Subgroups — #26377374

Order 12032.

2718 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246361	C₂	1	1	yes	maximal, characteristic, complemented
2	#20246337	C₂	1	1	yes	maximal, characteristic, complemented
3	#20246328	C₂	1	2	yes	maximal, complemented
4	#20246317	C₂	1	2	yes	maximal, complemented
5	#20246298	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	#20246281	C₂	1	1	yes	maximal, characteristic, complemented
8	#20246273	C₂	1	1	yes	maximal, characteristic, complemented
9	#20246237	C₂	1	2	yes	maximal, complemented
10	#20246237	C₂	1	2	yes	maximal, complemented
11	D₄×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
12	D₄×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
13	#20246031	C₂	1	1	yes	maximal, characteristic, complemented
14	#20246021	C₂	1	2	yes	maximal, complemented
15	#20245997	C₂	1	1	yes	maximal, characteristic, complemented
16	#20245986	C₂	1	2	yes	maximal, complemented
17	#20245886	C₂	1	1	yes	maximal, characteristic, complemented
18	#20245853	C₂	1	1	yes	maximal, characteristic, complemented
19	#20245833	C₂	1	2	yes	maximal, complemented
20	C₂×#15689016	C₂	1	2	yes	maximal, complemented
21	#20245749	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄₇×#518	C₂	1	1	yes	maximal, characteristic
24	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
27	C₂×D₄×Dic₄₇	C₂²	1	1	yes	characteristic
28	C₂×#13093983	C₂²	1	2	yes	complemented
29	C₂×#13093983	C₂²	1	2	yes	complemented
30	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
31	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
32	C₂²×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
33	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	complemented
34	#15689026	C₂²	1	1	yes	characteristic
35	#15689026	C₂²	1	1	yes	characteristic
36	#15689026	C₂²	1	1	yes	characteristic
37	#15689026	C₂²	1	1	yes	characteristic
38	#15689022	C₂²	1	1	yes	characteristic, complemented
39	#15689022	C₂²	1	1	yes	characteristic, complemented
40	#15689022	C₂²	1	1	yes	characteristic, complemented
41	#15689022	C₂²	1	1	yes	characteristic, complemented
42	#15689016	C₂²	1	2	yes	—
43	#15689016	C₂²	1	2	yes	—
44	#15689016	C₂²	1	2	yes	—
45	#15689016	C₂²	1	2	yes	—
46	#15689016	C₂²	1	1	yes	characteristic
47	#15689016	C₂²	1	2	yes	—
48	#15689016	C₂²	1	1	yes	characteristic
49	#15689016	C₂²	1	1	yes	characteristic
50	#15689016	C₂²	1	1	yes	characteristic
51	#15689016	C₂²	1	2	yes	—
52	#15689016	C₂²	1	2	yes	complemented
53	#15689016	C₂²	1	2	yes	complemented
54	#15689016	C₂²	1	2	yes	complemented
55	#15689016	C₂²	1	2	yes	complemented
56	#15689016	C₂²	1	2	yes	complemented
57	#15689016	C₂²	1	2	yes	complemented
58	#15689016	C₂²	1	2	yes	complemented
59	#15689016	C₂²	1	2	yes	complemented
60	#15689009	C₂²	1	1	yes	characteristic, complemented
61	#15689009	C₂²	1	2	yes	complemented
62	#15689009	C₂²	1	1	yes	characteristic, complemented
63	#15689009	C₂²	1	2	yes	complemented
64	#15689009	C₂²	1	1	yes	characteristic, complemented
65	#15689009	C₂²	1	1	yes	characteristic, complemented
66	#15689003	C₂²	1	2	yes	—
67	#15689003	C₂²	1	2	yes	—
68	#15689003	C₂²	1	2	yes	—
69	#15689003	C₂²	1	2	yes	—
70	#15688998	C₂²	1	2	yes	complemented
71	#15688998	C₂²	1	2	yes	complemented
72	#15688998	C₂²	1	2	yes	complemented
73	#15688998	C₂²	1	2	yes	complemented
74	#15688993	C₂²	1	1	yes	characteristic, complemented
75	#15688991	C₂²	1	2	yes	complemented
76	#15688989	C₂²	1	2	yes	complemented
77	#15688989	C₂²	1	1	yes	characteristic, complemented
78	#15688986	C₂²	1	2	yes	complemented
79	#15688986	C₂²	1	2	yes	complemented
80	#15688983	C₂²	1	1	yes	characteristic
81	#15688983	C₂²	1	1	yes	characteristic
82	#15688983	C₂²	1	2	yes	complemented
83	#15688983	C₂²	1	2	yes	complemented
84	#15688983	C₂²	1	2	yes	complemented
85	#15688983	C₂²	1	2	yes	complemented
86	#15688979	C₂²	1	2	yes	—
87	#15688979	C₂²	1	2	yes	—
88	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
89	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
90	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
91	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	complemented
93	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
94	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
95	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
96	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
97	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	complemented
98	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	complemented
99	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	complemented
100	C₂²⋊C₄×Dic₄₇	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
103	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
105	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
