Subgroups — C₂×#20257621 #27123511

Order 12032.

8890 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257621	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689862	C₂	1	2	yes	maximal, complemented
3	C₂×#15689860	C₂	1	2	yes	maximal, complemented
4	C₂×#15689820	C₂	1	2	yes	maximal, complemented
5	C₂×#15689817	C₂	1	2	yes	maximal, complemented
6	C₂×#15689758	C₂	1	2	yes	maximal, complemented
7	C₂×#15689757	C₂	1	2	yes	maximal, complemented
8	C₂×D₄×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
9	C₂×#15689755	C₂	1	2	yes	maximal, complemented
10	C₂×#15689726	C₂	1	2	yes	maximal, complemented
11	C₂×#15689707	C₂	1	4	yes	maximal, complemented
12	C₂×#15689687	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#15689683	C₂	1	4	yes	maximal, complemented
14	C₂×#15689630	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#121×D₄₇	C₂	1	2	yes	maximal, complemented
16	C₂×C₄₇×#535	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
18	C₂³×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
19	C₂²×D₄×D₄₇	C₂²	1	4	yes	complemented
20	C₂²×D₄×D₄₇	C₂²	1	2	yes	complemented
21	C₂²×D₄×D₄₇	C₂²	1	4	yes	complemented
22	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
23	#15689862	C₂²	1	32	yes	complemented
24	#15689860	C₂²	1	32	yes	complemented
25	#15689820	C₂²	1	32	yes	complemented
26	#15689817	C₂²	1	32	yes	complemented
27	#15689758	C₂²	1	32	yes	complemented
28	#15689757	C₂²	1	32	yes	complemented
29	D₄×C₂²⋊D₄₇	C₂²	1	32	yes	complemented
30	#15689755	C₂²	1	32	yes	complemented
31	#15689726	C₂²	1	32	yes	complemented
32	#15689707	C₂²	1	64	yes	complemented
33	#15689687	C₂²	1	16	yes	complemented
34	#15689683	C₂²	1	64	yes	complemented
35	C₂×#13094020	C₂²	1	2	yes	complemented
36	C₂×#13094020	C₂²	1	2	yes	complemented
37	C₂×#13094018	C₂²	1	4	yes	complemented
38	C₂×#13094017	C₂²	1	4	yes	complemented
39	C₂×#13094015	C₂²	1	2	yes	complemented
40	C₂×#13094013	C₂²	1	2	yes	complemented
41	#15689630	C₂²	1	16	yes	complemented
42	C₂×#13094008	C₂²	1	4	yes	complemented
43	C₂×#13094006	C₂²	1	4	yes	complemented
44	C₂×#13094006	C₂²	1	4	yes	complemented
45	C₂×#13094005	C₂²	1	1	yes	characteristic, complemented
46	C₂×#13094005	C₂²	1	1	yes	characteristic, complemented
47	C₂×#13094005	C₂²	1	4	yes	complemented
48	C₂×#13094000	C₂²	1	2	yes	complemented
49	C₂×#13093999	C₂²	1	2	yes	complemented
50	C₂×#13093998	C₂²	1	2	yes	complemented
51	C₂×#13093998	C₂²	1	2	yes	complemented
52	C₂×#13093997	C₂²	1	4	yes	complemented
53	C₂×#13093997	C₂²	1	4	yes	complemented
54	C₂×#13093997	C₂²	1	4	yes	complemented
55	C₂×#13093996	C₂²	1	4	yes	complemented
56	C₂×#13093996	C₂²	1	4	yes	complemented
57	C₂×#13093996	C₂²	1	4	yes	complemented
58	C₂×#13093995	C₂²	1	2	yes	complemented
59	C₂×#13093995	C₂²	1	4	yes	complemented
60	C₂×#13093995	C₂²	1	4	yes	complemented
61	C₂×#13093995	C₂²	1	2	yes	complemented
62	#121×D₄₇	C₂²	1	32	yes	complemented
63	C₂×#13093994	C₂²	1	4	yes	complemented
64	C₂×#13093993	C₂²	1	4	yes	complemented
65	C₂×#13093992	C₂²	1	1	yes	characteristic, complemented
66	C₂×#13093992	C₂²	1	4	yes	complemented
67	C₂×#13093992	C₂²	1	4	yes	complemented
68	C₂×#13093992	C₂²	1	1	yes	characteristic, complemented
69	C₂×#13093992	C₂²	1	2	yes	complemented
70	C₂×#13093992	C₂²	1	2	yes	complemented
71	C₂×C₄×D₁₈₈	C₂²	1	4	yes	complemented
72	C₂×D₄×Dic₄₇	C₂²	1	2	yes	complemented
73	C₂×#13093986	C₂²	1	2	yes	complemented
74	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
75	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
76	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
77	C₂×#13093983	C₂²	1	1	yes	characteristic, complemented
78	C₂×#13093983	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
80	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	complemented
81	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
82	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
83	C₄₇×#535	C₂²	1	16	yes	complemented
84	C₂×#127×C₄₇	C₂²	1	2	yes	complemented
85	C₂×#124×C₄₇	C₂²	1	2	yes	complemented
86	C₂×#121×C₄₇	C₂²	1	2	yes	complemented
87	C₂×#121×C₄₇	C₂²	1	2	yes	complemented
88	C₂×#120×C₄₇	C₂²	1	2	yes	complemented
89	C₂×#120×C₄₇	C₂²	1	2	yes	complemented
90	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
92	C₂⁴×D₄₇	C₂³	1	4	yes	—
93	C₂⁴×D₄₇	C₂³	1	2	yes	—
94	C₂²×D₁₈₈	—	4	4	no	—
95	C₂²×D₁₈₈	C₂³	1	2	yes	—
96	C₂²×D₁₈₈	C₂³	1	4	yes	—
97	C₂²×D₁₈₈	C₂³	1	2	yes	—
98	C₂²×D₁₈₈	C₂³	1	8	yes	complemented
99	C₂²×C₂²⋊D₄₇	—	4	16	no	—
100	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
101	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
102	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
