Subgroups — #27124817

Order 12032.

11534 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689960	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#41×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#20257067	C₂	1	8	yes	maximal, complemented
4	#20257056	C₂	1	8	yes	maximal, complemented
5	#20257046	C₂	1	1	yes	maximal, characteristic, complemented
6	#20257040	C₂	1	1	yes	maximal, characteristic, complemented
7	#20257036	C₂	1	1	yes	maximal, characteristic, complemented
8	#20257030	C₂	1	6	yes	maximal, complemented
9	#20257022	C₂	1	6	yes	maximal, complemented
10	#20256878	C₂	1	8	yes	maximal, complemented
11	#20256877	C₂	1	8	yes	maximal, complemented
12	#20256719	C₂	1	6	yes	maximal, complemented
13	#525×D₄₇	C₂	1	6	yes	maximal, complemented
14	#20256590	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#3487	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689960	—	2	16	no	—
17	C₂×#13094072	C₂²	1	1	yes	characteristic, complemented
18	C₂×#13094072	C₂²	1	4	yes	complemented
19	C₂×#13094070	C₂²	1	6	yes	complemented
20	C₂×#13094070	C₂²	1	4	yes	complemented
21	C₂²×#10625354	C₂²	1	1	yes	characteristic
22	C₂²×#10625354	C₂²	1	4	yes	complemented
23	C₂²×#10625350	C₂²	1	3	yes	complemented
24	C₂²×#10625352	C₂²	1	3	yes	complemented
25	C₂×#41×D₄₇	—	2	16	no	—
26	C₂×#41×D₄₇	C₂²	1	8	yes	complemented
27	C₂×#41×D₄₇	C₂²	1	8	yes	complemented
28	C₂×#41×D₄₇	C₂²	1	6	yes	complemented
29	C₂×#41×D₄₇	C₂²	1	4	yes	complemented
30	C₂²×Q₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₄×D₄₇	C₂²	1	3	yes	complemented
32	C₂³×C₄×D₄₇	C₂²	1	3	yes	complemented
33	#15689792	C₂²	1	8	yes	complemented
34	Q₈×D₁₈₈	C₂²	1	8	yes	complemented
35	Q₈×C₂²⋊D₄₇	C₂²	1	8	yes	complemented
36	#15689785	C₂²	1	8	yes	complemented
37	#15689780	C₂²	1	8	yes	complemented
38	#15689780	C₂²	1	8	yes	complemented
39	#15689778	C₂²	1	24	yes	complemented
40	#15689775	C₂²	1	24	yes	complemented
41	#15689770	C₂²	1	24	yes	complemented
42	#15689770	C₂²	1	24	yes	complemented
43	#15689769	C₂²	1	24	yes	complemented
44	#15689766	C₂²	1	24	yes	complemented
45	#15689758	C₂²	1	24	yes	complemented
46	#15689757	C₂²	1	24	yes	complemented
47	#15689702	C₂²	1	24	yes	complemented
48	#15689699	C₂²	1	6	yes	complemented
49	#15689694	C₂²	1	6	yes	complemented
50	#15689693	C₂²	1	12	yes	complemented
51	#15689690	C₂²	1	6	yes	complemented
52	#15689686	C₂²	1	12	yes	complemented
53	#15689683	C₂²	1	24	yes	complemented
54	#15689672	C₂²	1	12	yes	complemented
55	#15689671	C₂²	1	12	yes	complemented
56	#15689636	C₂²	1	12	yes	complemented
57	#15689635	C₂²	1	6	yes	complemented
58	#15689634	C₂²	1	6	yes	complemented
59	#15689633	C₂²	1	12	yes	complemented
60	#15689633	C₂²	1	24	yes	complemented
61	#15689632	C₂²	1	24	yes	complemented
62	#15689631	C₂²	1	4	yes	complemented
63	#15689630	C₂²	1	6	yes	complemented
64	#15689629	C₂²	1	12	yes	complemented
65	#123×D₄₇	C₂²	1	12	yes	complemented
66	C₂²⋊Q₈×D₄₇	C₂²	1	12	yes	complemented
67	#121×D₄₇	C₂²	1	12	yes	complemented
68	#120×D₄₇	C₂²	1	12	yes	complemented
69	#15689605	C₂²	1	8	yes	complemented
70	#15689601	C₂²	1	1	yes	characteristic, complemented
71	#15689597	C₂²	1	6	yes	complemented
72	C₄×#10625354	C₂²	1	8	yes	complemented
73	C₄×D₄×D₄₇	C₂²	1	24	yes	complemented
74	#117×D₄₇	C₂²	1	6	yes	complemented
75	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic, complemented
76	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
77	C₄₇×#550	C₂²	1	8	yes	complemented
78	C₄₇×#548	C₂²	1	8	yes	complemented
79	C₄₇×#535	C₂²	1	6	yes	complemented
80	C₄₇×#525	C₂²	1	6	yes	complemented
81	C₄₇×#519	C₂²	1	1	yes	characteristic, complemented
82	C₂⁴×D₄₇	C₂³	1	3	yes	—
83	#13094072	—	2	8	no	—
84	#13094072	—	2	32	no	—
85	#13094070	—	2	32	no	—
