Subgroups — C₂×#13114453 #15850613

Order 3328.

878 conjugacy classes of subgroups.

The subgroup lattice has 244 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	C₂×#11718739	C₂	1	2	yes	maximal
3	C₂×#11718753	C₂	1	2	yes	maximal
4	#13114453	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₈×#1055	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₂²×#6107	—	2	4	no	—
9	C₂×#88123	C₂²	1	2	yes	—
10	C₁₃×#500	—	2	2	no	—
11	C₁₃×#500	C₂²	1	4	yes	—
12	C₂×C₁₃×#107	—	2	2	no	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×#88058	—	2	2	no	—
15	#11718753	—	2	4	no	—
16	#11718753	C₂²	1	8	yes	—
17	#11718739	—	2	4	no	—
18	#11718739	C₂²	1	8	yes	—
19	C₂×#88047	—	2	4	no	—
20	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
21	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
22	#11718343	—	2	2	no	—
23	#11718343	C₂²	1	4	yes	—
24	C₈×#1055	C₂²	1	4	yes	—
25	C₂²×Q₈×C₁₃	—	2	2	no	—
26	C₂²×Dic₂₆	—	2	2	no	—
27	C₂²×C₈×C₁₃	D₄	1	2	yes	—
28	C₁₃×C₄⋊Q₈	—	2	2	no	—
29	C₁₃×C₄⋊Q₈	—	2	2	no	—
30	C₁₃×C₄⋊Q₈	—	2	2	no	—
31	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
32	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
33	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
34	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
35	C₂×#6107	—	2	16	no	—
36	C₂×#6107	—	4	16	no	—
37	C₂×C₄⋊Dic₁₃	—	2	2	no	—
38	C₂×C₄⋊Dic₁₃	—	2	2	no	—
39	C₂²×#1055	D₄	1	2	yes	—
40	C₂²×#1055	D₄	1	2	yes	—
41	#88123	—	2	2	no	—
42	#88123	—	2	2	no	—
43	#88123	—	2	2	no	—
44	#88123	C₂³	1	4	yes	—
45	C₁₃×#107	—	2	8	no	—
46	C₄×C₈×C₁₃	D₄	1	2	yes	—
47	C₄×C₈×C₁₃	C₂³	1	2	yes	—
48	#88058	—	2	8	no	—
49	#88047	—	2	16	no	—
50	C₄×#1055	D₄	1	2	yes	—
51	C₄×#1055	D₄	1	2	yes	—
52	C₄×#1055	C₂³	1	2	yes	—
53	C₄×#1055	C₂³	1	2	yes	—
54	C₂×#1713	—	13	1	no	maximal, Sylow
55	C₂×Q₈×C₁₃	—	2	4	no	—
56	C₂×Q₈×C₁₃	—	4	2	no	—
57	C₂×Q₈×C₁₃	—	4	8	no	—
58	C₂²×C₄×C₁₃	—	4	2	no	—
59	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
62	C₂²×Dic₁₃	—	4	2	no	—
63	C₂×Dic₂₆	—	2	4	no	—
64	C₂×Dic₂₆	—	4	8	no	—
65	C₂×Dic₂₆	—	4	2	no	—
66	C₂×C₈×C₁₃	Q₁₆	1	8	yes	complemented
67	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
68	C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₁₃×C₄⋊C₄	—	2	4	no	—
70	C₁₃×C₄⋊C₄	—	4	2	no	—
71	C₁₃×C₄⋊C₄	—	4	2	no	—
72	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
76	#6107	—	4	32	no	—
77	C₄⋊Dic₁₃	—	2	4	no	—
78	C₄⋊Dic₁₃	—	2	4	no	—
79	C₄⋊Dic₁₃	—	4	2	no	—
80	C₄⋊Dic₁₃	—	4	2	no	—
81	C₂×#1055	D₈	1	8	yes	—
82	C₂×#1055	Q₁₆	1	8	yes	complemented
83	C₂×#1055	C₂×D₄	1	4	yes	—
84	C₂×#1055	C₂×D₄	1	4	yes	—
85	C₂×#500	—	13	1	no	—
86	C₂×#500	—	13	2	no	—
87	C₂×#500	D₁₃	1	1	yes	characteristic
88	C₂×#494	—	13	2	no	—
89	#1713	—	13	8	no	—
90	C₂×C₈²	—	13	1	no	—
