Subgroups — C₂×#541×D₄₇ #27123089

Order 12032.

7110 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689736	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689735	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689734	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689733	C₂	1	2	yes	maximal, complemented
5	C₂×#15689732	C₂	1	4	yes	maximal, complemented
6	C₂×#15689731	C₂	1	2	yes	maximal, complemented
7	C₂×#15689730	C₂	1	4	yes	maximal, complemented
8	#541×D₄₇	C₂	1	32	yes	maximal, direct product factor
9	C₂×C₄⋊Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#126×D₄₇	C₂	1	4	yes	maximal
11	C₂×#125×D₄₇	C₂	1	4	yes	maximal, complemented
12	C₂×#125×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂²⋊Q₈×D₄₇	C₂	1	2	yes	maximal
14	C₂×C₄×Q₈×D₄₇	C₂	1	2	yes	maximal, complemented
15	C₂×#117×D₄₇	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄₇×#541	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₈×D₄₇	C₂²	1	2	yes	—
18	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic
19	#15689736	C₂²	1	16	yes	complemented
20	#15689735	C₂²	1	16	yes	complemented
21	#15689734	C₂²	1	16	yes	complemented
22	#15689733	C₂²	1	32	yes	complemented
23	#15689732	C₂²	1	64	yes	complemented
24	#15689731	C₂²	1	32	yes	complemented
25	#15689730	C₂²	1	64	yes	complemented
26	C₂×#13094024	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13094023	C₂²	1	4	yes	complemented
28	C₂×#13094022	C₂²	1	2	yes	complemented
29	C₄⋊Q₈×D₄₇	C₂²	1	16	yes	complemented
30	C₂×#13094019	C₂²	1	4	yes	—
31	C₂×#13094019	C₂²	1	4	yes	—
32	C₂×#13094019	C₂²	1	4	yes	—
33	C₂×#13094018	C₂²	1	4	yes	—
34	C₂×#13094017	C₂²	1	4	yes	—
35	C₂×#13094017	C₂²	1	4	yes	—
36	C₂×#13094017	C₂²	1	4	yes	—
37	#126×D₄₇	C₂²	1	64	yes	—
38	C₂×#13094016	C₂²	1	4	yes	complemented
39	C₂×#13094016	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13094015	C₂²	1	4	yes	complemented
41	C₂×#13094015	C₂²	1	2	yes	complemented
42	C₂×#13094015	C₂²	1	4	yes	complemented
43	C₂×#13094014	C₂²	1	4	yes	complemented
44	C₂×#13094014	C₂²	1	4	yes	complemented
45	C₂×#13094014	C₂²	1	4	yes	complemented
46	C₂×#13094014	C₂²	1	4	yes	complemented
47	C₂×#13094014	C₂²	1	4	yes	complemented
48	#125×D₄₇	C₂²	1	64	yes	complemented
49	#125×D₄₇	C₂²	1	16	yes	complemented
50	C₂×#13094004	C₂²	1	2	yes	—
51	C₂×#13094003	C₂²	1	2	yes	—
52	C₂×#13094002	C₂²	1	4	yes	—
53	C₂×#13094001	C₂²	1	4	yes	—
54	C₂×#13094000	C₂²	1	2	yes	—
55	C₂²⋊Q₈×D₄₇	C₂²	1	32	yes	—
56	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	complemented
57	C₂×C₄×Dic₉₄	C₂²	1	4	yes	complemented
58	C₂×C₄×Dic₉₄	C₂²	1	2	yes	complemented
59	C₂×#13093989	C₂²	1	4	yes	complemented
60	C₂×#13093989	C₂²	1	2	yes	complemented
61	C₄×Q₈×D₄₇	C₂²	1	32	yes	complemented
62	C₂×#13093983	C₂²	1	1	yes	characteristic
63	C₂×#13093982	C₂²	1	2	yes	—
64	C₂×#13093981	C₂²	1	1	yes	characteristic
65	C₂×#13093981	C₂²	1	1	yes	characteristic
66	C₂×#13093980	C₂²	1	2	yes	—
67	#117×D₄₇	C₂²	1	16	yes	—
68	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
69	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
70	C₂×C₄⋊C₄×D₄₇	C₂²	1	4	yes	—
71	C₂×C₄⋊C₄×D₄₇	C₂²	1	4	yes	—
72	C₂×C₄⋊C₄×D₄₇	C₂²	1	4	yes	—
73	C₂×C₄⋊C₄×D₄₇	C₂²	1	4	yes	—
74	C₂×C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
75	C₂×C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
76	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
77	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
78	C₂×C₄²×D₄₇	C₂²	1	4	yes	—
79	C₄₇×#541	C₂²	1	16	yes	complemented
