Subgroups — C₂×C₄₇×#2005 #26063096

Order 12032.

1998 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#536	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#104×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#419	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#101×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#2005	C₂	1	8	yes	maximal, direct product factor
8	C₂×C₄₇×#339	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×#137×C₄₇	—	2	2	no	—
13	C₂×#137×C₄₇	—	2	4	no	—
14	C₂×#137×C₄₇	—	2	4	no	—
15	C₂×#137×C₄₇	C₂²	1	4	yes	—
16	C₂²×Q₁₆×C₄₇	—	2	1	no	—
17	C₂²×SD₁₆×C₄₇	—	2	1	no	—
18	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#536	—	2	2	no	—
21	C₄₇×#536	—	2	2	no	—
22	C₄₇×#536	—	2	2	no	—
23	C₄₇×#536	C₂²	1	4	yes	—
24	C₂×C₄⋊Q₈×C₄₇	—	2	4	no	—
25	C₂×C₄⋊Q₈×C₄₇	—	2	2	no	—
26	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
27	C₂×C₄⋊Q₈×C₄₇	—	2	4	no	—
28	C₂×C₄⋊Q₈×C₄₇	C₂²	1	4	yes	complemented
29	C₂×#124×C₄₇	—	2	1	no	—
30	C₂×#123×C₄₇	—	2	2	no	—
31	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
32	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₄₇	—	2	2	no	—
34	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#104×C₄₇	—	2	4	no	—
36	C₂×#104×C₄₇	C₂²	1	4	yes	—
37	C₄₇×#419	—	2	2	no	—
38	C₄₇×#419	C₂²	1	4	yes	complemented
39	C₂×#103×C₄₇	—	2	2	no	—
40	C₂×#101×C₄₇	—	2	4	no	—
41	C₂×#101×C₄₇	C₂²	1	4	yes	complemented
42	C₄₇×#339	C₂²	1	4	yes	complemented
43	C₂×#41×C₄₇	—	2	1	no	—
44	C₂×#41×C₄₇	—	2	1	no	—
45	C₂×#41×C₄₇	—	2	2	no	—
46	C₂×#41×C₄₇	—	2	2	no	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	—	2	2	no	—
49	C₂×#41×C₄₇	D₄	1	2	yes	—
50	C₂×#41×C₄₇	C₂³	1	2	yes	—
51	C₂²×Q₈×C₄₇	—	2	1	no	—
52	C₂²×Q₈×C₄₇	—	2	1	no	—
53	C₂²×Q₈×C₄₇	—	2	2	no	—
54	C₂²×Q₈×C₄₇	—	2	2	no	—
55	C₂²×Q₈×C₄₇	—	2	2	no	—
56	C₂²×Q₈×C₄₇	—	2	1	no	—
57	C₂²×Q₈×C₄₇	—	2	1	no	—
58	C₂²×Q₈×C₄₇	—	2	1	no	—
59	C₂²×Q₈×C₄₇	—	2	2	no	—
60	C₂²×Q₈×C₄₇	—	2	2	no	—
61	C₂²×Q₈×C₄₇	—	2	1	no	—
62	C₂²×Q₈×C₄₇	—	2	1	no	—
63	C₂²×Q₈×C₄₇	—	2	2	no	—
64	C₂²×Q₈×C₄₇	—	2	1	no	—
65	C₂²×Q₈×C₄₇	—	2	1	no	—
66	C₂²×Q₈×C₄₇	—	2	2	no	—
67	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
68	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
69	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
70	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
71	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
72	C₂²×D₄×C₄₇	—	2	1	no	—
73	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
74	C₂³×C₄×C₄₇	—	2	1	no	—
75	C₂³×C₄×C₄₇	—	2	1	no	—
76	C₂³×C₄×C₄₇	—	2	1	no	—
77	C₂³×C₄×C₄₇	D₄	1	2	yes	—
78	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	#137×C₄₇	—	2	16	no	—
