Subgroups — C₂×#20257123 #27124625

Order 12032.

8006 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257123	C₂	1	32	yes	maximal, direct product factor
2	C₂×#15689836	C₂	1	2	yes	maximal, complemented
3	C₂×#15689821	C₂	1	2	yes	maximal, complemented
4	C₂×#15689817	C₂	1	2	yes	maximal, complemented
5	C₂×#15689797	C₂	1	4	yes	maximal, complemented
6	C₂×#15689774	C₂	1	2	yes	maximal, complemented
7	C₂×#15689763	C₂	1	4	yes	maximal, complemented
8	C₂×#15689751	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15689744	C₂	1	2	yes	maximal, complemented
10	C₂×#15689728	C₂	1	2	yes	maximal, complemented
11	C₂×#15689692	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15689673	C₂	1	2	yes	maximal, complemented
13	C₂×#15689657	C₂	1	2	yes	maximal, complemented
14	C₂×#15689634	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#13093998	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15689603	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#15689597	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#117×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#10625350	C₂²	1	1	yes	characteristic
20	C₂²×#10625350	C₂²	1	4	yes	complemented
21	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
22	C₂³×C₂²⋊D₄₇	C₂²	1	2	yes	—
23	#15689836	C₂²	1	32	yes	complemented
24	#15689821	C₂²	1	32	yes	complemented
25	#15689817	C₂²	1	32	yes	complemented
26	#15689797	C₂²	1	64	yes	complemented
27	#15689774	C₂²	1	32	yes	complemented
28	#15689763	C₂²	1	64	yes	complemented
29	#15689751	C₂²	1	16	yes	complemented
30	#15689744	C₂²	1	32	yes	complemented
31	#15689728	C₂²	1	32	yes	complemented
32	#15689692	C₂²	1	16	yes	complemented
33	#15689673	C₂²	1	32	yes	complemented
34	C₂×#13094024	C₂²	1	2	yes	complemented
35	C₂×#13094023	C₂²	1	2	yes	complemented
36	C₂×#13094021	C₂²	1	2	yes	complemented
37	#15689657	C₂²	1	32	yes	complemented
38	C₂×#13094019	C₂²	1	4	yes	complemented
39	C₂×#13094018	C₂²	1	4	yes	complemented
40	C₂×#13094016	C₂²	1	2	yes	complemented
41	C₂×#13094015	C₂²	1	2	yes	complemented
42	C₂×#13094012	C₂²	1	4	yes	complemented
43	C₂×#13094012	C₂²	1	2	yes	complemented
44	C₂×#13094010	C₂²	1	4	yes	complemented
45	#15689634	C₂²	1	16	yes	complemented
46	C₂×#13094009	C₂²	1	4	yes	complemented
47	C₂×#13094009	C₂²	1	4	yes	complemented
48	C₂×#13094007	C₂²	1	2	yes	—
49	C₂×#13094007	C₂²	1	4	yes	complemented
50	C₂×#13094006	C₂²	1	4	yes	complemented
51	C₂×#13094003	C₂²	1	1	yes	characteristic, complemented
52	C₂×#13094003	C₂²	1	1	yes	characteristic, complemented
53	C₂×#13094002	C₂²	1	4	yes	complemented
54	C₂×#13094001	C₂²	1	4	yes	—
55	C₂×#13093999	C₂²	1	2	yes	complemented
56	C₂×#13093999	C₂²	1	2	yes	complemented
57	C₂×#13093998	C₂²	1	2	yes	—
58	C₂×#13093998	C₂²	1	2	yes	—
59	C₂×#13093998	C₂²	1	2	yes	—
60	C₂×#13093998	C₂²	1	2	yes	—
61	C₂×#13093998	C₂²	1	16	yes	complemented
62	C₂×#13093998	C₂²	1	4	yes	complemented
63	C₂×#13093998	C₂²	1	1	yes	characteristic, complemented
64	C₂×#13093998	C₂²	1	1	yes	characteristic, complemented
65	C₂×#13093997	C₂²	1	4	yes	complemented
66	C₂×#13093997	C₂²	1	4	yes	complemented
67	C₂×#13093994	C₂²	1	4	yes	—
68	C₂×#13093993	C₂²	1	2	yes	—
69	#15689603	C₂²	1	16	yes	complemented
70	#15689597	C₂²	1	16	yes	complemented
71	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
72	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
73	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
74	C₂×C₄×D₁₈₈	C₂²	1	2	yes	complemented
75	C₂×C₄×D₁₈₈	C₂²	1	4	yes	complemented
76	C₂×#13093986	C₂²	1	2	yes	complemented
77	C₂×#13093986	C₂²	1	2	yes	complemented
78	C₂×C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
79	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
80	C₂×C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
81	C₂×(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	—
82	C₂×#13093983	C₂²	1	1	yes	characteristic
83	C₂×#13093982	C₂²	1	2	yes	complemented
84	C₂×#13093981	C₂²	1	4	yes	complemented
85	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
86	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
87	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
88	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
89	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
90	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
91	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
92	C₂×#117×C₄₇	C₂²	1	2	yes	—
93	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
94	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
95	C₂×#117×C₄₇	C₂²	1	2	yes	complemented
96	C₂×#117×C₄₇	C₂²	1	16	yes	complemented
97	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
98	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
