Subgroups — C₄×#15689075 #26213609

Order 12032.

1734 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689075	C₂	1	4	yes	maximal
2	C₂×C₄×#10625324	C₂	1	2	yes	maximal
3	C₄³×D₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄×#13093935	C₂	1	1	yes	maximal, characteristic, complemented
5	#97×Dic₄₇	C₂	1	4	yes	maximal, complemented
6	C₄×C₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
7	C₄×#97×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625324	C₂²	1	4	yes	—
9	C₂×C₄²×D₄₇	C₄	1	4	yes	—
10	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄²×D₄₇	C₂²	1	2	yes	—
12	#15689075	C₄	1	32	yes	direct product factor
13	C₄×#10625324	C₄	1	16	yes	complemented
14	C₂×#13093935	C₂²	1	4	yes	—
15	C₂×#13093934	C₂²	1	4	yes	—
16	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂×C₈×Dic₄₇	C₂²	1	8	yes	—
18	C₄²×Dic₄₇	C₄	1	4	yes	—
19	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₄²×Dic₄₇	C₂²	1	2	yes	—
21	C₂×#97×C₄₇	C₂²	1	4	yes	—
22	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
23	C₄³×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
25	C₂²×C₄×D₄₇	C₂×C₄	1	4	yes	—
26	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
27	C₂×#10625324	C₂×C₄	1	16	yes	—
28	C₂×#10625324	C₂×C₄	1	32	yes	—
29	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
30	C₂×C₄×Dic₄₇	C₂×C₄	1	8	yes	—
31	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
32	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
33	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
34	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
35	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
36	C₄²×D₄₇	—	2	16	no	—
37	C₄²×D₄₇	C₂×C₄	1	8	yes	—
38	C₄²×D₄₇	C₂×C₄	1	16	yes	—
39	#13093935	C₂×C₄	1	16	yes	complemented
40	#13093934	C₂×C₄	1	16	yes	complemented
41	C₄×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
42	C₈×Dic₄₇	C₂×C₄	1	32	yes	complemented
43	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
44	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
46	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
47	#97×C₄₇	C₂×C₄	1	16	yes	complemented
48	C₄×C₈×C₄₇	C₂×C₄	1	8	yes	complemented
49	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
51	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
52	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
53	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
54	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
55	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
56	C₂×C₄×D₄₇	—	2	8	no	—
57	C₂×C₄×D₄₇	—	2	16	no	—
58	C₂×C₄×D₄₇	C₄²	1	8	yes	—
59	C₂×C₄×D₄₇	C₄²	1	16	yes	—
60	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
61	C₂×C₄×D₄₇	C₂²×C₄	1	8	yes	—
62	C₂×C₈×C₄₇	C₂²×C₄	1	16	yes	—
63	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
64	C₄²×C₄₇	—	2	8	no	—
65	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
66	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
67	C₄×Dic₄₇	—	2	16	no	—
68	C₄×Dic₄₇	C₄²	1	8	yes	—
69	C₄×Dic₄₇	C₄²	1	16	yes	—
70	C₄×Dic₄₇	M₁₆	1	16	yes	complemented
