Subgroups — C₂×C₄₇×#1829 #26060409

Order 12032.

1434 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#518	C₂	1	1	yes	maximal, characteristic
2	C₂²×#100×C₄₇	C₂	1	2	yes	maximal
3	C₄₇×#1829	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄₇×#344	C₂	1	4	yes	maximal, complemented
5	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
6	C₂²×M₁₆×C₄₇	C₂²	1	4	yes	—
7	C₄₇×#518	—	2	4	no	—
8	C₄₇×#518	C₄	1	4	yes	—
9	C₄₇×#518	C₂²	1	4	yes	—
10	C₂×C₄×D₄×C₄₇	—	2	4	no	—
11	C₂×#117×C₄₇	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₄₇	C₄	1	4	yes	—
13	C₂×#100×C₄₇	—	2	4	no	—
14	C₂×#100×C₄₇	—	2	4	no	—
15	C₂×#100×C₄₇	C₂²	1	8	yes	—
16	C₄₇×#344	C₂²	1	16	yes	complemented
17	C₂⁵×C₄₇	C₂×C₄	1	2	yes	—
18	C₂²×D₄×C₄₇	—	2	4	no	—
19	C₂²×D₄×C₄₇	—	2	4	no	—
20	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
21	C₂²×D₄×C₄₇	D₄	1	4	yes	—
22	C₂²×D₄×C₄₇	D₄	1	4	yes	—
23	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
24	C₂³×C₄×C₄₇	—	2	4	no	—
25	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
26	C₂×M₁₆×C₄₇	—	2	4	no	—
27	C₂×M₁₆×C₄₇	—	2	4	no	—
28	C₂×M₁₆×C₄₇	—	2	4	no	—
29	C₂×M₁₆×C₄₇	—	2	4	no	—
30	C₂×M₁₆×C₄₇	—	2	4	no	—
31	C₂×M₁₆×C₄₇	C₂³	1	8	yes	—
32	C₂²×C₈×C₄₇	—	2	4	no	—
33	C₄×D₄×C₄₇	—	2	16	no	—
34	C₄×D₄×C₄₇	—	2	16	no	—
35	#117×C₄₇	—	2	2	no	—
36	#117×C₄₇	—	2	2	no	—
37	#117×C₄₇	C₂×C₄	1	4	yes	—
38	#117×C₄₇	C₂³	1	4	yes	—
39	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
41	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
42	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
43	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	—
44	C₂×C₄²×C₄₇	—	2	2	no	—
45	#100×C₄₇	—	2	16	no	—
46	C₂⁴×C₄₇	—	2	4	no	—
47	C₂⁴×C₄₇	—	2	4	no	—
48	C₂⁴×C₄₇	—	8	4	no	—
49	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
50	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
51	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
52	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
53	C₂×D₄×C₄₇	—	2	8	no	—
54	C₂×D₄×C₄₇	—	2	8	no	—
55	C₂×D₄×C₄₇	—	2	8	no	—
56	C₂×D₄×C₄₇	—	2	8	no	—
57	C₂×D₄×C₄₇	—	2	8	no	—
58	C₂×D₄×C₄₇	—	2	8	no	—
59	C₂×D₄×C₄₇	C₂²⋊C₄	1	8	yes	—
60	C₂×D₄×C₄₇	C₂×D₄	1	8	yes	—
61	C₂²×C₄×C₄₇	—	2	4	no	—
62	C₂²×C₄×C₄₇	—	2	16	no	—
63	C₂²×C₄×C₄₇	—	8	8	no	—
64	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
67	C₂²×C₄×C₄₇	#41	1	4	yes	—
68	C₂²×C₄×C₄₇	#41	1	4	yes	—