80	#137×C₄₇	—	2	8	no	—
81	#137×C₄₇	—	2	8	no	—
82	C₂×Q₁₆×C₄₇	—	2	8	no	—
83	C₂×Q₁₆×C₄₇	—	2	4	no	—
84	C₂×SD₁₆×C₄₇	—	2	8	no	—
85	C₂×SD₁₆×C₄₇	—	2	4	no	—
86	C₂×M₁₆×C₄₇	—	2	2	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	—	2	1	no	—
89	C₂×M₁₆×C₄₇	—	2	2	no	—
90	C₂×M₁₆×C₄₇	—	2	2	no	—
91	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
92	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
93	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
94	C₂²×C₈×C₄₇	—	2	1	no	—
95	C₂²×C₈×C₄₇	—	2	1	no	—
96	C₄⋊Q₈×C₄₇	—	2	16	no	—
97	C₄⋊Q₈×C₄₇	—	2	4	no	—
98	C₄⋊Q₈×C₄₇	—	2	8	no	—
99	C₄⋊Q₈×C₄₇	—	2	4	no	—
100	C₄⋊Q₈×C₄₇	—	2	8	no	—
101	#124×C₄₇	—	2	4	no	—
102	#124×C₄₇	—	2	4	no	—
103	#123×C₄₇	—	2	8	no	—
104	#123×C₄₇	—	2	8	no	—
105	C₂²⋊Q₈×C₄₇	—	2	8	no	—
106	C₂²⋊Q₈×C₄₇	—	2	8	no	—
107	#117×C₄₇	—	2	1	no	—
108	#117×C₄₇	—	2	1	no	—
109	#117×C₄₇	D₄	1	2	yes	—
110	#117×C₄₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₄₇	—	2	16	no	—
112	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
113	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
114	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
115	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
116	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
117	C₂×C₄²×C₄₇	—	2	1	no	—
118	C₂×C₄²×C₄₇	—	2	2	no	—
119	C₂×C₄²×C₄₇	—	2	1	no	—
120	C₂×C₄²×C₄₇	D₄	1	4	yes	—
121	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
122	#104×C₄₇	—	2	8	no	—
123	#103×C₄₇	—	2	8	no	—
124	#101×C₄₇	—	2	8	no	—
125	C₂⁴×C₄₇	—	2	1	no	—
126	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
127	#41×C₄₇	—	2	4	no	—
128	#41×C₄₇	—	2	4	no	—
129	#41×C₄₇	—	2	2	no	—
130	#41×C₄₇	—	2	2	no	—
131	#41×C₄₇	—	2	2	no	—
132	#41×C₄₇	—	2	2	no	—
133	#41×C₄₇	—	4	2	no	—
134	#41×C₄₇	—	4	2	no	—
135	#41×C₄₇	—	4	2	no	—
136	#41×C₄₇	—	4	2	no	—
137	C₂×Q₈×C₄₇	—	2	2	no	—
138	C₂×Q₈×C₄₇	—	2	2	no	—
139	C₂×Q₈×C₄₇	—	2	4	no	—
140	C₂×Q₈×C₄₇	—	2	4	no	—
141	C₂×Q₈×C₄₇	—	2	1	no	—
142	C₂×Q₈×C₄₇	—	2	4	no	—
143	C₂×Q₈×C₄₇	—	2	2	no	—
144	C₂×Q₈×C₄₇	—	2	2	no	—
145	C₂×Q₈×C₄₇	—	2	2	no	—
146	C₂×Q₈×C₄₇	—	2	2	no	—
147	C₂×Q₈×C₄₇	—	2	2	no	—
148	C₂×Q₈×C₄₇	—	2	2	no	—
149	C₂×Q₈×C₄₇	—	2	2	no	—
150	C₂×Q₈×C₄₇	—	2	4	no	—
151	C₂×Q₈×C₄₇	—	2	2	no	—
152	C₂×Q₈×C₄₇	—	2	4	no	—
153	C₂×Q₈×C₄₇	—	2	4	no	—
154	C₂×Q₈×C₄₇	—	2	4	no	—
155	C₂×Q₈×C₄₇	—	2	2	no	—
156	C₂×Q₈×C₄₇	—	2	2	no	—
157	C₂×Q₈×C₄₇	—	2	2	no	—
158	C₂×Q₈×C₄₇	—	2	2	no	—
159	C₂×Q₈×C₄₇	—	2	2	no	—
160	C₂×Q₈×C₄₇	—	4	1	no	—
161	C₂×Q₈×C₄₇	—	4	1	no	—
162	C₂×Q₈×C₄₇	—	4	2	no	—
163	C₂×Q₈×C₄₇	—	4	2	no	—
164	C₂×Q₈×C₄₇	—	4	2	no	—
165	C₂×Q₈×C₄₇	—	4	2	no	—