103	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
104	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
105	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
106	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
107	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
108	C₂²×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
109	C₂×D₄×D₄₇	—	4	8	no	—
110	C₂×D₄×D₄₇	—	4	16	no	—
111	C₂×D₄×D₄₇	—	4	16	no	—
112	C₂×D₄×D₄₇	C₂³	1	32	yes	complemented
113	C₂×D₄×D₄₇	C₂³	1	16	yes	complemented
114	C₂×D₄×D₄₇	C₂³	1	32	yes	complemented
115	C₂³×Dic₄₇	C₂³	1	4	yes	—
116	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
117	C₂²×C₄×D₄₇	—	4	4	no	—
118	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
119	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
120	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
121	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
122	C₂²×C₄×D₄₇	C₂³	1	8	yes	complemented
123	#13094020	C₂³	1	16	yes	complemented
124	#13094020	C₂³	1	16	yes	complemented
125	#13094018	C₂³	1	32	yes	complemented
126	#13094017	C₂³	1	32	yes	complemented
127	#13094015	C₂³	1	16	yes	complemented
128	#13094013	C₂³	1	16	yes	complemented
129	#13094008	C₂³	1	32	yes	complemented
130	#13094006	C₂³	1	32	yes	complemented
131	#13094006	C₂³	1	32	yes	complemented
132	#13094005	C₂³	1	32	yes	complemented
133	#13094005	C₂³	1	8	yes	complemented
134	#13094005	C₂³	1	8	yes	complemented
135	#13094000	C₂³	1	16	yes	complemented
136	#13093999	C₂³	1	16	yes	complemented
137	#13093998	C₂³	1	16	yes	complemented
138	#13093998	C₂³	1	16	yes	complemented
139	#13093997	C₂³	1	32	yes	complemented
140	#13093997	C₂³	1	32	yes	complemented
141	#13093997	C₂³	1	32	yes	complemented
142	#13093996	C₂³	1	32	yes	complemented
143	#13093996	C₂³	1	32	yes	complemented
144	#13093996	C₂³	1	32	yes	complemented
145	#13093995	C₂³	1	16	yes	complemented
146	#13093995	C₂³	1	32	yes	complemented
147	#13093995	C₂³	1	32	yes	complemented
148	#13093995	C₂³	1	16	yes	complemented
149	#13093994	C₂³	1	32	yes	complemented
150	#13093993	C₂³	1	32	yes	complemented
151	#13093992	C₂³	1	8	yes	complemented
152	#13093992	C₂³	1	32	yes	complemented
153	#13093992	C₂³	1	32	yes	complemented
154	#13093992	C₂³	1	8	yes	complemented
155	#13093992	C₂³	1	16	yes	complemented
156	#13093992	C₂³	1	16	yes	complemented
157	C₄×D₁₈₈	C₂³	1	32	yes	complemented
158	D₄×Dic₄₇	C₂³	1	16	yes	complemented
159	#13093986	C₂³	1	16	yes	complemented
160	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
161	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
162	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	complemented
163	#13093983	C₂³	1	8	yes	complemented
164	#13093983	C₂³	1	8	yes	complemented
165	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
166	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
167	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
168	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
169	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
170	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
171	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
172	C₄⋊C₄×D₄₇	C₂³	1	16	yes	complemented
173	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
174	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
175	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
176	C₂×C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
177	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
179	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
180	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
181	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
182	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
183	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
184	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
185	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
186	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	complemented
187	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
188	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
189	C₂⁵×C₄₇	C₂³	1	2	yes	—
190	C₂×#41×C₄₇	—	4	4	no	—
191	C₂×#41×C₄₇	C₂³	1	8	yes	complemented
192	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
193	C₂²×D₄×C₄₇	—	4	4	no	—
194	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
195	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
196	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
197	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
198	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
