Subgroups — C₂×#13129803 #16787352

Order 3328.

382 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#6092	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6092	C₂	1	1	yes	maximal, characteristic
3	#13129803	C₂	1	4	yes	maximal, direct product factor
4	C₂×#11718491	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Dic₂₆	C₄	1	1	yes	characteristic
6	C₂²×#6092	—	2	1	no	—
7	C₂²×#6092	—	2	1	no	—
8	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
9	C₂×#88054	—	2	1	no	—
10	C₂×C₈×Dic₁₃	—	2	1	no	—
11	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
12	#11718491	—	2	1	no	—
13	#11718491	—	2	1	no	—
14	#11718491	C₄	1	2	yes	—
15	#11718491	C₂²	1	2	yes	—
16	C₄⋊#6092	—	2	1	no	—
17	C₄⋊#6092	C₂²	1	2	yes	—
18	C₄×#6092	—	2	1	no	—
19	C₄×#6092	C₂²	1	2	yes	—
20	C₂²×Dic₂₆	C₈	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	—	2	1	no	—
22	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₃	C₈	1	1	yes	characteristic
24	C₂×#6101	—	2	1	no	—
25	C₂×C₄×Dic₁₃	—	2	1	no	—
26	C₂²×#1055	D₄	1	1	yes	characteristic
27	C₂²×#1055	D₄	1	1	yes	characteristic
28	C₄×Dic₂₆	—	2	1	no	—
29	C₄×Dic₂₆	—	2	1	no	—
30	C₄×Dic₂₆	C₈	1	2	yes	—
31	C₄×Dic₂₆	C₂×C₄	1	2	yes	—
32	C₂×#6092	—	2	4	no	—
33	C₂×#6092	—	2	2	no	—
34	C₂×#6092	—	2	2	no	—
35	C₂×#6092	—	4	2	no	—
36	C₁₃×C₄⋊C₈	—	2	1	no	—
37	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
38	#88054	—	2	2	no	—
39	#88054	—	2	2	no	—
40	C₈×Dic₁₃	—	2	2	no	—
41	C₈×Dic₁₃	—	2	2	no	—
42	C₄×#1055	C₂×C₄	1	1	yes	characteristic
43	C₄×#1055	D₄	1	1	yes	characteristic
44	C₄×#1055	D₄	1	1	yes	characteristic
45	C₄×#1055	C₂³	1	1	yes	characteristic
46	C₂×Q₈⋊C₁₆	—	13	1	no	maximal, Sylow
47	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
50	C₂²×Dic₁₃	—	2	1	no	—
51	C₂²×Dic₁₃	—	2	1	no	—
52	C₂×Dic₂₆	—	2	1	no	—
53	C₂×Dic₂₆	—	2	2	no	—
54	C₂×Dic₂₆	C₁₆	1	4	yes	complemented
55	C₂×Dic₂₆	C₂×C₈	1	2	yes	—
56	C₂×C₈×C₁₃	—	2	2	no	—
57	C₂×C₈×C₁₃	—	4	2	no	—
58	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
59	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
60	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
61	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
62	C₄⋊Dic₁₃	—	2	1	no	—
63	C₄⋊Dic₁₃	C₂×C₈	1	2	yes	—
64	#6101	—	2	2	no	—
65	#6101	—	2	2	no	—
66	C₄×Dic₁₃	—	2	2	no	—
67	C₄×Dic₁₃	—	2	2	no	—
68	C₂×#1055	—	2	2	no	—
69	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×#1055	SD₁₆	1	2	yes	—
72	C₂×#1055	Q₁₆	1	2	yes	—
73	C₂×#1055	C₂×D₄	1	1	yes	characteristic
74	C₂×#1055	C₂×D₄	1	1	yes	characteristic
75	#6092	—	2	4	no	—
76	#6092	—	4	2	no	—
77	C₂×C₈×Q₈	—	13	1	no	—
78	C₂×C₄⋊C₁₆	—	13	1	no	—
79	C₂×C₄×C₁₆	—	13	1	no	—
80	Q₈⋊C₁₆	—	13	4	no	—
81	C₂³×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