80	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
81	C₂×#126×C₄₇	C₂²	1	4	yes	—
82	C₂×#125×C₄₇	C₂²	1	4	yes	complemented
83	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
85	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
86	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
87	C₂⁴×D₄₇	C₂³	1	1	yes	characteristic
88	C₂²×Dic₉₄	C₂³	1	4	yes	—
89	C₂²×Dic₉₄	C₂³	1	2	yes	—
90	C₂×Q₈×D₄₇	—	2	16	no	—
91	C₂×Q₈×D₄₇	C₂³	1	16	yes	—
92	C₂³×Dic₄₇	C₂³	1	1	yes	characteristic
93	C₂²×C₄×D₄₇	—	2	8	no	—
94	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
95	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
96	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
97	C₂²×C₄×D₄₇	C₂³	1	4	yes	—
98	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
99	C₂²×C₄×D₄₇	C₂³	1	8	yes	—
100	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
101	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
103	#13094024	C₂³	1	8	yes	complemented
104	#13094023	C₂³	1	32	yes	complemented
105	#13094022	C₂³	1	16	yes	complemented
106	#13094019	C₂³	1	32	yes	—
107	#13094019	C₂³	1	32	yes	—
108	#13094019	C₂³	1	32	yes	—
109	#13094018	C₂³	1	32	yes	—
110	#13094017	C₂³	1	32	yes	—
111	#13094017	C₂³	1	32	yes	—
112	#13094017	C₂³	1	32	yes	—
113	#13094016	C₂³	1	32	yes	complemented
114	#13094016	C₂³	1	8	yes	complemented
115	#13094015	C₂³	1	32	yes	complemented
116	#13094015	C₂³	1	16	yes	complemented
117	#13094015	C₂³	1	32	yes	complemented
118	#13094014	C₂³	1	32	yes	complemented
119	#13094014	C₂³	1	32	yes	complemented
120	#13094014	C₂³	1	32	yes	complemented
121	#13094014	C₂³	1	32	yes	complemented
122	#13094014	C₂³	1	32	yes	complemented
123	#13094004	C₂³	1	16	yes	—
124	#13094003	C₂³	1	16	yes	—
125	#13094002	C₂³	1	32	yes	—
126	#13094001	C₂³	1	32	yes	—
127	#13094000	C₂³	1	16	yes	—
128	Q₈×Dic₄₇	C₂³	1	16	yes	complemented
129	C₄×Dic₉₄	C₂³	1	32	yes	complemented
130	C₄×Dic₉₄	C₂³	1	16	yes	complemented
131	#13093989	C₂³	1	32	yes	complemented
132	#13093989	C₂³	1	16	yes	complemented
133	#13093983	C₂³	1	8	yes	—
134	#13093982	C₂³	1	16	yes	—
135	#13093981	C₂³	1	8	yes	—
136	#13093981	C₂³	1	8	yes	—
137	#13093980	C₂³	1	16	yes	—
138	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
139	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
140	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
141	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
142	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
143	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
144	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
145	C₂×Dic₄₇⋊C₄	C₂³	1	2	yes	—
146	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
147	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
148	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
149	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
150	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
151	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
152	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
153	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
154	C₂×Dic₄₇⋊C₄	C₂³	1	4	yes	—
155	C₄⋊C₄×D₄₇	C₂³	1	16	yes	—
156	C₄⋊C₄×D₄₇	C₂³	1	16	yes	—
157	C₄⋊C₄×D₄₇	C₂³	1	32	yes	—
158	C₄⋊C₄×D₄₇	C₂³	1	32	yes	—
159	C₄⋊C₄×D₄₇	C₂³	1	32	yes	—
160	C₄⋊C₄×D₄₇	C₂³	1	32	yes	—
161	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
163	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
164	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
165	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