99	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
100	C₂²×C₄²×C₄₇	C₂²	1	2	yes	complemented
101	C₂⁴×D₄₇	C₂³	1	2	yes	—
102	C₂×#10625350	—	2	8	no	—
103	C₂×#10625350	—	4	16	no	—
104	C₂×#10625350	C₂³	1	8	yes	—
105	C₂×#10625350	C₂³	1	32	yes	complemented
106	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
107	C₂²×Dic₉₄	C₂³	1	4	yes	—
108	C₂²×D₁₈₈	—	2	8	no	—
109	C₂²×D₁₈₈	C₂³	1	2	yes	—
110	C₂²×D₁₈₈	C₂³	1	2	yes	—
111	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
112	C₂²×D₁₈₈	C₂³	1	8	yes	—
113	C₂²×D₁₈₈	C₂³	1	4	yes	—
114	C₂²×D₁₈₈	C₂³	1	4	yes	—
115	C₂²×C₂²⋊D₄₇	—	4	8	no	—
116	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
117	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
118	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
119	C₂²×C₂²⋊D₄₇	C₂³	1	16	yes	—
120	C₂²×C₂²⋊D₄₇	C₂³	1	2	yes	—
121	C₂²×C₂²⋊D₄₇	C₂³	1	4	yes	—
122	C₂³×Dic₄₇	C₂³	1	2	yes	—
123	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
124	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
125	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
126	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
127	#13094024	C₂³	1	16	yes	complemented
128	#13094023	C₂³	1	16	yes	complemented
129	#13094021	C₂³	1	16	yes	complemented
130	#13094019	C₂³	1	32	yes	complemented
131	#13094018	C₂³	1	32	yes	complemented
132	#13094016	C₂³	1	16	yes	complemented
133	#13094015	C₂³	1	16	yes	complemented
134	#13094012	C₂³	1	16	yes	complemented
135	#13094012	C₂³	1	32	yes	complemented
136	#13094010	C₂³	1	32	yes	complemented
137	#13094009	C₂³	1	32	yes	complemented
138	#13094009	C₂³	1	32	yes	complemented
139	#13094007	C₂³	1	16	yes	—
140	#13094007	C₂³	1	32	yes	complemented
141	#13094006	C₂³	1	32	yes	complemented
142	#13094003	C₂³	1	8	yes	complemented
143	#13094003	C₂³	1	8	yes	complemented
144	#13094002	C₂³	1	32	yes	complemented
145	#13094001	C₂³	1	32	yes	—
146	#13093999	C₂³	1	16	yes	complemented
147	#13093999	C₂³	1	16	yes	complemented
148	#13093998	C₂³	1	16	yes	—
149	#13093998	C₂³	1	16	yes	—
150	#13093998	C₂³	1	16	yes	—
151	#13093998	C₂³	1	16	yes	—
152	#13093998	C₂³	1	8	yes	complemented
153	#13093998	C₂³	1	32	yes	complemented
154	#13093998	C₂³	1	8	yes	complemented
155	#13093997	C₂³	1	32	yes	complemented
156	#13093997	C₂³	1	32	yes	complemented
157	#13093994	C₂³	1	32	yes	—
158	#13093993	C₂³	1	16	yes	—
159	C₄×Dic₉₄	C₂³	1	16	yes	complemented
160	C₄×D₁₈₈	C₂³	1	16	yes	complemented
161	C₄×D₁₈₈	C₂³	1	16	yes	complemented
162	C₄×D₁₈₈	C₂³	1	16	yes	complemented
163	C₄×D₁₈₈	C₂³	1	32	yes	complemented
164	#13093986	C₂³	1	16	yes	complemented
165	#13093986	C₂³	1	16	yes	complemented
166	C₄×C₂²⋊D₄₇	C₂³	1	32	yes	complemented
167	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
168	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	complemented
169	(C₂²⋊D₄₇)⋊C₄	C₂³	1	32	yes	—
170	#13093983	C₂³	1	8	yes	—
171	#13093982	C₂³	1	16	yes	complemented
172	#13093981	C₂³	1	32	yes	complemented
173	C₂×C₄⋊Dic₄₇	C₂³	1	8	yes	—
174	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
175	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
176	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
178	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
179	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
180	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
181	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
182	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
183	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
184	C₄⋊C₄×D₄₇	C₂³	1	16	yes	complemented
185	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
188	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	16	yes	—
189	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
190	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
191	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
192	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
193	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
194	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
195	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
196	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
197	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
198	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	—
199	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
200	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
201	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₄₇	—	2	8	no	—
203	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
205	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
210	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
211	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
