Subgroups — #15750098

Order 3328.

222 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718055	C₂	1	1	yes	maximal, characteristic
2	#13115000	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#364	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×M₃₂	—	2	1	no	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×#88058	—	2	1	no	—
7	C₂×#88057	—	2	1	no	—
8	C₂×#88052	—	2	1	no	—
9	#11718597	C₄	1	2	yes	—
10	C₁₃×#364	—	2	1	no	—
11	C₁₃×#364	C₄	1	2	yes	complemented
12	#11718055	—	2	1	no	—
13	#11718055	C₄	1	2	yes	complemented
14	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₃	—	2	2	no	—
18	C₁₃×M₃₂	—	2	2	no	—
19	C₁₃×M₃₂	—	4	1	no	—
20	C₂×C₁₃×C₁₆	—	4	1	no	—
21	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
24	C₄×C₈×C₁₃	Q₈	1	1	yes	characteristic
25	#88071	—	4	2	no	—
26	#88058	—	4	1	no	—
27	#88058	—	4	1	no	—
28	#88057	—	4	1	no	—
29	#88057	—	4	1	no	—
30	#88052	—	2	2	no	—
31	#88052	—	4	1	no	—
32	C₂×#6090	—	4	1	no	—
33	#7271	—	13	1	no	maximal, Sylow
34	C₂²×C₄×C₁₃	—	2	1	no	—
35	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×Dic₁₃	—	4	2	no	—
37	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
42	C₂×C₈×C₁₃	D₈	1	1	yes	characteristic
43	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
44	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
45	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
46	C₂×C₈×C₁₃	SD₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
48	C₂×C₈×C₁₃	Q₁₆	1	1	yes	characteristic
49	C₄²×C₁₃	—	2	1	no	—
50	C₄²×C₁₃	C₄²	1	1	yes	characteristic
51	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
52	C₄⋊Dic₁₃	—	4	2	no	—
53	C₄⋊Dic₁₃	—	4	2	no	—
54	C₁₃×C₁₆	—	4	2	no	—
55	#6090	—	4	2	no	—
56	C₂×#364	—	13	1	no	—
57	C₂×#364	D₁₃	1	1	yes	characteristic
58	#1846	—	13	1	no	—
59	C₂³×C₁₃	#100	1	1	yes	characteristic
60	C₂×C₄×C₁₃	—	2	1	no	—
61	C₂×C₄×C₁₃	—	2	1	no	—
62	C₂×C₄×C₁₃	—	4	2	no	—
63	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
64	C₂×C₄×C₁₃	#101	1	1	yes	characteristic
65	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
66	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
67	C₂×C₄×C₁₃	#103	1	1	yes	characteristic
68	C₂×C₄×C₁₃	#103	1	1	yes	characteristic
69	C₂×Dic₁₃	—	8	4	no	—
70	C₂×Dic₁₃	—	8	2	no	—
71	C₈×C₁₃	#102	1	1	yes	characteristic
72	C₈×C₁₃	#102	1	1	yes	characteristic
73	C₈×C₁₃	#103	1	1	yes	characteristic
74	C₈×C₁₃	#103	1	1	yes	characteristic
75	C₈×C₁₃	#106	1	1	yes	characteristic
76	C₈×C₁₃	#106	1	1	yes	characteristic
77	C₈×C₁₃	#107	1	1	yes	characteristic
78	C₈×C₁₃	#107	1	1	yes	characteristic
79	C₂×M₃₂	—	2	1	no	—
80	C₂×M₃₂	—	26	1	no	—
81	C₂×#107	—	26	1	no	—
82	C₂×#106	—	26	1	no	—
83	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
84	#382	—	13	2	no	—
85	#364	—	2	1	no	—
86	#364	—	13	2	no	—
87	#364	—	26	1	no	—
88	#364	Dic₁₃	1	2	yes	complemented
89	C₂²×C₁₃	—	2	2	no	—
90	C₂²×C₁₃	#331	1	1	yes	characteristic
91	C₂²×C₁₃	#333	1	1	yes	characteristic
92	C₂²×C₁₃	#343	1	1	yes	characteristic
93	C₄×C₁₃	—	4	1	no	—
94	C₄×C₁₃	—	4	1	no	—
95	C₄×C₁₃	#332	1	1	yes	characteristic
96	C₄×C₁₃	#332	1	1	yes	characteristic
97	C₄×C₁₃	#340	1	1	yes	characteristic
98	C₄×C₁₃	#340	1	1	yes	characteristic
99	Dic₁₃	—	16	2	no	—
100	C₂²×C₈	D₅₂	1	1	yes	characteristic