71	C₄×Dic₄₇	C₂²×C₄	1	8	yes	—
72	C₄×Dic₄₇	C₂²×C₄	1	4	yes	—
73	C₂×C₄₇⋊C₈	C₂²×C₄	1	16	yes	—
74	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
75	#10625324	C₄²	1	64	yes	complemented
76	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
77	C₂²×D₄₇	—	2	4	no	—
78	C₂²×D₄₇	C₂×C₄²	1	4	yes	—
79	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
80	C₂×C₄×C₄₇	—	2	8	no	—
81	C₂×C₄×C₄₇	C₂×C₄²	1	8	yes	—
82	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
83	C₂×C₄×C₄₇	C₂×M₁₆	1	8	yes	—
84	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
85	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
86	C₂×Dic₄₇	—	2	4	no	—
87	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
88	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
89	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
90	C₂×Dic₄₇	C₂×C₄²	1	8	yes	—
91	C₂×Dic₄₇	C₂×M₁₆	1	16	yes	—
92	C₄×D₄₇	—	2	16	no	—
93	C₄×D₄₇	—	2	32	no	—
94	C₄×D₄₇	C₂×C₄²	1	16	yes	—
95	C₈×C₄₇	C₂×C₄²	1	16	yes	complemented
96	C₄₇⋊C₈	C₂×C₄²	1	16	yes	complemented
97	C₄²×M₁₆	—	47	1	no	maximal, Sylow
98	C₂²×C₄₇	C₂²×C₄²	1	2	yes	—
99	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
100	C₂²×C₄₇	C₂²×M₁₆	1	4	yes	—
101	C₂×D₄₇	—	2	8	no	—
102	C₂×D₄₇	—	2	4	no	—
103	C₂×D₄₇	C₄³	1	4	yes	—
104	C₄×C₄₇	—	2	8	no	—
105	C₄×C₄₇	C₄×M₁₆	1	8	yes	complemented
106	C₄×C₄₇	C₂²×C₄²	1	4	yes	—
107	Dic₄₇	—	2	4	no	—
108	Dic₄₇	C₄³	1	4	yes	—
109	Dic₄₇	C₄×M₁₆	1	16	yes	complemented
110	C₂×C₄×M₁₆	—	47	4	no	—
111	C₂×C₄×M₁₆	—	47	2	no	—
112	C₂×C₄³	—	47	1	no	—
113	C₄×#97	—	47	4	no	—
114	C₄×#97	—	47	1	no	—
115	C₄×#97	D₄₇	1	1	yes	characteristic, complemented
116	C₄²×C₈	—	47	2	no	—
117	C₂×C₄₇	C₂×C₄³	1	1	yes	characteristic
118	C₂×C₄₇	C₂×C₄×M₁₆	1	4	yes	—
119	C₂×C₄₇	C₂×C₄×M₁₆	1	2	yes	—
120	D₄₇	—	2	4	no	—
121	C₂²×M₁₆	—	47	4	no	—
122	C₂²×C₄²	—	47	2	no	—
123	C₂²×C₄²	—	47	1	no	—
124	C₂²×C₄²	—	47	4	no	—
125	C₄×M₁₆	—	47	32	no	—
126	C₄×M₁₆	—	47	16	no	—
127	C₂×#97	—	47	4	no	—
128	C₂×#97	—	47	4	no	—
129	C₂×#97	C₂×D₄₇	1	4	yes	—
130	C₂×C₄×C₈	—	47	8	no	—
131	C₂×C₄×C₈	—	47	2	no	—
132	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
133	C₄³	—	47	4	no	—
134	C₄³	—	47	2	no	—
135	C₄³	—	47	1	no	—
136	C₄³	C₂×D₄₇	1	1	yes	characteristic
137	C₄₇	C₄²×M₁₆	1	1	yes	characteristic, complemented, Sylow
138	C₂³×C₄	—	47	1	no	—
139	C₂³×C₄	—	47	4	no	—
140	C₂³×C₄	—	47	2	no	—
141	C₂×M₁₆	—	47	32	no	—
142	C₂×M₁₆	—	47	16	no	—
143	C₂²×C₈	—	47	4	no	—
144	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
145	C₂×C₄²	—	47	4	no	—
146	C₂×C₄²	—	47	2	no	—
147	C₂×C₄²	—	47	4	no	—
148	C₂×C₄²	—	47	2	no	—
149	C₂×C₄²	—	47	1	no	—
150	C₂×C₄²	—	47	16	no	—
151	C₂×C₄²	—	47	8	no	—
152	C₂×C₄²	—	47	8	no	—
153	C₂×C₄²	—	94	16	no	—
154	C₂×C₄²	C₄×D₄₇	1	4	yes	—
155	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
156	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
157	#97	—	47	16	no	—
158	#97	—	47	16	no	—
159	#97	C₄×D₄₇	1	16	yes	complemented
160	C₄×C₈	—	47	32	no	—
161	C₄×C₈	—	47	8	no	—
162	C₄×C₈	C₄×D₄₇	1	8	yes	complemented
163	C₂⁴	—	47	1	no	—
164	C₂²×C₄	—	47	1	no	—
