Subgroups — #15794119

Order 3328.

1422 conjugacy classes of subgroups.

The subgroup lattice has 172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718597	C₂	1	2	yes	maximal
2	#13113066	C₂	1	4	yes	maximal
3	#13113063	C₂	1	8	yes	maximal
4	C₂×C₄³×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₃	C₂²	1	4	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₁₃	C₂²	1	4	yes	—
9	C₄³×C₁₃	C₄	1	8	yes	complemented
10	C₂×#88071	C₂²	1	8	yes	—
11	C₂×#88071	C₂²	1	16	yes	—
12	#11718597	—	2	8	no	—
13	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
14	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
15	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂³×Dic₁₃	C₂³	1	8	yes	—
17	C₂×C₄²×C₁₃	—	2	16	no	—
18	C₂×C₄²×C₁₃	—	2	8	no	—
19	C₂×C₄²×C₁₃	C₂×C₄	1	16	yes	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
22	C₂×C₄²×C₁₃	D₄	1	4	yes	—
23	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
24	C₂×C₄⋊Dic₁₃	—	2	8	no	—
25	C₂×C₄⋊Dic₁₃	—	2	16	no	—
26	#88071	—	2	16	no	—
27	#88071	—	2	32	no	—
28	#14689	—	13	1	no	maximal, Sylow
29	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
30	C₂²×C₄×C₁₃	—	2	8	no	—
31	C₂²×C₄×C₁₃	—	2	8	no	—
32	C₂²×C₄×C₁₃	—	2	8	no	—
33	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
34	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
35	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
36	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
37	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
39	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
40	C₂²×C₄×C₁₃	#41	1	16	yes	—
41	C₂²×C₄×C₁₃	#41	1	8	yes	—
42	C₂²×Dic₁₃	—	2	8	no	—
43	C₂²×Dic₁₃	—	2	32	no	—
44	C₂²×Dic₁₃	—	2	16	no	—
45	C₄²×C₁₃	—	2	32	no	—
46	C₄²×C₁₃	—	2	16	no	—
47	C₄²×C₁₃	C₄⋊C₄	1	16	yes	—
48	C₄⋊Dic₁₃	—	4	16	no	—
49	C₂×#382	—	13	2	no	—
50	C₂×C₄³	D₁₃	1	1	yes	characteristic
51	C₄⋊#95	—	13	4	no	—
52	#1434	—	13	8	no	—
53	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
54	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
55	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
56	C₂³×C₁₃	C₂×#41	1	4	yes	—
57	C₂³×C₁₃	C₂×#41	1	8	yes	—
58	C₂×C₄×C₁₃	—	2	8	no	—
59	C₂×C₄×C₁₃	—	2	8	no	—
60	C₂×C₄×C₁₃	—	2	8	no	—
61	C₂×C₄×C₁₃	—	2	32	no	—
62	C₂×C₄×C₁₃	—	2	8	no	—
63	C₂×C₄×C₁₃	—	2	8	no	—
64	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
65	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
66	C₂×C₄×C₁₃	#117	1	16	yes	—
67	C₂×C₄×C₁₃	#117	1	8	yes	—
68	C₂×C₄×C₁₃	#124	1	8	yes	—
69	C₂×C₄×C₁₃	#125	1	8	yes	—
70	C₂×Dic₁₃	—	4	8	no	—
71	C₂×Dic₁₃	—	4	32	no	—
72	C₂×Dic₁₃	—	4	16	no	—
73	C₂²×C₄⋊C₄	—	13	4	no	—
74	C₂²×C₄²	C₂×D₁₃	1	4	yes	—
75	C₂²×C₄²	C₂×D₁₃	1	2	yes	—
76	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
77	#382	—	26	8	no	—
78	C₂×#95	—	13	16	no	—
79	C₂×#95	—	13	8	no	—
80	C₄³	Dic₁₃	1	8	yes	complemented
81	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₁₃	C₂×#117	1	2	yes	—
83	C₂²×C₁₃	C₂×#117	1	4	yes	—
84	C₂²×C₁₃	C₂×#124	1	2	yes	—
85	C₂²×C₁₃	C₂×#125	1	2	yes	—
86	C₂²×C₁₃	#529	1	16	yes	—
87	C₂²×C₁₃	#532	1	4	yes	—
