Subgroups — C₄×#11718091 #15783096

Order 3328.

250 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718091	C₂	1	2	yes	maximal
2	#13112970	C₂	1	2	yes	maximal, complemented
3	C₄×#88034	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
8	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic
9	C₄×C₁₃×C₁₆	C₄	1	1	yes	characteristic
10	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
11	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
12	#11718091	C₄	1	8	yes	direct product factor
13	C₂×#88034	C₂²	1	4	yes	—
14	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₃	C₈	1	1	yes	characteristic
17	C₂×C₁₃×C₁₆	C₈	1	4	yes	—
18	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
21	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
23	C₄×C₈×C₁₃	C₈	1	1	yes	characteristic
24	C₄×C₈×C₁₃	C₈	1	1	yes	characteristic
25	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	#88034	C₂×C₄	1	8	yes	complemented
28	C₄×M₆₄	—	13	1	no	maximal, Sylow
29	C₂²×C₄×C₁₃	C₁₆	1	2	yes	—
30	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₁₃	C₁₆	1	4	yes	—
32	C₂×C₈×C₁₃	C₄²	1	2	yes	—
33	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
35	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₄²×C₁₃	C₁₆	1	2	yes	—
39	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
40	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
41	C₁₃×C₁₆	C₄²	1	2	yes	—
42	C₁₃×C₁₆	C₂×C₈	1	2	yes	—
43	C₁₃×C₁₆	C₂×C₈	1	2	yes	—
44	C₁₃×C₁₆	C₂²×C₄	1	2	yes	—
45	C₂×M₆₄	—	13	2	no	—
46	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic
47	#1397	—	13	2	no	—
48	C₄×C₃₂	—	13	2	no	—
49	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
50	C₂×C₄×C₁₃	—	2	4	no	—
51	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
52	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
53	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
54	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
55	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
56	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
57	C₈×C₁₃	C₄×C₈	1	2	yes	—
58	C₈×C₁₃	C₂×C₁₆	1	2	yes	—
59	C₈×C₁₃	C₂×C₁₆	1	2	yes	—
60	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
61	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
62	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
63	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
64	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
65	M₆₄	—	13	8	no	—
66	C₂×C₃₂	—	13	4	no	—
67	C₄×C₁₆	Dic₁₃	1	1	yes	characteristic
68	C₄×C₁₆	Dic₁₃	1	1	yes	characteristic
69	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
70	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
71	C₂²×C₁₃	—	2	2	no	—
72	C₂²×C₁₃	C₄×C₁₆	1	2	yes	—
73	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
74	C₄×C₁₃	—	2	2	no	—
75	C₄×C₁₃	C₄×C₁₆	1	2	yes	—
76	C₄×C₁₃	M₆₄	1	4	yes	complemented
77	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
78	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
79	C₂²×C₈	#1055	1	1	yes	characteristic
80	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
81	C₂×C₄²	#1055	1	1	yes	characteristic
82	C₂×C₁₆	#1055	1	4	yes	—
83	C₂×C₁₆	C₄×D₁₃	1	4	yes	—
84	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
85	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
86	C₂×C₁₆	C₂×Dic₁₃	1	1	yes	characteristic
87	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
88	C₄×C₈	#1055	1	1	yes	characteristic
89	C₄×C₈	#1055	1	1	yes	characteristic
90	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
91	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
92	C₃₂	—	13	8	no	—
93	C₂×C₁₃	—	2	2	no	—
94	C₂×C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic
95	C₂×C₁₃	C₂×M₆₄	1	2	yes	—
96	C₂²×C₄	#6090	1	2	yes	—
97	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
98	C₂×C₈	#6090	1	4	yes	—
99	C₂×C₈	C₂×#1055	1	2	yes	—
100	C₂×C₈	C₂×#1055	1	1	yes	characteristic
101	C₂×C₈	C₂×#1055	1	1	yes	characteristic
102	C₂×C₈	C₂×#1055	1	1	yes	characteristic
103	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
104	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
105	C₄²	#6090	1	2	yes	—
106	C₄²	C₂×#1055	1	1	yes	characteristic
107	C₄²	C₂×#1055	1	1	yes	characteristic
108	C₁₆	C₂×#1055	1	2	yes	—
109	C₁₆	C₂×#1055	1	2	yes	—
110	C₁₆	C₄×Dic₁₃	1	2	yes	—
111	C₁₆	C₂×C₄×D₁₃	1	2	yes	—
112	C₁₃	C₄×M₆₄	1	1	yes	characteristic, complemented, Sylow
113	C₂³	C₂×#6090	1	1	yes	characteristic
114	C₂×C₄	—	2	4	no	—
115	C₂×C₄	C₄×#1055	1	2	yes	—
116	C₂×C₄	C₂×#6090	1	2	yes	—
117	C₂×C₄	C₂×#6090	1	2	yes	—
118	C₂×C₄	C₂×#6090	1	1	yes	characteristic
119	C₂×C₄	C₂×#6090	1	2	yes	—
120	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
121	C₈	C₄×#1055	1	2	yes	—
122	C₈	C₂×#6090	1	2	yes	—
123	C₈	C₂×#6090	1	2	yes	—
124	C₈	C₂²×#1055	1	1	yes	characteristic
125	C₈	C₂×C₄×Dic₁₃	1	1	yes	characteristic
126	C₂²	—	2	2	no	—
127	C₂²	C₄×#6090	1	2	yes	—
128	C₂²	C₂²×#6090	1	1	yes	characteristic
129	C₄	—	2	2	no	—
130	C₄	C₄×#6090	1	2	yes	—
131	C₄	#11718091	1	4	yes	direct product factor
132	C₄	C₂×C₄×#1055	1	1	yes	characteristic
133	C₄	C₂²×#6090	1	1	yes	characteristic
134	C₂	—	2	2	no	—
135	C₂	C₂×C₄×#6090	1	1	yes	characteristic
136	C₂	C₂×#11718091	1	2	yes	—

	subgroup	G/H
center	C₄×C₁₆	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₄×C₁₆
Frattini	C₂×C₁₆	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle	C₂²×C₁₃	C₂²×C₁₆
prime radical	C₂³×C₁₃	C₂×C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂³
hypercenter	C₂×C₄×C₁₆	D₁₃
hypocenter	C₁₃	C₄×M₆₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₁₆ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13112970	C₂	semidirect
3. C₄×#88034	C₂	semidirect
12. #11718091	C₄	direct (N × H)
27. #88034	C₂×C₄	semidirect
76. C₄×C₁₃	M₆₄	semidirect
112. C₁₃	C₄×M₆₄	semidirect
131. C₄	#11718091	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×#11718091	2
#13112970	2
C₄×#88034	2
C₂×C₄×C₁₃×C₁₆	2
C₄×M₆₄	13

Subgroups — C4×#11718091 #15783096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718091 #15783096