91	C₂³×C₁₃	#127	1	1	yes	characteristic
92	Q₈×C₁₃	—	4	8	no	—
93	Q₈×C₁₃	—	8	4	no	—
94	C₂×C₄×C₁₃	—	4	4	no	—
95	C₂×C₄×C₁₃	—	8	4	no	—
96	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
97	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
98	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
99	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
100	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
101	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
102	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
105	C₂×Dic₁₃	—	4	4	no	—
106	C₂×Dic₁₃	—	8	4	no	—
107	Dic₂₆	—	4	8	no	—
108	Dic₂₆	—	8	4	no	—
109	C₈×C₁₃	C₂×Q₁₆	1	8	yes	complemented
110	#1055	C₂×D₈	1	8	yes	—
111	#1055	C₂×Q₁₆	1	8	yes	complemented
112	C₂²×Q₁₆	—	26	4	no	—
113	C₂×C₄⋊Q₈	—	13	2	no	—
114	C₂×C₄⋊Q₈	C₂×D₁₃	1	2	yes	—
115	#500	—	2	2	no	—
116	#500	—	13	8	no	—
117	#500	—	13	4	no	—
118	#500	—	26	4	no	—
119	#500	—	26	2	no	—
120	#500	C₂×D₁₃	1	4	yes	—
121	#494	—	13	8	no	—
122	#494	—	26	4	no	—
123	C₂×#107	—	2	2	no	—
124	C₂×#107	—	26	4	no	—
125	C₂×#107	—	26	2	no	—
126	C₂×C₄×C₈	—	13	1	no	—
127	C₂×C₄×C₈	—	13	1	no	—
128	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
129	C₈²	—	13	4	no	—
130	C₂²×C₁₃	#493	1	2	yes	—
131	C₂²×C₁₃	#494	1	2	yes	—
132	C₂²×C₁₃	#494	1	2	yes	—
133	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
134	C₄×C₁₃	—	8	4	no	—
135	C₄×C₁₃	#493	1	2	yes	—
136	C₄×C₁₃	#494	1	2	yes	—
137	C₄×C₁₃	#494	1	2	yes	—
138	C₄×C₁₃	C₂²×D₈	1	2	yes	—
139	C₄×C₁₃	C₂²×Q₁₆	1	2	yes	—
140	C₄×C₁₃	C₂²×Q₁₆	1	2	yes	—
141	Dic₁₃	—	8	4	no	—
142	C₂²×Q₈	—	2	2	no	—
143	C₂²×Q₈	—	26	2	no	—
144	C₂×Q₁₆	—	26	16	no	—
145	C₂×Q₁₆	—	52	16	no	—
146	C₂²×C₈	—	13	2	no	—
147	C₂²×C₈	—	13	2	no	—
148	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	—	2	2	no	—
151	C₄⋊Q₈	—	2	2	no	—
152	C₄⋊Q₈	—	13	4	no	—
153	C₄⋊Q₈	—	26	2	no	—
154	C₄⋊Q₈	—	26	2	no	—
155	C₄⋊Q₈	—	26	2	no	—
156	C₄⋊Q₈	C₂²×D₁₃	1	4	yes	—
157	C₂×C₄⋊C₄	—	2	2	no	—
158	C₂×C₄⋊C₄	—	2	2	no	—
159	C₂×C₄⋊C₄	—	26	2	no	—
160	C₂×C₄⋊C₄	—	26	2	no	—
161	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
162	#107	—	2	8	no	—
163	#107	—	26	16	no	—
164	#107	—	26	8	no	—
165	C₄×C₈	—	13	2	no	—
166	C₄×C₈	—	13	2	no	—
167	C₄×C₈	—	13	2	no	—
168	C₄×C₈	—	13	2	no	—
169	C₄×C₈	C₂²⋊D₁₃	1	2	yes	—
170	C₄×C₈	C₂²×D₁₃	1	2	yes	—
171	C₂×C₁₃	#1713	1	4	yes	complemented
172	C₂×C₁₃	C₂×#493	1	1	yes	characteristic
173	C₂×C₁₃	C₂×#494	1	1	yes	characteristic
174	C₂×C₁₃	C₂×#494	1	1	yes	characteristic
175	C₂×Q₈	—	2	4	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	—	4	8	no	—
178	C₂×Q₈	—	26	4	no	—
179	C₂×Q₈	—	52	2	no	—
180	C₂×Q₈	—	52	8	no	—
181	C₂²×C₄	—	4	2	no	—
182	C₂²×C₄	—	52	2	no	—
183	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
184	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