86	#13094070	—	2	48	no	—
87	C₂×#10625354	—	2	32	no	—
88	C₂×#10625354	D₄	1	16	yes	complemented
89	C₂×#10625354	C₂³	1	4	yes	—
90	C₂×#10625354	C₂³	1	4	yes	—
91	C₂×#10625354	C₂³	1	12	yes	complemented
92	C₂×#10625354	C₂³	1	4	yes	complemented
93	C₂×#10625354	C₂³	1	6	yes	complemented
94	C₂×#10625350	—	2	24	no	—
95	C₂×#10625350	C₂³	1	24	yes	—
96	C₂×#10625350	C₂³	1	6	yes	—
97	C₂×#10625350	C₂³	1	12	yes	complemented
98	C₂×#10625350	C₂³	1	12	yes	complemented
99	C₂×#10625352	—	2	24	no	—
100	C₂×#10625352	C₂³	1	4	yes	—
101	C₂×#10625352	C₂³	1	12	yes	—
102	C₂×#10625352	C₂³	1	12	yes	—
103	C₂×#10625352	C₂³	1	6	yes	complemented
104	#41×D₄₇	—	2	64	no	—
105	#41×D₄₇	—	2	64	no	—
106	#41×D₄₇	—	2	32	no	—
107	#41×D₄₇	—	2	48	no	—
108	C₂²×Dic₉₄	C₂³	1	3	yes	—
109	C₂×Q₈×D₄₇	—	2	8	no	—
110	C₂×Q₈×D₄₇	C₂³	1	8	yes	—
111	C₂×Q₈×D₄₇	C₂³	1	4	yes	complemented
112	C₂×Q₈×D₄₇	C₂³	1	6	yes	complemented
113	C₂²×D₁₈₈	C₂³	1	3	yes	—
114	C₂²×D₁₈₈	C₂³	1	12	yes	complemented
115	C₂²×C₂²⋊D₄₇	C₂³	1	6	yes	—
116	C₂×D₄×D₄₇	—	2	24	no	—
117	C₂×D₄×D₄₇	C₂³	1	24	yes	—
118	C₂×D₄×D₄₇	C₂³	1	12	yes	—
119	C₂×D₄×D₄₇	C₂³	1	24	yes	—
120	C₂×D₄×D₄₇	C₂³	1	12	yes	complemented
121	C₂×D₄×D₄₇	C₂³	1	6	yes	complemented
122	C₂³×Dic₄₇	C₂³	1	3	yes	—
123	C₂²×C₄×D₄₇	—	2	24	no	—
124	C₂²×C₄×D₄₇	C₂³	1	12	yes	—
125	C₂²×C₄×D₄₇	C₂³	1	12	yes	—
126	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
127	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
128	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×D₄₇	C₂³	1	3	yes	—
130	C₂²×C₄×D₄₇	C₂³	1	12	yes	complemented
131	#13094024	C₂³	1	12	yes	complemented
132	#13094022	C₂³	1	12	yes	complemented
133	#13094020	C₂³	1	12	yes	complemented
134	#13094012	C₂³	1	12	yes	complemented
135	#13094011	C₂³	1	12	yes	complemented
136	#13094011	C₂³	1	12	yes	complemented
137	#13094009	C₂³	1	24	yes	complemented
138	#13094008	C₂³	1	12	yes	—
139	#13094007	C₂³	1	4	yes	—
140	#13094006	C₂³	1	48	yes	complemented
141	#13094006	C₂³	1	24	yes	complemented
142	#13094005	C₂³	1	12	yes	—
143	#13094004	C₂³	1	12	yes	—
144	#13094004	C₂³	1	24	yes	complemented
145	#13094003	C₂³	1	24	yes	complemented
146	#13094003	C₂³	1	12	yes	complemented
147	#13094002	C₂³	1	8	yes	—
148	#13094001	C₂³	1	24	yes	complemented
149	#13094000	C₂³	1	12	yes	—
150	#13093999	C₂³	1	12	yes	—
151	#13093998	C₂³	1	12	yes	complemented
152	#13093997	C₂³	1	8	yes	—
153	#13093997	C₂³	1	48	yes	complemented
154	#13093996	C₂³	1	24	yes	complemented
155	#13093995	C₂³	1	12	yes	—
156	#13093995	C₂³	1	24	yes	complemented
157	#13093995	C₂³	1	48	yes	complemented
158	#13093994	C₂³	1	24	yes	—
159	#13093994	C₂³	1	4	yes	—
160	#13093993	C₂³	1	12	yes	—
161	#13093992	C₂³	1	24	yes	—
162	#13093992	C₂³	1	4	yes	—
163	#13093992	C₂³	1	48	yes	complemented
164	Q₈×Dic₄₇	C₂³	1	8	yes	complemented
165	C₄×D₁₈₈	C₂³	1	24	yes	—
166	C₄×D₁₈₈	C₂³	1	24	yes	complemented
167	D₄×Dic₄₇	C₂³	1	24	yes	complemented
168	#13093986	C₂³	1	8	yes	—
169	#13093986	C₂³	1	24	yes	complemented
170	C₄×C₂²⋊D₄₇	C₂³	1	24	yes	—
171	C₄×C₂²⋊D₄₇	C₂³	1	24	yes	complemented
172	(C₂²⋊D₄₇)⋊C₄	C₂³	1	8	yes	—
173	(C₂²⋊D₄₇)⋊C₄	C₂³	1	24	yes	complemented
174	#13093983	C₂³	1	6	yes	—
175	#13093982	C₂³	1	12	yes	complemented
176	#13093981	C₂³	1	12	yes	complemented
177	#13093980	C₂³	1	4	yes	—
178	C₄⋊C₄×D₄₇	C₂³	1	24	yes	complemented
179	C₄⋊C₄×D₄₇	C₂³	1	12	yes	complemented
180	C₂²⋊C₄×D₄₇	C₂³	1	24	yes	—
181	C₂²⋊C₄×D₄₇	C₂³	1	12	yes	—
182	C₂²⋊C₄×D₄₇	C₂³	1	24	yes	complemented
183	C₄²×D₄₇	C₂³	1	12	yes	complemented
184	2₋¹⁺⁴×C₄₇	—	2	8	no	—
185	C₂×#41×C₄₇	—	2	8	no	—
186	C₂×#41×C₄₇	C₂³	1	8	yes	—
187	C₂×#41×C₄₇	C₂³	1	6	yes	—
188	C₂×#41×C₄₇	C₂³	1	4	yes	complemented
189	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
190	C₂²×Q₈×C₄₇	C₂³	1	4	yes	complemented
