Subgroups — C₂×#21445575 #29677517

Order 15616.

930 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16839720	C₂	1	3	yes	maximal
2	#21445575	C₂	1	8	yes	maximal, direct product factor
3	C₂×#16839519	C₂	1	3	yes	maximal
4	C₂×C₆₁×#338	C₂	1	1	yes	maximal, characteristic
5	C₂³×#92418	C₂²	1	1	yes	characteristic
6	C₂×#14519736	C₂²	1	3	yes	—
7	#16839720	C₄	1	12	yes	complemented
8	#16839720	C₂²	1	12	yes	—
9	C₂×#14519687	C₄	1	6	yes	complemented
10	C₂×C₈×Dic₆₁	C₄	1	6	yes	complemented
11	#16839519	C₂²	1	12	yes	—
12	C₂²×M₁₆×C₆₁	C₂²	1	3	yes	—
13	C₆₁×#338	C₂²	1	4	yes	—
14	C₂²×#92418	C₂×C₄	1	3	yes	—
15	C₂²×#92418	C₂×C₄	1	3	yes	—
16	C₂²×#92418	C₂×C₄	1	6	yes	—
17	C₂²×#92418	C₂³	1	2	yes	—
18	#14519736	—	2	3	no	—
19	#14519736	—	2	3	no	—
20	#14519736	C₂×C₄	1	6	yes	—
21	#14519736	C₂³	1	6	yes	—
22	C₂×C₄⋊Dic₆₁	—	2	3	no	—
23	C₂×C₂²⋊Dic₆₁	—	2	3	no	—
24	C₂×C₄×Dic₆₁	C₂×C₄	1	6	yes	—
25	#14519687	C₂×C₄	1	24	yes	complemented
26	C₈×Dic₆₁	C₂×C₄	1	24	yes	complemented
27	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
28	C₂×M₁₆×C₆₁	—	2	6	no	—
29	C₂×M₁₆×C₆₁	—	2	6	no	—
30	C₂×M₁₆×C₆₁	C₂×C₄	1	6	yes	—
31	C₂×M₁₆×C₆₁	C₂³	1	6	yes	—
32	C₂²×C₈×C₆₁	C₂×C₄	1	6	yes	—
33	C₂⁴×C₆₁	#41	1	1	yes	characteristic
34	C₂²×C₄×C₆₁	C₂²×C₄	1	3	yes	—
35	C₂²×C₄×C₆₁	C₂²×C₄	1	3	yes	—
36	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
37	C₂²×C₄×C₆₁	#41	1	3	yes	—
38	C₂²×C₄×C₆₁	#41	1	3	yes	—
39	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
40	C₂²×Dic₆₁	—	2	6	no	—
41	M₁₆×C₆₁	—	2	12	no	—
42	M₁₆×C₆₁	—	2	12	no	—
43	C₂×C₈×C₆₁	—	2	6	no	—
44	C₂×C₈×C₆₁	—	2	6	no	—
45	C₂×C₈×C₆₁	C₂²×C₄	1	12	yes	—
46	C₂²⋊Dic₆₁	—	2	6	no	—
47	C₂²⋊Dic₆₁	—	2	6	no	—
48	C₄⋊Dic₆₁	—	2	6	no	—
49	C₄⋊Dic₆₁	—	2	6	no	—
50	C₄×Dic₆₁	—	2	6	no	—
51	C₄×Dic₆₁	C₂²×C₄	1	12	yes	—
52	C₂×#92418	C₄²	1	6	yes	—
53	C₂×#92418	C₄²	1	6	yes	—
54	C₂×#92418	C₄²	1	1	yes	characteristic
55	C₂×#92418	C₄²	1	3	yes	—
56	C₂×#92418	C₂²×C₄	1	6	yes	—
57	C₂×#92418	C₂²×C₄	1	6	yes	—
58	C₂³×C₆₁	—	4	2	no	—
59	C₂³×C₆₁	#117	1	3	yes	—
60	C₂³×C₆₁	#117	1	3	yes	—
61	C₂³×C₆₁	C₂×#41	1	1	yes	characteristic
62	C₂×C₄×C₆₁	C₂×C₄²	1	3	yes	—
63	C₂×C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