69	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
70	M₁₆×C₄₇	—	2	8	no	—
71	M₁₆×C₄₇	—	2	8	no	—
72	M₁₆×C₄₇	—	4	4	no	—
73	M₁₆×C₄₇	—	4	4	no	—
74	C₂×C₈×C₄₇	—	2	8	no	—
75	C₂×C₈×C₄₇	—	4	4	no	—
76	C₂×C₈×C₄₇	—	4	4	no	—
77	C₄⋊C₄×C₄₇	—	2	4	no	—
78	C₄⋊C₄×C₄₇	—	2	4	no	—
79	C₂²⋊C₄×C₄₇	—	2	4	no	—
80	C₂²⋊C₄×C₄₇	—	2	16	no	—
81	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
82	C₄²×C₄₇	—	2	4	no	—
83	C₄²×C₄₇	—	2	4	no	—
84	C₂³×C₄₇	—	2	4	no	—
85	C₂³×C₄₇	—	2	4	no	—
86	C₂³×C₄₇	—	2	8	no	—
87	C₂³×C₄₇	—	2	8	no	—
88	C₂³×C₄₇	—	4	2	no	—
89	C₂³×C₄₇	—	4	8	no	—
90	C₂³×C₄₇	—	8	8	no	—
91	C₂³×C₄₇	—	8	4	no	—
92	C₂³×C₄₇	—	8	4	no	—
93	C₂³×C₄₇	—	8	8	no	—
94	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂³×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
96	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂³×C₄₇	#117	1	2	yes	—
98	C₂³×C₄₇	#117	1	2	yes	—
99	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
100	D₄×C₄₇	—	2	16	no	—
101	D₄×C₄₇	—	2	16	no	—
102	C₂×C₄×C₄₇	—	2	8	no	—
103	C₂×C₄×C₄₇	—	4	8	no	—
104	C₂×C₄×C₄₇	—	8	16	no	—
105	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
106	C₂×C₄×C₄₇	#117	1	4	yes	—
107	C₂×C₄×C₄₇	#123	1	4	yes	—
108	C₂×C₄×C₄₇	#123	1	4	yes	—
109	C₂×C₄×C₄₇	#123	1	4	yes	—
110	C₂×C₄×C₄₇	#123	1	4	yes	—
111	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
112	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
113	C₈×C₄₇	—	4	8	no	—
114	C₂×#1829	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂²×C₄₇	—	2	2	no	—
116	C₂²×C₄₇	—	2	4	no	—
117	C₂²×C₄₇	—	2	8	no	—
118	C₂²×C₄₇	—	4	1	no	—
119	C₂²×C₄₇	—	4	2	no	—
120	C₂²×C₄₇	—	4	1	no	—
121	C₂²×C₄₇	—	4	8	no	—
122	C₂²×C₄₇	—	4	8	no	—
123	C₂²×C₄₇	—	4	8	no	—
124	C₂²×C₄₇	—	8	8	no	—
125	C₂²×C₄₇	—	8	8	no	—
126	C₂²×C₄₇	#381	1	1	yes	characteristic
127	C₂²×C₄₇	#381	1	2	yes	—
128	C₂²×C₄₇	#381	1	1	yes	characteristic
129	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×C₄₇	C₂×#117	1	2	yes	—
131	C₄×C₄₇	—	4	8	no	—
132	C₄×C₄₇	#381	1	4	yes	—
133	C₄×C₄₇	C₂×#123	1	4	yes	—
134	C₂×#518	C₂×C₄₇	1	1	yes	characteristic
135	C₂²×#100	C₂×C₄₇	1	2	yes	—
136	#1829	C₂×C₄₇	1	8	yes	direct product factor
137	C₂×#344	C₂×C₄₇	1	4	yes	complemented
138	C₂×C₄₇	—	2	1	no	—
139	C₂×C₄₇	—	2	1	no	—
140	C₂×C₄₇	—	2	2	no	—
141	C₂×C₄₇	—	2	2	no	—
142	C₂×C₄₇	—	4	8	no	—
143	C₂×C₄₇	#1829	1	2	yes	direct product factor
144	C₂×C₄₇	C₂×#381	1	1	yes	characteristic
