Subgroups — #15779299

Order 3328.

342 conjugacy classes of subgroups.

The subgroup lattice has 142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13114996	C₂	1	2	yes	maximal
2	#13112928	C₂	1	4	yes	maximal
3	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
5	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×#88058	—	2	2	no	—
7	C₂×#88058	C₂²	1	4	yes	—
8	#11718596	—	2	2	no	—
9	C₄×C₁₃×C₁₆	C₄	1	4	yes	complemented
10	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
12	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
13	C₂×C₄⋊Dic₁₃	—	2	4	no	—
14	C₂×C₄⋊Dic₁₃	—	4	2	no	—
15	C₂×C₄⋊Dic₁₃	—	4	2	no	—
16	C₂×C₁₃×C₁₆	—	2	4	no	—
17	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
18	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₃	Q₈	1	2	yes	—
20	#88058	—	2	8	no	—
21	#88058	—	4	4	no	—
22	#12888	—	13	1	no	maximal, Sylow
23	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
24	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
25	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
26	C₂²×Dic₁₃	—	4	4	no	—
27	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
28	C₂×C₈×C₁₃	SD₁₆	1	4	yes	—
29	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
31	C₂×C₈×C₁₃	#41	1	4	yes	—
32	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
33	C₄²×C₁₃	Q₁₆	1	2	yes	—
34	C₄⋊Dic₁₃	—	4	4	no	—
35	C₄⋊Dic₁₃	—	4	4	no	—
36	C₄⋊Dic₁₃	—	8	4	no	—
37	C₄⋊Dic₁₃	—	8	4	no	—
38	C₁₃×C₁₆	—	2	4	no	—
39	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic
40	#1845	—	13	2	no	—
41	#1380	—	13	4	no	—
42	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
43	C₂×C₄×C₁₃	#107	1	2	yes	—
44	C₂×C₄×C₁₃	#107	1	2	yes	—
45	C₂×C₄×C₁₃	D₁₆	1	2	yes	—
46	C₂×C₄×C₁₃	SD₃₂	1	4	yes	—
47	C₂×C₄×C₁₃	Q₃₂	1	2	yes	—
48	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₄×C₁₃	#124	1	2	yes	—
50	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
51	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
52	C₂×Dic₁₃	—	8	4	no	—
53	C₂×Dic₁₃	—	8	4	no	—
54	C₂×Dic₁₃	—	8	4	no	—
55	C₈×C₁₃	#106	1	4	yes	—
56	C₈×C₁₃	#117	1	2	yes	—
57	C₈×C₁₃	#125	1	2	yes	—
58	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
59	C₂×#107	—	13	4	no	—
60	C₂×#107	—	26	2	no	—
61	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
62	#384	—	26	2	no	—
63	C₄×C₁₆	Dic₁₃	1	4	yes	complemented
64	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
65	C₂²×C₁₃	#486	1	2	yes	—
66	C₂²×C₁₃	C₂×D₁₆	1	1	yes	characteristic
67	C₂²×C₁₃	C₂×SD₃₂	1	2	yes	—
68	C₂²×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
69	C₄×C₁₃	#366	1	4	yes	—
70	C₄×C₁₃	#367	1	4	yes	—
71	C₄×C₁₃	#382	1	1	yes	characteristic
72	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
73	C₄×C₁₃	#487	1	2	yes	—
74	Dic₁₃	—	16	4	no	—
75	C₂²×C₈	D₅₂	1	1	yes	characteristic
76	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
77	C₂×C₄⋊C₄	—	26	4	no	—
78	C₂×C₄⋊C₄	—	52	2	no	—
79	C₂×C₄⋊C₄	—	52	2	no	—
80	C₂×C₄²	D₅₂	1	1	yes	characteristic
81	C₂×C₁₆	—	2	4	no	—
82	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
83	#107	—	26	8	no	—
84	#107	—	52	4	no	—
85	C₄×C₈	Dic₂₆	1	2	yes	—
86	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
87	C₂×C₁₃	#1834	1	1	yes	characteristic
88	C₂×C₁₃	C₂×#366	1	1	yes	characteristic
89	C₂×C₁₃	C₂×#367	1	1	yes	characteristic
90	C₂×C₁₃	#2240	1	2	yes	—
91	C₂×C₁₃	#2241	1	2	yes	—
92	C₂²×C₄	—	52	4	no	—
93	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
94	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
95	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
96	C₂×C₈	#6095	1	4	yes	—
97	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
98	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
99	C₂×C₈	#6127	1	4	yes	—
100	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
101	C₄⋊C₄	—	52	4	no	—
102	C₄⋊C₄	—	52	4	no	—
103	C₄⋊C₄	—	104	4	no	—
104	C₄⋊C₄	—	104	4	no	—
105	C₄²	Dic₅₂	1	2	yes	—
106	C₄²	C₄⋊Dic₁₃	1	2	yes	—
107	C₁₆	—	2	4	no	—
108	C₁₃	#12888	1	1	yes	characteristic, complemented, Sylow
109	C₂³	C₂×D₁₀₄	1	1	yes	characteristic
110	C₂×C₄	—	104	4	no	—
111	C₂×C₄	—	104	4	no	—
112	C₂×C₄	—	104	4	no	—
113	C₂×C₄	D₂₀₈	1	2	yes	—
114	C₂×C₄	#88040	1	4	yes	—
115	C₂×C₄	Dic₁₀₄	1	2	yes	—
116	C₂×C₄	#88058	1	2	yes	—
117	C₂×C₄	#88058	1	2	yes	—
118	C₂×C₄	#88129	1	2	yes	—
119	C₂×C₄	C₂×#6095	1	2	yes	—
120	C₂×C₄	C₂×Dic₅₂	1	1	yes	characteristic
121	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
122	C₈	#88057	1	4	yes	—
123	C₈	#88124	1	2	yes	—
124	C₈	#88180	1	2	yes	—
125	C₂²	#11718355	1	2	yes	—
126	C₂²	C₂×D₂₀₈	1	1	yes	characteristic
127	C₂²	C₂×#88040	1	2	yes	—
128	C₂²	C₂×Dic₁₀₄	1	1	yes	characteristic
129	C₂²	C₂×#88058	1	1	yes	characteristic
130	C₄	—	208	4	no	—
131	C₄	#11718096	1	4	yes	—
132	C₄	#11718097	1	4	yes	—
133	C₄	#11718342	1	2	yes	—
134	C₄	#11718597	1	1	yes	characteristic
135	C₄	C₂×#88057	1	1	yes	characteristic
136	C₂	#13114964	1	1	yes	characteristic
137	C₂	C₂×#11718096	1	1	yes	characteristic
138	C₂	C₂×#11718097	1	1	yes	characteristic
139	C₂	#13117060	1	2	yes	—
140	C₂	#13117064	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₁₀₄
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×C₄×C₁₆	D₁₃
hypocenter	C₁₃	#12888
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
9. C₄×C₁₃×C₁₆	C₄	semidirect
63. C₄×C₁₆	Dic₁₃	semidirect
108. C₁₃	#12888	semidirect

Maximal subgroups

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

subgroup	index
#13114996	2
#13112928	2
C₂×C₄×C₁₃×C₁₆	2
#12888	13