106	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	complemented
107	#15688969	C₂²	1	2	yes	complemented
108	#15688969	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄₇⋊#95	C₂²	1	2	yes	complemented
110	C₂×C₄₇⋊#95	C₂²	1	2	yes	complemented
111	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
112	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
113	C₄₇×#518	C₄	1	16	yes	complemented
114	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
115	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
116	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
117	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
118	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
119	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
120	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
121	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
122	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
123	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
124	C₂³×Dic₄₇	C₂³	1	2	yes	—
125	C₂³×Dic₄₇	C₂³	1	2	yes	—
126	C₂³×Dic₄₇	C₂³	1	2	yes	—
127	C₂³×Dic₄₇	C₂³	1	2	yes	—
128	D₄×Dic₄₇	—	2	4	no	—
129	D₄×Dic₄₇	—	2	4	no	—
130	D₄×Dic₄₇	—	2	4	no	—
131	D₄×Dic₄₇	—	2	4	no	—
132	#13093983	—	4	4	no	—
133	#13093983	—	4	4	no	—
134	C₂×C₄⋊Dic₄₇	—	4	4	no	—
135	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
141	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
144	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
146	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
147	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
148	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
149	C₂×C₂²⋊Dic₄₇	—	4	4	no	—
150	C₂×C₂²⋊Dic₄₇	—	4	4	no	—
151	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
160	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
161	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
163	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
164	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
165	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
166	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
167	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
168	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
169	C₂×C₄×Dic₄₇	—	4	4	no	—
170	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
171	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
172	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
173	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
174	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
175	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
176	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
177	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
178	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
179	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
180	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
181	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
182	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
183	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
184	C₄₇⋊#95	C₂³	1	1	yes	characteristic
185	C₄₇⋊#95	C₂³	1	1	yes	characteristic
186	C₄₇⋊#95	C₂³	1	2	yes	—
187	C₄₇⋊#95	C₂³	1	2	yes	—
188	C₄₇⋊#95	C₂³	1	2	yes	—
189	C₄₇⋊#95	C₂³	1	2	yes	—
190	C₄₇⋊#95	C₂³	1	2	yes	—
191	C₄₇⋊#95	C₂³	1	2	yes	—
192	C₄₇⋊#95	C₂³	1	1	yes	characteristic
193	C₄₇⋊#95	C₂³	1	1	yes	characteristic
194	C₄₇⋊#95	C₂³	1	1	yes	characteristic
195	C₄₇⋊#95	C₂³	1	1	yes	characteristic
196	C₄₇⋊#95	C₂³	1	2	yes	—
197	C₄₇⋊#95	C₂³	1	2	yes	—
198	C₄₇⋊#95	C₂³	1	1	yes	characteristic
199	C₄₇⋊#95	C₂³	1	1	yes	characteristic
200	C₄₇⋊#95	C₂³	1	1	yes	characteristic
201	C₄₇⋊#95	C₂³	1	1	yes	characteristic
202	C₄₇⋊#95	C₂³	1	2	yes	—
203	C₄₇⋊#95	C₂³	1	2	yes	—
204	C₄₇⋊#95	C₂³	1	2	yes	—
205	C₄₇⋊#95	C₂³	1	2	yes	—
206	C₄₇⋊#95	C₂³	1	2	yes	—
207	C₄₇⋊#95	C₂³	1	2	yes	—
208	C₄₇⋊#95	C₂³	1	1	yes	characteristic
209	C₄₇⋊#95	C₂³	1	1	yes	characteristic
210	C₂⁵×C₄₇	C₂³	1	2	yes	—
211	C₂²×D₄×C₄₇	—	2	4	no	—
212	C₂²×D₄×C₄₇	—	2	4	no	—
213	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
214	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
215	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
216	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
217	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
218	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
219	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
220	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
221	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
222	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
223	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
224	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
