Subgroups — #27081465

Order 12032.

1908 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256685	C₂	1	1	yes	maximal, characteristic
2	#20252551	C₂	1	2	yes	maximal, complemented
3	#20252547	C₂	1	2	yes	maximal, complemented
4	#20252540	C₂	1	2	yes	maximal, complemented
5	#20252536	C₂	1	2	yes	maximal, complemented
6	#20252519	C₂	1	2	yes	maximal, complemented
7	#20252512	C₂	1	2	yes	maximal, complemented
8	#20252504	C₂	1	2	yes	maximal, complemented
9	#20252498	C₂	1	2	yes	maximal, complemented
10	#20252323	C₂	1	1	yes	maximal, characteristic, complemented
11	#20252116	C₂	1	2	yes	maximal, complemented
12	#20252112	C₂	1	2	yes	maximal, complemented
13	#20252101	C₂	1	1	yes	maximal, characteristic, complemented
14	#20252099	C₂	1	1	yes	maximal, characteristic, complemented
15	#20252052	C₂	1	2	yes	maximal, complemented
16	C₂×#15689174	C₂	1	1	yes	maximal, characteristic, complemented
17	#20251955	C₂	1	2	yes	maximal, complemented
18	#423×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₇×#2960	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13094032	C₂²	1	2	yes	—
21	C₂×#13094030	C₂²	1	2	yes	—
22	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
23	#15689678	C₄	1	1	yes	characteristic
24	#15689678	C₄	1	1	yes	characteristic
25	#15689674	C₄	1	1	yes	characteristic
26	#15689674	C₄	1	1	yes	characteristic
27	#15689673	C₂²	1	1	yes	characteristic
28	#15689660	C₂²	1	2	yes	—
29	#15689660	C₂²	1	2	yes	—
30	#15689659	C₄	1	2	yes	—
31	#15689659	C₄	1	2	yes	—
32	#15689658	C₄	1	2	yes	—
33	#15689658	C₄	1	2	yes	—
34	#15689636	C₄	1	2	yes	—
35	#15689636	C₄	1	2	yes	—
36	#15689635	C₂²	1	2	yes	—
37	C₄×#10625354	C₂²	1	2	yes	—
38	C₄×#10625354	C₂²	1	2	yes	—
39	#15689591	C₂²	1	2	yes	—
40	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
41	#15689254	C₂²	1	2	yes	complemented
42	#15689254	C₂²	1	2	yes	complemented
43	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
44	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
45	#15689202	C₂²	1	4	yes	—
46	#15689202	C₂²	1	2	yes	complemented
47	#15689202	C₂²	1	2	yes	complemented
48	#15689200	C₂²	1	4	yes	—
49	#15689200	C₂²	1	2	yes	complemented
50	#15689200	C₂²	1	2	yes	complemented
51	#15689196	C₂²	1	4	yes	—
52	#15689196	C₂²	1	4	yes	—
53	#15689193	C₂²	1	4	yes	—
54	#15689193	C₂²	1	4	yes	—
55	C₈×D₁₈₈	C₂²	1	4	yes	—
56	C₈×D₁₈₈	C₂²	1	2	yes	complemented
57	C₈×D₁₈₈	C₂²	1	2	yes	complemented
58	#15689188	C₂²	1	4	yes	—
59	#15689188	C₂²	1	2	yes	complemented
60	#15689188	C₂²	1	2	yes	complemented
61	#15689185	C₂²	1	4	yes	complemented
62	#15689182	C₂²	1	4	yes	complemented
63	#15689178	C₂²	1	4	yes	complemented
64	#15689174	C₂²	1	1	yes	characteristic
65	#15689174	C₂²	1	1	yes	characteristic
66	#15689174	C₂²	1	1	yes	characteristic
67	#15689174	C₂²	1	1	yes	characteristic
68	#15689174	C₂²	1	1	yes	characteristic
69	#15689174	C₂²	1	1	yes	characteristic
70	#15689174	C₂²	1	1	yes	characteristic
71	#15689174	C₂²	1	1	yes	characteristic
72	#15689174	C₂²	1	4	yes	complemented
73	#15689150	C₂²	1	2	yes	—
74	#15689148	C₂²	1	4	yes	complemented
75	#15689148	C₂²	1	4	yes	complemented
76	#15689147	C₂²	1	1	yes	characteristic
77	#15689146	C₂²	1	2	yes	—
78	#15689145	C₂²	1	2	yes	—
79	#15689145	C₂²	1	2	yes	—
80	#15689145	C₂²	1	4	yes	complemented
81	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
82	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
83	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
84	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
85	C₄⋊C₈×D₄₇	C₂²	1	4	yes	complemented
86	#15689091	C₂²	1	2	yes	—
87	#15689089	C₂²	1	2	yes	—
88	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
89	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
90	#15689079	C₂²	1	2	yes	—
91	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
92	C₄₇×#533	C₂²	1	1	yes	characteristic
93	C₄₇×#446	C₂²	1	2	yes	complemented
94	C₄₇×#446	C₂²	1	2	yes	complemented
95	C₈×Q₈×C₄₇	C₂²	1	2	yes	complemented
96	C₈×Q₈×C₄₇	C₂²	1	2	yes	complemented
