	C₂×C₄⋊C₄	—	47	4	no	—
490	C₂×C₄⋊C₄	—	188	4	no	—
491	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
492	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
493	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
494	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
495	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
496	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
497	C₂×C₂²⋊C₄	—	47	2	no	—
498	C₂×C₂²⋊C₄	—	47	4	no	—
499	C₂×C₂²⋊C₄	—	47	2	no	—
500	C₂×C₂²⋊C₄	—	47	4	no	—
501	C₂×C₂²⋊C₄	—	47	4	no	—
502	C₂×C₂²⋊C₄	—	47	4	no	—
503	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
504	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
508	C₂×C₄²	—	47	2	no	—
509	C₂×C₄²	—	47	2	no	—
510	C₂×C₄²	—	47	4	no	—
511	C₂×C₄²	—	47	4	no	—
512	C₂×C₄²	—	47	4	no	—
513	C₂×C₄²	—	47	4	no	—
514	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
515	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
516	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
517	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
518	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
519	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
520	#95	—	47	2	no	—
521	#95	—	47	4	no	—
522	#95	—	47	2	no	—
523	#95	—	47	2	no	—
524	#95	—	47	4	no	—
525	#95	—	47	4	no	—
526	#95	—	47	2	no	—
527	#95	—	47	4	no	—
528	#95	—	47	4	no	—
529	#95	—	47	4	no	—
530	#95	—	47	4	no	—
531	#95	—	47	4	no	—
532	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
533	C₂⁴	C₂³×D₄₇	1	2	yes	—
534	C₂×Q₈	—	2	2	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
537	C₂×D₄	—	2	2	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	4	2	no	—
540	C₂×D₄	—	4	2	no	—
541	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
542	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
543	C₂²×C₄	—	2	4	no	—
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	4	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	4	1	no	—
550	C₂²×C₄	—	4	1	no	—
551	C₂²×C₄	—	47	2	no	—
552	C₂²×C₄	—	47	2	no	—
553	C₂²×C₄	—	47	4	no	—
554	C₂²×C₄	—	47	2	no	—
555	C₂²×C₄	—	47	4	no	—
556	C₂²×C₄	—	47	2	no	—
557	C₂²×C₄	—	188	4	no	—
558	C₂²×C₄	—	188	4	no	—
559	C₂²×C₄	—	188	4	no	—
560	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
561	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
562	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
563	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
564	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
565	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
566	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
567	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
568	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
569	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
570	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
571	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
572	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
573	C₄⋊C₄	—	94	2	no	—
574	C₄⋊C₄	—	94	4	no	—
575	C₄⋊C₄	—	94	4	no	—
576	C₄⋊C₄	—	94	2	no	—
577	C₄⋊C₄	—	94	4	no	—
578	C₄⋊C₄	—	94	2	no	—
579	C₄⋊C₄	—	94	2	no	—
580	C₄⋊C₄	—	94	4	no	—
581	C₄⋊C₄	—	188	2	no	—
582	C₄⋊C₄	—	188	2	no	—
583	C₄⋊C₄	—	188	2	no	—
584	C₄⋊C₄	—	188	2	no	—
585	C₄⋊C₄	—	188	4	no	—
586	C₄⋊C₄	—	188	4	no	—
587	C₄⋊C₄	—	188	2	no	—
588	C₄⋊C₄	—	188	2	no	—
589	C₄⋊C₄	—	188	4	no	—
590	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
591	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
592	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
593	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
594	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
595	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
596	C₂²⋊C₄	—	188	4	no	—
597	C₂²⋊C₄	—	188	2	no	—
598	C₂²⋊C₄	—	188	2	no	—
599	C₂²⋊C₄	—	188	4	no	—
600	C₂²⋊C₄	—	188	4	no	—
601	C₂²⋊C₄	—	188	4	no	—
602	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
603	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
604	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
605	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
606	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
607	C₄²	—	94	4	no	—
608	C₄²	—	94	4	no	—
609	C₄²	—	188	4	no	—
610	C₄²	—	188	4	no	—
611	C₄²	—	188	4	no	—
612	C₄²	—	188	4	no	—
613	C₄²	C₂²×Dic₄₇	1	4	yes	—
614	C₄²	C₂²×Dic₄₇	1	4	yes	—
615	C₄²	C₂²×Dic₄₇	1	4	yes	—
616	C₄²	C₂²×Dic₄₇	1	4	yes	—
