Subgroups — C₂×#20257073 #27124188

Order 12032.

9502 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257073	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689802	C₂	1	4	yes	maximal, complemented
3	C₂×#15689797	C₂	1	4	yes	maximal, complemented
4	C₂×#15689769	C₂	1	4	yes	maximal, complemented
5	C₂×#15689763	C₂	1	4	yes	maximal, complemented
6	C₂×#15689749	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15689706	C₂	1	4	yes	maximal, complemented
8	C₂×#15689682	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689632	C₂	1	4	yes	maximal, complemented
10	C₂²×#13093994	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#13093992	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15689596	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₂²⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂⁵×D₄₇	C₂²	1	1	yes	characteristic
16	C₂²×#10625350	C₂²	1	4	yes	complemented
17	C₂³×D₁₈₈	C₂²	1	2	yes	complemented
18	C₂³×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
19	C₂³×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
20	C₂³×C₄×D₄₇	C₂²	1	2	yes	complemented
21	#15689802	C₂²	1	64	yes	complemented
22	#15689797	C₂²	1	64	yes	complemented
23	#15689769	C₂²	1	64	yes	complemented
24	#15689763	C₂²	1	64	yes	complemented
25	#15689749	C₂²	1	16	yes	complemented
26	#15689706	C₂²	1	64	yes	complemented
27	#15689682	C₂²	1	16	yes	complemented
28	C₂×#13094019	C₂²	1	4	yes	complemented
29	C₂×#13094018	C₂²	1	4	yes	complemented
30	C₂×#13094012	C₂²	1	4	yes	complemented
31	C₂×#13094010	C₂²	1	4	yes	complemented
32	#15689632	C₂²	1	64	yes	complemented
33	C₂×#13094009	C₂²	1	4	yes	complemented
34	C₂×#13094009	C₂²	1	4	yes	complemented
35	C₂×#13094007	C₂²	1	2	yes	complemented
36	C₂×#13094007	C₂²	1	4	yes	complemented
37	C₂×#13094006	C₂²	1	4	yes	complemented
38	C₂×#13094005	C₂²	1	2	yes	complemented
39	C₂×#13094003	C₂²	1	4	yes	complemented
40	C₂×#13094002	C₂²	1	4	yes	complemented
41	C₂×#13094001	C₂²	1	4	yes	complemented
42	C₂×#13094001	C₂²	1	4	yes	complemented
43	C₂×#13093998	C₂²	1	4	yes	complemented
44	C₂×#13093997	C₂²	1	4	yes	complemented
45	C₂×#13093997	C₂²	1	4	yes	complemented
46	C₂×#13093996	C₂²	1	4	yes	complemented
47	C₂×#13093994	C₂²	1	4	yes	—
48	C₂×#13093994	C₂²	1	2	yes	complemented
49	C₂×#13093994	C₂²	1	2	yes	complemented
50	C₂×#13093994	C₂²	1	16	yes	complemented
51	C₂×#13093993	C₂²	1	2	yes	complemented
52	C₂×#13093992	C₂²	1	4	yes	—
53	C₂×#13093992	C₂²	1	2	yes	complemented
54	C₂×#13093992	C₂²	1	2	yes	complemented
55	C₂×#13093992	C₂²	1	16	yes	complemented
56	C₂×#13093992	C₂²	1	2	yes	complemented
57	#15689596	C₂²	1	16	yes	complemented
58	C₂×C₄×D₁₈₈	C₂²	1	4	yes	complemented
59	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
60	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
61	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
62	C₂×#13093981	C₂²	1	4	yes	complemented
63	C₂×#13093980	C₂²	1	2	yes	complemented
64	C₂²×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
65	C₂²×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
66	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
67	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
68	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	complemented
69	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
70	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
71	C₂×C₂²⋊C₄×D₄₇	C₂²	1	16	yes	complemented
72	C₂×C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
73	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
74	C₄₇×#518	C₂²	1	16	yes	complemented
75	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	complemented
76	C₂×C₄×D₄×C₄₇	C₂²	1	4	yes	complemented
77	C₂×#117×C₄₇	C₂²	1	2	yes	complemented
78	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
79	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
80	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	complemented
81	C₂⁴×D₄₇	—	2	8	no	—
82	C₂⁴×D₄₇	—	4	8	no	—
83	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
84	C₂⁴×D₄₇	C₂³	1	2	yes	—
85	C₂⁴×D₄₇	C₂³	1	2	yes	—
86	C₂⁴×D₄₇	C₂³	1	8	yes	—
87	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
88	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
89	C₂×#10625350	—	4	16	no	—
90	C₂×#10625350	C₂³	1	32	yes	complemented
91	C₂²×Dic₉₄	C₂³	1	4	yes	complemented
92	C₂²×D₁₈₈	—	4	8	no	—
93	C₂²×D₁₈₈	C₂³	1	4	yes	—
94	C₂²×D₁₈₈	C₂³	1	4	yes	—
95	C₂²×D₁₈₈	C₂³	1	16	yes	complemented