225	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
226	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
227	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
228	#117×C₄₇	C₂×C₄	1	8	yes	complemented
229	#117×C₄₇	C₂×C₄	1	8	yes	complemented
230	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
235	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
236	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
238	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
239	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
242	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
243	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
244	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
245	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
246	C₂⁴×C₄₇	—	2	4	no	—
247	C₂⁴×C₄₇	—	2	4	no	—
248	C₂⁴×C₄₇	—	4	2	no	—
249	C₂⁴×C₄₇	—	4	2	no	—
250	C₂⁴×C₄₇	—	4	2	no	—
251	C₂⁴×C₄₇	—	4	2	no	—
252	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
253	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
254	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
255	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
256	C₂×D₄×C₄₇	—	2	4	no	—
257	C₂×D₄×C₄₇	—	2	4	no	—
258	C₂×D₄×C₄₇	—	2	32	no	—
259	C₂×D₄×C₄₇	—	2	2	no	—
260	C₂×D₄×C₄₇	—	2	2	no	—
261	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
262	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
263	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
264	C₂×D₄×C₄₇	#41	1	4	yes	—
265	C₂×D₄×C₄₇	#41	1	4	yes	—
266	C₂²×C₄×C₄₇	—	2	2	no	—
267	C₂²×C₄×C₄₇	—	2	2	no	—
268	C₂²×C₄×C₄₇	—	4	2	no	—
269	C₂²×C₄×C₄₇	—	4	2	no	—
270	C₂²×C₄×C₄₇	—	4	2	no	—
271	C₂²×C₄×C₄₇	—	4	2	no	—
272	C₂²×C₄×C₄₇	—	4	2	no	—
273	C₂²×C₄×C₄₇	—	4	2	no	—
274	C₂²×C₄×C₄₇	—	4	2	no	—
275	C₂²×C₄×C₄₇	—	4	2	no	—
276	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
277	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
278	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
279	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
280	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
281	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
289	C₂²×Dic₄₇	—	2	4	no	—
290	C₂²×Dic₄₇	—	2	4	no	—
291	C₂²×Dic₄₇	—	2	4	no	—
292	C₂²×Dic₄₇	—	2	4	no	—
293	C₂²×Dic₄₇	—	2	4	no	—
294	C₂²×Dic₄₇	—	2	4	no	—
295	C₂²×Dic₄₇	—	4	2	no	—
296	C₂²×Dic₄₇	—	4	2	no	—
297	C₂²×Dic₄₇	—	4	2	no	—
298	C₂²×Dic₄₇	—	4	2	no	—
299	C₂²×Dic₄₇	—	4	2	no	—
300	C₂²×Dic₄₇	—	4	2	no	—
301	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
302	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
303	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
304	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
305	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
306	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
307	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
308	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
309	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
310	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
311	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
312	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
313	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
314	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
315	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
316	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
317	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
318	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
319	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
320	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
321	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
322	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
323	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
324	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
325	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
326	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
327	C₂²⋊Dic₄₇	—	2	4	no	—
328	C₂²⋊Dic₄₇	—	2	4	no	—
329	C₂²⋊Dic₄₇	—	2	4	no	—
330	C₂²⋊Dic₄₇	—	2	4	no	—
331	C₂²⋊Dic₄₇	—	2	2	no	—
332	C₂²⋊Dic₄₇	—	2	2	no	—
333	C₂²⋊Dic₄₇	—	2	4	no	—
334	C₂²⋊Dic₄₇	—	2	4	no	—
335	C₂²⋊Dic₄₇	—	4	2	no	—
336	C₂²⋊Dic₄₇	—	4	2	no	—
337	C₂²⋊Dic₄₇	—	4	2	no	—
338	C₂²⋊Dic₄₇	—	4	2	no	—
339	C₂²⋊Dic₄₇	—	4	1	no	—
340	C₂²⋊Dic₄₇	—	4	1	no	—
341	C₂²⋊Dic₄₇	—	4	2	no	—
342	C₂²⋊Dic₄₇	—	4	2	no	—
343	C₂²⋊Dic₄₇	—	4	2	no	—
344	C₂²⋊Dic₄₇	—	4	2	no	—
345	C₄⋊Dic₄₇	—	2	2	no	—
346	C₄⋊Dic₄₇	—	2	2	no	—
347	C₄⋊Dic₄₇	—	2	2	no	—
348	C₄⋊Dic₄₇	—	2	2	no	—
349	C₄⋊Dic₄₇	—	2	2	no	—
350	C₄⋊Dic₄₇	—	2	4	no	—
351	C₄⋊Dic₄₇	—	2	2	no	—
352	C₄⋊Dic₄₇	—	4	2	no	—
353	C₄⋊Dic₄₇	—	4	2	no	—
354	C₄⋊Dic₄₇	—	4	1	no	—
