Subgroups — C₂×#13113745 #15832683

Order 3328.

654 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718685	C₂	1	2	yes	maximal
2	#13113745	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718049	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈⋊#1055	C₂	1	2	yes	maximal
5	C₂×#11718047	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×Q₁₆	C₄	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
9	C₄×C₁₃×Q₁₆	C₄	1	4	yes	—
10	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	—
11	C₂×C₁₃×#107	C₄	1	1	yes	characteristic
12	C₂×C₁₃×#103	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	#11718685	—	2	4	no	—
15	#11718685	C₂²	1	8	yes	—
16	C₂×C₄⋊#1055	—	2	2	no	—
17	C₂×C₄⋊#1055	C₂²	1	2	yes	—
18	C₂×#88043	—	2	2	no	—
19	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
20	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
21	Q₈⋊#1055	C₂²	1	8	yes	—
22	#11718049	C₂²	1	4	yes	—
23	#11718047	C₂²	1	4	yes	—
24	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₁₃×Q₁₆	—	2	4	no	—
26	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₄×Q₈×C₁₃	—	2	2	no	—
30	C₄×Q₈×C₁₃	—	2	2	no	—
31	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	—
32	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
35	C₂×C₄²×C₁₃	—	2	2	no	—
36	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×#1055	—	2	2	no	—
38	C₂²×#1055	—	2	1	no	—
39	C₂²×#1055	D₄	1	2	yes	—
40	C₁₃×#107	C₂×C₄	1	4	yes	—
41	C₁₃×#103	C₂×C₄	1	8	yes	—
42	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
43	C₄×C₈×C₁₃	C₂³	1	2	yes	—
44	C₄⋊#1055	—	2	2	no	—
45	C₄⋊#1055	—	2	8	no	—
46	C₄⋊#1055	C₂³	1	4	yes	—
47	#88043	—	2	8	no	—
48	C₄×#1055	—	2	1	no	—
49	C₄×#1055	D₄	1	2	yes	—
50	C₄×#1055	C₂³	1	2	yes	—
51	C₄×#1055	C₂³	1	2	yes	—
52	C₂×#1593	—	13	1	no	maximal, Sylow
53	C₂×Q₈×C₁₃	—	2	2	no	—
54	C₂×Q₈×C₁₃	—	2	4	no	—
55	C₂×Q₈×C₁₃	—	2	4	no	—
56	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
57	C₂²×C₄×C₁₃	—	2	2	no	—
58	C₂²×C₄×C₁₃	—	2	2	no	—
59	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
62	C₁₃×Q₁₆	—	2	8	no	—
63	C₂×C₈×C₁₃	—	2	2	no	—
64	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
65	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
66	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
67	C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₁₃×C₄⋊C₄	—	2	4	no	—
70	C₁₃×C₄⋊C₄	C₂²×C₄	1	4	yes	—
71	C₄²×C₁₃	—	2	4	no	—
72	C₄²×C₁₃	—	2	4	no	—
73	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₃	#41	1	1	yes	characteristic
76	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
77	C₂×#1055	—	2	4	no	—
78	C₂×#1055	—	2	4	no	—
79	C₂×#1055	—	2	2	no	—
80	C₂×#1055	—	4	2	no	—
81	C₂×#1055	—	4	4	no	—
82	C₂×#1055	C₂×D₄	1	4	yes	—
83	C₂×#446	—	13	2	no	—
84	C₂×C₄×Q₁₆	D₁₃	1	1	yes	characteristic
85	#1593	—	13	8	no	—
86	C₂×#334	—	13	1	no	—
87	C₂×Q₈⋊C₈	—	13	2	no	—
88	C₂×#322	—	13	1	no	—
89	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
90	Q₈×C₁₃	—	2	4	no	—
91	Q₈×C₁₃	—	2	4	no	—
92	Q₈×C₁₃	—	4	4	no	—
93	C₂×C₄×C₁₃	—	2	2	no	—
94	C₂×C₄×C₁₃	—	2	4	no	—
95	C₂×C₄×C₁₃	—	2	4	no	—
96	C₂×C₄×C₁₃	—	4	4	no	—
97	C₂×C₄×C₁₃	—	4	4	no	—
98	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
101	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
102	C₂×C₄×C₁₃	#131	1	2	yes	—
103	C₂×C₄×C₁₃	#137	1	4	yes	—
104	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
106	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
107	C₈×C₁₃	—	2	2	no	—
108	C₈×C₁₃	C₂×M₁₆	1	4	yes	—
109	#1055	—	2	4	no	—
110	#1055	—	4	2	no	—
111	#1055	—	4	4	no	—
112	C₂²×Q₁₆	Dic₁₃	1	1	yes	characteristic
113	C₂×C₄×Q₈	C₂×D₁₃	1	2	yes	—
114	#446	—	13	8	no	—
115	#446	—	26	4	no	—
116	C₄×Q₁₆	Dic₁₃	1	4	yes	—
117	C₄×Q₁₆	C₂×D₁₃	1	4	yes	—
118	C₂×#107	Dic₁₃	1	1	yes	characteristic
119	C₂×C₄⋊C₈	—	13	2	no	—
120	C₂×C₄⋊C₈	—	26	2	no	—
121	C₂×#103	Dic₁₃	1	2	yes	—
122	C₂×#97	—	26	2	no	—
123	C₂×C₄×C₈	—	13	1	no	—
124	C₂×C₄×C₈	—	13	1	no	—
125	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
126	#334	—	13	4	no	—
127	Q₈⋊C₈	—	13	8	no	—
128	#322	—	13	4	no	—
129	C₂²×C₁₃	#436	1	2	yes	—
130	C₂²×C₁₃	#441	1	2	yes	—
131	C₂²×C₁₃	#444	1	2	yes	—
132	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
133	C₄×C₁₃	—	2	1	no	—
