Subgroups — C₂²×C₈×#1057 #16792561

Order 3328.

1342 conjugacy classes of subgroups.

The subgroup lattice has 148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×#1057	C₂	1	2	yes	maximal
2	C₂×C₈×#1057	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×#1057	C₄	1	4	yes	—
5	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
7	C₂³×#1055	C₄	1	1	yes	characteristic
8	C₂×C₄×#1057	C₄	1	12	yes	—
9	C₂×C₄×#1057	C₂²	1	12	yes	—
10	C₂×C₈×Dic₁₃	C₄	1	6	yes	—
11	C₂×C₈×Dic₁₃	C₂²	1	6	yes	—
12	C₈×#1057	C₂²	1	16	yes	direct product factor
13	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂³×Dic₁₃	C₂×C₄	1	2	yes	—
15	C₂²×#1057	C₈	1	32	yes	direct product factor
16	C₂²×#1057	C₂×C₄	1	24	yes	—
17	C₂²×C₈×C₁₃	C₈	1	8	yes	complemented
18	C₂²×C₈×C₁₃	C₂×C₄	1	6	yes	—
19	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
20	C₂×C₄×Dic₁₃	C₂×C₄	1	6	yes	—
21	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
22	C₂²×#1055	C₈	1	8	yes	complemented
23	C₂²×#1055	C₂×C₄	1	6	yes	—
24	C₄×#1057	C₂×C₄	1	24	yes	—
25	C₄×#1057	C₂³	1	8	yes	—
26	C₈×Dic₁₃	C₂×C₄	1	12	yes	—
27	C₈×Dic₁₃	C₂³	1	4	yes	—
28	C₂²×C₈²	—	13	1	no	maximal, Sylow
29	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
30	C₂²×C₄×C₁₃	C₄²	1	3	yes	—
31	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
32	C₂²×C₄×C₁₃	C₂×C₈	1	4	yes	—
33	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
34	C₂²×Dic₁₃	C₄²	1	6	yes	—
35	C₂²×Dic₁₃	C₂×C₈	1	16	yes	—
36	C₂²×Dic₁₃	C₂²×C₄	1	6	yes	—
37	C₂×#1057	C₂×C₈	1	96	yes	direct product factor
38	C₂×#1057	C₂²×C₄	1	16	yes	—
39	C₂×C₈×C₁₃	C₂×C₈	1	24	yes	complemented
40	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
41	C₄×Dic₁₃	C₄²	1	6	yes	—
42	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
43	C₄×Dic₁₃	C₂²×C₄	1	6	yes	—
44	C₄×Dic₁₃	C₂⁴	1	1	yes	characteristic
45	C₂×#1055	C₂×C₈	1	24	yes	complemented
46	C₂×#1055	C₂²×C₄	1	4	yes	—
47	C₂²×C₄×C₈	—	13	2	no	—
48	C₂²×C₄×C₈	—	13	1	no	—
49	C₂×C₈²	—	13	12	no	—
50	C₂³×C₁₃	C₄×C₈	1	8	yes	—
51	C₂³×C₁₃	C₄×C₈	1	4	yes	—
52	C₂³×C₁₃	C₂×C₄²	1	3	yes	—
53	C₂×C₄×C₁₃	C₄×C₈	1	12	yes	—
54	C₂×C₄×C₁₃	C₂×C₄²	1	3	yes	—
55	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
56	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
57	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
58	C₂×Dic₁₃	C₄×C₈	1	24	yes	—
59	C₂×Dic₁₃	C₂×C₄²	1	6	yes	—
60	C₂×Dic₁₃	C₂²×C₈	1	24	yes	—
61	C₂×Dic₁₃	C₂³×C₄	1	2	yes	—
62	#1057	C₂²×C₈	1	32	yes	direct product factor
63	C₈×C₁₃	C₂²×C₈	1	8	yes	complemented
64	#1055	C₂²×C₈	1	8	yes	complemented
65	C₂³×C₈	—	13	4	no	—
66	C₂³×C₈	—	13	1	no	—
67	C₂³×C₈	#261	1	1	yes	characteristic
68	C₂²×C₄²	—	13	1	no	—
69	C₂×C₄×C₈	—	13	12	no	—
70	C₂×C₄×C₈	—	13	12	no	—
71	C₂×C₄×C₈	—	13	6	no	—
72	C₂×C₄×C₈	—	13	6	no	—
73	C₈²	—	13	16	no	—
74	C₂²×C₁₃	C₈²	1	16	yes	complemented
75	C₂²×C₁₃	C₂×C₄×C₈	1	12	yes	—
76	C₂²×C₁₃	C₂×C₄×C₈	1	6	yes	—
77	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
78	C₄×C₁₃	C₂×C₄×C₈	1	6	yes	—
79	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
80	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
