Subgroups — #15779366

Order 3328.

314 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718098	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718085	C₂	1	2	yes	maximal
3	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#13115006	C₂	1	2	yes	maximal
5	C₂×C₁₃×#368	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#108	C₂²	1	2	yes	—
8	C₂×#88062	—	2	2	no	—
9	#11718779	—	2	2	no	—
10	C₂×#88059	C₂²	1	2	yes	—
11	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂²×#6090	C₂²	1	1	yes	characteristic
13	C₁₃×#368	—	2	2	no	—
14	#11718098	—	2	2	no	—
15	C₁₆×Dic₁₃	C₄	1	2	yes	—
16	C₁₆×Dic₁₃	C₄	1	2	yes	—
17	#11718085	—	2	4	no	—
18	C₂×C₁₃×M₁₆	—	2	2	no	—
19	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
21	C₂×#6099	—	2	2	no	—
22	C₂²×#1055	D₄	1	1	yes	characteristic
23	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
24	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
25	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
26	C₁₃×#108	—	2	2	no	—
27	C₁₃×#108	—	2	2	no	—
28	#88062	—	4	4	no	—
29	#88059	—	2	2	no	—
30	#88059	—	2	2	no	—
31	#88054	—	4	4	no	—
32	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
33	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
34	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
35	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
36	C₂×#6090	C₂×C₄	1	2	yes	—
37	C₂×#6090	D₄	1	2	yes	—
38	C₂×#6090	Q₈	1	2	yes	—
39	#12909	—	13	1	no	maximal, Sylow
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×Dic₁₃	Q₁₆	1	2	yes	—
42	C₁₃×M₁₆	—	4	2	no	—
43	C₁₃×M₁₆	—	4	2	no	—
44	C₂×C₈×C₁₃	—	4	2	no	—
45	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
51	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
52	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
53	C₄×Dic₁₃	D₈	1	2	yes	—
54	#6099	—	4	2	no	—
55	#6099	—	4	2	no	—
56	C₂×#1055	—	4	2	no	—
57	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
58	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
59	C₂×#1055	D₈	1	2	yes	—
60	C₂×#1055	Q₁₆	1	2	yes	—
61	C₁₃×C₁₆	C₄⋊C₄	1	4	yes	—
62	#6090	C₄⋊C₄	1	4	yes	—
63	C₂×#368	—	13	1	no	—
64	C₂×#368	—	13	2	no	—
65	C₂×#368	D₁₃	1	1	yes	characteristic
66	C₂×C₄×C₁₆	—	13	1	no	—
67	#1848	—	13	2	no	—
68	C₂³×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
75	C₂×Dic₁₃	—	2	4	no	—
76	C₂×Dic₁₃	#107	1	2	yes	—
77	C₂×Dic₁₃	#107	1	2	yes	—
78	C₈×C₁₃	—	8	2	no	—
79	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
82	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
83	#1055	—	8	2	no	—
84	#1055	#107	1	2	yes	—
85	#1055	#107	1	2	yes	—
86	C₂²×C₁₆	—	13	1	no	—
87	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
88	C₂×#108	—	13	2	no	—
89	C₂×#108	—	26	2	no	—
90	C₂×#108	C₂×D₁₃	1	2	yes	—
91	#423	—	26	2	no	—
92	C₂×C₄×C₈	—	13	1	no	—
93	#368	—	2	2	no	—
94	#368	—	26	4	no	—
95	#368	—	26	2	no	—
96	C₄×C₁₆	—	13	2	no	—
97	C₄×C₁₆	—	13	2	no	—
98	C₂²×C₁₃	—	2	2	no	—
99	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
100	C₂²×C₁₃	#494	1	1	yes	characteristic
101	C₂²×C₁₃	#500	1	1	yes	characteristic
102	C₄×C₁₃	#384	1	1	yes	characteristic
103	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
104	C₄×C₁₃	#493	1	1	yes	characteristic
105	C₄×C₁₃	#500	1	1	yes	characteristic