82	C₂×C₄×C₁₃	—	2	2	no	—
83	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
86	C₂×C₄×C₁₃	#103	1	2	yes	—
87	C₂×C₄×C₁₃	#104	1	2	yes	—
88	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
89	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
90	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
92	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
93	C₂×Dic₁₃	—	2	4	no	—
94	C₂×Dic₁₃	—	2	2	no	—
95	C₂×Dic₁₃	—	2	2	no	—
96	C₂×Dic₁₃	—	4	2	no	—
97	Dic₂₆	—	2	4	no	—
98	Dic₂₆	—	2	2	no	—
99	Dic₂₆	C₂×C₁₆	1	4	yes	complemented
100	C₈×C₁₃	—	4	2	no	—
101	#1055	—	2	1	no	—
102	#1055	—	2	1	no	—
103	#1055	#103	1	2	yes	—
104	#1055	C₂×SD₁₆	1	1	yes	characteristic
105	#1055	C₂×Q₁₆	1	1	yes	characteristic
106	C₂×C₄×Q₈	—	13	1	no	—
107	C₂²×C₁₆	—	26	1	no	—
108	C₂²×C₁₆	—	26	1	no	—
109	C₈×Q₈	—	13	2	no	—
110	C₈×Q₈	—	13	2	no	—
111	C₈×Q₈	—	26	1	no	—
112	C₈×Q₈	—	26	1	no	—
113	C₂×C₄⋊C₈	—	26	1	no	—
114	C₂×C₄⋊C₈	#261	1	1	yes	characteristic
115	C₂×C₄×C₈	—	13	1	no	—
116	C₂×C₄×C₈	—	26	1	no	—
117	C₄⋊C₁₆	—	13	2	no	—
118	C₄⋊C₁₆	—	26	1	no	—
119	C₄×C₁₆	—	13	2	no	—
120	C₄×C₁₆	—	26	1	no	—
121	C₂²×C₁₃	Q₈⋊C₈	1	2	yes	—
122	C₂²×C₁₃	C₂²⋊C₁₆	1	2	yes	—
123	C₂²×C₁₃	#350	1	2	yes	—
124	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
125	C₄×C₁₃	—	2	1	no	—
126	C₄×C₁₃	—	2	1	no	—
127	C₄×C₁₃	Q₈⋊C₈	1	2	yes	—
128	C₄×C₁₃	C₂²⋊C₁₆	1	2	yes	—
129	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
130	C₄×C₁₃	C₂×#104	1	1	yes	characteristic
131	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
132	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
133	Dic₁₃	—	2	4	no	—
134	Dic₁₃	—	4	2	no	—
135	C₂²×Q₈	—	13	1	no	—
136	C₂²×C₈	—	2	1	no	—
137	C₂²×C₈	—	13	1	no	—
138	C₂²×C₈	—	13	1	no	—
139	C₄×Q₈	—	13	2	no	—
140	C₄×Q₈	—	13	2	no	—
141	C₄×Q₈	—	26	1	no	—
142	C₄×Q₈	—	26	1	no	—
143	C₂×C₄⋊C₄	—	13	1	no	—
144	C₂×C₄⋊C₄	—	26	1	no	—
145	C₂×C₄²	—	26	1	no	—
146	C₂×C₄²	C₂×#261	1	1	yes	characteristic
147	C₂×C₁₆	—	26	2	no	—
148	C₂×C₁₆	—	26	4	no	—
149	C₂×C₁₆	—	26	2	no	—
150	C₂×C₁₆	—	52	2	no	—
151	C₄⋊C₈	—	2	1	no	—
152	C₄⋊C₈	—	26	2	no	—
153	C₄⋊C₈	—	26	2	no	—
154	C₄⋊C₈	C₂×#261	1	2	yes	—
155	C₄×C₈	—	13	1	no	—
156	C₄×C₈	—	13	1	no	—
157	C₄×C₈	—	13	1	no	—
158	C₄×C₈	—	13	1	no	—
159	C₄×C₈	—	26	2	no	—
160	C₄×C₈	—	26	2	no	—
161	C₂×C₁₃	Q₈⋊C₁₆	1	4	yes	complemented
162	C₂×C₁₃	C₂×Q₈⋊C₈	1	1	yes	characteristic
163	C₂×C₁₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
164	C₂×C₁₃	C₂×#350	1	1	yes	characteristic
165	C₂×Q₈	—	13	4	no	—
166	C₂×Q₈	—	13	2	no	—
167	C₂×Q₈	—	26	2	no	—
168	C₂×Q₈	—	26	1	no	—
169	C₂²×C₄	—	26	1	no	—
170	C₂²×C₄	—	26	1	no	—
171	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
172	C₂²×C₄	#6118	1	1	yes	characteristic