212	#117×C₄₇	C₂³	1	8	yes	—
213	#117×C₄₇	C₂³	1	16	yes	—
214	#117×C₄₇	C₂³	1	8	yes	—
215	#117×C₄₇	C₂³	1	16	yes	complemented
216	#117×C₄₇	C₂³	1	8	yes	complemented
217	#117×C₄₇	C₂³	1	8	yes	complemented
218	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
223	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
224	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	complemented
225	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	complemented
226	C₂×C₂²⋊C₄×C₄₇	C₂³	1	16	yes	—
227	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
230	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
231	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
232	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
233	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
234	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
235	C₂×C₄²×C₄₇	C₂³	1	16	yes	complemented
236	C₂⁴×C₄₇	—	2	4	no	—
237	C₂⁴×C₄₇	—	2	4	no	—
238	C₂⁴×C₄₇	—	4	2	no	—
239	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
241	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
242	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₂³×D₄₇	—	2	8	no	—
244	C₂³×D₄₇	—	4	4	no	—
245	C₂³×D₄₇	—	4	4	no	—
246	C₂³×D₄₇	C₂⁴	1	4	yes	—
247	C₂³×D₄₇	C₂⁴	1	2	yes	—
248	C₂³×D₄₇	C₂⁴	1	8	yes	—
249	C₂²×C₄×C₄₇	—	2	4	no	—
250	C₂²×C₄×C₄₇	—	2	8	no	—
251	C₂²×C₄×C₄₇	—	2	4	no	—
252	C₂²×C₄×C₄₇	—	2	4	no	—
253	C₂²×C₄×C₄₇	—	2	4	no	—
254	C₂²×C₄×C₄₇	—	2	4	no	—
255	C₂²×C₄×C₄₇	—	2	32	no	—
256	C₂²×C₄×C₄₇	—	4	4	no	—
257	C₂²×C₄×C₄₇	#41	1	8	yes	complemented
258	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
265	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
267	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₄₇	C₂⁴	1	8	yes	—
271	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
274	C₂×C₂²⋊D₄₇	—	2	8	no	—
275	C₂×C₂²⋊D₄₇	—	2	16	no	—
276	C₂×C₂²⋊D₄₇	—	2	8	no	—
277	C₂×C₂²⋊D₄₇	—	4	8	no	—
278	C₂×C₂²⋊D₄₇	—	4	4	no	—
279	C₂×C₂²⋊D₄₇	—	4	32	no	—
280	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
281	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
282	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
283	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
284	C₂×C₂²⋊D₄₇	C₂⁴	1	16	yes	—
285	C₂²×Dic₄₇	—	4	4	no	—
286	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
287	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
288	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
289	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
290	C₂²×Dic₄₇	C₂⁴	1	8	yes	—
291	#10625350	—	2	32	no	—
292	#10625350	—	4	64	no	—
293	C₂×D₁₈₈	—	2	8	no	—
294	C₂×D₁₈₈	—	2	8	no	—
295	C₂×D₁₈₈	—	2	4	no	—
296	C₂×D₁₈₈	—	2	32	no	—
297	C₂×D₁₈₈	—	4	8	no	—
298	C₂×D₁₈₈	—	4	8	no	—
299	C₂×D₁₈₈	C₂⁴	1	8	yes	—
300	C₂×D₁₈₈	C₂⁴	1	8	yes	—
301	C₂×D₁₈₈	C₂⁴	1	4	yes	—
302	C₂×D₁₈₈	C₂⁴	1	16	yes	—
303	C₂×D₁₈₈	C₂⁴	1	16	yes	—
304	C₂×C₄×D₄₇	—	2	8	no	—
305	C₂×C₄×D₄₇	—	4	8	no	—
306	C₂×C₄×D₄₇	—	4	8	no	—
307	C₂×C₄×D₄₇	—	4	8	no	—
308	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
309	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
310	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
311	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
312	C₂×Dic₉₄	—	2	4	no	—
313	C₂×Dic₉₄	—	4	8	no	—
314	C₂×Dic₉₄	C₂⁴	1	4	yes	—
315	C₂×Dic₉₄	C₂⁴	1	16	yes	—
316	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
317	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
318	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
319	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
320	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
321	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
322	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
323	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
324	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
325	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
326	C₄²×C₄₇	C₂⁴	1	8	yes	—
327	C₄²×C₄₇	C₂⁴	1	8	yes	—
328	C₄²×C₄₇	C₂⁴	1	8	yes	—
329	C₄²×C₄₇	C₂⁴	1	8	yes	—
330	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
331	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
332	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
333	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
334	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
335	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
336	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
337	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
338	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
339	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
340	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
341	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