166	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
167	C₂²⋊C₄×D₄₇	C₂³	1	16	yes	—
168	C₂²⋊C₄×D₄₇	C₂³	1	32	yes	—
169	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
170	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
171	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
172	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
173	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
174	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
175	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
176	C₄²×D₄₇	C₂³	1	8	yes	—
177	C₄²×D₄₇	C₂³	1	8	yes	—
178	C₄²×D₄₇	C₂³	1	32	yes	—
179	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
180	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
181	C₄⋊Q₈×C₄₇	C₂³	1	8	yes	complemented
182	#126×C₄₇	C₂³	1	32	yes	—
183	#125×C₄₇	C₂³	1	32	yes	complemented
184	#125×C₄₇	C₂³	1	8	yes	complemented
185	C₂²⋊Q₈×C₄₇	C₂³	1	16	yes	—
186	C₄×Q₈×C₄₇	C₂³	1	16	yes	complemented
187	#117×C₄₇	C₂³	1	8	yes	—
188	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
191	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
192	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
193	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
194	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
196	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
199	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
200	C₂³×D₄₇	—	2	4	no	—
201	C₂³×D₄₇	—	2	8	no	—
202	C₂³×D₄₇	C₂⁴	1	4	yes	—
203	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
204	C₂³×D₄₇	C₂⁴	1	1	yes	characteristic
205	C₂×Q₈×C₄₇	—	2	8	no	—
206	C₂×Q₈×C₄₇	C₂⁴	1	8	yes	—
207	C₂²×C₄×C₄₇	—	2	4	no	—
208	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
209	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
212	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
215	C₂²×Dic₄₇	—	2	4	no	—
216	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
217	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
218	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
219	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
220	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
221	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
222	C₂²×Dic₄₇	C₂⁴	1	1	yes	characteristic
223	Q₈×D₄₇	—	2	64	no	—
224	C₂×C₄×D₄₇	—	2	4	no	—
225	C₂×C₄×D₄₇	—	2	16	no	—
226	C₂×C₄×D₄₇	—	2	8	no	—
227	C₂×C₄×D₄₇	—	2	8	no	—
228	C₂×C₄×D₄₇	—	2	16	no	—
229	C₂×C₄×D₄₇	—	2	4	no	—
230	C₂×C₄×D₄₇	—	2	4	no	—
231	C₂×C₄×D₄₇	—	2	32	no	—
232	C₂×C₄×D₄₇	#41	1	8	yes	—
233	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
234	C₂×C₄×D₄₇	C₂⁴	1	8	yes	—
235	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
236	C₂×C₄×D₄₇	C₂⁴	1	16	yes	—
237	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
238	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
239	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
240	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
241	C₂×Dic₉₄	—	2	8	no	—
242	C₂×Dic₉₄	—	2	16	no	—
243	C₂×Dic₉₄	C₂⁴	1	16	yes	—
244	C₂×Dic₉₄	C₂⁴	1	8	yes	—
245	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
246	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
247	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
248	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
249	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
250	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
251	C₂²⋊C₄×C₄₇	C₂⁴	1	8	yes	—
252	C₂²⋊C₄×C₄₇	C₂⁴	1	16	yes	—
253	C₄²×C₄₇	C₂⁴	1	4	yes	—
254	C₄²×C₄₇	C₂⁴	1	4	yes	—
