Subgroups — C₂×#13117109 #16018394

Order 3328.

558 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718343	C₂	1	1	yes	maximal, characteristic
2	#13117109	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718081	C₂	1	4	yes	maximal
4	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
7	C₂×#88123	—	2	1	no	—
8	C₁₃×#500	—	2	2	no	—
9	C₁₃×#500	C₂²	1	4	yes	—
10	C₂×C₁₃×#107	—	2	1	no	—
11	C₂×C₁₃×#107	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×#88058	—	2	1	no	—
14	C₂×#88058	C₂²	1	2	yes	—
15	C₂²×#6090	C₂²	1	2	yes	—
16	#11718343	—	2	2	no	—
17	#11718343	C₂²	1	4	yes	—
18	#11718081	C₂²	1	16	yes	—
19	C₄×#6090	C₂²	1	4	yes	—
20	C₂²×Q₈×C₁₃	—	4	1	no	—
21	C₂²×Dic₂₆	—	4	1	no	—
22	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₁₃×C₄⋊Q₈	—	2	4	no	—
25	C₁₃×C₄⋊Q₈	—	4	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
28	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₃	—	2	2	no	—
30	C₂×C₄⋊Dic₁₃	—	4	1	no	—
31	#88123	—	2	4	no	—
32	#88123	—	4	2	no	—
33	C₁₃×#107	—	2	4	no	—
34	C₁₃×#107	—	2	2	no	—
35	C₁₃×#107	C₂³	1	4	yes	—
36	C₄×C₈×C₁₃	D₄	1	2	yes	—
37	C₄×C₈×C₁₃	C₂³	1	2	yes	—
38	#88058	—	2	4	no	—
39	#88058	—	2	2	no	—
40	#88058	C₂³	1	4	yes	—
41	C₂×#6090	Q₈	1	8	yes	complemented
42	C₂×#6090	C₂³	1	4	yes	—
43	C₂×#2252	—	13	1	no	maximal, Sylow
44	C₂×Q₈×C₁₃	—	4	4	no	—
45	C₂×Q₈×C₁₃	—	8	4	no	—
46	C₂²×C₄×C₁₃	—	4	2	no	—
47	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₁₃	—	4	2	no	—
51	C₂×Dic₂₆	—	4	4	no	—
52	C₂×Dic₂₆	—	8	4	no	—
53	C₂×C₈×C₁₃	Q₁₆	1	4	yes	—
54	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
56	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
57	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
58	C₁₃×C₄⋊C₄	—	2	4	no	—
59	C₁₃×C₄⋊C₄	—	4	2	no	—
60	C₁₃×C₄⋊C₄	—	4	4	no	—
61	C₄²×C₁₃	D₈	1	2	yes	—
62	C₄²×C₁₃	C₂×D₄	1	2	yes	—
63	C₄⋊Dic₁₃	—	2	4	no	—
64	C₄⋊Dic₁₃	—	4	4	no	—
65	C₄⋊Dic₁₃	—	4	2	no	—
66	#6090	C₂×Q₈	1	8	yes	complemented
67	C₂×#500	—	13	1	no	—
68	C₂×#500	D₁₃	1	1	yes	characteristic
69	#2252	—	13	8	no	—
70	C₂×#366	—	13	4	no	—
71	C₂×C₄×C₁₆	—	13	1	no	—
72	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
73	Q₈×C₁₃	—	8	8	no	—
74	C₂×C₄×C₁₃	—	4	4	no	—
75	C₂×C₄×C₁₃	—	8	4	no	—
76	C₂×C₄×C₁₃	D₁₆	1	4	yes	—
77	C₂×C₄×C₁₃	Q₃₂	1	4	yes	—
78	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
79	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
81	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
82	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
83	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
84	C₂×Dic₁₃	—	4	4	no	—
85	C₂×Dic₁₃	—	8	4	no	—
86	Dic₂₆	—	8	8	no	—
87	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
88	C₈×C₁₃	C₂×Q₁₆	1	4	yes	—
89	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
90	C₂×C₄⋊Q₈	—	2	1	no	—
91	C₂×C₄⋊Q₈	—	26	1	no	—
92	C₂²×C₁₆	—	13	2	no	—
93	#500	—	2	2	no	—
94	#500	—	13	4	no	—
95	#500	—	26	2	no	—
96	#500	C₂×D₁₃	1	4	yes	—
97	C₂×#107	—	2	1	no	—
98	C₂×#107	—	13	2	no	—
99	C₂×#107	—	26	1	no	—
100	C₂×#107	C₂×D₁₃	1	2	yes	—
101	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
102	#366	—	13	16	no	—
103	C₄×C₁₆	—	13	4	no	—
104	C₂²×C₁₃	#500	1	2	yes	—
105	C₂²×C₁₃	C₂×D₁₆	1	2	yes	—
106	C₂²×C₁₃	C₂×Q₃₂	1	2	yes	—
107	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
108	C₄×C₁₃	—	8	4	no	—
109	C₄×C₁₃	#500	1	2	yes	—
110	C₄×C₁₃	C₂×D₁₆	1	4	yes	—
111	C₄×C₁₃	C₂×Q₃₂	1	4	yes	—
112	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
113	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