64	C₂×C₄×C₆₁	#117	1	3	yes	—
65	C₂×C₄×C₆₁	#117	1	3	yes	—
66	C₂×C₄×C₆₁	#117	1	6	yes	—
67	C₂×C₄×C₆₁	#117	1	3	yes	—
68	C₂×C₄×C₆₁	#117	1	3	yes	—
69	C₂×C₄×C₆₁	C₂³×C₄	1	3	yes	—
70	C₂×C₄×C₆₁	C₂×#41	1	3	yes	—
71	C₂×Dic₆₁	—	2	12	no	—
72	C₂×Dic₆₁	—	4	12	no	—
73	C₈×C₆₁	—	2	12	no	—
74	#92418	C₂×C₄²	1	2	yes	—
75	#92418	C₂×C₄²	1	6	yes	—
76	C₂×#1747	—	61	1	no	maximal, Sylow
77	C₂²×C₆₁	—	2	6	no	—
78	C₂²×C₆₁	—	4	3	no	—
79	C₂²×C₆₁	—	4	1	no	—
80	C₂²×C₆₁	#376	1	3	yes	—
81	C₂²×C₆₁	#376	1	1	yes	characteristic
82	C₂²×C₆₁	C₂×#117	1	3	yes	—
83	C₄×C₆₁	#376	1	3	yes	—
84	C₄×C₆₁	#376	1	1	yes	characteristic
85	C₄×C₆₁	C₂²×C₄²	1	1	yes	characteristic
86	C₄×C₆₁	C₂×#117	1	3	yes	—
87	Dic₆₁	—	4	12	no	—
88	C₂×#405	—	61	3	no	—
89	#1747	—	61	8	no	—
90	C₂×#338	D₆₁	1	1	yes	characteristic
91	C₂×H(3,ℤ/4)	—	61	3	no	—
92	C₂×C₆₁	—	2	3	no	—
93	C₂×C₆₁	—	2	3	no	—
94	C₂×C₆₁	#1747	1	2	yes	complemented
95	C₂×C₆₁	C₂×#376	1	1	yes	characteristic
96	C₂²×M₁₆	C₂×D₆₁	1	3	yes	—
97	C₂³×C₈	—	61	1	no	—
98	C₂×#117	—	61	3	no	—
99	#405	—	61	12	no	—
100	#405	—	61	12	no	—
101	C₂×#97	—	61	6	no	—
102	C₂×C₄×C₈	—	61	6	no	—
103	#338	C₂×D₆₁	1	4	yes	—
104	H(3,ℤ/4)	—	61	12	no	—
105	C₆₁	C₂×#1747	1	1	yes	characteristic, complemented, Sylow
106	C₂³×C₄	C₂²×D₆₁	1	1	yes	characteristic
107	C₂×M₁₆	—	2	6	no	—
108	C₂×M₁₆	—	2	6	no	—
109	C₂×M₁₆	C₄×D₆₁	1	6	yes	—
110	C₂×M₁₆	C₂²×D₆₁	1	6	yes	—
111	C₂²×C₈	—	61	3	no	—
112	C₂²×C₈	—	61	3	no	—
113	C₂²×C₈	—	61	6	no	—
114	C₂²×C₈	—	61	2	no	—
115	C₂²×C₈	C₄×D₆₁	1	6	yes	—
116	#117	—	61	6	no	—
117	#117	—	61	6	no	—
118	#117	—	122	3	no	—
119	#117	—	122	3	no	—
120	C₂×C₄⋊C₄	—	122	3	no	—
121	C₂×C₂²⋊C₄	—	122	3	no	—
122	C₂×C₄²	—	61	6	no	—
123	#97	—	61	24	no	—
124	C₄×C₈	—	61	24	no	—
125	C₂⁴	#11758226	1	1	yes	characteristic
126	C₂²×C₄	—	122	6	no	—
127	C₂²×C₄	C₂×C₄×D₆₁	1	3	yes	—
128	C₂²×C₄	C₂×C₄×D₆₁	1	3	yes	—
129	C₂²×C₄	#11758224	1	3	yes	—
130	C₂²×C₄	#11758224	1	3	yes	—
131	C₂²×C₄	#11758226	1	1	yes	characteristic
132	C₂²×C₄	C₂³×D₆₁	1	1	yes	characteristic
133	M₁₆	—	2	12	no	—
134	M₁₆	—	2	12	no	—
135	C₂×C₈	—	2	6	no	—
136	C₂×C₈	—	2	6	no	—
137	C₂×C₈	—	61	6	no	—
138	C₂×C₈	—	61	6	no	—
