Finite Group Databasebeta

← #15782008

Subgroups — #15782008

Order 3328.

370 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 99 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
1#13125360C211yesmaximal, characteristic
2#13116556C212yesmaximal
3#13112943C212yesmaximal
4#13112920C211yesmaximal, characteristic
5C13×#1971C211yesmaximal, characteristic
6C22×C13×Q16C2211yescharacteristic
7#11719175—21no—
8C2×C13×#106C2211yescharacteristic
9C2×C13×#103—21no—
10C2×C13×#97C2211yescharacteristic
11C13×#391—21no—
12#11718767—21no—
13#11718767C2212yes—
14C2×#88052C2212yes—
15#11718363—24no—
16#11718156—24no—
17C22×Q8×C13—21no—
18C2×C13×Q16—22no—
19C2×C13×Q16—22no—
20C2×C13×Q16—21no—
21C2×C13×Q16Q812yescomplemented
22C22×C8×C13D411yescharacteristic
23C22×C8×C13C2311yescharacteristic
24C2×C13×C4⋊C4—21no—
25C2×C42×C13D411yescharacteristic
26#88180—22no—
27#88178—42no—
28#88124—22no—
29#88123—22no—
30C4×Dic26—42no—
31C13×#106—22no—
32C13×#103—42no—
33C13×#97—22no—
34C13×#95—42no—
35#88058—22no—
36#88058D414yes—
37#88057—22no—
38#88057—22no—
39#88052—22no—
40#88052—22no—
41C2×#6090—22no—
42#13368—131nomaximal, Sylow
43C2×Q8×C13—22no—
44C2×Q8×C13—41no—
45C2×Q8×C13—41no—
46C2×Q8×C13—41no—
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C22×C4×C13—41no—
50C22×C4×C13—41no—
51C22×C4×C13D812yes—
52C22×C4×C13C2×D411yescharacteristic
53C2×Dic26—42no—
54C13×Q16—24no—
55C13×Q16—42no—
56C2×C8×C13—21no—
57C2×C8×C13—21no—
58C2×C8×C13SD1612yes—
59C2×C8×C13C2×D412yes—
60C2×C8×C13C2×Q811yescharacteristic
61C2×C8×C13#4112yes—
62C2×C8×C13#4111yescharacteristic
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C42×C13—21no—
66C42×C13—21no—
67C22⋊Dic13—42no—
68C4⋊Dic13—24no—
69C4⋊Dic13—42no—
70#6101—44no—
71C4×Dic13—42no—
72#6090—42no—
73#3162—131no—
74#2141—132no—
75#1971D1311yescharacteristic
76#1386—132no—
77#1377—131no—
78C23×C13C2×D811yescharacteristic
79Q8×C13—42no—
80Q8×C13—42no—
81Q8×C13—81no—
82Q8×C13—81no—
83C2×C4×C13—22no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—81no—
87C2×C4×C13—81no—
88C2×C4×C13—82no—
89C2×C4×C13—81no—
90C2×C4×C13#12011yescharacteristic
91C2×C4×C13C22⋊Q811yescharacteristic
92C2×C4×C13#12411yescharacteristic
93C2×C4×C13C2×SD1611yescharacteristic
94C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
95C2×C4×C13#13711yescharacteristic
96C2×Dic13—44no—
97Dic26—84no—
98C8×C13—22no—
99C8×C13C22⋊Q812yes—
100C8×C13#12412yes—
101C22×Q16C2×D1311yescharacteristic
102#533—261no—
103C2×M32—132no—
104#501—264no—
105#427—132no—
106#427—261no—
107C2×#106C2×D1311yescharacteristic
108C2×#103—21no—
109C2×#97C2×D1311yescharacteristic
110#391—21no—
111#358—264no—
112C22×C13—22no—
113C22×C13#44711yescharacteristic
114C22×C13#47411yescharacteristic
115C22×C13#48611yescharacteristic
116C4×C13—42no—
117C4×C13—82no—
118C4×C13—161no—
119C4×C13#39311yescharacteristic
120C4×C13#44811yescharacteristic
121C4×C13#47611yescharacteristic
122C4×C13#48911yescharacteristic
123Dic13—84no—
124C22×Q8—21no—
125C2×Q16—21no—
126C2×Q16—22no—
127C2×Q16—22no—
128C2×Q16Dic2612yescomplemented
129C22×C8C22⋊D1311yescharacteristic
130C22×C8C22×D1311yescharacteristic
131C4⋊Q8—262no—
132#125—262no—
133C22⋊Q8—522no—
134C4×Q8—522no—
135#117—262no—
136C2×C4⋊C4—21no—
137C2×C42C22⋊D1311yescharacteristic
138M32—262no—
139M32—262no—
140C2×C16—262no—
141#107—134no—
142#107—262no—
143#106—22no—
144#106—262no—
145#106—262no—
146#103—42no—
147#97—22no—
148#95—42no—
149C2×C13—21no—
150C2×C13—21no—
151C2×C13#202311yescharacteristic
152C2×C13#219112yes—
153C2×Q8—22no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—522no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4#610412yes—
163C22×C4C2×C22⋊D1311yescharacteristic
164Q16—24no—
165Q16—42no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8#610512yes—
169C2×C8C2×Dic2611yescharacteristic
170C2×C8#612711yescharacteristic
171C2×C8D4×D1312yes—
172C2×C8#612912yes—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—264no—
176C4⋊C4—524no—
177C4⋊C4—522no—
178C22⋊C4—522no—
179C42—21no—
180C42—21no—
181C42—522no—
182C16—522no—
183C13#1336811yescharacteristic, complemented, Sylow
184C23C2×#610411yescharacteristic
185Q8—42no—
186Q8—42no—
187Q8—81no—
188Q8—81no—
189Q8—1044no—
190C2×C4—22no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4—524no—
198C2×C4#8817811yescharacteristic
199C2×C4C2×#610511yescharacteristic
200C2×C4#8819011yescharacteristic
201C2×C4#8819111yescharacteristic
202C2×C4#8820311yescharacteristic
203C2×C4#8820511yescharacteristic
204C8—22no—
205C8#8813212yes—
206C8#8813912yes—
207C22—22no—
208C22#1171866811yescharacteristic
209C22#1171869711yescharacteristic
210C22#1171873111yescharacteristic
211C4—42no—
212C4—82no—
213C4—161no—
214C4—1044no—
215C4#1171860811yescharacteristic
216C4#1171866911yescharacteristic
217C4#1171870111yescharacteristic
218C4#1171871611yescharacteristic
219C2—21no—
220C2—21no—
221C2#1311597211yescharacteristic
222C2#1311678612yes—
subgroupG/H
centerC22#11718697
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC13×#1971C2
socleC22×C13#447
prime radicalC23×C13C2×D8
hypercenter#1971D13
hypocenterC13#13368
LCSG ▷ C22×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #1971

Complements

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

NH ≅ G/Ntype
21. C2×C13×Q16Q8semidirect
128. C2×Q16Dic26semidirect
183. C13#13368semidirect

Maximal subgroups

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

subgroupindex
#131253602
#131165562
#131129432
#131129202
C13×#19712
#1336813