97	C₄₇×#424	C₂²	1	2	yes	—
98	C₄₇×#423	C₂²	1	1	yes	characteristic
99	C₄₇×#405	C₂²	1	2	yes	—
100	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
101	C₂×#10625354	C₂×C₄	1	2	yes	—
102	C₂×#10625354	C₂×C₄	1	2	yes	—
103	C₂×#10625350	C₂³	1	2	yes	—
104	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
106	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
107	#13094032	—	4	4	no	—
108	#13094030	—	4	4	no	—
109	C₂×#10625329	C₂³	1	2	yes	—
110	C₂×#10625324	C₂³	1	4	yes	—
111	C₂×#10625324	C₂³	1	4	yes	—
112	C₂×#10625324	C₂³	1	4	yes	—
113	M₁₆×D₄₇	—	4	4	no	—
114	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
115	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
116	C₂×C₈×D₄₇	C₂³	1	4	yes	—
117	C₂×C₈×D₄₇	C₂³	1	4	yes	—
118	C₂×C₈×D₄₇	C₂³	1	4	yes	—
119	#13094024	C₂×C₄	1	1	yes	characteristic
120	#13094021	C₂×C₄	1	1	yes	characteristic
121	#13094019	C₂×C₄	1	4	yes	—
122	#13094019	C₂×C₄	1	4	yes	—
123	#13094015	C₂×C₄	1	2	yes	—
124	#13094015	C₂×C₄	1	2	yes	—
125	#13094013	C₂×C₄	1	2	yes	—
126	#13094013	C₂×C₄	1	2	yes	—
127	#13094012	C₂×C₄	1	2	yes	—
128	#13094009	C₂×C₄	1	4	yes	—
129	#13094009	C₂×C₄	1	4	yes	—
130	#13094008	C₂×C₄	1	4	yes	—
131	#13094004	C₂×C₄	1	2	yes	—
132	#13094004	C₂×C₄	1	2	yes	—
133	#13094000	C₂×C₄	1	2	yes	—
134	#13094000	C₂×C₄	1	2	yes	—
135	#13093999	C₂×C₄	1	2	yes	—
136	#13093999	C₂×C₄	1	2	yes	—
137	#13093999	C₂×C₄	1	2	yes	—
138	#13093999	C₂×C₄	1	2	yes	—
139	#13093998	C₂×C₄	1	2	yes	—
140	#13093998	C₂×C₄	1	2	yes	—
141	#13093994	C₂×C₄	1	4	yes	—
142	Q₈×Dic₄₇	C₂×C₄	1	2	yes	—
143	Q₈×Dic₄₇	C₂×C₄	1	2	yes	—
144	#13093989	C₂×C₄	1	2	yes	—
145	#13093989	C₂×C₄	1	2	yes	—
146	C₄×D₁₈₈	C₂³	1	4	yes	—
147	C₄×D₁₈₈	C₂³	1	4	yes	—
148	C₄×D₁₈₈	C₂³	1	2	yes	—
149	C₄×D₁₈₈	C₂³	1	2	yes	—
150	#13093986	C₂×C₄	1	2	yes	—
151	#13093986	C₂×C₄	1	2	yes	—
152	#13093986	C₂×C₄	1	4	yes	—
153	#13093986	C₂×C₄	1	4	yes	—
154	#13093986	C₂×C₄	1	2	yes	—
155	#13093986	C₂×C₄	1	2	yes	—
156	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
157	(C₂²⋊D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
158	#13093982	C₂×C₄	1	2	yes	—
159	#13093982	C₂×C₄	1	2	yes	—
160	#13093982	C₂×C₄	1	4	yes	—
161	#13093982	C₂×C₄	1	4	yes	—
162	#13093981	C₂³	1	4	yes	—
163	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
164	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
165	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
166	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
167	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
168	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
169	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
170	C₄²×D₄₇	C₂³	1	1	yes	characteristic
171	C₄²×D₄₇	C₂³	1	1	yes	characteristic
172	C₄²×D₄₇	C₂³	1	1	yes	characteristic
173	C₄²×D₄₇	C₂³	1	1	yes	characteristic
174	C₄²×D₄₇	C₂³	1	4	yes	—
175	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
176	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
177	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
178	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
179	Dic₄₇⋊C₈	C₂³	1	4	yes	—
180	Dic₄₇⋊C₈	C₂³	1	4	yes	—
181	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
182	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
183	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
184	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
185	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
186	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
187	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
188	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
189	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
190	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
191	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
192	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
193	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
194	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
195	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