355	C₄⋊Dic₄₇	—	4	1	no	—
356	C₄⋊Dic₄₇	—	4	2	no	—
357	C₄⋊Dic₄₇	—	4	2	no	—
358	C₄⋊Dic₄₇	—	4	2	no	—
359	C₄×Dic₄₇	—	2	2	no	—
360	C₄×Dic₄₇	—	2	2	no	—
361	C₄×Dic₄₇	—	2	2	no	—
362	C₄×Dic₄₇	—	2	2	no	—
363	C₄×Dic₄₇	—	2	2	no	—
364	C₄×Dic₄₇	—	2	4	no	—
365	C₄×Dic₄₇	—	2	2	no	—
366	C₄×Dic₄₇	—	4	2	no	—
367	C₄×Dic₄₇	—	4	2	no	—
368	C₄×Dic₄₇	—	4	1	no	—
369	C₄×Dic₄₇	—	4	2	no	—
370	C₄×Dic₄₇	—	4	1	no	—
371	C₄×Dic₄₇	—	4	2	no	—
372	C₄×Dic₄₇	—	4	2	no	—
373	C₂³×C₄₇	—	2	2	no	—
374	C₂³×C₄₇	—	2	2	no	—
375	C₂³×C₄₇	—	2	2	no	—
376	C₂³×C₄₇	—	2	2	no	—
377	C₂³×C₄₇	—	2	1	no	—
378	C₂³×C₄₇	—	2	1	no	—
379	C₂³×C₄₇	—	2	2	no	—
380	C₂³×C₄₇	—	2	2	no	—
381	C₂³×C₄₇	—	2	2	no	—
382	C₂³×C₄₇	—	2	2	no	—
383	C₂³×C₄₇	—	2	1	no	—
384	C₂³×C₄₇	—	2	1	no	—
385	C₂³×C₄₇	—	2	2	no	—
386	C₂³×C₄₇	—	2	2	no	—
387	C₂³×C₄₇	—	2	1	no	—
388	C₂³×C₄₇	—	2	1	no	—
389	C₂³×C₄₇	—	2	16	no	—
390	C₂³×C₄₇	—	4	8	no	—
391	C₂³×C₄₇	—	4	8	no	—
392	C₂³×C₄₇	—	8	4	no	—
393	C₂³×C₄₇	—	8	4	no	—
394	C₂³×C₄₇	—	8	4	no	—
395	C₂³×C₄₇	—	8	4	no	—
396	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
397	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
398	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
399	C₂³×C₄₇	C₂×#41	1	4	yes	—
400	C₂³×C₄₇	C₂×#41	1	4	yes	—
401	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
402	D₄×C₄₇	—	2	16	no	—
403	D₄×C₄₇	—	2	8	no	—
404	D₄×C₄₇	#117	1	16	yes	complemented
405	C₂×C₄×C₄₇	—	2	1	no	—
406	C₂×C₄×C₄₇	—	2	1	no	—
407	C₂×C₄×C₄₇	—	2	1	no	—
408	C₂×C₄×C₄₇	—	2	2	no	—
409	C₂×C₄×C₄₇	—	2	1	no	—
410	C₂×C₄×C₄₇	—	2	1	no	—
411	C₂×C₄×C₄₇	—	2	1	no	—
412	C₂×C₄×C₄₇	—	2	2	no	—
413	C₂×C₄×C₄₇	—	2	1	no	—
414	C₂×C₄×C₄₇	—	2	2	no	—
415	C₂×C₄×C₄₇	—	2	1	no	—
416	C₂×C₄×C₄₇	—	2	1	no	—
417	C₂×C₄×C₄₇	—	2	2	no	—
418	C₂×C₄×C₄₇	—	2	1	no	—
419	C₂×C₄×C₄₇	—	2	8	no	—
420	C₂×C₄×C₄₇	—	4	8	no	—
421	C₂×C₄×C₄₇	—	4	8	no	—
422	C₂×C₄×C₄₇	—	4	8	no	—
423	C₂×C₄×C₄₇	—	4	8	no	—
424	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
425	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
426	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
427	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
428	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
429	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
430	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
431	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
432	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
433	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
434	C₂×Dic₄₇	—	2	1	no	—
435	C₂×Dic₄₇	—	2	1	no	—
436	C₂×Dic₄₇	—	2	1	no	—
437	C₂×Dic₄₇	—	2	1	no	—
438	C₂×Dic₄₇	—	2	1	no	—
439	C₂×Dic₄₇	—	2	1	no	—
440	C₂×Dic₄₇	—	2	1	no	—
441	C₂×Dic₄₇	—	2	1	no	—
442	C₂×Dic₄₇	—	2	1	no	—
443	C₂×Dic₄₇	—	2	1	no	—
444	C₂×Dic₄₇	—	2	2	no	—
445	C₂×Dic₄₇	—	2	2	no	—
446	C₂×Dic₄₇	—	2	2	no	—
447	C₂×Dic₄₇	—	2	2	no	—
448	C₂×Dic₄₇	—	2	2	no	—
449	C₂×Dic₄₇	—	2	1	no	—
450	C₂×Dic₄₇	—	2	1	no	—
451	C₂×Dic₄₇	—	2	2	no	—
452	C₂×Dic₄₇	—	2	2	no	—
453	C₂×Dic₄₇	—	2	2	no	—
454	C₂×Dic₄₇	—	2	2	no	—
455	C₂×Dic₄₇	—	2	1	no	—
456	C₂×Dic₄₇	—	2	2	no	—
457	C₂×Dic₄₇	—	2	1	no	—
458	C₂×Dic₄₇	—	2	1	no	—
459	C₂×Dic₄₇	—	2	1	no	—
460	C₂×Dic₄₇	—	2	1	no	—
461	C₂×Dic₄₇	—	2	1	no	—
462	C₂×Dic₄₇	—	2	1	no	—
463	C₂×Dic₄₇	—	2	2	no	—
464	C₂×Dic₄₇	—	2	1	no	—
465	C₂×Dic₄₇	—	2	1	no	—
466	C₂×Dic₄₇	—	2	2	no	—
467	C₂×Dic₄₇	—	2	1	no	—
468	C₂×Dic₄₇	—	4	8	no	—
469	C₂×Dic₄₇	—	4	8	no	—
470	C₂×Dic₄₇	—	8	4	no	—
471	C₂×Dic₄₇	—	8	4	no	—
472	C₂×Dic₄₇	H(5,𝔽₂)	1	2	yes	—
473	C₂×Dic₄₇	H(5,𝔽₂)	1	2	yes	—
474	#34261	—	47	1	no	maximal, Sylow
475	C₂²×C₄₇	—	2	4	no	—
476	C₂²×C₄₇	—	2	4	no	—
477	C₂²×C₄₇	—	2	4	no	—
478	C₂²×C₄₇	—	2	4	no	—
479	C₂²×C₄₇	—	2	4	no	—
480	C₂²×C₄₇	—	2	4	no	—
481	C₂²×C₄₇	—	2	2	no	—
482	C₂²×C₄₇	—	2	4	no	—
483	C₂²×C₄₇	—	2	4	no	—
484	C₂²×C₄₇	—	2	4	no	—
485	C₂²×C₄₇	—	2	2	no	—
486	C₂²×C₄₇	—	2	2	no	—
487	C₂²×C₄₇	—	4	2	no	—
488	C₂²×C₄₇	—	4	1	no	—
489	C₂²×C₄₇	—	4	2	no	—
490	C₂²×C₄₇	—	4	1	no	—
491	C₂²×C₄₇	—	4	2	no	—
492	C₂²×C₄₇	—	4	1	no	—
493	C₂²×C₄₇	—	4	2	no	—
494	C₂²×C₄₇	—	4	1	no	—
495	C₂²×C₄₇	—	8	16	no	—
496	C₂²×C₄₇	C₂×#117	1	8	yes	—
497	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
498	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
499	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
500	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
502	C₂²×C₄₇	#585	1	1	yes	characteristic
503	C₂²×C₄₇	#585	1	1	yes	characteristic
504	C₄×C₄₇	—	2	2	no	—
505	C₄×C₄₇	—	2	2	no	—
506	C₄×C₄₇	—	2	4	no	—
507	C₄×C₄₇	—	2	2	no	—
508	C₄×C₄₇	—	2	2	no	—
509	C₄×C₄₇	—	2	2	no	—
510	C₄×C₄₇	—	2	4	no	—
511	C₄×C₄₇	C₂×#117	1	4	yes	—
512	Dic₄₇	—	2	2	no	—
513	Dic₄₇	—	2	2	no	—
514	Dic₄₇	—	4	1	no	—
515	Dic₄₇	—	4	2	no	—
516	Dic₄₇	—	4	1	no	—
517	Dic₄₇	—	4	2	no	—
518	Dic₄₇	—	4	1	no	—
519	Dic₄₇	—	4	2	no	—
520	Dic₄₇	—	4	2	no	—
521	Dic₄₇	—	4	1	no	—
