Subgroups — C₈×#88055 #15752269

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13114581	C₂	1	1	yes	maximal, characteristic
2	C₄×#88055	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11718046	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718047	C₂	1	1	yes	maximal, characteristic
6	C₂×C₈×#1055	C₂	1	1	yes	maximal, characteristic
7	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×#88055	C₄	1	4	yes	—
12	C₂×C₈×Dic₁₃	C₄	1	4	yes	—
13	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
15	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
16	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
17	C₈²×C₁₃	C₄	1	4	yes	complemented
18	#11718142	C₄	1	4	yes	—
19	#11718047	C₄	1	4	yes	complemented
20	#11718046	C₄	1	4	yes	complemented
21	C₈×#1055	C₄	1	4	yes	complemented
22	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
26	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
27	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
28	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
29	C₂²×#1055	C₂×C₄	1	2	yes	—
30	C₂²×#1055	C₂×C₄	1	2	yes	—
31	C₂²×#1055	C₂×C₄	1	2	yes	—
32	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
36	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
37	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
38	#88055	C₈	1	16	yes	direct product factor
39	C₈×Dic₁₃	—	2	8	no	—
40	C₄×#1055	C₂×C₄	1	2	yes	—
41	C₄×#1055	C₂×C₄	1	2	yes	—
42	C₄×#1055	C₂×C₄	1	2	yes	—
43	C₄×#1055	C₂×C₄	1	2	yes	—
44	C₄×#1055	C₂×C₄	1	2	yes	—
45	C₄×#1055	C₂×C₄	1	2	yes	—
46	C₈×#97	—	13	1	no	maximal, Sylow
47	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×Dic₁₃	C₄²	1	4	yes	—
51	C₂×C₈×C₁₃	—	2	4	no	—
52	C₂×C₈×C₁₃	C₄²	1	4	yes	—
53	C₂×C₈×C₁₃	C₄²	1	4	yes	—
54	C₂×C₈×C₁₃	C₄²	1	4	yes	—
55	C₂×C₈×C₁₃	C₂×C₈	1	8	yes	—
56	C₂×C₈×C₁₃	M₁₆	1	8	yes	—
57	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
59	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₄×Dic₁₃	—	2	4	no	—
62	C₄×Dic₁₃	—	2	4	no	—
63	C₄×Dic₁₃	C₂×C₈	1	8	yes	—
64	C₂×#1055	—	2	4	no	—
65	C₂×#1055	—	2	4	no	—
66	C₂×#1055	C₄²	1	4	yes	—
67	C₂×#1055	C₄²	1	4	yes	—
68	C₂×#1055	C₄²	1	4	yes	—
69	C₂×#1055	C₂×C₈	1	8	yes	—
70	#1744	—	13	1	no	—
71	C₄×#97	—	13	1	no	—
72	C₄²×C₈	—	13	1	no	—
73	C₂×#322	—	13	1	no	—
74	C₂×#322	—	13	1	no	—
75	C₂×C₈²	—	13	1	no	—
76	C₂×C₈²	D₁₃	1	1	yes	characteristic
77	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
85	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
86	C₂×C₄×C₁₃	#131	1	4	yes	—
87	C₂×Dic₁₃	—	2	4	no	—
88	C₂×Dic₁₃	—	2	4	no	—
89	C₂×Dic₁₃	C₄×C₈	1	8	yes	—
90	C₈×C₁₃	—	2	4	no	—
91	C₈×C₁₃	C₄×C₈	1	8	yes	complemented
92	C₈×C₁₃	#97	1	8	yes	complemented
93	#1055	—	2	4	no	—
94	#1055	—	2	4	no	—
95	#1055	C₄×C₈	1	8	yes	complemented
96	C₂×#97	—	13	4	no	—
97	C₂×C₄×C₈	—	13	1	no	—
98	C₂×C₄×C₈	—	13	1	no	—
99	C₂×C₄×C₈	—	13	1	no	—
100	C₂×C₄×C₈	—	13	4	no	—
101	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
102	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
103	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
104	C₄³	—	13	1	no	—
105	#336	—	13	4	no	—
106	#322	—	13	4	no	—
107	#322	—	13	4	no	—
108	C₈²	—	13	4	no	—
109	C₈²	Dic₁₃	1	4	yes	complemented
110	C₂²×C₁₃	C₄³	1	1	yes	characteristic
111	C₂²×C₁₃	C₂×C₄×C₈	1	2	yes	—
112	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
113	C₂²×C₁₃	#405	1	2	yes	—
114	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
115	C₄×C₁₃	C₂×C₄×C₈	1	2	yes	—
116	C₄×C₁₃	C₂×#97	1	2	yes	—
117	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
118	C₄×C₁₃	#405	1	2	yes	—
119	C₄×C₁₃	#405	1	2	yes	—
120	Dic₁₃	—	2	8	no	—
121	C₂²×C₈	—	13	2	no	—
122	C₂²×C₈	—	13	2	no	—
123	C₂²×C₈	—	13	2	no	—
124	C₂²×C₈	C₄×D₁₃	1	2	yes	—
125	C₂²×C₈	C₄×D₁₃	1	2	yes	—