166	C₂×Q₈×C₄₇	—	4	2	no	—
167	C₂×Q₈×C₄₇	—	4	2	no	—
168	C₂×Q₈×C₄₇	—	4	2	no	—
169	C₂×Q₈×C₄₇	—	4	2	no	—
170	C₂×Q₈×C₄₇	—	4	2	no	—
171	C₂×Q₈×C₄₇	—	4	2	no	—
172	C₂×Q₈×C₄₇	—	4	2	no	—
173	C₂×Q₈×C₄₇	—	4	2	no	—
174	C₂×Q₈×C₄₇	—	4	2	no	—
175	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
176	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
177	C₂×D₄×C₄₇	—	2	2	no	—
178	C₂×D₄×C₄₇	—	2	2	no	—
179	C₂×D₄×C₄₇	—	2	2	no	—
180	C₂×D₄×C₄₇	—	2	1	no	—
181	C₂×D₄×C₄₇	—	2	2	no	—
182	C₂×D₄×C₄₇	—	4	2	no	—
183	C₂×D₄×C₄₇	—	4	2	no	—
184	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₄₇	—	2	8	no	—
186	C₂²×C₄×C₄₇	—	2	4	no	—
187	C₂²×C₄×C₄₇	—	2	2	no	—
188	C₂²×C₄×C₄₇	—	2	4	no	—
189	C₂²×C₄×C₄₇	—	2	4	no	—
190	C₂²×C₄×C₄₇	—	2	2	no	—
191	C₂²×C₄×C₄₇	—	2	2	no	—
192	C₂²×C₄×C₄₇	—	2	2	no	—
193	C₂²×C₄×C₄₇	—	2	1	no	—
194	C₂²×C₄×C₄₇	—	2	4	no	—
195	C₂²×C₄×C₄₇	—	2	2	no	—
196	C₂²×C₄×C₄₇	—	2	2	no	—
197	C₂²×C₄×C₄₇	—	2	2	no	—
198	C₂²×C₄×C₄₇	—	4	1	no	—
199	C₂²×C₄×C₄₇	—	4	1	no	—
200	C₂²×C₄×C₄₇	—	4	2	no	—
201	C₂²×C₄×C₄₇	—	4	2	no	—
202	C₂²×C₄×C₄₇	—	4	2	no	—
203	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
204	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
205	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
206	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
210	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₄₇	#41	1	2	yes	—
213	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
214	Q₁₆×C₄₇	—	2	16	no	—
215	SD₁₆×C₄₇	—	2	16	no	—
216	M₁₆×C₄₇	—	2	4	no	—
217	M₁₆×C₄₇	—	2	2	no	—
218	M₁₆×C₄₇	—	2	2	no	—
219	M₁₆×C₄₇	—	2	2	no	—
220	M₁₆×C₄₇	—	4	2	no	—
221	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
222	C₂×C₈×C₄₇	—	2	4	no	—
223	C₂×C₈×C₄₇	—	2	2	no	—
224	C₂×C₈×C₄₇	—	2	2	no	—
225	C₂×C₈×C₄₇	—	4	2	no	—
226	C₄⋊C₄×C₄₇	—	2	32	no	—
227	C₄⋊C₄×C₄₇	—	2	16	no	—
228	C₄⋊C₄×C₄₇	—	2	2	no	—
229	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
230	C₂²⋊C₄×C₄₇	—	2	16	no	—
231	C₂²⋊C₄×C₄₇	—	2	2	no	—
232	C₂²⋊C₄×C₄₇	—	2	2	no	—
233	C₄²×C₄₇	—	2	4	no	—
234	C₄²×C₄₇	—	2	2	no	—
235	C₄²×C₄₇	—	2	2	no	—
236	C₄²×C₄₇	—	2	2	no	—
237	C₄²×C₄₇	C₂×D₄	1	4	yes	—
238	C₂³×C₄₇	—	2	4	no	—
239	C₂³×C₄₇	—	2	2	no	—
240	C₂³×C₄₇	—	4	2	no	—
241	C₂³×C₄₇	—	4	4	no	—
242	C₂³×C₄₇	#120	1	1	yes	characteristic
243	C₂³×C₄₇	#120	1	2	yes	—
244	C₂³×C₄₇	#120	1	1	yes	characteristic
245	C₂³×C₄₇	#121	1	2	yes	—
246	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
247	Q₈×C₄₇	—	2	4	no	—
248	Q₈×C₄₇	—	2	2	no	—
249	Q₈×C₄₇	—	2	4	no	—
250	Q₈×C₄₇	—	2	2	no	—
251	Q₈×C₄₇	—	4	2	no	—
252	Q₈×C₄₇	—	4	2	no	—
253	Q₈×C₄₇	—	4	2	no	—
254	Q₈×C₄₇	—	4	2	no	—
255	Q₈×C₄₇	—	4	2	no	—