96	C₂²×C₂²⋊D₄₇	—	2	8	no	—
97	C₂²×C₂²⋊D₄₇	—	4	8	no	—
98	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
99	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
100	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
101	C₂²×C₂²⋊D₄₇	C₂³	1	8	yes	—
102	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
103	C₂²×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
104	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	complemented
105	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
106	C₂³×Dic₄₇	C₂³	1	2	yes	—
107	C₂³×Dic₄₇	C₂³	1	2	yes	—
108	C₂²×C₄×D₄₇	—	4	8	no	—
109	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
110	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
111	C₂²×C₄×D₄₇	C₂³	1	16	yes	complemented
112	C₂²×C₄×D₄₇	C₂³	1	4	yes	complemented
113	#13094019	C₂³	1	32	yes	complemented
114	#13094018	C₂³	1	32	yes	complemented
115	#13094012	C₂³	1	32	yes	complemented
116	#13094010	C₂³	1	32	yes	complemented
117	#13094009	C₂³	1	32	yes	complemented
118	#13094009	C₂³	1	32	yes	complemented
119	#13094007	C₂³	1	32	yes	complemented
120	#13094007	C₂³	1	16	yes	complemented
121	#13094006	C₂³	1	32	yes	complemented
122	#13094005	C₂³	1	16	yes	complemented
123	#13094003	C₂³	1	32	yes	complemented
124	#13094002	C₂³	1	32	yes	complemented
125	#13094001	C₂³	1	32	yes	complemented
126	#13094001	C₂³	1	32	yes	complemented
127	#13093998	C₂³	1	32	yes	complemented
128	#13093997	C₂³	1	32	yes	complemented
129	#13093997	C₂³	1	32	yes	complemented
130	#13093996	C₂³	1	32	yes	complemented
131	#13093994	C₂³	1	32	yes	—
132	#13093994	C₂³	1	16	yes	complemented
133	#13093994	C₂³	1	16	yes	complemented
134	#13093993	C₂³	1	16	yes	complemented
135	#13093992	C₂³	1	32	yes	—
136	#13093992	C₂³	1	16	yes	complemented
137	#13093992	C₂³	1	16	yes	complemented
138	#13093992	C₂³	1	16	yes	complemented
139	C₄×D₁₈₈	C₂³	1	32	yes	complemented
140	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
141	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
142	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
143	#13093981	C₂³	1	32	yes	complemented
144	#13093980	C₂³	1	16	yes	complemented
145	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	complemented
146	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
147	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
148	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
149	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	complemented
150	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
151	C₂×C₂²⋊Dic₄₇	C₂³	1	8	yes	—
152	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
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	4	yes	complemented
157	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
158	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
159	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
160	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
161	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
162	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
163	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	complemented
164	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	complemented
165	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	complemented
166	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	complemented
167	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	complemented
168	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	complemented
169	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	complemented
170	C₂²⋊C₄×D₄₇	C₂³	1	16	yes	complemented
171	C₂×C₄×Dic₄₇	C₂³	1	4	yes	complemented
172	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
173	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
174	C₂²×D₄×C₄₇	—	2	8	no	—
175	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
176	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
177	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
178	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
179	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
180	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
181	C₂³×C₄×C₄₇	C₂³	1	4	yes	complemented
182	C₄×D₄×C₄₇	C₂³	1	32	yes	complemented
183	C₄×D₄×C₄₇	C₂³	1	32	yes	complemented
184	#117×C₄₇	C₂³	1	16	yes	complemented
185	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	complemented
186	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