173	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	4	2	no	—
176	C₂×C₈	—	13	2	no	—
177	C₂×C₈	—	13	2	no	—
178	C₂×C₈	—	13	1	no	—
179	C₂×C₈	—	13	1	no	—
180	C₂×C₈	—	13	1	no	—
181	C₂×C₈	—	13	1	no	—
182	C₂×C₈	—	26	2	no	—
183	C₄⋊C₄	—	13	2	no	—
184	C₄⋊C₄	—	26	1	no	—
185	C₄⋊C₄	—	26	2	no	—
186	C₄⋊C₄	—	26	2	no	—
187	C₄²	—	26	2	no	—
188	C₄²	—	26	2	no	—
189	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
190	C₄²	#6118	1	1	yes	characteristic
191	C₄²	C₂²⋊#261	1	1	yes	characteristic
192	C₄²	C₂²×#261	1	1	yes	characteristic
193	C₁₆	—	26	4	no	—
194	C₁₆	—	52	2	no	—
195	C₁₃	C₂×Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
196	C₂³	#88111	1	1	yes	characteristic
197	Q₈	—	13	4	no	—
198	Q₈	—	26	4	no	—
199	Q₈	—	26	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	26	4	no	—
202	C₂×C₄	—	26	2	no	—
203	C₂×C₄	—	26	2	no	—
204	C₂×C₄	—	52	2	no	—
205	C₂×C₄	D₁₃⋊C₁₆	1	2	yes	—
206	C₂×C₄	#88098	1	2	yes	—
207	C₂×C₄	#88111	1	1	yes	characteristic
208	C₂×C₄	#88111	1	1	yes	characteristic
209	C₂×C₄	#88111	1	1	yes	characteristic
210	C₂×C₄	#88116	1	2	yes	—
211	C₂×C₄	#88117	1	2	yes	—
212	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
213	C₂×C₄	C₂×#6118	1	1	yes	characteristic
214	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
215	C₈	—	4	2	no	—
216	C₈	—	13	1	no	—
217	C₈	—	13	2	no	—
218	C₈	—	13	1	no	—
219	C₈	—	26	1	no	—
220	C₈	—	26	1	no	—
221	C₂²	#11718244	1	2	yes	—
222	C₂²	#11718259	1	2	yes	—
223	C₂²	#11718270	1	2	yes	—
224	C₂²	C₂×#88111	1	1	yes	characteristic
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	26	4	no	—
228	C₄	—	52	2	no	—
229	C₄	#11718244	1	2	yes	—
230	C₄	#11718259	1	2	yes	—
231	C₄	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
232	C₄	C₂×#88098	1	1	yes	characteristic
233	C₄	C₂×#88116	1	1	yes	characteristic
234	C₄	C₂×#88117	1	1	yes	characteristic
235	C₂	#13129803	1	4	yes	direct product factor
236	C₂	C₂×#11718244	1	1	yes	characteristic
237	C₂	C₂×#11718259	1	1	yes	characteristic
238	C₂	C₂×#11718270	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂²⋊#261
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₄²	C₂²×#261
Fitting	C₂×C₁₃×C₄⋊C₈	C₄
socle, prime radical	C₂³×C₁₃	C₂²⋊C₈
cosocle	C₄×#1055	C₂³
hypercenter	C₂×C₄⋊C₈	#261
hypocenter	C₁₃	C₂×Q₈⋊C₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13129803	C₂	direct (N × H)
54. C₂×Dic₂₆	C₁₆	semidirect
99. Dic₂₆	C₂×C₁₆	semidirect
161. C₂×C₁₃	Q₈⋊C₁₆	semidirect
195. C₁₃	C₂×Q₈⋊C₁₆	semidirect
235. C₂	#13129803	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×C₄⋊#6092	2
C₂×C₄×#6092	2
#13129803	2
C₂×#11718491	2
C₂×Q₈⋊C₁₆	13

Subgroups — C2×#13129803 #16787352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129803 #16787352