Subgroups — C₂×#13117115 #16018401

Order 3328.

494 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	C₂×#11718344	C₂	1	2	yes	maximal
2	#13117115	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718097	C₂	1	2	yes	maximal
4	C₂×#11718096	C₂	1	2	yes	maximal
5	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂×#88124	—	2	2	no	—
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88058	C₂²	1	4	yes	—
11	C₂×#88057	—	2	2	no	—
12	#11718344	—	2	4	no	—
13	#11718344	C₂²	1	8	yes	—
14	C₄×C₁₃×C₁₆	C₂²	1	4	yes	—
15	#11718097	C₂²	1	8	yes	—
16	#11718096	C₂²	1	8	yes	—
17	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₃	—	2	4	no	—
21	C₂×#6101	—	4	4	no	—
22	#88124	—	2	8	no	—
23	#88124	—	4	4	no	—
24	C₂×C₁₃×C₁₆	Q₈	1	4	yes	—
25	C₂×C₁₃×C₁₆	Q₈	1	4	yes	—
26	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
27	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
28	C₄×C₈×C₁₃	D₄	1	2	yes	—
29	C₄×C₈×C₁₃	C₂³	1	2	yes	—
30	#88058	—	2	4	no	—
31	#88058	C₂³	1	8	yes	—
32	#88057	—	2	8	no	—
33	C₂×#2253	—	13	1	no	maximal, Sylow
34	C₂²×C₄×C₁₃	D₈	1	2	yes	—
35	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
36	C₂²×Dic₁₃	—	4	4	no	—
37	C₂×C₈×C₁₃	Q₁₆	1	4	yes	—
38	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
40	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
41	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
42	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
43	C₄²×C₁₃	D₈	1	2	yes	—
44	C₄²×C₁₃	C₂×D₄	1	2	yes	—
45	C₄⋊Dic₁₃	—	2	8	no	—
46	C₄⋊Dic₁₃	—	4	4	no	—
47	#6101	—	4	16	no	—
48	C₁₃×C₁₆	C₂×Q₈	1	4	yes	—
49	C₁₃×C₁₆	C₂×Q₈	1	4	yes	—
50	C₂×#499	—	13	2	no	—
51	#2253	—	13	8	no	—
52	C₂×#367	—	13	2	no	—
53	C₂×#366	—	13	2	no	—
54	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic
55	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
56	C₂×C₄×C₁₃	—	2	4	no	—
57	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
58	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
59	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
60	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
61	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
62	C₂×Dic₁₃	—	4	8	no	—
63	C₂×Dic₁₃	—	8	8	no	—
64	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
65	C₈×C₁₃	C₂×Q₁₆	1	4	yes	—
66	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
67	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
68	C₂×#125	—	26	2	no	—
69	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
70	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
71	#499	—	13	8	no	—
72	#499	—	26	4	no	—
73	C₂×#107	—	13	4	no	—
74	C₂×#106	—	26	2	no	—
75	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
76	#367	—	13	8	no	—
77	#366	—	13	8	no	—
78	C₄×C₁₆	C₂×D₁₃	1	4	yes	—
79	C₂²×C₁₃	#500	1	2	yes	—
80	C₂²×C₁₃	#508	1	4	yes	—
81	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
82	C₄×C₁₃	—	2	4	no	—
83	C₄×C₁₃	#500	1	2	yes	—
84	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
85	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
86	Dic₁₃	—	8	8	no	—
87	C₂²×C₈	D₅₂	1	1	yes	characteristic
88	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
89	#125	—	26	8	no	—
90	#125	—	52	4	no	—
91	C₂×C₄⋊C₄	—	26	4	no	—
92	C₂×C₄⋊C₄	—	52	4	no	—
93	C₂×C₄²	D₅₂	1	1	yes	characteristic
94	C₂×C₁₆	Dic₂₆	1	4	yes	—
95	C₂×C₁₆	Dic₂₆	1	4	yes	—
96	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
97	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
98	#107	—	13	8	no	—
99	#107	—	26	4	no	—
100	#106	—	26	8	no	—
101	C₄×C₈	D₅₂	1	2	yes	—
102	C₄×C₈	C₂²×D₁₃	1	2	yes	—
103	C₂×C₁₃	#2253	1	4	yes	complemented
104	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
105	C₂×C₁₃	C₂×#508	1	2	yes	—
106	C₂²×C₄	—	52	4	no	—
107	C₂²×C₄	D₁₀₄	1	2	yes	—
108	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
109	C₂×C₈	Dic₅₂	1	4	yes	—
110	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
111	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
112	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
113	C₂×C₈	C₂×D₅₂	1	2	yes	—
114	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
115	C₄⋊C₄	—	26	8	no	—
116	C₄⋊C₄	—	52	4	no	—
117	C₄⋊C₄	—	52	16	no	—
118	C₄²	D₁₀₄	1	2	yes	—
119	C₄²	C₂×D₅₂	1	2	yes	—
120	C₁₆	C₂×Dic₂₆	1	4	yes	—
121	C₁₆	C₂×Dic₂₆	1	4	yes	—
122	C₁₃	C₂×#2253	1	1	yes	characteristic, complemented, Sylow
123	C₂³	C₂×D₁₀₄	1	1	yes	characteristic
124	C₂×C₄	—	2	4	no	—
125	C₂×C₄	—	52	8	no	—
126	C₂×C₄	—	104	8	no	—
127	C₂×C₄	#88123	1	2	yes	—
128	C₂×C₄	C₂×D₁₀₄	1	4	yes	—
129	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
130	C₂×C₄	C₂×Dic₅₂	1	2	yes	—
131	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
132	C₈	#88123	1	2	yes	—
133	C₈	C₂×Dic₅₂	1	4	yes	—
134	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
135	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
136	C₂²	#11718343	1	2	yes	—
137	C₂²	#11718565	1	4	yes	—
138	C₂²	C₂²×D₁₀₄	1	1	yes	characteristic
139	C₄	—	2	4	no	—
140	C₄	—	104	8	no	—
141	C₄	#11718343	1	2	yes	—
142	C₄	C₂×#88123	1	1	yes	characteristic
143	C₄	C₂²×Dic₅₂	1	1	yes	characteristic
144	C₂	#13117115	1	4	yes	direct product factor
145	C₂	C₂×#11718343	1	1	yes	characteristic
146	C₂	C₂×#11718565	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₁₀₄
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
hypercenter	C₂×C₄×C₁₆	D₁₃
hypocenter	C₁₃	C₂×#2253
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13117115	C₂	direct (N × H)
103. C₂×C₁₃	#2253	semidirect
122. C₁₃	C₂×#2253	semidirect
144. C₂	#13117115	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×#11718344	2
#13117115	2
C₂×#11718097	2
C₂×#11718096	2
C₂×C₄×C₁₃×C₁₆	2
C₂×#2253	13

Subgroups — C2×#13117115 #16018401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13117115 #16018401