Subgroups — C₂×#13112912 #15774512

Order 3328.

230 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718055	C₂	1	2	yes	maximal
2	#13112912	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	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88052	—	2	2	no	—
8	C₄×C₁₃×C₁₆	C₄	1	2	yes	—
9	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
10	#11718055	—	2	2	no	—
11	#11718055	C₂²	1	4	yes	—
12	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₃	Q₈	1	1	yes	characteristic
15	C₂×C₁₃×C₁₆	—	2	1	no	—
16	C₂×C₁₃×C₁₆	—	2	1	no	—
17	C₂×C₁₃×C₁₆	C₈	1	2	yes	—
18	C₂×C₁₃×C₁₆	C₈	1	2	yes	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
20	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
21	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
24	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	#88052	—	2	4	no	—
26	#88052	—	4	2	no	—
27	C₂×#6090	—	4	2	no	—
28	C₂×#1373	—	13	1	no	maximal, Sylow
29	C₂²×C₄×C₁₃	—	2	1	no	—
30	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
36	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
37	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
38	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
39	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
40	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₄²×C₁₃	—	2	1	no	—
44	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
45	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
46	C₁₃×C₁₆	—	2	2	no	—
47	C₁₃×C₁₆	C₂×C₈	1	4	yes	—
48	#6090	—	4	4	no	—
49	C₂×#364	—	13	2	no	—
50	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic
51	#1373	—	13	4	no	—
52	C₂³×C₁₃	#108	1	1	yes	characteristic
53	C₂×C₄×C₁₃	—	2	4	no	—
54	C₂×C₄×C₁₃	—	2	1	no	—
55	C₂×C₄×C₁₃	—	2	1	no	—
56	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
58	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
59	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
60	C₂×C₄×C₁₃	#108	1	1	yes	characteristic
61	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
63	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
64	C₈×C₁₃	#107	1	1	yes	characteristic
65	C₈×C₁₃	#107	1	1	yes	characteristic
66	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
67	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
68	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
69	C₈×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
70	C₂×M₃₂	—	26	2	no	—
71	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
72	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
73	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
74	#364	—	13	4	no	—
75	#364	—	26	2	no	—
76	C₄×C₁₆	Dic₁₃	1	2	yes	—
77	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
78	C₂²×C₁₃	—	2	2	no	—
79	C₂²×C₁₃	#335	1	1	yes	characteristic
80	C₂²×C₁₃	#335	1	1	yes	characteristic
81	C₂²×C₁₃	C₂×#108	1	1	yes	characteristic
82	C₄×C₁₃	—	2	2	no	—
83	C₄×C₁₃	—	2	2	no	—
84	C₄×C₁₃	#335	1	1	yes	characteristic
85	C₄×C₁₃	#335	1	1	yes	characteristic
86	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
87	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
88	C₂²×C₈	D₅₂	1	1	yes	characteristic
89	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
90	C₂×C₄²	Dic₂₆	1	1	yes	characteristic
91	M₃₂	—	26	4	no	—
92	M₃₂	—	52	2	no	—
93	C₂×C₁₆	—	2	1	no	—
94	C₂×C₁₆	—	2	1	no	—
95	C₂×C₁₆	—	52	2	no	—
96	C₂×C₁₆	#1055	1	2	yes	—
97	C₂×C₁₆	#1055	1	2	yes	—
98	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
99	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
100	C₄×C₈	Dic₂₆	1	1	yes	characteristic
101	C₄×C₈	D₅₂	1	1	yes	characteristic
102	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
103	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
104	C₂×C₁₃	—	2	1	no	—
105	C₂×C₁₃	—	2	1	no	—
106	C₂×C₁₃	#1373	1	2	yes	complemented
107	C₂×C₁₃	C₂×#335	1	1	yes	characteristic
108	C₂²×C₄	—	2	1	no	—
109	C₂²×C₄	C₄⋊Dic₁₃	1	1	yes	characteristic
110	C₂×C₈	D₁₀₄	1	1	yes	characteristic
111	C₂×C₈	D₁₀₄	1	1	yes	characteristic
112	C₂×C₈	Dic₅₂	1	1	yes	characteristic
113	C₂×C₈	Dic₅₂	1	1	yes	characteristic
114	C₂×C₈	C₂×#1055	1	1	yes	characteristic
115	C₂×C₈	C₂×#1055	1	1	yes	characteristic
116	C₂×C₈	#6099	1	1	yes	characteristic
117	C₂×C₈	#6099	1	1	yes	characteristic
118	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
119	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
120	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
121	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
122	C₄²	—	2	1	no	—
123	C₄²	C₄⋊Dic₁₃	1	1	yes	characteristic
124	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
125	C₁₆	—	2	2	no	—
126	C₁₆	—	52	4	no	—
127	C₁₆	C₂×#1055	1	4	yes	—
128	C₁₃	C₂×#1373	1	1	yes	characteristic, complemented, Sylow
129	C₂³	#88059	1	1	yes	characteristic
130	C₂×C₄	—	2	4	no	—
131	C₂×C₄	—	2	1	no	—
132	C₂×C₄	—	2	1	no	—
133	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
134	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
135	C₂×C₄	#88058	1	1	yes	characteristic
136	C₂×C₄	#88058	1	1	yes	characteristic
137	C₂×C₄	#88059	1	1	yes	characteristic
138	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
139	C₈	C₄⋊#1055	1	1	yes	characteristic
140	C₈	C₄⋊#1055	1	1	yes	characteristic
141	C₈	#88058	1	1	yes	characteristic
142	C₈	#88058	1	1	yes	characteristic
143	C₈	C₂×D₁₀₄	1	1	yes	characteristic
144	C₈	C₂×Dic₅₂	1	1	yes	characteristic
145	C₈	C₂²×#1055	1	1	yes	characteristic
146	C₈	C₂×#6099	1	1	yes	characteristic
147	C₂²	—	2	2	no	—
148	C₂²	#11718050	1	1	yes	characteristic
149	C₂²	#11718050	1	1	yes	characteristic
150	C₂²	C₂×#88059	1	1	yes	characteristic
151	C₄	—	2	2	no	—
152	C₄	—	2	2	no	—
153	C₄	#11718050	1	1	yes	characteristic
154	C₄	#11718050	1	1	yes	characteristic
155	C₄	C₂×C₄⋊#1055	1	1	yes	characteristic
156	C₄	C₂×#88058	1	1	yes	characteristic
157	C₂	—	2	1	no	—
158	C₂	—	2	1	no	—
159	C₂	#13112912	1	2	yes	direct product factor
160	C₂	C₂×#11718050	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₁₀₄
commutator	C₈×C₁₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle	C₂²×C₁₃	#335
prime radical	C₂³×C₁₃	#108
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×C₄×C₁₆	D₁₃
hypocenter	C₁₃	C₂×#1373
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13112912	C₂	direct (N × H)
106. C₂×C₁₃	#1373	semidirect
128. C₁₃	C₂×#1373	semidirect
159. C₂	#13112912	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×#11718055	2
#13112912	2
C₂×C₄×C₁₃×C₁₆	2
C₂×#1373	13

Subgroups — C2×#13112912 #15774512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112912 #15774512