342	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
343	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
344	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
345	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
346	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
347	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
348	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
349	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
350	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
351	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
352	C₄×Dic₄₇	C₂⁴	1	16	yes	—
353	C₄×Dic₄₇	C₂⁴	1	8	yes	—
354	C₂³×C₄₇	—	2	2	no	—
355	C₂³×C₄₇	—	2	2	no	—
356	C₂³×C₄₇	—	2	2	no	—
357	C₂³×C₄₇	—	2	2	no	—
358	C₂³×C₄₇	—	2	8	no	—
359	C₂³×C₄₇	—	2	2	no	—
360	C₂³×C₄₇	—	2	8	no	—
361	C₂³×C₄₇	—	2	2	no	—
362	C₂³×C₄₇	—	2	2	no	—
363	C₂³×C₄₇	—	4	4	no	—
364	C₂³×C₄₇	—	4	16	no	—
365	C₂³×C₄₇	C₂×#41	1	4	yes	—
366	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
367	C₂³×C₄₇	C₂⁵	1	2	yes	—
368	C₂³×C₄₇	C₂⁵	1	2	yes	—
369	C₂³×C₄₇	C₂⁵	1	2	yes	—
370	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
371	C₂²×D₄₇	—	2	4	no	—
372	C₂²×D₄₇	—	2	8	no	—
373	C₂²×D₄₇	—	2	4	no	—
374	C₂²×D₄₇	—	2	8	no	—
375	C₂²×D₄₇	—	2	8	no	—
376	C₂²×D₄₇	—	2	4	no	—
377	C₂²×D₄₇	—	2	16	no	—
378	C₂²×D₄₇	—	4	8	no	—
379	C₂²×D₄₇	—	4	8	no	—
380	C₂²×D₄₇	—	8	16	no	—
381	C₂²×D₄₇	C₂⁵	1	8	yes	—
382	C₂²×D₄₇	C₂⁵	1	4	yes	—
383	C₂×C₄×C₄₇	—	2	8	no	—
384	C₂×C₄×C₄₇	—	2	2	no	—
385	C₂×C₄×C₄₇	—	2	2	no	—
386	C₂×C₄×C₄₇	—	2	4	no	—
387	C₂×C₄×C₄₇	—	2	4	no	—
388	C₂×C₄×C₄₇	—	2	16	no	—
389	C₂×C₄×C₄₇	—	2	4	no	—
390	C₂×C₄×C₄₇	—	2	4	no	—
391	C₂×C₄×C₄₇	—	2	8	no	—
392	C₂×C₄×C₄₇	—	2	8	no	—
393	C₂×C₄×C₄₇	—	2	8	no	—
394	C₂×C₄×C₄₇	—	2	8	no	—
395	C₂×C₄×C₄₇	—	4	8	no	—
396	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
397	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
398	C₂×C₄×C₄₇	C₂×#41	1	16	yes	complemented
399	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
400	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
401	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
402	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
403	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
404	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
405	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
406	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
407	C₂²⋊D₄₇	—	2	16	no	—
408	C₂²⋊D₄₇	—	2	16	no	—
409	C₂²⋊D₄₇	—	2	32	no	—
410	C₂²⋊D₄₇	—	4	16	no	—
411	C₂²⋊D₄₇	—	4	8	no	—
412	C₂×Dic₄₇	—	2	4	no	—
413	C₂×Dic₄₇	—	2	4	no	—
414	C₂×Dic₄₇	—	2	8	no	—
415	C₂×Dic₄₇	—	2	4	no	—
416	C₂×Dic₄₇	—	4	8	no	—
417	C₂×Dic₄₇	C₂⁵	1	4	yes	—
418	C₂×Dic₄₇	C₂⁵	1	4	yes	—
419	C₂×Dic₄₇	C₂⁵	1	8	yes	—
420	C₂×Dic₄₇	C₂⁵	1	4	yes	—
421	D₁₈₈	—	2	16	no	—
422	D₁₈₈	—	2	16	no	—
423	D₁₈₈	—	2	8	no	—
424	D₁₈₈	—	4	16	no	—
425	D₁₈₈	—	4	16	no	—
426	C₄×D₄₇	—	2	16	no	—
427	C₄×D₄₇	—	4	16	no	—
428	C₄×D₄₇	—	4	16	no	—
429	C₄×D₄₇	—	4	16	no	—
430	Dic₉₄	—	2	8	no	—
431	Dic₉₄	—	4	16	no	—
432	C₂×#3494	—	47	1	no	maximal, Sylow
433	C₂²×C₄₇	—	2	2	no	—
434	C₂²×C₄₇	—	2	2	no	—
435	C₂²×C₄₇	—	2	2	no	—
436	C₂²×C₄₇	—	2	2	no	—
437	C₂²×C₄₇	—	2	8	no	—
438	C₂²×C₄₇	—	2	8	no	—
439	C₂²×C₄₇	—	2	2	no	—
440	C₂²×C₄₇	—	2	2	no	—
441	C₂²×C₄₇	—	2	2	no	—
442	C₂²×C₄₇	—	4	16	no	—
443	C₂²×C₄₇	—	4	4	no	—
444	C₂²×C₄₇	C₂²×#41	1	4	yes	—
445	C₂²×C₄₇	C₂²×#41	1	2	yes	—
446	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	4	yes	—
447	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	2	yes	—
448	C₂²×C₄₇	#585	1	2	yes	—
449	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
450	C₂×D₄₇	—	2	4	no	—
451	C₂×D₄₇	—	2	8	no	—
452	C₂×D₄₇	—	2	4	no	—
453	C₂×D₄₇	—	2	8	no	—
454	C₂×D₄₇	—	2	8	no	—
455	C₂×D₄₇	—	2	4	no	—
456	C₂×D₄₇	—	4	8	no	—
457	C₂×D₄₇	—	4	16	no	—
458	C₂×D₄₇	—	8	16	no	—
459	C₄×C₄₇	—	2	2	no	—
460	C₄×C₄₇	—	2	2	no	—
461	C₄×C₄₇	—	2	4	no	—
462	C₄×C₄₇	—	2	4	no	—
463	C₄×C₄₇	—	2	4	no	—
464	C₄×C₄₇	—	2	4	no	—
465	C₄×C₄₇	C₂²×#41	1	4	yes	—
466	C₄×C₄₇	C₂²×#41	1	4	yes	—
467	Dic₄₇	—	2	4	no	—
468	Dic₄₇	—	2	4	no	—
469	Dic₄₇	—	2	8	no	—
470	Dic₄₇	—	2	4	no	—
471	#3494	—	47	32	no	—
472	C₂×#555	—	47	2	no	—
473	C₂×#553	—	47	2	no	—
474	C₂×#553	—	47	2	no	—
475	C₂×#551	—	47	4	no	—
476	C₂×#547	—	47	2	no	—
477	C₂×#546	—	47	4	no	—
478	C₂×#544	—	47	1	no	—
479	C₂×#542	—	47	2	no	—
480	C₂×#540	—	47	2	no	—
481	C₂×#535	—	47	1	no	—
482	C₂×#532	—	47	2	no	—
483	C₂×#529	—	47	2	no	—
484	C₂×#525	—	47	1	no	—
485	C₂²×#121	—	47	1	no	—
486	C₂×#520	—	47	1	no	—
487	C₂×#518	—	47	1	no	—
488	C₂²×#117	D₄₇	1	1	yes	characteristic, complemented
489	C₂×C₄₇	—	2	4	no	—
490	C₂×C₄₇	—	2	4	no	—
491	C₂×C₄₇	—	4	2	no	—
492	C₂×C₄₇	#3494	1	4	yes	complemented
493	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
