Subgroups — C₂²×#11718094 #16015544

Order 3328.

942 conjugacy classes of subgroups.

The subgroup lattice has 150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#6090	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718094	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₄×Dic₁₃	C₄	1	1	yes	characteristic
7	C₂³×#1055	C₄	1	1	yes	characteristic
8	C₂²×C₁₃×C₁₆	C₄	1	8	yes	complemented
9	C₂²×C₁₃×C₁₆	C₂²	1	6	yes	—
10	C₂×C₈×Dic₁₃	C₄	1	6	yes	—
11	C₂×C₈×Dic₁₃	C₂²	1	6	yes	—
12	C₂²×#6090	C₄	1	8	yes	complemented
13	C₂²×#6090	C₂²	1	6	yes	—
14	#11718094	C₂²	1	16	yes	direct product factor
15	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂³×Dic₁₃	C₈	1	2	yes	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	3	yes	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
20	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
21	C₂×C₄×Dic₁₃	C₈	1	6	yes	—
22	C₂×C₄×Dic₁₃	C₂×C₄	1	6	yes	—
23	C₂²×#1055	C₈	1	8	yes	—
24	C₂²×#1055	C₂×C₄	1	6	yes	—
25	C₂×C₁₃×C₁₆	C₂×C₄	1	24	yes	complemented
26	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
27	C₈×Dic₁₃	C₂×C₄	1	12	yes	—
28	C₈×Dic₁₃	C₂³	1	4	yes	—
29	C₂×#6090	C₂×C₄	1	24	yes	complemented
30	C₂×#6090	C₂³	1	4	yes	—
31	C₂²×#346	—	13	1	no	maximal, Sylow
32	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
33	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
34	C₂²×C₄×C₁₃	C₂×C₈	1	3	yes	—
35	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
36	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
37	C₂²×Dic₁₃	—	2	8	no	—
38	C₂²×Dic₁₃	C₂×C₈	1	12	yes	—
39	C₂×C₈×C₁₃	C₄²	1	12	yes	—
40	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
41	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
42	C₂×C₈×C₁₃	C₂²×C₄	1	6	yes	—
43	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
44	C₄×Dic₁₃	C₂×C₈	1	12	yes	—
45	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
46	C₂×#1055	C₂×C₈	1	24	yes	—
47	C₂×#1055	C₂²×C₄	1	4	yes	—
48	C₁₃×C₁₆	C₂²×C₄	1	8	yes	complemented
49	#6090	C₂²×C₄	1	8	yes	complemented
50	C₂³×C₁₆	—	13	1	no	—
51	C₂³×C₁₆	D₁₃	1	1	yes	characteristic
52	C₂²×C₄×C₈	—	13	1	no	—
53	C₂×#346	—	13	12	no	—
54	C₂³×C₁₃	C₄×C₈	1	4	yes	—
55	C₂³×C₁₃	M₃₂	1	8	yes	—
56	C₂³×C₁₃	C₂²×C₈	1	3	yes	—
57	C₂×C₄×C₁₃	C₄×C₈	1	12	yes	—
58	C₂×C₄×C₁₃	C₂×C₄²	1	6	yes	—
59	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
60	C₂×C₄×C₁₃	C₂²×C₈	1	3	yes	—
61	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
62	C₂×Dic₁₃	—	2	24	no	—
63	C₂×Dic₁₃	C₂²×C₈	1	8	yes	—
64	C₈×C₁₃	C₂×C₄²	1	6	yes	—
65	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
66	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
67	#1055	C₂²×C₈	1	8	yes	—
68	C₂³×C₈	—	13	1	no	—
69	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
70	C₂²×C₄²	—	13	1	no	—
71	C₂²×C₁₆	—	13	8	no	—
72	C₂²×C₁₆	—	13	6	no	—
73	C₂²×C₁₆	Dic₁₃	1	8	yes	complemented
74	C₂²×C₁₆	C₂×D₁₃	1	6	yes	—
75	C₂×C₄×C₈	—	13	6	no	—
76	C₂×C₄×C₈	—	13	6	no	—
77	#346	—	13	16	no	—
78	C₂²×C₁₃	#346	1	16	yes	complemented
79	C₂²×C₁₃	C₂×C₄×C₈	1	6	yes	—
80	C₂²×C₁₃	C₂×M₃₂	1	12	yes	—
81	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
82	C₄×C₁₃	C₂×C₄×C₈	1	6	yes	—
83	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
84	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
85	Dic₁₃	—	2	8	no	—
86	C₂³×C₄	—	13	2	no	—
87	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
88	C₂²×C₈	—	13	8	no	—
89	C₂²×C₈	—	13	6	no	—
90	C₂²×C₈	C₄×D₁₃	1	3	yes	—
91	C₂²×C₈	C₄×D₁₃	1	4	yes	—
92	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
93	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
94	C₂×C₄²	—	13	6	no	—
95	C₂×C₄²	—	13	6	no	—
96	C₂×C₁₆	—	13	24	no	—
97	C₂×C₁₆	—	13	4	no	—
98	C₂×C₁₆	C₂×Dic₁₃	1	24	yes	complemented
99	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
100	C₄×C₈	—	13	12	no	—
101	C₄×C₈	—	13	4	no	—
102	C₂×C₁₃	C₂×#346	1	12	yes	complemented
103	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
104	C₂×C₁₃	C₂²×M₃₂	1	2	yes	—
105	C₂⁴	C₈×D₁₃	1	1	yes	characteristic
106	C₂²×C₄	—	13	12	no	—
107	C₂²×C₄	—	26	8	no	—
108	C₂²×C₄	C₈×D₁₃	1	4	yes	—
109	C₂²×C₄	C₈×D₁₃	1	3	yes	—
110	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
111	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
112	C₂×C₈	—	13	24	no	—
113	C₂×C₈	—	13	4	no	—
114	C₂×C₈	C₄×Dic₁₃	1	12	yes	—
115	C₂×C₈	C₂×C₄×D₁₃	1	3	yes	—
116	C₂×C₈	C₂×C₄×D₁₃	1	6	yes	—
117	C₂×C₈	C₂²×Dic₁₃	1	6	yes	—
118	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
119	C₄²	—	13	12	no	—
120	C₄²	—	13	4	no	—
121	C₁₆	—	13	8	no	—
122	C₁₆	C₂²×Dic₁₃	1	8	yes	complemented
123	C₁₃	C₂²×#346	1	1	yes	characteristic, complemented, Sylow
124	C₂³	#88038	1	8	yes	—
125	C₂³	C₈×Dic₁₃	1	4	yes	—
126	C₂³	C₂×C₈×D₁₃	1	3	yes	—
127	C₂×C₄	—	13	8	no	—
128	C₂×C₄	—	26	24	no	—
129	C₂×C₄	C₈×Dic₁₃	1	12	yes	—
130	C₂×C₄	C₂×C₈×D₁₃	1	6	yes	—
131	C₂×C₄	C₂×C₈×D₁₃	1	3	yes	—
132	C₂×C₄	C₂×C₄×Dic₁₃	1	6	yes	—
133	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
134	C₈	—	13	8	no	—
135	C₈	C₂×C₄×Dic₁₃	1	6	yes	—
136	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
137	C₈	C₂³×Dic₁₃	1	1	yes	characteristic
138	C₂²	#11718094	1	16	yes	direct product factor
139	C₂²	C₂×#88038	1	12	yes	—
140	C₂²	C₂×C₈×Dic₁₃	1	6	yes	—
141	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
142	C₄	—	26	8	no	—
143	C₄	C₂×C₈×Dic₁₃	1	6	yes	—
144	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
145	C₄	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
146	C₂	C₂×#11718094	1	12	yes	direct product factor
147	C₂	C₂²×C₈×Dic₁₃	1	1	yes	characteristic
148	C₂	C₂²×#88038	1	2	yes	—