101	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
102	C₂×C₄⋊C₄	—	26	2	no	—
103	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
104	M₃₂	—	2	2	no	—
105	M₃₂	—	4	1	no	—
106	M₃₂	—	26	2	no	—
107	M₃₂	—	52	1	no	—
108	C₂×C₁₆	—	4	1	no	—
109	C₂×C₁₆	—	52	1	no	—
110	#107	—	52	1	no	—
111	#107	—	52	1	no	—
112	#106	—	52	1	no	—
113	#106	—	52	1	no	—
114	C₄×C₈	Dic₂₆	1	1	yes	characteristic
115	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
116	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
117	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
118	#95	—	52	2	no	—
119	C₂×C₁₃	—	2	1	no	—
120	C₂×C₁₃	—	2	1	no	—
121	C₂×C₁₃	#1296	1	1	yes	characteristic
122	C₂×C₁₃	#1366	1	2	yes	—
123	C₂²×C₄	—	2	1	no	—
124	C₂²×C₄	—	52	2	no	—
125	C₂²×C₄	#6103	1	1	yes	characteristic
126	C₂×C₈	#6095	1	1	yes	characteristic
127	C₂×C₈	#6095	1	1	yes	characteristic
128	C₂×C₈	D₁₀₄	1	1	yes	characteristic
129	C₂×C₈	Dic₅₂	1	1	yes	characteristic
130	C₂×C₈	#6101	1	1	yes	characteristic
131	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
132	C₂×C₈	#6103	1	1	yes	characteristic
133	C₂×C₈	#6104	1	1	yes	characteristic
134	C₂×C₈	#6105	1	1	yes	characteristic
135	C₂×C₈	#6106	1	1	yes	characteristic
136	C₂×C₈	#6107	1	1	yes	characteristic
137	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
138	C₄⋊C₄	—	52	2	no	—
139	C₄⋊C₄	—	52	2	no	—
140	C₄²	—	2	1	no	—
141	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
142	C₄²	#6101	1	1	yes	characteristic
143	C₁₆	—	4	2	no	—
144	C₁₆	—	52	2	no	—
145	C₁₃	#7271	1	1	yes	characteristic, complemented, Sylow
146	C₂³	#88063	1	1	yes	characteristic
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	4	2	no	—
150	C₂×C₄	—	104	4	no	—
151	C₂×C₄	—	104	2	no	—
152	C₂×C₄	#88049	1	1	yes	characteristic
153	C₂×C₄	#88050	1	1	yes	characteristic
154	C₂×C₄	#88056	1	1	yes	characteristic
155	C₂×C₄	#88061	1	1	yes	characteristic
156	C₂×C₄	#88064	1	1	yes	characteristic
157	C₂×C₄	#88071	1	1	yes	characteristic
158	C₈	#88047	1	1	yes	characteristic
159	C₈	#88048	1	1	yes	characteristic
160	C₈	#88056	1	1	yes	characteristic
161	C₈	#88057	1	1	yes	characteristic
162	C₈	#88058	1	1	yes	characteristic
163	C₈	#88061	1	1	yes	characteristic
164	C₈	#88072	1	1	yes	characteristic
165	C₈	#88075	1	1	yes	characteristic
166	C₂²	—	2	2	no	—
167	C₂²	#11718073	1	1	yes	characteristic
168	C₂²	#11718077	1	1	yes	characteristic
169	C₂²	#11718146	1	1	yes	characteristic
170	C₄	—	4	1	no	—
171	C₄	—	4	1	no	—
172	C₄	—	208	2	no	—
173	C₄	#11718074	1	1	yes	characteristic
174	C₄	#11718078	1	1	yes	characteristic
175	C₄	#11718121	1	1	yes	characteristic
176	C₄	#11718143	1	1	yes	characteristic
177	C₂	—	2	1	no	—
178	C₂	—	2	1	no	—
179	C₂	#13112720	1	1	yes	characteristic
180	C₂	#13112898	1	2	yes	—

	subgroup	G/H
center	C₂²	#11718073
commutator	C₄²×C₁₃	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₃
Fitting	C₂×C₁₃×#364	C₂
socle	C₂²×C₁₃	#333
prime radical	C₂³×C₁₃	#100
cosocle	C₂×C₄×C₈×C₁₃	C₂²
hypercenter	C₂×#364	D₁₃
hypocenter	C₁₃	#7271
LCS	G ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
11. C₁₃×#364	C₄	semidirect
13. #11718055	C₄	semidirect
88. #364	Dic₁₃	semidirect
145. C₁₃	#7271	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718055	2
#13115000	2
C₂×C₁₃×#364	2
#7271	13