494	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
495	C₂×C₄₇	C₂×#585	1	1	yes	characteristic
496	D₄₇	—	4	4	no	—
497	D₄₇	—	4	8	no	—
498	C₂²×#41	—	47	1	no	—
499	C₂²×#41	—	47	4	no	—
500	C₂³×D₄	—	47	2	no	—
501	C₂³×D₄	—	47	1	no	—
502	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
503	#555	—	47	32	no	—
504	#553	—	47	32	no	—
505	#553	—	47	32	no	—
506	#551	—	47	64	no	—
507	#547	—	47	32	no	—
508	#546	—	47	64	no	—
509	#544	—	47	16	no	—
510	#542	—	47	32	no	—
511	#540	—	47	32	no	—
512	#535	—	47	16	no	—
513	#532	—	47	32	no	—
514	C₂×C₄⋊Q₈	—	47	2	no	—
515	C₂×C₄⋊Q₈	—	47	2	no	—
516	C₂×#127	—	47	2	no	—
517	#529	—	47	32	no	—
518	C₂×#126	—	47	4	no	—
519	C₂×#126	—	47	4	no	—
520	C₂×#125	—	47	2	no	—
521	C₂×#125	—	47	2	no	—
522	C₂×#124	—	47	4	no	—
523	C₂×#124	—	47	2	no	—
524	C₂×#124	—	47	4	no	—
525	#525	—	47	16	no	—
526	C₂×#123	—	47	2	no	—
527	C₂×#123	—	47	4	no	—
528	C₂×#123	—	47	4	no	—
529	C₂×#123	—	47	4	no	—
530	C₂×#123	—	47	4	no	—
531	C₂×C₂²⋊Q₈	—	47	1	no	—
532	C₂×C₂²⋊Q₈	—	47	1	no	—
533	C₂×C₂²⋊Q₈	—	47	4	no	—
534	C₂×C₂²⋊Q₈	—	47	4	no	—
535	C₂×#121	—	47	2	no	—
536	C₂×#121	—	47	2	no	—
537	C₂×#121	—	47	2	no	—
538	C₂×#121	—	47	2	no	—
539	C₂×#121	—	47	16	no	—
540	C₂×#121	—	47	1	no	—
541	C₂×#121	—	47	1	no	—
542	C₂×#121	—	47	4	no	—
543	C₂×#121	—	47	2	no	—
544	C₂×#121	—	47	2	no	—
545	C₂×#121	—	47	4	no	—
546	C₂×#121	—	47	4	no	—
547	C₂×#120	—	47	2	no	—
548	C₂×#120	—	47	4	no	—
549	#520	—	47	16	no	—
550	#518	—	47	16	no	—
551	C₂×C₄×Q₈	—	47	2	no	—
552	C₂×C₄×D₄	—	47	2	no	—
553	C₂×C₄×D₄	—	47	2	no	—
554	C₂×C₄×D₄	—	47	4	no	—
555	C₂×C₄×D₄	—	47	2	no	—
556	C₂×C₄×D₄	—	47	2	no	—
557	C₂×C₄×D₄	—	47	4	no	—
558	C₂×C₄×D₄	—	47	2	no	—
559	C₂×C₄×D₄	—	47	2	no	—
560	C₂×C₄×D₄	—	47	2	no	—
561	C₂×C₄×D₄	—	47	4	no	—
562	C₂×#117	—	47	1	no	—
563	C₂×#117	—	47	2	no	—
564	C₂×#117	—	47	4	no	—
565	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
566	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
567	C₂×#117	C₂×D₄₇	1	2	yes	—
568	C₂×#117	C₂×D₄₇	1	2	yes	complemented
569	C₂×#117	C₂×D₄₇	1	1	yes	characteristic, complemented
570	C₂×#117	C₂×D₄₇	1	1	yes	characteristic, complemented
571	C₂×#117	C₂×D₄₇	1	16	yes	complemented
572	C₂²×C₄⋊C₄	—	47	1	no	—
573	C₂²×C₄⋊C₄	—	47	2	no	—
574	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
575	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
576	C₂²×C₂²⋊C₄	—	47	2	no	—
577	C₂²×C₂²⋊C₄	—	47	4	no	—
578	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
579	C₂²×C₄²	C₂×D₄₇	1	2	yes	complemented
580	C₄₇	C₂×#3494	1	1	yes	characteristic, complemented, Sylow
581	C₂⁵	—	47	2	no	—
582	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
583	C₂×#41	—	47	8	no	—
584	C₂×#41	—	47	32	no	—
585	C₂×#41	—	94	8	no	—
586	C₂×#41	—	188	16	no	—
587	C₂²×Q₈	—	47	1	no	—
588	C₂²×Q₈	—	47	4	no	—
589	C₂²×D₄	—	47	2	no	—
590	C₂²×D₄	—	47	2	no	—
591	C₂²×D₄	—	47	4	no	—
592	C₂²×D₄	—	47	2	no	—
593	C₂²×D₄	—	47	4	no	—
594	C₂²×D₄	—	47	16	no	—
595	C₂²×D₄	—	47	2	no	—
596	C₂²×D₄	—	47	2	no	—
597	C₂²×D₄	—	47	1	no	—
598	C₂²×D₄	—	47	8	no	—
599	C₂²×D₄	—	47	4	no	—
600	C₂²×D₄	—	47	4	no	—
601	C₂²×D₄	—	94	8	no	—
602	C₂²×D₄	—	188	8	no	—
603	C₂³×C₄	—	2	8	no	—
604	C₂³×C₄	—	47	2	no	—
605	C₂³×C₄	—	47	2	no	—
606	C₂³×C₄	—	47	4	no	—
607	C₂³×C₄	—	47	4	no	—
608	C₂³×C₄	—	47	4	no	—
609	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
610	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
611	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
612	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
613	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
614	C₂³×C₄	C₂²×D₄₇	1	8	yes	—
615	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
616	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
617	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
618	C₄⋊Q₈	—	47	16	no	—
619	C₄⋊Q₈	—	47	16	no	—
620	#127	—	47	16	no	—
621	#126	—	47	32	no	—
622	#126	—	47	32	no	—
623	#125	—	47	16	no	—
624	#125	—	47	16	no	—
625	#124	—	47	32	no	—
626	#124	—	47	16	no	—
627	#124	—	47	32	no	—
628	#123	—	47	16	no	—
629	#123	—	47	32	no	—
630	#123	—	47	32	no	—
631	#123	—	47	32	no	—
632	#123	—	47	32	no	—
633	C₂²⋊Q₈	—	47	8	no	—
634	C₂²⋊Q₈	—	47	8	no	—
635	C₂²⋊Q₈	—	47	32	no	—
636	C₂²⋊Q₈	—	47	32	no	—
637	#121	—	47	16	no	—
638	#121	—	47	16	no	—
639	#121	—	47	16	no	—
640	#121	—	47	16	no	—
641	#121	—	47	8	no	—
642	#121	—	47	8	no	—
643	#121	—	47	32	no	—
644	#121	—	47	16	no	—
645	#121	—	47	16	no	—
646	#121	—	47	32	no	—
647	#121	—	47	32	no	—
648	#120	—	47	16	no	—
649	#120	—	47	32	no	—
650	C₄×Q₈	—	47	16	no	—
651	C₄×D₄	—	47	16	no	—
652	C₄×D₄	—	47	16	no	—
653	C₄×D₄	—	47	32	no	—
654	C₄×D₄	—	47	16	no	—
655	C₄×D₄	—	47	16	no	—
656	C₄×D₄	—	47	32	no	—
657	C₄×D₄	—	47	16	no	—
658	C₄×D₄	—	47	16	no	—
659	C₄×D₄	—	47	16	no	—