187	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
189	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
192	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	complemented
193	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	complemented
194	C₂×C₄²×C₄₇	C₂³	1	4	yes	complemented
195	C₂⁴×C₄₇	—	2	4	no	—
196	C₂⁴×C₄₇	—	4	4	no	—
197	C₂⁴×C₄₇	—	4	4	no	—
198	C₂⁴×C₄₇	#41	1	8	yes	complemented
199	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
200	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
201	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
202	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
203	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
204	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
205	C₂³×D₄₇	—	2	4	no	—
206	C₂³×D₄₇	—	2	8	no	—
207	C₂³×D₄₇	—	2	8	no	—
208	C₂³×D₄₇	—	2	8	no	—
209	C₂³×D₄₇	—	2	4	no	—
210	C₂³×D₄₇	—	2	32	no	—
211	C₂³×D₄₇	—	2	4	no	—
212	C₂³×D₄₇	—	2	8	no	—
213	C₂³×D₄₇	—	2	8	no	—
214	C₂³×D₄₇	—	4	32	no	—
215	C₂³×D₄₇	—	4	4	no	—
216	C₂³×D₄₇	—	4	4	no	—
217	C₂³×D₄₇	—	4	4	no	—
218	C₂³×D₄₇	—	4	4	no	—
219	C₂³×D₄₇	—	4	64	no	—
220	C₂³×D₄₇	C₂⁴	1	2	yes	—
221	C₂³×D₄₇	C₂⁴	1	2	yes	—
222	C₂³×D₄₇	C₂⁴	1	4	yes	—
223	C₂³×D₄₇	C₂⁴	1	8	yes	—
224	C₂³×D₄₇	C₂⁴	1	8	yes	—
225	C₂³×D₄₇	C₂⁴	1	2	yes	—
226	C₂³×D₄₇	C₂⁴	1	4	yes	—
227	C₂³×D₄₇	C₂⁴	1	4	yes	—
228	C₂×D₄×C₄₇	—	2	8	no	—
229	C₂×D₄×C₄₇	—	2	8	no	—
230	C₂×D₄×C₄₇	—	2	32	no	—
231	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
232	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
233	C₂²×C₄×C₄₇	—	2	4	no	—
234	C₂²×C₄×C₄₇	—	4	4	no	—
235	C₂²×C₄×C₄₇	—	4	4	no	—
236	C₂²×C₄×C₄₇	—	4	8	no	—
237	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
239	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
240	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
241	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
242	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
243	C₂²×C₄×C₄₇	C₂⁴	1	16	yes	complemented
244	C₂×C₂²⋊D₄₇	—	2	8	no	—
245	C₂×C₂²⋊D₄₇	—	2	8	no	—
246	C₂×C₂²⋊D₄₇	—	2	32	no	—
247	C₂×C₂²⋊D₄₇	—	2	16	no	—
248	C₂×C₂²⋊D₄₇	—	4	8	no	—
249	C₂×C₂²⋊D₄₇	—	4	8	no	—
250	C₂×C₂²⋊D₄₇	—	4	32	no	—
251	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
252	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
253	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
254	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
255	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	complemented
256	C₂²×Dic₄₇	—	2	4	no	—
257	C₂²×Dic₄₇	—	4	4	no	—
258	C₂²×Dic₄₇	—	4	4	no	—
259	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
260	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
261	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
262	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
263	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
264	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
265	#10625350	—	4	64	no	—
266	C₂×D₁₈₈	—	2	16	no	—
267	C₂×D₁₈₈	—	4	32	no	—
268	C₂×D₁₈₈	—	4	8	no	—
269	C₂×D₁₈₈	C₂⁴	1	16	yes	—
270	C₂×D₁₈₈	C₂⁴	1	16	yes	—
271	C₂×C₄×D₄₇	—	2	16	no	—
272	C₂×C₄×D₄₇	—	4	32	no	—
273	C₂×C₄×D₄₇	—	4	8	no	—
274	C₂×C₄×D₄₇	—	4	8	no	—
275	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
276	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
277	C₂×C₄×D₄₇	C₂⁴	1	16	yes	complemented
278	C₂×Dic₉₄	—	4	8	no	—
279	C₂×Dic₉₄	C₂⁴	1	16	yes	complemented
280	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	complemented
281	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
282	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
283	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
284	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
285	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	complemented
286	C₄²×C₄₇	C₂⁴	1	16	yes	complemented
287	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
288	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
289	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
290	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
291	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	complemented
292	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
293	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
294	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
295	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