196	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
197	(C₂×D₄₇)⋊C₈	C₂³	1	4	yes	—
198	(C₂×D₄₇)⋊C₈	C₂³	1	4	yes	—
199	(C₂×D₄₇)⋊C₈	C₂³	1	4	yes	—
200	(C₂×D₄₇)⋊C₈	C₂³	1	4	yes	—
201	#13093935	C₂³	1	4	yes	—
202	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
203	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
204	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
205	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
206	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
207	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
208	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
209	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
210	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
211	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
212	#125×C₄₇	C₂×C₄	1	2	yes	—
213	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
214	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
215	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
216	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
217	#117×C₄₇	C₂³	1	2	yes	—
218	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
219	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
220	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
221	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
222	C₄⋊C₈×C₄₇	C₂³	1	4	yes	—
223	#97×C₄₇	C₂³	1	4	yes	—
224	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
225	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
226	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
227	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
228	C₄×C₈×C₄₇	C₂³	1	4	yes	—
229	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
230	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
231	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
232	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
233	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
234	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
235	C₂×C₂²⋊D₄₇	C₂²×C₄	1	4	yes	—
236	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
237	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
238	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
239	#10625354	—	2	8	no	—
240	#10625354	—	4	4	no	—
241	#10625350	—	2	4	no	—
242	#10625350	—	2	4	no	—
243	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
244	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
245	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
246	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
247	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
248	C₂×C₄×D₄₇	—	2	2	no	—
249	C₂×C₄×D₄₇	—	2	2	no	—
250	C₂×C₄×D₄₇	—	2	4	no	—
251	C₂×C₄×D₄₇	—	4	2	no	—
252	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
253	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
254	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
255	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
256	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
257	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
258	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
259	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
260	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
261	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
262	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
263	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
264	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
265	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
266	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
267	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
268	M₁₆×C₄₇	—	2	4	no	—
269	C₂×C₈×C₄₇	—	2	2	no	—
270	C₂×C₈×C₄₇	—	2	2	no	—
271	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
272	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
273	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
274	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
