Subgroups — C₂×#13129896 #16789103

Order 3328.

574 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88104	C₂	1	2	yes	maximal
2	#13129896	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#6118	—	2	2	no	—
5	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
6	C₂×#88104	—	2	2	no	—
7	C₂×#88104	—	2	4	no	—
8	C₂×#88104	C₄	1	8	yes	—
9	C₂×#88104	C₂²	1	4	yes	—
10	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
11	C₂²×#6090	C₄	1	1	yes	characteristic
12	C₂×C₁₆×D₁₃	—	2	4	no	—
13	C₂×C₁₆×D₁₃	C₄	1	2	yes	—
14	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
15	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
16	C₂²×#1057	—	4	2	no	—
17	C₂×#6118	—	2	8	no	—
18	C₂×#6118	—	2	4	no	—
19	C₂×#6118	—	4	2	no	—
20	C₂×#6118	—	4	4	no	—
21	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×#1055	Q₈	1	1	yes	characteristic
23	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
25	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
26	C₂×C₈×D₁₃	D₄	1	4	yes	—
27	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
28	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
29	#88104	—	2	8	no	—
30	#88104	—	2	4	no	—
31	#88104	C₂×C₄	1	8	yes	—
32	C₂×C₁₃×C₁₆	—	2	2	no	—
33	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
34	C₂×#6090	—	2	2	no	—
35	C₂×#6090	C₂×C₄	1	2	yes	—
36	C₁₆×D₁₃	—	2	4	no	—
37	C₁₆×D₁₃	—	2	4	no	—
38	C₂×#1381	—	13	1	no	maximal, Sylow
39	C₂³×D₁₃	Q₁₆	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
41	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
42	C₂×C₄×D₁₃	C₂²⋊C₄	1	4	yes	—
43	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
45	C₂×C₄×D₁₃	SD₁₆	1	4	yes	—
46	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
47	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂×#1057	—	4	8	no	—
49	C₂×#1057	—	4	4	no	—
50	#6118	—	2	8	no	—
51	#6118	—	4	8	no	—
52	#6118	—	4	4	no	—
53	C₂×C₈×C₁₃	C₄²	1	2	yes	—
54	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
58	C₂×#1055	C₄⋊C₄	1	4	yes	—
59	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
60	C₈×D₁₃	C₄²	1	2	yes	—
61	C₈×D₁₃	C₂²⋊C₄	1	4	yes	—
62	C₈×D₁₃	C₂²⋊C₄	1	2	yes	—
63	C₈×D₁₃	C₄⋊C₄	1	4	yes	—
64	C₈×D₁₃	C₂²×C₄	1	2	yes	—
65	C₈×D₁₃	C₂×D₄	1	2	yes	—
66	C₁₃×C₁₆	—	2	2	no	—
67	#6090	—	2	2	no	—
68	C₂³×C₁₆	—	13	1	no	—
69	C₂²×#108	—	13	2	no	—
70	#1381	—	13	4	no	—
71	C₂³×C₁₃	#107	1	1	yes	characteristic
72	C₂²×D₁₃	—	2	2	no	—
73	C₂²×D₁₃	—	2	2	no	—
74	C₂²×D₁₃	#103	1	4	yes	—
75	C₂²×D₁₃	#107	1	1	yes	characteristic
76	C₂²×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