256	Q₈×C₄₇	—	4	2	no	—
257	Q₈×C₄₇	—	4	4	no	—
258	Q₈×C₄₇	—	4	4	no	—
259	Q₈×C₄₇	—	4	4	no	—
260	Q₈×C₄₇	—	4	4	no	—
261	Q₈×C₄₇	—	4	2	no	—
262	D₄×C₄₇	—	2	2	no	—
263	D₄×C₄₇	—	2	2	no	—
264	D₄×C₄₇	—	4	2	no	—
265	D₄×C₄₇	—	4	2	no	—
266	D₄×C₄₇	—	4	4	no	—
267	D₄×C₄₇	—	4	2	no	—
268	C₂×C₄×C₄₇	—	2	8	no	—
269	C₂×C₄×C₄₇	—	2	16	no	—
270	C₂×C₄×C₄₇	—	2	4	no	—
271	C₂×C₄×C₄₇	—	2	4	no	—
272	C₂×C₄×C₄₇	—	2	4	no	—
273	C₂×C₄×C₄₇	—	2	2	no	—
274	C₂×C₄×C₄₇	—	2	4	no	—
275	C₂×C₄×C₄₇	—	2	4	no	—
276	C₂×C₄×C₄₇	—	2	4	no	—
277	C₂×C₄×C₄₇	—	4	2	no	—
278	C₂×C₄×C₄₇	—	4	2	no	—
279	C₂×C₄×C₄₇	—	4	4	no	—
280	C₂×C₄×C₄₇	—	4	4	no	—
281	C₂×C₄×C₄₇	—	4	2	no	—
282	C₂×C₄×C₄₇	—	4	4	no	—
283	C₂×C₄×C₄₇	—	4	4	no	—
284	C₂×C₄×C₄₇	—	4	4	no	—
285	C₂×C₄×C₄₇	—	4	2	no	—
286	C₂×C₄×C₄₇	—	4	2	no	—
287	C₂×C₄×C₄₇	—	4	4	no	—
288	C₂×C₄×C₄₇	#120	1	2	yes	—
289	C₂×C₄×C₄₇	#120	1	2	yes	—
290	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
291	C₂×C₄×C₄₇	#120	1	2	yes	—
292	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
293	C₂×C₄×C₄₇	#121	1	2	yes	—
294	C₂×C₄×C₄₇	#121	1	2	yes	—
295	C₂×C₄×C₄₇	#121	1	2	yes	—
296	C₂×C₄×C₄₇	#121	1	2	yes	—
297	C₂×C₄×C₄₇	#121	1	2	yes	—
298	C₂×C₄×C₄₇	#127	1	2	yes	—
299	C₂×C₄×C₄₇	#127	1	2	yes	—
300	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
303	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
304	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
306	C₈×C₄₇	—	2	4	no	—
307	C₈×C₄₇	—	4	2	no	—
308	C₂×#2005	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
309	C₂²×C₄₇	—	2	2	no	—
310	C₂²×C₄₇	—	2	2	no	—
311	C₂²×C₄₇	—	2	4	no	—
312	C₂²×C₄₇	—	2	4	no	—
313	C₂²×C₄₇	—	4	2	no	—
314	C₂²×C₄₇	—	4	4	no	—
315	C₂²×C₄₇	—	8	4	no	—
316	C₂²×C₄₇	#392	1	2	yes	—
317	C₂²×C₄₇	#392	1	2	yes	—
318	C₂²×C₄₇	#456	1	4	yes	—
319	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
320	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
321	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
322	C₄×C₄₇	—	2	8	no	—
323	C₄×C₄₇	—	4	4	no	—
324	C₄×C₄₇	—	4	2	no	—
325	C₄×C₄₇	—	4	4	no	—
326	C₄×C₄₇	—	4	4	no	—
327	C₄×C₄₇	#392	1	2	yes	—
328	C₄×C₄₇	#392	1	2	yes	—
329	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
330	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
331	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
332	C₄×C₄₇	C₂×#127	1	1	yes	characteristic
333	C₂²×#137	C₂×C₄₇	1	1	yes	characteristic
334	C₂×#536	C₂×C₄₇	1	1	yes	characteristic
335	C₂²×C₄⋊Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
336	C₂²×#104	C₂×C₄₇	1	1	yes	characteristic
337	C₂×#419	C₂×C₄₇	1	1	yes	characteristic, complemented
338	C₂²×#101	C₂×C₄₇	1	1	yes	characteristic, complemented
