Subgroups — C₂×C₄₇×#1912 #26060709

Order 12032.

1694 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#421	C₂	1	2	yes	maximal
4	C₂²×#101×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1912	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₇×H(3,ℤ/4)	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
8	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
10	C₄₇×#536	—	2	2	no	—
11	C₄₇×#536	—	2	2	no	—
12	C₄₇×#536	C₄	1	4	yes	complemented
13	C₄₇×#536	C₂²	1	4	yes	—
14	C₂×C₄⋊Q₈×C₄₇	C₄	1	2	yes	complemented
15	C₂×#124×C₄₇	C₄	1	2	yes	complemented
16	C₂×#123×C₄₇	—	2	2	no	—
17	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
18	C₄₇×#519	—	2	2	no	—
19	C₄₇×#519	—	2	4	no	—
20	C₄₇×#519	C₂²	1	4	yes	complemented
21	C₂×C₄×Q₈×C₄₇	—	2	4	no	—
22	C₂×#117×C₄₇	—	2	2	no	—
23	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#117×C₄₇	C₂²	1	2	yes	—
25	C₄₇×#421	—	2	4	no	—
26	C₄₇×#421	C₂²	1	8	yes	—
27	C₂×#104×C₄₇	—	2	4	no	—
28	C₂×#101×C₄₇	—	2	2	no	—
29	C₂×#101×C₄₇	—	2	2	no	—
30	C₂×#101×C₄₇	C₂²	1	4	yes	complemented
31	C₄₇×H(3,ℤ/4)	C₂²	1	8	yes	complemented
32	C₂×#41×C₄₇	—	2	1	no	—
33	C₂×#41×C₄₇	—	2	1	no	—
34	C₂×#41×C₄₇	—	2	2	no	—
35	C₂×#41×C₄₇	—	2	2	no	—
36	C₂×#41×C₄₇	—	2	2	no	—
37	C₂×#41×C₄₇	—	2	2	no	—
38	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
39	C₂×#41×C₄₇	C₂³	1	2	yes	—
40	C₂²×Q₈×C₄₇	—	2	2	no	—
41	C₂²×Q₈×C₄₇	—	2	2	no	—
42	C₂²×Q₈×C₄₇	—	2	2	no	—
43	C₂²×Q₈×C₄₇	—	2	2	no	—
44	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
46	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
47	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
48	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
49	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
50	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
51	C₂²×D₄×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	—	2	1	no	—
54	C₂³×C₄×C₄₇	D₄	1	2	yes	—
55	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₄₇	—	2	2	no	—
57	C₂×M₁₆×C₄₇	—	2	2	no	—
58	C₂×M₁₆×C₄₇	—	2	2	no	—
59	C₂×M₁₆×C₄₇	—	2	2	no	—
60	C₂×M₁₆×C₄₇	—	2	2	no	—
61	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
62	C₂²×C₈×C₄₇	—	2	2	no	—
63	C₄⋊Q₈×C₄₇	—	2	4	no	—
64	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
65	#124×C₄₇	—	2	4	no	—
66	#124×C₄₇	C₂×C₄	1	8	yes	complemented
67	#123×C₄₇	—	2	8	no	—
68	#123×C₄₇	—	2	8	no	—
69	C₂²⋊Q₈×C₄₇	—	2	8	no	—
70	C₂²⋊Q₈×C₄₇	—	2	8	no	—
71	C₄×Q₈×C₄₇	—	2	16	no	—
72	C₄×Q₈×C₄₇	—	2	16	no	—
73	#117×C₄₇	—	2	8	no	—
74	#117×C₄₇	—	2	8	no	—
75	#117×C₄₇	—	2	2	no	—
76	#117×C₄₇	—	2	2	no	—
77	#117×C₄₇	—	2	1	no	—
78	#117×C₄₇	—	2	1	no	—
79	#117×C₄₇	C₂×C₄	1	2	yes	—
80	#117×C₄₇	D₄	1	4	yes	—
81	#117×C₄₇	C₂³	1	2	yes	—
82	#117×C₄₇	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
84	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
85	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
86	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
90	C₂×C₄²×C₄₇	—	2	4	no	—
91	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
92	C₂×C₄²×C₄₇	D₄	1	4	yes	—
93	#104×C₄₇	—	2	16	no	—
94	#101×C₄₇	—	2	8	no	—
95	C₂⁴×C₄₇	—	2	1	no	—
96	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
97	#41×C₄₇	—	2	4	no	—
98	#41×C₄₇	—	2	4	no	—
99	#41×C₄₇	—	2	4	no	—