77	C₂×C₄×C₁₃	#95	1	2	yes	—
78	C₂×C₄×C₁₃	#106	1	2	yes	—
79	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₂×Dic₁₃	#102	1	4	yes	—
82	C₂×Dic₁₃	#107	1	1	yes	characteristic
83	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
84	C₄×D₁₃	#95	1	2	yes	—
85	C₄×D₁₃	#102	1	4	yes	—
86	C₄×D₁₃	#103	1	4	yes	—
87	C₄×D₁₃	#106	1	2	yes	—
88	C₄×D₁₃	C₂×C₂²⋊C₄	1	2	yes	—
89	C₄×D₁₃	C₂×SD₁₆	1	2	yes	—
90	#1057	—	4	8	no	—
91	C₈×C₁₃	#95	1	2	yes	—
92	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
93	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	#1055	#95	1	2	yes	—
95	#1055	C₂×C₄⋊C₄	1	2	yes	—
96	C₂²×M₁₆	—	26	2	no	—
97	C₂³×C₈	—	13	1	no	—
98	C₂²×C₁₆	—	13	1	no	—
99	C₂²×C₁₆	—	13	2	no	—
100	C₂²×C₁₆	—	13	2	no	—
101	C₂²×C₁₆	—	26	4	no	—
102	C₂²×C₁₆	#261	1	1	yes	characteristic
103	C₂×#108	—	13	4	no	—
104	C₂×#108	—	13	8	no	—
105	C₂×#108	—	26	2	no	—
106	C₂×#108	—	26	4	no	—
107	C₂²×C₁₃	#340	1	2	yes	—
108	C₂²×C₁₃	#368	1	2	yes	—
109	C₂²×C₁₃	#368	1	2	yes	—
110	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
111	C₂×D₁₃	—	2	8	no	—
112	C₂×D₁₃	—	2	1	no	—
113	C₂×D₁₃	—	2	1	no	—
114	C₂×D₁₃	—	2	1	no	—
115	C₂×D₁₃	—	2	1	no	—
116	C₂×D₁₃	#340	1	2	yes	—
117	C₂×D₁₃	C₂×#103	1	2	yes	—
118	C₄×C₁₃	#340	1	2	yes	—
119	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
120	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
121	Dic₁₃	#340	1	2	yes	—
122	Dic₁₃	C₂×#102	1	2	yes	—
123	C₂³×C₄	—	13	1	no	—
124	C₂×M₁₆	—	26	8	no	—
125	C₂×M₁₆	—	26	4	no	—
126	C₂×M₁₆	—	52	4	no	—
127	C₂×M₁₆	—	52	2	no	—
128	C₂²×C₈	—	13	1	no	—
129	C₂²×C₈	—	13	4	no	—
130	C₂²×C₈	—	13	1	no	—
131	C₂²×C₈	—	13	1	no	—
132	C₂²×C₈	—	13	4	no	—
133	C₂²×C₈	—	13	1	no	—
134	C₂²×C₈	—	13	1	no	—
135	C₂²×C₈	—	52	2	no	—
136	C₂²×C₈	C₂×#261	1	1	yes	characteristic
137	C₂×C₁₆	—	2	2	no	—
138	C₂×C₁₆	—	13	2	no	—
139	C₂×C₁₆	—	26	4	no	—
140	C₂×C₁₆	—	26	4	no	—
141	C₂×C₁₆	—	26	2	no	—
142	C₂×C₁₆	C₂×#261	1	2	yes	—
143	#108	—	13	8	no	—
144	#108	—	26	8	no	—
145	#108	—	26	4	no	—
146	C₂×C₁₃	#1381	1	4	yes	complemented
147	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
148	C₂×C₁₃	C₂×#368	1	1	yes	characteristic
149	C₂×C₁₃	C₂×#368	1	1	yes	characteristic
150	D₁₃	—	2	2	no	—
151	D₁₃	—	2	2	no	—
152	C₂⁴	—	13	1	no	—
153	C₂²×C₄	—	13	1	no	—
154	C₂²×C₄	—	13	4	no	—
155	C₂²×C₄	—	13	1	no	—
156	C₂²×C₄	—	13	1	no	—
157	C₂²×C₄	—	13	4	no	—
158	C₂²×C₄	—	13	1	no	—
159	C₂²×C₄	—	13	1	no	—
160	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
161	M₁₆	—	26	8	no	—
162	M₁₆	—	52	8	no	—