255	C₄²×C₄₇	C₂⁴	1	16	yes	—
256	C₂²⋊Dic₄₇	C₂⁴	1	8	yes	—
257	C₂²⋊Dic₄₇	C₂⁴	1	16	yes	—
258	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
259	(C₂×D₄₇)⋊C₄	C₂⁴	1	8	yes	—
260	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
261	(C₂×D₄₇)⋊C₄	C₂⁴	1	16	yes	—
262	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
263	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
264	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
265	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
266	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
267	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
268	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
269	Dic₄₇⋊C₄	C₂⁴	1	8	yes	—
270	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
271	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
272	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
273	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
274	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
275	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
276	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
277	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
278	Dic₄₇⋊C₄	C₂⁴	1	16	yes	—
279	C₄×Dic₄₇	C₂⁴	1	8	yes	—
280	C₄×Dic₄₇	C₂⁴	1	8	yes	—
281	C₄×Dic₄₇	C₂⁴	1	4	yes	—
282	C₄×Dic₄₇	C₂⁴	1	4	yes	—
283	C₄×Dic₄₇	C₂⁴	1	16	yes	—
284	C₄×Dic₄₇	C₂⁴	1	16	yes	—
285	C₄×Dic₄₇	C₂⁴	1	16	yes	—
286	C₂³×C₄₇	—	2	2	no	—
287	C₂³×C₄₇	—	2	4	no	—
288	C₂³×C₄₇	C₂⁵	1	2	yes	—
289	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
290	C₂²×D₄₇	—	2	2	no	—
291	C₂²×D₄₇	—	2	4	no	—
292	C₂²×D₄₇	—	2	8	no	—
293	C₂²×D₄₇	—	2	16	no	—
294	C₂²×D₄₇	—	4	16	no	—
295	C₂²×D₄₇	C₂×#41	1	4	yes	—
296	C₂²×D₄₇	2₋¹⁺⁴	1	8	yes	—
297	C₂²×D₄₇	C₂⁵	1	2	yes	—
298	C₂²×D₄₇	C₂⁵	1	2	yes	—
299	Q₈×C₄₇	—	2	16	no	—
300	C₂×C₄×C₄₇	—	2	8	no	—
301	C₂×C₄×C₄₇	—	2	2	no	—
302	C₂×C₄×C₄₇	—	2	4	no	—
303	C₂×C₄×C₄₇	—	2	4	no	—
304	C₂×C₄×C₄₇	—	2	8	no	—
305	C₂×C₄×C₄₇	—	2	8	no	—
306	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
307	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
308	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
309	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
310	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
311	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
312	C₂×C₄×C₄₇	C₂⁵	1	2	yes	—
313	C₂×Dic₄₇	—	2	8	no	—
314	C₂×Dic₄₇	—	2	2	no	—
315	C₂×Dic₄₇	—	2	4	no	—
316	C₂×Dic₄₇	—	2	4	no	—
317	C₂×Dic₄₇	—	2	8	no	—
318	C₂×Dic₄₇	—	2	8	no	—
319	C₂×Dic₄₇	C₂×#41	1	4	yes	—
320	C₂×Dic₄₇	C₂⁵	1	4	yes	—
321	C₂×Dic₄₇	C₂⁵	1	4	yes	—
322	C₂×Dic₄₇	C₂⁵	1	8	yes	—
323	C₂×Dic₄₇	C₂⁵	1	8	yes	—
324	C₂×Dic₄₇	C₂⁵	1	2	yes	—
325	C₂×Dic₄₇	C₂⁵	1	2	yes	—
326	C₄×D₄₇	—	2	8	no	—
327	C₄×D₄₇	—	2	32	no	—
328	C₄×D₄₇	—	2	16	no	—
329	C₄×D₄₇	—	2	16	no	—
330	C₄×D₄₇	—	2	32	no	—
331	C₄×D₄₇	—	2	8	no	—
332	C₄×D₄₇	—	2	8	no	—
333	C₄×D₄₇	C₂×#41	1	16	yes	—
334	Dic₉₄	—	2	16	no	—
335	Dic₉₄	—	2	32	no	—
336	C₂²×#541	—	47	1	no	maximal, Sylow
337	C₂²×C₄₇	—	2	2	no	—
338	C₂²×C₄₇	—	2	4	no	—
339	C₂²×C₄₇	—	4	4	no	—
340	C₂²×C₄₇	C₂²×#41	1	2	yes	—
341	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	4	yes	—
342	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
343	C₂×D₄₇	—	2	2	no	—
344	C₂×D₄₇	—	2	4	no	—
345	C₂×D₄₇	—	4	4	no	—
346	C₂×D₄₇	—	4	16	no	—
347	C₂×D₄₇	#541	1	16	yes	direct product factor
348	C₂×D₄₇	C₂²×#41	1	4	yes	—
349	C₂×D₄₇	C₂×2₋¹⁺⁴	1	8	yes	—
350	C₄×C₄₇	—	2	8	no	—
351	C₄×C₄₇	—	2	2	no	—
352	C₄×C₄₇	—	2	4	no	—
353	C₄×C₄₇	—	2	4	no	—
354	C₄×C₄₇	—	2	8	no	—
355	C₄×C₄₇	C₂²×#41	1	4	yes	—