339	#2005	C₂×C₄₇	1	8	yes	direct product factor
340	C₂×#339	C₂×C₄₇	1	1	yes	characteristic, complemented
341	C₂×C₄₇	—	2	1	no	—
342	C₂×C₄₇	—	2	1	no	—
343	C₂×C₄₇	—	2	2	no	—
344	C₂×C₄₇	—	8	2	no	—
345	C₂×C₄₇	#2005	1	4	yes	direct product factor
346	C₂×C₄₇	C₂×#392	1	1	yes	characteristic
347	C₂×C₄₇	C₂×#456	1	2	yes	—
348	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
349	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
350	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
351	C₂×#137	—	2	2	no	—
352	C₂×#137	—	2	4	no	—
353	C₂×#137	—	2	4	no	—
354	C₂×#137	C₂²×C₄₇	1	4	yes	—
355	C₂²×Q₁₆	—	2	1	no	—
356	C₂²×SD₁₆	—	2	1	no	—
357	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
358	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
359	#536	—	2	2	no	—
360	#536	—	2	2	no	—
361	#536	—	2	2	no	—
362	#536	C₂²×C₄₇	1	4	yes	—
363	C₂×C₄⋊Q₈	—	2	4	no	—
364	C₂×C₄⋊Q₈	—	2	2	no	—
365	C₂×C₄⋊Q₈	—	2	1	no	—
366	C₂×C₄⋊Q₈	—	2	4	no	—
367	C₂×C₄⋊Q₈	C₂²×C₄₇	1	4	yes	complemented
368	C₂×#124	—	2	1	no	—
369	C₂×#123	—	2	2	no	—
370	C₂×C₂²⋊Q₈	—	2	2	no	—
371	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
372	C₂²×C₄⋊C₄	—	2	2	no	—
373	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
374	C₂×#104	—	2	4	no	—
375	C₂×#104	C₂²×C₄₇	1	4	yes	—
376	#419	—	2	2	no	—
377	#419	C₂²×C₄₇	1	4	yes	complemented
378	C₂×#103	—	2	2	no	—
379	C₂×#101	—	2	4	no	—
380	C₂×#101	C₂²×C₄₇	1	4	yes	complemented
381	#339	C₂²×C₄₇	1	4	yes	complemented
382	C₄₇	C₂×#2005	1	1	yes	characteristic, direct product factor, Sylow
383	C₂×#41	—	2	1	no	—
384	C₂×#41	—	2	1	no	—
385	C₂×#41	—	2	2	no	—
386	C₂×#41	—	2	2	no	—
387	C₂×#41	—	2	2	no	—
388	C₂×#41	—	2	2	no	—
389	C₂×#41	D₄×C₄₇	1	2	yes	—
390	C₂×#41	C₂³×C₄₇	1	2	yes	—
391	C₂²×Q₈	—	2	1	no	—
392	C₂²×Q₈	—	2	1	no	—
393	C₂²×Q₈	—	2	2	no	—
394	C₂²×Q₈	—	2	2	no	—
395	C₂²×Q₈	—	2	2	no	—
396	C₂²×Q₈	—	2	1	no	—
397	C₂²×Q₈	—	2	1	no	—
398	C₂²×Q₈	—	2	1	no	—
399	C₂²×Q₈	—	2	2	no	—
400	C₂²×Q₈	—	2	2	no	—
401	C₂²×Q₈	—	2	1	no	—
402	C₂²×Q₈	—	2	1	no	—
403	C₂²×Q₈	—	2	2	no	—
404	C₂²×Q₈	—	2	1	no	—
405	C₂²×Q₈	—	2	1	no	—
406	C₂²×Q₈	—	2	2	no	—
407	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
408	C₂²×Q₈	D₄×C₄₇	1	4	yes	—
409	C₂²×Q₈	D₄×C₄₇	1	2	yes	—
410	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
411	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
412	C₂²×D₄	—	2	1	no	—
413	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	—	2	1	no	—
416	C₂³×C₄	—	2	1	no	—
417	C₂³×C₄	D₄×C₄₇	1	2	yes	—
418	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
419	#137	—	2	16	no	—
420	#137	—	2	8	no	—
421	#137	—	2	8	no	—
