Subgroups — C₂×#1057⋊C₁₆ #16786590

Order 3328.

350 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718257	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×#1057	C₂	1	1	yes	maximal, characteristic
3	#1057⋊C₁₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#1057	C₄	1	1	yes	characteristic
6	C₂×C₄×#1057	C₄	1	1	yes	characteristic
7	C₂²×#6092	C₄	1	2	yes	—
8	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
9	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₂²×#6090	C₄	1	1	yes	characteristic
11	#11718257	C₄	1	2	yes	—
12	#11718257	C₂²	1	2	yes	—
13	C₈×#1057	C₄	1	2	yes	—
14	C₈×#1057	C₂²	1	2	yes	—
15	C₁₆×Dic₁₃	C₄	1	2	yes	—
16	C₁₆×Dic₁₃	C₂²	1	2	yes	—
17	C₂²×#1057	C₈	1	2	yes	—
18	C₂²×#1057	C₈	1	2	yes	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
22	C₄×#1057	C₈	1	2	yes	—
23	C₄×#1057	C₈	1	2	yes	—
24	C₄×#1057	C₂×C₄	1	2	yes	—
25	C₄×#1057	C₂×C₄	1	2	yes	—
26	C₂×#6092	—	2	4	no	—
27	C₂×#6092	C₂×C₄	1	4	yes	—
28	C₂×C₁₃×C₁₆	—	2	2	no	—
29	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
30	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
33	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
34	C₂×#6090	—	2	2	no	—
35	C₂×#6090	C₂×C₄	1	2	yes	—
36	C₂×#1312	—	13	1	no	maximal, Sylow
37	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
38	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
39	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
40	C₂×#1057	—	2	4	no	—
41	C₂×#1057	C₁₆	1	8	yes	complemented
42	C₂×#1057	C₂×C₈	1	4	yes	—
43	C₂×#1057	C₂×C₈	1	4	yes	—
44	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
45	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
46	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
47	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
49	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
50	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
51	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×#1055	C₄²	1	1	yes	characteristic
53	C₂×#1055	M₁₆	1	4	yes	—
54	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
55	#6092	—	2	4	no	—
56	C₁₃×C₁₆	—	2	2	no	—
57	#6090	—	2	2	no	—
58	C₂×C₄×C₁₆	—	13	1	no	—
59	C₂×C₄×C₁₆	—	13	1	no	—
60	C₂×C₈²	—	13	1	no	—
61	#1312	—	13	4	no	—
62	C₂³×C₁₃	C₄×C₈	1	1	yes	characteristic
63	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	#97	1	2	yes	—
65	C₂×C₄×C₁₃	#97	1	2	yes	—
66	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
67	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
68	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
69	C₂×Dic₁₃	C₂×C₁₆	1	4	yes	—
70	C₂×Dic₁₃	M₃₂	1	4	yes	—
71	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
72	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
73	#1057	—	2	4	no	—
74	#1057	C₂×C₁₆	1	8	yes	complemented
75	C₈×C₁₃	#97	1	2	yes	—
76	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
77	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
78	#1055	#97	1	2	yes	—
79	#1055	C₂×M₁₆	1	2	yes	—
80	C₂²×C₁₆	—	13	2	no	—
81	C₂²×C₁₆	—	13	1	no	—
82	C₂²×C₁₆	#261	1	1	yes	characteristic
83	C₂×C₄×C₈	—	13	1	no	—
84	C₂×C₄×C₈	—	13	1	no	—
85	C₂×C₄×C₈	—	13	1	no	—
86	C₄×C₁₆	—	13	2	no	—
87	C₄×C₁₆	—	13	2	no	—
88	C₄×C₁₆	—	13	2	no	—
89	C₄×C₁₆	—	13	2	no	—
90	C₈²	—	13	2	no	—
91	C₈²	—	13	2	no	—
92	C₂²×C₁₃	#322	1	2	yes	—