134	C₄×C₁₃	—	2	1	no	—
135	C₄×C₁₃	—	4	4	no	—
136	C₄×C₁₃	—	4	4	no	—
137	C₄×C₁₃	#436	1	2	yes	—
138	C₄×C₁₃	#441	1	2	yes	—
139	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
140	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
141	C₄×C₁₃	C₂×#137	1	2	yes	—
142	C₂²×Q₈	C₂×Dic₁₃	1	2	yes	—
143	C₂×Q₁₆	—	2	4	no	—
144	C₂×Q₁₆	C₂×Dic₁₃	1	4	yes	—
145	C₂²×C₈	—	13	2	no	—
146	C₂²×C₈	—	26	2	no	—
147	C₂²×C₈	—	26	1	no	—
148	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
149	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
150	C₄×Q₈	—	2	2	no	—
151	C₄×Q₈	—	2	2	no	—
152	C₄×Q₈	C₂×Dic₁₃	1	4	yes	—
153	C₄×Q₈	C₂²×D₁₃	1	4	yes	—
154	C₂×C₄⋊C₄	—	2	2	no	—
155	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
156	C₂×C₄²	—	2	2	no	—
157	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
158	#107	C₂×Dic₁₃	1	4	yes	—
159	C₄⋊C₈	—	13	4	no	—
160	C₄⋊C₈	—	26	8	no	—
161	C₄⋊C₈	—	26	2	no	—
162	#103	C₂×Dic₁₃	1	8	yes	—
163	#97	—	26	8	no	—
164	C₄×C₈	—	13	2	no	—
165	C₄×C₈	—	13	2	no	—
166	C₄×C₈	—	13	2	no	—
167	C₄×C₈	—	26	1	no	—
168	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
169	C₄×C₈	C₂²×D₁₃	1	2	yes	—
170	C₂×C₁₃	#1593	1	4	yes	complemented
171	C₂×C₁₃	C₂×#436	1	1	yes	characteristic
172	C₂×C₁₃	C₂×#441	1	1	yes	characteristic
173	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	2	4	no	—
176	C₂×Q₈	—	2	4	no	—
177	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	2	2	no	—
180	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
181	C₂²×C₄	#6129	1	1	yes	characteristic
182	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
183	Q₁₆	—	2	8	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	13	4	no	—
186	C₂×C₈	—	26	4	no	—
187	C₂×C₈	—	26	4	no	—
188	C₂×C₈	—	26	2	no	—
189	C₂×C₈	—	52	2	no	—
190	C₂×C₈	—	52	4	no	—
191	C₂×C₈	#6099	1	4	yes	—
192	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
193	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	2	2	no	—
196	C₄⋊C₄	—	2	4	no	—
197	C₄⋊C₄	C₂²×Dic₁₃	1	4	yes	—
198	C₄²	—	2	4	no	—
199	C₄²	—	2	4	no	—
200	C₄²	D₄×D₁₃	1	1	yes	characteristic
201	C₄²	#6129	1	1	yes	characteristic
202	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
203	C₄²	C₂³×D₁₃	1	1	yes	characteristic
204	C₁₃	C₂×#1593	1	1	yes	characteristic, complemented, Sylow
205	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
206	Q₈	—	2	4	no	—
207	Q₈	—	2	4	no	—
208	Q₈	—	4	4	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	4	no	—
211	C₂×C₄	—	2	4	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	—	4	4	no	—
214	C₂×C₄	#88172	1	4	yes	—
215	C₂×C₄	C₂×#6099	1	2	yes	—
216	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
217	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
218	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
219	C₂×C₄	#88202	1	2	yes	—
220	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
221	C₂×C₄	C₂×#6129	1	1	yes	characteristic
222	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
223	C₈	—	2	2	no	—
224	C₈	—	26	4	no	—
225	C₈	—	52	2	no	—
226	C₈	—	52	4	no	—
227	C₈	C₂×#6099	1	4	yes	—
228	C₂²	#11718673	1	2	yes	—
229	C₂²	#11718845	1	2	yes	—
230	C₂²	#11718858	1	2	yes	—
231	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	4	no	—
235	C₄	—	4	4	no	—
236	C₄	#11718673	1	2	yes	—
237	C₄	#11718845	1	2	yes	—
238	C₄	C₂×#88172	1	2	yes	—
239	C₄	C₂²×#6099	1	1	yes	characteristic
240	C₄	C₂×#88202	1	1	yes	characteristic
241	C₂	#13113745	1	4	yes	direct product factor
242	C₂	C₂×#11718673	1	1	yes	characteristic
243	C₂	C₂×#11718845	1	1	yes	characteristic
244	C₂	C₂×#11718858	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×Q₁₆	C₂
socle, prime radical	C₂³×C₁₃	C₄×D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×C₄×Q₁₆	D₁₃
hypocenter	C₁₃	C₂×#1593
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
2. #13113745	C₂	direct (N × H)
170. C₂×C₁₃	#1593	semidirect
204. C₁₃	C₂×#1593	semidirect
241. C₂	#13113745	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×#11718685	2
#13113745	2
C₂×#11718049	2
C₂×Q₈⋊#1055	2
C₂×#11718047	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×#1593	13

Subgroups — C2×#13113745 #15832683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13113745 #15832683