522	Dic₄₇	—	4	1	no	—
523	Dic₄₇	—	4	1	no	—
524	C₂×#518	D₄₇	1	1	yes	characteristic
525	#2357	—	47	1	no	—
526	#2354	—	47	1	no	—
527	#2353	—	47	2	no	—
528	#2352	—	47	2	no	—
529	#2349	—	47	1	no	—
530	D₄×C₄⋊C₄	—	47	1	no	—
531	#2347	—	47	1	no	—
532	#2346	—	47	1	no	—
533	#2342	—	47	2	no	—
534	#2342	—	47	2	no	—
535	D₄×C₂²⋊C₄	—	47	1	no	—
536	D₄×C₂²⋊C₄	—	47	1	no	—
537	#2319	—	47	1	no	—
538	#2318	—	47	2	no	—
539	#2314	—	47	1	no	—
540	#2312	—	47	2	no	—
541	#2298	—	47	1	no	—
542	#2293	—	47	1	no	—
543	#2290	—	47	2	no	—
544	C₂×#388	—	47	2	no	—
545	#2275	—	47	1	no	—
546	C₄²×D₄	—	47	1	no	—
547	C₂×C₄₇	—	2	8	no	—
548	C₂×C₄₇	—	4	4	no	—
549	C₂×C₄₇	—	4	2	no	—
550	C₂×C₄₇	C₂²×#117	1	1	yes	characteristic
551	C₂×C₄₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
552	C₂×C₄₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
553	C₂×C₄₇	#3513	1	1	yes	characteristic
554	C₂×C₄₇	#3514	1	1	yes	characteristic
555	C₂×C₄₇	#3519	1	1	yes	characteristic
556	C₂×C₄₇	#3521	1	1	yes	characteristic
557	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
558	#518	Dic₄₇	1	16	yes	complemented
559	C₂×C₄×D₄	—	47	1	no	—
560	C₂×C₄×D₄	—	47	1	no	—
561	C₂×C₄×D₄	—	47	1	no	—
562	C₂×C₄×D₄	—	47	1	no	—
563	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
564	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
565	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
566	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
567	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
568	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
569	C₂×#117	—	47	2	no	—
570	C₂×#117	—	47	2	no	—
571	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
572	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
573	C₂²×C₄⋊C₄	—	47	2	no	—
574	C₂²×C₂²⋊C₄	—	47	2	no	—
575	C₂²×C₂²⋊C₄	—	47	2	no	—
576	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
577	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
578	C₂²×C₄²	—	47	2	no	—
579	#390	—	47	1	no	—
580	#390	—	47	1	no	—
581	#390	—	47	1	no	—
582	#390	—	47	1	no	—
583	#389	—	47	1	no	—
584	#389	—	47	1	no	—
585	#389	—	47	1	no	—
586	#389	—	47	1	no	—
587	#388	—	47	1	no	—
588	#388	—	47	2	no	—
589	#388	—	47	2	no	—
590	#388	—	47	2	no	—
591	#388	—	47	2	no	—
592	#388	—	47	2	no	—
593	#388	—	47	2	no	—
594	#388	—	47	2	no	—
595	#388	—	47	2	no	—
596	#388	—	47	2	no	—
597	#388	—	47	1	no	—
598	#388	—	47	1	no	—
599	#388	—	47	2	no	—
600	#388	—	47	2	no	—
601	#388	—	47	2	no	—
602	#388	—	47	2	no	—
603	#388	—	47	1	no	—
604	#388	—	47	2	no	—
605	#387	—	47	2	no	—
606	#387	—	47	2	no	—
607	#387	—	47	1	no	—
608	#387	—	47	1	no	—
609	#387	—	47	1	no	—
610	#387	—	47	1	no	—
611	#386	—	47	2	no	—
612	#386	—	47	2	no	—
613	#386	—	47	2	no	—
614	#386	—	47	2	no	—
615	#385	—	47	2	no	—
616	#385	—	47	2	no	—
617	#385	—	47	2	no	—
618	#385	—	47	2	no	—
619	#384	—	47	1	no	—
620	#383	—	47	2	no	—
621	#382	—	47	1	no	—
622	#382	—	47	2	no	—
623	#381	—	47	2	no	—
624	#381	—	47	2	no	—
625	#380	—	47	2	no	—
626	#380	—	47	2	no	—
627	#380	—	47	1	no	—
628	#380	—	47	1	no	—
629	#380	—	47	2	no	—
630	#380	—	47	2	no	—
631	#379	—	47	2	no	—
632	#379	—	47	2	no	—
633	C₄×C₄⋊C₄	—	47	1	no	—
634	C₄×C₄⋊C₄	—	47	1	no	—
635	C₄×C₄⋊C₄	—	47	1	no	—
636	C₄×C₄⋊C₄	—	47	1	no	—
637	C₄×C₄⋊C₄	—	47	1	no	—
638	C₄×C₄⋊C₄	—	47	1	no	—
639	C₄×C₄⋊C₄	—	47	2	no	—
640	C₄×C₄⋊C₄	—	47	1	no	—
641	C₄×C₄⋊C₄	—	47	1	no	—
642	C₄×C₂²⋊C₄	—	47	2	no	—
643	C₄×C₂²⋊C₄	—	47	2	no	—
644	C₄×C₂²⋊C₄	—	47	1	no	—
645	C₄×C₂²⋊C₄	—	47	1	no	—
646	C₄×C₂²⋊C₄	—	47	2	no	—
647	C₄×C₂²⋊C₄	—	47	2	no	—
648	C₄×C₂²⋊C₄	—	47	2	no	—
649	C₄×C₂²⋊C₄	—	47	2	no	—
650	C₄×C₂²⋊C₄	—	47	2	no	—
651	C₄×C₂²⋊C₄	—	47	2	no	—
652	#376	—	47	1	no	—
653	#376	—	47	2	no	—
654	C₂×#95	—	47	2	no	—
655	C₂×#95	—	47	2	no	—
656	C₄³	—	47	1	no	—
657	C₄₇	#34261	1	1	yes	characteristic, complemented, Sylow
658	C₂⁵	C₂²×D₄₇	1	2	yes	—
659	C₂²×D₄	—	2	4	no	—
660	C₂²×D₄	—	2	4	no	—
661	C₂²×D₄	C₂×Dic₄₇	1	8	yes	—
662	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
663	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
664	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
665	C₂³×C₄	—	47	2	no	—
666	C₂³×C₄	—	47	2	no	—
667	C₂³×C₄	—	47	2	no	—
668	C₂³×C₄	—	47	2	no	—
669	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
670	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
671	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
672	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
673	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
674	C₄×D₄	—	94	4	no	—
675	C₄×D₄	—	94	4	no	—
676	C₄×D₄	—	94	4	no	—
677	C₄×D₄	—	94	4	no	—
678	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
679	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
680	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
