Subgroups — C₂×C₄₇⋊#1309 #26106691

Order 12032.

658 conjugacy classes of subgroups.

The subgroup lattice has 268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	2	yes	maximal
2	C₄₇⋊#1309	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄₇×#423	C₂	1	1	yes	maximal, characteristic
4	C₂²×#10625329	C₄	1	4	yes	—
5	#15689147	—	2	2	no	—
6	#15689147	—	2	2	no	—
7	#15689147	C₄	1	4	yes	—
8	#15689147	C₂²	1	4	yes	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
11	C₂²×M₁₆×C₄₇	C₄	1	2	yes	—
12	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
13	C₄₇×#423	—	2	2	no	—
14	C₄₇×#423	C₄	1	2	yes	—
15	C₄₇×#423	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
17	C₂×#10625329	—	2	4	no	—
18	C₂×#10625329	—	4	8	no	—
19	C₂×#10625329	C₂×C₄	1	8	yes	—
20	C₂²×C₄₇⋊C₈	—	2	4	no	—
21	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
22	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
23	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
24	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
25	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
26	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
27	C₂×M₁₆×C₄₇	—	2	2	no	—
28	C₂×M₁₆×C₄₇	—	4	4	no	—
29	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
30	C₂²×C₈×C₄₇	—	2	2	no	—
31	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₄₇	D₄	1	2	yes	—
36	C₂×C₄²×C₄₇	D₄	1	2	yes	—
37	C₂×C₄²×C₄₇	Q₈	1	1	yes	characteristic
38	C₂×C₄²×C₄₇	Q₈	1	1	yes	characteristic
39	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₄₇	—	2	4	no	—
41	C₄⋊C₈×C₄₇	—	2	4	no	—
42	C₂⁴×C₄₇	C₄²	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	—	2	2	no	—
44	C₂²×C₄×C₄₇	—	2	4	no	—
45	C₂²×C₄×C₄₇	—	2	4	no	—
46	C₂²×C₄×C₄₇	—	2	2	no	—
47	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
48	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
49	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
52	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
54	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
55	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
58	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
59	M₁₆×C₄₇	—	4	4	no	—
60	M₁₆×C₄₇	—	4	4	no	—
61	C₂×C₈×C₄₇	—	2	4	no	—
62	C₂×C₈×C₄₇	—	4	4	no	—
63	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
64	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
66	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
67	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
68	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
69	C₄²×C₄₇	C₄⋊C₄	1	1	yes	characteristic
70	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₄₇	C₂×D₄	1	2	yes	—
72	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
73	#10625329	—	4	8	no	—
74	#10625329	—	4	8	no	—
75	C₂×C₄₇⋊C₈	—	2	8	no	—
76	C₂×C₄₇⋊C₈	—	4	8	no	—
77	C₂³×C₄₇	—	2	4	no	—
78	C₂³×C₄₇	—	2	2	no	—
79	C₂³×C₄₇	#95	1	1	yes	characteristic
80	C₂³×C₄₇	#95	1	1	yes	characteristic
81	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
82	C₂×C₄×C₄₇	—	2	4	no	—
83	C₂×C₄×C₄₇	—	2	2	no	—
84	C₂×C₄×C₄₇	—	2	4	no	—
85	C₂×C₄×C₄₇	—	2	2	no	—
86	C₂×C₄×C₄₇	—	2	4	no	—
87	C₂×C₄×C₄₇	—	2	2	no	—
88	C₂×C₄×C₄₇	—	2	2	no	—
89	C₂×C₄×C₄₇	—	2	2	no	—
90	C₂×C₄×C₄₇	—	2	1	no	—