163	M₁₆	—	52	4	no	—
164	C₂×C₈	—	13	4	no	—
165	C₂×C₈	—	13	1	no	—
166	C₂×C₈	—	13	1	no	—
167	C₂×C₈	—	13	4	no	—
168	C₂×C₈	—	13	4	no	—
169	C₂×C₈	—	13	2	no	—
170	C₂×C₈	—	13	2	no	—
171	C₂×C₈	—	13	2	no	—
172	C₂×C₈	—	13	2	no	—
173	C₂×C₈	—	52	8	no	—
174	C₂×C₈	—	52	4	no	—
175	C₂×C₈	C₄×#261	1	2	yes	—
176	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
177	C₂×C₈	C₂²⋊#261	1	2	yes	—
178	C₂×C₈	C₂²×#261	1	1	yes	characteristic
179	C₁₆	—	2	2	no	—
180	C₁₆	—	26	2	no	—
181	C₁₃	C₂×#1381	1	1	yes	characteristic, complemented, Sylow
182	C₂³	—	13	4	no	—
183	C₂³	—	13	1	no	—
184	C₂³	—	13	1	no	—
185	C₂³	—	26	2	no	—
186	C₂³	—	26	2	no	—
187	C₂³	#88102	1	1	yes	characteristic
188	C₂×C₄	—	13	4	no	—
189	C₂×C₄	—	13	1	no	—
190	C₂×C₄	—	13	1	no	—
191	C₂×C₄	—	13	4	no	—
192	C₂×C₄	—	13	4	no	—
193	C₂×C₄	—	13	2	no	—
194	C₂×C₄	—	13	2	no	—
195	C₂×C₄	—	13	2	no	—
196	C₂×C₄	—	13	2	no	—
197	C₂×C₄	#88101	1	2	yes	—
198	C₂×C₄	#88102	1	1	yes	characteristic
199	C₂×C₄	(C₂×#261)⋊C₄	1	2	yes	—
200	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
201	C₈	—	13	2	no	—
202	C₈	—	13	2	no	—
203	C₈	—	52	8	no	—
204	C₈	(C₂×#261)⋊C₄	1	2	yes	—
205	C₈	C₂×C₄×#261	1	1	yes	characteristic
206	C₈	C₂×C₂²⋊#261	1	1	yes	characteristic
207	C₂²	—	13	2	no	—
208	C₂²	—	13	2	no	—
209	C₂²	—	26	8	no	—
210	C₂²	—	26	1	no	—
211	C₂²	—	26	1	no	—
212	C₂²	—	26	1	no	—
213	C₂²	—	26	1	no	—
214	C₂²	#11718223	1	2	yes	—
215	C₂²	#11718224	1	2	yes	—
216	C₂²	#11718265	1	2	yes	—
217	C₂²	C₂×#88102	1	1	yes	characteristic
218	C₄	—	13	2	no	—
219	C₄	—	13	2	no	—
220	C₄	#11718265	1	2	yes	—
221	C₄	C₂×#88101	1	1	yes	characteristic
222	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
223	C₂	—	26	2	no	—
224	C₂	—	26	2	no	—
225	C₂	#13129896	1	4	yes	direct product factor
226	C₂	C₂×#11718265	1	1	yes	characteristic
227	C₂	C₂×#11718223	1	1	yes	characteristic
228	C₂	C₂×#11718224	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#88102
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×#261
Fitting	C₂²×C₁₃×C₁₆	C₄
socle	C₂³×C₁₃	#107
prime radical	C₂³×D₁₃	Q₁₆
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	C₂²×C₁₆	#261
hypocenter	C₁₃	C₂×#1381
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #13129896	C₂	direct (N × H)
146. C₂×C₁₃	#1381	semidirect
181. C₁₃	C₂×#1381	semidirect
225. C₂	#13129896	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#88104	2
#13129896	2
C₂²×C₁₆×D₁₃	2
C₂×#1381	13

Subgroups — C2×#13129896 #16789103

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129896 #16789103