191	C₂²×D₄×C₄₇	C₂³	1	3	yes	—
192	C₂³×C₄×C₄₇	C₂³	1	3	yes	—
193	#127×C₄₇	C₂³	1	12	yes	complemented
194	#124×C₄₇	C₂³	1	12	yes	complemented
195	#123×C₄₇	C₂³	1	4	yes	—
196	C₂²⋊Q₈×C₄₇	C₂³	1	12	yes	complemented
197	#121×C₄₇	C₂³	1	24	yes	complemented
198	#121×C₄₇	C₂³	1	12	yes	complemented
199	#120×C₄₇	C₂³	1	12	yes	—
200	C₄×Q₈×C₄₇	C₂³	1	8	yes	complemented
201	C₄×D₄×C₄₇	C₂³	1	24	yes	complemented
202	#117×C₄₇	C₂³	1	6	yes	—
203	C₂⁴×C₄₇	C₂⁴	1	3	yes	—
204	C₂³×D₄₇	—	2	12	no	—
205	C₂³×D₄₇	—	4	12	no	—
206	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
207	C₂³×D₄₇	C₂⁴	1	12	yes	—
208	C₂³×D₄₇	C₂⁴	1	12	yes	—
209	C₂³×D₄₇	C₂⁴	1	3	yes	—
210	#41×C₄₇	—	2	32	no	—
211	#41×C₄₇	—	2	16	no	—
212	#41×C₄₇	—	2	24	no	—
213	C₂×Q₈×C₄₇	—	2	16	no	—
214	C₂×Q₈×C₄₇	C₂×D₄	1	8	yes	complemented
215	C₂×Q₈×C₄₇	C₂⁴	1	6	yes	—
216	C₂×Q₈×C₄₇	C₂⁴	1	4	yes	—
217	C₂×D₄×C₄₇	—	2	12	no	—
218	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
219	C₂×D₄×C₄₇	C₂⁴	1	12	yes	—
220	C₂×D₄×C₄₇	C₂⁴	1	6	yes	—
221	C₂×D₄×C₄₇	C₂⁴	1	24	yes	—
222	C₂²×C₄×C₄₇	—	2	12	no	—
223	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
224	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
225	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
227	C₂×C₂²⋊D₄₇	—	2	24	no	—
228	C₂×C₂²⋊D₄₇	C₂⁴	1	8	yes	—
229	C₂×C₂²⋊D₄₇	C₂⁴	1	12	yes	—
230	C₂×C₂²⋊D₄₇	C₂⁴	1	24	yes	—
231	C₂×C₂²⋊D₄₇	C₂⁴	1	4	yes	—
232	C₂×C₂²⋊D₄₇	C₂⁴	1	4	yes	—
233	C₂×C₂²⋊D₄₇	C₂⁴	1	24	yes	—
234	C₂²×Dic₄₇	—	2	12	no	—
235	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
236	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
237	C₂²×Dic₄₇	C₂⁴	1	6	yes	—
238	C₂²×Dic₄₇	C₂⁴	1	3	yes	—
239	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
240	#10625354	—	2	16	no	—
241	#10625354	—	2	48	no	—
242	#10625354	—	2	24	no	—
243	#10625354	C₂×D₄	1	32	yes	complemented
244	#10625354	C₂×D₄	1	32	yes	complemented
245	Q₈×D₄₇	—	2	32	no	—
246	Q₈×D₄₇	—	2	16	no	—
247	Q₈×D₄₇	—	2	24	no	—
248	#10625352	—	2	16	no	—
249	#10625352	—	2	24	no	—
250	#10625352	—	2	48	no	—
251	#10625352	—	2	48	no	—
252	D₄×D₄₇	—	2	48	no	—
253	D₄×D₄₇	—	2	96	no	—
254	D₄×D₄₇	—	2	48	no	—
255	D₄×D₄₇	—	2	24	no	—
256	D₄×D₄₇	—	4	48	no	—
257	#10625350	—	2	24	no	—
258	#10625350	—	2	96	no	—
259	#10625350	—	2	48	no	—
260	#10625350	—	2	48	no	—
261	C₂×D₁₈₈	—	2	48	no	—
262	C₂×D₁₈₈	C₂×D₄	1	24	yes	complemented
263	C₂×D₁₈₈	C₂⁴	1	8	yes	—
264	C₂×D₁₈₈	C₂⁴	1	12	yes	—
265	C₂×D₁₈₈	C₂⁴	1	6	yes	—
266	C₂×D₁₈₈	C₂⁴	1	12	yes	—
267	C₂×C₄×D₄₇	—	2	12	no	—
268	C₂×C₄×D₄₇	—	2	12	no	—
269	C₂×C₄×D₄₇	—	2	4	no	—
270	C₂×C₄×D₄₇	—	2	48	no	—
271	C₂×C₄×D₄₇	—	2	48	no	—
272	C₂×C₄×D₄₇	—	2	48	no	—
273	C₂×C₄×D₄₇	C₂×D₄	1	24	yes	complemented
274	C₂×C₄×D₄₇	C₂⁴	1	12	yes	—
275	C₂×C₄×D₄₇	C₂⁴	1	12	yes	—
276	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
277	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
278	C₂×C₄×D₄₇	C₂⁴	1	12	yes	—
279	C₂×C₄×D₄₇	C₂⁴	1	12	yes	—
280	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
281	C₂×C₄×D₄₇	C₂⁴	1	24	yes	—
282	C₂×C₄×D₄₇	C₂⁴	1	6	yes	—
283	C₂×C₄×D₄₇	C₂⁴	1	6	yes	—
284	C₂×Dic₉₄	—	2	12	no	—
285	C₂×Dic₉₄	C₂⁴	1	4	yes	—
286	C₂×Dic₉₄	C₂⁴	1	6	yes	—
287	C₂×Dic₉₄	C₂⁴	1	12	yes	—
288	C₄⋊C₄×C₄₇	C₂⁴	1	12	yes	—
289	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
290	C₂²⋊C₄×C₄₇	C₂⁴	1	4	yes	—
291	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
292	C₂²⋊C₄×C₄₇	C₂⁴	1	24	yes	—
293	C₄²×C₄₇	C₂⁴	1	12	yes	—
294	C₂²⋊Dic₄₇	C₂⁴	1	4	yes	—
295	C₂²⋊Dic₄₇	C₂⁴	1	24	yes	—
296	C₂²⋊Dic₄₇	C₂⁴	1	24	yes	—
297	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
298	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
299	(C₂×D₄₇)⋊C₄	C₂⁴	1	24	yes	—
300	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
301	(C₂×D₄₇)⋊C₄	C₂⁴	1	24	yes	—