93	C₂²×C₁₃	C₄×C₁₆	1	2	yes	—
94	C₂²×C₁₃	#346	1	2	yes	—
95	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
96	C₄×C₁₃	#322	1	2	yes	—
97	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
98	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
99	Dic₁₃	C₄×C₁₆	1	2	yes	—
100	Dic₁₃	#346	1	2	yes	—
101	Dic₁₃	C₂²×C₁₆	1	2	yes	—
102	Dic₁₃	C₂×M₃₂	1	2	yes	—
103	C₂²×C₈	—	13	2	no	—
104	C₂²×C₈	—	13	1	no	—
105	C₂²×C₈	—	13	2	no	—
106	C₂²×C₈	C₂×#261	1	1	yes	characteristic
107	C₂×C₄²	—	13	1	no	—
108	C₂×C₁₆	—	2	2	no	—
109	C₂×C₁₆	—	13	4	no	—
110	C₂×C₁₆	—	13	2	no	—
111	C₂×C₁₆	—	26	4	no	—
112	C₂×C₁₆	—	26	2	no	—
113	C₂×C₁₆	C₂×#261	1	2	yes	—
114	C₄×C₈	—	13	2	no	—
115	C₄×C₈	—	13	2	no	—
116	C₄×C₈	—	13	2	no	—
117	C₄×C₈	—	13	2	no	—
118	C₄×C₈	—	13	1	no	—
119	C₄×C₈	—	13	1	no	—
120	C₄×C₈	—	13	1	no	—
121	C₄×C₈	—	13	1	no	—
122	C₂×C₁₃	#1312	1	4	yes	complemented
123	C₂×C₁₃	C₂×#322	1	1	yes	characteristic
124	C₂×C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic
125	C₂×C₁₃	C₂×#346	1	1	yes	characteristic
126	C₂²×C₄	—	13	1	no	—
127	C₂²×C₄	—	13	1	no	—
128	C₂²×C₄	C₄×#261	1	1	yes	characteristic
129	C₂×C₈	—	13	4	no	—
130	C₂×C₈	—	13	8	no	—
131	C₂×C₈	—	13	4	no	—
132	C₂×C₈	—	13	1	no	—
133	C₂×C₈	—	13	1	no	—
134	C₂×C₈	—	13	4	no	—
135	C₂×C₈	—	26	4	no	—
136	C₂×C₈	#6118	1	2	yes	—
137	C₂×C₈	C₄×#261	1	1	yes	characteristic
138	C₂×C₈	#6122	1	2	yes	—
139	C₂×C₈	C₂²×#261	1	1	yes	characteristic
140	C₄²	—	13	1	no	—
141	C₄²	—	13	1	no	—
142	C₄²	—	13	1	no	—
143	C₄²	—	13	1	no	—
144	C₁₆	—	2	2	no	—
145	C₁₆	—	26	4	no	—
146	C₁₆	—	26	2	no	—
147	C₁₃	C₂×#1312	1	1	yes	characteristic, complemented, Sylow
148	C₂³	C₈×#261	1	1	yes	characteristic
149	C₂×C₄	—	13	4	no	—
150	C₂×C₄	—	13	4	no	—
151	C₂×C₄	—	13	1	no	—
152	C₂×C₄	—	13	1	no	—
153	C₂×C₄	—	13	1	no	—
154	C₂×C₄	—	13	1	no	—
155	C₂×C₄	C₈×#261	1	1	yes	characteristic
156	C₂×C₄	#88100	1	2	yes	—
157	C₂×C₄	#88110	1	2	yes	—
158	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
159	C₈	—	13	8	no	—
160	C₈	—	13	2	no	—
161	C₈	—	13	2	no	—
162	C₈	—	26	4	no	—
163	C₈	#88110	1	2	yes	—
164	C₈	C₂×#6118	1	1	yes	characteristic
165	C₈	C₂×#6122	1	1	yes	characteristic
166	C₂²	C₁₆×#261	1	2	yes	—
167	C₂²	#11718216	1	2	yes	—
168	C₂²	#1057⋊C₈	1	2	yes	—
169	C₂²	C₂×C₈×#261	1	1	yes	characteristic
170	C₄	—	13	2	no	—
171	C₄	—	13	2	no	—
172	C₄	—	13	2	no	—
173	C₄	—	13	2	no	—
174	C₄	#1057⋊C₈	1	2	yes	—
175	C₄	C₂×#88100	1	1	yes	characteristic
176	C₄	C₂×#88110	1	1	yes	characteristic
177	C₂	#1057⋊C₁₆	1	4	yes	direct product factor
178	C₂	C₂×#1057⋊C₈	1	1	yes	characteristic
179	C₂	C₂×C₁₆×#261	1	1	yes	characteristic
180	C₂	C₂×#11718216	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂×#261
commutator	C₂×C₁₃	C₂×C₄×C₁₆
Frattini	C₂×C₈	C₂²×#261
Fitting	C₂²×C₁₃×C₁₆	C₄
socle, prime radical	C₂³×C₁₃	C₄×C₈
cosocle	C₈×Dic₁₃	C₂³
hypercenter	C₂²×C₁₆	#261
hypocenter	C₁₃	C₂×#1312
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
3. #1057⋊C₁₆	C₂	direct (N × H)
41. C₂×#1057	C₁₆	semidirect
74. #1057	C₂×C₁₆	semidirect
122. C₂×C₁₃	#1312	semidirect
147. C₁₃	C₂×#1312	semidirect
177. C₂	#1057⋊C₁₆	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×#11718257	2
C₂×C₈×#1057	2
#1057⋊C₁₆	2
C₂×C₁₆×Dic₁₃	2
C₂×#1312	13

Subgroups — C2×#1057⋊C16 #16786590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1057⋊C₁₆ #16786590