275	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
276	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
277	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
278	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
279	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
280	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
281	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
282	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
283	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
284	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
285	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
286	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
287	C₄²×C₄₇	C₂⁴	1	4	yes	—
288	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	4	yes	—
289	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	4	yes	—
290	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	4	yes	—
291	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	4	yes	—
292	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	4	yes	—
293	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	4	yes	—
294	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	4	yes	—
295	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	4	yes	—
296	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
297	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
298	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
299	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
300	Dic₄₇⋊C₄	C₂²×C₄	1	4	yes	—
301	Dic₄₇⋊C₄	C₂²×C₄	1	4	yes	—
302	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
303	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
304	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
305	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
306	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
307	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
308	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
309	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
310	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
311	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
312	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
313	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
314	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
315	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
316	#10625329	—	2	4	no	—
317	C₂×C₄₇⋊C₈	—	2	2	no	—
318	C₂×C₄₇⋊C₈	—	2	2	no	—
319	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
320	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
321	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
322	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
323	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
324	#10625324	—	4	4	no	—
325	#10625324	—	4	4	no	—
326	#10625324	—	4	4	no	—
327	C₈×D₄₇	—	4	4	no	—
328	C₈×D₄₇	—	4	4	no	—
329	C₈×D₄₇	—	4	4	no	—
330	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
331	C₂²×D₄₇	—	2	2	no	—
332	C₂²×D₄₇	—	2	2	no	—
333	C₂²×D₄₇	—	4	1	no	—
334	C₂²×D₄₇	C₂³×C₄	1	4	yes	—
335	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
336	C₂²×D₄₇	C₂³×C₄	1	1	yes	characteristic
337	Q₈×C₄₇	—	2	4	no	—
338	Q₈×C₄₇	—	2	4	no	—
339	C₂×C₄×C₄₇	—	2	2	no	—
340	C₂×C₄×C₄₇	—	2	2	no	—
341	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
342	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
343	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
344	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
345	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
346	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
347	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
348	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
349	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
350	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
351	C₂²⋊D₄₇	—	2	8	no	—
352	C₂×Dic₄₇	—	2	2	no	—
353	C₂×Dic₄₇	—	2	2	no	—
354	C₂×Dic₄₇	—	4	1	no	—
355	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