617	C₄²	C₂²×Dic₄₇	1	8	yes	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	2	no	—
621	C₂³	—	2	2	no	—
622	C₂³	—	2	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	2	no	—
625	C₂³	—	2	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	2	no	—
630	C₂³	C₂³×Dic₄₇	1	4	yes	—
631	C₂³	C₂³×Dic₄₇	1	2	yes	—
632	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
633	Q₈	—	2	8	no	—
634	D₄	—	2	8	no	—
635	D₄	—	4	8	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	16	no	—
651	C₂×C₄	—	2	8	no	—
652	C₂×C₄	—	2	8	no	—
653	C₂×C₄	—	4	4	no	—
654	C₂×C₄	—	94	2	no	—
655	C₂×C₄	—	94	2	no	—
656	C₂×C₄	—	94	2	no	—
657	C₂×C₄	—	94	2	no	—
658	C₂×C₄	—	94	4	no	—
659	C₂×C₄	—	94	2	no	—
660	C₂×C₄	—	94	4	no	—
661	C₂×C₄	—	94	4	no	—
662	C₂×C₄	—	94	2	no	—
663	C₂×C₄	—	94	4	no	—
664	C₂×C₄	—	94	2	no	—
665	C₂×C₄	—	94	2	no	—
666	C₂×C₄	—	94	2	no	—
667	C₂×C₄	—	94	4	no	—
668	C₂×C₄	—	94	2	no	—
669	C₂×C₄	—	94	2	no	—
670	C₂×C₄	—	94	4	no	—
671	C₂×C₄	—	94	2	no	—
672	C₂×C₄	—	376	8	no	—
673	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
674	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
675	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
676	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
677	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
678	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
679	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
680	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
681	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
682	C₂×C₄	#13094070	1	2	yes	—
683	C₂×C₄	#13094070	1	2	yes	—
684	C₂×C₄	#13094071	1	2	yes	—
685	C₂×C₄	#13094071	1	2	yes	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	2	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	2	2	no	—
691	C₂²	—	2	4	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	2	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	2	no	—
700	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
701	C₂²	C₂×#13094070	1	1	yes	characteristic
702	C₂²	C₂×#13094070	1	1	yes	characteristic
703	C₂²	C₂×#13094071	1	1	yes	characteristic
704	C₂²	C₂×#13094071	1	1	yes	characteristic
705	C₂²	#15689959	1	1	yes	characteristic
706	C₂²	#15689959	1	1	yes	characteristic
707	C₄	—	2	2	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	4	no	—
711	C₄	—	2	2	no	—
712	C₄	—	2	2	no	—
713	C₄	—	2	4	no	—
714	C₄	—	188	4	no	—
715	C₄	—	188	2	no	—
716	C₄	—	188	4	no	—
717	C₄	—	188	2	no	—
718	C₄	—	188	2	no	—
719	C₄	—	188	2	no	—
720	C₄	#15689606	1	4	yes	—
721	C₄	#15689606	1	4	yes	—
722	C₂	—	4	2	no	—
723	C₂	—	4	4	no	—
724	C₂	C₂×#15689606	1	1	yes	characteristic
725	C₂	C₂×#15689606	1	1	yes	characteristic
726	C₂	#20256591	1	1	yes	characteristic
727	C₂	#20257762	1	1	yes	characteristic
728	C₂	#20257779	1	1	yes	characteristic
729	C₂	#20257861	1	1	yes	characteristic
730	C₂	#20257878	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂×C₄₇×#529	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂×#121×C₄₇	C₂²
hypercenter	C₂×#529	D₄₇
hypocenter	C₄₇	#34383
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #20246536	C₂	semidirect
2. #20246488	C₂	semidirect
3. #20246463	C₂	semidirect
4. #20246345	C₂	semidirect
5. #20246337	C₂	semidirect
6. #20246337	C₂	semidirect
7. #20246317	C₂	semidirect
8. Q₈×C₄⋊Dic₄₇	C₂	semidirect
9. D₄×C₄⋊Dic₄₇	C₂	semidirect
10. #20246167	C₂	semidirect
12. #20246072	C₂	semidirect
13. #20246011	C₂	semidirect
14. #20245997	C₂	semidirect
15. #20245795	C₂	semidirect
16. #20245795	C₂	semidirect
72. C₄₇×#529	C₄	semidirect
139. #126×C₄₇	C₂×C₄	semidirect
140. #125×C₄₇	C₂×C₄	semidirect
142. #123×C₄₇	C₂×C₄	semidirect
143. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
145. C₄×Q₈×C₄₇	C₂×C₄	semidirect
147. C₄×D₄×C₄₇	C₂×C₄	semidirect
148. #117×C₄₇	C₂×C₄	semidirect
160. C₂×C₄²×C₄₇	C₂×C₄	semidirect
383. #529	Dic₄₇	semidirect
449. C₄₇	#34383	semidirect
458. #126	C₂×Dic₄₇	semidirect
459. #125	C₂×Dic₄₇	semidirect
461. #123	C₂×Dic₄₇	semidirect
462. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
465. C₄×Q₈	C₂×Dic₄₇	semidirect
468. C₄×D₄	C₂×Dic₄₇	semidirect
472. #117	C₂×Dic₄₇	semidirect
514. C₂×C₄²	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246536	2
#20246488	2
#20246463	2
#20246345	2
#20246337	2
#20246317	2
Q₈×C₄⋊Dic₄₇	2
D₄×C₄⋊Dic₄₇	2
#20246167	2
#20246083	2
#20246072	2
#20246011	2
#20245997	2
#20245795	2
C₂×C₄₇×#529	2
#34383	47