199	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
200	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
201	C₂²×D₄×C₄₇	C₂³	1	8	yes	complemented
202	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
205	#127×C₄₇	C₂³	1	16	yes	complemented
206	#124×C₄₇	C₂³	1	16	yes	complemented
207	#121×C₄₇	C₂³	1	16	yes	complemented
208	#121×C₄₇	C₂³	1	16	yes	complemented
209	#120×C₄₇	C₂³	1	16	yes	complemented
210	#120×C₄₇	C₂³	1	16	yes	complemented
211	#117×C₄₇	C₂³	1	8	yes	complemented
212	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
215	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
216	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
217	C₂⁴×C₄₇	—	4	4	no	—
218	C₂⁴×C₄₇	—	4	8	no	—
219	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
221	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
222	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
223	C₂⁴×C₄₇	C₂⁴	1	8	yes	—
224	C₂³×D₄₇	—	2	8	no	—
225	C₂³×D₄₇	—	2	16	no	—
226	C₂³×D₄₇	—	4	2	no	—
227	C₂³×D₄₇	—	4	8	no	—
228	C₂³×D₄₇	—	4	8	no	—
229	C₂³×D₄₇	—	4	8	no	—
230	C₂³×D₄₇	—	4	4	no	—
231	C₂³×D₄₇	C₂⁴	1	4	yes	—
232	C₂³×D₄₇	C₂⁴	1	4	yes	—
233	C₂³×D₄₇	C₂⁴	1	2	yes	—
234	C₂³×D₄₇	C₂⁴	1	16	yes	—
235	C₂³×D₄₇	C₂⁴	1	8	yes	—
236	#41×C₄₇	—	4	16	no	—
237	C₂×Q₈×C₄₇	—	4	2	no	—
238	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
239	C₂×D₄×C₄₇	—	2	8	no	—
240	C₂×D₄×C₄₇	—	4	16	no	—
241	C₂×D₄×C₄₇	—	4	4	no	—
242	C₂×D₄×C₄₇	—	4	2	no	—
243	C₂×D₄×C₄₇	—	4	2	no	—
244	C₂×D₄×C₄₇	—	4	2	no	—
245	C₂×D₄×C₄₇	—	4	8	no	—
246	C₂×D₄×C₄₇	—	4	8	no	—
247	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
248	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
249	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
250	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
251	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
252	C₂×D₄×C₄₇	C₂⁴	1	8	yes	—
253	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
254	C₂²×C₄×C₄₇	—	2	4	no	—
255	C₂²×C₄×C₄₇	—	2	4	no	—
256	C₂²×C₄×C₄₇	—	2	4	no	—
257	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
262	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
265	C₂×C₂²⋊D₄₇	—	2	8	no	—
266	C₂×C₂²⋊D₄₇	—	2	16	no	—
267	C₂×C₂²⋊D₄₇	—	2	8	no	—
268	C₂×C₂²⋊D₄₇	—	4	8	no	—
269	C₂×C₂²⋊D₄₇	—	4	8	no	—
270	C₂×C₂²⋊D₄₇	—	4	8	no	—
271	C₂×C₂²⋊D₄₇	—	4	8	no	—
272	C₂×C₂²⋊D₄₇	—	4	8	no	—
273	C₂×C₂²⋊D₄₇	—	4	64	no	—
274	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
275	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
276	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
277	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
278	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
279	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
280	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
281	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
282	C₂²×Dic₄₇	—	4	2	no	—
283	C₂²×Dic₄₇	—	4	8	no	—
284	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
285	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
286	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
287	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
288	C₂²×Dic₄₇	C₂⁴	1	16	yes	—
289	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
290	D₄×D₄₇	—	4	32	no	—
291	D₄×D₄₇	—	4	64	no	—
292	D₄×D₄₇	—	4	64	no	—
293	C₂×D₁₈₈	—	2	16	no	—
294	C₂×D₁₈₈	—	2	8	no	—
295	C₂×D₁₈₈	—	4	16	no	—
296	C₂×D₁₈₈	—	4	4	no	—
297	C₂×D₁₈₈	C₂⁴	1	8	yes	—
298	C₂×D₁₈₈	C₂⁴	1	16	yes	—
299	C₂×D₁₈₈	C₂⁴	1	8	yes	—
300	C₂×C₄×D₄₇	—	2	8	no	—
301	C₂×C₄×D₄₇	—	4	16	no	—
302	C₂×C₄×D₄₇	—	4	4	no	—
303	C₂×C₄×D₄₇	—	4	8	no	—
304	C₂×C₄×D₄₇	—	4	8	no	—
305	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
306	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
307	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
308	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
309	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
310	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
311	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
312	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
313	C₄²×C₄₇	C₂⁴	1	8	yes	—
314	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
315	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
316	C₂²⋊Dic₄₇	C₂⁴	1	4	yes	—
317	C₂²⋊Dic₄₇	C₂⁴	1	4	yes	—
318	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
319	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
320	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
321	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
322	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