681	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
682	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
683	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
684	#117	—	188	4	no	—
685	#117	—	188	4	no	—
686	#117	C₂×Dic₄₇	1	8	yes	complemented
687	#117	C₂×Dic₄₇	1	8	yes	complemented
688	C₂×C₄⋊C₄	—	47	1	no	—
689	C₂×C₄⋊C₄	—	47	2	no	—
690	C₂×C₄⋊C₄	—	47	1	no	—
691	C₂×C₄⋊C₄	—	47	1	no	—
692	C₂×C₄⋊C₄	—	47	1	no	—
693	C₂×C₄⋊C₄	—	47	1	no	—
694	C₂×C₄⋊C₄	—	47	1	no	—
695	C₂×C₄⋊C₄	—	47	2	no	—
696	C₂×C₄⋊C₄	—	47	2	no	—
697	C₂×C₄⋊C₄	—	47	2	no	—
698	C₂×C₄⋊C₄	—	47	2	no	—
699	C₂×C₄⋊C₄	—	47	1	no	—
700	C₂×C₄⋊C₄	—	47	2	no	—
701	C₂×C₄⋊C₄	—	47	1	no	—
702	C₂×C₄⋊C₄	—	188	4	no	—
703	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
704	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
707	C₂×C₂²⋊C₄	—	47	1	no	—
708	C₂×C₂²⋊C₄	—	47	1	no	—
709	C₂×C₂²⋊C₄	—	47	2	no	—
710	C₂×C₂²⋊C₄	—	47	2	no	—
711	C₂×C₂²⋊C₄	—	47	2	no	—
712	C₂×C₂²⋊C₄	—	47	2	no	—
713	C₂×C₂²⋊C₄	—	47	2	no	—
714	C₂×C₂²⋊C₄	—	47	2	no	—
715	C₂×C₂²⋊C₄	—	47	2	no	—
716	C₂×C₂²⋊C₄	—	47	2	no	—
717	C₂×C₂²⋊C₄	—	47	2	no	—
718	C₂×C₂²⋊C₄	—	47	2	no	—
719	C₂×C₂²⋊C₄	—	47	2	no	—
720	C₂×C₂²⋊C₄	—	47	2	no	—
721	C₂×C₂²⋊C₄	—	47	1	no	—
722	C₂×C₂²⋊C₄	—	47	1	no	—
723	C₂×C₂²⋊C₄	—	47	2	no	—
724	C₂×C₂²⋊C₄	—	47	2	no	—
725	C₂×C₂²⋊C₄	—	188	4	no	—
726	C₂×C₂²⋊C₄	—	188	4	no	—
727	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
728	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	16	yes	complemented
729	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
730	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
732	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
736	C₂×C₄²	—	47	1	no	—
737	C₂×C₄²	—	47	2	no	—
738	C₂×C₄²	—	47	1	no	—
739	C₂×C₄²	—	47	1	no	—
740	C₂×C₄²	—	47	1	no	—
741	C₂×C₄²	—	47	1	no	—
742	C₂×C₄²	—	47	1	no	—
743	C₂×C₄²	—	47	2	no	—
744	C₂×C₄²	—	47	2	no	—
745	C₂×C₄²	—	47	1	no	—
746	C₂×C₄²	—	47	1	no	—
747	C₂×C₄²	—	47	2	no	—
748	C₂×C₄²	—	47	2	no	—
749	C₂×C₄²	—	47	2	no	—
750	C₂×C₄²	—	188	4	no	—
751	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
752	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
753	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
754	#95	—	47	1	no	—
755	#95	—	47	1	no	—
756	#95	—	47	2	no	—
757	#95	—	47	2	no	—
758	#95	—	47	2	no	—
759	#95	—	47	2	no	—
760	#95	—	47	2	no	—
761	#95	—	47	2	no	—
762	#95	—	47	1	no	—
763	#95	—	47	1	no	—
764	#95	—	47	1	no	—
765	#95	—	47	1	no	—
766	#95	—	47	2	no	—
767	#95	—	47	2	no	—
768	#95	—	47	2	no	—
769	#95	—	47	2	no	—
770	#95	—	47	2	no	—
771	#95	—	47	1	no	—
772	#95	—	47	1	no	—
773	#95	—	47	2	no	—
774	#95	—	47	2	no	—
775	#95	—	47	1	no	—
776	#95	—	47	1	no	—
777	#95	—	47	1	no	—
778	#95	—	47	2	no	—
779	#95	—	47	1	no	—
780	C₂⁴	—	2	4	no	—
781	C₂⁴	—	2	4	no	—
782	C₂⁴	—	4	2	no	—
783	C₂⁴	—	4	2	no	—
784	C₂⁴	—	4	2	no	—
785	C₂⁴	—	4	2	no	—
786	C₂⁴	C₂²×Dic₄₇	1	8	yes	—
787	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
788	C₂⁴	C₂³×D₄₇	1	2	yes	—
789	C₂⁴	C₂³×D₄₇	1	2	yes	—
790	C₂×D₄	—	2	4	no	—
791	C₂×D₄	—	2	4	no	—
792	C₂×D₄	—	2	32	no	—
793	C₂×D₄	—	2	2	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	#10625350	1	4	yes	—
796	C₂×D₄	#10625350	1	4	yes	—
797	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
798	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
799	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	4	2	no	—
803	C₂²×C₄	—	4	2	no	—
804	C₂²×C₄	—	4	2	no	—
805	C₂²×C₄	—	4	2	no	—
806	C₂²×C₄	—	4	2	no	—
807	C₂²×C₄	—	4	2	no	—
808	C₂²×C₄	—	4	2	no	—
809	C₂²×C₄	—	4	2	no	—
810	C₂²×C₄	—	47	1	no	—
811	C₂²×C₄	—	47	1	no	—
812	C₂²×C₄	—	47	1	no	—
813	C₂²×C₄	—	47	1	no	—
814	C₂²×C₄	—	47	1	no	—
815	C₂²×C₄	—	47	2	no	—
816	C₂²×C₄	—	47	2	no	—
817	C₂²×C₄	—	47	1	no	—
818	C₂²×C₄	—	47	1	no	—
819	C₂²×C₄	—	47	1	no	—
820	C₂²×C₄	—	47	2	no	—
821	C₂²×C₄	—	47	2	no	—
822	C₂²×C₄	—	94	4	no	—
823	C₂²×C₄	—	94	4	no	—
824	C₂²×C₄	—	94	4	no	—
825	C₂²×C₄	—	94	4	no	—
826	C₂²×C₄	—	94	4	no	—
827	C₂²×C₄	—	94	4	no	—
828	C₂²×C₄	—	188	2	no	—
829	C₂²×C₄	—	188	2	no	—
830	C₂²×C₄	—	188	2	no	—
831	C₂²×C₄	—	188	2	no	—
832	C₂²×C₄	—	188	2	no	—
833	C₂²×C₄	—	188	2	no	—
834	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
835	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
836	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
837	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
838	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
839	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
840	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
841	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
842	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
843	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
844	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