185	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
186	Q₁₆	—	52	32	no	—
187	C₂×C₈	—	13	8	no	—
188	C₂×C₈	—	13	8	no	—
189	C₂×C₈	—	13	4	no	—
190	C₂×C₈	—	13	4	no	—
191	C₂×C₈	#6107	1	8	yes	complemented
192	C₂×C₈	C₂×C₂²⋊D₁₃	1	4	yes	—
193	C₄⋊C₄	—	2	4	no	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	26	4	no	—
198	C₄⋊C₄	—	26	4	no	—
199	C₄⋊C₄	—	52	2	no	—
200	C₄⋊C₄	—	52	2	no	—
201	C₄²	D₄×D₁₃	1	1	yes	characteristic
202	C₄²	D₄×D₁₃	1	1	yes	characteristic
203	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
204	C₄²	C₂³×D₁₃	1	1	yes	characteristic
205	C₁₃	C₂×#1713	1	1	yes	characteristic, complemented, Sylow
206	C₂³	#88194	1	1	yes	characteristic
207	Q₈	—	4	8	no	—
208	Q₈	—	8	4	no	—
209	Q₈	—	52	8	no	—
210	Q₈	—	104	4	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	8	4	no	—
213	C₂×C₄	—	52	4	no	—
214	C₂×C₄	—	104	4	no	—
215	C₂×C₄	D₈×D₁₃	1	4	yes	—
216	C₂×C₄	Q₁₆×D₁₃	1	4	yes	—
217	C₂×C₄	#88194	1	1	yes	characteristic
218	C₂×C₄	#88194	1	1	yes	characteristic
219	C₂×C₄	#88194	1	1	yes	characteristic
220	C₂×C₄	C₂×#6107	1	4	yes	—
221	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
222	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
223	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
224	C₈	—	13	8	no	—
225	C₈	—	13	8	no	—
226	C₈	C₂×#6107	1	8	yes	complemented
227	C₂²	#11718753	1	2	yes	—
228	C₂²	#11718812	1	2	yes	—
229	C₂²	#11718842	1	2	yes	—
230	C₂²	C₂×#88194	1	1	yes	characteristic
231	C₄	—	8	4	no	—
232	C₄	—	104	4	no	—
233	C₄	#11718753	1	2	yes	—
234	C₄	#11718812	1	2	yes	—
235	C₄	#11718842	1	2	yes	—
236	C₄	C₂×D₈×D₁₃	1	2	yes	—
237	C₄	C₂×Q₁₆×D₁₃	1	2	yes	—
238	C₄	C₂²×#6107	1	2	yes	—
239	C₂	#13114453	1	4	yes	direct product factor
240	C₂	C₂×#11718812	1	1	yes	characteristic
241	C₂	C₂×#11718842	1	1	yes	characteristic
242	C₂	C₂×#11718753	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#88194
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₁₃×#500	C₂
socle, prime radical	C₂³×C₁₃	#127
hypercenter	C₂×#500	D₁₃
hypocenter	C₁₃	C₂×#1713
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#500

Complements

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

N	H ≅ G/N	type
4. #13114453	C₂	direct (N × H)
66. C₂×C₈×C₁₃	Q₁₆	semidirect
82. C₂×#1055	Q₁₆	semidirect
109. C₈×C₁₃	C₂×Q₁₆	semidirect
111. #1055	C₂×Q₁₆	semidirect
171. C₂×C₁₃	#1713	semidirect
191. C₂×C₈	#6107	semidirect
205. C₁₃	C₂×#1713	semidirect
226. C₈	C₂×#6107	semidirect
239. C₂	#13114453	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
C₂×#11718739	2
C₂×#11718753	2
#13114453	2
C₂×C₈×#1055	2
C₂×C₁₃×#500	2
C₂×#1713	13

Subgroups — C2×#13114453 #15850613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13114453 #15850613