323	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
324	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
325	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
326	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
327	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
328	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
329	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
330	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
331	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
332	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
333	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
334	C₄×Dic₄₇	C₂⁴	1	8	yes	—
335	C₄×Dic₄₇	C₂⁴	1	8	yes	—
336	C₂³×C₄₇	—	2	8	no	—
337	C₂³×C₄₇	—	2	2	no	—
338	C₂³×C₄₇	—	2	4	no	—
339	C₂³×C₄₇	—	2	8	no	—
340	C₂³×C₄₇	—	2	4	no	—
341	C₂³×C₄₇	—	2	4	no	—
342	C₂³×C₄₇	—	2	8	no	—
343	C₂³×C₄₇	—	2	2	no	—
344	C₂³×C₄₇	—	2	2	no	—
345	C₂³×C₄₇	—	4	16	no	—
346	C₂³×C₄₇	—	4	8	no	—
347	C₂³×C₄₇	—	8	16	no	—
348	C₂³×C₄₇	C₂⁵	1	2	yes	—
349	C₂³×C₄₇	C₂⁵	1	8	yes	—
350	C₂³×C₄₇	C₂⁵	1	2	yes	—
351	C₂³×C₄₇	C₂⁵	1	2	yes	—
352	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
353	C₂²×D₄₇	—	2	4	no	—
354	C₂²×D₄₇	—	2	4	no	—
355	C₂²×D₄₇	—	2	8	no	—
356	C₂²×D₄₇	—	2	8	no	—
357	C₂²×D₄₇	—	2	8	no	—
358	C₂²×D₄₇	—	2	16	no	—
359	C₂²×D₄₇	—	2	32	no	—
360	C₂²×D₄₇	—	4	4	no	—
361	C₂²×D₄₇	—	4	16	no	—
362	C₂²×D₄₇	—	4	8	no	—
363	C₂²×D₄₇	—	4	16	no	—
364	C₂²×D₄₇	—	4	16	no	—
365	C₂²×D₄₇	—	4	16	no	—
366	C₂²×D₄₇	—	8	32	no	—
367	C₂²×D₄₇	—	8	16	no	—
368	C₂²×D₄₇	H(5,𝔽₂)	1	8	yes	—
369	C₂²×D₄₇	C₂⁵	1	8	yes	—
370	C₂²×D₄₇	C₂⁵	1	4	yes	—
371	Q₈×C₄₇	—	4	4	no	—
372	D₄×C₄₇	—	2	16	no	—
373	D₄×C₄₇	—	4	16	no	—
374	D₄×C₄₇	—	4	16	no	—
375	D₄×C₄₇	—	4	8	no	—
376	D₄×C₄₇	—	4	4	no	—
377	D₄×C₄₇	—	4	4	no	—
378	D₄×C₄₇	—	4	4	no	—
379	C₂×C₄×C₄₇	—	2	8	no	—
380	C₂×C₄×C₄₇	—	2	2	no	—
381	C₂×C₄×C₄₇	—	2	2	no	—
382	C₂×C₄×C₄₇	—	2	2	no	—
383	C₂×C₄×C₄₇	—	2	8	no	—
384	C₂×C₄×C₄₇	—	2	8	no	—
385	C₂×C₄×C₄₇	—	2	8	no	—
386	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
387	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
388	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
389	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
390	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
391	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
392	C₂²⋊D₄₇	—	2	16	no	—
393	C₂²⋊D₄₇	—	2	32	no	—
394	C₂²⋊D₄₇	—	2	16	no	—
395	C₂²⋊D₄₇	—	4	16	no	—
396	C₂²⋊D₄₇	—	4	16	no	—
397	C₂²⋊D₄₇	—	4	16	no	—
398	C₂²⋊D₄₇	—	4	16	no	—
399	C₂²⋊D₄₇	—	4	16	no	—
400	C₂×Dic₄₇	—	2	4	no	—
401	C₂×Dic₄₇	—	2	4	no	—
402	C₂×Dic₄₇	—	2	8	no	—
403	C₂×Dic₄₇	—	2	4	no	—
404	C₂×Dic₄₇	—	4	4	no	—
405	C₂×Dic₄₇	—	4	16	no	—
406	C₂×Dic₄₇	C₂⁵	1	4	yes	—
407	C₂×Dic₄₇	C₂⁵	1	8	yes	—
408	C₂×Dic₄₇	C₂⁵	1	4	yes	—
409	C₂×Dic₄₇	C₂⁵	1	4	yes	—
410	D₁₈₈	—	2	32	no	—
411	D₁₈₈	—	2	16	no	—
412	D₁₈₈	—	4	8	no	—
413	C₄×D₄₇	—	2	16	no	—
414	C₄×D₄₇	—	4	8	no	—
415	C₄×D₄₇	—	4	16	no	—
416	C₄×D₄₇	—	4	16	no	—
417	C₂×#3537	—	47	1	no	maximal, Sylow
418	C₂²×C₄₇	—	2	8	no	—
419	C₂²×C₄₇	—	2	2	no	—
420	C₂²×C₄₇	—	2	4	no	—
421	C₂²×C₄₇	—	2	8	no	—
422	C₂²×C₄₇	—	2	4	no	—
423	C₂²×C₄₇	—	2	4	no	—
424	C₂²×C₄₇	—	2	8	no	—
425	C₂²×C₄₇	—	2	2	no	—
426	C₂²×C₄₇	—	2	2	no	—
427	C₂²×C₄₇	—	4	4	no	—
428	C₂²×C₄₇	—	4	4	no	—
429	C₂²×C₄₇	—	4	16	no	—
430	C₂²×C₄₇	—	4	4	no	—
431	C₂²×C₄₇	—	8	16	no	—
432	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
433	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
434	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
435	C₂×D₄₇	—	2	4	no	—
436	C₂×D₄₇	—	2	4	no	—
437	C₂×D₄₇	—	2	16	no	—
438	C₂×D₄₇	—	2	8	no	—
439	C₂×D₄₇	—	2	8	no	—
440	C₂×D₄₇	—	2	8	no	—
441	C₂×D₄₇	—	4	16	no	—
442	C₂×D₄₇	—	4	16	no	—
443	C₂×D₄₇	—	8	32	no	—
444	C₂×D₄₇	—	8	16	no	—
445	C₂×D₄₇	C₂×H(5,𝔽₂)	1	8	yes	—
446	C₄×C₄₇	—	2	8	no	—
447	C₄×C₄₇	—	2	2	no	—
448	C₄×C₄₇	—	2	2	no	—
449	C₄×C₄₇	—	2	2	no	—
450	C₄×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
451	Dic₄₇	—	2	4	no	—
452	Dic₄₇	—	2	4	no	—
453	Dic₄₇	—	2	8	no	—
454	Dic₄₇	—	2	4	no	—
455	#3537	—	47	32	no	—
456	C₂×#560	—	47	2	no	—
457	C₂×#560	—	47	2	no	—
458	C₂×#553	—	47	2	no	—
459	C₂×#553	—	47	2	no	—
460	C₂×D₄²	—	47	2	no	—
461	C₂×D₄²	—	47	2	no	—
462	C₂×D₄²	—	47	2	no	—
463	C₂×D₄²	—	47	2	no	—
464	C₂×#540	—	47	2	no	—
465	C₂×#538	—	47	4	no	—
466	C₂×#535	—	47	1	no	—
467	C₂×#535	D₄₇	1	1	yes	characteristic, complemented
468	C₂×#534	—	47	4	no	—
469	C₂×#525	—	47	1	no	—
470	C₂²×#121	—	47	2	no	—
471	C₂×C₄₇	—	4	2	no	—
472	C₂×C₄₇	—	4	2	no	—
473	C₂×C₄₇	—	4	8	no	—
474	C₂×C₄₇	—	4	2	no	—
475	C₂×C₄₇	#3537	1	4	yes	complemented
476	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	2	yes	—
