Finite Group Databasebeta

← #15782308

Subgroups — #15782308

Order 3328.

436 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 101 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×#11718157C212yesmaximal
2#13116556C212yesmaximal
3#13115584C211yesmaximal, characteristic
4#13112918C211yesmaximal, characteristic
5C2×C13×#494C211yesmaximal, characteristic
6C22×C13×Q16—21no—
7C22×C13×Q16C2212yes—
8C2×C13×C4⋊Q8—21no—
9C13×#494—24no—
10C2×C4×C8×C13C2211yescharacteristic
11C2×#88059C2211yescharacteristic
12#11718767C2211yescharacteristic
13#11718763—21no—
14C2×#88052C2212yes—
15#11718157—24no—
16#11718156—24no—
17#11718115—21no—
18C22×Q8×C13—22no—
19C2×C13×Q16—24no—
20C2×C13×Q16—22no—
21C2×C13×Q16—22no—
22C2×C13×Q16—22no—
23C2×C13×Q16—22no—
24C2×C13×Q16—22no—
25C2×C13×Q16—42no—
26C2×C13×Q16—42no—
27C2×C13×Q16D414yes—
28C22×C8×C13D411yescharacteristic
29C22×C8×C13C2311yescharacteristic
30C13×C4⋊Q8—24no—
31C13×C4⋊Q8—42no—
32C2×C13×C4⋊C4—42no—
33C2×C42×C13D411yescharacteristic
34#88180—21no—
35C2×#6099—21no—
36C4×C8×C13—22no—
37#88059—22no—
38#88058D412yes—
39#88057—21no—
40#88054—42no—
41#88052—22no—
42#88052—22no—
43C2×#6090—22no—
44#13415—131nomaximal, Sylow
45C2×Q8×C13—24no—
46C2×Q8×C13—42no—
47C2×Q8×C13—42no—
48C2×Q8×C13—42no—
49C2×Q8×C13—42no—
50C2×Q8×C13—42no—
51C22×C4×C13—21no—
52C22×C4×C13—42no—
53C22×C4×C13C2×D411yescharacteristic
54C13×Q16—24no—
55C13×Q16—24no—
56C13×Q16—48no—
57C13×Q16—42no—
58C13×Q16—42no—
59C2×C8×C13—21no—
60C2×C8×C13—21no—
61C2×C8×C13D812yes—
62C2×C8×C13C2×D411yescharacteristic
63C2×C8×C13C2×D412yes—
64C2×C8×C13#4112yes—
65C2×C8×C13#4111yescharacteristic
66C13×C4⋊C4—48no—
67C42×C13—21no—
68C42×C13SD1612yes—
69C22⋊Dic13—41no—
70C4⋊Dic13—22no—
71C4×Dic13—41no—
72#6099—41no—
73#6099—41no—
74C2×#1055—41no—
75#6090—42no—
76C2×#494D1311yescharacteristic
77C2×#362—132no—
78#2141—132no—
79#1945—131no—
80#1376—131no—
81C23×C13AGL(1,ℤ/8)11yescharacteristic
82Q8×C13—44no—
83Q8×C13—44no—
84Q8×C13—82no—
85Q8×C13—82no—
86C2×C4×C13—24no—
87C2×C4×C13—22no—
88C2×C4×C13—44no—
89C2×C4×C13—82no—
90C2×C4×C13—82no—
91C2×C4×C13#12011yescharacteristic
92C2×C4×C13#12111yescharacteristic
93C2×C4×C13#12411yescharacteristic
94C2×C4×C13C2×D811yescharacteristic
95C2×C4×C13C2×SD1611yescharacteristic
96C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
97C2×Dic13—42no—
98C8×C13—22no—
99C8×C13#12112yes—
100C8×C13#12312yes—
101#1055—81no—
102C22×Q16—21no—
103C22×Q16C2×D1312yes—
104C2×C4⋊Q8—21no—
105C2×M32—132no—
106#494—24no—
107C2×#108—131no—
108#427—131no—
109#424—261no—
110C2×C4×C8C2×D1311yescharacteristic
111#362—264no—
112#358—264no—
113#339—261no—
114C22×C13—22no—
115C22×C13#45011yescharacteristic