139	C₂×C₈	—	61	6	no	—
140	C₂×C₈	—	61	6	no	—
141	C₂×C₈	—	61	1	no	—
142	C₂×C₈	—	61	3	no	—
143	C₂×C₈	C₂×C₄×D₆₁	1	12	yes	—
144	C₄⋊C₄	—	122	6	no	—
145	C₄⋊C₄	—	122	6	no	—
146	C₂²⋊C₄	—	122	6	no	—
147	C₂²⋊C₄	—	122	6	no	—
148	C₄²	—	61	12	no	—
149	C₄²	—	122	6	no	—
150	C₂³	—	4	2	no	—
151	C₂³	#14519735	1	3	yes	—
152	C₂³	#14519735	1	3	yes	—
153	C₂³	C₂×#11758226	1	1	yes	characteristic
154	C₂×C₄	—	122	12	no	—
155	C₂×C₄	—	244	12	no	—
156	C₂×C₄	C₄²×D₆₁	1	3	yes	—
157	C₂×C₄	C₄²×D₆₁	1	1	yes	characteristic
158	C₂×C₄	#14519733	1	3	yes	—
159	C₂×C₄	#14519733	1	3	yes	—
160	C₂×C₄	#14519733	1	6	yes	—
161	C₂×C₄	#14519735	1	3	yes	—
162	C₂×C₄	#14519735	1	3	yes	—
163	C₂×C₄	C₂²×C₄×D₆₁	1	3	yes	—
164	C₂×C₄	C₂×#11758224	1	3	yes	—
165	C₈	—	2	12	no	—
166	C₈	—	61	2	no	—
167	C₈	—	61	6	no	—
168	C₂²	—	2	6	no	—
169	C₂²	—	4	1	no	—
170	C₂²	—	4	3	no	—
171	C₂²	#16839607	1	3	yes	—
172	C₂²	#16839607	1	1	yes	characteristic
173	C₂²	C₂×#14519735	1	3	yes	—
174	C₄	—	244	12	no	—
175	C₄	#16839607	1	3	yes	—
176	C₄	#16839607	1	1	yes	characteristic
177	C₄	C₂×C₄²×D₆₁	1	1	yes	characteristic
178	C₄	C₂×#14519733	1	3	yes	—
179	C₂	—	2	3	no	—
180	C₂	—	2	3	no	—
181	C₂	#21445575	1	2	yes	direct product factor
182	C₂	C₂×#16839607	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄²×D₆₁
commutator	C₄×C₆₁	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₆₁
Fitting	C₂×C₆₁×#338	C₂
socle	C₂²×C₆₁	#376
prime radical	C₂⁴×C₆₁	#41
cosocle	C₂²×C₄×C₆₁	C₂⁴
hypercenter	C₂×#338	D₆₁
hypocenter	C₆₁	C₂×#1747
LCS	G ▷ C₄×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#338

Complements

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

N	H ≅ G/N	type
2. #21445575	C₂	direct (N × H)
7. #16839720	C₄	semidirect
9. C₂×#14519687	C₄	semidirect
10. C₂×C₈×Dic₆₁	C₄	semidirect
25. #14519687	C₂×C₄	semidirect
26. C₈×Dic₆₁	C₂×C₄	semidirect
94. C₂×C₆₁	#1747	semidirect
105. C₆₁	C₂×#1747	semidirect
181. C₂	#21445575	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×#16839720	2
#21445575	2
C₂×#16839519	2
C₂×C₆₁×#338	2
C₂×#1747	61

Subgroups — C2×#21445575 #29677517

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#21445575 #29677517