296	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
297	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
298	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	complemented
299	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	complemented
300	C₄⋊Dic₄₇	C₂⁴	1	16	yes	complemented
301	Dic₄₇⋊C₄	C₂⁴	1	16	yes	complemented
302	Dic₄₇⋊C₄	C₂⁴	1	16	yes	complemented
303	Dic₄₇⋊C₄	C₂⁴	1	16	yes	complemented
304	Dic₄₇⋊C₄	C₂⁴	1	16	yes	complemented
305	C₄×Dic₄₇	C₂⁴	1	16	yes	complemented
306	C₂³×C₄₇	—	2	4	no	—
307	C₂³×C₄₇	—	2	4	no	—
308	C₂³×C₄₇	—	2	4	no	—
309	C₂³×C₄₇	—	2	4	no	—
310	C₂³×C₄₇	—	2	8	no	—
311	C₂³×C₄₇	—	2	8	no	—
312	C₂³×C₄₇	—	4	16	no	—
313	C₂³×C₄₇	—	4	8	no	—
314	C₂³×C₄₇	—	4	8	no	—
315	C₂³×C₄₇	—	8	8	no	—
316	C₂³×C₄₇	C₂×#41	1	4	yes	—
317	C₂³×C₄₇	C₂×#41	1	4	yes	—
318	C₂³×C₄₇	C₂×#41	1	4	yes	—
319	C₂³×C₄₇	C₂×#41	1	16	yes	complemented
320	C₂³×C₄₇	C₂⁵	1	4	yes	—
321	C₂³×C₄₇	C₂⁵	1	2	yes	—
322	C₂³×C₄₇	C₂⁵	1	2	yes	—
323	C₂³×C₄₇	C₂⁵	1	2	yes	—
324	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
325	C₂²×D₄₇	—	2	32	no	—
326	C₂²×D₄₇	—	2	8	no	—
327	C₂²×D₄₇	—	2	4	no	—
328	C₂²×D₄₇	—	2	4	no	—
329	C₂²×D₄₇	—	2	16	no	—
330	C₂²×D₄₇	—	2	4	no	—
331	C₂²×D₄₇	—	2	16	no	—
332	C₂²×D₄₇	—	2	16	no	—
333	C₂²×D₄₇	—	2	8	no	—
334	C₂²×D₄₇	—	2	4	no	—
335	C₂²×D₄₇	—	2	8	no	—
336	C₂²×D₄₇	—	2	4	no	—
337	C₂²×D₄₇	—	2	4	no	—
338	C₂²×D₄₇	—	2	8	no	—
339	C₂²×D₄₇	—	2	16	no	—
340	C₂²×D₄₇	—	2	16	no	—
341	C₂²×D₄₇	—	4	8	no	—
342	C₂²×D₄₇	—	4	8	no	—
343	C₂²×D₄₇	—	4	8	no	—
344	C₂²×D₄₇	—	4	8	no	—
345	C₂²×D₄₇	—	4	32	no	—
346	C₂²×D₄₇	—	4	32	no	—
347	C₂²×D₄₇	—	4	128	no	—
348	C₂²×D₄₇	—	4	16	no	—
349	C₂²×D₄₇	—	8	8	no	—
350	C₂²×D₄₇	H(5,𝔽₂)	1	8	yes	—
351	C₂²×D₄₇	C₂⁵	1	4	yes	—
352	C₂²×D₄₇	C₂⁵	1	4	yes	—
353	C₂²×D₄₇	C₂⁵	1	4	yes	—
354	D₄×C₄₇	—	2	16	no	—
355	D₄×C₄₇	—	2	16	no	—
356	C₂×C₄×C₄₇	—	2	8	no	—
357	C₂×C₄×C₄₇	—	2	4	no	—
358	C₂×C₄×C₄₇	—	2	8	no	—
359	C₂×C₄×C₄₇	—	2	8	no	—
360	C₂×C₄×C₄₇	—	4	8	no	—
361	C₂×C₄×C₄₇	—	4	8	no	—
362	C₂×C₄×C₄₇	—	4	16	no	—
363	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
364	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
365	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
366	C₂²⋊D₄₇	—	2	16	no	—
367	C₂²⋊D₄₇	—	2	16	no	—
368	C₂²⋊D₄₇	—	2	32	no	—
369	C₂²⋊D₄₇	—	4	16	no	—
370	C₂²⋊D₄₇	—	4	16	no	—
371	C₂×Dic₄₇	—	2	8	no	—
372	C₂×Dic₄₇	—	2	4	no	—
373	C₂×Dic₄₇	—	2	8	no	—
374	C₂×Dic₄₇	—	2	8	no	—
375	C₂×Dic₄₇	—	4	8	no	—
376	C₂×Dic₄₇	—	4	8	no	—
377	C₂×Dic₄₇	C₂⁵	1	4	yes	—
378	C₂×Dic₄₇	C₂⁵	1	8	yes	—
379	C₂×Dic₄₇	C₂⁵	1	8	yes	—
380	D₁₈₈	—	2	32	no	—
381	D₁₈₈	—	4	16	no	—
382	C₄×D₄₇	—	2	32	no	—
383	C₄×D₄₇	—	4	16	no	—
384	C₄×D₄₇	—	4	16	no	—
385	Dic₉₄	—	4	16	no	—
386	C₂×#3490	—	47	1	no	maximal, Sylow
387	C₂²×C₄₇	—	2	4	no	—
388	C₂²×C₄₇	—	2	4	no	—
389	C₂²×C₄₇	—	2	4	no	—
390	C₂²×C₄₇	—	2	8	no	—
391	C₂²×C₄₇	—	2	8	no	—
392	C₂²×C₄₇	—	2	8	no	—
393	C₂²×C₄₇	—	2	4	no	—
394	C₂²×C₄₇	—	2	8	no	—
395	C₂²×C₄₇	—	4	16	no	—
396	C₂²×C₄₇	—	4	8	no	—
397	C₂²×C₄₇	—	8	8	no	—
398	C₂²×C₄₇	C₂²×#41	1	4	yes	—
399	C₂²×C₄₇	C₂²×#41	1	4	yes	—
400	C₂²×C₄₇	C₂²×#41	1	4	yes	—
401	C₂²×C₄₇	C₂²×#41	1	2	yes	—
402	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
403	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
404	C₂×D₄₇	—	2	32	no	—
405	C₂×D₄₇	—	2	4	no	—
406	C₂×D₄₇	—	2	4	no	—
407	C₂×D₄₇	—	2	16	no	—
408	C₂×D₄₇	—	2	4	no	—
409	C₂×D₄₇	—	2	4	no	—
410	C₂×D₄₇	—	2	8	no	—
411	C₂×D₄₇	—	2	4	no	—
412	C₂×D₄₇	—	2	4	no	—
413	C₂×D₄₇	—	4	32	no	—
414	C₂×D₄₇	—	4	32	no	—
415	C₂×D₄₇	—	4	16	no	—
416	C₂×D₄₇	—	4	8	no	—
417	C₂×D₄₇	—	4	8	no	—
418	C₂×D₄₇	—	8	8	no	—
419	C₂×D₄₇	C₂×H(5,𝔽₂)	1	8	yes	—
420	C₄×C₄₇	—	2	4	no	—
421	C₄×C₄₇	—	2	8	no	—
422	C₄×C₄₇	—	2	8	no	—
423	Dic₄₇	—	2	4	no	—
424	Dic₄₇	—	2	8	no	—
425	Dic₄₇	—	2	8	no	—
426	#3490	—	47	32	no	—
427	C₂×#551	—	47	4	no	—
428	C₂×#551	—	47	4	no	—
429	C₂×#546	—	47	4	no	—
430	C₂×#546	—	47	4	no	—
431	C₂×#543	—	47	1	no	—
432	C₂×#538	—	47	4	no	—
433	C₂×#534	—	47	1	no	—
434	C₂×#525	—	47	4	no	—
435	C₂²×#120	—	47	1	no	—
436	C₂²×#120	—	47	1	no	—
437	C₂×#518	—	47	1	no	—
438	C₂×#518	D₄₇	1	1	yes	characteristic, complemented
439	C₂³×C₂²⋊C₄	—	47	1	no	—
440	C₂×C₄₇	—	2	4	no	—
441	C₂×C₄₇	—	2	4	no	—
442	C₂×C₄₇	—	2	4	no	—
443	C₂×C₄₇	—	4	4	no	—
444	C₂×C₄₇	#3490	1	4	yes	complemented
445	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
446	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	2	yes	—
447	D₄₇	—	2	8	no	—
448	D₄₇	—	4	4	no	—
449	D₄₇	—	4	4	no	—
450	C₂⁶	—	47	1	no	—
451	C₂²×#41	—	47	4	no	—
452	C₂³×D₄	—	47	1	no	—
