Subgroups — C₂×#13114967 #15863107

Order 3328.

1006 conjugacy classes of subgroups.

The subgroup lattice has 166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718597	C₂	1	2	yes	maximal
2	#13114967	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718143	C₂	1	4	yes	maximal
4	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₁₃	C₂²	1	4	yes	—
8	C₂×C₄×C₈×C₁₃	C₄	1	8	yes	complemented
9	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
10	C₂×#88071	—	2	4	no	—
11	#11718597	—	2	4	no	—
12	#11718597	C₂²	1	8	yes	—
13	#11718143	C₂²	1	16	yes	—
14	C₂³×C₄×C₁₃	D₄	1	2	yes	—
15	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂³×Dic₁₃	—	2	4	no	—
17	C₂²×C₈×C₁₃	—	2	8	no	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
19	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₃	D₄	1	2	yes	—
22	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
23	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
24	C₂×C₄⋊Dic₁₃	—	2	16	no	—
25	C₂×C₄⋊Dic₁₃	—	2	4	no	—
26	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
27	C₄×C₈×C₁₃	C₂×C₄	1	16	yes	complemented
28	#88071	—	2	16	no	—
29	C₂×#1835	—	13	1	no	maximal, Sylow
30	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₄×C₁₃	—	2	8	no	—
32	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
33	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
34	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
35	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
37	C₂²×C₄×C₁₃	#41	1	8	yes	—
38	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
39	C₂²×Dic₁₃	—	2	8	no	—
40	C₂²×Dic₁₃	—	4	8	no	—
41	C₂²×Dic₁₃	—	4	16	no	—
42	C₂×C₈×C₁₃	—	2	16	no	—
43	C₂×C₈×C₁₃	—	2	8	no	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
45	C₄²×C₁₃	C₄⋊C₄	1	8	yes	—
46	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
47	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
48	C₄⋊Dic₁₃	—	2	16	no	—
49	C₄⋊Dic₁₃	—	4	8	no	—
50	C₂²×C₄×C₈	D₁₃	1	1	yes	characteristic
51	C₂×#382	—	13	2	no	—
52	#1835	—	13	8	no	—
53	C₂×#340	—	13	4	no	—
54	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
55	C₂³×C₁₃	#124	1	4	yes	—
56	C₂³×C₁₃	#135	1	8	yes	—
57	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
58	C₂×C₄×C₁₃	—	2	8	no	—
59	C₂×C₄×C₁₃	—	2	16	no	—
60	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
61	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
62	C₂×C₄×C₁₃	#117	1	8	yes	—
63	C₂×C₄×C₁₃	#124	1	4	yes	—
64	C₂×C₄×C₁₃	#125	1	8	yes	—
65	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
66	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
67	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
68	C₂×Dic₁₃	—	4	8	no	—
69	C₂×Dic₁₃	—	4	16	no	—
70	C₂×Dic₁₃	—	8	16	no	—
71	C₈×C₁₃	—	2	8	no	—
72	C₂³×C₈	C₂×D₁₃	1	2	yes	—
73	C₂²×C₄⋊C₄	—	13	4	no	—
74	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
75	C₂×C₄×C₈	Dic₁₃	1	8	yes	complemented
76	C₂×C₄×C₈	C₂×D₁₃	1	4	yes	—
77	#382	—	13	8	no	—
78	#382	—	26	4	no	—
79	C₂×#95	—	26	4	no	—
80	#340	—	13	16	no	—
81	C₂²×C₁₃	#382	1	4	yes	—
82	C₂²×C₁₃	#427	1	8	yes	—
83	C₂²×C₁₃	#488	1	16	yes	—
84	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₁₃	C₂×#124	1	2	yes	—
86	C₂²×C₁₃	C₂×#135	1	4	yes	—
87	C₄×C₁₃	—	2	8	no	—
88	C₄×C₁₃	#382	1	4	yes	—
89	C₄×C₁₃	C₂×#117	1	2	yes	—
