Finite Group Databasebeta

← #13115975

Subgroups — #13115975

Order 1664.

290 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#88142C211yesmaximal, characteristic
2C2×C13×#103C211yesmaximal, characteristic
3#11718891C211yesmaximal, characteristic
4C2×#88075C211yesmaximal, characteristic
5#11718143C211yesmaximal, characteristic
6#11718142C211yesmaximal, characteristic
7#11718121C211yesmaximal, characteristic
8C22×Q8×C13C2211yescharacteristic
9C22×Dic26—21no—
10C22×C8×C13C2211yescharacteristic
11C2×C13×C4⋊C4C2211yescharacteristic
12C2×C4⋊Dic13C2211yescharacteristic
13C2×C4⋊Dic13C2211yescharacteristic
14C2×#6101—21no—
15C2×C4×Dic13C2211yescharacteristic
16C22×#1055C2211yescharacteristic
17#88142—22no—
18#88142—22no—
19C13×#103—22no—
20#88075—22no—
21#88071—21no—
22#88071—21no—
23C2×Q8×C13—21no—
24C2×Q8×C13—21no—
25C2×Q8×C13—21no—
26C2×Q8×C13—21no—
27C2×Q8×C13—21no—
28C2×Q8×C13Q812yescomplemented
29C22×C4×C13—21no—
30C22×C4×C13—21no—
31C22×C4×C13C2311yescharacteristic
32C22×Dic13—21no—
33C22×Dic13—21no—
34C22×Dic13D411yescharacteristic
35C22×Dic13D411yescharacteristic
36C2×Dic26—24no—
37C2×Dic26—42no—
38C2×Dic26—42no—
39C2×C8×C13—21no—
40C2×C8×C13—21no—
41C2×C8×C13—21no—
42C13×C4⋊C4—21no—
43C13×C4⋊C4D412yes—
44C4⋊Dic13—21no—
45C4⋊Dic13—21no—
46C4⋊Dic13—21no—
47C4⋊Dic13D412yes—
48#6101—24no—
49C4×Dic13—21no—
50C4×Dic13—21no—
51C2×#1055—21no—
52C2×#1055—21no—
53C2×#1055—21no—
54#2024—131nomaximal, Sylow
55C23×C13C2×D411yescharacteristic
56Q8×C13—22no—
57Q8×C13—22no—
58Q8×C13—41no—
59Q8×C13—41no—
60C2×C4×C13—22no—
61C2×C4×C13—22no—
62C2×C4×C13—41no—
63C2×C4×C13—41no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13C2×D411yescharacteristic
67C2×C4×C13C2×D411yescharacteristic
68C2×C4×C13C2×Q811yescharacteristic
69C2×C4×C13#4111yescharacteristic
70C2×C4×C13#4111yescharacteristic
71C2×C4×C13#4111yescharacteristic
72C2×Dic13—21no—
73C2×Dic13—21no—
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—22no—
77C2×Dic13—41no—
78C2×Dic13—41no—
79C2×Dic13—41no—
80C2×Dic13—41no—
81C2×Dic13—41no—
82C2×Dic13SD1612yes—
83C2×Dic13Q1612yes—
84Dic26—48no—
85C8×C13—41no—
86#1055—41no—
87C2×C4⋊Q8—131no—
88C2×#103—131no—
89C2×#103D1311yescharacteristic
90#391—131no—
91#340—131no—
92#340—131no—
93#336—131no—
94C22×C13#12011yescharacteristic
95C22×C13C22⋊Q811yescharacteristic
96C22×C13#12411yescharacteristic
97C22×C13C2×SD1611yescharacteristic
98C22×C13C2×Q1611yescharacteristic
99C22×C13AGL(1,ℤ/8)11yescharacteristic
100C22×C13#13711yescharacteristic
101C4×C13—42no—
102C4×C13—42no—
103C4×C13C22⋊Q811yescharacteristic
104C4×C13C22⋊Q811yescharacteristic
105C4×C13#12411yescharacteristic
106C4×C13#12411yescharacteristic
107Dic13—22no—
108Dic13—22no—
109Dic13—42no—
110Dic13—81no—
111C22×Q8—261no—
112C22×Q8C2×D1311yescharacteristic
113C22×C8—131no—
114C22×C8C2×D1311yescharacteristic
115C4⋊Q8—262no—
116C4⋊Q8—262no—
117C2×C4⋊C4—131no—
118C2×C4⋊C4—131no—
119C2×C4⋊C4—261no—
120C2×C4⋊C4C2×D1311yescharacteristic
121C2×C42—131no—
122#103—22no—
123#103—262no—
124#95—261no—
125#95—261no—
126C2×C13#39311yescharacteristic
127C2×C13#45011yescharacteristic
128C2×C13#45111yescharacteristic
129C2×C13#47511yescharacteristic
130C2×C13#47711yescharacteristic
131C2×C13#48711yescharacteristic
132C2×C13#48911yescharacteristic
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—264no—
139C2×Q8—522no—
140C2×Q8—522no—
141C2×Q8Dic2612yescomplemented
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—131no—
145C22×C4—131no—
146C22×C4—261no—
147C22×C4—261no—
148C22×C4C22×D1311yescharacteristic
149C2×C8—21no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—261no—
153C2×C8—261no—
154C2×C8—261no—
155C4⋊C4—21no—
156C4⋊C4—132no—
157C4⋊C4—264no—
158C4⋊C4—261no—
159C4⋊C4—261no—
160C4⋊C4—261no—
161C4⋊C4C22⋊D1312yes—
162C42—261no—
163C42—261no—
164C13#202411yescharacteristic, complemented, Sylow
165C23D4×D1311yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—528no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—132no—
178C2×C4—132no—
179C2×C4—261no—
180C2×C4—261no—
181C2×C4—261no—
182C2×C4—261no—
183C2×C4—262no—
184C2×C4—521no—
185C2×C4—521no—
186C2×C4—521no—
187C2×C4—521no—
188C2×C4—521no—
189C2×C4C2×Dic2611yescharacteristic
190C2×C4#612711yescharacteristic
191C2×C4D4×D1311yescharacteristic
192C2×C4#612911yescharacteristic
193C2×C4#612911yescharacteristic
194C2×C4C2×C22⋊D1311yescharacteristic
195C8—41no—
196C8—521no—
197C22#8813211yescharacteristic
198C22#8813911yescharacteristic
199C22SD16×D1311yescharacteristic
200C22#8816811yescharacteristic
201C22Q16×D1311yescharacteristic
202C22#8817211yescharacteristic
203C22#8819111yescharacteristic
204C4—42no—
205C4—42no—
206C4—262no—
207C4—262no—
208C4—522no—
209C4—1041no—
210C4#8813211yescharacteristic
211C4#8813911yescharacteristic
212C4#8817811yescharacteristic
213C4#8819011yescharacteristic
214C2#1171845211yescharacteristic
215C2#1171845311yescharacteristic
216C2#1171845511yescharacteristic
217C2#1171845611yescharacteristic
218C2#1171860811yescharacteristic
219C2#1171883011yescharacteristic
220C2#1171884711yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC2×C13×#103C2
socle, prime radicalC23×C13C2×D4
hypercenterC2×#103D13
hypocenterC13#2024
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
28. C2×Q8×C13Q8semidirect
141. C2×Q8Dic26semidirect
164. C13#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#881422
C2×C13×#1032
#117188912
C2×#880752
#117181432
#117181422
#117181212
#202413