Subgroups — #15762930

Order 3328.

494 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88124	C₂	1	1	yes	maximal, characteristic
2	#13114953	C₂	1	1	yes	maximal, characteristic
3	#13112676	C₂	1	4	yes	maximal
4	C₄²×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#88124	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	—	2	2	no	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
8	C₄³×C₁₃	C₂²	1	1	yes	characteristic
9	#11718597	C₄	1	1	yes	characteristic
10	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	#11718594	—	2	2	no	—
12	C₄×#6101	—	2	2	no	—
13	#11718589	C₄	1	2	yes	—
14	C₂×C₄⋊#1055	C₂²	1	2	yes	—
15	#11718116	—	2	2	no	—
16	C₂²×C₈×C₁₃	—	2	2	no	—
17	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	D₄	1	2	yes	—
20	C₂×C₄²×C₁₃	D₄	1	2	yes	—
21	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
23	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
24	C₂×#6101	—	2	2	no	—
25	C₂×#6101	—	2	2	no	—
26	C₂×C₄×Dic₁₃	—	2	2	no	—
27	C₂²×#1055	—	2	2	no	—
28	#88124	—	2	2	no	—
29	#88124	C₈	1	4	yes	complemented
30	C₄×C₈×C₁₃	—	2	8	no	—
31	C₄×C₈×C₁₃	—	2	2	no	—
32	C₄×C₈×C₁₃	Q₈	1	4	yes	—
33	#88071	—	2	2	no	—
34	#88071	—	2	2	no	—
35	#88071	—	2	2	no	—
36	C₄⋊#1055	—	2	4	no	—
37	#9871	—	13	1	no	maximal, Sylow
38	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₁₃	—	2	2	no	—
44	C₂²×Dic₁₃	—	2	2	no	—
45	C₂×C₈×C₁₃	—	2	8	no	—
46	C₂×C₈×C₁₃	—	2	4	no	—
47	C₄²×C₁₃	—	2	4	no	—
48	C₄²×C₁₃	—	2	2	no	—
49	C₄²×C₁₃	—	2	4	no	—
50	C₄²×C₁₃	C₂×C₈	1	2	yes	—
51	C₄²×C₁₃	M₁₆	1	2	yes	—
52	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
53	C₄²×C₁₃	#41	1	2	yes	—
54	C₄⋊Dic₁₃	—	2	2	no	—
55	C₄⋊Dic₁₃	—	2	4	no	—
56	C₄⋊Dic₁₃	C₂×C₈	1	4	yes	—
57	#6101	—	2	8	no	—
58	#6101	—	4	4	no	—
59	C₄×Dic₁₃	—	4	4	no	—
60	C₂×#1055	—	4	2	no	—
61	C₂×#1055	—	4	4	no	—
62	C₄×#125	—	13	1	no	—
63	#1831	—	13	1	no	—
64	C₄²×C₈	D₁₃	1	1	yes	characteristic
65	#1279	—	13	4	no	—
66	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	2	no	—
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	C₂²⋊C₈	1	4	yes	—
73	C₂×C₄×C₁₃	#104	1	4	yes	—
74	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
75	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
76	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₃	#131	1	2	yes	—
81	C₂×C₄×C₁₃	#135	1	4	yes	—
82	C₂×Dic₁₃	—	2	4	no	—
83	C₂×Dic₁₃	—	4	2	no	—
84	C₂×Dic₁₃	—	4	2	no	—
85	C₂×Dic₁₃	—	4	2	no	—
86	C₂×Dic₁₃	—	4	2	no	—
87	C₂×Dic₁₃	—	4	2	no	—
88	C₈×C₁₃	—	2	8	no	—
89	#1055	—	8	2	no	—
90	C₂×#125	—	13	1	no	—
91	C₂×C₄⋊C₈	—	13	2	no	—
92	C₂×C₄×C₈	—	2	2	no	—
93	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
94	#389	—	13	2	no	—
95	#387	—	26	2	no	—
96	#382	—	13	1	no	—
97	C₄×C₄⋊C₄	—	13	2	no	—
98	C₄×C₄⋊C₄	—	26	2	no	—
99	C₄³	C₂×D₁₃	1	1	yes	characteristic
100	#336	—	26	2	no	—
101	C₂²×C₁₃	#391	1	1	yes	characteristic
102	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
103	C₂²×C₁₃	#408	1	1	yes	characteristic
104	C₂²×C₁₃	#416	1	2	yes	—
105	C₂²×C₁₃	C₂×#104	1	2	yes	—
106	C₄×C₁₃	—	2	4	no	—
107	C₄×C₁₃	—	2	2	no	—
108	C₄×C₁₃	—	2	4	no	—
109	C₄×C₁₃	C₈×Q₈	1	2	yes	—
110	C₄×C₁₃	#446	1	2	yes	—
111	C₄×C₁₃	#488	1	2	yes	—
112	C₄×C₁₃	#499	1	2	yes	—
