Subgroups — #15779374

Order 3328.

266 conjugacy classes of subgroups.

The subgroup lattice has 188 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	#13116608	C₂	1	2	yes	maximal
3	#13116432	C₂	1	1	yes	maximal, characteristic
4	#13114959	C₂	1	2	yes	maximal
5	C₁₃×#2158	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₁₃×#427	C₂²	1	2	yes	—
8	C₂×#88059	C₂²	1	2	yes	—
9	#11718762	C₂²	1	1	yes	characteristic
10	C₂×#88052	C₂²	1	1	yes	characteristic
11	C₁₃×#367	—	2	1	no	—
12	C₁₃×#366	—	2	1	no	—
13	#11718125	—	2	2	no	—
14	#11718123	—	2	2	no	—
15	#11718098	—	2	1	no	—
16	#11718098	—	2	1	no	—
17	#11718094	C₄	1	2	yes	complemented
18	C₁₆×Dic₁₃	C₄	1	2	yes	complemented
19	#11718079	—	2	4	no	—
20	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₁₃×#117	—	2	2	no	—
22	#88180	D₄	1	1	yes	characteristic
23	C₂×#6099	—	2	2	no	—
24	C₂×#6099	D₄	1	1	yes	characteristic
25	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
26	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
27	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
28	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
29	C₂×C₁₃×C₁₆	Q₈	1	1	yes	characteristic
30	C₂×C₁₃×C₁₆	Q₈	1	1	yes	characteristic
31	C₁₃×#107	—	2	2	no	—
32	C₁₃×#106	—	2	2	no	—
33	#88059	—	2	2	no	—
34	#88059	—	2	2	no	—
35	#88055	Q₈	1	2	yes	—
36	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
37	#88052	D₄	1	2	yes	—
38	#88052	Q₈	1	2	yes	—
39	C₂×#6090	C₂×C₄	1	2	yes	—
40	#12911	—	13	1	no	maximal, Sylow
41	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₁₃×C₄⋊C₄	—	4	2	no	—
49	C₁₃×C₂²⋊C₄	—	4	2	no	—
50	C₄²×C₁₃	—	4	2	no	—
51	C₂²⋊Dic₁₃	—	2	1	no	—
52	C₄⋊Dic₁₃	—	2	1	no	—
53	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
54	#6099	—	2	1	no	—
55	#6099	—	2	1	no	—
56	#6099	—	4	2	no	—
57	#6099	—	4	2	no	—
58	C₂×#1055	—	4	2	no	—
59	C₂×#1055	C₄⋊C₄	1	2	yes	—
60	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
61	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
62	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
63	C₁₃×C₁₆	C₄⋊C₄	1	1	yes	characteristic
64	#6090	C₄⋊C₄	1	4	yes	—
65	C₂×#368	—	13	1	no	—
66	#2158	D₁₃	1	1	yes	characteristic
67	#2155	—	13	2	no	—
68	#2108	—	13	1	no	—
69	#1833	—	13	2	no	—
70	C₂³×C₁₃	#135	1	1	yes	characteristic
71	C₂×C₄×C₁₃	—	8	2	no	—
72	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
77	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
78	C₂×Dic₁₃	—	2	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	—	2	2	no	—
84	#1055	—	8	2	no	—
85	C₂×M₃₂	—	13	1	no	—
86	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
87	C₂×#108	—	13	2	no	—
88	#427	C₂×D₁₃	1	2	yes	—
89	#405	—	13	1	no	—
90	#368	—	26	1	no	—
91	#368	—	26	1	no	—
92	#367	—	2	1	no	—
93	#366	—	2	1	no	—
94	#365	—	26	4	no	—
95	#346	—	13	2	no	—
96	C₄×C₁₆	—	13	2	no	—
97	#344	—	26	2	no	—
98	H(3,ℤ/4)	—	26	2	no	—
99	C₂²×C₁₃	—	4	1	no	—
100	C₂²×C₁₃	#427	1	1	yes	characteristic
101	C₂²×C₁₃	#495	1	1	yes	characteristic
102	C₂²×C₁₃	#499	1	1	yes	characteristic
103	C₄×C₁₃	—	16	2	no	—
104	C₄×C₁₃	#384	1	1	yes	characteristic
105	C₄×C₁₃	#427	1	1	yes	characteristic
106	C₄×C₁₃	#495	1	1	yes	characteristic
107	C₄×C₁₃	#499	1	1	yes	characteristic
108	Dic₁₃	—	4	2	no	—
109	C₂×M₁₆	—	13	1	no	—
110	C₂×M₁₆	—	26	2	no	—