845	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
846	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
847	C₄⋊C₄	—	94	2	no	—
848	C₄⋊C₄	—	94	4	no	—
849	C₄⋊C₄	—	94	2	no	—
850	C₄⋊C₄	—	94	2	no	—
851	C₄⋊C₄	—	94	2	no	—
852	C₄⋊C₄	—	94	2	no	—
853	C₄⋊C₄	—	94	2	no	—
854	C₄⋊C₄	—	188	1	no	—
855	C₄⋊C₄	—	188	1	no	—
856	C₄⋊C₄	—	188	2	no	—
857	C₄⋊C₄	—	188	2	no	—
858	C₄⋊C₄	—	188	2	no	—
859	C₄⋊C₄	—	188	2	no	—
860	C₄⋊C₄	—	188	2	no	—
861	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
862	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
863	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
864	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
865	C₂²⋊C₄	—	94	2	no	—
866	C₂²⋊C₄	—	94	2	no	—
867	C₂²⋊C₄	—	94	4	no	—
868	C₂²⋊C₄	—	94	4	no	—
869	C₂²⋊C₄	—	94	4	no	—
870	C₂²⋊C₄	—	94	4	no	—
871	C₂²⋊C₄	—	94	4	no	—
872	C₂²⋊C₄	—	94	4	no	—
873	C₂²⋊C₄	—	188	1	no	—
874	C₂²⋊C₄	—	188	2	no	—
875	C₂²⋊C₄	—	188	1	no	—
876	C₂²⋊C₄	—	188	2	no	—
877	C₂²⋊C₄	—	188	2	no	—
878	C₂²⋊C₄	—	188	2	no	—
879	C₂²⋊C₄	—	188	2	no	—
880	C₂²⋊C₄	—	188	2	no	—
881	C₂²⋊C₄	—	188	2	no	—
882	C₂²⋊C₄	—	188	2	no	—
883	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
884	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
885	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
886	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
887	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
888	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
889	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
890	C₄²	—	94	2	no	—
891	C₄²	—	94	4	no	—
892	C₄²	—	94	2	no	—
893	C₄²	—	94	2	no	—
894	C₄²	—	94	2	no	—
895	C₄²	—	94	2	no	—
896	C₄²	—	94	2	no	—
897	C₄²	—	188	1	no	—
898	C₄²	—	188	2	no	—
899	C₄²	—	188	1	no	—
900	C₄²	—	188	2	no	—
901	C₄²	—	188	2	no	—
902	C₄²	—	188	2	no	—
903	C₄²	—	188	2	no	—
904	C₄²	C₂²×Dic₄₇	1	4	yes	—
905	C₄²	C₂²×Dic₄₇	1	4	yes	—
906	C₄²	C₂²×Dic₄₇	1	8	yes	—
907	C₂³	—	2	2	no	—
908	C₂³	—	2	2	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	2	no	—
916	C₂³	—	2	2	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	16	no	—
924	C₂³	—	4	8	no	—
925	C₂³	—	4	8	no	—
926	C₂³	—	8	4	no	—
927	C₂³	—	8	4	no	—
928	C₂³	—	8	4	no	—
929	C₂³	—	8	4	no	—
930	C₂³	C₂³×Dic₄₇	1	2	yes	—
931	C₂³	C₂³×Dic₄₇	1	4	yes	—
932	C₂³	C₂³×Dic₄₇	1	4	yes	—
933	C₂³	C₂×#10625350	1	4	yes	—
934	C₂³	C₂×#10625350	1	4	yes	—
935	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
936	D₄	—	2	16	no	—
937	D₄	—	2	8	no	—
938	D₄	#13093983	1	16	yes	complemented
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	8	no	—
954	C₂×C₄	—	4	8	no	—
955	C₂×C₄	—	4	8	no	—
956	C₂×C₄	—	4	8	no	—
957	C₂×C₄	—	4	8	no	—
958	C₂×C₄	—	47	2	no	—
959	C₂×C₄	—	47	2	no	—
960	C₂×C₄	—	94	1	no	—
961	C₂×C₄	—	94	1	no	—
962	C₂×C₄	—	94	1	no	—
963	C₂×C₄	—	94	1	no	—
964	C₂×C₄	—	94	1	no	—
965	C₂×C₄	—	94	1	no	—
966	C₂×C₄	—	94	1	no	—
967	C₂×C₄	—	94	1	no	—
968	C₂×C₄	—	94	1	no	—
969	C₂×C₄	—	94	1	no	—
970	C₂×C₄	—	94	2	no	—
971	C₂×C₄	—	94	2	no	—
972	C₂×C₄	—	94	2	no	—
973	C₂×C₄	—	94	2	no	—
974	C₂×C₄	—	94	2	no	—
975	C₂×C₄	—	94	1	no	—
976	C₂×C₄	—	94	1	no	—
977	C₂×C₄	—	94	2	no	—
978	C₂×C₄	—	94	2	no	—
979	C₂×C₄	—	94	2	no	—
980	C₂×C₄	—	94	2	no	—
981	C₂×C₄	—	94	1	no	—
982	C₂×C₄	—	94	1	no	—
983	C₂×C₄	—	94	2	no	—
984	C₂×C₄	—	94	1	no	—
985	C₂×C₄	—	94	1	no	—
986	C₂×C₄	—	94	1	no	—
987	C₂×C₄	—	94	1	no	—
988	C₂×C₄	—	94	1	no	—
989	C₂×C₄	—	94	2	no	—
990	C₂×C₄	—	94	1	no	—
991	C₂×C₄	—	94	1	no	—
992	C₂×C₄	—	94	2	no	—
993	C₂×C₄	—	94	1	no	—
994	C₂×C₄	—	376	4	no	—
995	C₂×C₄	—	376	4	no	—
996	C₂×C₄	—	188	8	no	—
997	C₂×C₄	—	188	8	no	—
998	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
999	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
1000	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
1001	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
1002	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
1003	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
1004	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
1005	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
1006	C₂×C₄	C₂×#10625350	1	2	yes	—
1007	C₂×C₄	C₂×#10625350	1	2	yes	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	2	4	no	—
1012	C₂²	—	2	4	no	—
1013	C₂²	—	2	4	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	4	no	—
1016	C₂²	—	2	4	no	—
1017	C₂²	—	2	4	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	4	1	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	1	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	1	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	2	no	—
1028	C₂²	—	8	16	no	—
1029	C₂²	C₂×#13093983	1	8	yes	—
1030	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
1031	C₂²	C₂²×#10625350	1	1	yes	characteristic
1032	C₂²	C₂²×#10625350	1	1	yes	characteristic