477	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
478	D₄₇	—	2	8	no	—
479	D₄₇	—	4	8	no	—
480	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
481	C₂³×D₄	—	47	4	no	—
482	C₂³×D₄	—	47	2	no	—
483	C₂³×D₄	—	47	4	no	—
484	C₂³×D₄	—	47	4	no	—
485	C₂³×D₄	—	47	1	no	—
486	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
487	C₂⁴×C₄	—	47	1	no	—
488	#560	—	47	32	no	—
489	#560	—	47	32	no	—
490	#553	—	47	32	no	—
491	#553	—	47	32	no	—
492	D₄²	—	47	32	no	—
493	D₄²	—	47	32	no	—
494	D₄²	—	47	32	no	—
495	D₄²	—	47	32	no	—
496	#540	—	47	32	no	—
497	#538	—	47	64	no	—
498	#535	—	47	16	no	—
499	#535	C₂×D₄₇	1	16	yes	complemented
500	#534	—	47	64	no	—
501	C₂×#127	—	47	2	no	—
502	C₂×#127	—	47	2	no	—
503	C₂×#127	C₂×D₄₇	1	2	yes	complemented
504	C₂×#126	—	47	4	no	—
505	C₂×#126	—	47	4	no	—
506	C₂×#125	—	47	2	no	—
507	C₂×#124	—	47	2	no	—
508	C₂×#124	C₂×D₄₇	1	2	yes	complemented
509	#525	—	47	16	no	—
510	C₂×#123	—	47	1	no	—
511	C₂×#123	—	47	1	no	—
512	C₂×#123	—	47	4	no	—
513	C₂×#123	—	47	4	no	—
514	C₂×#123	—	47	4	no	—
515	C₂×#123	—	47	4	no	—
516	C₂×C₂²⋊Q₈	—	47	2	no	—
517	C₂×#121	—	47	2	no	—
518	C₂×#121	—	47	4	no	—
519	C₂×#121	—	47	2	no	—
520	C₂×#121	—	47	4	no	—
521	C₂×#121	—	47	4	no	—
522	C₂×#121	—	47	4	no	—
523	C₂×#121	—	47	4	no	—
524	C₂×#121	—	47	2	no	—
525	C₂×#121	—	47	2	no	—
526	C₂×#121	—	47	32	no	—
527	C₂×#121	—	47	2	no	—
528	C₂×#121	—	47	4	no	—
529	C₂×#121	—	47	4	no	—
530	C₂×#121	—	47	4	no	—
531	C₂×#121	C₂×D₄₇	1	2	yes	complemented
532	C₂×#121	C₂×D₄₇	1	2	yes	complemented
533	C₂×#120	—	47	4	no	—
534	C₂×#120	—	47	1	no	—
535	C₂×#120	—	47	1	no	—
536	C₂×#120	—	47	2	no	—
537	C₂×#120	—	47	4	no	—
538	C₂×#120	—	47	2	no	—
539	C₂×#120	—	47	4	no	—
540	C₂×#120	—	47	4	no	—
541	C₂×#120	C₂×D₄₇	1	2	yes	complemented
542	C₂×#120	C₂×D₄₇	1	2	yes	complemented
543	C₂×C₄×D₄	—	47	2	no	—
544	C₂×C₄×D₄	—	47	2	no	—
545	C₂×C₄×D₄	—	47	2	no	—
546	C₂×C₄×D₄	—	47	2	no	—
547	C₂×C₄×D₄	—	47	4	no	—
548	C₂×C₄×D₄	—	47	4	no	—
549	C₂×#117	—	47	1	no	—
550	C₂×#117	—	47	1	no	—
551	C₂×#117	C₂×D₄₇	1	1	yes	characteristic, complemented
552	C₂²×C₄⋊C₄	—	47	2	no	—
553	C₂²×C₂²⋊C₄	—	47	4	no	—
554	C₄₇	C₂×#3537	1	1	yes	characteristic, complemented, Sylow
555	C₂⁵	—	47	1	no	—
556	C₂⁵	—	47	4	no	—
557	C₂⁵	—	47	2	no	—
558	C₂⁵	C₂²×D₄₇	1	2	yes	—
559	C₂×#41	—	4	4	no	—
560	C₂×#41	C₂²×D₄₇	1	8	yes	complemented
561	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
562	C₂²×D₄	—	4	4	no	—
563	C₂²×D₄	—	47	2	no	—
564	C₂²×D₄	—	47	4	no	—
565	C₂²×D₄	—	47	2	no	—
566	C₂²×D₄	—	47	4	no	—
567	C₂²×D₄	—	47	4	no	—
568	C₂²×D₄	—	47	4	no	—
569	C₂²×D₄	—	47	4	no	—
570	C₂²×D₄	—	47	4	no	—
571	C₂²×D₄	—	47	32	no	—
572	C₂²×D₄	—	47	16	no	—
573	C₂²×D₄	—	47	32	no	—
574	C₂²×D₄	—	47	32	no	—
575	C₂²×D₄	—	47	4	no	—
576	C₂²×D₄	—	47	2	no	—
577	C₂²×D₄	—	47	2	no	—
578	C₂²×D₄	—	47	8	no	—
579	C₂²×D₄	—	188	4	no	—
580	C₂²×D₄	—	188	8	no	—
581	C₂²×D₄	—	188	16	no	—
582	C₂²×D₄	—	188	16	no	—
583	C₂²×D₄	—	188	16	no	—
584	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
585	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
586	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
587	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
588	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
589	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
590	C₂²×D₄	C₂²×D₄₇	1	4	yes	—
591	C₂²×D₄	C₂²×D₄₇	1	8	yes	complemented
592	C₂³×C₄	—	47	4	no	—
593	C₂³×C₄	—	47	1	no	—
594	C₂³×C₄	—	47	2	no	—
595	C₂³×C₄	—	47	2	no	—
596	C₂³×C₄	—	47	4	no	—
597	C₂³×C₄	—	47	4	no	—
598	C₂³×C₄	—	47	8	no	—
599	C₂³×C₄	—	188	4	no	—
600	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
601	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
602	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
603	#127	—	47	16	no	—
604	#127	—	47	16	no	—
605	#127	C₂²×D₄₇	1	16	yes	complemented
606	#126	—	47	32	no	—
607	#126	—	47	32	no	—
608	#125	—	47	16	no	—
609	#124	—	47	16	no	—
610	#124	C₂²×D₄₇	1	16	yes	complemented
611	#123	—	47	8	no	—
612	#123	—	47	8	no	—
613	#123	—	47	32	no	—
614	#123	—	47	32	no	—
615	#123	—	47	32	no	—
616	#123	—	47	32	no	—
617	C₂²⋊Q₈	—	47	16	no	—
618	#121	—	47	16	no	—
619	#121	—	47	32	no	—
620	#121	—	47	16	no	—
621	#121	—	47	32	no	—
622	#121	—	47	32	no	—
623	#121	—	47	32	no	—
624	#121	—	47	32	no	—
625	#121	—	47	16	no	—
626	#121	—	47	16	no	—
627	#121	—	47	16	no	—
628	#121	—	47	32	no	—
629	#121	—	47	32	no	—
630	#121	—	47	32	no	—
631	#121	C₂²×D₄₇	1	16	yes	complemented
632	#121	C₂²×D₄₇	1	16	yes	complemented
633	#120	—	47	32	no	—
634	#120	—	47	8	no	—
635	#120	—	47	8	no	—
636	#120	—	47	16	no	—
637	#120	—	47	32	no	—
638	#120	—	47	16	no	—