302	C₄⋊Dic₄₇	C₂⁴	1	12	yes	—
303	C₄⋊Dic₄₇	C₂⁴	1	24	yes	—
304	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
305	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
306	Dic₄₇⋊C₄	C₂⁴	1	24	yes	—
307	C₄×Dic₄₇	C₂⁴	1	8	yes	—
308	C₄×Dic₄₇	C₂⁴	1	12	yes	—
309	C₂³×C₄₇	—	2	6	no	—
310	C₂³×C₄₇	—	4	6	no	—
311	C₂³×C₄₇	C₂⁵	1	4	yes	—
312	C₂³×C₄₇	C₂⁵	1	6	yes	—
313	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
314	C₂²×D₄₇	—	2	2	no	—
315	C₂²×D₄₇	—	2	4	no	—
316	C₂²×D₄₇	—	2	24	no	—
317	C₂²×D₄₇	—	2	24	no	—
318	C₂²×D₄₇	—	2	24	no	—
319	C₂²×D₄₇	—	4	6	no	—
320	C₂²×D₄₇	—	4	12	no	—
321	C₂²×D₄₇	—	4	24	no	—
322	C₂²×D₄₇	—	4	48	no	—
323	C₂²×D₄₇	C₂²×D₄	1	12	yes	—
324	C₂²×D₄₇	C₂⁵	1	4	yes	—
325	C₂²×D₄₇	C₂⁵	1	6	yes	—
326	C₂²×D₄₇	C₂⁵	1	2	yes	—
327	Q₈×C₄₇	—	2	12	no	—
328	Q₈×C₄₇	C₂²×D₄	1	16	yes	—
329	D₄×C₄₇	—	2	8	no	—
330	D₄×C₄₇	—	2	12	no	—
331	D₄×C₄₇	—	2	24	no	—
332	D₄×C₄₇	—	4	24	no	—
333	C₂×C₄×C₄₇	—	2	2	no	—
334	C₂×C₄×C₄₇	—	2	24	no	—
335	C₂×C₄×C₄₇	—	2	24	no	—
336	C₂×C₄×C₄₇	C₂²×D₄	1	12	yes	—
337	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
338	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
339	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
340	C₂×C₄×C₄₇	C₂⁵	1	6	yes	—
341	C₂²⋊D₄₇	—	2	8	no	—
342	C₂²⋊D₄₇	—	2	24	no	—
343	C₂²⋊D₄₇	—	2	48	no	—
344	C₂²⋊D₄₇	—	2	16	no	—
345	C₂²⋊D₄₇	—	2	8	no	—
346	C₂²⋊D₄₇	—	4	24	no	—
347	C₂×Dic₄₇	—	2	6	no	—
348	C₂×Dic₄₇	—	2	8	no	—
349	C₂×Dic₄₇	—	2	12	no	—
350	C₂×Dic₄₇	—	2	12	no	—
351	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
352	C₂×Dic₄₇	C₂⁵	1	8	yes	—
353	C₂×Dic₄₇	C₂⁵	1	6	yes	—
354	C₂×Dic₄₇	C₂⁵	1	4	yes	—
355	C₂×Dic₄₇	C₂⁵	1	1	yes	characteristic
356	C₂×Dic₄₇	C₂⁵	1	1	yes	characteristic
357	D₁₈₈	—	2	24	no	—
358	D₁₈₈	—	2	16	no	—
359	D₁₈₈	—	2	12	no	—
360	D₁₈₈	C₂²×D₄	1	48	yes	—
361	C₄×D₄₇	—	2	24	no	—
362	C₄×D₄₇	—	2	24	no	—
363	C₄×D₄₇	—	2	24	no	—
364	C₄×D₄₇	—	2	24	no	—
365	C₄×D₄₇	—	2	4	no	—
366	C₄×D₄₇	—	2	4	no	—
367	C₄×D₄₇	—	2	8	no	—
368	C₄×D₄₇	—	4	24	no	—
369	C₄×D₄₇	C₂²×D₄	1	24	yes	—
370	C₄×D₄₇	C₂²×D₄	1	24	yes	—
371	Dic₉₄	—	2	24	no	—
372	Dic₉₄	—	2	12	no	—
373	Dic₉₄	—	2	8	no	—
374	#62811	—	47	1	no	maximal, Sylow
375	C₂²×C₄₇	—	2	2	no	—
376	C₂²×C₄₇	—	2	6	no	—
377	C₂²×C₄₇	—	2	4	no	—
378	C₂²×C₄₇	—	2	8	no	—
379	C₂²×C₄₇	—	2	12	no	—
380	C₂²×C₄₇	—	4	12	no	—
381	C₂²×C₄₇	C₂³×D₄	1	2	yes	—
382	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
383	C₂×D₄₇	—	2	8	no	—
384	C₂×D₄₇	—	2	2	no	—
385	C₂×D₄₇	—	2	12	no	—
386	C₂×D₄₇	—	2	2	no	—
387	C₂×D₄₇	—	2	4	no	—
388	C₂×D₄₇	—	2	8	no	—
389	C₂×D₄₇	—	4	12	no	—
390	C₂×D₄₇	—	4	48	no	—
391	C₂×D₄₇	—	8	24	no	—
392	C₂×D₄₇	C₂³×D₄	1	12	yes	—
393	C₂×D₄₇	#585	1	4	yes	complemented
394	C₄×C₄₇	—	2	4	no	—
395	C₄×C₄₇	—	2	2	no	—
396	C₄×C₄₇	—	2	8	no	—
397	C₄×C₄₇	C₂³×D₄	1	12	yes	—
398	Dic₄₇	—	2	4	no	—
399	Dic₄₇	—	2	6	no	—
400	Dic₄₇	—	2	8	no	—
401	Dic₄₇	C₂³×D₄	1	2	yes	—
402	Dic₄₇	C₂³×D₄	1	2	yes	—
403	C₂×#585	—	47	1	no	—
404	C₂³×#41	—	47	1	no	—
405	#3489	—	47	8	no	—
406	#3488	—	47	8	no	—
407	#3487	—	47	1	no	—
408	#3487	D₄₇	1	1	yes	characteristic, complemented
409	#3486	—	47	1	no	—
410	#3486	—	47	1	no	—
411	#3485	—	47	6	no	—
412	#3484	—	47	6	no	—
413	D₄×#41	—	47	8	no	—
414	D₄×#41	—	47	8	no	—
415	#3449	—	47	6	no	—
416	C₂×#525	—	47	6	no	—
417	#3428	—	47	1	no	—
418	C₂×C₄₇	—	2	2	no	—
419	C₂×C₄₇	—	4	6	no	—
420	C₂×C₄₇	—	4	4	no	—
421	C₂×C₄₇	C₂⁴×D₄	1	1	yes	characteristic
422	C₂×C₄₇	C₂×#585	1	2	yes	—
423	D₄₇	—	2	4	no	—
424	D₄₇	—	2	12	no	—
425	D₄₇	—	4	4	no	—
426	#585	—	94	16	no	—
427	C₂×2₋¹⁺⁴	—	47	1	no	—
428	C₂×2₋¹⁺⁴	—	47	4	no	—
429	C₂×2₋¹⁺⁴	C₂×D₄₇	1	1	yes	characteristic, complemented
430	C₂×H(5,𝔽₂)	—	47	6	no	—
431	C₂×H(5,𝔽₂)	—	47	4	no	—
432	C₂²×#41	—	47	8	no	—
433	C₂²×#41	—	47	8	no	—
434	C₂²×#41	—	47	6	no	—
435	C₂²×#41	—	47	4	no	—
