Subgroups — C₄×#11718046 #15752268

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×#1055	C₂	1	1	yes	maximal, characteristic
2	C₄²×#1055	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718046	C₂	1	4	yes	maximal
4	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₈×C₁₃	C₄	1	4	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
7	C₄³×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×#1055	C₄	1	4	yes	—
9	C₂×C₄×#1055	C₄	1	4	yes	—
10	C₂×C₄×#1055	C₂²	1	2	yes	—
11	C₂×C₄×#1055	C₂²	1	2	yes	—
12	#11718046	C₄	1	16	yes	direct product factor
13	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
14	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
18	C₂²×#1055	C₂×C₄	1	4	yes	—
19	C₂²×#1055	C₂×C₄	1	4	yes	—
20	C₄×C₈×C₁₃	—	2	8	no	—
21	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
22	C₄×#1055	—	2	8	no	—
23	C₄×#1055	C₈	1	16	yes	complemented
24	C₄×#1055	C₂×C₄	1	8	yes	—
25	C₄×#1055	C₂×C₄	1	8	yes	—
26	C₄×#322	—	13	1	no	maximal, Sylow
27	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
28	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₃	—	2	8	no	—
32	C₂×C₈×C₁₃	C₄²	1	8	yes	—
33	C₄²×C₁₃	C₂×C₈	1	8	yes	—
34	C₄²×C₁₃	M₁₆	1	8	yes	—
35	C₄²×C₁₃	M₁₆	1	8	yes	—
36	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
37	C₂×#1055	—	2	8	no	—
38	C₂×#1055	C₄²	1	8	yes	—
39	C₂×#1055	C₄²	1	8	yes	—
40	C₂×#1055	C₂×C₈	1	16	yes	—
41	C₄²×C₈	—	13	1	no	—
42	C₄²×C₈	—	13	1	no	—
43	C₄²×C₈	D₁₃	1	1	yes	characteristic
44	C₂×#322	—	13	4	no	—
45	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
46	C₂×C₄×C₁₃	C₄×C₈	1	8	yes	—
47	C₂×C₄×C₁₃	#97	1	8	yes	—
48	C₂×C₄×C₁₃	#97	1	8	yes	—
49	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
50	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
51	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
52	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
53	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
54	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
55	C₈×C₁₃	—	2	8	no	—
56	#1055	—	2	8	no	—
57	#1055	C₄×C₈	1	16	yes	complemented
58	C₂×C₄×C₈	—	13	4	no	—
59	C₂×C₄×C₈	—	13	2	no	—
60	C₂×C₄×C₈	—	13	2	no	—
61	C₂×C₄×C₈	—	13	4	no	—
62	C₂×C₄×C₈	Dic₁₃	1	4	yes	—
63	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
64	C₄³	C₂×D₁₃	1	1	yes	characteristic
65	#322	—	13	16	no	—
66	C₂²×C₁₃	C₄³	1	1	yes	characteristic
67	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
68	C₂²×C₁₃	C₂×#97	1	2	yes	—
69	C₂²×C₁₃	C₂×#97	1	2	yes	—
70	C₄×C₁₃	#322	1	16	yes	complemented
71	C₄×C₁₃	C₂×C₄×C₈	1	4	yes	—
72	C₄×C₁₃	C₄×M₁₆	1	4	yes	—
73	C₄×C₁₃	C₄×M₁₆	1	4	yes	—
74	C₂²×C₈	—	13	4	no	—
75	C₂²×C₈	—	13	4	no	—
76	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
77	C₂×C₄²	C₄×D₁₃	1	2	yes	—
78	C₂×C₄²	C₄×D₁₃	1	2	yes	—
79	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
80	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
81	C₄×C₈	—	2	8	no	—
82	C₄×C₈	—	13	16	no	—
83	C₄×C₈	—	13	8	no	—
84	C₄×C₈	—	13	8	no	—
85	C₄×C₈	—	26	8	no	—
86	C₄×C₈	C₄×D₁₃	1	8	yes	—
87	C₂×C₁₃	C₂×#322	1	4	yes	—
88	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
89	C₂×C₁₃	C₄×#97	1	1	yes	characteristic
90	C₂×C₁₃	C₄×#97	1	1	yes	characteristic
91	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
92	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
93	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
94	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
95	C₂×C₈	—	2	8	no	—
96	C₂×C₈	—	13	8	no	—
97	C₂×C₈	—	13	16	no	—
98	C₂×C₈	—	13	8	no	—
99	C₂×C₈	—	26	8	no	—
100	C₂×C₈	C₄×Dic₁₃	1	8	yes	—
101	C₄²	C₈×D₁₃	1	8	yes	—
102	C₄²	#6094	1	8	yes	—
103	C₄²	#6099	1	8	yes	—
104	C₄²	C₂×C₄×D₁₃	1	4	yes	—
105	C₁₃	C₄×#322	1	1	yes	characteristic, complemented, Sylow
106	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
107	C₂×C₄	#88043	1	8	yes	—
108	C₂×C₄	C₈×Dic₁₃	1	8	yes	—
109	C₂×C₄	#88055	1	8	yes	—
110	C₂×C₄	C₄²×D₁₃	1	2	yes	—
111	C₂×C₄	C₄²×D₁₃	1	2	yes	—
112	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
113	C₂×C₄	C₂×#6094	1	4	yes	—
114	C₂×C₄	C₂×#6099	1	4	yes	—
115	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
116	C₈	—	2	8	no	—
117	C₈	—	13	16	no	—
118	C₈	—	26	8	no	—
119	C₂²	C₂×#88043	1	2	yes	—
120	C₂²	C₄²×Dic₁₃	1	1	yes	characteristic
121	C₂²	C₂×C₈×Dic₁₃	1	2	yes	—
122	C₂²	C₂×#88055	1	2	yes	—
123	C₄	#11718046	1	16	yes	direct product factor
124	C₄	C₄×C₈×D₁₃	1	4	yes	—
125	C₄	C₄×#6094	1	4	yes	—
126	C₄	C₄×#6099	1	4	yes	—
127	C₂	C₂×#11718046	1	4	yes	—
128	C₂	C₄×C₈×Dic₁₃	1	1	yes	characteristic
129	C₂	C₄×#88055	1	1	yes	characteristic
130	C₂	C₄×#88043	1	1	yes	characteristic

	subgroup	G/H
center	C₄³	C₂×D₁₃
commutator	C₂×C₁₃	C₄²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₄²×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄²×C₈	D₁₃
hypocenter	C₁₃	C₄×#322
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
12. #11718046	C₄	direct (N × H)
23. C₄×#1055	C₈	semidirect
57. #1055	C₄×C₈	semidirect
70. C₄×C₁₃	#322	semidirect
105. C₁₃	C₄×#322	semidirect
123. C₄	#11718046	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×#1055	2
C₂×#11718046	2
C₄²×C₈×C₁₃	2
C₄×#322	13

Subgroups — C4×#11718046 #15752268

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718046 #15752268