639	#120	—	47	32	no	—
640	#120	—	47	32	no	—
641	#120	C₂²×D₄₇	1	16	yes	complemented
642	#120	C₂²×D₄₇	1	16	yes	complemented
643	C₄×D₄	—	47	16	no	—
644	C₄×D₄	—	47	16	no	—
645	C₄×D₄	—	47	16	no	—
646	C₄×D₄	—	47	16	no	—
647	C₄×D₄	—	47	32	no	—
648	C₄×D₄	—	47	32	no	—
649	#117	—	47	8	no	—
650	#117	—	47	8	no	—
651	#117	C₂²×D₄₇	1	8	yes	complemented
652	C₂×C₄⋊C₄	—	47	2	no	—
653	C₂×C₄⋊C₄	—	47	4	no	—
654	C₂×C₄⋊C₄	—	47	2	no	—
655	C₂×C₄⋊C₄	—	47	2	no	—
656	C₂×C₄⋊C₄	—	47	2	no	—
657	C₂×C₄⋊C₄	—	47	4	no	—
658	C₂×C₄⋊C₄	—	47	4	no	—
659	C₂×C₄⋊C₄	—	47	16	no	—
660	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
661	C₂×C₂²⋊C₄	—	47	4	no	—
662	C₂×C₂²⋊C₄	—	47	2	no	—
663	C₂×C₂²⋊C₄	—	47	1	no	—
664	C₂×C₂²⋊C₄	—	47	1	no	—
665	C₂×C₂²⋊C₄	—	47	4	no	—
666	C₂×C₂²⋊C₄	—	47	2	no	—
667	C₂×C₂²⋊C₄	—	47	2	no	—
668	C₂×C₂²⋊C₄	—	47	4	no	—
669	C₂×C₂²⋊C₄	—	47	4	no	—
670	C₂×C₂²⋊C₄	—	47	2	no	—
671	C₂×C₂²⋊C₄	—	47	2	no	—
672	C₂×C₂²⋊C₄	—	47	4	no	—
673	C₂×C₂²⋊C₄	—	47	4	no	—
674	C₂×C₂²⋊C₄	—	47	32	no	—
675	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
676	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
677	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
678	C₂×C₄²	—	47	2	no	—
679	C₂×C₄²	—	47	2	no	—
680	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
681	C₂⁴	—	4	4	no	—
682	C₂⁴	—	4	8	no	—
683	C₂⁴	—	47	2	no	—
684	C₂⁴	—	47	4	no	—
685	C₂⁴	—	47	4	no	—
686	C₂⁴	—	47	16	no	—
687	C₂⁴	—	47	8	no	—
688	C₂⁴	—	94	16	no	—
689	C₂⁴	—	94	8	no	—
690	C₂⁴	—	188	8	no	—
691	C₂⁴	—	188	8	no	—
692	C₂⁴	—	188	4	no	—
693	C₂⁴	—	188	8	no	—
694	C₂⁴	—	188	2	no	—
695	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
696	C₂⁴	C₂³×D₄₇	1	4	yes	—
697	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
698	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
699	C₂⁴	C₂³×D₄₇	1	8	yes	—
700	#41	—	4	16	no	—
701	C₂×Q₈	—	4	2	no	—
702	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
703	C₂×D₄	—	2	8	no	—
704	C₂×D₄	—	4	16	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	—	4	8	no	—
707	C₂×D₄	—	4	8	no	—
708	C₂×D₄	—	4	2	no	—
709	C₂×D₄	—	4	2	no	—
710	C₂×D₄	—	4	2	no	—
711	C₂×D₄	—	47	8	no	—
712	C₂×D₄	—	47	16	no	—
713	C₂×D₄	—	47	8	no	—
714	C₂×D₄	—	47	16	no	—
715	C₂×D₄	—	47	16	no	—
716	C₂×D₄	—	47	16	no	—
717	C₂×D₄	—	47	16	no	—
718	C₂×D₄	—	47	16	no	—
719	C₂×D₄	—	47	16	no	—
720	C₂×D₄	—	47	8	no	—
721	C₂×D₄	—	47	8	no	—
722	C₂×D₄	—	94	16	no	—
723	C₂×D₄	—	94	8	no	—
724	C₂×D₄	—	94	16	no	—
725	C₂×D₄	—	94	8	no	—
726	C₂×D₄	—	94	8	no	—
727	C₂×D₄	—	188	16	no	—
728	C₂×D₄	—	188	4	no	—
729	C₂×D₄	—	188	32	no	—
730	C₂×D₄	—	188	8	no	—
731	C₂×D₄	—	188	8	no	—
732	C₂×D₄	—	188	8	no	—
733	C₂×D₄	—	188	8	no	—
734	C₂×D₄	—	188	8	no	—
735	C₂×D₄	—	188	64	no	—
736	C₂×D₄	—	188	64	no	—
737	C₂×D₄	—	188	64	no	—
738	C₂×D₄	C₂³×D₄₇	1	8	yes	—
739	C₂×D₄	C₂³×D₄₇	1	4	yes	—
740	C₂×D₄	C₂³×D₄₇	1	4	yes	—
741	C₂×D₄	C₂³×D₄₇	1	8	yes	—
742	C₂×D₄	C₂³×D₄₇	1	4	yes	—
743	C₂×D₄	C₂³×D₄₇	1	16	yes	—
744	C₂×D₄	C₂³×D₄₇	1	16	yes	—
745	C₂²×C₄	—	2	4	no	—
746	C₂²×C₄	—	2	4	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	47	2	no	—
749	C₂²×C₄	—	47	4	no	—
750	C₂²×C₄	—	47	2	no	—
751	C₂²×C₄	—	47	2	no	—
752	C₂²×C₄	—	47	16	no	—
753	C₂²×C₄	—	47	4	no	—
754	C₂²×C₄	—	47	8	no	—
755	C₂²×C₄	—	47	8	no	—
756	C₂²×C₄	—	47	16	no	—
757	C₂²×C₄	—	47	16	no	—
758	C₂²×C₄	—	94	8	no	—
759	C₂²×C₄	—	188	16	no	—
760	C₂²×C₄	—	188	4	no	—
761	C₂²×C₄	—	188	8	no	—
762	C₂²×C₄	—	188	8	no	—
763	C₂²×C₄	—	188	2	no	—
764	C₂²×C₄	—	188	8	no	—
765	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
766	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
767	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
768	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
769	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
770	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
771	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
772	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
773	C₄⋊C₄	—	47	16	no	—
774	C₄⋊C₄	—	47	8	no	—
775	C₄⋊C₄	—	47	8	no	—
776	C₄⋊C₄	—	47	16	no	—
777	C₄⋊C₄	—	47	8	no	—
778	C₄⋊C₄	—	47	8	no	—
779	C₄⋊C₄	—	47	16	no	—
780	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
781	C₂²⋊C₄	—	47	16	no	—
782	C₂²⋊C₄	—	47	8	no	—
783	C₂²⋊C₄	—	47	4	no	—
784	C₂²⋊C₄	—	47	4	no	—
785	C₂²⋊C₄	—	47	16	no	—
786	C₂²⋊C₄	—	47	8	no	—
787	C₂²⋊C₄	—	47	8	no	—
788	C₂²⋊C₄	—	47	16	no	—
789	C₂²⋊C₄	—	47	16	no	—
790	C₂²⋊C₄	—	47	8	no	—
791	C₂²⋊C₄	—	47	8	no	—
792	C₂²⋊C₄	—	47	16	no	—
793	C₂²⋊C₄	—	47	16	no	—
794	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
795	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
796	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