356	Dic₄₇	—	2	8	no	—
357	Dic₄₇	—	2	2	no	—
358	Dic₄₇	—	2	4	no	—
359	Dic₄₇	—	2	4	no	—
360	Dic₄₇	—	2	8	no	—
361	Dic₄₇	C₂²×#41	1	4	yes	—
362	C₂×#541	—	47	32	no	—
363	C₂×#541	—	47	1	no	—
364	C₂×#541	—	47	4	no	—
365	C₂×#541	—	47	4	no	—
366	C₂×#541	—	47	1	no	—
367	C₂×#541	—	47	2	no	—
368	C₂×#541	—	47	2	no	—
369	C₂×#541	—	47	1	no	—
370	C₂×#541	D₄₇	1	1	yes	characteristic, direct product factor
371	C₂²×C₄⋊Q₈	—	47	1	no	—
372	C₂²×#126	—	47	4	no	—
373	C₂²×#125	—	47	4	no	—
374	C₂²×#125	—	47	1	no	—
375	C₂²×C₂²⋊Q₈	—	47	2	no	—
376	C₂²×C₄×Q₈	—	47	2	no	—
377	C₂²×#117	—	47	1	no	—
378	C₂×C₄₇	—	4	2	no	—
379	C₂×C₄₇	C₂×#541	1	4	yes	complemented
380	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
381	C₂×C₄₇	C₂²×2₋¹⁺⁴	1	2	yes	—
382	D₄₇	—	4	2	no	—
383	D₄₇	C₂×#541	1	8	yes	direct product factor
384	C₂³×Q₈	—	47	2	no	—
385	C₂⁴×C₄	—	47	1	no	—
386	#541	—	47	16	no	—
387	#541	—	47	64	no	—
388	#541	—	47	64	no	—
389	#541	—	47	16	no	—
390	#541	—	47	32	no	—
391	#541	—	47	32	no	—
392	#541	—	47	16	no	—
393	#541	C₂×D₄₇	1	16	yes	direct product factor
394	C₂×C₄⋊Q₈	—	47	2	no	—
395	C₂×C₄⋊Q₈	—	47	16	no	—
396	C₂×C₄⋊Q₈	—	47	4	no	—
397	C₂×C₄⋊Q₈	—	47	1	no	—
398	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
399	C₂×#126	—	47	64	no	—
400	C₂×#126	—	47	4	no	—
401	C₂×#126	—	47	4	no	—
402	C₂×#126	—	47	4	no	—
403	C₂×#126	—	47	4	no	—
404	C₂×#126	—	47	4	no	—
405	C₂×#126	—	47	4	no	—
406	C₂×#126	—	47	4	no	—
407	C₂×#126	C₂×D₄₇	1	4	yes	—
408	C₂×#125	—	47	16	no	—
409	C₂×#125	—	47	64	no	—
410	C₂×#125	—	47	4	no	—
411	C₂×#125	—	47	4	no	—
412	C₂×#125	—	47	4	no	—
413	C₂×#125	—	47	4	no	—
414	C₂×#125	—	47	4	no	—
415	C₂×#125	—	47	2	no	—
416	C₂×#125	—	47	4	no	—
417	C₂×#125	—	47	4	no	—
418	C₂×#125	—	47	1	no	—
419	C₂×#125	—	47	4	no	—
420	C₂×#125	C₂×D₄₇	1	1	yes	characteristic, complemented
421	C₂×#125	C₂×D₄₇	1	4	yes	complemented
422	C₂×C₂²⋊Q₈	—	47	2	no	—
423	C₂×C₂²⋊Q₈	—	47	2	no	—
424	C₂×C₂²⋊Q₈	—	47	32	no	—
425	C₂×C₂²⋊Q₈	—	47	4	no	—
426	C₂×C₂²⋊Q₈	—	47	2	no	—
427	C₂×C₂²⋊Q₈	—	47	4	no	—
428	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
429	C₂×C₄×Q₈	—	47	2	no	—
430	C₂×C₄×Q₈	—	47	32	no	—
431	C₂×C₄×Q₈	—	47	4	no	—
432	C₂×C₄×Q₈	—	47	2	no	—
433	C₂×C₄×Q₈	—	47	4	no	—
434	C₂×C₄×Q₈	—	47	2	no	—
435	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	complemented
436	C₂×#117	—	47	1	no	—
437	C₂×#117	—	47	16	no	—
438	C₂×#117	—	47	2	no	—
439	C₂×#117	—	47	2	no	—
440	C₂×#117	—	47	1	no	—
441	C₂×#117	—	47	1	no	—
442	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
443	C₂²×C₄⋊C₄	—	47	2	no	—
444	C₂²×C₄⋊C₄	—	47	2	no	—
445	C₂²×C₄⋊C₄	—	47	4	no	—
446	C₂²×C₄⋊C₄	—	47	4	no	—
447	C₂²×C₄⋊C₄	—	47	4	no	—
448	C₂²×C₄⋊C₄	—	47	4	no	—
449	C₂²×C₂²⋊C₄	—	47	2	no	—
450	C₂²×C₂²⋊C₄	—	47	4	no	—
451	C₂²×C₄²	—	47	1	no	—
452	C₂²×C₄²	—	47	1	no	—
453	C₂²×C₄²	—	47	4	no	—
454	C₄₇	C₂²×#541	1	1	yes	characteristic, complemented, Sylow
455	C₂⁵	—	47	1	no	—
456	C₂²×Q₈	—	47	16	no	—
457	C₂²×Q₈	—	47	4	no	—
458	C₂²×Q₈	—	47	2	no	—
459	C₂²×Q₈	—	94	16	no	—
460	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
461	C₂³×C₄	—	47	1	no	—
462	C₂³×C₄	—	47	1	no	—
463	C₂³×C₄	—	47	2	no	—
464	C₂³×C₄	—	47	4	no	—
465	C₂³×C₄	—	47	4	no	—
466	C₂³×C₄	—	47	2	no	—
467	C₂³×C₄	—	47	1	no	—
468	C₂³×C₄	—	47	1	no	—
469	C₂³×C₄	—	47	8	no	—
470	C₂³×C₄	—	47	1	no	—
471	C₂³×C₄	—	94	8	no	—
472	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
473	C₄⋊Q₈	—	47	16	no	—
474	C₄⋊Q₈	—	47	32	no	—
475	C₄⋊Q₈	—	47	8	no	—
476	C₄⋊Q₈	C₂²×D₄₇	1	8	yes	complemented
477	#126	—	47	32	no	—
478	#126	—	47	32	no	—