81	Dic₁₃	C₂×C₄×C₈	1	12	yes	—
82	Dic₁₃	C₂³×C₈	1	4	yes	—
83	C₂³×C₄	—	13	2	no	—
84	C₂³×C₄	C₂×#261	1	1	yes	characteristic
85	C₂²×C₈	—	13	24	no	—
86	C₂²×C₈	—	13	32	no	—
87	C₂²×C₈	—	13	8	no	—
88	C₂²×C₈	—	13	6	no	—
89	C₂²×C₈	#1057	1	8	yes	direct product factor
90	C₂²×C₈	C₂×#261	1	6	yes	—
91	C₂×C₄²	—	13	6	no	—
92	C₂×C₄²	—	13	3	no	—
93	C₂×C₄²	—	13	3	no	—
94	C₄×C₈	—	13	24	no	—
95	C₄×C₈	—	13	8	no	—
96	C₄×C₈	—	13	4	no	—
97	C₄×C₈	—	13	12	no	—
98	C₂×C₁₃	C₂×C₈²	1	12	yes	complemented
99	C₂×C₁₃	C₂²×C₄×C₈	1	2	yes	—
100	C₂×C₁₃	C₂²×C₄×C₈	1	1	yes	characteristic
101	C₂⁴	C₄×#261	1	1	yes	characteristic
102	C₂²×C₄	—	13	16	no	—
103	C₂²×C₄	—	13	6	no	—
104	C₂²×C₄	—	13	6	no	—
105	C₂²×C₄	D₁₃⋊C₈	1	4	yes	—
106	C₂²×C₄	C₄×#261	1	3	yes	—
107	C₂²×C₄	C₂×#1057	1	4	yes	—
108	C₂²×C₄	C₂²×#261	1	3	yes	—
109	C₂×C₈	—	13	16	no	—
110	C₂×C₈	—	13	96	no	—
111	C₂×C₈	—	13	24	no	—
112	C₂×C₈	—	13	4	no	—
113	C₂×C₈	C₂×#1057	1	24	yes	direct product factor
114	C₂×C₈	C₂²×#261	1	4	yes	—
115	C₄²	—	13	6	no	—
116	C₄²	—	13	6	no	—
117	C₄²	—	13	1	no	—
118	C₄²	—	13	3	no	—
119	C₁₃	C₂²×C₈²	1	1	yes	characteristic, complemented, Sylow
120	C₂³	C₈×#261	1	8	yes	—
121	C₂³	C₄×#1057	1	4	yes	—
122	C₂³	C₂×C₄×#261	1	3	yes	—
123	C₂×C₄	—	13	24	no	—
124	C₂×C₄	—	13	24	no	—
125	C₂×C₄	—	13	2	no	—
126	C₂×C₄	—	13	6	no	—
127	C₂×C₄	C₄×#1057	1	12	yes	—
128	C₂×C₄	C₂×D₁₃⋊C₈	1	6	yes	—
129	C₂×C₄	C₂×C₄×#261	1	3	yes	—
130	C₂×C₄	C₂²×#1057	1	6	yes	—
131	C₂×C₄	C₂³×#261	1	1	yes	characteristic
132	C₈	—	13	32	no	—
133	C₈	—	13	8	no	—
134	C₈	C₂²×#1057	1	8	yes	direct product factor
135	C₂²	C₈×#1057	1	16	yes	direct product factor
136	C₂²	C₂×C₈×#261	1	12	yes	—
137	C₂²	C₂×C₄×#1057	1	6	yes	—
138	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
139	C₄	—	13	4	no	—
140	C₄	—	13	12	no	—
141	C₄	C₂×C₄×#1057	1	6	yes	—
142	C₄	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
143	C₄	C₂³×#1057	1	1	yes	characteristic
144	C₂	C₂×C₈×#1057	1	12	yes	direct product factor
145	C₂	C₂²×C₈×#261	1	2	yes	—
146	C₂	C₂²×C₄×#1057	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₈	#261
commutator, hypocenter	C₁₃	C₂²×C₈²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂³×C₈×C₁₃	C₄
socle, prime radical	C₂⁴×C₁₃	C₄²
cosocle	C₄×Dic₁₃	C₂⁴
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×#1057	C₂	direct (N × H)
12. C₈×#1057	C₂²	direct (N × H)
15. C₂²×#1057	C₈	direct (N × H)
17. C₂²×C₈×C₁₃	C₈	semidirect
22. C₂²×#1055	C₈	semidirect
37. C₂×#1057	C₂×C₈	direct (N × H)
39. C₂×C₈×C₁₃	C₂×C₈	semidirect
45. C₂×#1055	C₂×C₈	semidirect
62. #1057	C₂²×C₈	direct (N × H)
63. C₈×C₁₃	C₂²×C₈	semidirect
64. #1055	C₂²×C₈	semidirect
74. C₂²×C₁₃	C₈²	semidirect
89. C₂²×C₈	#1057	direct (N × H)
98. C₂×C₁₃	C₂×C₈²	semidirect
113. C₂×C₈	C₂×#1057	direct (N × H)
119. C₁₃	C₂²×C₈²	semidirect
134. C₈	C₂²×#1057	direct (N × H)
135. C₂²	C₈×#1057	direct (N × H)
144. C₂	C₂×C₈×#1057	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×C₄×#1057	2
C₂×C₈×#1057	2
C₂²×C₈×Dic₁₃	2
C₂²×C₈²	13

Subgroups — C22×C8×#1057 #16792561

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₈×#1057 #16792561