100	#41×C₄₇	—	2	4	no	—
101	#41×C₄₇	—	4	2	no	—
102	#41×C₄₇	—	4	2	no	—
103	#41×C₄₇	—	4	2	no	—
104	#41×C₄₇	—	4	2	no	—
105	C₂×Q₈×C₄₇	—	2	1	no	—
106	C₂×Q₈×C₄₇	—	2	4	no	—
107	C₂×Q₈×C₄₇	—	2	4	no	—
108	C₂×Q₈×C₄₇	—	2	4	no	—
109	C₂×Q₈×C₄₇	—	2	4	no	—
110	C₂×Q₈×C₄₇	—	2	4	no	—
111	C₂×Q₈×C₄₇	—	2	4	no	—
112	C₂×Q₈×C₄₇	—	2	4	no	—
113	C₂×Q₈×C₄₇	—	2	4	no	—
114	C₂×Q₈×C₄₇	—	2	4	no	—
115	C₂×Q₈×C₄₇	—	2	4	no	—
116	C₂×Q₈×C₄₇	—	2	4	no	—
117	C₂×Q₈×C₄₇	—	2	4	no	—
118	C₂×Q₈×C₄₇	—	2	2	no	—
119	C₂×Q₈×C₄₇	—	2	2	no	—
120	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
121	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
122	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
124	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	—	2	2	no	—
127	C₂×D₄×C₄₇	—	2	1	no	—
128	C₂×D₄×C₄₇	—	2	2	no	—
129	C₂×D₄×C₄₇	—	2	2	no	—
130	C₂×D₄×C₄₇	—	4	1	no	—
131	C₂×D₄×C₄₇	—	4	1	no	—
132	C₂×D₄×C₄₇	—	4	1	no	—
133	C₂×D₄×C₄₇	—	4	1	no	—
134	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₄₇	—	2	2	no	—
136	C₂²×C₄×C₄₇	—	2	2	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	2	2	no	—
140	C₂²×C₄×C₄₇	—	2	1	no	—
141	C₂²×C₄×C₄₇	—	2	4	no	—
142	C₂²×C₄×C₄₇	—	2	2	no	—
143	C₂²×C₄×C₄₇	—	2	2	no	—
144	C₂²×C₄×C₄₇	—	4	2	no	—
145	C₂²×C₄×C₄₇	—	4	2	no	—
146	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
147	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
148	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₄₇	#41	1	2	yes	—
157	C₂²×C₄×C₄₇	#41	1	2	yes	—
158	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
159	M₁₆×C₄₇	—	2	4	no	—
160	M₁₆×C₄₇	—	2	4	no	—
161	M₁₆×C₄₇	—	4	2	no	—
162	M₁₆×C₄₇	—	4	2	no	—
163	C₂×C₈×C₄₇	—	2	4	no	—
164	C₂×C₈×C₄₇	—	4	2	no	—
165	C₂×C₈×C₄₇	—	4	2	no	—
166	C₄⋊C₄×C₄₇	—	2	16	no	—
167	C₄⋊C₄×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	—	2	16	no	—
169	C₄⋊C₄×C₄₇	—	2	4	no	—
170	C₄⋊C₄×C₄₇	—	2	4	no	—
171	C₄⋊C₄×C₄₇	—	2	2	no	—
172	C₂²⋊C₄×C₄₇	—	2	2	no	—
173	C₂²⋊C₄×C₄₇	—	2	4	no	—
174	C₂²⋊C₄×C₄₇	—	2	4	no	—
175	C₂²⋊C₄×C₄₇	—	2	2	no	—
176	C₂²⋊C₄×C₄₇	—	2	16	no	—
177	C₄²×C₄₇	—	2	16	no	—
178	C₄²×C₄₇	—	2	2	no	—
179	C₄²×C₄₇	—	2	4	no	—
180	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
181	C₄²×C₄₇	C₂×D₄	1	8	yes	—
182	C₂³×C₄₇	—	2	2	no	—
183	C₂³×C₄₇	—	4	2	no	—
184	C₂³×C₄₇	—	4	4	no	—
185	C₂³×C₄₇	—	4	1	no	—
186	C₂³×C₄₇	—	4	1	no	—
187	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₄₇	#120	1	1	yes	characteristic
190	C₂³×C₄₇	#120	1	1	yes	characteristic
191	C₂³×C₄₇	#123	1	1	yes	characteristic
192	C₂³×C₄₇	#123	1	1	yes	characteristic
193	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
194	Q₈×C₄₇	—	2	8	no	—
195	Q₈×C₄₇	—	2	8	no	—
196	Q₈×C₄₇	—	2	8	no	—
197	Q₈×C₄₇	—	2	8	no	—
198	Q₈×C₄₇	—	2	4	no	—
199	Q₈×C₄₇	—	4	2	no	—
200	D₄×C₄₇	—	2	4	no	—
201	D₄×C₄₇	—	4	2	no	—
202	D₄×C₄₇	—	4	2	no	—
203	D₄×C₄₇	—	4	2	no	—
204	D₄×C₄₇	—	4	2	no	—
205	D₄×C₄₇	—	4	2	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	2	4	no	—
209	C₂×C₄×C₄₇	—	2	4	no	—
210	C₂×C₄×C₄₇	—	2	4	no	—
211	C₂×C₄×C₄₇	—	2	4	no	—
212	C₂×C₄×C₄₇	—	2	4	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	2	8	no	—
215	C₂×C₄×C₄₇	—	4	8	no	—
216	C₂×C₄×C₄₇	—	4	4	no	—
217	C₂×C₄×C₄₇	—	4	1	no	—
218	C₂×C₄×C₄₇	—	4	1	no	—
219	C₂×C₄×C₄₇	—	4	4	no	—
220	C₂×C₄×C₄₇	—	4	4	no	—