91	C₂×C₄×C₄₇	—	2	1	no	—
92	C₂×C₄×C₄₇	—	2	2	no	—
93	C₂×C₄×C₄₇	—	2	1	no	—
94	C₂×C₄×C₄₇	—	2	2	no	—
95	C₂×C₄×C₄₇	—	2	1	no	—
96	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
97	C₂×C₄×C₄₇	#95	1	2	yes	—
98	C₂×C₄×C₄₇	#95	1	2	yes	—
99	C₂×C₄×C₄₇	#95	1	1	yes	characteristic
100	C₂×C₄×C₄₇	#100	1	4	yes	—
101	C₂×C₄×C₄₇	#100	1	2	yes	—
102	C₂×C₄×C₄₇	#101	1	4	yes	—
103	C₂×C₄×C₄₇	#101	1	2	yes	—
104	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
105	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
107	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
108	C₈×C₄₇	—	4	4	no	—
109	C₄₇⋊C₈	—	4	8	no	—
110	C₂×#1309	—	47	1	no	maximal, Sylow
111	C₂²×C₄₇	—	2	2	no	—
112	C₂²×C₄₇	—	2	1	no	—
113	C₂²×C₄₇	—	2	2	no	—
114	C₂²×C₄₇	—	2	1	no	—
115	C₂²×C₄₇	—	4	4	no	—
116	C₂²×C₄₇	#343	1	4	yes	—
117	C₂²×C₄₇	#343	1	2	yes	—
118	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
119	C₄×C₄₇	—	2	2	no	—
120	C₄×C₄₇	—	2	1	no	—
121	C₄×C₄₇	—	2	2	no	—
122	C₄×C₄₇	—	2	1	no	—
123	C₄×C₄₇	#343	1	4	yes	—
124	C₄×C₄₇	#343	1	2	yes	—
125	C₄×C₄₇	C₂×#100	1	2	yes	—
126	C₄×C₄₇	C₂×#100	1	1	yes	characteristic
127	C₄×C₄₇	C₂×#101	1	2	yes	—
128	C₄×C₄₇	C₂×#101	1	1	yes	characteristic
129	C₂×#423	—	47	2	no	—
130	C₂×#423	D₄₇	1	1	yes	characteristic
131	#1309	—	47	4	no	—
132	C₂×C₄₇	—	4	1	no	—
133	C₂×C₄₇	—	4	1	no	—
134	C₂×C₄₇	#1309	1	4	yes	complemented
135	C₂×C₄₇	C₂×#343	1	2	yes	—
136	C₂×C₄₇	C₂×#343	1	1	yes	characteristic
137	C₂²×M₁₆	—	47	4	no	—
138	C₂²×M₁₆	Dic₄₇	1	2	yes	—
139	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
140	#423	—	2	2	no	—
141	#423	—	47	4	no	—
142	#423	—	47	4	no	—
143	#423	—	94	2	no	—
144	#423	—	94	2	no	—
145	#423	Dic₄₇	1	2	yes	—
146	#423	C₂×D₄₇	1	2	yes	—
147	C₂×C₄⋊C₈	—	2	2	no	—
148	C₂×C₄⋊C₈	—	94	2	no	—
149	C₂×C₄⋊C₈	—	94	2	no	—
150	C₄₇	C₂×#1309	1	1	yes	characteristic, complemented, Sylow
151	C₂³×C₄	C₄×D₄₇	1	2	yes	—
152	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
153	C₂×M₁₆	—	2	2	no	—
154	C₂×M₁₆	—	4	4	no	—
155	C₂×M₁₆	—	47	8	no	—
156	C₂×M₁₆	—	94	4	no	—
157	C₂×M₁₆	—	188	8	no	—
158	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
159	C₂²×C₈	—	2	2	no	—
160	C₂²×C₈	—	94	4	no	—
161	C₂×C₄²	Dic₉₄	1	1	yes	characteristic
162	C₂×C₄²	Dic₉₄	1	1	yes	characteristic
163	C₂×C₄²	C₄×D₄₇	1	2	yes	—
164	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
165	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
166	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
167	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
168	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
169	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
170	C₄⋊C₈	—	2	4	no	—
171	C₄⋊C₈	—	2	4	no	—
172	C₄⋊C₈	—	94	4	no	—
173	C₄⋊C₈	—	94	4	no	—
174	C₄⋊C₈	—	94	4	no	—
175	C₄⋊C₈	—	94	4	no	—
176	C₂⁴	C₄×Dic₄₇	1	1	yes	characteristic
177	C₂²×C₄	—	2	4	no	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	2	4	no	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
182	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
183	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
184	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
185	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
186	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