356	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
357	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
358	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
359	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
360	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
361	C₂×Dic₄₇	C₂³×C₄	1	1	yes	characteristic
362	D₁₈₈	—	2	8	no	—
363	D₁₈₈	—	2	4	no	—
364	D₁₈₈	—	2	4	no	—
365	D₁₈₈	—	2	4	no	—
366	D₁₈₈	—	4	4	no	—
367	C₄×D₄₇	—	2	2	no	—
368	C₄×D₄₇	—	2	2	no	—
369	C₄×D₄₇	—	2	2	no	—
370	C₄×D₄₇	—	2	2	no	—
371	C₄×D₄₇	—	2	2	no	—
372	C₄×D₄₇	—	2	2	no	—
373	C₄×D₄₇	—	2	1	no	—
374	C₄×D₄₇	—	2	4	no	—
375	C₄×D₄₇	—	2	1	no	—
376	C₄×D₄₇	—	2	1	no	—
377	C₄×D₄₇	—	2	1	no	—
378	C₄×D₄₇	—	2	4	no	—
379	C₄×D₄₇	—	2	2	no	—
380	C₄×D₄₇	—	2	8	no	—
381	C₄×D₄₇	—	4	1	no	—
382	C₄×D₄₇	—	4	1	no	—
383	C₄×D₄₇	—	4	4	no	—
384	C₄×D₄₇	#131	1	4	yes	complemented
385	Dic₉₄	—	2	4	no	—
386	C₈×C₄₇	—	2	1	no	—
387	C₈×C₄₇	—	2	4	no	—
388	C₈×C₄₇	—	2	1	no	—
389	C₈×C₄₇	—	2	1	no	—
390	C₈×C₄₇	—	2	1	no	—
391	C₄₇⋊C₈	—	2	1	no	—
392	C₄₇⋊C₈	—	2	4	no	—
393	C₄₇⋊C₈	—	2	1	no	—
394	C₄₇⋊C₈	—	2	1	no	—
395	C₄₇⋊C₈	—	2	1	no	—
396	#60268	—	47	1	no	maximal, Sylow
397	C₂²×C₄₇	—	2	1	no	—
398	C₂²×C₄₇	—	2	1	no	—
399	C₂²×C₄₇	#520	1	2	yes	—
400	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
401	C₂×D₄₇	—	2	1	no	—
402	C₂×D₄₇	—	2	1	no	—
403	C₂×D₄₇	—	2	1	no	—
404	C₂×D₄₇	—	2	4	no	—
405	C₂×D₄₇	—	2	1	no	—
406	C₂×D₄₇	—	2	4	no	—
407	C₂×D₄₇	—	2	1	no	—
408	C₂×D₄₇	—	2	4	no	—
409	C₂×D₄₇	—	4	4	no	—
410	C₂×D₄₇	C₂×#131	1	2	yes	—
411	C₄×C₄₇	—	2	1	no	—
412	C₄×C₄₇	—	2	4	no	—
413	C₄×C₄₇	—	2	1	no	—
414	C₄×C₄₇	—	2	4	no	—
415	C₄×C₄₇	#520	1	2	yes	—
416	C₄×C₄₇	C₂×#131	1	2	yes	—
417	C₄×C₄₇	#568	1	2	yes	—
418	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
419	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
420	Dic₄₇	—	2	4	no	—
421	Dic₄₇	—	2	1	no	—
422	Dic₄₇	—	2	1	no	—
423	Dic₄₇	—	2	1	no	—
424	Dic₄₇	—	2	1	no	—
425	Dic₄₇	—	2	1	no	—
426	Dic₄₇	C₂×#131	1	2	yes	—
427	#3444	—	47	1	no	—
428	#2994	—	47	2	no	—
429	#2994	—	47	2	no	—
430	#2993	—	47	2	no	—
431	#2993	—	47	2	no	—
432	#2991	—	47	2	no	—
433	#2990	—	47	2	no	—
434	#2989	—	47	2	no	—
435	#2988	—	47	2	no	—
436	#2960	—	47	1	no	—
437	#2960	D₄₇	1	1	yes	characteristic, complemented
438	#2933	—	47	2	no	—
439	#2933	—	47	2	no	—
440	#2931	—	47	1	no	—
441	#2931	—	47	1	no	—
442	#2925	—	47	2	no	—
443	C₂×#431	—	47	1	no	—
444	#2906	—	47	2	no	—
445	C₂×#423	—	47	1	no	—
446	C₂×C₄₇	—	2	2	no	—
447	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
448	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
449	C₂×C₄₇	C₂×#568	1	1	yes	characteristic
450	D₄₇	—	2	2	no	—
451	D₄₇	—	4	4	no	—
452	D₄₇	—	4	1	no	—
453	C₂×#131	—	47	2	no	—
454	C₂×#131	—	47	2	no	—
455	C₂²×M₁₆	—	47	2	no	—
456	#533	—	47	1	no	—
457	#533	—	47	1	no	—
458	#533	C₂×D₄₇	1	1	yes	characteristic
459	#532	—	47	1	no	—
460	#532	—	47	1	no	—
461	#532	—	47	1	no	—
462	#529	—	47	2	no	—
463	#529	—	47	2	no	—
464	#529	—	47	2	no	—
465	#529	—	47	2	no	—
466	#529	—	47	2	no	—
467	#529	—	47	2	no	—
468	#525	—	47	2	no	—
469	#525	—	47	2	no	—
470	#525	—	47	2	no	—
471	C₄×#41	—	47	2	no	—
472	C₄×#41	—	47	2	no	—
473	C₄×#41	—	47	2	no	—
474	C₂²×C₄²	—	47	1	no	—
475	#446	—	47	2	no	—
476	#446	—	47	2	no	—
477	#446	C₂×D₄₇	1	2	yes	complemented
478	#446	C₂×D₄₇	1	2	yes	complemented
479	C₈×Q₈	—	47	2	no	—
480	C₈×Q₈	—	47	2	no	—
481	C₈×Q₈	C₂×D₄₇	1	2	yes	complemented
482	C₈×Q₈	C₂×D₄₇	1	2	yes	complemented
483	#436	—	47	2	no	—
484	#436	—	47	2	no	—
485	#436	—	47	4	no	—
486	#436	—	47	2	no	—
487	#436	—	47	2	no	—
488	#436	—	47	4	no	—
489	#435	—	47	4	no	—
490	#435	—	47	4	no	—
491	#435	—	47	4	no	—
492	#435	—	47	4	no	—
493	C₈×D₄	—	47	2	no	—
494	C₈×D₄	—	47	2	no	—
495	C₈×D₄	—	47	4	no	—
496	C₈×D₄	—	47	2	no	—
497	C₈×D₄	—	47	2	no	—
498	C₈×D₄	—	47	4	no	—
499	#433	—	47	4	no	—
500	#433	—	47	4	no	—
501	#432	—	47	4	no	—
502	#431	—	47	1	no	—
503	#431	—	47	1	no	—
504	#431	—	47	1	no	—
505	#431	—	47	1	no	—
506	#431	—	47	1	no	—
507	#431	—	47	1	no	—
