Subgroups — C₂×#13117112 #16018398

Order 3328.

494 conjugacy classes of subgroups.

The subgroup lattice has 188 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	1	yes	maximal, characteristic
2	#13117112	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718082	C₂	1	2	yes	maximal
4	C₂×#11718081	C₂	1	2	yes	maximal
5	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×#125	—	2	1	no	—
8	C₂×#88124	—	2	1	no	—
9	C₁₃×#499	—	2	2	no	—
10	C₁₃×#499	C₂²	1	4	yes	—
11	C₂×C₁₃×#107	C₂²	1	2	yes	—
12	C₂×C₁₃×#106	—	2	1	no	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88058	C₂²	1	2	yes	—
15	C₂×#88057	—	2	1	no	—
16	C₂²×#6090	C₂²	1	1	yes	characteristic
17	C₂²×#6090	C₂²	1	1	yes	characteristic
18	#11718344	—	2	2	no	—
19	#11718344	C₂²	1	4	yes	—
20	#11718082	C₂²	1	8	yes	—
21	#11718081	C₂²	1	8	yes	—
22	C₄×#6090	C₂²	1	4	yes	—
23	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
25	C₁₃×#125	—	2	4	no	—
26	C₁₃×#125	—	4	2	no	—
27	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
29	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
30	C₂×C₄⋊Dic₁₃	—	2	2	no	—
31	C₂×#6101	—	4	2	no	—
32	#88124	—	2	4	no	—
33	#88124	—	4	2	no	—
34	C₁₃×#107	—	2	2	no	—
35	C₁₃×#107	C₂³	1	4	yes	—
36	C₁₃×#106	—	2	4	no	—
37	C₄×C₈×C₁₃	D₄	1	2	yes	—
38	C₄×C₈×C₁₃	C₂³	1	2	yes	—
39	#88058	—	2	2	no	—
40	#88058	C₂³	1	4	yes	—
41	#88057	—	2	4	no	—
42	C₂×#6090	Q₈	1	4	yes	—
43	C₂×#6090	Q₈	1	4	yes	—
44	C₂×#6090	C₂³	1	2	yes	—
45	C₂×#6090	C₂³	1	2	yes	—
46	C₂×#2253	—	13	1	no	maximal, Sylow
47	C₂²×C₄×C₁₃	—	4	2	no	—
48	C₂²×C₄×C₁₃	D₈	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₁₃	—	4	2	no	—
51	C₂×C₈×C₁₃	Q₁₆	1	4	yes	—
52	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
54	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
55	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
56	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
57	C₁₃×C₄⋊C₄	—	2	4	no	—
58	C₁₃×C₄⋊C₄	—	4	2	no	—
59	C₁₃×C₄⋊C₄	—	4	8	no	—
60	C₄²×C₁₃	D₈	1	2	yes	—
61	C₄²×C₁₃	C₂×D₄	1	2	yes	—
62	C₄⋊Dic₁₃	—	2	4	no	—
63	C₄⋊Dic₁₃	—	4	2	no	—
64	#6101	—	4	8	no	—
65	#6090	C₂×Q₈	1	4	yes	—
66	#6090	C₂×Q₈	1	4	yes	—
67	C₂×#499	—	13	1	no	—
68	C₂×#499	D₁₃	1	1	yes	characteristic
69	#2253	—	13	8	no	—
70	C₂×#367	—	13	2	no	—
71	C₂×#366	—	13	2	no	—
72	C₂×C₄×C₁₆	—	13	1	no	—
73	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
74	C₂×C₄×C₁₃	—	2	4	no	—
75	C₂×C₄×C₁₃	—	4	4	no	—
76	C₂×C₄×C₁₃	—	8	4	no	—
77	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
78	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
79	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
81	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
82	C₂×Dic₁₃	—	4	4	no	—
83	C₂×Dic₁₃	—	8	4	no	—
84	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
85	C₈×C₁₃	C₂×Q₁₆	1	4	yes	—
86	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
87	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
88	C₂×#125	—	2	1	no	—
89	C₂×#125	—	26	1	no	—
90	C₂²×C₁₆	—	13	1	no	—
91	C₂²×C₁₆	—	13	1	no	—
92	#499	—	2	2	no	—
93	#499	—	13	4	no	—
94	#499	—	26	2	no	—
95	#499	C₂×D₁₃	1	4	yes	—
96	C₂×#107	—	13	2	no	—
97	C₂×#107	C₂×D₁₃	1	2	yes	—
98	C₂×#106	—	2	1	no	—
99	C₂×#106	—	26	1	no	—
100	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
101	#367	—	13	8	no	—
102	#366	—	13	8	no	—
103	C₄×C₁₆	—	13	4	no	—
104	C₂²×C₁₃	#500	1	2	yes	—
105	C₂²×C₁₃	#508	1	4	yes	—
