Subgroups — C₂×#13116620 #16015948

Order 3328.

694 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718767	C₂	1	2	yes	maximal
2	#13116620	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718097	C₂	1	2	yes	maximal, complemented
4	C₂×#11718096	C₂	1	2	yes	maximal, complemented
5	C₂³×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88180	—	2	2	no	—
8	C₂²×C₁₃×C₁₆	C₄	1	8	yes	complemented
9	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×C₁₆	C₂²	1	4	yes	—
12	#11718767	—	2	4	no	—
13	#11718767	C₂²	1	8	yes	—
14	C₂×#88058	C₂²	1	4	yes	—
15	C₂×#88057	—	2	2	no	—
16	#11718097	C₂²	1	8	yes	complemented
17	#11718096	C₂²	1	8	yes	complemented
18	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
20	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	D₄	1	2	yes	—
22	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
23	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
25	C₂×C₂²⋊Dic₁₃	—	4	2	no	—
26	#88180	—	2	8	no	—
27	#88180	—	4	4	no	—
28	C₂×C₄⋊Dic₁₃	—	2	4	no	—
29	C₂×C₄×Dic₁₃	—	4	2	no	—
30	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
31	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
32	C₂×C₁₃×C₁₆	C₂×C₄	1	16	yes	complemented
33	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
34	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
35	#88058	—	2	4	no	—
36	#88058	C₂³	1	8	yes	—
37	#88057	—	2	8	no	—
38	C₂×#2158	—	13	1	no	maximal, Sylow
39	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
41	C₂²×C₄×C₁₃	D₈	1	2	yes	—
42	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	Q₁₆	1	4	yes	—
44	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
46	C₂²×Dic₁₃	—	4	4	no	—
47	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
48	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	—
49	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
50	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
51	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
52	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
54	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
55	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
56	C₂²⋊Dic₁₃	—	4	8	no	—
57	C₄⋊Dic₁₃	—	2	8	no	—
58	C₄⋊Dic₁₃	—	4	4	no	—
59	C₄×Dic₁₃	—	4	8	no	—
60	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
61	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
62	C₂³×C₁₆	D₁₃	1	1	yes	characteristic
63	C₂×#427	—	13	2	no	—
64	#2158	—	13	8	no	—
65	C₂×#367	—	13	2	no	—
66	C₂×#366	—	13	2	no	—
67	C₂³×C₁₃	—	2	4	no	—
68	C₂³×C₁₃	#107	1	4	yes	—
69	C₂³×C₁₃	C₂×D₈	1	2	yes	—
70	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
71	C₂×C₄×C₁₃	#107	1	8	yes	—
72	C₂×C₄×C₁₃	#107	1	4	yes	—
73	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
74	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
75	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
76	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
78	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
79	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
80	C₂×Dic₁₃	—	4	8	no	—
81	C₂×Dic₁₃	—	8	8	no	—
82	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
83	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
84	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
85	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
86	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
87	C₂×#117	—	26	2	no	—
88	C₂²×C₁₆	Dic₁₃	1	8	yes	complemented
89	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
90	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
91	C₂²×C₁₆	C₂×D₁₃	1	4	yes	—
92	#427	—	13	8	no	—
93	#427	—	26	4	no	—
94	C₂×#107	—	13	4	no	—
95	C₂×#106	—	26	2	no	—
96	#367	—	13	8	no	—
97	#366	—	13	8	no	—
98	C₂²×C₁₃	—	2	4	no	—
99	C₂²×C₁₃	—	2	8	no	—
100	C₂²×C₁₃	C₂×#107	1	4	yes	—
101	C₂²×C₁₃	C₂×#107	1	2	yes	—
102	C₂²×C₁₃	#508	1	4	yes	—
103	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
104	C₄×C₁₃	C₂×#107	1	4	yes	—
105	C₄×C₁₃	C₂×#107	1	2	yes	—
106	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
107	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