422	C₂×Q₁₆	—	2	8	no	—
423	C₂×Q₁₆	—	2	4	no	—
424	C₂×SD₁₆	—	2	8	no	—
425	C₂×SD₁₆	—	2	4	no	—
426	C₂×M₁₆	—	2	2	no	—
427	C₂×M₁₆	—	2	1	no	—
428	C₂×M₁₆	—	2	1	no	—
429	C₂×M₁₆	—	2	2	no	—
430	C₂×M₁₆	—	2	2	no	—
431	C₂×M₁₆	D₄×C₄₇	1	4	yes	—
432	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
433	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
434	C₂²×C₈	—	2	1	no	—
435	C₂²×C₈	—	2	1	no	—
436	C₄⋊Q₈	—	2	16	no	—
437	C₄⋊Q₈	—	2	4	no	—
438	C₄⋊Q₈	—	2	8	no	—
439	C₄⋊Q₈	—	2	4	no	—
440	C₄⋊Q₈	—	2	8	no	—
441	#124	—	2	4	no	—
442	#124	—	2	4	no	—
443	#123	—	2	8	no	—
444	#123	—	2	8	no	—
445	C₂²⋊Q₈	—	2	8	no	—
446	C₂²⋊Q₈	—	2	8	no	—
447	#117	—	2	1	no	—
448	#117	—	2	1	no	—
449	#117	D₄×C₄₇	1	2	yes	—
450	#117	C₂³×C₄₇	1	2	yes	—
451	C₂×C₄⋊C₄	—	2	16	no	—
452	C₂×C₄⋊C₄	—	2	4	no	—
453	C₂×C₄⋊C₄	—	2	8	no	—
454	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
455	C₂×C₂²⋊C₄	—	2	4	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₄²	—	2	1	no	—
458	C₂×C₄²	—	2	1	no	—
459	C₂×C₄²	—	2	2	no	—
460	C₂×C₄²	D₄×C₄₇	1	4	yes	—
461	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
462	#104	—	2	8	no	—
463	#103	—	2	8	no	—
464	#101	—	2	8	no	—
465	C₂⁴	—	2	1	no	—
466	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
467	#41	—	2	4	no	—
468	#41	—	2	4	no	—
469	#41	—	2	2	no	—
470	#41	—	2	2	no	—
471	#41	—	2	2	no	—
472	#41	—	2	2	no	—
473	#41	—	4	2	no	—
474	#41	—	4	2	no	—
475	#41	—	4	2	no	—
476	#41	—	4	2	no	—
477	C₂×Q₈	—	2	2	no	—
478	C₂×Q₈	—	2	2	no	—
479	C₂×Q₈	—	2	4	no	—
480	C₂×Q₈	—	2	4	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	4	no	—
483	C₂×Q₈	—	2	2	no	—
484	C₂×Q₈	—	2	2	no	—
485	C₂×Q₈	—	2	2	no	—
486	C₂×Q₈	—	2	2	no	—
487	C₂×Q₈	—	2	2	no	—
488	C₂×Q₈	—	2	2	no	—
489	C₂×Q₈	—	2	2	no	—
490	C₂×Q₈	—	2	4	no	—
491	C₂×Q₈	—	2	2	no	—
492	C₂×Q₈	—	2	4	no	—
493	C₂×Q₈	—	2	4	no	—
494	C₂×Q₈	—	2	4	no	—
495	C₂×Q₈	—	2	2	no	—
496	C₂×Q₈	—	2	2	no	—
497	C₂×Q₈	—	2	2	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	—	4	1	no	—
501	C₂×Q₈	—	4	1	no	—
502	C₂×Q₈	—	4	2	no	—
503	C₂×Q₈	—	4	2	no	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×Q₈	—	4	2	no	—
506	C₂×Q₈	—	4	2	no	—
507	C₂×Q₈	—	4	2	no	—
508	C₂×Q₈	—	4	2	no	—
509	C₂×Q₈	—	4	2	no	—
510	C₂×Q₈	—	4	2	no	—
511	C₂×Q₈	—	4	2	no	—
512	C₂×Q₈	—	4	2	no	—
513	C₂×Q₈	—	4	2	no	—
514	C₂×Q₈	—	4	2	no	—
515	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
516	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
517	C₂×D₄	—	2	2	no	—
518	C₂×D₄	—	2	2	no	—
519	C₂×D₄	—	2	2	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	2	2	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
525	C₂²×C₄	—	2	8	no	—