797	C₄²	—	47	8	no	—
798	C₄²	—	47	8	no	—
799	C₄²	C₂³×D₄₇	1	8	yes	—
800	C₂³	—	2	8	no	—
801	C₂³	—	2	4	no	—
802	C₂³	—	2	4	no	—
803	C₂³	—	2	8	no	—
804	C₂³	—	2	4	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	8	no	—
809	C₂³	—	4	8	no	—
810	C₂³	—	4	16	no	—
811	C₂³	—	8	16	no	—
812	C₂³	—	47	8	no	—
813	C₂³	—	47	4	no	—
814	C₂³	—	47	8	no	—
815	C₂³	—	94	32	no	—
816	C₂³	—	94	16	no	—
817	C₂³	—	94	4	no	—
818	C₂³	—	94	4	no	—
819	C₂³	—	94	8	no	—
820	C₂³	—	94	8	no	—
821	C₂³	—	94	8	no	—
822	C₂³	—	376	32	no	—
823	C₂³	—	376	16	no	—
824	C₂³	—	188	16	no	—
825	C₂³	—	188	16	no	—
826	C₂³	—	188	8	no	—
827	C₂³	—	188	16	no	—
828	C₂³	—	188	4	no	—
829	C₂³	—	188	16	no	—
830	C₂³	C₂⁴×D₄₇	1	2	yes	—
831	C₂³	C₂⁴×D₄₇	1	8	yes	—
832	C₂³	C₂⁴×D₄₇	1	2	yes	—
833	C₂³	C₂⁴×D₄₇	1	2	yes	—
834	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
835	Q₈	—	4	4	no	—
836	D₄	—	2	16	no	—
837	D₄	—	4	8	no	—
838	D₄	—	4	16	no	—
839	D₄	—	4	16	no	—
840	D₄	—	4	4	no	—
841	D₄	—	4	4	no	—
842	D₄	—	4	4	no	—
843	D₄	—	94	32	no	—
844	D₄	—	94	16	no	—
845	D₄	—	94	32	no	—
846	D₄	—	94	16	no	—
847	D₄	—	94	16	no	—
848	D₄	—	188	8	no	—
849	D₄	—	188	16	no	—
850	D₄	—	188	16	no	—
851	D₄	—	188	16	no	—
852	D₄	—	188	16	no	—
853	D₄	—	188	16	no	—
854	C₂×C₄	—	2	8	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	8	no	—
859	C₂×C₄	—	2	8	no	—
860	C₂×C₄	—	2	8	no	—
861	C₂×C₄	—	47	4	no	—
862	C₂×C₄	—	47	8	no	—
863	C₂×C₄	—	47	4	no	—
864	C₂×C₄	—	47	4	no	—
865	C₂×C₄	—	94	4	no	—
866	C₂×C₄	—	94	8	no	—
867	C₂×C₄	—	94	4	no	—
868	C₂×C₄	—	94	4	no	—
869	C₂×C₄	—	94	16	no	—
870	C₂×C₄	—	188	8	no	—
871	C₂×C₄	—	188	16	no	—
872	C₂×C₄	—	188	16	no	—
873	C₂×C₄	—	188	4	no	—
874	C₂×C₄	—	188	16	no	—
875	C₂×C₄	#13094069	1	4	yes	—
876	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
877	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
878	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
879	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
880	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
881	C₂²	—	2	8	no	—
882	C₂²	—	2	4	no	—
883	C₂²	—	2	4	no	—
884	C₂²	—	2	8	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	8	no	—
890	C₂²	—	4	4	no	—
891	C₂²	—	4	16	no	—
892	C₂²	—	4	4	no	—
893	C₂²	—	4	4	no	—
894	C₂²	—	8	16	no	—
895	C₂²	—	47	8	no	—
896	C₂²	—	94	16	no	—
897	C₂²	—	94	4	no	—
898	C₂²	—	94	4	no	—
899	C₂²	—	94	8	no	—
900	C₂²	—	94	8	no	—
901	C₂²	—	94	8	no	—
902	C₂²	—	376	32	no	—
903	C₂²	—	376	16	no	—
904	C₂²	—	188	16	no	—
905	C₂²	—	188	16	no	—
906	C₂²	H(5,𝔽₂)×D₄₇	1	4	yes	—
907	C₂²	C₂×#13094069	1	2	yes	—
908	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
909	C₄	—	2	8	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	2	2	no	—
913	C₄	—	94	4	no	—
914	C₄	—	94	8	no	—
915	C₄	—	94	4	no	—
916	C₄	—	94	4	no	—
917	C₄	C₂×#13094069	1	4	yes	—
918	C₂	—	4	2	no	—
919	C₂	—	4	8	no	—
920	C₂	—	4	2	no	—
921	C₂	—	4	2	no	—
922	C₂	—	94	8	no	—
923	C₂	—	188	8	no	—
924	C₂	#20257621	1	4	yes	direct product factor
925	C₂	C₂×H(5,𝔽₂)×D₄₇	1	2	yes	—
926	C₂	C₂²×#13094069	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#535	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂×#535	D₄₇
hypocenter	C₄₇	C₂×#3537
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#535

Complements

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

N	H ≅ G/N	type
1. #20257621	C₂	direct (N × H)
2. C₂×#15689862	C₂	semidirect
3. C₂×#15689860	C₂	semidirect
4. C₂×#15689820	C₂	semidirect
5. C₂×#15689817	C₂	semidirect
6. C₂×#15689758	C₂	semidirect
7. C₂×#15689757	C₂	semidirect
8. C₂×D₄×C₂²⋊D₄₇	C₂	semidirect
9. C₂×#15689755	C₂	semidirect
10. C₂×#15689726	C₂	semidirect
11. C₂×#15689707	C₂	semidirect
12. C₂×#15689687	C₂	semidirect
13. C₂×#15689683	C₂	semidirect
14. C₂×#15689630	C₂	semidirect
15. C₂×#121×D₄₇	C₂	semidirect
16. C₂×C₄₇×#535	C₂	semidirect
17. C₂³×D₁₈₈	C₂²	semidirect
18. C₂³×C₂²⋊D₄₇	C₂²	semidirect
19. C₂²×D₄×D₄₇	C₂²	semidirect
20. C₂²×D₄×D₄₇	C₂²	semidirect
21. C₂²×D₄×D₄₇	C₂²	semidirect
22. C₂³×C₄×D₄₇	C₂²	semidirect
23. #15689862	C₂²	semidirect
24. #15689860	C₂²	semidirect
25. #15689820	C₂²	semidirect
26. #15689817	C₂²	semidirect
27. #15689758	C₂²	semidirect
28. #15689757	C₂²	semidirect
29. D₄×C₂²⋊D₄₇	C₂²	semidirect
30. #15689755	C₂²	semidirect
31. #15689726	C₂²	semidirect
32. #15689707	C₂²	semidirect
33. #15689687	C₂²	semidirect
34. #15689683	C₂²	semidirect
35. C₂×#13094020	C₂²	semidirect
36. C₂×#13094020	C₂²	semidirect
37. C₂×#13094018	C₂²	semidirect
38. C₂×#13094017	C₂²	semidirect
39. C₂×#13094015	C₂²	semidirect
40. C₂×#13094013	C₂²	semidirect
41. #15689630	C₂²	semidirect
42. C₂×#13094008	C₂²	semidirect