479	#126	—	47	32	no	—
480	#126	—	47	32	no	—
481	#126	—	47	32	no	—
482	#126	—	47	32	no	—
483	#126	—	47	32	no	—
484	#126	C₂²×D₄₇	1	32	yes	—
485	#125	—	47	32	no	—
486	#125	—	47	32	no	—
487	#125	—	47	32	no	—
488	#125	—	47	32	no	—
489	#125	—	47	32	no	—
490	#125	—	47	16	no	—
491	#125	—	47	32	no	—
492	#125	—	47	32	no	—
493	#125	—	47	8	no	—
494	#125	—	47	32	no	—
495	#125	C₂²×D₄₇	1	8	yes	complemented
496	#125	C₂²×D₄₇	1	32	yes	complemented
497	C₂²⋊Q₈	—	47	16	no	—
498	C₂²⋊Q₈	—	47	16	no	—
499	C₂²⋊Q₈	—	47	32	no	—
500	C₂²⋊Q₈	—	47	16	no	—
501	C₂²⋊Q₈	—	47	32	no	—
502	C₂²⋊Q₈	C₂²×D₄₇	1	16	yes	—
503	C₄×Q₈	—	47	16	no	—
504	C₄×Q₈	—	47	32	no	—
505	C₄×Q₈	—	47	16	no	—
506	C₄×Q₈	—	47	32	no	—
507	C₄×Q₈	—	47	16	no	—
508	C₄×Q₈	C₂²×D₄₇	1	16	yes	complemented
509	#117	—	47	8	no	—
510	#117	—	47	16	no	—
511	#117	—	47	16	no	—
512	#117	—	47	8	no	—
513	#117	—	47	8	no	—
514	#117	C₂²×D₄₇	1	8	yes	—
515	C₂×C₄⋊C₄	—	47	2	no	—
516	C₂×C₄⋊C₄	—	47	2	no	—
517	C₂×C₄⋊C₄	—	47	2	no	—
518	C₂×C₄⋊C₄	—	47	4	no	—
519	C₂×C₄⋊C₄	—	47	2	no	—
520	C₂×C₄⋊C₄	—	47	4	no	—
521	C₂×C₄⋊C₄	—	47	4	no	—
522	C₂×C₄⋊C₄	—	47	4	no	—
523	C₂×C₄⋊C₄	—	47	4	no	—
524	C₂×C₄⋊C₄	—	47	4	no	—
525	C₂×C₄⋊C₄	—	47	4	no	—
526	C₂×C₄⋊C₄	—	47	4	no	—
527	C₂×C₄⋊C₄	—	47	4	no	—
528	C₂×C₄⋊C₄	—	47	4	no	—
529	C₂×C₄⋊C₄	—	47	4	no	—
530	C₂×C₄⋊C₄	—	47	4	no	—
531	C₂×C₄⋊C₄	—	47	4	no	—
532	C₂×C₄⋊C₄	—	47	16	no	—
533	C₂×C₄⋊C₄	—	47	16	no	—
534	C₂×C₄⋊C₄	—	47	32	no	—
535	C₂×C₄⋊C₄	—	47	32	no	—
536	C₂×C₄⋊C₄	—	47	32	no	—
537	C₂×C₄⋊C₄	—	47	32	no	—
538	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
539	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
540	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
541	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
542	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
543	C₂×C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
544	C₂×C₂²⋊C₄	—	47	2	no	—
545	C₂×C₂²⋊C₄	—	47	4	no	—
546	C₂×C₂²⋊C₄	—	47	2	no	—
547	C₂×C₂²⋊C₄	—	47	2	no	—
548	C₂×C₂²⋊C₄	—	47	4	no	—
549	C₂×C₂²⋊C₄	—	47	4	no	—
550	C₂×C₂²⋊C₄	—	47	16	no	—
551	C₂×C₂²⋊C₄	—	47	32	no	—
552	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
554	C₂×C₄²	—	47	2	no	—
555	C₂×C₄²	—	47	1	no	—
556	C₂×C₄²	—	47	2	no	—
557	C₂×C₄²	—	47	1	no	—
558	C₂×C₄²	—	47	4	no	—
559	C₂×C₄²	—	47	4	no	—
560	C₂×C₄²	—	47	4	no	—
561	C₂×C₄²	—	47	8	no	—
562	C₂×C₄²	—	47	8	no	—
563	C₂×C₄²	—	47	32	no	—
564	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
565	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
566	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
567	C₂⁴	—	47	1	no	—
568	C₂⁴	—	47	4	no	—
569	C₂⁴	—	47	1	no	—
570	C₂⁴	—	94	4	no	—
571	C₂⁴	—	94	8	no	—
572	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
573	C₂×Q₈	—	2	8	no	—
574	C₂×Q₈	—	47	16	no	—
575	C₂×Q₈	—	47	8	no	—
576	C₂×Q₈	—	94	16	no	—
577	C₂×Q₈	—	94	64	no	—
578	C₂×Q₈	—	94	8	no	—
579	C₂×Q₈	C₂³×D₄₇	1	8	yes	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	47	1	no	—
582	C₂²×C₄	—	47	8	no	—
583	C₂²×C₄	—	47	4	no	—
584	C₂²×C₄	—	47	4	no	—
585	C₂²×C₄	—	47	2	no	—
586	C₂²×C₄	—	47	2	no	—
587	C₂²×C₄	—	47	4	no	—
588	C₂²×C₄	—	47	4	no	—
589	C₂²×C₄	—	47	1	no	—
590	C₂²×C₄	—	47	8	no	—
591	C₂²×C₄	—	47	8	no	—
592	C₂²×C₄	—	47	16	no	—
593	C₂²×C₄	—	47	16	no	—
594	C₂²×C₄	—	47	4	no	—
595	C₂²×C₄	—	47	4	no	—
596	C₂²×C₄	—	47	4	no	—
597	C₂²×C₄	—	94	4	no	—
598	C₂²×C₄	—	94	32	no	—
599	C₂²×C₄	—	94	8	no	—
600	C₂²×C₄	—	94	16	no	—
601	C₂²×C₄	—	94	8	no	—
602	C₂²×C₄	—	94	4	no	—
603	C₂²×C₄	—	94	16	no	—
604	C₂²×C₄	—	94	4	no	—
605	C₂²×C₄	—	94	4	no	—