508	#431	—	47	1	no	—
509	#431	—	47	1	no	—
510	#431	—	47	4	no	—
511	#424	—	47	2	no	—
512	#424	—	47	4	no	—
513	#424	—	47	4	no	—
514	#424	C₂×D₄₇	1	2	yes	—
515	#423	—	47	2	no	—
516	#423	—	47	1	no	—
517	#423	—	47	2	no	—
518	#423	—	47	2	no	—
519	#423	—	47	4	no	—
520	#423	C₂×D₄₇	1	1	yes	characteristic
521	C₂×C₄⋊C₈	—	47	1	no	—
522	C₂×C₄⋊C₈	—	47	1	no	—
523	C₂×C₄⋊C₈	—	47	2	no	—
524	C₂×C₄⋊C₈	—	47	2	no	—
525	C₂×C₄⋊C₈	—	47	4	no	—
526	#408	—	47	2	no	—
527	#408	—	47	2	no	—
528	C₂×C₂²⋊C₈	—	47	1	no	—
529	C₂×C₂²⋊C₈	—	47	1	no	—
530	#405	—	47	2	no	—
531	#405	C₂×D₄₇	1	2	yes	—
532	C₂×C₄×C₈	—	47	1	no	—
533	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
534	C₄₇	#60268	1	1	yes	characteristic, complemented, Sylow
535	C₂×#41	—	47	2	no	—
536	C₂×#41	—	47	2	no	—
537	C₂×#41	—	47	2	no	—
538	C₂³×C₄	—	47	1	no	—
539	C₂³×C₄	—	47	1	no	—
540	C₂³×C₄	—	47	1	no	—
541	#131	—	188	4	no	—
542	#131	—	188	4	no	—
543	C₂×M₁₆	—	47	2	no	—
544	C₂×M₁₆	—	47	4	no	—
545	C₂×M₁₆	—	47	4	no	—
546	C₂×M₁₆	—	47	4	no	—
547	C₂×M₁₆	—	188	4	no	—
548	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
549	C₂²×C₈	—	47	1	no	—
550	C₂²×C₈	—	47	1	no	—
551	C₂²×C₈	—	47	4	no	—
552	C₂²×C₈	—	47	4	no	—
553	C₂²×C₈	—	47	4	no	—
554	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
555	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
556	C₄⋊Q₈	—	47	1	no	—
557	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
558	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
559	#127	—	47	1	no	—
560	#126	—	47	4	no	—
561	#126	—	47	4	no	—
562	#125	—	47	2	no	—
563	#125	—	47	2	no	—
564	#125	C₄×D₄₇	1	2	yes	—
565	#124	—	47	2	no	—
566	#124	—	47	2	no	—
567	#124	—	47	2	no	—
568	#123	—	47	4	no	—
569	#123	—	47	4	no	—
570	#123	—	47	4	no	—
571	C₂²⋊Q₈	—	47	2	no	—
572	C₂²⋊Q₈	—	47	2	no	—
573	C₂²⋊Q₈	—	47	2	no	—
574	C₂²⋊Q₈	—	47	2	no	—
575	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
576	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
577	#121	—	47	2	no	—
578	#121	—	47	2	no	—
579	#121	—	47	2	no	—
580	#121	—	47	2	no	—
581	#121	—	47	2	no	—
582	#121	—	47	2	no	—
583	#120	—	47	4	no	—
584	C₄×Q₈	—	47	2	no	—
585	C₄×Q₈	—	47	2	no	—
586	C₄×Q₈	—	47	2	no	—
587	C₄×Q₈	—	47	2	no	—
588	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
589	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
590	C₄×D₄	—	47	4	no	—
591	C₄×D₄	—	47	4	no	—
592	C₄×D₄	—	47	2	no	—
593	C₄×D₄	—	47	2	no	—
594	C₄×D₄	—	47	2	no	—
595	C₄×D₄	—	47	2	no	—
596	C₄×D₄	—	47	4	no	—
597	C₄×D₄	—	47	4	no	—
598	C₄×D₄	—	47	4	no	—
599	C₄×D₄	—	47	4	no	—
600	C₄×D₄	—	47	2	no	—
601	C₄×D₄	—	47	2	no	—
602	#117	—	47	2	no	—
603	#117	—	47	2	no	—
604	#117	—	47	4	no	—
605	#117	—	47	4	no	—
606	#117	—	47	4	no	—
607	#117	C₂²×D₄₇	1	2	yes	—
608	C₂×C₄²	—	47	1	no	—
609	C₂×C₄²	—	47	1	no	—
610	C₂×C₄²	—	47	1	no	—
611	C₂×C₄²	—	47	1	no	—
612	C₂×C₄²	—	47	1	no	—
613	C₂×C₄²	—	47	1	no	—
614	C₂×C₄²	—	47	1	no	—
615	C₂×C₄²	—	47	4	no	—
616	C₂×C₄²	—	47	1	no	—
617	C₂×C₄²	—	47	1	no	—
618	C₂×C₄²	—	47	1	no	—
619	C₂×C₄²	—	47	1	no	—
620	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
621	C₄⋊C₈	—	47	1	no	—
622	C₄⋊C₈	—	47	4	no	—
623	C₄⋊C₈	—	47	1	no	—
624	C₄⋊C₈	—	47	4	no	—
625	C₄⋊C₈	—	47	1	no	—
626	C₄⋊C₈	—	47	1	no	—
627	C₄⋊C₈	—	47	1	no	—
628	C₄⋊C₈	—	47	1	no	—
629	C₄⋊C₈	—	47	1	no	—
630	C₄⋊C₈	—	47	1	no	—
631	C₄⋊C₈	—	47	2	no	—
632	C₄⋊C₈	—	47	2	no	—
633	C₄⋊C₈	—	47	4	no	—
634	C₄⋊C₈	—	47	4	no	—
635	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
636	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
637	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
638	C₄⋊C₈	C₂²×D₄₇	1	4	yes	—
639	C₂²⋊C₈	—	47	1	no	—
640	C₂²⋊C₈	—	47	1	no	—
641	C₂²⋊C₈	—	47	1	no	—
642	C₂²⋊C₈	—	47	1	no	—
643	C₂²⋊C₈	—	47	1	no	—
644	C₂²⋊C₈	—	47	1	no	—
645	C₂²⋊C₈	—	47	1	no	—
646	C₂²⋊C₈	—	47	1	no	—
647	C₂²⋊C₈	—	47	4	no	—
648	C₂²⋊C₈	—	47	4	no	—
649	C₂²⋊C₈	—	47	4	no	—
650	C₂²⋊C₈	—	47	4	no	—
651	#97	—	47	4	no	—
652	#97	C₂²×D₄₇	1	4	yes	—
653	C₄×C₈	—	47	1	no	—
654	C₄×C₈	—	47	1	no	—
655	C₄×C₈	—	47	1	no	—
656	C₄×C₈	—	47	1	no	—