145	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
146	C₂²×M₁₆	C₂²×C₄₇	1	4	yes	—
147	#518	—	2	4	no	—
148	#518	C₄×C₄₇	1	4	yes	—
149	#518	C₂²×C₄₇	1	4	yes	—
150	C₂×C₄×D₄	—	2	4	no	—
151	C₂×#117	C₂²×C₄₇	1	2	yes	—
152	C₂²×C₂²⋊C₄	C₄×C₄₇	1	4	yes	—
153	C₂×#100	—	2	4	no	—
154	C₂×#100	—	2	4	no	—
155	C₂×#100	C₂²×C₄₇	1	8	yes	—
156	#344	C₂²×C₄₇	1	16	yes	complemented
157	C₄₇	C₂×#1829	1	1	yes	characteristic, direct product factor, Sylow
158	C₂⁵	C₂×C₄×C₄₇	1	2	yes	—
159	C₂²×D₄	—	2	4	no	—
160	C₂²×D₄	—	2	4	no	—
161	C₂²×D₄	C₂×C₄×C₄₇	1	2	yes	—
162	C₂²×D₄	D₄×C₄₇	1	4	yes	—
163	C₂²×D₄	D₄×C₄₇	1	4	yes	—
164	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
165	C₂³×C₄	—	2	4	no	—
166	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
167	C₂×M₁₆	—	2	4	no	—
168	C₂×M₁₆	—	2	4	no	—
169	C₂×M₁₆	—	2	4	no	—
170	C₂×M₁₆	—	2	4	no	—
171	C₂×M₁₆	—	2	4	no	—
172	C₂×M₁₆	C₂³×C₄₇	1	8	yes	—
173	C₂²×C₈	—	2	4	no	—
174	C₄×D₄	—	2	16	no	—
175	C₄×D₄	—	2	16	no	—
176	#117	—	2	2	no	—
177	#117	—	2	2	no	—
178	#117	C₂×C₄×C₄₇	1	4	yes	—
179	#117	C₂³×C₄₇	1	4	yes	—
180	C₂×C₄⋊C₄	—	2	2	no	—
181	C₂×C₂²⋊C₄	—	2	4	no	—
182	C₂×C₂²⋊C₄	—	2	8	no	—
183	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
184	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	16	yes	—
185	C₂×C₄²	—	2	2	no	—
186	#100	—	2	16	no	—
187	C₂⁴	—	2	4	no	—
188	C₂⁴	—	2	4	no	—
189	C₂⁴	—	8	4	no	—
190	C₂⁴	C₂²⋊C₄×C₄₇	1	4	yes	—
191	C₂⁴	C₂²⋊C₄×C₄₇	1	4	yes	—
192	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
193	C₂⁴	C₂²×C₄×C₄₇	1	1	yes	characteristic
194	C₂×D₄	—	2	8	no	—
195	C₂×D₄	—	2	8	no	—
196	C₂×D₄	—	2	8	no	—
197	C₂×D₄	—	2	8	no	—
198	C₂×D₄	—	2	8	no	—
199	C₂×D₄	—	2	8	no	—
200	C₂×D₄	C₂²⋊C₄×C₄₇	1	8	yes	—
201	C₂×D₄	C₂×D₄×C₄₇	1	8	yes	—
202	C₂²×C₄	—	2	4	no	—
203	C₂²×C₄	—	2	16	no	—
204	C₂²×C₄	—	8	8	no	—
205	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
206	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
207	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
208	C₂²×C₄	#41×C₄₇	1	4	yes	—
209	C₂²×C₄	#41×C₄₇	1	4	yes	—
210	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
211	M₁₆	—	2	8	no	—
212	M₁₆	—	2	8	no	—
213	M₁₆	—	4	4	no	—
214	M₁₆	—	4	4	no	—
215	C₂×C₈	—	2	8	no	—
216	C₂×C₈	—	4	4	no	—
217	C₂×C₈	—	4	4	no	—
218	C₄⋊C₄	—	2	4	no	—
219	C₄⋊C₄	—	2	4	no	—
220	C₂²⋊C₄	—	2	4	no	—
221	C₂²⋊C₄	—	2	16	no	—