436	C₂²×#41	—	47	1	no	—
437	C₂²×#41	—	47	4	no	—
438	C₂²×#41	—	47	3	no	—
439	C₂²×#41	—	47	3	no	—
440	C₂²×#41	—	94	16	no	—
441	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
442	C₂³×Q₈	—	47	1	no	—
443	C₂³×D₄	—	47	3	no	—
444	C₂⁴×C₄	—	47	3	no	—
445	#550	—	47	8	no	—
446	#550	C₂×D₄₇	1	8	yes	complemented
447	D₄×Q₈	—	47	8	no	—
448	D₄×Q₈	—	47	8	no	—
449	#548	—	47	8	no	—
450	#548	—	47	8	no	—
451	#548	—	47	8	no	—
452	#548	C₂×D₄₇	1	8	yes	complemented
453	#547	—	47	24	no	—
454	#547	—	47	24	no	—
455	#546	—	47	24	no	—
456	#546	—	47	24	no	—
457	#546	—	47	24	no	—
458	#546	—	47	24	no	—
459	D₄²	—	47	24	no	—
460	D₄²	—	47	24	no	—
461	#537	—	47	24	no	—
462	#536	—	47	6	no	—
463	#536	—	47	12	no	—
464	#536	—	47	6	no	—
465	#535	—	47	6	no	—
466	#535	—	47	12	no	—
467	#535	C₂×D₄₇	1	6	yes	complemented
468	#534	—	47	24	no	—
469	#532	—	47	12	no	—
470	#532	—	47	12	no	—
471	#525	—	47	6	no	—
472	#525	—	47	6	no	—
473	#525	—	47	4	no	—
474	#525	—	47	12	no	—
475	#525	—	47	12	no	—
476	#525	—	47	24	no	—
477	#525	—	47	12	no	—
478	#525	—	47	24	no	—
479	#525	—	47	6	no	—
480	#525	C₂×D₄₇	1	6	yes	complemented
481	C₂×#123	—	47	12	no	—
482	C₂×C₂²⋊Q₈	—	47	12	no	—
483	C₂×#121	—	47	12	no	—
484	C₂×#120	—	47	12	no	—
485	#520	—	47	8	no	—
486	#519	—	47	1	no	—
487	#519	C₂×D₄₇	1	1	yes	characteristic, complemented
488	#518	—	47	6	no	—
489	C₄×#41	—	47	8	no	—
490	C₂×C₄×D₄	—	47	24	no	—
491	C₂×#117	—	47	6	no	—
492	C₄₇	#62811	1	1	yes	characteristic, complemented, Sylow
493	C₂⁵	—	47	3	no	—
494	2₋¹⁺⁴	—	2	8	no	—
495	2₋¹⁺⁴	—	94	32	no	—
496	2₋¹⁺⁴	—	94	8	no	—
497	H(5,𝔽₂)	—	94	48	no	—
498	H(5,𝔽₂)	—	94	32	no	—
499	C₂×#41	—	2	8	no	—
500	C₂×#41	—	47	16	no	—
501	C₂×#41	—	47	4	no	—
502	C₂×#41	—	47	4	no	—
503	C₂×#41	—	47	6	no	—
504	C₂×#41	—	47	12	no	—
505	C₂×#41	—	47	4	no	—
506	C₂×#41	—	47	4	no	—
507	C₂×#41	—	47	12	no	—
508	C₂×#41	—	47	6	no	—
509	C₂×#41	—	47	12	no	—
510	C₂×#41	—	47	6	no	—
511	C₂×#41	—	47	12	no	—
512	C₂×#41	—	47	24	no	—
513	C₂×#41	—	47	12	no	—
514	C₂×#41	—	94	24	no	—
515	C₂×#41	—	94	24	no	—
516	C₂×#41	—	94	48	no	—
517	C₂×#41	—	94	32	no	—
518	C₂×#41	—	94	64	no	—
519	C₂×#41	—	94	64	no	—
520	C₂×#41	—	94	32	no	—
521	C₂×#41	C₂²×D₄₇	1	6	yes	—
522	C₂×#41	C₂²×D₄₇	1	8	yes	—
523	C₂×#41	C₂²×D₄₇	1	4	yes	complemented
524	C₂²×Q₈	—	47	6	no	—
525	C₂²×Q₈	—	47	8	no	—
526	C₂²×Q₈	—	47	4	no	—
527	C₂²×Q₈	—	47	3	no	—
528	C₂²×Q₈	—	94	8	no	—
529	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
530	C₂²×Q₈	C₂²×D₄₇	1	4	yes	complemented
531	C₂²×D₄	—	47	6	no	—
532	C₂²×D₄	—	47	12	no	—
533	C₂²×D₄	—	47	6	no	—
534	C₂²×D₄	—	47	24	no	—
535	C₂²×D₄	—	47	12	no	—
536	C₂²×D₄	—	47	24	no	—
537	C₂²×D₄	—	47	3	no	—
538	C₂²×D₄	—	47	12	no	—
539	C₂²×D₄	—	94	24	no	—
540	C₂²×D₄	C₂²×D₄₇	1	3	yes	—
541	C₂³×C₄	—	47	3	no	—
542	C₂³×C₄	—	47	3	no	—
543	C₂³×C₄	—	47	12	no	—
544	C₂³×C₄	—	47	12	no	—
545	C₂³×C₄	—	47	12	no	—
546	C₂³×C₄	—	47	3	no	—
547	C₂³×C₄	—	47	1	no	—
548	C₂³×C₄	—	47	3	no	—
549	C₂³×C₄	—	94	24	no	—
550	C₂³×C₄	C₂²×D₄₇	1	3	yes	—
551	C₄⋊Q₈	—	47	12	no	—
552	C₄⋊Q₈	—	47	12	no	—
553	#127	—	47	12	no	—
554	#127	C₂²×D₄₇	1	12	yes	complemented
555	#124	—	47	12	no	—
556	#124	—	47	12	no	—
557	#124	—	47	12	no	—
558	#124	C₂²×D₄₇	1	12	yes	complemented
559	#123	—	47	12	no	—
560	#123	—	47	4	no	—
561	#123	—	47	24	no	—
562	#123	—	47	12	no	—
563	#123	—	47	24	no	—
564	#123	—	47	48	no	—
565	#123	C₂²×D₄₇	1	4	yes	—
566	C₂²⋊Q₈	—	47	12	no	—
567	C₂²⋊Q₈	—	47	12	no	—
568	C₂²⋊Q₈	—	47	24	no	—
569	C₂²⋊Q₈	—	47	8	no	—
570	C₂²⋊Q₈	—	47	12	no	—
571	C₂²⋊Q₈	—	47	24	no	—
572	C₂²⋊Q₈	—	47	24	no	—
573	C₂²⋊Q₈	C₂²×D₄₇	1	12	yes	complemented
574	#121	—	47	24	no	—
575	#121	—	47	12	no	—
576	#121	—	47	24	no	—
577	#121	—	47	48	no	—
578	#121	—	47	12	no	—
579	#121	—	47	12	no	—
580	#121	—	47	8	no	—
581	#121	—	47	48	no	—
