Subgroups — #15754053

Order 3328.

494 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊#1055	C₂	1	2	yes	maximal
2	C₂×#11718047	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×#1055	C₂	1	1	yes	maximal, characteristic
4	#13112663	C₂	1	2	yes	maximal
5	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#97	C₄	1	2	yes	—
7	C₂×C₁₃×#97	C₄	1	2	yes	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₄³×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊#1055	C₄	1	4	yes	—
12	C₂×C₄×#1055	C₂²	1	2	yes	—
13	C₂×C₄×#1055	C₂²	1	2	yes	—
14	#11718116	C₄	1	4	yes	—
15	#11718047	—	2	2	no	—
16	C₈×#1055	—	2	2	no	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²×#1055	C₂×C₄	1	4	yes	—
25	C₂²×#1055	C₂×C₄	1	4	yes	—
26	C₁₃×#97	—	2	4	no	—
27	C₁₃×#97	C₈	1	8	yes	complemented
28	C₄×C₈×C₁₃	—	2	2	no	—
29	C₄×C₈×C₁₃	D₄	1	2	yes	—
30	C₄×C₈×C₁₃	Q₈	1	2	yes	—
31	C₄⋊#1055	—	2	8	no	—
32	C₄×#1055	—	2	2	no	—
33	C₄×#1055	—	2	2	no	—
34	C₄×#1055	—	2	2	no	—
35	C₄×#1055	—	2	2	no	—
36	#8262	—	13	1	no	maximal, Sylow
37	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
41	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	—	2	2	no	—
43	C₂×C₈×C₁₃	—	2	2	no	—
44	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
45	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
46	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
47	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
48	C₄²×C₁₃	—	2	2	no	—
49	C₄²×C₁₃	—	2	4	no	—
50	C₄²×C₁₃	—	2	4	no	—
51	C₄²×C₁₃	C₂×C₈	1	4	yes	—
52	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
54	C₄²×C₁₃	#41	1	2	yes	—
55	C₂×#1055	—	2	4	no	—
56	C₂×#1055	—	2	4	no	—
57	C₂×#1055	—	2	4	no	—
58	C₂×#1055	—	2	4	no	—
59	C₂×#1055	—	2	4	no	—
60	C₂×#1055	M₁₆	1	8	yes	—
61	C₄×C₄⋊C₈	—	13	2	no	—
62	C₄×#97	D₁₃	1	1	yes	characteristic
63	C₂×#322	—	13	1	no	—
64	C₂×C₈²	—	13	1	no	—
65	#1273	—	13	2	no	—
66	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	—	2	1	no	—
70	C₂×C₄×C₁₃	—	2	2	no	—
71	C₂×C₄×C₁₃	—	2	1	no	—
72	C₂×C₄×C₁₃	—	2	2	no	—
73	C₂×C₄×C₁₃	C₄×C₈	1	4	yes	—
74	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
77	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
78	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
79	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
80	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
81	C₂×C₄×C₁₃	#131	1	4	yes	—
82	C₈×C₁₃	—	2	4	no	—
83	C₈×C₁₃	C₄⋊C₈	1	8	yes	complemented
84	#1055	—	2	8	no	—
85	#1055	—	4	4	no	—
86	C₂×C₄⋊C₈	—	13	4	no	—
87	C₂×#97	Dic₁₃	1	2	yes	—
88	C₂×#97	Dic₁₃	1	2	yes	—
89	C₂×C₄×C₈	—	13	2	no	—
90	C₂×C₄×C₈	—	13	2	no	—
91	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
92	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
93	C₄³	C₂×D₁₃	1	1	yes	characteristic
94	#336	—	13	4	no	—
95	#322	—	26	2	no	—
96	C₈²	—	26	2	no	—
97	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
98	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
99	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
100	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
101	C₂²×C₁₃	#405	1	2	yes	—
102	C₄×C₁₃	—	2	4	no	—
103	C₄×C₁₃	—	4	1	no	—
104	C₄×C₁₃	—	4	1	no	—