657	C₄×C₈	—	47	4	no	—
658	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
659	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
660	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
661	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
662	C₄×C₈	C₂²×D₄₇	1	4	yes	—
663	C₂⁴	—	47	1	no	—
664	#41	—	94	8	no	—
665	#41	—	94	4	no	—
666	#41	—	94	4	no	—
667	#41	—	188	4	no	—
668	C₂×Q₈	—	47	2	no	—
669	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
670	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
671	C₂×D₄	—	47	4	no	—
672	C₂×D₄	—	47	4	no	—
673	C₂×D₄	—	47	2	no	—
674	C₂×D₄	—	47	2	no	—
675	C₂×D₄	—	47	2	no	—
676	C₂×D₄	—	47	4	no	—
677	C₂²×C₄	—	47	1	no	—
678	C₂²×C₄	—	47	1	no	—
679	C₂²×C₄	—	47	1	no	—
680	C₂²×C₄	—	47	1	no	—
681	C₂²×C₄	—	47	1	no	—
682	C₂²×C₄	—	47	1	no	—
683	C₂²×C₄	—	47	1	no	—
684	C₂²×C₄	—	47	1	no	—
685	C₂²×C₄	—	47	1	no	—
686	C₂²×C₄	—	47	1	no	—
687	C₂²×C₄	—	47	1	no	—
688	C₂²×C₄	—	47	4	no	—
689	C₂²×C₄	—	47	1	no	—
690	C₂²×C₄	—	47	1	no	—
691	C₂²×C₄	—	47	4	no	—
692	C₂²×C₄	—	47	1	no	—
693	C₂²×C₄	—	47	1	no	—
694	C₂²×C₄	—	47	4	no	—
695	C₂²×C₄	—	94	4	no	—
696	C₂²×C₄	—	94	2	no	—
697	C₂²×C₄	—	94	2	no	—
698	C₂²×C₄	—	188	2	no	—
699	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
700	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
701	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
702	M₁₆	—	2	4	no	—
703	M₁₆	—	94	4	no	—
704	M₁₆	—	188	4	no	—
705	M₁₆	—	188	4	no	—
706	M₁₆	—	188	4	no	—
707	C₂×C₈	—	2	2	no	—
708	C₂×C₈	—	2	2	no	—
709	C₂×C₈	—	47	1	no	—
710	C₂×C₈	—	47	1	no	—
711	C₂×C₈	—	47	1	no	—
712	C₂×C₈	—	47	1	no	—
713	C₂×C₈	—	47	4	no	—
714	C₂×C₈	—	94	2	no	—
715	C₂×C₈	—	94	2	no	—
716	C₂×C₈	—	188	4	no	—
717	C₂×C₈	—	188	4	no	—
718	C₂×C₈	—	188	4	no	—
719	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
720	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
721	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
722	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
723	C₂×C₈	C₂³×D₄₇	1	4	yes	—
724	C₄⋊C₄	—	47	4	no	—
725	C₄⋊C₄	—	47	4	no	—
726	C₄⋊C₄	—	47	2	no	—
727	C₄⋊C₄	—	47	2	no	—
728	C₄⋊C₄	—	47	4	no	—
729	C₄⋊C₄	—	47	4	no	—
730	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
731	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
732	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
733	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
734	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
735	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
736	C₂²⋊C₄	—	47	4	no	—
737	C₂²⋊C₄	—	47	4	no	—
738	C₂²⋊C₄	—	47	4	no	—
739	C₂²⋊C₄	—	47	4	no	—
740	C₂²⋊C₄	—	47	4	no	—
741	C₂²⋊C₄	—	47	4	no	—
742	C₂²⋊C₄	—	47	4	no	—
743	C₂²⋊C₄	—	47	4	no	—
744	C₂²⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
745	C₄²	—	47	1	no	—
746	C₄²	—	47	1	no	—
747	C₄²	—	47	1	no	—
748	C₄²	—	47	1	no	—
749	C₄²	—	47	1	no	—
750	C₄²	—	47	1	no	—
751	C₄²	—	47	1	no	—
752	C₄²	—	47	1	no	—
753	C₄²	—	47	1	no	—
754	C₄²	—	47	1	no	—
755	C₄²	—	47	4	no	—
756	C₄²	—	47	4	no	—
757	C₄²	—	47	1	no	—
758	C₄²	—	47	1	no	—
759	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
760	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
761	C₄²	C₂³×D₄₇	1	1	yes	characteristic
762	C₄²	C₂³×D₄₇	1	1	yes	characteristic
763	C₄²	C₂³×D₄₇	1	4	yes	—
764	C₂³	—	47	1	no	—
765	C₂³	—	47	4	no	—
766	C₂³	—	47	1	no	—
767	C₂³	—	94	2	no	—
768	C₂³	—	94	2	no	—
769	C₂³	—	188	1	no	—
770	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
771	Q₈	—	2	4	no	—
772	Q₈	—	2	4	no	—
773	Q₈	—	94	4	no	—
774	D₄	—	94	8	no	—
775	D₄	—	94	8	no	—
776	D₄	—	94	4	no	—
777	D₄	—	94	4	no	—
778	D₄	—	94	4	no	—
779	D₄	—	188	4	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	47	1	no	—
783	C₂×C₄	—	47	4	no	—
784	C₂×C₄	—	47	1	no	—
785	C₂×C₄	—	47	1	no	—
786	C₂×C₄	—	47	1	no	—
787	C₂×C₄	—	47	1	no	—
788	C₂×C₄	—	47	1	no	—
789	C₂×C₄	—	47	4	no	—
790	C₂×C₄	—	94	2	no	—
791	C₂×C₄	—	94	8	no	—
792	C₂×C₄	—	94	2	no	—
793	C₂×C₄	—	94	2	no	—
794	C₂×C₄	—	94	2	no	—
795	C₂×C₄	—	94	2	no	—
796	C₂×C₄	—	94	2	no	—