187	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
188	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
189	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
190	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
191	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
192	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
193	M₁₆	—	4	4	no	—
194	M₁₆	—	4	4	no	—
195	M₁₆	—	188	8	no	—
196	M₁₆	—	188	8	no	—
197	C₂×C₈	—	2	4	no	—
198	C₂×C₈	—	4	4	no	—
199	C₂×C₈	—	94	8	no	—
200	C₂×C₈	—	188	8	no	—
201	C₄²	Dic₄₇⋊C₄	1	2	yes	—
202	C₄²	Dic₄₇⋊C₄	1	2	yes	—
203	C₄²	C₄⋊Dic₄₇	1	1	yes	characteristic
204	C₄²	C₄⋊Dic₄₇	1	1	yes	characteristic
205	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
206	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
207	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
208	C₄²	C₂×Dic₉₄	1	1	yes	characteristic
209	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
210	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
211	C₂³	—	2	4	no	—
212	C₂³	—	2	2	no	—
213	C₂³	C₄₇⋊#95	1	1	yes	characteristic
214	C₂³	C₄₇⋊#95	1	1	yes	characteristic
215	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
216	C₂×C₄	—	2	4	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	2	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	4	no	—
227	C₂×C₄	—	2	4	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
231	C₂×C₄	C₄₇⋊#95	1	2	yes	—
232	C₂×C₄	C₄₇⋊#95	1	2	yes	—
233	C₂×C₄	C₄₇⋊#95	1	1	yes	characteristic
234	C₂×C₄	#13093940	1	4	yes	—
235	C₂×C₄	#13093941	1	2	yes	—
236	C₂×C₄	#13093942	1	4	yes	—
237	C₂×C₄	#13093943	1	2	yes	—
238	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
239	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
240	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
241	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
242	C₈	—	4	4	no	—
243	C₈	—	188	8	no	—
244	C₂²	—	2	2	no	—
245	C₂²	—	2	2	no	—
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	4	4	no	—
249	C₂²	#15688891	1	4	yes	—
250	C₂²	#15688892	1	2	yes	—
251	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
252	C₄	—	2	2	no	—
253	C₄	—	2	2	no	—
254	C₄	—	2	1	no	—
255	C₄	—	2	1	no	—
256	C₄	#15688891	1	4	yes	—
257	C₄	#15688892	1	2	yes	—
258	C₄	C₂×#13093940	1	2	yes	—
259	C₄	C₂×#13093941	1	1	yes	characteristic
260	C₄	C₂×#13093942	1	2	yes	—
261	C₄	C₂×#13093943	1	1	yes	characteristic
262	C₂	—	4	1	no	—
263	C₂	—	4	1	no	—
264	C₂	C₄₇⋊#1309	1	4	yes	direct product factor
265	C₂	C₂×#15688891	1	2	yes	—
266	C₂	C₂×#15688892	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₄₇⋊#95
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#423	C₂
socle	C₂³×C₄₇	#95
prime radical	C₂⁴×C₄₇	C₄²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#423	D₄₇
hypocenter	C₄₇	C₂×#1309
LCS	G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
2. C₄₇⋊#1309	C₂	direct (N × H)
134. C₂×C₄₇	#1309	semidirect
150. C₄₇	C₂×#1309	semidirect
264. C₂	C₄₇⋊#1309	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×#15689147	2
C₄₇⋊#1309	2
C₂×C₄₇×#423	2
C₂×#1309	47

Subgroups — C2×C47⋊#1309 #26106691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇⋊#1309 #26106691