108	Dic₁₃	—	8	8	no	—
109	C₂³×C₄	D₅₂	1	1	yes	characteristic
110	C₂²×C₈	Dic₂₆	1	4	yes	—
111	C₂²×C₈	D₅₂	1	1	yes	characteristic
112	C₂²×C₈	D₅₂	1	2	yes	—
113	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
114	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
115	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
116	#117	—	26	8	no	—
117	#117	—	52	4	no	—
118	C₂×C₄⋊C₄	—	26	4	no	—
119	C₂×C₂²⋊C₄	—	52	2	no	—
120	C₂×C₄²	—	52	2	no	—
121	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
122	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
123	C₂×C₁₆	C₂×Dic₁₃	1	16	yes	complemented
124	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
125	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
126	#107	—	13	8	no	—
127	#107	—	26	4	no	—
128	#106	—	26	8	no	—
129	C₂×C₁₃	—	2	4	no	—
130	C₂×C₁₃	#2158	1	4	yes	complemented
131	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
132	C₂×C₁₃	C₂×#508	1	2	yes	—
133	C₂⁴	D₁₀₄	1	1	yes	characteristic
134	C₂²×C₄	—	52	4	no	—
135	C₂²×C₄	D₁₀₄	1	2	yes	—
136	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
137	C₂²×C₄	Dic₅₂	1	4	yes	—
138	C₂²×C₄	C₄⋊Dic₁₃	1	4	yes	—
139	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
140	C₂²×C₄	C₂×D₅₂	1	2	yes	—
141	C₂×C₈	C₄⋊Dic₁₃	1	4	yes	—
142	C₂×C₈	C₄⋊Dic₁₃	1	8	yes	—
143	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
144	C₂×C₈	C₂×Dic₂₆	1	4	yes	—
145	C₂×C₈	C₂×D₅₂	1	2	yes	—
146	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
147	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
148	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
149	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
150	C₄⋊C₄	—	26	8	no	—
151	C₄⋊C₄	—	52	4	no	—
152	C₂²⋊C₄	—	52	8	no	—
153	C₄²	—	52	8	no	—
154	C₁₆	C₂²×Dic₁₃	1	4	yes	—
155	C₁₆	C₂²×Dic₁₃	1	4	yes	—
156	C₁₃	C₂×#2158	1	1	yes	characteristic, complemented, Sylow
157	C₂³	—	2	4	no	—
158	C₂³	#88058	1	4	yes	—
159	C₂³	C₂×D₁₀₄	1	2	yes	—
160	C₂³	C₂×D₁₀₄	1	1	yes	characteristic
161	C₂×C₄	—	52	8	no	—
162	C₂×C₄	—	104	8	no	—
163	C₂×C₄	#88058	1	8	yes	—
164	C₂×C₄	#88058	1	4	yes	—
165	C₂×C₄	C₂×D₁₀₄	1	2	yes	—
166	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
167	C₂×C₄	C₂×Dic₅₂	1	4	yes	—
168	C₂×C₄	C₂×Dic₅₂	1	2	yes	—
169	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
170	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
171	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
172	C₈	C₂×C₄⋊Dic₁₃	1	4	yes	—
173	C₈	C₂×C₄⋊Dic₁₃	1	2	yes	—
174	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
175	C₈	C₂³×Dic₁₃	1	1	yes	characteristic
176	C₂²	—	2	4	no	—
177	C₂²	—	2	8	no	—
178	C₂²	#11718565	1	4	yes	—
179	C₂²	C₂×#88058	1	4	yes	—
180	C₂²	C₂×#88058	1	2	yes	—
181	C₂²	C₂²×D₁₀₄	1	1	yes	characteristic
182	C₄	—	104	8	no	—
183	C₄	C₂×#88058	1	4	yes	—
184	C₄	C₂×#88058	1	2	yes	—
185	C₄	C₂²×Dic₅₂	1	1	yes	characteristic
186	C₄	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
187	C₂	—	2	4	no	—
188	C₂	#13116620	1	4	yes	direct product factor
189	C₂	C₂²×#88058	1	1	yes	characteristic
190	C₂	C₂×#11718565	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₁₀₄
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂³×C₁₃×C₁₆	C₂
socle	C₂³×C₁₃	C₂×D₈
prime radical	C₂⁴×C₁₃	D₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂³×C₁₆	D₁₃
hypocenter	C₁₃	C₂×#2158
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂³×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13116620	C₂	direct (N × H)
3. C₂×#11718097	C₂	semidirect
4. C₂×#11718096	C₂	semidirect
8. C₂²×C₁₃×C₁₆	C₄	semidirect
16. #11718097	C₂²	semidirect
17. #11718096	C₂²	semidirect
32. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
88. C₂²×C₁₆	Dic₁₃	semidirect
123. C₂×C₁₆	C₂×Dic₁₃	semidirect
130. C₂×C₁₃	#2158	semidirect
156. C₁₃	C₂×#2158	semidirect
188. C₂	#13116620	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×#11718767	2
#13116620	2
C₂×#11718097	2
C₂×#11718096	2
C₂³×C₁₃×C₁₆	2
C₂×#2158	13

Subgroups — C2×#13116620 #16015948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116620 #16015948