165	C₂²×C₄	—	47	4	no	—
166	C₂²×C₄	—	47	8	no	—
167	C₂²×C₄	—	47	4	no	—
168	C₂²×C₄	—	47	2	no	—
169	C₂²×C₄	—	47	16	no	—
170	C₂²×C₄	—	47	8	no	—
171	C₂²×C₄	—	94	16	no	—
172	C₂²×C₄	—	94	8	no	—
173	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
174	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
175	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
176	M₁₆	—	47	64	no	—
177	C₂×C₈	—	47	16	no	—
178	C₂×C₈	—	47	8	no	—
179	C₂×C₈	C₂×C₄×D₄₇	1	16	yes	—
180	C₂×C₈	C₂×C₄×D₄₇	1	8	yes	—
181	C₄²	—	2	8	no	—
182	C₄²	—	47	16	no	—
183	C₄²	—	47	8	no	—
184	C₄²	—	47	16	no	—
185	C₄²	—	47	8	no	—
186	C₄²	—	47	4	no	—
187	C₄²	—	94	16	no	—
188	C₄²	C₂×C₄×D₄₇	1	4	yes	—
189	C₄²	C₂×C₄×D₄₇	1	8	yes	—
190	C₂³	—	47	4	no	—
191	C₂³	—	47	2	no	—
192	C₂³	—	94	4	no	—
193	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
194	C₂×C₄	—	2	8	no	—
195	C₂×C₄	—	47	8	no	—
196	C₂×C₄	—	47	4	no	—
197	C₂×C₄	—	47	2	no	—
198	C₂×C₄	—	47	16	no	—
199	C₂×C₄	—	47	16	no	—
200	C₂×C₄	—	47	4	no	—
201	C₂×C₄	—	94	32	no	—
202	C₂×C₄	—	94	4	no	—
203	C₂×C₄	—	94	16	no	—
204	C₂×C₄	C₄²×D₄₇	1	8	yes	—
205	C₂×C₄	C₄²×D₄₇	1	4	yes	—
206	C₂×C₄	M₁₆×D₄₇	1	8	yes	—
207	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
208	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
209	C₈	—	47	16	no	—
210	C₈	C₄²×D₄₇	1	16	yes	complemented
211	C₂²	—	47	4	no	—
212	C₂²	—	94	8	no	—
213	C₂²	—	94	4	no	—
214	C₂²	C₂×C₄²×D₄₇	1	2	yes	—
215	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
216	C₂²	C₂×M₁₆×D₄₇	1	4	yes	—
217	C₄	—	2	8	no	—
218	C₄	—	47	16	no	—
219	C₄	—	47	4	no	—
220	C₄	—	94	4	no	—
221	C₄	#15689075	1	8	yes	direct product factor
222	C₄	C₂×C₄²×D₄₇	1	4	yes	—
223	C₂	—	94	4	no	—
224	C₂	C₄³×D₄₇	1	1	yes	characteristic
225	C₂	C₄×M₁₆×D₄₇	1	4	yes	—
226	C₂	C₂×#15689075	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²×D₄₇
commutator	C₂×C₄₇	C₂×C₄³
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#97×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×#97	D₄₇
hypocenter	C₄₇	C₄²×M₁₆
LCS	G ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
4. C₄×#13093935	C₂	semidirect
5. #97×Dic₄₇	C₂	semidirect
6. C₄×C₈×Dic₄₇	C₂	semidirect
7. C₄×#97×C₄₇	C₂	semidirect
12. #15689075	C₄	direct (N × H)
13. C₄×#10625324	C₄	semidirect
39. #13093935	C₂×C₄	semidirect
40. #13093934	C₂×C₄	semidirect
41. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
42. C₈×Dic₄₇	C₂×C₄	semidirect
47. #97×C₄₇	C₂×C₄	semidirect
48. C₄×C₈×C₄₇	C₂×C₄	semidirect
70. C₄×Dic₄₇	M₁₆	semidirect
75. #10625324	C₄²	semidirect
95. C₈×C₄₇	C₂×C₄²	semidirect
96. C₄₇⋊C₈	C₂×C₄²	semidirect
105. C₄×C₄₇	C₄×M₁₆	semidirect
109. Dic₄₇	C₄×M₁₆	semidirect
115. C₄×#97	D₄₇	semidirect
137. C₄₇	C₄²×M₁₆	semidirect
159. #97	C₄×D₄₇	semidirect
162. C₄×C₈	C₄×D₄₇	semidirect
210. C₈	C₄²×D₄₇	semidirect
221. C₄	#15689075	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×#15689075	2
C₂×C₄×#10625324	2
C₄³×D₄₇	2
C₄×#13093935	2
#97×Dic₄₇	2
C₄×C₈×Dic₄₇	2
C₄×#97×C₄₇	2
C₄²×M₁₆	47

Subgroups — C4×#15689075 #26213609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15689075 #26213609