113	Dic₁₃	—	4	4	no	—
114	Dic₁₃	—	8	2	no	—
115	C₂²×C₈	—	2	2	no	—
116	C₂²×C₈	—	26	2	no	—
117	#125	—	13	4	no	—
118	#125	—	26	2	no	—
119	C₂×C₄⋊C₄	—	13	2	no	—
120	C₂×C₄⋊C₄	—	13	2	no	—
121	C₂×C₄⋊C₄	—	26	2	no	—
122	C₂×C₄⋊C₄	—	26	2	no	—
123	C₂×C₄²	—	26	2	no	—
124	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
125	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
126	C₂×C₄²	D₅₂	1	2	yes	—
127	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
128	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
129	C₄⋊C₈	—	26	4	no	—
130	C₄×C₈	—	2	8	no	—
131	C₄×C₈	—	2	2	no	—
132	C₄×C₈	Dic₂₆	1	4	yes	—
133	#95	—	26	2	no	—
134	#95	—	26	2	no	—
135	#95	—	26	2	no	—
136	C₂×C₁₃	#1476	1	2	yes	—
137	C₂×C₁₃	#1494	1	2	yes	—
138	C₂×C₁₃	#1984	1	1	yes	characteristic
139	C₂×C₁₃	#1991	1	1	yes	characteristic
140	C₂×C₁₃	#1994	1	1	yes	characteristic
141	C₂²×C₄	—	26	2	no	—
142	C₂²×C₄	—	26	2	no	—
143	C₂²×C₄	#6103	1	2	yes	—
144	C₂²×C₄	#6103	1	2	yes	—
145	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
146	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
147	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
148	C₂×C₈	—	2	8	no	—
149	C₂×C₈	—	2	4	no	—
150	C₂×C₈	—	52	2	no	—
151	C₂×C₈	—	52	4	no	—
152	C₄⋊C₄	—	13	4	no	—
153	C₄⋊C₄	—	26	2	no	—
154	C₄⋊C₄	—	26	8	no	—
155	C₄⋊C₄	—	26	4	no	—
156	C₄⋊C₄	—	52	4	no	—
157	C₄²	—	2	2	no	—
158	C₄²	—	2	4	no	—
159	C₄²	—	2	4	no	—
160	C₄²	—	52	4	no	—
161	C₄²	C₈×D₁₃	1	2	yes	—
162	C₄²	#6094	1	2	yes	—
163	C₄²	C₂×Dic₂₆	1	2	yes	—
164	C₄²	#6127	1	2	yes	—
165	C₁₃	#9871	1	1	yes	characteristic, complemented, Sylow
166	C₂³	C₂×#6103	1	1	yes	characteristic
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	2	2	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	26	4	no	—
173	C₂×C₄	—	52	2	no	—
174	C₂×C₄	—	52	2	no	—
175	C₂×C₄	—	52	2	no	—
176	C₂×C₄	—	52	2	no	—
177	C₂×C₄	—	52	2	no	—
178	C₂×C₄	#88045	1	4	yes	—
179	C₂×C₄	#88060	1	4	yes	—
180	C₂×C₄	C₄×Dic₂₆	1	2	yes	—
181	C₂×C₄	#88123	1	1	yes	characteristic
182	C₂×C₄	#88129	1	1	yes	characteristic
183	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
184	C₂×C₄	C₂×#6094	1	1	yes	characteristic
185	C₂×C₄	#88155	1	2	yes	—
186	C₂×C₄	#88158	1	4	yes	—
187	C₂×C₄	#88178	1	2	yes	—
188	C₈	—	2	8	no	—
189	C₈	—	104	2	no	—
190	C₂²	C₂×#88045	1	2	yes	—
191	C₂²	#11718590	1	1	yes	characteristic
192	C₂²	C₂×#88060	1	1	yes	characteristic
193	C₂²	#11718771	1	1	yes	characteristic
194	C₂²	#11718774	1	2	yes	—
195	C₄	—	2	4	no	—
196	C₄	—	2	2	no	—
197	C₄	—	2	4	no	—
198	C₄	—	52	4	no	—
199	C₄	—	104	2	no	—
200	C₄	C₈×Dic₂₆	1	2	yes	—
201	C₄	#11718340	1	2	yes	—
202	C₄	#11718344	1	2	yes	—
203	C₄	#11718358	1	2	yes	—
204	C₂	#13113219	1	2	yes	—
205	C₂	#13113297	1	2	yes	—
206	C₂	#13115772	1	1	yes	characteristic
207	C₂	#13115801	1	1	yes	characteristic
208	C₂	#13115813	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₄²×C₈×C₁₃	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄²×C₈	D₁₃
hypocenter	C₁₃	#9871
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
29. #88124	C₈	semidirect
165. C₁₃	#9871	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88124	2
#13114953	2
#13112676	2
C₄²×C₈×C₁₃	2
#9871	13