606	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
607	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
608	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
609	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
610	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
611	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
612	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
613	C₄⋊C₄	—	47	8	no	—
614	C₄⋊C₄	—	47	8	no	—
615	C₄⋊C₄	—	47	16	no	—
616	C₄⋊C₄	—	47	16	no	—
617	C₄⋊C₄	—	47	16	no	—
618	C₄⋊C₄	—	47	16	no	—
619	C₄⋊C₄	—	47	16	no	—
620	C₄⋊C₄	—	47	16	no	—
621	C₄⋊C₄	—	47	16	no	—
622	C₄⋊C₄	—	47	16	no	—
623	C₄⋊C₄	—	47	16	no	—
624	C₄⋊C₄	—	47	8	no	—
625	C₄⋊C₄	—	47	8	no	—
626	C₄⋊C₄	—	47	16	no	—
627	C₄⋊C₄	—	47	16	no	—
628	C₄⋊C₄	—	47	16	no	—
629	C₄⋊C₄	—	47	16	no	—
630	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
631	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
632	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
633	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
634	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
635	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
636	C₂²⋊C₄	—	47	8	no	—
637	C₂²⋊C₄	—	47	16	no	—
638	C₂²⋊C₄	—	47	8	no	—
639	C₂²⋊C₄	—	47	8	no	—
640	C₂²⋊C₄	—	47	16	no	—
641	C₂²⋊C₄	—	47	16	no	—
642	C₂²⋊C₄	C₂³×D₄₇	1	8	yes	—
643	C₂²⋊C₄	C₂³×D₄₇	1	16	yes	—
644	C₄²	—	47	8	no	—
645	C₄²	—	47	4	no	—
646	C₄²	—	47	8	no	—
647	C₄²	—	47	4	no	—
648	C₄²	—	47	16	no	—
649	C₄²	—	47	16	no	—
650	C₄²	—	47	16	no	—
651	C₄²	C₂³×D₄₇	1	4	yes	—
652	C₄²	C₂³×D₄₇	1	4	yes	—
653	C₄²	C₂³×D₄₇	1	16	yes	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	4	no	—
656	C₂³	—	47	4	no	—
657	C₂³	—	47	8	no	—
658	C₂³	—	47	2	no	—
659	C₂³	—	47	2	no	—
660	C₂³	—	94	8	no	—
661	C₂³	—	94	16	no	—
662	C₂³	—	94	2	no	—
663	C₂³	—	94	4	no	—
664	C₂³	—	188	16	no	—
665	C₂³	C₂⁴×D₄₇	1	2	yes	—
666	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
667	Q₈	—	2	16	no	—
668	Q₈	—	94	32	no	—
669	Q₈	—	94	16	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	8	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	8	no	—
675	C₂×C₄	—	2	8	no	—
676	C₂×C₄	—	47	4	no	—
677	C₂×C₄	—	47	2	no	—
678	C₂×C₄	—	47	16	no	—
679	C₂×C₄	—	47	4	no	—
680	C₂×C₄	—	47	4	no	—
681	C₂×C₄	—	47	8	no	—
682	C₂×C₄	—	47	8	no	—
683	C₂×C₄	—	47	2	no	—
684	C₂×C₄	—	94	8	no	—
685	C₂×C₄	—	94	16	no	—
686	C₂×C₄	—	94	16	no	—
687	C₂×C₄	—	94	32	no	—
688	C₂×C₄	—	94	8	no	—
689	C₂×C₄	—	94	32	no	—
690	C₂×C₄	—	94	8	no	—
691	C₂×C₄	—	94	2	no	—
692	C₂×C₄	—	94	8	no	—
693	C₂×C₄	—	94	4	no	—
694	C₂×C₄	—	94	4	no	—
695	C₂×C₄	—	94	8	no	—
696	C₂×C₄	—	94	8	no	—
697	C₂×C₄	#41×D₄₇	1	4	yes	—
698	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
699	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
700	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
701	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
702	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
703	C₂×C₄	C₂⁴×D₄₇	1	2	yes	—
704	C₂²	—	2	2	no	—
705	C₂²	—	2	4	no	—
706	C₂²	—	4	4	no	—
707	C₂²	—	47	4	no	—
708	C₂²	—	47	8	no	—
709	C₂²	—	47	16	no	—
710	C₂²	—	94	2	no	—
711	C₂²	—	94	4	no	—
712	C₂²	—	188	16	no	—
713	C₂²	—	188	4	no	—
714	C₂²	C₂×#41×D₄₇	1	2	yes	—
715	C₂²	2₋¹⁺⁴×D₄₇	1	4	yes	—
716	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
717	C₄	—	2	2	no	—
718	C₄	—	2	8	no	—
719	C₄	—	2	4	no	—
720	C₄	—	2	4	no	—
721	C₄	—	2	8	no	—
722	C₄	—	47	4	no	—
723	C₄	—	94	2	no	—
724	C₄	—	94	8	no	—
725	C₄	—	94	4	no	—
726	C₄	—	94	4	no	—
727	C₄	—	94	8	no	—
728	C₄	C₂×#41×D₄₇	1	4	yes	—