582	#121	C₂²×D₄₇	1	12	yes	complemented
583	#121	C₂²×D₄₇	1	24	yes	complemented
584	#120	—	47	12	no	—
585	#120	—	47	4	no	—
586	#120	—	47	24	no	—
587	#120	—	47	48	no	—
588	#120	—	47	4	no	—
589	#120	—	47	24	no	—
590	#120	C₂²×D₄₇	1	12	yes	—
591	C₄×Q₈	—	47	8	no	—
592	C₄×Q₈	C₂²×D₄₇	1	8	yes	complemented
593	C₄×D₄	—	47	24	no	—
594	C₄×D₄	—	47	24	no	—
595	C₄×D₄	—	47	24	no	—
596	C₄×D₄	—	47	8	no	—
597	C₄×D₄	—	47	24	no	—
598	C₄×D₄	—	47	8	no	—
599	C₄×D₄	—	47	24	no	—
600	C₄×D₄	—	47	24	no	—
601	C₄×D₄	—	47	24	no	—
602	C₄×D₄	C₂²×D₄₇	1	24	yes	complemented
603	#117	—	47	6	no	—
604	#117	—	47	12	no	—
605	#117	—	47	4	no	—
606	#117	—	47	12	no	—
607	#117	C₂²×D₄₇	1	6	yes	—
608	C₂×C₄⋊C₄	—	47	12	no	—
609	C₂×C₄⋊C₄	—	47	24	no	—
610	C₂×C₂²⋊C₄	—	47	12	no	—
611	C₂×C₂²⋊C₄	—	47	24	no	—
612	C₂×C₂²⋊C₄	—	47	24	no	—
613	C₂×C₄²	—	47	12	no	—
614	C₂⁴	—	47	3	no	—
615	C₂⁴	—	47	1	no	—
616	C₂⁴	—	47	12	no	—
617	C₂⁴	—	47	12	no	—
618	C₂⁴	—	94	12	no	—
619	C₂⁴	—	188	12	no	—
620	C₂⁴	C₂³×D₄₇	1	3	yes	—
621	#41	—	2	32	no	—
622	#41	—	2	16	no	—
623	#41	—	2	24	no	—
624	#41	—	47	32	no	—
625	#41	—	47	32	no	—
626	#41	—	94	48	no	—
627	#41	—	94	96	no	—
628	#41	—	94	48	no	—
629	#41	—	94	16	no	—
630	#41	—	94	48	no	—
631	#41	—	94	24	no	—
632	#41	—	94	48	no	—
633	#41	—	94	24	no	—
634	#41	—	94	48	no	—
635	#41	—	94	16	no	—
636	#41	—	94	24	no	—
637	C₂×Q₈	—	2	16	no	—
638	C₂×Q₈	—	47	4	no	—
639	C₂×Q₈	—	47	6	no	—
640	C₂×Q₈	—	47	12	no	—
641	C₂×Q₈	—	94	24	no	—
642	C₂×Q₈	—	94	32	no	—
643	C₂×Q₈	—	94	16	no	—
644	C₂×Q₈	—	94	12	no	—
645	C₂×Q₈	D₄×D₄₇	1	8	yes	complemented
646	C₂×Q₈	C₂³×D₄₇	1	6	yes	—
647	C₂×Q₈	C₂³×D₄₇	1	4	yes	—
648	C₂×D₄	—	2	12	no	—
649	C₂×D₄	—	47	8	no	—
650	C₂×D₄	—	47	4	no	—
651	C₂×D₄	—	47	12	no	—
652	C₂×D₄	—	47	24	no	—
653	C₂×D₄	—	47	4	no	—
654	C₂×D₄	—	47	24	no	—
655	C₂×D₄	—	47	24	no	—
656	C₂×D₄	—	47	12	no	—
657	C₂×D₄	—	47	8	no	—
658	C₂×D₄	—	47	12	no	—
659	C₂×D₄	—	47	6	no	—
660	C₂×D₄	—	94	48	no	—
661	C₂×D₄	—	94	24	no	—
662	C₂×D₄	—	94	96	no	—
663	C₂×D₄	—	94	48	no	—
664	C₂×D₄	—	94	48	no	—
665	C₂×D₄	—	94	24	no	—
666	C₂×D₄	—	188	48	no	—
667	C₂×D₄	C₂³×D₄₇	1	4	yes	—
668	C₂×D₄	C₂³×D₄₇	1	6	yes	—
669	C₂×D₄	C₂³×D₄₇	1	12	yes	—
670	C₂×D₄	C₂³×D₄₇	1	24	yes	—
671	C₂²×C₄	—	2	12	no	—
672	C₂²×C₄	—	47	1	no	—
673	C₂²×C₄	—	47	24	no	—
674	C₂²×C₄	—	47	6	no	—
675	C₂²×C₄	—	47	6	no	—
676	C₂²×C₄	—	47	4	no	—
677	C₂²×C₄	—	47	6	no	—
678	C₂²×C₄	—	47	6	no	—
679	C₂²×C₄	—	47	3	no	—
680	C₂²×C₄	—	47	12	no	—
681	C₂²×C₄	—	47	12	no	—
682	C₂²×C₄	—	47	2	no	—
683	C₂²×C₄	—	47	4	no	—
684	C₂²×C₄	—	47	12	no	—
685	C₂²×C₄	—	47	12	no	—
686	C₂²×C₄	—	47	2	no	—
687	C₂²×C₄	—	47	24	no	—
688	C₂²×C₄	—	94	4	no	—
689	C₂²×C₄	—	94	48	no	—
690	C₂²×C₄	—	94	48	no	—
691	C₂²×C₄	—	94	48	no	—
692	C₂²×C₄	—	94	12	no	—
693	C₂²×C₄	—	94	12	no	—
694	C₂²×C₄	—	94	12	no	—
695	C₂²×C₄	C₂³×D₄₇	1	12	yes	—
696	C₂²×C₄	C₂³×D₄₇	1	12	yes	—
697	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
698	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
699	C₄⋊C₄	—	47	8	no	—
700	C₄⋊C₄	—	47	8	no	—
701	C₄⋊C₄	—	47	24	no	—
702	C₄⋊C₄	—	47	12	no	—
703	C₄⋊C₄	—	47	24	no	—
704	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
705	C₄⋊C₄	C₂³×D₄₇	1	12	yes	—
706	C₂²⋊C₄	—	47	4	no	—
707	C₂²⋊C₄	—	47	24	no	—
708	C₂²⋊C₄	—	47	24	no	—
709	C₂²⋊C₄	—	47	8	no	—
710	C₂²⋊C₄	—	47	8	no	—
711	C₂²⋊C₄	—	47	8	no	—
712	C₂²⋊C₄	—	47	24	no	—
713	C₂²⋊C₄	—	47	24	no	—
714	C₂²⋊C₄	C₂³×D₄₇	1	4	yes	—
715	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
716	C₂²⋊C₄	C₂³×D₄₇	1	24	yes	—
717	C₄²	—	47	8	no	—
718	C₄²	—	47	12	no	—
719	C₄²	C₂³×D₄₇	1	12	yes	—
720	C₂³	—	2	6	no	—
721	C₂³	—	4	6	no	—
722	C₂³	—	47	2	no	—
723	C₂³	—	47	6	no	—
724	C₂³	—	47	12	no	—
725	C₂³	—	47	4	no	—
726	C₂³	—	94	4	no	—
727	C₂³	—	94	24	no	—
728	C₂³	—	94	24	no	—
729	C₂³	—	94	24	no	—
