Subgroups — C₂×C₄×#88034 #15783089

Order 3328.

270 conjugacy classes of subgroups.

The subgroup lattice has 114 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₄×C₁₆	D₁₃
commutator, hypocenter	C₁₃	C₂×C₄×C₃₂
Frattini	C₂×C₁₆	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₁₆
cosocle	C₂×C₁₃×C₁₆	C₂³
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×#88034	C₂	direct (N × H)
9. C₂×#88034	C₄	direct (N × H)
21. #88034	C₂×C₄	direct (N × H)
40. C₂×C₄×C₁₃	C₃₂	semidirect
61. C₄×C₁₃	C₂×C₃₂	semidirect
75. C₂×C₁₃	C₄×C₃₂	semidirect
91. C₁₃	C₂×C₄×C₃₂	semidirect
93. C₂×C₄	#88034	direct (N × H)
107. C₄	C₂×#88034	direct (N × H)
110. C₂	C₄×#88034	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×#88034	2
C₄×#88034	2
C₂×C₄×C₁₃×C₁₆	2
C₂×C₄×C₃₂	13

Subgroups — C2×C4×#88034 #15783089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#88034 #15783089