729	C₂	—	4	2	no	—
730	C₂	—	47	8	no	—
731	C₂	—	188	2	no	—
732	C₂	#541×D₄₇	1	4	yes	direct product factor
733	C₂	C₂²×#41×D₄₇	1	1	yes	characteristic
734	C₂	C₂×2₋¹⁺⁴×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂×C₄₇×#541	C₂
socle	C₂³×C₄₇	C₂⁵
prime radical	C₂⁴×D₄₇	C₂³
hypercenter	C₂×#541	D₄₇
hypocenter	C₄₇	C₂²×#541
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#541

Complements

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

N	H ≅ G/N	type
1. C₂×#15689736	C₂	semidirect
2. C₂×#15689735	C₂	semidirect
3. C₂×#15689734	C₂	semidirect
4. C₂×#15689733	C₂	semidirect
5. C₂×#15689732	C₂	semidirect
6. C₂×#15689731	C₂	semidirect
7. C₂×#15689730	C₂	semidirect
8. #541×D₄₇	C₂	direct (N × H)
9. C₂×C₄⋊Q₈×D₄₇	C₂	semidirect
11. C₂×#125×D₄₇	C₂	semidirect
12. C₂×#125×D₄₇	C₂	semidirect
14. C₂×C₄×Q₈×D₄₇	C₂	semidirect
16. C₂×C₄₇×#541	C₂	semidirect
19. #15689736	C₂²	semidirect
20. #15689735	C₂²	semidirect
21. #15689734	C₂²	semidirect
22. #15689733	C₂²	semidirect
23. #15689732	C₂²	semidirect
24. #15689731	C₂²	semidirect
25. #15689730	C₂²	semidirect
26. C₂×#13094024	C₂²	semidirect
27. C₂×#13094023	C₂²	semidirect
28. C₂×#13094022	C₂²	semidirect
29. C₄⋊Q₈×D₄₇	C₂²	semidirect
38. C₂×#13094016	C₂²	semidirect
39. C₂×#13094016	C₂²	semidirect
40. C₂×#13094015	C₂²	semidirect
41. C₂×#13094015	C₂²	semidirect
42. C₂×#13094015	C₂²	semidirect
43. C₂×#13094014	C₂²	semidirect
44. C₂×#13094014	C₂²	semidirect
45. C₂×#13094014	C₂²	semidirect
46. C₂×#13094014	C₂²	semidirect
47. C₂×#13094014	C₂²	semidirect
48. #125×D₄₇	C₂²	semidirect
49. #125×D₄₇	C₂²	semidirect
56. C₂×Q₈×Dic₄₇	C₂²	semidirect
57. C₂×C₄×Dic₉₄	C₂²	semidirect
58. C₂×C₄×Dic₉₄	C₂²	semidirect
59. C₂×#13093989	C₂²	semidirect
60. C₂×#13093989	C₂²	semidirect
61. C₄×Q₈×D₄₇	C₂²	semidirect
79. C₄₇×#541	C₂²	semidirect
80. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
82. C₂×#125×C₄₇	C₂²	semidirect
83. C₂×#125×C₄₇	C₂²	semidirect
85. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
103. #13094024	C₂³	semidirect
104. #13094023	C₂³	semidirect
105. #13094022	C₂³	semidirect
113. #13094016	C₂³	semidirect
114. #13094016	C₂³	semidirect
115. #13094015	C₂³	semidirect
116. #13094015	C₂³	semidirect
117. #13094015	C₂³	semidirect
118. #13094014	C₂³	semidirect
119. #13094014	C₂³	semidirect
120. #13094014	C₂³	semidirect
121. #13094014	C₂³	semidirect
122. #13094014	C₂³	semidirect
128. Q₈×Dic₄₇	C₂³	semidirect
129. C₄×Dic₉₄	C₂³	semidirect
130. C₄×Dic₉₄	C₂³	semidirect
131. #13093989	C₂³	semidirect
132. #13093989	C₂³	semidirect
181. C₄⋊Q₈×C₄₇	C₂³	semidirect
183. #125×C₄₇	C₂³	semidirect
184. #125×C₄₇	C₂³	semidirect
186. C₄×Q₈×C₄₇	C₂³	semidirect
347. C₂×D₄₇	#541	direct (N × H)
370. C₂×#541	D₄₇	direct (N × H)
379. C₂×C₄₇	C₂×#541	semidirect
383. D₄₇	C₂×#541	direct (N × H)
393. #541	C₂×D₄₇	direct (N × H)
398. C₂×C₄⋊Q₈	C₂×D₄₇	semidirect
420. C₂×#125	C₂×D₄₇	semidirect
421. C₂×#125	C₂×D₄₇	semidirect
435. C₂×C₄×Q₈	C₂×D₄₇	semidirect
454. C₄₇	C₂²×#541	semidirect
476. C₄⋊Q₈	C₂²×D₄₇	semidirect
495. #125	C₂²×D₄₇	semidirect
496. #125	C₂²×D₄₇	semidirect
508. C₄×Q₈	C₂²×D₄₇	semidirect
732. C₂	#541×D₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#15689736	2
C₂×#15689735	2
C₂×#15689734	2
C₂×#15689733	2
C₂×#15689732	2
C₂×#15689731	2
C₂×#15689730	2
#541×D₄₇	2
C₂×C₄⋊Q₈×D₄₇	2
C₂×#126×D₄₇	2
C₂×#125×D₄₇	2
C₂×C₂²⋊Q₈×D₄₇	2
C₂×C₄×Q₈×D₄₇	2
C₂×#117×D₄₇	2
C₂×C₄₇×#541	2
C₂²×#541	47

Subgroups — C2×#541×D47 #27123089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#541×D₄₇ #27123089