660	C₄×D₄	—	47	32	no	—
661	#117	—	47	8	no	—
662	#117	—	47	16	no	—
663	#117	—	47	32	no	—
664	#117	C₂²×D₄₇	1	8	yes	—
665	#117	C₂²×D₄₇	1	8	yes	—
666	#117	C₂²×D₄₇	1	16	yes	—
667	#117	C₂²×D₄₇	1	16	yes	complemented
668	#117	C₂²×D₄₇	1	8	yes	complemented
669	#117	C₂²×D₄₇	1	8	yes	complemented
670	C₂×C₄⋊C₄	—	47	2	no	—
671	C₂×C₄⋊C₄	—	47	2	no	—
672	C₂×C₄⋊C₄	—	47	4	no	—
673	C₂×C₄⋊C₄	—	47	8	no	—
674	C₂×C₄⋊C₄	—	47	2	no	—
675	C₂×C₄⋊C₄	—	47	1	no	—
676	C₂×C₄⋊C₄	—	47	1	no	—
677	C₂×C₄⋊C₄	—	47	4	no	—
678	C₂×C₄⋊C₄	—	47	4	no	—
679	C₂×C₄⋊C₄	—	47	4	no	—
680	C₂×C₄⋊C₄	—	47	2	no	—
681	C₂×C₄⋊C₄	—	47	16	no	—
682	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
683	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
685	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
686	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
687	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
688	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	complemented
689	C₂×C₄⋊C₄	C₂²×D₄₇	1	8	yes	complemented
690	C₂×C₂²⋊C₄	—	47	2	no	—
691	C₂×C₂²⋊C₄	—	47	2	no	—
692	C₂×C₂²⋊C₄	—	47	2	no	—
693	C₂×C₂²⋊C₄	—	47	4	no	—
694	C₂×C₂²⋊C₄	—	47	4	no	—
695	C₂×C₂²⋊C₄	—	47	4	no	—
696	C₂×C₂²⋊C₄	—	47	4	no	—
697	C₂×C₂²⋊C₄	—	47	16	no	—
698	C₂×C₂²⋊C₄	—	47	4	no	—
699	C₂×C₂²⋊C₄	—	47	4	no	—
700	C₂×C₂²⋊C₄	—	47	2	no	—
701	C₂×C₂²⋊C₄	—	47	4	no	—
702	C₂×C₂²⋊C₄	—	47	2	no	—
703	C₂×C₂²⋊C₄	—	47	32	no	—
704	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂²×D₄₇	1	16	yes	—
709	C₂×C₄²	—	47	4	no	—
710	C₂×C₄²	—	47	2	no	—
711	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
712	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
713	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
714	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
715	C₂×C₄²	C₂²×D₄₇	1	16	yes	complemented
716	C₂⁴	—	2	4	no	—
717	C₂⁴	—	2	4	no	—
718	C₂⁴	—	4	2	no	—
719	C₂⁴	—	47	4	no	—
720	C₂⁴	—	47	2	no	—
721	C₂⁴	—	47	8	no	—
722	C₂⁴	—	94	8	no	—
723	C₂⁴	—	188	4	no	—
724	C₂⁴	—	188	4	no	—
725	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
726	C₂⁴	C₂³×D₄₇	1	4	yes	—
727	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
728	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
729	#41	—	94	32	no	—
730	#41	—	188	64	no	—
731	C₂×Q₈	—	47	4	no	—
732	C₂×Q₈	—	47	16	no	—
733	C₂×Q₈	—	94	4	no	—
734	C₂×Q₈	—	188	8	no	—
735	C₂×D₄	—	47	8	no	—
736	C₂×D₄	—	47	8	no	—
737	C₂×D₄	—	47	16	no	—
738	C₂×D₄	—	47	8	no	—
739	C₂×D₄	—	47	16	no	—
740	C₂×D₄	—	47	8	no	—
741	C₂×D₄	—	47	8	no	—
742	C₂×D₄	—	47	4	no	—
743	C₂×D₄	—	47	16	no	—
744	C₂×D₄	—	47	16	no	—
745	C₂×D₄	—	94	8	no	—
746	C₂×D₄	—	94	16	no	—
747	C₂×D₄	—	94	8	no	—
748	C₂×D₄	—	94	8	no	—
749	C₂×D₄	—	94	8	no	—
750	C₂×D₄	—	94	4	no	—
751	C₂×D₄	—	94	32	no	—
752	C₂×D₄	—	188	8	no	—
753	C₂×D₄	—	188	8	no	—
754	C₂×D₄	—	188	4	no	—
755	C₂×D₄	—	188	8	no	—
756	C₂×D₄	—	188	32	no	—
757	C₂²×C₄	—	2	4	no	—
758	C₂²×C₄	—	2	8	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	—	2	4	no	—
762	C₂²×C₄	—	2	4	no	—
763	C₂²×C₄	—	2	32	no	—
764	C₂²×C₄	—	4	4	no	—
765	C₂²×C₄	—	47	2	no	—
766	C₂²×C₄	—	47	2	no	—
767	C₂²×C₄	—	47	2	no	—
768	C₂²×C₄	—	47	4	no	—
769	C₂²×C₄	—	47	8	no	—
770	C₂²×C₄	—	47	8	no	—
771	C₂²×C₄	—	47	16	no	—
772	C₂²×C₄	—	47	16	no	—
773	C₂²×C₄	—	47	16	no	—
774	C₂²×C₄	—	94	8	no	—
775	C₂²×C₄	—	188	8	no	—
776	C₂²×C₄	—	188	8	no	—
777	C₂²×C₄	—	188	8	no	—
778	C₂²×C₄	—	188	4	no	—
779	C₂²×C₄	#10625350	1	8	yes	complemented
780	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
781	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
782	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
783	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
784	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
785	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
786	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
787	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
788	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
789	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
790	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
791	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
792	C₂²×C₄	C₂³×D₄₇	1	8	yes	—
793	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
794	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
795	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
796	C₄⋊C₄	—	47	16	no	—
797	C₄⋊C₄	—	47	8	no	—
798	C₄⋊C₄	—	47	16	no	—
799	C₄⋊C₄	—	47	16	no	—
800	C₄⋊C₄	—	47	8	no	—
801	C₄⋊C₄	—	47	8	no	—
802	C₄⋊C₄	—	47	8	no	—
803	C₄⋊C₄	—	47	4	no	—
804	C₄⋊C₄	—	47	4	no	—
805	C₄⋊C₄	—	47	16	no	—
806	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
807	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
808	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
