Subgroups — C₂×#13117119 #16018413

Order 3328.

518 conjugacy classes of subgroups.

The subgroup lattice has 220 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	#13117119	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×#11718053	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
8	C₂×#88124	—	2	1	no	—
9	C₁₃×#500	—	2	2	no	—
10	C₁₃×#500	C₂²	1	4	yes	—
11	C₂×C₁₃×#107	—	2	1	no	—
12	C₂×C₁₃×#107	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88058	C₂²	1	1	yes	characteristic
15	C₂×#88058	C₂²	1	1	yes	characteristic
16	C₂×#88057	—	2	1	no	—
17	C₂²×#6090	C₂²	1	2	yes	—
18	#11718344	—	2	2	no	—
19	#11718344	C₂²	1	4	yes	—
20	#11718082	C₂²	1	8	yes	—
21	#11718081	C₂²	1	8	yes	—
22	#11718053	C₂²	1	4	yes	—
23	C₂²×Q₈×C₁₃	—	4	1	no	—
24	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
26	C₁₃×C₄⋊Q₈	—	2	4	no	—
27	C₁₃×C₄⋊Q₈	—	4	2	no	—
28	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
30	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
31	C₂×C₄⋊Dic₁₃	—	2	1	no	—
32	C₂×C₄⋊Dic₁₃	—	2	1	no	—
33	C₂×#6101	—	4	1	no	—
34	C₂×#6101	—	4	1	no	—
35	#88124	—	2	4	no	—
36	#88124	—	4	2	no	—
37	C₁₃×#107	—	2	4	no	—
38	C₁₃×#107	—	2	2	no	—
39	C₁₃×#107	C₂³	1	4	yes	—
40	C₄×C₈×C₁₃	D₄	1	2	yes	—
41	C₄×C₈×C₁₃	C₂³	1	2	yes	—
42	#88058	—	2	1	no	—
43	#88058	—	2	1	no	—
44	#88058	C₂³	1	2	yes	—
45	#88058	C₂³	1	2	yes	—
46	#88057	—	2	4	no	—
47	C₂×#6090	Q₈	1	8	yes	complemented
48	C₂×#6090	C₂³	1	4	yes	—
49	C₂×#2255	—	13	1	no	maximal, Sylow
50	C₂×Q₈×C₁₃	—	4	4	no	—
51	C₂×Q₈×C₁₃	—	8	4	no	—
52	C₂²×C₄×C₁₃	—	4	2	no	—
53	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×Dic₁₃	—	4	1	no	—
57	C₂²×Dic₁₃	—	4	1	no	—
58	C₂×C₈×C₁₃	Q₁₆	1	4	yes	—
59	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
61	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
62	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
63	C₁₃×C₄⋊C₄	—	2	4	no	—
64	C₁₃×C₄⋊C₄	—	4	2	no	—
65	C₁₃×C₄⋊C₄	—	4	4	no	—
66	C₄²×C₁₃	D₈	1	2	yes	—
67	C₄²×C₁₃	C₂×D₄	1	2	yes	—
68	C₄⋊Dic₁₃	—	2	2	no	—
69	C₄⋊Dic₁₃	—	2	2	no	—
70	C₄⋊Dic₁₃	—	4	1	no	—
71	C₄⋊Dic₁₃	—	4	1	no	—
72	#6101	—	4	4	no	—
73	#6101	—	4	4	no	—
74	#6090	C₂×Q₈	1	8	yes	complemented
75	C₂×#500	D₁₃	1	1	yes	characteristic
76	C₂×#499	—	13	1	no	—
77	#2255	—	13	8	no	—
78	C₂×#367	—	13	2	no	—
79	C₂×#366	—	13	2	no	—
80	C₂×#346	—	13	1	no	—
81	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
82	Q₈×C₁₃	—	8	8	no	—
83	C₂×C₄×C₁₃	—	2	2	no	—
84	C₂×C₄×C₁₃	—	2	2	no	—
85	C₂×C₄×C₁₃	—	4	4	no	—
86	C₂×C₄×C₁₃	—	8	4	no	—
87	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
88	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
89	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
90	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
92	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
93	C₂×Dic₁₃	—	4	2	no	—
94	C₂×Dic₁₃	—	4	2	no	—
95	C₂×Dic₁₃	—	8	2	no	—
96	C₂×Dic₁₃	—	8	2	no	—
97	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
98	C₈×C₁₃	C₂×Q₁₆	1	4	yes	—
99	C₈×C₁₃	C₂²×Q₈	1	2	yes	—
100	C₂×C₄⋊Q₈	—	2	1	no	—
101	C₂×#125	—	26	1	no	—
102	C₂²×C₁₆	—	13	2	no	—
103	#500	—	2	2	no	—
104	#500	C₂×D₁₃	1	4	yes	—
105	#499	—	13	4	no	—
106	#499	—	26	2	no	—
107	C₂×#107	—	2	1	no	—
108	C₂×#107	—	13	1	no	—
109	C₂×#107	—	13	1	no	—
110	C₂×#107	C₂×D₁₃	1	2	yes	—
111	C₂×#106	—	26	1	no	—
112	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
113	#367	—	13	8	no	—
114	#366	—	13	8	no	—
115	#346	—	13	4	no	—
116	C₂²×C₁₃	#500	1	2	yes	—
117	C₂²×C₁₃	#509	1	2	yes	—
118	C₂²×C₁₃	#510	1	2	yes	—
119	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
120	C₄×C₁₃	—	2	2	no	—
121	C₄×C₁₃	—	2	2	no	—