526	C₂²×C₄	—	2	4	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	2	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	4	no	—
532	C₂²×C₄	—	2	4	no	—
533	C₂²×C₄	—	2	2	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	2	no	—
536	C₂²×C₄	—	2	2	no	—
537	C₂²×C₄	—	2	2	no	—
538	C₂²×C₄	—	4	1	no	—
539	C₂²×C₄	—	4	1	no	—
540	C₂²×C₄	—	4	2	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
544	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
545	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
547	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
549	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
550	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
551	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
552	C₂²×C₄	#41×C₄₇	1	2	yes	—
553	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
554	Q₁₆	—	2	16	no	—
555	SD₁₆	—	2	16	no	—
556	M₁₆	—	2	4	no	—
557	M₁₆	—	2	2	no	—
558	M₁₆	—	2	2	no	—
559	M₁₆	—	2	2	no	—
560	M₁₆	—	4	2	no	—
561	M₁₆	C₂×D₄×C₄₇	1	4	yes	—
562	C₂×C₈	—	2	4	no	—
563	C₂×C₈	—	2	2	no	—
564	C₂×C₈	—	2	2	no	—
565	C₂×C₈	—	4	2	no	—
566	C₄⋊C₄	—	2	32	no	—
567	C₄⋊C₄	—	2	16	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
570	C₂²⋊C₄	—	2	16	no	—
571	C₂²⋊C₄	—	2	2	no	—
572	C₂²⋊C₄	—	2	2	no	—
573	C₄²	—	2	4	no	—
574	C₄²	—	2	2	no	—
575	C₄²	—	2	2	no	—
576	C₄²	—	2	2	no	—
577	C₄²	C₂×D₄×C₄₇	1	4	yes	—
578	C₂³	—	2	4	no	—
579	C₂³	—	2	2	no	—
580	C₂³	—	4	4	no	—
581	C₂³	—	4	2	no	—
582	C₂³	#120×C₄₇	1	1	yes	characteristic
583	C₂³	#120×C₄₇	1	2	yes	—
584	C₂³	#120×C₄₇	1	1	yes	characteristic
585	C₂³	#121×C₄₇	1	2	yes	—
586	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
587	Q₈	—	2	4	no	—
588	Q₈	—	2	2	no	—
589	Q₈	—	2	4	no	—
590	Q₈	—	2	2	no	—
591	Q₈	—	4	2	no	—
592	Q₈	—	4	2	no	—
593	Q₈	—	4	2	no	—
594	Q₈	—	4	2	no	—
595	Q₈	—	4	2	no	—
596	Q₈	—	4	2	no	—
597	Q₈	—	4	4	no	—
598	Q₈	—	4	4	no	—
599	Q₈	—	4	4	no	—
600	Q₈	—	4	4	no	—
601	Q₈	—	4	2	no	—
602	D₄	—	2	2	no	—
603	D₄	—	2	2	no	—
604	D₄	—	4	2	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	4	no	—
607	D₄	—	4	2	no	—
608	C₂×C₄	—	2	8	no	—
609	C₂×C₄	—	2	16	no	—
610	C₂×C₄	—	2	4	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	4	4	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	4	no	—
621	C₂×C₄	—	4	4	no	—
622	C₂×C₄	—	4	2	no	—
623	C₂×C₄	—	4	4	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	#120×C₄₇	1	2	yes	—
629	C₂×C₄	#120×C₄₇	1	2	yes	—
630	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
631	C₂×C₄	#120×C₄₇	1	2	yes	—
632	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
633	C₂×C₄	#121×C₄₇	1	2	yes	—
634	C₂×C₄	#121×C₄₇	1	2	yes	—
