Subgroups — #15771910

Order 3328.

298 conjugacy classes of subgroups.

The subgroup lattice has 136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic
2	#13113119	C₂	1	1	yes	maximal, characteristic
3	#13112755	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×M₃₂	C₄	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×#6090	C₄	1	2	yes	—
8	#11718586	C₄	1	2	yes	—
9	C₁₃×#346	C₄	1	2	yes	—
10	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
11	C₄×#6090	C₄	1	2	yes	—
12	C₄×#6090	C₂²	1	2	yes	—
13	#11718047	C₄	1	2	yes	—
14	C₈×#1055	C₂²	1	2	yes	—
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₁₃×M₃₂	—	2	4	no	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
20	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²⋊#1055	C₈	1	4	yes	—
25	C₂×#6090	—	2	4	no	—
26	C₂×#6090	C₂×C₄	1	4	yes	—
27	C₄⋊#1055	C₈	1	4	yes	—
28	C₄×#1055	C₂×C₄	1	4	yes	—
29	#11401	—	13	1	no	maximal, Sylow
30	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
31	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
32	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
33	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
34	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
35	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
36	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₄²×C₁₃	C₄²	1	1	yes	characteristic
39	C₄²×C₁₃	C₂×C₈	1	2	yes	—
40	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×#1055	C₂×C₈	1	8	yes	—
42	C₁₃×C₁₆	—	2	4	no	—
43	#6090	—	2	4	no	—
44	C₄×M₃₂	D₁₃	1	1	yes	characteristic
45	C₂×C₄×C₁₆	—	13	1	no	—
46	#1450	—	13	1	no	—
47	#1312	—	13	4	no	—
48	C₂³×C₁₃	C₄×C₈	1	1	yes	characteristic
49	C₂×C₄×C₁₃	—	2	4	no	—
50	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
51	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₃	#97	1	2	yes	—
53	C₂×C₄×C₁₃	#97	1	2	yes	—
54	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
55	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
56	C₈×C₁₃	#97	1	2	yes	—
57	C₈×C₁₃	#97	1	2	yes	—
58	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
59	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
60	#1055	—	2	8	no	—
61	C₂×M₃₂	Dic₁₃	1	2	yes	—
62	C₂²×C₁₆	—	13	2	no	—
63	#431	—	13	2	no	—
64	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
65	#346	Dic₁₃	1	2	yes	—
66	C₄×C₁₆	—	13	2	no	—
67	C₄×C₁₆	—	13	2	no	—
68	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
69	#322	—	13	2	no	—
70	C₈²	—	13	2	no	—
71	C₂²×C₁₃	—	2	2	no	—
72	C₂²×C₁₃	#322	1	2	yes	—
73	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
74	C₄×C₁₃	—	2	2	no	—
75	C₄×C₁₃	#322	1	2	yes	—
76	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
77	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
78	C₄×C₁₃	#504	1	4	yes	—
79	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
80	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
81	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
82	M₃₂	—	2	4	no	—
83	C₂×C₁₆	—	13	4	no	—
84	C₂×C₁₆	—	26	4	no	—
85	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
86	C₄⋊C₈	—	13	4	no	—
87	C₂²⋊C₈	—	13	4	no	—
88	C₄×C₈	—	13	4	no	—
89	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
90	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
91	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
92	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
93	C₂×C₁₃	—	2	2	no	—
94	C₂×C₁₃	C₂×#322	1	1	yes	characteristic
95	C₂×C₁₃	#2108	1	2	yes	—
96	C₂²×C₄	C₈×D₁₃	1	2	yes	—
97	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
98	C₂×C₈	—	13	8	no	—
99	C₂×C₈	#6094	1	4	yes	—
100	C₂×C₈	#6099	1	4	yes	—
101	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
102	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
103	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
104	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
105	C₄²	C₈×D₁₃	1	2	yes	—
106	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
107	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
108	C₁₆	—	2	4	no	—
109	C₁₆	—	26	4	no	—
110	C₁₃	#11401	1	1	yes	characteristic, complemented, Sylow
111	C₂³	C₈×Dic₁₃	1	1	yes	characteristic
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	#88043	1	2	yes	—
114	C₂×C₄	C₈×Dic₁₃	1	2	yes	—
115	C₂×C₄	C₈×Dic₁₃	1	1	yes	characteristic
116	C₂×C₄	#88055	1	2	yes	—
117	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
118	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
119	C₈	—	26	8	no	—
120	C₈	#88043	1	2	yes	—
121	C₈	#88055	1	2	yes	—
122	C₈	C₂×#6094	1	2	yes	—
123	C₈	C₂×#6099	1	2	yes	—
124	C₂²	—	2	2	no	—
125	C₂²	#11718046	1	2	yes	—
126	C₂²	C₂×C₈×Dic₁₃	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	#11718046	1	2	yes	—
129	C₄	#11718568	1	4	yes	—
130	C₄	C₂×#88043	1	1	yes	characteristic
131	C₄	C₂×#88055	1	1	yes	characteristic
132	C₂	—	2	2	no	—
133	C₂	C₂×#11718046	1	1	yes	characteristic
134	C₂	#13116435	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₁₃
commutator, socle	C₂²×C₁₃	C₂×C₄×C₈
Fitting	C₄×C₁₃×M₃₂	C₂
prime radical	C₂³×C₁₃	C₄×C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₄×M₃₂	D₁₃
hypocenter	C₁₃	#11401
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
3. #13112755	C₂	semidirect
110. C₁₃	#11401	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#6090	2
#13113119	2
#13112755	2
C₄×C₁₃×M₃₂	2
#11401	13