221	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
222	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
225	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₄₇	#120	1	2	yes	—
229	C₂×C₄×C₄₇	#121	1	2	yes	—
230	C₂×C₄×C₄₇	#121	1	2	yes	—
231	C₂×C₄×C₄₇	#121	1	2	yes	—
232	C₂×C₄×C₄₇	#121	1	2	yes	—
233	C₂×C₄×C₄₇	#123	1	2	yes	—
234	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
236	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
238	C₈×C₄₇	—	4	4	no	—
239	C₂×#1912	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂²×C₄₇	—	2	2	no	—
241	C₂²×C₄₇	—	2	2	no	—
242	C₂²×C₄₇	—	2	2	no	—
243	C₂²×C₄₇	—	4	1	no	—
244	C₂²×C₄₇	—	4	1	no	—
245	C₂²×C₄₇	—	4	1	no	—
246	C₂²×C₄₇	—	4	1	no	—
247	C₂²×C₄₇	—	4	4	no	—
248	C₂²×C₄₇	—	4	2	no	—
249	C₂²×C₄₇	—	8	2	no	—
250	C₂²×C₄₇	—	8	2	no	—
251	C₂²×C₄₇	#386	1	1	yes	characteristic
252	C₂²×C₄₇	#386	1	1	yes	characteristic
253	C₂²×C₄₇	#386	1	1	yes	characteristic
254	C₂²×C₄₇	#386	1	1	yes	characteristic
255	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
257	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
258	C₄×C₄₇	—	2	8	no	—
259	C₄×C₄₇	—	4	8	no	—
260	C₄×C₄₇	—	4	4	no	—
261	C₄×C₄₇	—	4	2	no	—
262	C₄×C₄₇	#386	1	2	yes	—
263	C₄×C₄₇	#386	1	2	yes	—
264	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
265	C₄×C₄₇	C₂×#121	1	2	yes	—
266	C₂×#536	C₂×C₄₇	1	1	yes	characteristic
267	C₂×#519	C₂×C₄₇	1	1	yes	characteristic, complemented
268	C₂×#421	C₂×C₄₇	1	2	yes	—
269	C₂²×#101	C₂×C₄₇	1	1	yes	characteristic, complemented
270	#1912	C₂×C₄₇	1	8	yes	direct product factor
271	C₂×H(3,ℤ/4)	C₂×C₄₇	1	2	yes	complemented
272	C₂×C₄₇	—	2	1	no	—
273	C₂×C₄₇	—	2	1	no	—
274	C₂×C₄₇	—	2	1	no	—
275	C₂×C₄₇	—	2	1	no	—
276	C₂×C₄₇	—	2	1	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	8	2	no	—
279	C₂×C₄₇	#1912	1	2	yes	direct product factor
280	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
281	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
282	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
283	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
284	#536	—	2	2	no	—
285	#536	—	2	2	no	—
286	#536	C₄×C₄₇	1	4	yes	complemented
287	#536	C₂²×C₄₇	1	4	yes	—
288	C₂×C₄⋊Q₈	C₄×C₄₇	1	2	yes	complemented
289	C₂×#124	C₄×C₄₇	1	2	yes	complemented
290	C₂×#123	—	2	2	no	—
291	C₂×C₂²⋊Q₈	—	2	2	no	—
292	#519	—	2	2	no	—
293	#519	—	2	4	no	—
294	#519	C₂²×C₄₇	1	4	yes	complemented
295	C₂×C₄×Q₈	—	2	4	no	—
296	C₂×#117	—	2	2	no	—
297	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
298	C₂×#117	C₂²×C₄₇	1	2	yes	—
299	#421	—	2	4	no	—
300	#421	C₂²×C₄₇	1	8	yes	—
301	C₂×#104	—	2	4	no	—
302	C₂×#101	—	2	2	no	—
303	C₂×#101	—	2	2	no	—
304	C₂×#101	C₂²×C₄₇	1	4	yes	complemented
305	H(3,ℤ/4)	C₂²×C₄₇	1	8	yes	complemented
306	C₄₇	C₂×#1912	1	1	yes	characteristic, direct product factor, Sylow
307	C₂×#41	—	2	1	no	—
308	C₂×#41	—	2	1	no	—
309	C₂×#41	—	2	2	no	—
310	C₂×#41	—	2	2	no	—
311	C₂×#41	—	2	2	no	—
312	C₂×#41	—	2	2	no	—
313	C₂×#41	C₂×C₄×C₄₇	1	2	yes	—
314	C₂×#41	C₂³×C₄₇	1	2	yes	—
315	C₂²×Q₈	—	2	2	no	—
316	C₂²×Q₈	—	2	2	no	—
317	C₂²×Q₈	—	2	2	no	—
318	C₂²×Q₈	—	2	2	no	—
319	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
320	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
321	C₂²×Q₈	C₂×C₄×C₄₇	1	2	yes	—