126	C₂²×C₈	C₄×D₁₃	1	2	yes	—
127	C₂×C₄²	—	13	2	no	—
128	C₂×C₄²	—	13	2	no	—
129	C₂×C₄²	—	13	2	no	—
130	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
131	#97	—	13	16	no	—
132	C₄×C₈	—	13	2	no	—
133	C₄×C₈	—	13	2	no	—
134	C₄×C₈	—	13	2	no	—
135	C₄×C₈	—	13	2	no	—
136	C₄×C₈	—	13	2	no	—
137	C₄×C₈	—	13	2	no	—
138	C₄×C₈	—	26	8	no	—
139	C₄×C₈	C₄×D₁₃	1	2	yes	—
140	C₄×C₈	C₄×D₁₃	1	2	yes	—
141	C₄×C₈	C₄×D₁₃	1	2	yes	—
142	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
143	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
144	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
145	C₂×C₁₃	C₈×M₁₆	1	4	yes	—
146	C₂×C₁₃	C₄²×C₈	1	1	yes	characteristic
147	C₂×C₁₃	C₄×#97	1	1	yes	characteristic
148	C₂×C₁₃	#1726	1	1	yes	characteristic
149	C₂²×C₄	—	13	4	no	—
150	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
152	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
153	C₂×C₈	—	2	4	no	—
154	C₂×C₈	—	13	4	no	—
155	C₂×C₈	—	13	8	no	—
156	C₂×C₈	—	13	4	no	—
157	C₂×C₈	—	13	4	no	—
158	C₂×C₈	—	26	4	no	—
159	C₂×C₈	—	26	4	no	—
160	C₂×C₈	C₈×D₁₃	1	8	yes	—
161	C₂×C₈	#6094	1	8	yes	—
162	C₂×C₈	C₄×Dic₁₃	1	4	yes	—
163	C₂×C₈	C₄×Dic₁₃	1	4	yes	—
164	C₂×C₈	C₄×Dic₁₃	1	4	yes	—
165	C₄²	—	13	8	no	—
166	C₄²	—	26	4	no	—
167	C₄²	—	26	4	no	—
168	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
169	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
170	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
171	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
172	C₁₃	C₈×#97	1	1	yes	characteristic, complemented, Sylow
173	C₂³	C₄²×D₁₃	1	1	yes	characteristic
174	C₂×C₄	—	13	8	no	—
175	C₂×C₄	—	26	4	no	—
176	C₂×C₄	—	26	4	no	—
177	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
178	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
179	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
180	C₂×C₄	C₂×C₈×D₁₃	1	4	yes	—
181	C₂×C₄	C₂×#6094	1	4	yes	—
182	C₂×C₄	#88155	1	4	yes	—
183	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
184	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
185	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
186	C₈	—	2	4	no	—
187	C₈	—	13	8	no	—
188	C₈	—	26	4	no	—
189	C₈	—	26	4	no	—
190	C₈	C₈×Dic₁₃	1	8	yes	complemented
191	C₈	#88055	1	8	yes	direct product factor
192	C₂²	C₄×C₈×D₁₃	1	2	yes	—
193	C₂²	C₄×#6094	1	2	yes	—
194	C₂²	#11718350	1	2	yes	—
195	C₂²	C₄²×Dic₁₃	1	1	yes	characteristic
196	C₄	—	26	8	no	—
197	C₄	C₄×C₈×D₁₃	1	2	yes	—
198	C₄	C₄×#6094	1	2	yes	—
199	C₄	#11718350	1	2	yes	—
200	C₄	C₂×C₈×Dic₁₃	1	2	yes	—
201	C₄	C₂×#88055	1	2	yes	—
202	C₄	#11718762	1	2	yes	—
203	C₂	C₈×#6094	1	4	yes	—
204	C₂	C₄×C₈×Dic₁₃	1	1	yes	characteristic
205	C₂	C₄×#88055	1	1	yes	characteristic
206	C₂	#13114522	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₈	C₂×D₁₃
commutator	C₂×C₁₃	C₄²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₂×C₈²×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₂×C₈²	D₁₃
hypocenter	C₁₃	C₈×#97
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄×C₈ ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
17. C₈²×C₁₃	C₄	semidirect
19. #11718047	C₄	semidirect
20. #11718046	C₄	semidirect
21. C₈×#1055	C₄	semidirect
38. #88055	C₈	direct (N × H)
91. C₈×C₁₃	C₄×C₈	semidirect
92. C₈×C₁₃	#97	semidirect
95. #1055	C₄×C₈	semidirect
109. C₈²	Dic₁₃	semidirect
172. C₁₃	C₈×#97	semidirect
190. C₈	C₈×Dic₁₃	semidirect
191. C₈	#88055	direct (N × H)

Maximal subgroups

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

subgroup	index
#13114581	2
C₄×#88055	2
C₄×C₈×Dic₁₃	2
C₂×#11718046	2
C₂×#11718047	2
C₂×C₈×#1055	2
C₂×C₈²×C₁₃	2
C₈×#97	13

Subgroups — C8×#88055 #15752269

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#88055 #15752269