111	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
112	#117	—	2	2	no	—
113	#117	—	13	1	no	—
114	M₃₂	—	13	2	no	—
115	M₃₂	—	13	2	no	—
116	C₂×C₁₆	—	13	2	no	—
117	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
118	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
119	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
120	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
121	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
122	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
123	#108	—	26	2	no	—
124	#108	—	26	2	no	—
125	#107	—	2	2	no	—
126	#106	—	2	2	no	—
127	#97	—	13	2	no	—
128	C₄×C₈	—	13	2	no	—
129	C₂×C₁₃	—	2	1	no	—
130	C₂×C₁₃	—	2	1	no	—
131	C₂×C₁₃	—	2	1	no	—
132	C₂×C₁₃	#1846	1	1	yes	characteristic
133	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
134	M₁₆	—	26	1	no	—
135	M₁₆	—	26	1	no	—
136	M₁₆	—	52	2	no	—
137	M₁₆	—	52	2	no	—
138	C₂×C₈	—	13	2	no	—
139	C₂×C₈	—	52	2	no	—
140	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
141	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
142	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
143	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
144	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
145	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
146	C₄⋊C₄	—	4	2	no	—
147	C₄⋊C₄	—	26	1	no	—
148	C₂²⋊C₄	—	4	2	no	—
149	C₂²⋊C₄	—	26	1	no	—
150	C₄²	—	4	2	no	—
151	C₄²	—	13	2	no	—
152	C₁₆	—	13	4	no	—
153	C₁₆	#6101	1	1	yes	characteristic
154	C₁₆	#6101	1	1	yes	characteristic
155	C₁₆	#6101	1	1	yes	characteristic
156	C₁₆	#6101	1	1	yes	characteristic
157	C₁₃	#12911	1	1	yes	characteristic, complemented, Sylow
158	C₂³	#88166	1	1	yes	characteristic
159	C₂×C₄	—	8	2	no	—
160	C₂×C₄	—	26	2	no	—
161	C₂×C₄	#88142	1	1	yes	characteristic
162	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
163	C₂×C₄	#88166	1	1	yes	characteristic
164	C₂×C₄	#88173	1	1	yes	characteristic
165	C₂×C₄	#88173	1	1	yes	characteristic
166	C₂×C₄	#88194	1	1	yes	characteristic
167	C₈	—	26	2	no	—
168	C₈	—	104	2	no	—
169	C₈	#88142	1	1	yes	characteristic
170	C₈	C₄⋊C₄×D₁₃	1	1	yes	characteristic
171	C₈	C₂×#6101	1	1	yes	characteristic
172	C₈	#88198	1	1	yes	characteristic
173	C₂²	—	4	1	no	—
174	C₂²	#11718539	1	1	yes	characteristic
175	C₂²	#11718541	1	1	yes	characteristic
176	C₂²	#11718816	1	1	yes	characteristic
177	C₄	—	16	2	no	—
178	C₄	—	52	2	no	—
179	C₄	#11718539	1	1	yes	characteristic
180	C₄	#11718541	1	1	yes	characteristic
181	C₄	#11718637	1	1	yes	characteristic
182	C₄	#11718852	1	1	yes	characteristic
183	C₂	—	2	1	no	—
184	C₂	—	2	1	no	—
185	C₂	—	2	1	no	—
186	C₂	#13114999	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11718541
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#2158	C₂
socle	C₂×C₁₃	#1846
prime radical	C₂³×C₁₃	#135
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#2158	D₁₃
hypocenter	C₁₃	#12911
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2158

Complements

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

N	H ≅ G/N	type
17. #11718094	C₄	semidirect
18. C₁₆×Dic₁₃	C₄	semidirect
157. C₁₃	#12911	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
#13116608	2
#13116432	2
#13114959	2
C₁₃×#2158	2
#12911	13