90	C₄×C₁₃	C₂×#125	1	2	yes	—
91	Dic₁₃	—	8	8	no	—
92	C₂³×C₄	—	26	4	no	—
93	C₂³×C₄	D₅₂	1	2	yes	—
94	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
95	C₂²×C₈	—	2	8	no	—
96	C₂²×C₈	C₂×Dic₁₃	1	8	yes	—
97	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
98	C₂×C₄⋊C₄	—	13	8	no	—
99	C₂×C₄⋊C₄	—	26	16	no	—
100	C₂×C₄⋊C₄	—	26	4	no	—
101	C₂×C₄²	Dic₂₆	1	4	yes	—
102	C₂×C₄²	D₅₂	1	2	yes	—
103	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
104	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
105	C₄×C₈	C₂×Dic₁₃	1	16	yes	complemented
106	#95	—	26	16	no	—
107	C₂×C₁₃	#1835	1	8	yes	complemented
108	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
109	C₂×C₁₃	C₂×#427	1	2	yes	—
110	C₂×C₁₃	C₂×#488	1	4	yes	—
111	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
112	C₂²×C₄	—	2	8	no	—
113	C₂²×C₄	—	26	8	no	—
114	C₂²×C₄	—	52	8	no	—
115	C₂²×C₄	—	52	16	no	—
116	C₂²×C₄	C₄⋊Dic₁₃	1	8	yes	—
117	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
118	C₂²×C₄	C₂×D₅₂	1	4	yes	—
119	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
120	C₂²×C₄	#6127	1	8	yes	—
121	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
122	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
123	C₂×C₈	—	2	16	no	—
124	C₂×C₈	—	2	8	no	—
125	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
126	C₄⋊C₄	—	26	16	no	—
127	C₄⋊C₄	—	52	8	no	—
128	C₄²	C₄⋊Dic₁₃	1	8	yes	—
129	C₄²	C₂×Dic₂₆	1	4	yes	—
130	C₄²	C₂²×Dic₁₃	1	4	yes	—
131	C₁₃	C₂×#1835	1	1	yes	characteristic, complemented, Sylow
132	C₂³	#88129	1	4	yes	—
133	C₂³	#88158	1	8	yes	—
134	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
135	C₂³	C₂²×D₅₂	1	1	yes	characteristic
136	C₂×C₄	—	2	8	no	—
137	C₂×C₄	—	2	16	no	—
138	C₂×C₄	—	52	8	no	—
139	C₂×C₄	—	52	16	no	—
140	C₂×C₄	—	104	16	no	—
141	C₂×C₄	#88124	1	8	yes	—
142	C₂×C₄	#88129	1	4	yes	—
143	C₂×C₄	C₂×C₄⋊Dic₁₃	1	8	yes	—
144	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
145	C₂×C₄	#88180	1	8	yes	—
146	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
147	C₂×C₄	C₂×#6127	1	4	yes	—
148	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
149	C₈	—	2	8	no	—
150	C₂²	#11718358	1	16	yes	—
151	C₂²	#11718597	1	4	yes	—
152	C₂²	#11718767	1	8	yes	—
153	C₂²	C₂×#88129	1	2	yes	—
154	C₂²	C₂×#88158	1	4	yes	—
155	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
156	C₄	—	2	8	no	—
157	C₄	—	104	8	no	—
158	C₄	#11718597	1	4	yes	—
159	C₄	C₂×#88124	1	2	yes	—
160	C₄	C₂×#88180	1	2	yes	—
161	C₂	#13114967	1	8	yes	direct product factor
162	C₂	C₂×#11718597	1	1	yes	characteristic
163	C₂	C₂×#11718767	1	2	yes	—
164	C₂	C₂×#11718358	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₄×C₈×C₁₃	C₂
socle, prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×C₄×C₈	D₁₃
hypocenter	C₁₃	C₂×#1835
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13114967	C₂	direct (N × H)
8. C₂×C₄×C₈×C₁₃	C₄	semidirect
27. C₄×C₈×C₁₃	C₂×C₄	semidirect
75. C₂×C₄×C₈	Dic₁₃	semidirect
105. C₄×C₈	C₂×Dic₁₃	semidirect
107. C₂×C₁₃	#1835	semidirect
131. C₁₃	C₂×#1835	semidirect
161. C₂	#13114967	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×#11718597	2
#13114967	2
C₂×#11718143	2
C₂²×C₄×C₈×C₁₃	2
C₂×#1835	13

Subgroups — C2×#13114967 #15863107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13114967 #15863107