88	C₂²×C₁₃	#533	1	4	yes	—
89	C₄×C₁₃	—	2	16	no	—
90	C₄×C₁₃	—	2	8	no	—
91	C₄×C₁₃	#382	1	8	yes	—
92	Dic₁₃	—	8	8	no	—
93	C₂³×C₄	—	13	8	no	—
94	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
95	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
96	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
97	C₂×C₄⋊C₄	—	26	8	no	—
98	C₂×C₄⋊C₄	—	26	16	no	—
99	C₂×C₄²	—	2	16	no	—
100	C₂×C₄²	—	2	8	no	—
101	C₂×C₄²	Dic₂₆	1	4	yes	—
102	C₂×C₄²	D₅₂	1	4	yes	—
103	C₂×C₄²	C₂×Dic₁₃	1	16	yes	—
104	C₂×C₄²	C₂×Dic₁₃	1	8	yes	—
105	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
106	#95	—	26	16	no	—
107	#95	—	26	32	no	—
108	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
109	C₂×C₁₃	#2283	1	4	yes	—
110	C₂×C₁₃	#2285	1	2	yes	—
111	C₂×C₁₃	#2861	1	4	yes	—
112	C₂×C₁₃	#2864	1	4	yes	—
113	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
114	C₂²×C₄	—	2	8	no	—
115	C₂²×C₄	—	2	8	no	—
116	C₂²×C₄	—	2	8	no	—
117	C₂²×C₄	—	26	8	no	—
118	C₂²×C₄	—	26	32	no	—
119	C₂²×C₄	—	26	16	no	—
120	C₂²×C₄	C₂×Dic₂₆	1	4	yes	—
121	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
122	C₂²×C₄	C₂×D₅₂	1	4	yes	—
123	C₂²×C₄	C₂×D₅₂	1	2	yes	—
124	C₂²×C₄	#6127	1	16	yes	—
125	C₂²×C₄	#6127	1	8	yes	—
126	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
127	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
128	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
129	C₄⋊C₄	—	52	16	no	—
130	C₄²	—	2	32	no	—
131	C₄²	—	2	16	no	—
132	C₄²	C₄⋊Dic₁₃	1	16	yes	—
133	C₁₃	#14689	1	1	yes	characteristic, complemented, Sylow
134	C₂³	C₂²×Dic₂₆	1	1	yes	characteristic
135	C₂³	C₂²×D₅₂	1	1	yes	characteristic
136	C₂³	C₂×#6127	1	4	yes	—
137	C₂³	C₂×#6127	1	8	yes	—
138	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
139	C₂×C₄	—	2	8	no	—
140	C₂×C₄	—	2	8	no	—
141	C₂×C₄	—	2	32	no	—
142	C₂×C₄	—	2	8	no	—
143	C₂×C₄	—	2	8	no	—
144	C₂×C₄	—	2	8	no	—
145	C₂×C₄	—	52	8	no	—
146	C₂×C₄	—	52	16	no	—
147	C₂×C₄	—	52	32	no	—
148	C₂×C₄	#88124	1	8	yes	—
149	C₂×C₄	#88129	1	8	yes	—
150	C₂×C₄	C₂×C₄⋊Dic₁₃	1	8	yes	—
151	C₂×C₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
152	C₂×C₄	#88180	1	16	yes	—
153	C₂×C₄	#88180	1	8	yes	—
154	C₂²	C₂×#88124	1	2	yes	—
155	C₂²	#11719175	1	4	yes	—
156	C₂²	C₂×#88129	1	2	yes	—
157	C₂²	#11719182	1	4	yes	—
158	C₂²	#11719184	1	16	yes	—
159	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
160	C₂²	C₂×#88180	1	2	yes	—
161	C₂²	C₂×#88180	1	4	yes	—
162	C₄	—	2	16	no	—
163	C₄	—	2	8	no	—
164	C₄	—	104	8	no	—
165	C₄	#11718597	1	8	yes	—
166	C₂	C₂×#11718597	1	1	yes	characteristic
167	C₂	#13117234	1	4	yes	—
168	C₂	#13117243	1	2	yes	—
169	C₂	#13123208	1	4	yes	—
170	C₂	#13123223	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₁₃
commutator	C₂³×C₁₃	C₂³×C₄
Fitting	C₂×C₄³×C₁₃	C₂
socle, prime radical, cosocle	C₂⁴×C₁₃	C₂⁴
hypercenter	C₂×C₄³	D₁₃
hypocenter	C₁₃	#14689
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
9. C₄³×C₁₃	C₄	semidirect
80. C₄³	Dic₁₃	semidirect
133. C₁₃	#14689	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718597	2
#13113066	2
#13113063	2
C₂×C₄³×C₁₃	2
#14689	13