122	C₄×C₁₃	—	8	4	no	—
123	C₄×C₁₃	#500	1	2	yes	—
124	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
125	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
126	Dic₁₃	—	8	2	no	—
127	Dic₁₃	—	8	2	no	—
128	C₂²×Q₈	—	4	1	no	—
129	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
130	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
131	C₄⋊Q₈	—	2	4	no	—
132	C₄⋊Q₈	—	4	2	no	—
133	#125	—	26	4	no	—
134	#125	—	52	2	no	—
135	C₂×C₄⋊C₄	—	2	2	no	—
136	C₂×C₄⋊C₄	—	4	1	no	—
137	C₂×C₄⋊C₄	—	26	1	no	—
138	C₂×C₄⋊C₄	—	26	1	no	—
139	C₂×C₄⋊C₄	—	52	1	no	—
140	C₂×C₄⋊C₄	—	52	1	no	—
141	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
142	C₂×C₁₆	—	13	8	no	—
143	C₂×C₁₆	—	13	4	no	—
144	#107	—	2	4	no	—
145	#107	—	2	2	no	—
146	#107	—	13	2	no	—
147	#107	—	13	2	no	—
148	#107	—	26	1	no	—
149	#107	—	26	1	no	—
150	#107	C₂²×D₁₃	1	4	yes	—
151	#106	—	26	4	no	—
152	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
153	C₄×C₈	C₂²×D₁₃	1	2	yes	—
154	C₂×C₁₃	#2255	1	4	yes	complemented
155	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
156	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
157	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
158	C₂×Q₈	—	4	4	no	—
159	C₂×Q₈	—	8	4	no	—
160	C₂²×C₄	—	4	2	no	—
161	C₂²×C₄	—	52	1	no	—
162	C₂²×C₄	—	52	1	no	—
163	C₂²×C₄	#6104	1	1	yes	characteristic
164	C₂²×C₄	#6104	1	1	yes	characteristic
165	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
166	C₂×C₈	#6107	1	4	yes	—
167	C₂×C₈	Q₈×D₁₃	1	4	yes	—
168	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
169	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
170	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
171	C₄⋊C₄	—	2	4	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	4	4	no	—
174	C₄⋊C₄	—	26	2	no	—
175	C₄⋊C₄	—	26	2	no	—
176	C₄⋊C₄	—	52	1	no	—
177	C₄⋊C₄	—	52	1	no	—
178	C₄⋊C₄	—	52	4	no	—
179	C₄⋊C₄	—	52	4	no	—
180	C₄²	#6104	1	2	yes	—
181	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
182	C₁₆	—	13	8	no	—
183	C₁₃	C₂×#2255	1	1	yes	characteristic, complemented, Sylow
184	C₂³	C₂×#6104	1	1	yes	characteristic
185	Q₈	—	8	8	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	4	4	no	—
189	C₂×C₄	—	8	4	no	—
190	C₂×C₄	—	52	2	no	—
191	C₂×C₄	—	52	2	no	—
192	C₂×C₄	—	104	2	no	—
193	C₂×C₄	—	104	2	no	—
194	C₂×C₄	C₂×#6104	1	2	yes	—
195	C₂×C₄	C₂×#6104	1	2	yes	—
196	C₂×C₄	C₂×#6104	1	1	yes	characteristic
197	C₂×C₄	C₂×#6107	1	2	yes	—
198	C₂×C₄	#88198	1	2	yes	—
199	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
200	C₈	C₂×#6107	1	4	yes	—
201	C₈	#88198	1	2	yes	—
202	C₈	C₂×Q₈×D₁₃	1	2	yes	—
203	C₂²	#11718739	1	2	yes	—
204	C₂²	#11718808	1	2	yes	—
205	C₂²	#11718840	1	2	yes	—
206	C₂²	C₂²×#6104	1	1	yes	characteristic
207	C₄	—	2	2	no	—
208	C₄	—	2	2	no	—
209	C₄	—	8	4	no	—
210	C₄	—	104	2	no	—
211	C₄	—	104	2	no	—
212	C₄	#11718739	1	2	yes	—
213	C₄	C₂²×#6107	1	1	yes	characteristic
214	C₄	C₂×#88198	1	1	yes	characteristic
215	C₂	#13117119	1	4	yes	direct product factor
216	C₂	C₂×#11718739	1	1	yes	characteristic
217	C₂	C₂×#11718808	1	1	yes	characteristic
218	C₂	C₂×#11718840	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×#2255
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. #13117119	C₂	direct (N × H)
47. C₂×#6090	Q₈	semidirect
74. #6090	C₂×Q₈	semidirect
154. C₂×C₁₃	#2255	semidirect
183. C₁₃	C₂×#2255	semidirect
215. C₂	#13117119	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
#13117119	2
C₂×#11718082	2
C₂×#11718081	2
C₂×#11718053	2
C₂×C₁₃×#500	2
C₂×#2255	13

Subgroups — C2×#13117119 #16018413

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13117119 #16018413