809	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
810	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
811	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
812	C₂²⋊C₄	—	47	8	no	—
813	C₂²⋊C₄	—	47	8	no	—
814	C₂²⋊C₄	—	47	8	no	—
815	C₂²⋊C₄	—	47	16	no	—
816	C₂²⋊C₄	—	47	16	no	—
817	C₂²⋊C₄	—	47	16	no	—
818	C₂²⋊C₄	—	47	16	no	—
819	C₂²⋊C₄	—	47	16	no	—
820	C₂²⋊C₄	—	47	16	no	—
821	C₂²⋊C₄	—	47	8	no	—
822	C₂²⋊C₄	—	47	16	no	—
823	C₂²⋊C₄	—	47	8	no	—
824	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
825	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
826	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
827	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
828	C₄²	—	47	16	no	—
829	C₄²	—	47	8	no	—
830	C₄²	C₂³×D₄₇	1	8	yes	—
831	C₄²	C₂³×D₄₇	1	8	yes	—
832	C₄²	C₂³×D₄₇	1	8	yes	—
833	C₄²	C₂³×D₄₇	1	8	yes	—
834	C₂³	—	2	2	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	2	no	—
837	C₂³	—	2	2	no	—
838	C₂³	—	2	8	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	2	8	no	—
841	C₂³	—	2	2	no	—
842	C₂³	—	2	2	no	—
843	C₂³	—	4	4	no	—
844	C₂³	—	4	16	no	—
845	C₂³	—	47	8	no	—
846	C₂³	—	47	4	no	—
847	C₂³	—	94	16	no	—
848	C₂³	—	94	4	no	—
849	C₂³	—	94	8	no	—
850	C₂³	—	94	4	no	—
851	C₂³	—	94	8	no	—
852	C₂³	—	94	8	no	—
853	C₂³	—	94	4	no	—
854	C₂³	—	376	16	no	—
855	C₂³	—	188	8	no	—
856	C₂³	—	188	8	no	—
857	C₂³	C₂×#10625350	1	4	yes	—
858	C₂³	#13094070	1	4	yes	—
859	C₂³	C₂⁴×D₄₇	1	2	yes	—
860	C₂³	C₂⁴×D₄₇	1	2	yes	—
861	C₂³	C₂⁴×D₄₇	1	2	yes	—
862	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
863	Q₈	—	94	8	no	—
864	Q₈	—	188	16	no	—
865	D₄	—	94	16	no	—
866	D₄	—	94	32	no	—
867	D₄	—	94	16	no	—
868	D₄	—	94	16	no	—
869	D₄	—	94	16	no	—
870	D₄	—	94	8	no	—
871	D₄	—	188	16	no	—
872	D₄	—	188	16	no	—
873	D₄	—	188	8	no	—
874	D₄	—	188	16	no	—
875	C₂×C₄	—	2	8	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	4	no	—
879	C₂×C₄	—	2	4	no	—
880	C₂×C₄	—	2	16	no	—
881	C₂×C₄	—	2	4	no	—
882	C₂×C₄	—	2	4	no	—
883	C₂×C₄	—	2	8	no	—
884	C₂×C₄	—	2	8	no	—
885	C₂×C₄	—	2	8	no	—
886	C₂×C₄	—	2	8	no	—
887	C₂×C₄	—	4	8	no	—
888	C₂×C₄	—	47	4	no	—
889	C₂×C₄	—	47	4	no	—
890	C₂×C₄	—	47	4	no	—
891	C₂×C₄	—	47	8	no	—
892	C₂×C₄	—	94	4	no	—
893	C₂×C₄	—	94	8	no	—
894	C₂×C₄	—	94	4	no	—
895	C₂×C₄	—	94	4	no	—
896	C₂×C₄	—	94	16	no	—
897	C₂×C₄	—	188	16	no	—
898	C₂×C₄	—	188	16	no	—
899	C₂×C₄	—	188	16	no	—
900	C₂×C₄	—	188	8	no	—
901	C₂×C₄	C₂×#10625350	1	4	yes	—
902	C₂×C₄	C₂×#10625350	1	4	yes	—
903	C₂×C₄	C₂×#10625350	1	16	yes	complemented
904	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
905	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
906	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
907	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
908	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
909	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
910	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
911	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
912	C₂²	—	2	8	no	—
913	C₂²	—	2	8	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	4	16	no	—
922	C₂²	—	4	4	no	—
923	C₂²	—	94	4	no	—
924	C₂²	—	94	8	no	—
925	C₂²	—	94	4	no	—
926	C₂²	—	94	8	no	—
927	C₂²	—	94	8	no	—
928	C₂²	—	94	4	no	—
929	C₂²	—	376	16	no	—
930	C₂²	—	188	16	no	—
931	C₂²	—	188	8	no	—
932	C₂²	C₂²×#10625350	1	4	yes	—
933	C₂²	C₂²×#10625350	1	2	yes	—
934	C₂²	C₂×#13094070	1	4	yes	—
935	C₂²	C₂×#13094070	1	2	yes	—
936	C₂²	#15689959	1	2	yes	—
937	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
938	C₄	—	2	2	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	4	no	—
941	C₄	—	2	4	no	—
942	C₄	—	2	4	no	—
943	C₄	—	2	4	no	—
944	C₄	—	94	4	no	—
945	C₄	—	94	8	no	—
946	C₄	—	94	4	no	—
947	C₄	—	94	4	no	—
948	C₄	C₂²×#10625350	1	4	yes	—
949	C₄	C₂²×#10625350	1	4	yes	—
950	C₂	—	2	4	no	—
951	C₂	—	2	4	no	—
952	C₂	—	4	2	no	—
953	C₂	—	188	8	no	—
954	C₂	—	188	4	no	—
955	C₂	#20257123	1	4	yes	direct product factor
956	C₂	C₂³×#10625350	1	1	yes	characteristic
957	C₂	C₂²×#13094070	1	1	yes	characteristic
958	C₂	C₂×#15689959	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×#117×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁵
hypercenter	C₂²×#117	D₄₇
hypocenter	C₄₇	C₂×#3494
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. #20257123	C₂	direct (N × H)
2. C₂×#15689836	C₂	semidirect
3. C₂×#15689821	C₂	semidirect
4. C₂×#15689817	C₂	semidirect
5. C₂×#15689797	C₂	semidirect
6. C₂×#15689774	C₂	semidirect
7. C₂×#15689763	C₂	semidirect
8. C₂×#15689751	C₂	semidirect
9. C₂×#15689744	C₂	semidirect
10. C₂×#15689728	C₂	semidirect
11. C₂×#15689692	C₂	semidirect
12. C₂×#15689673	C₂	semidirect
13. C₂×#15689657	C₂	semidirect
14. C₂×#15689634	C₂	semidirect
15. C₂²×#13093998	C₂	semidirect