797	C₂×C₄	—	94	2	no	—
798	C₂×C₄	—	94	2	no	—
799	C₂×C₄	—	94	2	no	—
800	C₂×C₄	—	94	1	no	—
801	C₂×C₄	—	94	4	no	—
802	C₂×C₄	—	94	1	no	—
803	C₂×C₄	—	94	1	no	—
804	C₂×C₄	—	94	1	no	—
805	C₂×C₄	—	94	4	no	—
806	C₂×C₄	—	188	1	no	—
807	C₂×C₄	—	188	1	no	—
808	C₂×C₄	—	188	4	no	—
809	C₂×C₄	—	188	1	no	—
810	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
811	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
812	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
813	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
814	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
815	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
816	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
817	C₂×C₄	#13094070	1	2	yes	—
818	C₂×C₄	#13094072	1	2	yes	—
819	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
820	C₈	—	2	1	no	—
821	C₈	—	2	1	no	—
822	C₈	—	2	4	no	—
823	C₈	—	2	1	no	—
824	C₈	—	2	1	no	—
825	C₈	—	94	1	no	—
826	C₈	—	94	1	no	—
827	C₈	—	94	4	no	—
828	C₈	—	94	1	no	—
829	C₈	—	94	1	no	—
830	C₂²	—	2	1	no	—
831	C₂²	—	2	1	no	—
832	C₂²	—	47	2	no	—
833	C₂²	—	94	1	no	—
834	C₂²	—	94	1	no	—
835	C₂²	—	94	1	no	—
836	C₂²	—	94	4	no	—
837	C₂²	—	94	1	no	—
838	C₂²	—	94	4	no	—
839	C₂²	—	94	1	no	—
840	C₂²	—	94	4	no	—
841	C₂²	—	188	4	no	—
842	C₂²	#15689605	1	2	yes	—
843	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
844	C₄	—	2	1	no	—
845	C₄	—	2	4	no	—
846	C₄	—	2	1	no	—
847	C₄	—	2	4	no	—
848	C₄	—	47	2	no	—
849	C₄	—	94	1	no	—
850	C₄	—	94	1	no	—
851	C₄	—	94	1	no	—
852	C₄	—	94	1	no	—
853	C₄	—	94	1	no	—
854	C₄	—	94	4	no	—
855	C₄	#15689605	1	2	yes	—
856	C₄	#131×D₄₇	1	2	yes	—
857	C₄	#15689888	1	2	yes	—
858	C₄	C₂×#13094070	1	1	yes	characteristic
859	C₄	C₂×#13094072	1	1	yes	characteristic
860	C₂	—	2	2	no	—
861	C₂	—	94	2	no	—
862	C₂	—	188	1	no	—
863	C₂	—	188	4	no	—
864	C₂	C₂×#15689605	1	1	yes	characteristic
865	C₂	C₂×#131×D₄₇	1	1	yes	characteristic
866	C₂	C₂×#15689888	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₄₇×#2960	C₂
prime radical	#20256685	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2960	D₄₇
hypocenter	C₄₇	#60268
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #2960

Complements

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

N	H ≅ G/N	type
2. #20252551	C₂	semidirect
3. #20252547	C₂	semidirect
4. #20252540	C₂	semidirect
5. #20252536	C₂	semidirect
6. #20252519	C₂	semidirect
7. #20252512	C₂	semidirect
8. #20252504	C₂	semidirect
9. #20252498	C₂	semidirect
10. #20252323	C₂	semidirect
11. #20252116	C₂	semidirect
12. #20252112	C₂	semidirect
13. #20252101	C₂	semidirect
14. #20252099	C₂	semidirect
15. #20252052	C₂	semidirect
16. C₂×#15689174	C₂	semidirect
17. #20251955	C₂	semidirect
18. #423×D₄₇	C₂	semidirect
19. C₄₇×#2960	C₂	semidirect
41. #15689254	C₂²	semidirect
42. #15689254	C₂²	semidirect
43. Q₈×C₄₇⋊C₈	C₂²	semidirect
44. Q₈×C₄₇⋊C₈	C₂²	semidirect
46. #15689202	C₂²	semidirect
47. #15689202	C₂²	semidirect
49. #15689200	C₂²	semidirect
50. #15689200	C₂²	semidirect
56. C₈×D₁₈₈	C₂²	semidirect
57. C₈×D₁₈₈	C₂²	semidirect
59. #15689188	C₂²	semidirect
60. #15689188	C₂²	semidirect
61. #15689185	C₂²	semidirect
62. #15689182	C₂²	semidirect
63. #15689178	C₂²	semidirect
72. #15689174	C₂²	semidirect
74. #15689148	C₂²	semidirect
75. #15689148	C₂²	semidirect
80. #15689145	C₂²	semidirect
85. C₄⋊C₈×D₄₇	C₂²	semidirect
93. C₄₇×#446	C₂²	semidirect
94. C₄₇×#446	C₂²	semidirect
95. C₈×Q₈×C₄₇	C₂²	semidirect
96. C₈×Q₈×C₄₇	C₂²	semidirect
384. C₄×D₄₇	#131	semidirect
437. #2960	D₄₇	semidirect
477. #446	C₂×D₄₇	semidirect
478. #446	C₂×D₄₇	semidirect
481. C₈×Q₈	C₂×D₄₇	semidirect
482. C₈×Q₈	C₂×D₄₇	semidirect
534. C₄₇	#60268	semidirect

Maximal subgroups

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

subgroup	index
#20256685	2
#20252551	2
#20252547	2
#20252540	2
#20252536	2
#20252519	2
#20252512	2
#20252504	2
#20252498	2
#20252323	2
#20252116	2
#20252112	2
#20252101	2
#20252099	2
#20252052	2
C₂×#15689174	2
#20251955	2
#423×D₄₇	2
C₄₇×#2960	2
#60268	47