730	C₂³	—	94	2	no	—
731	C₂³	—	188	24	no	—
732	C₂³	—	188	6	no	—
733	C₂³	—	188	12	no	—
734	C₂³	—	188	48	no	—
735	C₂³	C₂⁴×D₄₇	1	4	yes	—
736	C₂³	C₂⁴×D₄₇	1	6	yes	—
737	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
738	Q₈	—	2	12	no	—
739	Q₈	—	94	8	no	—
740	Q₈	—	94	24	no	—
741	Q₈	—	94	12	no	—
742	Q₈	C₂×D₄×D₄₇	1	16	yes	—
743	D₄	—	2	8	no	—
744	D₄	—	2	24	no	—
745	D₄	—	2	12	no	—
746	D₄	—	4	24	no	—
747	D₄	—	47	48	no	—
748	D₄	—	94	24	no	—
749	D₄	—	94	16	no	—
750	D₄	—	94	8	no	—
751	D₄	—	94	24	no	—
752	D₄	—	94	48	no	—
753	D₄	—	94	16	no	—
754	D₄	—	94	8	no	—
755	D₄	—	94	12	no	—
756	D₄	—	188	24	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	24	no	—
759	C₂×C₄	—	2	24	no	—
760	C₂×C₄	—	47	4	no	—
761	C₂×C₄	—	47	1	no	—
762	C₂×C₄	—	47	1	no	—
763	C₂×C₄	—	47	24	no	—
764	C₂×C₄	—	47	24	no	—
765	C₂×C₄	—	47	8	no	—
766	C₂×C₄	—	47	6	no	—
767	C₂×C₄	—	47	4	no	—
768	C₂×C₄	—	94	4	no	—
769	C₂×C₄	—	94	4	no	—
770	C₂×C₄	—	94	8	no	—
771	C₂×C₄	—	94	24	no	—
772	C₂×C₄	—	94	24	no	—
773	C₂×C₄	—	94	8	no	—
774	C₂×C₄	—	94	12	no	—
775	C₂×C₄	—	94	12	no	—
776	C₂×C₄	—	94	6	no	—
777	C₂×C₄	—	94	24	no	—
778	C₂×C₄	—	94	24	no	—
779	C₂×C₄	—	188	24	no	—
780	C₂×C₄	C₂×D₄×D₄₇	1	12	yes	—
781	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
782	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
783	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
784	C₂×C₄	C₂⁴×D₄₇	1	6	yes	—
785	C₂²	—	2	2	no	—
786	C₂²	—	2	4	no	—
787	C₂²	—	2	6	no	—
788	C₂²	—	2	8	no	—
789	C₂²	—	2	12	no	—
790	C₂²	—	4	12	no	—
791	C₂²	—	47	12	no	—
792	C₂²	—	47	4	no	—
793	C₂²	—	94	8	no	—
794	C₂²	—	94	2	no	—
795	C₂²	—	94	12	no	—
796	C₂²	—	94	2	no	—
797	C₂²	—	94	4	no	—
798	C₂²	—	94	8	no	—
799	C₂²	—	376	24	no	—
800	C₂²	—	188	12	no	—
801	C₂²	—	188	48	no	—
802	C₂²	C₂²×D₄×D₄₇	1	2	yes	—
803	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
804	C₄	—	2	2	no	—
805	C₄	—	2	4	no	—
806	C₄	—	2	8	no	—
807	C₄	—	47	2	no	—
808	C₄	—	47	2	no	—
809	C₄	—	94	6	no	—
810	C₄	—	94	4	no	—
811	C₄	—	94	8	no	—
812	C₄	C₂²×D₄×D₄₇	1	12	yes	—
813	C₂	—	2	2	no	—
814	C₂	—	4	6	no	—
815	C₂	—	4	4	no	—
816	C₂	—	94	4	no	—
817	C₂	—	94	12	no	—
818	C₂	—	188	4	no	—
819	C₂	C₂³×D₄×D₄₇	1	1	yes	characteristic
820	C₂	#585×D₄₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁶
Fitting	C₄₇×#3487	C₂
hypercenter	#3487	D₄₇
hypocenter	C₄₇	#62811
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #3487

Complements

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

N	H ≅ G/N	type
1. C₂×#15689960	C₂	semidirect
2. C₂²×#41×D₄₇	C₂	semidirect
3. #20257067	C₂	semidirect
4. #20257056	C₂	semidirect
5. #20257046	C₂	semidirect
6. #20257040	C₂	semidirect
7. #20257036	C₂	semidirect
8. #20257030	C₂	semidirect
9. #20257022	C₂	semidirect
10. #20256878	C₂	semidirect
11. #20256877	C₂	semidirect
12. #20256719	C₂	semidirect
13. #525×D₄₇	C₂	semidirect
14. #20256590	C₂	semidirect
15. C₄₇×#3487	C₂	semidirect
17. C₂×#13094072	C₂²	semidirect
18. C₂×#13094072	C₂²	semidirect
19. C₂×#13094070	C₂²	semidirect
20. C₂×#13094070	C₂²	semidirect
22. C₂²×#10625354	C₂²	semidirect
23. C₂²×#10625350	C₂²	semidirect
24. C₂²×#10625352	C₂²	semidirect
26. C₂×#41×D₄₇	C₂²	semidirect
27. C₂×#41×D₄₇	C₂²	semidirect
28. C₂×#41×D₄₇	C₂²	semidirect
29. C₂×#41×D₄₇	C₂²	semidirect
30. C₂²×Q₈×D₄₇	C₂²	semidirect
31. C₂²×D₄×D₄₇	C₂²	semidirect
32. C₂³×C₄×D₄₇	C₂²	semidirect
33. #15689792	C₂²	semidirect
34. Q₈×D₁₈₈	C₂²	semidirect
35. Q₈×C₂²⋊D₄₇	C₂²	semidirect
36. #15689785	C₂²	semidirect
37. #15689780	C₂²	semidirect
38. #15689780	C₂²	semidirect
39. #15689778	C₂²	semidirect
40. #15689775	C₂²	semidirect
41. #15689770	C₂²	semidirect
42. #15689770	C₂²	semidirect
43. #15689769	C₂²	semidirect
44. #15689766	C₂²	semidirect