43. C₂×#13094006	C₂²	semidirect
44. C₂×#13094006	C₂²	semidirect
45. C₂×#13094005	C₂²	semidirect
46. C₂×#13094005	C₂²	semidirect
47. C₂×#13094005	C₂²	semidirect
48. C₂×#13094000	C₂²	semidirect
49. C₂×#13093999	C₂²	semidirect
50. C₂×#13093998	C₂²	semidirect
51. C₂×#13093998	C₂²	semidirect
52. C₂×#13093997	C₂²	semidirect
53. C₂×#13093997	C₂²	semidirect
54. C₂×#13093997	C₂²	semidirect
55. C₂×#13093996	C₂²	semidirect
56. C₂×#13093996	C₂²	semidirect
57. C₂×#13093996	C₂²	semidirect
58. C₂×#13093995	C₂²	semidirect
59. C₂×#13093995	C₂²	semidirect
60. C₂×#13093995	C₂²	semidirect
61. C₂×#13093995	C₂²	semidirect
62. #121×D₄₇	C₂²	semidirect
63. C₂×#13093994	C₂²	semidirect
64. C₂×#13093993	C₂²	semidirect
65. C₂×#13093992	C₂²	semidirect
66. C₂×#13093992	C₂²	semidirect
67. C₂×#13093992	C₂²	semidirect
68. C₂×#13093992	C₂²	semidirect
69. C₂×#13093992	C₂²	semidirect
70. C₂×#13093992	C₂²	semidirect
71. C₂×C₄×D₁₈₈	C₂²	semidirect
72. C₂×D₄×Dic₄₇	C₂²	semidirect
73. C₂×#13093986	C₂²	semidirect
74. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
75. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
76. C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
77. C₂×#13093983	C₂²	semidirect
78. C₂×#13093983	C₂²	semidirect
79. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
80. C₂×C₂²⋊C₄×D₄₇	C₂²	semidirect
81. C₂²×#41×C₄₇	C₂²	semidirect
82. C₂³×D₄×C₄₇	C₂²	semidirect
83. C₄₇×#535	C₂²	semidirect
84. C₂×#127×C₄₇	C₂²	semidirect
85. C₂×#124×C₄₇	C₂²	semidirect
86. C₂×#121×C₄₇	C₂²	semidirect
87. C₂×#121×C₄₇	C₂²	semidirect
88. C₂×#120×C₄₇	C₂²	semidirect
89. C₂×#120×C₄₇	C₂²	semidirect
90. C₂×#117×C₄₇	C₂²	semidirect
98. C₂²×D₁₈₈	C₂³	semidirect
108. C₂²×C₂²⋊D₄₇	C₂³	semidirect
112. C₂×D₄×D₄₇	C₂³	semidirect
113. C₂×D₄×D₄₇	C₂³	semidirect
114. C₂×D₄×D₄₇	C₂³	semidirect
122. C₂²×C₄×D₄₇	C₂³	semidirect
123. #13094020	C₂³	semidirect
124. #13094020	C₂³	semidirect
125. #13094018	C₂³	semidirect
126. #13094017	C₂³	semidirect
127. #13094015	C₂³	semidirect
128. #13094013	C₂³	semidirect
129. #13094008	C₂³	semidirect
130. #13094006	C₂³	semidirect
131. #13094006	C₂³	semidirect
132. #13094005	C₂³	semidirect
133. #13094005	C₂³	semidirect
134. #13094005	C₂³	semidirect
135. #13094000	C₂³	semidirect
136. #13093999	C₂³	semidirect
137. #13093998	C₂³	semidirect
138. #13093998	C₂³	semidirect
139. #13093997	C₂³	semidirect
140. #13093997	C₂³	semidirect
141. #13093997	C₂³	semidirect
142. #13093996	C₂³	semidirect
143. #13093996	C₂³	semidirect
144. #13093996	C₂³	semidirect
145. #13093995	C₂³	semidirect
146. #13093995	C₂³	semidirect
147. #13093995	C₂³	semidirect
148. #13093995	C₂³	semidirect
149. #13093994	C₂³	semidirect
150. #13093993	C₂³	semidirect
151. #13093992	C₂³	semidirect
152. #13093992	C₂³	semidirect
153. #13093992	C₂³	semidirect
154. #13093992	C₂³	semidirect
155. #13093992	C₂³	semidirect
156. #13093992	C₂³	semidirect
157. C₄×D₁₈₈	C₂³	semidirect
158. D₄×Dic₄₇	C₂³	semidirect
159. #13093986	C₂³	semidirect
160. C₄×C₂²⋊D₄₇	C₂³	semidirect
161. C₄×C₂²⋊D₄₇	C₂³	semidirect
162. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
163. #13093983	C₂³	semidirect
164. #13093983	C₂³	semidirect
172. C₄⋊C₄×D₄₇	C₂³	semidirect
186. C₂²⋊C₄×D₄₇	C₂³	semidirect
191. C₂×#41×C₄₇	C₂³	semidirect
201. C₂²×D₄×C₄₇	C₂³	semidirect
205. #127×C₄₇	C₂³	semidirect
206. #124×C₄₇	C₂³	semidirect
207. #121×C₄₇	C₂³	semidirect
208. #121×C₄₇	C₂³	semidirect
209. #120×C₄₇	C₂³	semidirect
210. #120×C₄₇	C₂³	semidirect
211. #117×C₄₇	C₂³	semidirect
467. C₂×#535	D₄₇	semidirect
475. C₂×C₄₇	#3537	semidirect
480. C₂²×#41	C₂×D₄₇	semidirect
486. C₂³×D₄	C₂×D₄₇	semidirect
499. #535	C₂×D₄₇	semidirect
503. C₂×#127	C₂×D₄₇	semidirect
508. C₂×#124	C₂×D₄₇	semidirect
531. C₂×#121	C₂×D₄₇	semidirect
532. C₂×#121	C₂×D₄₇	semidirect
541. C₂×#120	C₂×D₄₇	semidirect
542. C₂×#120	C₂×D₄₇	semidirect
551. C₂×#117	C₂×D₄₇	semidirect
554. C₄₇	C₂×#3537	semidirect
560. C₂×#41	C₂²×D₄₇	semidirect
591. C₂²×D₄	C₂²×D₄₇	semidirect
605. #127	C₂²×D₄₇	semidirect
610. #124	C₂²×D₄₇	semidirect
631. #121	C₂²×D₄₇	semidirect
632. #121	C₂²×D₄₇	semidirect
641. #120	C₂²×D₄₇	semidirect
642. #120	C₂²×D₄₇	semidirect
651. #117	C₂²×D₄₇	semidirect
924. C₂	#20257621	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257621	2
C₂×#15689862	2
C₂×#15689860	2
C₂×#15689820	2
C₂×#15689817	2
C₂×#15689758	2
C₂×#15689757	2
C₂×D₄×C₂²⋊D₄₇	2
C₂×#15689755	2
C₂×#15689726	2
C₂×#15689707	2
C₂×#15689687	2
C₂×#15689683	2
C₂×#15689630	2
C₂×#121×D₄₇	2
C₂×C₄₇×#535	2
C₂×#3537	47

Subgroups — C2×#20257621 #27123511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257621 #27123511