106	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
107	C₄×C₁₃	—	2	4	no	—
108	C₄×C₁₃	—	8	4	no	—
109	C₄×C₁₃	#500	1	2	yes	—
110	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
111	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
112	Dic₁₃	—	8	4	no	—
113	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
114	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
115	#125	—	2	4	no	—
116	#125	—	4	2	no	—
117	#125	—	26	4	no	—
118	#125	—	52	2	no	—
119	C₂×C₄⋊C₄	—	2	2	no	—
120	C₂×C₄⋊C₄	—	4	2	no	—
121	C₂×C₄⋊C₄	—	26	2	no	—
122	C₂×C₄⋊C₄	—	52	2	no	—
123	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
124	C₂×C₁₆	—	13	4	no	—
125	C₂×C₁₆	—	13	4	no	—
126	C₂×C₁₆	—	13	2	no	—
127	C₂×C₁₆	—	13	2	no	—
128	#107	—	2	2	no	—
129	#107	—	13	4	no	—
130	#107	—	26	2	no	—
131	#107	C₂²×D₁₃	1	4	yes	—
132	#106	—	2	4	no	—
133	#106	—	26	4	no	—
134	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
135	C₄×C₈	C₂²×D₁₃	1	2	yes	—
136	C₂×C₁₃	#2253	1	4	yes	complemented
137	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
138	C₂×C₁₃	C₂×#508	1	2	yes	—
139	C₂²×C₄	—	4	2	no	—
140	C₂²×C₄	—	52	2	no	—
141	C₂²×C₄	#6104	1	2	yes	—
142	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
143	C₂×C₈	#6107	1	4	yes	—
144	C₂×C₈	Q₈×D₁₃	1	2	yes	—
145	C₂×C₈	Q₈×D₁₃	1	2	yes	—
146	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
147	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
148	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
149	C₄⋊C₄	—	2	4	no	—
150	C₄⋊C₄	—	4	2	no	—
151	C₄⋊C₄	—	4	8	no	—
152	C₄⋊C₄	—	26	4	no	—
153	C₄⋊C₄	—	52	2	no	—
154	C₄⋊C₄	—	52	8	no	—
155	C₄²	#6104	1	2	yes	—
156	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
157	C₁₆	—	13	4	no	—
158	C₁₆	—	13	4	no	—
159	C₁₃	C₂×#2253	1	1	yes	characteristic, complemented, Sylow
160	C₂³	C₂×#6104	1	1	yes	characteristic
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	4	4	no	—
163	C₂×C₄	—	8	4	no	—
164	C₂×C₄	—	52	4	no	—
165	C₂×C₄	—	104	4	no	—
166	C₂×C₄	C₂×#6104	1	4	yes	—
167	C₂×C₄	C₂×#6104	1	1	yes	characteristic
168	C₂×C₄	C₂×#6107	1	2	yes	—
169	C₂×C₄	#88198	1	2	yes	—
170	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
171	C₈	C₂×#6107	1	4	yes	—
172	C₈	#88198	1	2	yes	—
173	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
174	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
175	C₂²	#11718739	1	2	yes	—
176	C₂²	#11718855	1	4	yes	—
177	C₂²	C₂²×#6104	1	1	yes	characteristic
178	C₄	—	2	4	no	—
179	C₄	—	8	4	no	—
180	C₄	—	104	4	no	—
181	C₄	#11718739	1	2	yes	—
182	C₄	C₂²×#6107	1	1	yes	characteristic
183	C₄	C₂×#88198	1	1	yes	characteristic
184	C₂	#13117112	1	4	yes	direct product factor
185	C₂	C₂×#11718739	1	1	yes	characteristic
186	C₂	C₂×#11718855	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#499	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
hypercenter	C₂×#499	D₁₃
hypocenter	C₁₃	C₂×#2253
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#499

Complements

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

N	H ≅ G/N	type
2. #13117112	C₂	direct (N × H)
136. C₂×C₁₃	#2253	semidirect
159. C₁₃	C₂×#2253	semidirect
184. C₂	#13117112	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
#13117112	2
C₂×#11718082	2
C₂×#11718081	2
C₂×C₄×#6090	2
C₂×C₁₃×#499	2
C₂×#2253	13

Subgroups — C2×#13117112 #16018398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13117112 #16018398