Subgroups — C₂×#20243136 #26213743

Order 12032.

1310 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093935	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20243136	C₂	1	8	yes	maximal, direct product factor
4	C₂×#15688877	C₂	1	4	yes	maximal
5	C₂²×#97×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₄₇	C₄	1	4	yes	—
8	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
9	C₂×#13093935	C₄	1	8	yes	complemented
10	C₂×#13093935	C₂²	1	4	yes	—
11	C₄²×Dic₄₇	C₄	1	4	yes	—
12	C₄²×Dic₄₇	C₂²	1	4	yes	—
13	#15688877	C₂²	1	16	yes	—
14	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#97×C₄₇	C₄	1	8	yes	complemented
17	C₂×#97×C₄₇	C₂²	1	4	yes	—
18	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
19	C₂²×C₄₇⋊C₈	—	2	8	no	—
20	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	—
21	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
22	C₂×C₄×Dic₄₇	—	2	8	no	—
23	C₂×C₄×Dic₄₇	—	2	16	no	—
24	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
25	C₂×C₄×Dic₄₇	C₂×C₄	1	16	yes	—
26	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
27	#13093935	C₂×C₄	1	16	yes	complemented
28	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
29	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₄₇	—	2	8	no	—
31	C₂²×C₈×C₄₇	C₂×C₄	1	8	yes	—
32	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
33	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
35	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
36	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
37	#97×C₄₇	C₂×C₄	1	16	yes	complemented
38	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
39	C₂²×C₄×C₄₇	—	2	8	no	—
40	C₂²×C₄×C₄₇	C₄²	1	8	yes	—
41	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
42	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
44	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
45	C₂²×C₄×C₄₇	#41	1	8	yes	—
46	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
47	C₂²×Dic₄₇	—	2	8	no	—
48	C₂²×Dic₄₇	—	2	8	no	—
49	C₂²×Dic₄₇	M₁₆	1	16	yes	—
50	C₂²×Dic₄₇	C₂²×C₄	1	8	yes	—
51	C₂×C₈×C₄₇	—	2	16	no	—
52	C₂×C₈×C₄₇	—	2	8	no	—
53	C₂×C₈×C₄₇	C₂²×C₄	1	8	yes	—
54	C₄²×C₄₇	C₄²	1	8	yes	—
55	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
56	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
57	C₄×Dic₄₇	—	2	8	no	—
58	C₄×Dic₄₇	—	2	8	no	—
59	C₄×Dic₄₇	—	2	32	no	—
60	C₂×C₄₇⋊C₈	—	2	16	no	—
61	C₂×C₄₇⋊C₈	—	2	8	no	—
62	C₂×C₄₇⋊C₈	C₂²×C₄	1	8	yes	—
63	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
64	C₂³×C₄₇	#117	1	4	yes	—
65	C₂³×C₄₇	C₂×M₁₆	1	8	yes	—
66	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
67	C₂×C₄×C₄₇	—	2	8	no	—
68	C₂×C₄×C₄₇	—	2	16	no	—
69	C₂×C₄×C₄₇	C₂×C₄²	1	8	yes	—
70	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
71	C₂×C₄×C₄₇	#117	1	8	yes	—
72	C₂×C₄×C₄₇	#117	1	4	yes	—
73	C₂×C₄×C₄₇	#117	1	8	yes	—
74	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
75	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
76	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
77	C₂×Dic₄₇	—	2	8	no	—
78	C₂×Dic₄₇	—	2	8	no	—
79	C₂×Dic₄₇	—	2	32	no	—
80	C₂×Dic₄₇	C₂×M₁₆	1	16	yes	—
81	C₈×C₄₇	—	2	8	no	—
82	C₄₇⋊C₈	—	2	8	no	—
83	C₂×#1745	—	47	1	no	maximal, Sylow
84	C₂²×C₄₇	#376	1	4	yes	—
85	C₂²×C₄₇	C₄×M₁₆	1	8	yes	—
86	C₂²×C₄₇	#432	1	16	yes	—
87	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
88	C₂²×C₄₇	C₂×#117	1	2	yes	—
89	C₂²×C₄₇	C₂²×M₁₆	1	4	yes	—
90	C₄×C₄₇	—	2	8	no	—
91	C₄×C₄₇	#376	1	4	yes	—
92	C₄×C₄₇	C₂×#117	1	2	yes	—
93	C₄×C₄₇	C₂×#117	1	2	yes	—
94	Dic₄₇	—	2	16	no	—
95	C₂²×#97	—	47	1	no	—
96	C₂²×#97	D₄₇	1	1	yes	characteristic
97	C₂×C₄³	—	47	1	no	—
98	#1745	—	47	8	no	—
99	C₂×#336	—	47	4	no	—
100	C₂×C₄₇	#1745	1	8	yes	complemented
101	C₂×C₄₇	C₂×#376	1	1	yes	characteristic
102	C₂×C₄₇	C₂×C₄×M₁₆	1	2	yes	—
103	C₂×C₄₇	C₂×#432	1	4	yes	—