16. C₂×#15689603	C₂	semidirect
17. C₂×#15689597	C₂	semidirect
18. C₂²×#117×C₄₇	C₂	semidirect
20. C₂²×#10625350	C₂²	semidirect
23. #15689836	C₂²	semidirect
24. #15689821	C₂²	semidirect
25. #15689817	C₂²	semidirect
26. #15689797	C₂²	semidirect
27. #15689774	C₂²	semidirect
28. #15689763	C₂²	semidirect
29. #15689751	C₂²	semidirect
30. #15689744	C₂²	semidirect
31. #15689728	C₂²	semidirect
32. #15689692	C₂²	semidirect
33. #15689673	C₂²	semidirect
34. C₂×#13094024	C₂²	semidirect
35. C₂×#13094023	C₂²	semidirect
36. C₂×#13094021	C₂²	semidirect
37. #15689657	C₂²	semidirect
38. C₂×#13094019	C₂²	semidirect
39. C₂×#13094018	C₂²	semidirect
40. C₂×#13094016	C₂²	semidirect
41. C₂×#13094015	C₂²	semidirect
42. C₂×#13094012	C₂²	semidirect
43. C₂×#13094012	C₂²	semidirect
44. C₂×#13094010	C₂²	semidirect
45. #15689634	C₂²	semidirect
46. C₂×#13094009	C₂²	semidirect
47. C₂×#13094009	C₂²	semidirect
49. C₂×#13094007	C₂²	semidirect
50. C₂×#13094006	C₂²	semidirect
51. C₂×#13094003	C₂²	semidirect
52. C₂×#13094003	C₂²	semidirect
53. C₂×#13094002	C₂²	semidirect
55. C₂×#13093999	C₂²	semidirect
56. C₂×#13093999	C₂²	semidirect
61. C₂×#13093998	C₂²	semidirect
62. C₂×#13093998	C₂²	semidirect
63. C₂×#13093998	C₂²	semidirect
64. C₂×#13093998	C₂²	semidirect
65. C₂×#13093997	C₂²	semidirect
66. C₂×#13093997	C₂²	semidirect
69. #15689603	C₂²	semidirect
70. #15689597	C₂²	semidirect
71. C₂×C₄×Dic₉₄	C₂²	semidirect
72. C₂×C₄×D₁₈₈	C₂²	semidirect
73. C₂×C₄×D₁₈₈	C₂²	semidirect
74. C₂×C₄×D₁₈₈	C₂²	semidirect
75. C₂×C₄×D₁₈₈	C₂²	semidirect
76. C₂×#13093986	C₂²	semidirect
77. C₂×#13093986	C₂²	semidirect
78. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
79. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
80. C₂×C₄×C₂²⋊D₄₇	C₂²	semidirect
83. C₂×#13093982	C₂²	semidirect
84. C₂×#13093981	C₂²	semidirect
86. C₂×C₄⋊C₄×D₄₇	C₂²	semidirect
93. C₂×#117×C₄₇	C₂²	semidirect
94. C₂×#117×C₄₇	C₂²	semidirect
95. C₂×#117×C₄₇	C₂²	semidirect
96. C₂×#117×C₄₇	C₂²	semidirect
97. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
98. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
100. C₂²×C₄²×C₄₇	C₂²	semidirect
105. C₂×#10625350	C₂³	semidirect
127. #13094024	C₂³	semidirect
128. #13094023	C₂³	semidirect
129. #13094021	C₂³	semidirect
130. #13094019	C₂³	semidirect
131. #13094018	C₂³	semidirect
132. #13094016	C₂³	semidirect
133. #13094015	C₂³	semidirect
134. #13094012	C₂³	semidirect
135. #13094012	C₂³	semidirect
136. #13094010	C₂³	semidirect
137. #13094009	C₂³	semidirect
138. #13094009	C₂³	semidirect
140. #13094007	C₂³	semidirect
141. #13094006	C₂³	semidirect
142. #13094003	C₂³	semidirect
143. #13094003	C₂³	semidirect
144. #13094002	C₂³	semidirect
146. #13093999	C₂³	semidirect
147. #13093999	C₂³	semidirect
152. #13093998	C₂³	semidirect
153. #13093998	C₂³	semidirect
154. #13093998	C₂³	semidirect
155. #13093997	C₂³	semidirect
156. #13093997	C₂³	semidirect
159. C₄×Dic₉₄	C₂³	semidirect
160. C₄×D₁₈₈	C₂³	semidirect
161. C₄×D₁₈₈	C₂³	semidirect
162. C₄×D₁₈₈	C₂³	semidirect
163. C₄×D₁₈₈	C₂³	semidirect
164. #13093986	C₂³	semidirect
165. #13093986	C₂³	semidirect
166. C₄×C₂²⋊D₄₇	C₂³	semidirect
167. C₄×C₂²⋊D₄₇	C₂³	semidirect
168. C₄×C₂²⋊D₄₇	C₂³	semidirect
171. #13093982	C₂³	semidirect
172. #13093981	C₂³	semidirect
184. C₄⋊C₄×D₄₇	C₂³	semidirect
215. #117×C₄₇	C₂³	semidirect
216. #117×C₄₇	C₂³	semidirect
217. #117×C₄₇	C₂³	semidirect
224. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
225. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
235. C₂×C₄²×C₄₇	C₂³	semidirect
257. C₂²×C₄×C₄₇	#41	semidirect
398. C₂×C₄×C₄₇	C₂×#41	semidirect
488. C₂²×#117	D₄₇	semidirect
492. C₂×C₄₇	#3494	semidirect
568. C₂×#117	C₂×D₄₇	semidirect
569. C₂×#117	C₂×D₄₇	semidirect
570. C₂×#117	C₂×D₄₇	semidirect
571. C₂×#117	C₂×D₄₇	semidirect
574. C₂²×C₄⋊C₄	C₂×D₄₇	semidirect
575. C₂²×C₄⋊C₄	C₂×D₄₇	semidirect
579. C₂²×C₄²	C₂×D₄₇	semidirect
580. C₄₇	C₂×#3494	semidirect
667. #117	C₂²×D₄₇	semidirect
668. #117	C₂²×D₄₇	semidirect
669. #117	C₂²×D₄₇	semidirect
688. C₂×C₄⋊C₄	C₂²×D₄₇	semidirect
689. C₂×C₄⋊C₄	C₂²×D₄₇	semidirect
715. C₂×C₄²	C₂²×D₄₇	semidirect
779. C₂²×C₄	#10625350	semidirect
903. C₂×C₄	C₂×#10625350	semidirect
955. C₂	#20257123	direct (N × H)

Maximal subgroups

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

subgroup	index
#20257123	2
C₂×#15689836	2
C₂×#15689821	2
C₂×#15689817	2
C₂×#15689797	2
C₂×#15689774	2
C₂×#15689763	2
C₂×#15689751	2
C₂×#15689744	2
C₂×#15689728	2
C₂×#15689692	2
C₂×#15689673	2
C₂×#15689657	2
C₂×#15689634	2
C₂²×#13093998	2
C₂×#15689603	2
C₂×#15689597	2
C₂²×#117×C₄₇	2
C₂×#3494	47

Subgroups — C2×#20257123 #27124625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20257123 #27124625