453	C₂³×D₄	—	47	2	no	—
454	C₂³×D₄	—	47	2	no	—
455	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
456	C₂⁴×C₄	—	47	2	no	—
457	#551	—	47	64	no	—
458	#551	—	47	64	no	—
459	#546	—	47	64	no	—
460	#546	—	47	64	no	—
461	#543	—	47	16	no	—
462	#538	—	47	64	no	—
463	#534	—	47	16	no	—
464	C₂×#126	—	47	4	no	—
465	C₂×#126	—	47	4	no	—
466	C₂×#124	—	47	4	no	—
467	C₂×#124	—	47	4	no	—
468	#525	—	47	64	no	—
469	C₂×#123	—	47	2	no	—
470	C₂×#123	—	47	2	no	—
471	C₂×#123	—	47	4	no	—
472	C₂×#123	—	47	4	no	—
473	C₂×#123	—	47	4	no	—
474	C₂×#123	—	47	4	no	—
475	C₂×C₂²⋊Q₈	—	47	4	no	—
476	C₂×C₂²⋊Q₈	—	47	4	no	—
477	C₂×C₂²⋊Q₈	—	47	4	no	—
478	C₂×C₂²⋊Q₈	—	47	4	no	—
479	C₂×#121	—	47	4	no	—
480	C₂×#121	—	47	4	no	—
481	C₂×#121	—	47	4	no	—
482	C₂×#121	—	47	4	no	—
483	C₂×#120	—	47	2	no	—
484	C₂×#120	—	47	2	no	—
485	C₂×#120	—	47	2	no	—
486	C₂×#120	—	47	4	no	—
487	C₂×#120	—	47	16	no	—
488	C₂×#120	—	47	2	no	—
489	C₂×#120	—	47	2	no	—
490	C₂×#120	—	47	2	no	—
491	C₂×#120	—	47	4	no	—
492	C₂×#120	—	47	16	no	—
493	#518	—	47	16	no	—
494	#518	C₂×D₄₇	1	16	yes	complemented
495	C₂×C₄×D₄	—	47	4	no	—
496	C₂×C₄×D₄	—	47	4	no	—
497	C₂×C₄×D₄	—	47	4	no	—
498	C₂×C₄×D₄	—	47	4	no	—
499	C₂×C₄×D₄	C₂×D₄₇	1	4	yes	complemented
500	C₂×C₄×D₄	C₂×D₄₇	1	4	yes	complemented
501	C₂×#117	—	47	2	no	—
502	C₂×#117	—	47	4	no	—
503	C₂×#117	C₂×D₄₇	1	2	yes	complemented
504	C₂²×C₂²⋊C₄	—	47	1	no	—
505	C₂²×C₂²⋊C₄	—	47	1	no	—
506	C₂²×C₂²⋊C₄	—	47	2	no	—
507	C₂²×C₂²⋊C₄	—	47	2	no	—
508	C₂²×C₂²⋊C₄	—	47	2	no	—
509	C₂²×C₂²⋊C₄	—	47	4	no	—
510	C₂²×C₂²⋊C₄	—	47	4	no	—
511	C₂²×C₂²⋊C₄	—	47	16	no	—
512	C₂²×C₂²⋊C₄	—	47	2	no	—
513	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
514	C₂²×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
515	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	complemented
516	C₄₇	C₂×#3490	1	1	yes	characteristic, complemented, Sylow
517	C₂⁵	—	47	1	no	—
518	C₂⁵	—	47	2	no	—
519	C₂⁵	—	47	2	no	—
520	C₂⁵	—	47	8	no	—
521	C₂⁵	—	47	1	no	—
522	C₂⁵	—	47	1	no	—
523	C₂⁵	—	94	8	no	—
524	C₂⁵	—	188	8	no	—
525	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
526	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
527	C₂×#41	—	47	32	no	—
528	C₂×#41	—	188	16	no	—
529	C₂²×Q₈	—	47	4	no	—
530	C₂²×D₄	—	2	8	no	—
531	C₂²×D₄	—	47	2	no	—
532	C₂²×D₄	—	47	2	no	—
533	C₂²×D₄	—	47	4	no	—
534	C₂²×D₄	—	47	8	no	—
535	C₂²×D₄	—	47	4	no	—
536	C₂²×D₄	—	47	4	no	—
537	C₂²×D₄	—	47	16	no	—
538	C₂²×D₄	—	47	4	no	—
539	C₂²×D₄	—	47	4	no	—
540	C₂²×D₄	—	47	16	no	—
541	C₂²×D₄	—	94	8	no	—
542	C₂²×D₄	—	188	8	no	—
543	C₂²×D₄	—	188	8	no	—
544	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
545	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
546	C₂²×D₄	C₂²×D₄₇	1	8	yes	—
547	C₂³×C₄	—	47	1	no	—
548	C₂³×C₄	—	47	2	no	—
549	C₂³×C₄	—	47	2	no	—
550	C₂³×C₄	—	47	4	no	—
551	C₂³×C₄	—	47	4	no	—
552	C₂³×C₄	—	47	16	no	—
553	C₂³×C₄	—	47	4	no	—
554	C₂³×C₄	—	188	8	no	—
555	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
556	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
557	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
558	C₂³×C₄	C₂²×D₄₇	1	4	yes	complemented
559	#126	—	47	32	no	—
560	#126	—	47	32	no	—
561	#124	—	47	32	no	—
562	#124	—	47	32	no	—
563	#123	—	47	16	no	—
564	#123	—	47	16	no	—
565	#123	—	47	32	no	—
566	#123	—	47	32	no	—
567	#123	—	47	32	no	—
568	#123	—	47	32	no	—
569	C₂²⋊Q₈	—	47	32	no	—
570	C₂²⋊Q₈	—	47	32	no	—
571	C₂²⋊Q₈	—	47	32	no	—
572	C₂²⋊Q₈	—	47	32	no	—
573	#121	—	47	32	no	—
574	#121	—	47	32	no	—
575	#121	—	47	32	no	—
576	#121	—	47	32	no	—
577	#120	—	47	16	no	—
578	#120	—	47	16	no	—
579	#120	—	47	16	no	—
580	#120	—	47	32	no	—
581	#120	—	47	16	no	—
582	#120	—	47	16	no	—
583	#120	—	47	16	no	—
584	#120	—	47	32	no	—
585	C₄×D₄	—	47	32	no	—
586	C₄×D₄	—	47	32	no	—
587	C₄×D₄	—	47	32	no	—
588	C₄×D₄	—	47	32	no	—
589	C₄×D₄	C₂²×D₄₇	1	32	yes	complemented
590	C₄×D₄	C₂²×D₄₇	1	32	yes	complemented
591	#117	—	47	16	no	—
592	#117	—	47	32	no	—
593	#117	C₂²×D₄₇	1	16	yes	complemented
594	C₂×C₄⋊C₄	—	47	4	no	—
595	C₂×C₄⋊C₄	—	47	4	no	—
596	C₂×C₄⋊C₄	—	47	4	no	—
597	C₂×C₄⋊C₄	—	47	4	no	—
598	C₂×C₄⋊C₄	—	47	4	no	—
599	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	complemented
600	C₂×C₂²⋊C₄	—	47	2	no	—
601	C₂×C₂²⋊C₄	—	47	2	no	—
602	C₂×C₂²⋊C₄	—	47	8	no	—
603	C₂×C₂²⋊C₄	—	47	2	no	—
604	C₂×C₂²⋊C₄	—	47	2	no	—
605	C₂×C₂²⋊C₄	—	47	8	no	—
606	C₂×C₂²⋊C₄	—	47	4	no	—
607	C₂×C₂²⋊C₄	—	47	4	no	—
608	C₂×C₂²⋊C₄	—	47	4	no	—
609	C₂×C₂²⋊C₄	—	47	16	no	—