322	C₂²×Q₈	D₄×C₄₇	1	2	yes	—
323	C₂²×Q₈	D₄×C₄₇	1	2	yes	—
324	C₂²×Q₈	D₄×C₄₇	1	2	yes	—
325	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	D₄×C₄₇	1	2	yes	—
330	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	—	2	2	no	—
334	C₂×M₁₆	—	2	2	no	—
335	C₂×M₁₆	—	2	2	no	—
336	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
337	C₂²×C₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	4	no	—
339	C₄⋊Q₈	C₂×C₄×C₄₇	1	8	yes	complemented
340	#124	—	2	4	no	—
341	#124	C₂×C₄×C₄₇	1	8	yes	complemented
342	#123	—	2	8	no	—
343	#123	—	2	8	no	—
344	C₂²⋊Q₈	—	2	8	no	—
345	C₂²⋊Q₈	—	2	8	no	—
346	C₄×Q₈	—	2	16	no	—
347	C₄×Q₈	—	2	16	no	—
348	#117	—	2	8	no	—
349	#117	—	2	8	no	—
350	#117	—	2	2	no	—
351	#117	—	2	2	no	—
352	#117	—	2	1	no	—
353	#117	—	2	1	no	—
354	#117	C₂×C₄×C₄₇	1	2	yes	—
355	#117	D₄×C₄₇	1	4	yes	—
356	#117	C₂³×C₄₇	1	2	yes	—
357	#117	C₂³×C₄₇	1	4	yes	—
358	C₂×C₄⋊C₄	—	2	4	no	—
359	C₂×C₄⋊C₄	—	2	4	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	4	no	—
365	C₂×C₄²	—	2	4	no	—
366	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
367	C₂×C₄²	D₄×C₄₇	1	4	yes	—
368	#104	—	2	16	no	—
369	#101	—	2	8	no	—
370	C₂⁴	—	2	1	no	—
371	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
372	#41	—	2	4	no	—
373	#41	—	2	4	no	—
374	#41	—	2	4	no	—
375	#41	—	2	4	no	—
376	#41	—	4	2	no	—
377	#41	—	4	2	no	—
378	#41	—	4	2	no	—
379	#41	—	4	2	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	—	2	4	no	—
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	4	no	—
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	C₂²⋊C₄×C₄₇	1	4	yes	—
396	C₂×Q₈	C₂²⋊C₄×C₄₇	1	4	yes	—
397	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
398	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
399	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	4	1	no	—
406	C₂×D₄	—	4	1	no	—
407	C₂×D₄	—	4	1	no	—
408	C₂×D₄	—	4	1	no	—
409	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	2	no	—
421	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
422	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
423	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
424	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
426	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
431	C₂²×C₄	#41×C₄₇	1	2	yes	—
432	C₂²×C₄	#41×C₄₇	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
434	M₁₆	—	2	4	no	—
435	M₁₆	—	2	4	no	—
436	M₁₆	—	4	2	no	—
437	M₁₆	—	4	2	no	—
438	C₂×C₈	—	2	4	no	—
439	C₂×C₈	—	4	2	no	—
440	C₂×C₈	—	4	2	no	—
441	C₄⋊C₄	—	2	16	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	16	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	2	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	16	no	—
452	C₄²	—	2	16	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	2	4	no	—
455	C₄²	C₂²×C₄×C₄₇	1	4	yes	—
456	C₄²	C₂×D₄×C₄₇	1	8	yes	—
457	C₂³	—	2	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	4	1	no	—
461	C₂³	—	4	1	no	—
462	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
463	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
464	C₂³	#120×C₄₇	1	1	yes	characteristic
465	C₂³	#120×C₄₇	1	1	yes	characteristic
466	C₂³	#123×C₄₇	1	1	yes	characteristic
467	C₂³	#123×C₄₇	1	1	yes	characteristic
468	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