	subgroup	G/H
center	C₂³×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₂²×C₄×C₈
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂³×C₁₃×C₁₆	C₂
socle, prime radical	C₂⁴×C₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂³×C₁₆	D₁₃
hypocenter	C₁₃	C₂²×#346
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₈ ◁ C₂³×C₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×#11718094	C₂	direct (N × H)
8. C₂²×C₁₃×C₁₆	C₄	semidirect
12. C₂²×#6090	C₄	semidirect
14. #11718094	C₂²	direct (N × H)
25. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
29. C₂×#6090	C₂×C₄	semidirect
48. C₁₃×C₁₆	C₂²×C₄	semidirect
49. #6090	C₂²×C₄	semidirect
73. C₂²×C₁₆	Dic₁₃	semidirect
78. C₂²×C₁₃	#346	semidirect
98. C₂×C₁₆	C₂×Dic₁₃	semidirect
102. C₂×C₁₃	C₂×#346	semidirect
122. C₁₆	C₂²×Dic₁₃	semidirect
123. C₁₃	C₂²×#346	semidirect
138. C₂²	#11718094	direct (N × H)
146. C₂	C₂×#11718094	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×#6090	2
C₂²×C₈×Dic₁₃	2
C₂×#11718094	2
C₂³×C₁₃×C₁₆	2
C₂²×#346	13

Subgroups — C22×#11718094 #16015544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11718094 #16015544