106	Dic₁₃	—	2	2	no	—
107	Dic₁₃	#368	1	4	yes	complemented
108	C₂×M₁₆	—	2	2	no	—
109	C₂×M₁₆	—	26	2	no	—
110	C₂²×C₈	—	13	1	no	—
111	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
112	C₂×C₄²	—	13	1	no	—
113	C₂×C₁₆	—	13	2	no	—
114	C₂×C₁₆	—	13	2	no	—
115	C₂×C₁₆	—	13	2	no	—
116	C₂×C₁₆	Dic₂₆	1	2	yes	—
117	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
118	C₂×C₁₆	C₂²⋊D₁₃	1	2	yes	—
119	#108	—	2	2	no	—
120	#108	—	2	2	no	—
121	#108	—	26	2	no	—
122	#108	—	26	2	no	—
123	#108	—	52	4	no	—
124	C₄⋊C₈	—	52	4	no	—
125	C₄×C₈	—	13	1	no	—
126	C₄×C₈	—	13	1	no	—
127	C₄×C₈	—	13	1	no	—
128	C₄×C₈	—	13	1	no	—
129	C₂×C₁₃	—	2	1	no	—
130	C₂×C₁₃	—	2	1	no	—
131	C₂×C₁₃	#1845	1	1	yes	characteristic
132	C₂×C₁₃	C₂×#368	1	2	yes	—
133	C₂²×C₄	—	13	2	no	—
134	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
135	M₁₆	—	4	2	no	—
136	M₁₆	—	4	2	no	—
137	M₁₆	—	52	2	no	—
138	M₁₆	—	52	2	no	—
139	C₂×C₈	—	4	2	no	—
140	C₂×C₈	—	13	1	no	—
141	C₂×C₈	—	13	1	no	—
142	C₂×C₈	—	13	2	no	—
143	C₂×C₈	—	13	2	no	—
144	C₂×C₈	—	52	2	no	—
145	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
146	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
147	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
148	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
149	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
150	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
151	C₄²	—	13	1	no	—
152	C₄²	—	13	1	no	—
153	C₄²	—	13	2	no	—
154	C₁₆	—	13	4	no	—
155	C₁₆	#6101	1	4	yes	—
156	C₁₃	#12909	1	1	yes	characteristic, complemented, Sylow
157	C₂³	Q₁₆×D₁₃	1	1	yes	characteristic
158	C₂×C₄	—	13	2	no	—
159	C₂×C₄	—	13	2	no	—
160	C₂×C₄	—	26	4	no	—
161	C₂×C₄	#88142	1	1	yes	characteristic
162	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
163	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
164	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
165	C₂×C₄	Q₁₆×D₁₃	1	1	yes	characteristic
166	C₂×C₄	#88194	1	1	yes	characteristic
167	C₈	—	8	2	no	—
168	C₈	—	13	2	no	—
169	C₈	—	13	2	no	—
170	C₈	—	104	2	no	—
171	C₈	#88142	1	1	yes	characteristic
172	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
173	C₈	C₂×#6101	1	1	yes	characteristic
174	C₈	#88198	1	1	yes	characteristic
175	C₂²	—	2	2	no	—
176	C₂²	#11718535	1	1	yes	characteristic
177	C₂²	D₁₃×#107	1	1	yes	characteristic
178	C₂²	#11718842	1	1	yes	characteristic
179	C₄	—	13	4	no	—
180	C₄	—	26	2	no	—
181	C₄	#11718535	1	1	yes	characteristic
182	C₄	D₁₃×#107	1	1	yes	characteristic
183	C₄	#11718637	1	1	yes	characteristic
184	C₄	#11718812	1	1	yes	characteristic
185	C₂	—	2	1	no	—
186	C₂	—	2	1	no	—
187	C₂	#13114994	1	1	yes	characteristic
188	C₂	D₁₃×#368	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₈×D₁₃
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#368	C₂
socle	C₂²×C₁₃	C₂×#107
prime radical	C₂³×C₁₃	C₂×Q₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#368	D₁₃
hypocenter	C₁₃	#12909
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

Complements

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

N	H ≅ G/N	type
107. Dic₁₃	#368	semidirect
156. C₁₃	#12909	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718098	2
C₂×#11718085	2
C₂×C₁₆×Dic₁₃	2
#13115006	2
C₂×C₁₃×#368	2
#12909	13