635	C₂×C₄	#121×C₄₇	1	2	yes	—
636	C₂×C₄	#121×C₄₇	1	2	yes	—
637	C₂×C₄	#121×C₄₇	1	2	yes	—
638	C₂×C₄	#127×C₄₇	1	2	yes	—
639	C₂×C₄	#127×C₄₇	1	2	yes	—
640	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
641	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
642	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
643	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
644	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
645	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
646	C₈	—	2	4	no	—
647	C₈	—	4	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	4	no	—
651	C₂²	—	2	4	no	—
652	C₂²	—	4	2	no	—
653	C₂²	—	4	4	no	—
654	C₂²	—	8	4	no	—
655	C₂²	C₄₇×#392	1	2	yes	—
656	C₂²	C₄₇×#392	1	2	yes	—
657	C₂²	C₄₇×#456	1	4	yes	—
658	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
659	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
660	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
661	C₄	—	2	8	no	—
662	C₄	—	4	4	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	4	no	—
665	C₄	—	4	4	no	—
666	C₄	C₄₇×#392	1	2	yes	—
667	C₄	C₄₇×#392	1	2	yes	—
668	C₄	C₂×#120×C₄₇	1	1	yes	characteristic
669	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
670	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
671	C₄	C₂×#127×C₄₇	1	1	yes	characteristic
672	C₂	—	2	1	no	—
673	C₂	—	2	1	no	—
674	C₂	—	2	2	no	—
675	C₂	—	8	2	no	—
676	C₂	C₄₇×#2005	1	4	yes	direct product factor
677	C₂	C₂×C₄₇×#392	1	1	yes	characteristic
678	C₂	C₂×C₄₇×#456	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×#41×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄⋊Q₈×C₄₇	C₂	semidirect
5. C₂×C₄₇×#419	C₂	semidirect
6. C₂²×#101×C₄₇	C₂	semidirect
7. C₄₇×#2005	C₂	direct (N × H)
8. C₂×C₄₇×#339	C₂	semidirect
28. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
38. C₄₇×#419	C₂²	semidirect
41. C₂×#101×C₄₇	C₂²	semidirect
42. C₄₇×#339	C₂²	semidirect
308. C₂×#2005	C₄₇	direct (N × H)
335. C₂²×C₄⋊Q₈	C₂×C₄₇	semidirect
337. C₂×#419	C₂×C₄₇	semidirect
338. C₂²×#101	C₂×C₄₇	semidirect
339. #2005	C₂×C₄₇	direct (N × H)
340. C₂×#339	C₂×C₄₇	semidirect
345. C₂×C₄₇	#2005	direct (N × H)
367. C₂×C₄⋊Q₈	C₂²×C₄₇	semidirect
377. #419	C₂²×C₄₇	semidirect
380. C₂×#101	C₂²×C₄₇	semidirect
381. #339	C₂²×C₄₇	semidirect
382. C₄₇	C₂×#2005	direct (N × H)
676. C₂	C₄₇×#2005	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#137×C₄₇	2
C₂×C₄₇×#536	2
C₂²×C₄⋊Q₈×C₄₇	2
C₂²×#104×C₄₇	2
C₂×C₄₇×#419	2
C₂²×#101×C₄₇	2
C₄₇×#2005	2
C₂×C₄₇×#339	2
C₂×#2005	47

Subgroups — C2×C47×#2005 #26063096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2005 #26063096