610	C₂×C₂²⋊C₄	—	47	4	no	—
611	C₂×C₂²⋊C₄	—	47	4	no	—
612	C₂×C₂²⋊C₄	—	47	4	no	—
613	C₂×C₂²⋊C₄	—	47	4	no	—
614	C₂×C₂²⋊C₄	—	47	4	no	—
615	C₂×C₂²⋊C₄	—	47	16	no	—
616	C₂×C₂²⋊C₄	—	47	16	no	—
617	C₂×C₂²⋊C₄	—	47	4	no	—
618	C₂×C₂²⋊C₄	—	47	32	no	—
619	C₂×C₂²⋊C₄	—	47	32	no	—
620	C₂×C₂²⋊C₄	—	47	16	no	—
621	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
624	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
625	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂²×D₄₇	1	8	yes	—
627	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	complemented
628	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	complemented
629	C₂×C₄²	—	47	4	no	—
630	C₂×C₄²	C₂²×D₄₇	1	4	yes	complemented
631	C₂⁴	—	2	4	no	—
632	C₂⁴	—	4	4	no	—
633	C₂⁴	—	4	4	no	—
634	C₂⁴	—	47	2	no	—
635	C₂⁴	—	47	4	no	—
636	C₂⁴	—	47	2	no	—
637	C₂⁴	—	47	2	no	—
638	C₂⁴	—	47	8	no	—
639	C₂⁴	—	47	8	no	—
640	C₂⁴	—	47	4	no	—
641	C₂⁴	—	47	4	no	—
642	C₂⁴	—	94	8	no	—
643	C₂⁴	—	94	8	no	—
644	C₂⁴	—	94	8	no	—
645	C₂⁴	—	94	4	no	—
646	C₂⁴	—	94	4	no	—
647	C₂⁴	—	94	8	no	—
648	C₂⁴	—	94	8	no	—
649	C₂⁴	—	94	4	no	—
650	C₂⁴	—	94	32	no	—
651	C₂⁴	—	188	4	no	—
652	C₂⁴	—	188	4	no	—
653	C₂⁴	—	188	4	no	—
654	C₂⁴	—	188	4	no	—
655	C₂⁴	—	188	32	no	—
656	C₂⁴	—	188	64	no	—
657	C₂⁴	#10625350	1	8	yes	complemented
658	C₂⁴	C₂³×D₄₇	1	2	yes	—
659	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
660	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
661	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
662	C₂⁴	C₂³×D₄₇	1	4	yes	—
663	C₂⁴	C₂³×D₄₇	1	4	yes	—
664	#41	—	188	64	no	—
665	C₂×Q₈	—	47	16	no	—
666	C₂×Q₈	—	188	8	no	—
667	C₂×D₄	—	2	8	no	—
668	C₂×D₄	—	2	8	no	—
669	C₂×D₄	—	2	32	no	—
670	C₂×D₄	—	47	8	no	—
671	C₂×D₄	—	47	8	no	—
672	C₂×D₄	—	47	16	no	—
673	C₂×D₄	—	47	16	no	—
674	C₂×D₄	—	47	16	no	—
675	C₂×D₄	—	47	16	no	—
676	C₂×D₄	—	47	16	no	—
677	C₂×D₄	—	94	16	no	—
678	C₂×D₄	—	94	16	no	—
679	C₂×D₄	—	94	8	no	—
680	C₂×D₄	—	94	8	no	—
681	C₂×D₄	—	94	32	no	—
682	C₂×D₄	—	188	8	no	—
683	C₂×D₄	—	188	32	no	—
684	C₂×D₄	—	188	8	no	—
685	C₂×D₄	—	188	8	no	—
686	C₂×D₄	—	188	32	no	—
687	C₂×D₄	C₂³×D₄₇	1	8	yes	—
688	C₂×D₄	C₂³×D₄₇	1	8	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	4	4	no	—
691	C₂²×C₄	—	4	4	no	—
692	C₂²×C₄	—	4	8	no	—
693	C₂²×C₄	—	47	4	no	—
694	C₂²×C₄	—	47	2	no	—
695	C₂²×C₄	—	47	4	no	—
696	C₂²×C₄	—	47	4	no	—
697	C₂²×C₄	—	47	8	no	—
698	C₂²×C₄	—	47	8	no	—
699	C₂²×C₄	—	47	16	no	—
700	C₂²×C₄	—	47	16	no	—
701	C₂²×C₄	—	47	16	no	—
702	C₂²×C₄	—	94	16	no	—
703	C₂²×C₄	—	94	4	no	—
704	C₂²×C₄	—	188	8	no	—
705	C₂²×C₄	—	188	8	no	—
706	C₂²×C₄	—	188	32	no	—
707	C₂²×C₄	—	188	4	no	—
708	C₂²×C₄	—	188	4	no	—
709	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
710	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
711	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
712	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
713	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
714	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
715	C₂²×C₄	C₂³×D₄₇	1	16	yes	complemented
716	C₄⋊C₄	—	47	16	no	—
717	C₄⋊C₄	—	47	16	no	—
718	C₄⋊C₄	—	47	16	no	—
719	C₄⋊C₄	—	47	16	no	—
720	C₄⋊C₄	—	47	16	no	—
721	C₄⋊C₄	C₂³×D₄₇	1	16	yes	complemented
722	C₂²⋊C₄	—	47	8	no	—
723	C₂²⋊C₄	—	47	8	no	—
724	C₂²⋊C₄	—	47	8	no	—
725	C₂²⋊C₄	—	47	8	no	—
726	C₂²⋊C₄	—	47	16	no	—
727	C₂²⋊C₄	—	47	16	no	—
728	C₂²⋊C₄	—	47	16	no	—
729	C₂²⋊C₄	—	47	16	no	—
730	C₂²⋊C₄	—	47	16	no	—
731	C₂²⋊C₄	—	47	16	no	—
732	C₂²⋊C₄	—	47	16	no	—
733	C₂²⋊C₄	—	47	16	no	—
734	C₂²⋊C₄	—	47	16	no	—
735	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
736	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
737	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
738	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
739	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	complemented
740	C₄²	—	47	16	no	—
741	C₄²	C₂³×D₄₇	1	16	yes	complemented
742	C₂³	—	2	4	no	—
743	C₂³	—	2	4	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	4	no	—
746	C₂³	—	2	8	no	—
747	C₂³	—	2	8	no	—
748	C₂³	—	4	16	no	—
749	C₂³	—	4	8	no	—
750	C₂³	—	4	8	no	—
751	C₂³	—	8	8	no	—
752	C₂³	—	47	8	no	—
753	C₂³	—	47	4	no	—
754	C₂³	—	47	4	no	—
755	C₂³	—	47	4	no	—
756	C₂³	—	94	16	no	—
757	C₂³	—	94	16	no	—
758	C₂³	—	94	16	no	—
759	C₂³	—	94	32	no	—
760	C₂³	—	94	8	no	—
761	C₂³	—	94	4	no	—
762	C₂³	—	94	4	no	—
763	C₂³	—	94	8	no	—
764	C₂³	—	94	4	no	—
765	C₂³	—	94	16	no	—
766	C₂³	—	94	16	no	—
767	C₂³	—	94	8	no	—