469	Q₈	—	2	8	no	—
470	Q₈	—	2	8	no	—
471	Q₈	—	2	8	no	—
472	Q₈	—	2	8	no	—
473	Q₈	—	2	4	no	—
474	Q₈	—	4	2	no	—
475	D₄	—	2	4	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	2	no	—
480	D₄	—	4	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	4	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
497	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
498	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
499	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
500	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
501	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
502	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
503	C₂×C₄	#120×C₄₇	1	2	yes	—
504	C₂×C₄	#121×C₄₇	1	2	yes	—
505	C₂×C₄	#121×C₄₇	1	2	yes	—
506	C₂×C₄	#121×C₄₇	1	2	yes	—
507	C₂×C₄	#121×C₄₇	1	2	yes	—
508	C₂×C₄	#123×C₄₇	1	2	yes	—
509	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
511	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
512	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
513	C₈	—	4	4	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	1	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	C₄₇×#386	1	1	yes	characteristic
526	C₂²	C₄₇×#386	1	1	yes	characteristic
527	C₂²	C₄₇×#386	1	1	yes	characteristic
528	C₂²	C₄₇×#386	1	1	yes	characteristic
529	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
530	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
531	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
532	C₄	—	2	8	no	—
533	C₄	—	4	8	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	2	no	—
536	C₄	C₄₇×#386	1	2	yes	—
537	C₄	C₄₇×#386	1	2	yes	—
538	C₄	C₂×C₄×D₄×C₄₇	1	2	yes	—
539	C₄	C₂×#121×C₄₇	1	2	yes	—
540	C₂	—	2	1	no	—
541	C₂	—	2	1	no	—
542	C₂	—	2	1	no	—
543	C₂	—	2	1	no	—
544	C₂	—	2	1	no	—
545	C₂	—	2	1	no	—
546	C₂	—	8	2	no	—
547	C₂	C₄₇×#1912	1	2	yes	direct product factor
548	C₂	C₂×C₄₇×#386	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	#386
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×#41×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#519	C₂	semidirect
4. C₂²×#101×C₄₇	C₂	semidirect
5. C₄₇×#1912	C₂	direct (N × H)
6. C₂×C₄₇×H(3,ℤ/4)	C₂	semidirect
12. C₄₇×#536	C₄	semidirect
14. C₂×C₄⋊Q₈×C₄₇	C₄	semidirect
15. C₂×#124×C₄₇	C₄	semidirect
20. C₄₇×#519	C₂²	semidirect
30. C₂×#101×C₄₇	C₂²	semidirect
31. C₄₇×H(3,ℤ/4)	C₂²	semidirect
64. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
66. #124×C₄₇	C₂×C₄	semidirect
239. C₂×#1912	C₄₇	direct (N × H)
267. C₂×#519	C₂×C₄₇	semidirect
269. C₂²×#101	C₂×C₄₇	semidirect
270. #1912	C₂×C₄₇	direct (N × H)
271. C₂×H(3,ℤ/4)	C₂×C₄₇	semidirect
279. C₂×C₄₇	#1912	direct (N × H)
286. #536	C₄×C₄₇	semidirect
288. C₂×C₄⋊Q₈	C₄×C₄₇	semidirect
289. C₂×#124	C₄×C₄₇	semidirect
294. #519	C₂²×C₄₇	semidirect
304. C₂×#101	C₂²×C₄₇	semidirect
305. H(3,ℤ/4)	C₂²×C₄₇	semidirect
306. C₄₇	C₂×#1912	direct (N × H)
339. C₄⋊Q₈	C₂×C₄×C₄₇	semidirect
341. #124	C₂×C₄×C₄₇	semidirect
547. C₂	C₄₇×#1912	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×C₄₇×#536	2
C₂×C₄₇×#519	2
C₂×C₄₇×#421	2
C₂²×#101×C₄₇	2
C₄₇×#1912	2
C₂×C₄₇×H(3,ℤ/4)	2
C₂×#1912	47

Subgroups — C2×C47×#1912 #26060709

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1912 #26060709