1033	C₂²	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
1034	C₂²	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
1035	C₂²	#15689958	1	1	yes	characteristic
1036	C₂²	#15689958	1	1	yes	characteristic
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	4	no	—
1044	C₄	—	94	2	no	—
1045	C₄	—	94	2	no	—
1046	C₄	—	188	2	no	—
1047	C₄	—	188	1	no	—
1048	C₄	—	188	1	no	—
1049	C₄	—	188	2	no	—
1050	C₄	—	188	1	no	—
1051	C₄	—	188	1	no	—
1052	C₄	—	188	2	no	—
1053	C₄	—	188	2	no	—
1054	C₄	—	188	1	no	—
1055	C₄	—	188	1	no	—
1056	C₄	C₂×#13093983	1	4	yes	—
1057	C₂	—	2	8	no	—
1058	C₂	—	4	2	no	—
1059	C₂	—	4	4	no	—
1060	C₂	C₂²×#13093983	1	1	yes	characteristic
1061	C₂	H(5,𝔽₂)×Dic₄₇	1	1	yes	characteristic
1062	C₂	H(5,𝔽₂)×Dic₄₇	1	1	yes	characteristic
1063	C₂	#20257316	1	1	yes	characteristic
1064	C₂	#20257339	1	1	yes	characteristic
1065	C₂	#20257410	1	1	yes	characteristic
1066	C₂	#20257444	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂×C₄₇×#518	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂³×D₄×C₄₇	C₂²
hypercenter	C₂×#518	D₄₇
hypocenter	C₄₇	#34261
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
1. #20246361	C₂	semidirect
2. #20246337	C₂	semidirect
3. #20246328	C₂	semidirect
4. #20246317	C₂	semidirect
5. #20246298	C₂	semidirect
6. D₄×C₄⋊Dic₄₇	C₂	semidirect
7. #20246281	C₂	semidirect
8. #20246273	C₂	semidirect
9. #20246237	C₂	semidirect
10. #20246237	C₂	semidirect
13. #20246031	C₂	semidirect
14. #20246021	C₂	semidirect
15. #20245997	C₂	semidirect
16. #20245986	C₂	semidirect
17. #20245886	C₂	semidirect
18. #20245853	C₂	semidirect
19. #20245833	C₂	semidirect
20. C₂×#15689016	C₂	semidirect
21. #20245749	C₂	semidirect
22. C₄×D₄×Dic₄₇	C₂	semidirect
28. C₂×#13093983	C₂²	semidirect
29. C₂×#13093983	C₂²	semidirect
30. C₂²×C₄⋊Dic₄₇	C₂²	semidirect
33. C₂²×C₄×Dic₄₇	C₂²	semidirect
38. #15689022	C₂²	semidirect
39. #15689022	C₂²	semidirect
40. #15689022	C₂²	semidirect
41. #15689022	C₂²	semidirect
52. #15689016	C₂²	semidirect
53. #15689016	C₂²	semidirect
54. #15689016	C₂²	semidirect
55. #15689016	C₂²	semidirect
56. #15689016	C₂²	semidirect
57. #15689016	C₂²	semidirect
58. #15689016	C₂²	semidirect
59. #15689016	C₂²	semidirect
60. #15689009	C₂²	semidirect
61. #15689009	C₂²	semidirect
62. #15689009	C₂²	semidirect
63. #15689009	C₂²	semidirect
64. #15689009	C₂²	semidirect
65. #15689009	C₂²	semidirect
70. #15688998	C₂²	semidirect
71. #15688998	C₂²	semidirect
72. #15688998	C₂²	semidirect
73. #15688998	C₂²	semidirect
74. #15688993	C₂²	semidirect
75. #15688991	C₂²	semidirect
76. #15688989	C₂²	semidirect
77. #15688989	C₂²	semidirect
78. #15688986	C₂²	semidirect
79. #15688986	C₂²	semidirect
82. #15688983	C₂²	semidirect
83. #15688983	C₂²	semidirect
84. #15688983	C₂²	semidirect
85. #15688983	C₂²	semidirect
88. C₄⋊C₄×Dic₄₇	C₂²	semidirect
89. C₄⋊C₄×Dic₄₇	C₂²	semidirect
90. C₄⋊C₄×Dic₄₇	C₂²	semidirect
91. C₄⋊C₄×Dic₄₇	C₂²	semidirect
92. C₄×C₄⋊Dic₄₇	C₂²	semidirect
93. C₄×C₄⋊Dic₄₇	C₂²	semidirect
94. C₄×C₄⋊Dic₄₇	C₂²	semidirect
95. C₄×C₄⋊Dic₄₇	C₂²	semidirect
96. C₄×C₄⋊Dic₄₇	C₂²	semidirect
97. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
98. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
99. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
100. C₂²⋊C₄×Dic₄₇	C₂²	semidirect
103. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
104. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
105. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
106. C₄×C₂²⋊Dic₄₇	C₂²	semidirect
107. #15688969	C₂²	semidirect
108. #15688969	C₂²	semidirect
109. C₂×C₄₇⋊#95	C₂²	semidirect
110. C₂×C₄₇⋊#95	C₂²	semidirect
111. C₄²×Dic₄₇	C₂²	semidirect
113. C₄₇×#518	C₄	semidirect
224. C₄×D₄×C₄₇	C₂×C₄	semidirect
225. C₄×D₄×C₄₇	C₂×C₄	semidirect
226. C₄×D₄×C₄₇	C₂×C₄	semidirect
227. C₄×D₄×C₄₇	C₂×C₄	semidirect
228. #117×C₄₇	C₂×C₄	semidirect
229. #117×C₄₇	C₂×C₄	semidirect
234. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
235. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
404. D₄×C₄₇	#117	semidirect
558. #518	Dic₄₇	semidirect
657. C₄₇	#34261	semidirect
680. C₄×D₄	C₂×Dic₄₇	semidirect
681. C₄×D₄	C₂×Dic₄₇	semidirect
682. C₄×D₄	C₂×Dic₄₇	semidirect
683. C₄×D₄	C₂×Dic₄₇	semidirect
686. #117	C₂×Dic₄₇	semidirect
687. #117	C₂×Dic₄₇	semidirect
727. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
728. C₂×C₂²⋊C₄	C₂×Dic₄₇	semidirect
938. D₄	#13093983	semidirect

Maximal subgroups

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

subgroup	index
#20246361	2
#20246337	2
#20246328	2
#20246317	2
#20246298	2
D₄×C₄⋊Dic₄₇	2
#20246281	2
#20246273	2
#20246237	2
D₄×C₂²⋊Dic₄₇	2
#20246031	2
#20246021	2
#20245997	2
#20245986	2
#20245886	2
#20245853	2
#20245833	2
C₂×#15689016	2
#20245749	2
C₄×D₄×Dic₄₇	2
C₂×C₄₇×#518	2
#34261	47