222	C₂²⋊C₄	C₂²×C₄×C₄₇	1	8	yes	—
223	C₄²	—	2	4	no	—
224	C₄²	—	2	4	no	—
225	C₂³	—	2	4	no	—
226	C₂³	—	2	4	no	—
227	C₂³	—	2	8	no	—
228	C₂³	—	2	8	no	—
229	C₂³	—	4	2	no	—
230	C₂³	—	4	8	no	—
231	C₂³	—	8	8	no	—
232	C₂³	—	8	4	no	—
233	C₂³	—	8	4	no	—
234	C₂³	—	8	8	no	—
235	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
236	C₂³	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
237	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
238	C₂³	#117×C₄₇	1	2	yes	—
239	C₂³	#117×C₄₇	1	2	yes	—
240	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
241	D₄	—	2	16	no	—
242	D₄	—	2	16	no	—
243	C₂×C₄	—	2	8	no	—
244	C₂×C₄	—	4	8	no	—
245	C₂×C₄	—	8	16	no	—
246	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
247	C₂×C₄	#117×C₄₇	1	4	yes	—
248	C₂×C₄	#123×C₄₇	1	4	yes	—
249	C₂×C₄	#123×C₄₇	1	4	yes	—
250	C₂×C₄	#123×C₄₇	1	4	yes	—
251	C₂×C₄	#123×C₄₇	1	4	yes	—
252	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
253	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
254	C₈	—	4	8	no	—
255	C₂²	—	2	2	no	—
256	C₂²	—	2	4	no	—
257	C₂²	—	2	8	no	—
258	C₂²	—	4	1	no	—
259	C₂²	—	4	2	no	—
260	C₂²	—	4	1	no	—
261	C₂²	—	4	8	no	—
262	C₂²	—	4	8	no	—
263	C₂²	—	4	8	no	—
264	C₂²	—	8	8	no	—
265	C₂²	—	8	8	no	—
266	C₂²	C₄₇×#381	1	1	yes	characteristic
267	C₂²	C₄₇×#381	1	2	yes	—
268	C₂²	C₄₇×#381	1	1	yes	characteristic
269	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
270	C₂²	C₂×#117×C₄₇	1	2	yes	—
271	C₄	—	4	8	no	—
272	C₄	C₄₇×#381	1	4	yes	—
273	C₄	C₂×#123×C₄₇	1	4	yes	—
274	C₂	—	2	1	no	—
275	C₂	—	2	1	no	—
276	C₂	—	2	2	no	—
277	C₂	—	2	2	no	—
278	C₂	—	4	8	no	—
279	C₂	C₄₇×#1829	1	2	yes	direct product factor
280	C₂	C₂×C₄₇×#381	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	#381
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂³ ▷ 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
3. C₄₇×#1829	C₂	direct (N × H)
4. C₂×C₄₇×#344	C₂	semidirect
16. C₄₇×#344	C₂²	semidirect
114. C₂×#1829	C₄₇	direct (N × H)
136. #1829	C₂×C₄₇	direct (N × H)
137. C₂×#344	C₂×C₄₇	semidirect
143. C₂×C₄₇	#1829	direct (N × H)
156. #344	C₂²×C₄₇	semidirect
157. C₄₇	C₂×#1829	direct (N × H)
279. C₂	C₄₇×#1829	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×#518	2
C₂²×#100×C₄₇	2
C₄₇×#1829	2
C₂×C₄₇×#344	2
C₂×#1829	47

Subgroups — C2×C47×#1829 #26060409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1829 #26060409