105	C₄×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
106	C₄×C₁₃	#431	1	2	yes	—
107	C₄×C₁₃	#435	1	4	yes	—
108	C₄×C₁₃	#446	1	4	yes	—
109	C₂²×C₈	—	13	4	no	—
110	C₂²×C₈	—	13	4	no	—
111	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
112	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
113	C₂×C₄²	C₄×D₁₃	1	2	yes	—
114	C₂×C₄²	C₄×D₁₃	1	2	yes	—
115	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
116	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
117	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
118	C₄⋊C₈	—	26	8	no	—
119	#97	—	2	4	no	—
120	#97	#1055	1	8	yes	complemented
121	C₄×C₈	—	2	2	no	—
122	C₄×C₈	—	26	2	no	—
123	C₄×C₈	—	26	2	no	—
124	C₄×C₈	—	26	2	no	—
125	C₄×C₈	—	26	2	no	—
126	C₄×C₈	Dic₂₆	1	2	yes	—
127	C₄×C₈	D₅₂	1	2	yes	—
128	C₂×C₁₃	C₈×M₁₆	1	2	yes	—
129	C₂×C₁₃	#1453	1	1	yes	characteristic
130	C₂×C₁₃	#1455	1	1	yes	characteristic
131	C₂×C₁₃	C₄×C₄⋊C₈	1	1	yes	characteristic
132	C₂×C₁₃	#1771	1	2	yes	—
133	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
134	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
135	C₂²×C₄	C₄×Dic₁₃	1	2	yes	—
136	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
137	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	13	8	no	—
141	C₂×C₈	—	26	4	no	—
142	C₂×C₈	—	26	4	no	—
143	C₂×C₈	—	26	4	no	—
144	C₂×C₈	—	26	4	no	—
145	C₂×C₈	—	26	4	no	—
146	C₂×C₈	C₂×#1055	1	4	yes	—
147	C₂×C₈	C₂×#1055	1	4	yes	—
148	C₂×C₈	#6099	1	4	yes	—
149	C₂×C₈	C₄⋊Dic₁₃	1	4	yes	—
150	C₄²	—	2	4	no	—
151	C₄²	—	2	4	no	—
152	C₄²	—	2	2	no	—
153	C₄²	C₂×#1055	1	4	yes	—
154	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
155	C₄²	C₂×D₅₂	1	1	yes	characteristic
156	C₄²	#6127	1	2	yes	—
157	C₁₃	#8262	1	1	yes	characteristic, complemented, Sylow
158	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	C₄×#1055	1	4	yes	—
166	C₂×C₄	C₄×Dic₂₆	1	2	yes	—
167	C₂×C₄	C₄×D₅₂	1	2	yes	—
168	C₂×C₄	M₁₆×D₁₃	1	4	yes	—
169	C₂×C₄	#88161	1	4	yes	—
170	C₂×C₄	C₂²×#1055	1	2	yes	—
171	C₂×C₄	C₂×#6099	1	2	yes	—
172	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
173	C₂×C₄	#88180	1	1	yes	characteristic
174	C₈	—	2	4	no	—
175	C₈	—	26	8	no	—
176	C₈	—	52	4	no	—
177	C₈	C₄⋊#1055	1	8	yes	complemented
178	C₂²	C₂×C₄×#1055	1	1	yes	characteristic
179	C₂²	C₄×#6099	1	1	yes	characteristic
180	C₂²	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
181	C₂²	M₁₆×Dic₁₃	1	2	yes	—
182	C₂²	#11718783	1	2	yes	—
183	C₄	—	2	4	no	—
184	C₄	—	4	1	no	—
185	C₄	—	4	1	no	—
186	C₄	#11718362	1	4	yes	—
187	C₄	#11718367	1	4	yes	—
188	C₄	C₂×C₄⋊#1055	1	2	yes	—
189	C₄	#11718586	1	2	yes	—
190	C₂	M₁₆×#1055	1	2	yes	—
191	C₂	#13113133	1	1	yes	characteristic
192	C₂	#13113139	1	1	yes	characteristic
193	C₂	C₄×C₄⋊#1055	1	1	yes	characteristic
194	C₂	#13114708	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₄×C₁₃×#97	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄×#97	D₁₃
hypocenter	C₁₃	#8262
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
27. C₁₃×#97	C₈	semidirect
83. C₈×C₁₃	C₄⋊C₈	semidirect
120. #97	#1055	semidirect
157. C₁₃	#8262	semidirect
177. C₈	C₄⋊#1055	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊#1055	2
C₂×#11718047	2
C₂×C₈×#1055	2
#13112663	2
C₄×C₁₃×#97	2
#8262	13