116C22×C13#45911yescharacteristic
117C22×C13#49011yescharacteristic
118C4×C13—24no—
119C4×C13—84no—
120C4×C13#39411yescharacteristic
121C4×C13#44711yescharacteristic
122C4×C13#46011yescharacteristic
123C4×C13#48611yescharacteristic
124Dic13—82no—
125C22×Q8—22no—
126C2×Q16—24no—
127C2×Q16—22no—
128C2×Q16—22no—
129C2×Q16—22no—
130C2×Q16—22no—
131C2×Q16—22no—
132C2×Q16—42no—
133C2×Q16—42no—
134C2×Q16C22⋊D1314yes—
135C2×M16—261no—
136C22×C8C22⋊D1311yescharacteristic
137C22×C8C22×D1311yescharacteristic
138C4⋊Q8—24no—
139C4⋊Q8—42no—
140#117—261no—
141C2×C4⋊C4—42no—
142C2×C42C22⋊D1311yescharacteristic
143M32—262no—
144M32—262no—
145C2×C16—262no—
146#108—262no—
147#107—132no—
148#106—261no—
149C4⋊C8—522no—
150C4×C8—22no—
151C2×C13—21no—
152C2×C13—21no—
153C2×C13#204111yescharacteristic
154C2×C13#221412yes—
155C2×Q8—24no—
156C2×Q8—42no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8—42no—
160C2×Q8—42no—
161C22×C4—21no—
162C22×C4—42no—
163C22×C4C2×C22⋊D1311yescharacteristic
164Q16—24no—
165Q16—24no—
166Q16—48no—
167Q16—42no—
168Q16—42no—
169M16—521no—
170M16—521no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—521no—
174C2×C8#610412yes—
175C2×C8D4×D1311yescharacteristic
176C2×C8#612911yescharacteristic
177C2×C8#612912yes—
178C2×C8C2×C22⋊D1312yes—
179C4⋊C4—48no—
180C4⋊C4—262no—
181C22⋊C4—521no—
182C42—21no—
183C42—521no—
184C42#610512yes—
185C16—522no—
186C13#1341511yescharacteristic, complemented, Sylow
187C23#8818611yescharacteristic
188Q8—44no—
189Q8—44no—
190Q8—82no—
191Q8—82no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—82no—
196C2×C4—82no—
197C2×C4—522no—
198C2×C4C2×#610411yescharacteristic
199C2×C4#8818611yescharacteristic
200C2×C4C2×#610511yescharacteristic
201C2×C4#8819011yescharacteristic
202C2×C4#8819211yescharacteristic
203C2×C4#8820711yescharacteristic
204C8—22no—
205C8—1041no—
206C8#8818912yes—
207C8#8819312yes—
208C22—22no—
209C22#1171873211yescharacteristic
210C22#1171873311yescharacteristic
211C22#1171887911yescharacteristic
212C4—24no—
213C4—84no—
214C4—1042no—
215C4#1171873111yescharacteristic
216C4#1171873611yescharacteristic
217C4#1171887811yescharacteristic
218C4#1171888311yescharacteristic
219C2—21no—
220C2—21no—
221C2#1311606711yescharacteristic
222C2#1311691412yes—
subgroupG/H
centerC22#11718733
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
FittingC2×C13×#494C2
socleC22×C13#459
prime radicalC23×C13AGL(1,ℤ/8)
hypercenterC2×#494D13
hypocenterC13#13415
LCSG ▷ C22×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
186. C13#13415semidirect

Maximal subgroups

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

subgroupindex
C2×#117181572
#131165562
#131155842
#131129182
C2×C13×#4942
#1341513