114	Dic₁₃	—	8	4	no	—
115	C₂²×Q₈	—	4	1	no	—
116	C₂²×Q₈	—	52	1	no	—
117	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
118	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
119	C₄⋊Q₈	—	2	4	no	—
120	C₄⋊Q₈	—	4	2	no	—
121	C₄⋊Q₈	—	26	4	no	—
122	C₄⋊Q₈	—	52	2	no	—
123	C₂×C₄⋊C₄	—	2	2	no	—
124	C₂×C₄⋊C₄	—	4	1	no	—
125	C₂×C₄⋊C₄	—	26	2	no	—
126	C₂×C₄⋊C₄	—	52	1	no	—
127	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
128	C₂×C₁₆	—	13	8	no	—
129	C₂×C₁₆	—	13	4	no	—
130	#107	—	2	4	no	—
131	#107	—	2	2	no	—
132	#107	—	13	4	no	—
133	#107	—	26	2	no	—
134	#107	—	26	4	no	—
135	#107	C₂²×D₁₃	1	4	yes	—
136	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
137	C₄×C₈	C₂²×D₁₃	1	2	yes	—
138	C₂×C₁₃	#2252	1	4	yes	complemented
139	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
140	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
141	C₂×C₁₃	C₂²×Q₃₂	1	1	yes	characteristic
142	C₂×Q₈	—	4	4	no	—
143	C₂×Q₈	—	8	4	no	—
144	C₂×Q₈	—	52	4	no	—
145	C₂×Q₈	—	104	4	no	—
146	C₂²×C₄	—	4	2	no	—
147	C₂²×C₄	—	52	2	no	—
148	C₂²×C₄	#6104	1	1	yes	characteristic
149	C₂²×C₄	#6104	1	1	yes	characteristic
150	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
151	C₂×C₈	#6107	1	4	yes	—
152	C₂×C₈	Q₈×D₁₃	1	4	yes	—
153	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
154	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
155	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
156	C₄⋊C₄	—	2	4	no	—
157	C₄⋊C₄	—	4	2	no	—
158	C₄⋊C₄	—	4	4	no	—
159	C₄⋊C₄	—	26	4	no	—
160	C₄⋊C₄	—	52	2	no	—
161	C₄⋊C₄	—	52	4	no	—
162	C₄²	#6104	1	2	yes	—
163	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
164	C₁₆	—	13	8	no	—
165	C₁₃	C₂×#2252	1	1	yes	characteristic, complemented, Sylow
166	C₂³	C₂×#6104	1	1	yes	characteristic
167	Q₈	—	8	8	no	—
168	Q₈	—	104	8	no	—
169	C₂×C₄	—	4	4	no	—
170	C₂×C₄	—	8	4	no	—
171	C₂×C₄	—	52	4	no	—
172	C₂×C₄	—	104	4	no	—
173	C₂×C₄	#88066	1	4	yes	—
174	C₂×C₄	#88069	1	4	yes	—
175	C₂×C₄	C₂×#6104	1	1	yes	characteristic
176	C₂×C₄	C₂×#6104	1	2	yes	—
177	C₂×C₄	C₂×#6104	1	2	yes	—
178	C₂×C₄	C₂×#6107	1	2	yes	—
179	C₂×C₄	#88198	1	2	yes	—
180	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
181	C₈	C₂×#6107	1	4	yes	—
182	C₈	#88198	1	2	yes	—
183	C₈	C₂×Q₈×D₁₃	1	2	yes	—
184	C₂²	#11718739	1	2	yes	—
185	C₂²	C₂×#88066	1	2	yes	—
186	C₂²	C₂×#88069	1	2	yes	—
187	C₂²	C₂²×#6104	1	1	yes	characteristic
188	C₄	—	8	4	no	—
189	C₄	—	104	4	no	—
190	C₄	#11718739	1	2	yes	—
191	C₄	C₂×#88066	1	4	yes	—
192	C₄	C₂×#88069	1	4	yes	—
193	C₄	C₂²×#6107	1	1	yes	characteristic
194	C₄	C₂×#88198	1	1	yes	characteristic
195	C₂	#13117109	1	4	yes	direct product factor
196	C₂	C₂×#11718739	1	1	yes	characteristic
197	C₂	C₂²×#88066	1	1	yes	characteristic
198	C₂	C₂²×#88069	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#500	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
hypercenter	C₂×#500	D₁₃
hypocenter	C₁₃	C₂×#2252
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#500

Complements

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

N	H ≅ G/N	type
2. #13117109	C₂	direct (N × H)
41. C₂×#6090	Q₈	semidirect
66. #6090	C₂×Q₈	semidirect
138. C₂×C₁₃	#2252	semidirect
165. C₁₃	C₂×#2252	semidirect
195. C₂	#13117109	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×#11718343	2
#13117109	2
C₂×#11718081	2
C₂×C₄×#6090	2
C₂×C₁₃×#500	2
C₂×#2252	13

Subgroups — C2×#13117109 #16018394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13117109 #16018394