768	C₂³	—	94	4	no	—
769	C₂³	—	94	8	no	—
770	C₂³	—	94	4	no	—
771	C₂³	—	94	4	no	—
772	C₂³	—	376	8	no	—
773	C₂³	—	188	8	no	—
774	C₂³	—	188	8	no	—
775	C₂³	—	188	8	no	—
776	C₂³	—	188	8	no	—
777	C₂³	—	188	32	no	—
778	C₂³	—	188	32	no	—
779	C₂³	—	188	16	no	—
780	C₂³	—	188	128	no	—
781	C₂³	C₂×#10625350	1	4	yes	—
782	C₂³	C₂×#10625350	1	4	yes	—
783	C₂³	C₂×#10625350	1	4	yes	—
784	C₂³	C₂×#10625350	1	16	yes	complemented
785	C₂³	C₂⁴×D₄₇	1	4	yes	—
786	C₂³	C₂⁴×D₄₇	1	2	yes	—
787	C₂³	C₂⁴×D₄₇	1	2	yes	—
788	C₂³	C₂⁴×D₄₇	1	2	yes	—
789	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
790	Q₈	—	188	16	no	—
791	D₄	—	2	16	no	—
792	D₄	—	2	16	no	—
793	D₄	—	94	32	no	—
794	D₄	—	94	32	no	—
795	D₄	—	94	16	no	—
796	D₄	—	94	16	no	—
797	D₄	—	188	16	no	—
798	D₄	—	188	16	no	—
799	D₄	—	188	16	no	—
800	C₂×C₄	—	2	8	no	—
801	C₂×C₄	—	2	4	no	—
802	C₂×C₄	—	2	8	no	—
803	C₂×C₄	—	2	8	no	—
804	C₂×C₄	—	4	8	no	—
805	C₂×C₄	—	4	8	no	—
806	C₂×C₄	—	4	16	no	—
807	C₂×C₄	—	47	4	no	—
808	C₂×C₄	—	47	8	no	—
809	C₂×C₄	—	47	8	no	—
810	C₂×C₄	—	94	32	no	—
811	C₂×C₄	—	94	8	no	—
812	C₂×C₄	—	94	4	no	—
813	C₂×C₄	—	94	8	no	—
814	C₂×C₄	—	94	8	no	—
815	C₂×C₄	—	188	16	no	—
816	C₂×C₄	—	188	16	no	—
817	C₂×C₄	—	188	8	no	—
818	C₂×C₄	—	188	8	no	—
819	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
820	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
821	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
822	C₂²	—	2	8	no	—
823	C₂²	—	2	8	no	—
824	C₂²	—	2	8	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	8	no	—
830	C₂²	—	4	16	no	—
831	C₂²	—	4	8	no	—
832	C₂²	—	8	8	no	—
833	C₂²	—	47	8	no	—
834	C₂²	—	94	32	no	—
835	C₂²	—	94	16	no	—
836	C₂²	—	94	4	no	—
837	C₂²	—	94	4	no	—
838	C₂²	—	94	4	no	—
839	C₂²	—	94	4	no	—
840	C₂²	—	94	8	no	—
841	C₂²	—	94	4	no	—
842	C₂²	—	94	4	no	—
843	C₂²	—	376	8	no	—
844	C₂²	—	188	32	no	—
845	C₂²	—	188	32	no	—
846	C₂²	—	188	16	no	—
847	C₂²	—	188	8	no	—
848	C₂²	—	188	8	no	—
849	C₂²	C₂²×#10625350	1	4	yes	—
850	C₂²	C₂²×#10625350	1	4	yes	—
851	C₂²	C₂²×#10625350	1	4	yes	—
852	C₂²	C₂²×#10625350	1	2	yes	—
853	C₂²	H(5,𝔽₂)×D₄₇	1	4	yes	—
854	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
855	C₄	—	2	4	no	—
856	C₄	—	2	8	no	—
857	C₄	—	2	8	no	—
858	C₄	—	94	4	no	—
859	C₄	—	94	8	no	—
860	C₄	—	94	8	no	—
861	C₂	—	2	4	no	—
862	C₂	—	2	4	no	—
863	C₂	—	2	4	no	—
864	C₂	—	4	4	no	—
865	C₂	—	94	8	no	—
866	C₂	—	188	4	no	—
867	C₂	—	188	4	no	—
868	C₂	#20257073	1	4	yes	direct product factor
869	C₂	C₂³×#10625350	1	1	yes	characteristic
870	C₂	C₂×H(5,𝔽₂)×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#518	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#518	D₄₇
hypocenter	C₄₇	C₂×#3490
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. #20257073	C₂	direct (N × H)
2. C₂×#15689802	C₂	semidirect
3. C₂×#15689797	C₂	semidirect
4. C₂×#15689769	C₂	semidirect
5. C₂×#15689763	C₂	semidirect
6. C₂×#15689749	C₂	semidirect
7. C₂×#15689706	C₂	semidirect
8. C₂×#15689682	C₂	semidirect
9. C₂×#15689632	C₂	semidirect
10. C₂²×#13093994	C₂	semidirect
11. C₂²×#13093992	C₂	semidirect
12. C₂×#15689596	C₂	semidirect
13. C₂²×C₂²⋊C₄×D₄₇	C₂	semidirect
14. C₂×C₄₇×#518	C₂	semidirect
16. C₂²×#10625350	C₂²	semidirect
17. C₂³×D₁₈₈	C₂²	semidirect
19. C₂³×C₂²⋊D₄₇	C₂²	semidirect
20. C₂³×C₄×D₄₇	C₂²	semidirect
21. #15689802	C₂²	semidirect
22. #15689797	C₂²	semidirect
23. #15689769	C₂²	semidirect
24. #15689763	C₂²	semidirect
25. #15689749	C₂²	semidirect
26. #15689706	C₂²	semidirect
27. #15689682	C₂²	semidirect
28. C₂×#13094019	C₂²	semidirect
29. C₂×#13094018	C₂²	semidirect
30. C₂×#13094012	C₂²	semidirect
31. C₂×#13094010	C₂²	semidirect
32. #15689632	C₂²	semidirect
33. C₂×#13094009	C₂²	semidirect
34. C₂×#13094009	C₂²	semidirect
35. C₂×#13094007	C₂²	semidirect
36. C₂×#13094007	C₂²	semidirect
37. C₂×#13094006	C₂²	semidirect
38. C₂×#13094005	C₂²	semidirect
39. C₂×#13094003	C₂²	semidirect
40. C₂×#13094002	C₂²	semidirect
41. C₂×#13094001	C₂²	semidirect
42. C₂×#13094001	C₂²	semidirect
43. C₂×#13093998	C₂²	semidirect
44. C₂×#13093997	C₂²	semidirect
45. C₂×#13093997	C₂²	semidirect
46. C₂×#13093996	C₂²	semidirect
48. C₂×#13093994	C₂²	semidirect
49. C₂×#13093994	C₂²	semidirect
50. C₂×#13093994	C₂²	semidirect
51. C₂×#13093993	C₂²	semidirect
53. C₂×#13093992	C₂²	semidirect
54. C₂×#13093992	C₂²	semidirect
55. C₂×#13093992	C₂²	semidirect
56. C₂×#13093992	C₂²	semidirect
57. #15689596	C₂²	semidirect
58. C₂×C₄×D₁₈₈	C₂²	semidirect
59. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
60. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
61. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
62. C₂×#13093981	C₂²	semidirect
63. C₂×#13093980	C₂²	semidirect
66. C₂²×(C₂×D₄₇)⋊C₄	C₂²	semidirect
67. C₂²×(C₂×D₄₇)⋊C₄	C₂²	semidirect
68. C₂²×(C₂×D₄₇)⋊C₄	C₂²	semidirect
69. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
70. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
71. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
72. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
74. C₄₇×#518	C₂²	semidirect
75. C₂×C₄×D₄×C₄₇	C₂²	semidirect
76. C₂×C₄×D₄×C₄₇	C₂²	semidirect
77. C₂×#117×C₄₇	C₂²	semidirect
80. C₂²×C₂²⋊C₄×C₄₇	C₂²	semidirect
90. C₂×#10625350	C₂³	semidirect
91. C₂²×Dic₉₄	C₂³	semidirect
95. C₂²×D₁₈₈	C₂³	semidirect
103. C₂²×C₂²⋊D₄₇	C₂³	semidirect
104. C₂²×C₂²⋊D₄₇	C₂³	semidirect
111. C₂²×C₄×D₄₇	C₂³	semidirect
112. C₂²×C₄×D₄₇	C₂³	semidirect
113. #13094019	C₂³	semidirect
114. #13094018	C₂³	semidirect
115. #13094012	C₂³	semidirect
116. #13094010	C₂³	semidirect
117. #13094009	C₂³	semidirect
118. #13094009	C₂³	semidirect
119. #13094007	C₂³	semidirect
120. #13094007	C₂³	semidirect
121. #13094006	C₂³	semidirect
122. #13094005	C₂³	semidirect
123. #13094003	C₂³	semidirect
124. #13094002	C₂³	semidirect
125. #13094001	C₂³	semidirect
126. #13094001	C₂³	semidirect
127. #13093998	C₂³	semidirect
128. #13093997	C₂³	semidirect
129. #13093997	C₂³	semidirect
130. #13093996	C₂³	semidirect
132. #13093994	C₂³	semidirect
133. #13093994	C₂³	semidirect
134. #13093993	C₂³	semidirect
136. #13093992	C₂³	semidirect
137. #13093992	C₂³	semidirect
138. #13093992	C₂³	semidirect
139. C₄×D₁₈₈	C₂³	semidirect
140. C₄×C₂²⋊D₄₇	C₂³	semidirect
141. C₄×C₂²⋊D₄₇	C₂³	semidirect
142. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
143. #13093981	C₂³	semidirect
144. #13093980	C₂³	semidirect
145. C₂×C₄⋊Dic₄₇	C₂³	semidirect
146. C₂×Dic₄₇⋊C₄	C₂³	semidirect
147. C₂×Dic₄₇⋊C₄	C₂³	semidirect
148. C₂×Dic₄₇⋊C₄	C₂³	semidirect
149. C₂×Dic₄₇⋊C₄	C₂³	semidirect
156. C₂×C₂²⋊Dic₄₇	C₂³	semidirect
163. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
164. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
165. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
166. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
167. C₂×(C₂×D₄₇)⋊C₄	C₂³	semidirect
168. C₂²⋊C₄×D₄₇	C₂³	semidirect
169. C₂²⋊C₄×D₄₇	C₂³	semidirect
170. C₂²⋊C₄×D₄₇	C₂³	semidirect
171. C₂×C₄×Dic₄₇	C₂³	semidirect
181. C₂³×C₄×C₄₇	C₂³	semidirect
182. C₄×D₄×C₄₇	C₂³	semidirect
183. C₄×D₄×C₄₇	C₂³	semidirect
184. #117×C₄₇	C₂³	semidirect
185. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
192. C₂×C₂²⋊C₄×C₄₇	C₂³	semidirect
193. C₂×C₂²⋊C₄×C₄₇	C₂³	semidirect
194. C₂×C₄²×C₄₇	C₂³	semidirect
198. C₂⁴×C₄₇	#41	semidirect
243. C₂²×C₄×C₄₇	C₂⁴	semidirect
255. C₂×C₂²⋊D₄₇	C₂⁴	semidirect
277. C₂×C₄×D₄₇	C₂⁴	semidirect
279. C₂×Dic₉₄	C₂⁴	semidirect
280. C₄⋊C₄×C₄₇	C₂⁴	semidirect
285. C₂²⋊C₄×C₄₇	C₂⁴	semidirect
286. C₄²×C₄₇	C₂⁴	semidirect
291. C₂²⋊Dic₄₇	C₂⁴	semidirect
298. (C₂×D₄₇)⋊C₄	C₂⁴	semidirect
299. (C₂×D₄₇)⋊C₄	C₂⁴	semidirect
300. C₄⋊Dic₄₇	C₂⁴	semidirect
301. Dic₄₇⋊C₄	C₂⁴	semidirect
302. Dic₄₇⋊C₄	C₂⁴	semidirect
303. Dic₄₇⋊C₄	C₂⁴	semidirect
304. Dic₄₇⋊C₄	C₂⁴	semidirect
305. C₄×Dic₄₇	C₂⁴	semidirect
319. C₂³×C₄₇	C₂×#41	semidirect
438. C₂×#518	D₄₇	semidirect
444. C₂×C₄₇	#3490	semidirect
494. #518	C₂×D₄₇	semidirect
499. C₂×C₄×D₄	C₂×D₄₇	semidirect
500. C₂×C₄×D₄	C₂×D₄₇	semidirect
503. C₂×#117	C₂×D₄₇	semidirect
515. C₂²×C₂²⋊C₄	C₂×D₄₇	semidirect
516. C₄₇	C₂×#3490	semidirect
558. C₂³×C₄	C₂²×D₄₇	semidirect
589. C₄×D₄	C₂²×D₄₇	semidirect
590. C₄×D₄	C₂²×D₄₇	semidirect
593. #117	C₂²×D₄₇	semidirect
599. C₂×C₄⋊C₄	C₂²×D₄₇	semidirect
627. C₂×C₂²⋊C₄	C₂²×D₄₇	semidirect
628. C₂×C₂²⋊C₄	C₂²×D₄₇	semidirect
630. C₂×C₄²	C₂²×D₄₇	semidirect
657. C₂⁴	#10625350	semidirect
715. C₂²×C₄	C₂³×D₄₇	semidirect
721. C₄⋊C₄	C₂³×D₄₇	semidirect
739. C₂²⋊C₄	C₂³×D₄₇	semidirect
741. C₄²	C₂³×D₄₇	semidirect
784. C₂³	C₂×#10625350	semidirect
868. C₂	#20257073	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257073	2
C₂×#15689802	2
C₂×#15689797	2
C₂×#15689769	2
C₂×#15689763	2
C₂×#15689749	2
C₂×#15689706	2
C₂×#15689682	2
C₂×#15689632	2
C₂²×#13093994	2
C₂²×#13093992	2
C₂×#15689596	2
C₂²×C₂²⋊C₄×D₄₇	2
C₂×C₄₇×#518	2
C₂×#3490	47

Subgroups — C2×#20257073 #27124188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257073 #27124188