45. #15689758	C₂²	semidirect
46. #15689757	C₂²	semidirect
47. #15689702	C₂²	semidirect
48. #15689699	C₂²	semidirect
49. #15689694	C₂²	semidirect
50. #15689693	C₂²	semidirect
51. #15689690	C₂²	semidirect
52. #15689686	C₂²	semidirect
53. #15689683	C₂²	semidirect
54. #15689672	C₂²	semidirect
55. #15689671	C₂²	semidirect
56. #15689636	C₂²	semidirect
57. #15689635	C₂²	semidirect
58. #15689634	C₂²	semidirect
59. #15689633	C₂²	semidirect
60. #15689633	C₂²	semidirect
61. #15689632	C₂²	semidirect
62. #15689631	C₂²	semidirect
63. #15689630	C₂²	semidirect
64. #15689629	C₂²	semidirect
65. #123×D₄₇	C₂²	semidirect
66. C₂²⋊Q₈×D₄₇	C₂²	semidirect
67. #121×D₄₇	C₂²	semidirect
68. #120×D₄₇	C₂²	semidirect
69. #15689605	C₂²	semidirect
70. #15689601	C₂²	semidirect
71. #15689597	C₂²	semidirect
72. C₄×#10625354	C₂²	semidirect
73. C₄×D₄×D₄₇	C₂²	semidirect
74. #117×D₄₇	C₂²	semidirect
75. C₂×2₋¹⁺⁴×C₄₇	C₂²	semidirect
76. C₂²×#41×C₄₇	C₂²	semidirect
77. C₄₇×#550	C₂²	semidirect
78. C₄₇×#548	C₂²	semidirect
79. C₄₇×#535	C₂²	semidirect
80. C₄₇×#525	C₂²	semidirect
81. C₄₇×#519	C₂²	semidirect
88. C₂×#10625354	D₄	semidirect
91. C₂×#10625354	C₂³	semidirect
92. C₂×#10625354	C₂³	semidirect
93. C₂×#10625354	C₂³	semidirect
97. C₂×#10625350	C₂³	semidirect
98. C₂×#10625350	C₂³	semidirect
103. C₂×#10625352	C₂³	semidirect
111. C₂×Q₈×D₄₇	C₂³	semidirect
112. C₂×Q₈×D₄₇	C₂³	semidirect
114. C₂²×D₁₈₈	C₂³	semidirect
120. C₂×D₄×D₄₇	C₂³	semidirect
121. C₂×D₄×D₄₇	C₂³	semidirect
130. C₂²×C₄×D₄₇	C₂³	semidirect
131. #13094024	C₂³	semidirect
132. #13094022	C₂³	semidirect
133. #13094020	C₂³	semidirect
134. #13094012	C₂³	semidirect
135. #13094011	C₂³	semidirect
136. #13094011	C₂³	semidirect
137. #13094009	C₂³	semidirect
140. #13094006	C₂³	semidirect
141. #13094006	C₂³	semidirect
144. #13094004	C₂³	semidirect
145. #13094003	C₂³	semidirect
146. #13094003	C₂³	semidirect
148. #13094001	C₂³	semidirect
151. #13093998	C₂³	semidirect
153. #13093997	C₂³	semidirect
154. #13093996	C₂³	semidirect
156. #13093995	C₂³	semidirect
157. #13093995	C₂³	semidirect
163. #13093992	C₂³	semidirect
164. Q₈×Dic₄₇	C₂³	semidirect
166. C₄×D₁₈₈	C₂³	semidirect
167. D₄×Dic₄₇	C₂³	semidirect
169. #13093986	C₂³	semidirect
171. C₄×C₂²⋊D₄₇	C₂³	semidirect
173. (C₂²⋊D₄₇)⋊C₄	C₂³	semidirect
175. #13093982	C₂³	semidirect
176. #13093981	C₂³	semidirect
178. C₄⋊C₄×D₄₇	C₂³	semidirect
179. C₄⋊C₄×D₄₇	C₂³	semidirect
182. C₂²⋊C₄×D₄₇	C₂³	semidirect
183. C₄²×D₄₇	C₂³	semidirect
188. C₂×#41×C₄₇	C₂³	semidirect
190. C₂²×Q₈×C₄₇	C₂³	semidirect
193. #127×C₄₇	C₂³	semidirect
194. #124×C₄₇	C₂³	semidirect
196. C₂²⋊Q₈×C₄₇	C₂³	semidirect
197. #121×C₄₇	C₂³	semidirect
198. #121×C₄₇	C₂³	semidirect
200. C₄×Q₈×C₄₇	C₂³	semidirect
201. C₄×D₄×C₄₇	C₂³	semidirect
214. C₂×Q₈×C₄₇	C₂×D₄	semidirect
243. #10625354	C₂×D₄	semidirect
244. #10625354	C₂×D₄	semidirect
262. C₂×D₁₈₈	C₂×D₄	semidirect
273. C₂×C₄×D₄₇	C₂×D₄	semidirect
393. C₂×D₄₇	#585	semidirect
408. #3487	D₄₇	semidirect
429. C₂×2₋¹⁺⁴	C₂×D₄₇	semidirect
441. C₂²×#41	C₂×D₄₇	semidirect
446. #550	C₂×D₄₇	semidirect
452. #548	C₂×D₄₇	semidirect
467. #535	C₂×D₄₇	semidirect
480. #525	C₂×D₄₇	semidirect
487. #519	C₂×D₄₇	semidirect
492. C₄₇	#62811	semidirect
523. C₂×#41	C₂²×D₄₇	semidirect
530. C₂²×Q₈	C₂²×D₄₇	semidirect
554. #127	C₂²×D₄₇	semidirect
558. #124	C₂²×D₄₇	semidirect
573. C₂²⋊Q₈	C₂²×D₄₇	semidirect
582. #121	C₂²×D₄₇	semidirect
583. #121	C₂²×D₄₇	semidirect
592. C₄×Q₈	C₂²×D₄₇	semidirect
602. C₄×D₄	C₂²×D₄₇	semidirect
645. C₂×Q₈	D₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689960	2
C₂²×#41×D₄₇	2
#20257067	2
#20257056	2
#20257046	2
#20257040	2
#20257036	2
#20257030	2
#20257022	2
#20256878	2
#20256877	2
#20256719	2
#525×D₄₇	2
#20256590	2
C₄₇×#3487	2
#62811	47