104	C₂³×C₈	—	47	2	no	—
105	C₂³×C₈	C₂×D₄₇	1	2	yes	—
106	C₂²×C₄²	—	47	4	no	—
107	C₂²×C₄²	—	47	2	no	—
108	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
109	C₂×#97	—	47	8	no	—
110	C₂×#97	—	47	4	no	—
111	C₂×#97	Dic₄₇	1	8	yes	complemented
112	C₂×#97	C₂×D₄₇	1	4	yes	—
113	C₄³	—	47	4	no	—
114	C₄³	—	47	4	no	—
115	#336	—	47	16	no	—
116	C₄₇	C₂×#1745	1	1	yes	characteristic, complemented, Sylow
117	C₂³×C₄	—	47	4	no	—
118	C₂³×C₄	C₄×D₄₇	1	2	yes	—
119	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
120	C₂²×C₈	—	2	8	no	—
121	C₂²×C₈	—	47	8	no	—
122	C₂²×C₈	—	47	4	no	—
123	C₂²×C₈	—	94	8	no	—
124	C₂²×C₈	C₂×Dic₄₇	1	8	yes	—
125	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
126	C₂×C₄²	—	47	16	no	—
127	C₂×C₄²	—	47	4	no	—
128	C₂×C₄²	—	47	4	no	—
129	C₂×C₄²	—	94	16	no	—
130	C₂×C₄²	—	94	8	no	—
131	C₂×C₄²	C₄×D₄₇	1	2	yes	—
132	C₂×C₄²	C₄×D₄₇	1	4	yes	—
133	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
134	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
135	#97	—	47	16	no	—
136	#97	C₂×Dic₄₇	1	16	yes	complemented
137	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
138	C₂²×C₄	—	2	8	no	—
139	C₂²×C₄	—	47	16	no	—
140	C₂²×C₄	—	47	8	no	—
141	C₂²×C₄	—	94	8	no	—
142	C₂²×C₄	—	94	8	no	—
143	C₂²×C₄	C₄×Dic₄₇	1	8	yes	—
144	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
145	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
146	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
147	C₂²×C₄	#10625350	1	8	yes	—
148	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
149	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
150	C₂×C₈	—	2	16	no	—
151	C₂×C₈	—	2	8	no	—
152	C₂×C₈	—	47	8	no	—
153	C₂×C₈	—	94	16	no	—
154	C₂×C₈	—	94	8	no	—
155	C₂×C₈	C₂²×Dic₄₇	1	8	yes	—
156	C₄²	—	94	32	no	—
157	C₄²	—	94	8	no	—
158	C₄²	—	94	8	no	—
159	C₄²	C₄×Dic₄₇	1	8	yes	—
160	C₄²	C₂×C₄×D₄₇	1	4	yes	—
161	C₄²	C₂²×Dic₄₇	1	4	yes	—
162	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
163	C₂³	#13093981	1	4	yes	—
164	C₂³	M₁₆×D₄₇	1	8	yes	—
165	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
166	C₂×C₄	—	2	16	no	—
167	C₂×C₄	—	2	8	no	—
168	C₂×C₄	—	47	16	no	—
169	C₂×C₄	—	94	8	no	—
170	C₂×C₄	—	94	8	no	—
171	C₂×C₄	—	94	32	no	—
172	C₂×C₄	C₂×C₄×Dic₄₇	1	8	yes	—
173	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
174	C₂×C₄	#13093981	1	4	yes	—
175	C₂×C₄	#13093981	1	8	yes	—
176	C₂×C₄	#13093983	1	8	yes	—
177	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
178	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
179	C₂×C₄	C₂×#10625350	1	4	yes	—
180	C₈	—	2	8	no	—
181	C₈	—	94	8	no	—
182	C₂²	#15688969	1	4	yes	—
183	C₂²	M₁₆×Dic₄₇	1	8	yes	—
184	C₂²	#15689178	1	16	yes	—
185	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
186	C₂²	C₂×#13093981	1	2	yes	—
187	C₂²	C₂×M₁₆×D₄₇	1	4	yes	—
188	C₄	—	2	8	no	—
189	C₄	—	94	16	no	—
190	C₄	#15688969	1	4	yes	—
191	C₄	C₂×#13093981	1	2	yes	—
192	C₄	C₂×#13093983	1	2	yes	—
193	C₂	#20243136	1	8	yes	direct product factor
194	C₂	C₂×#15688969	1	1	yes	characteristic
195	C₂	C₂×M₁₆×Dic₄₇	1	2	yes	—
196	C₂	C₂×#15689178	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂²×#97×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×#97	D₄₇
hypocenter	C₄₇	C₂×#1745
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
3. #20243136	C₂	direct (N × H)
9. C₂×#13093935	C₄	semidirect
16. C₂×#97×C₄₇	C₄	semidirect
27. #13093935	C₂×C₄	semidirect
37. #97×C₄₇	C₂×C₄	semidirect
100. C₂×C₄₇	#1745	semidirect
111. C₂×#97	Dic₄₇	semidirect
116. C₄₇	C₂×#1745	semidirect
136. #97	C₂×Dic₄₇	semidirect
193. C₂	#20243136	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×#13093935	2
C₂×C₄²×Dic₄₇	2
#20243136	2
C₂×#15688877	2
C₂²×#97×C₄₇	2
C₂×#1745	47

Subgroups — C2×#20243136 #26213743

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20243136 #26213743