Finite Group Databasebeta

← #15766057

Subgroups — #15766057

Order 3328.

402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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#13118141C211yesmaximal, characteristic, complemented
2#13113331C212yesmaximal
3#13112737C212yesmaximal, complemented
4#13112665C211yesmaximal, characteristic, complemented
5C13×#1963C211yesmaximal, characteristic
6C13×#532C2211yescharacteristic
7C13×#423C2211yescharacteristic
8C2×C13×#104—22no—
9C13×#376C2211yescharacteristic
10C4×C4⋊Dic13C2212yes—
11C4×#6101—22no—
12#11718586C2212yes—
13#11718321—22no—
14#11718318—22no—
15#11718129—22no—
16#11718129—22no—
17C2×C13×#41—21no—
18C2×C13×M16—21no—
19C13×C4⋊Q8Q811yescharacteristic
20C13×#127Q811yescharacteristic
21C13×#124—21no—
22C13×#121—22no—
23C4×D4×C13—22no—
24C2×C42×C13D412yes—
25C2×C42×C13C2311yescharacteristic
26C2×C4⋊Dic13—22no—
27C2×#6101—22no—
28C2×#6101—22no—
29C2×C4×Dic13—22no—
30C13×C4⋊C8—22no—
31C13×#104—44no—
32C13×#95—22no—
33#88071—22no—
34#88071—22no—
35#88071D412yes—
36#88071D412yes—
37C22⋊#1055—22no—
38C4⋊#1055—22no—
39C4×#1055—22no—
40#10372—131nomaximal, Sylow
41C13×#41—42no—
42C13×#41—42no—
43C2×Q8×C13—21no—
44C2×D4×C13—21no—
45C2×D4×C13—22no—
46C2×D4×C13—41no—
47C22×C4×C13—22no—
48C22×C4×C13—41no—
49C22×C4×C13C2×D412yes—
50C22×C4×C13C2×D411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13—22no—
53C13×M16—42no—
54C2×C8×C13—41no—
55C13×C4⋊C4—22no—
56C13×C22⋊C4—42no—
57C42×C13—22no—
58C42×C13—22no—
59C42×C13C2×Q811yescharacteristic
60C42×C13#4111yescharacteristic
61C42×C13#4112yes—
62C4⋊Dic13—44no—
63#6101—44no—
64#6101—44no—
65C4×Dic13—42no—
66C4×Dic13—42no—
67C2×#1055—42no—
68#2402—131no—
69#1963D1311yescharacteristic
70#1502—132no—
71#1303—132no—
72#1274—131no—
73C23×C13—41no—
74C23×C13#12011yescharacteristic
75Q8×C13—42no—
76D4×C13—42no—
77D4×C13—82no—
78D4×C13—82no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—41no—
83C2×C4×C13—42no—
84C2×C4×C13—81no—
85C2×C4×C13—81no—
86C2×C4×C13C22⋊Q812yes—
87C2×C4×C13C22⋊Q811yescharacteristic
88C2×C4×C13#12412yes—
89C2×C4×C13#12411yescharacteristic
90C2×C4×C13#13512yes—
91C2×C4×C13AGL(1,ℤ/8)12yes—
92C2×Dic13—24no—
93C2×Dic13—42no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C8×C13—81no—
99#1055—82no—
100#532C2×D1311yescharacteristic
101#431—132no—
102#423C2×D1311yescharacteristic
103C2×#104—22no—
104#400—262no—
105#398—262no—
106C4×C4⋊C4—132no—
107C4×C4⋊C4—262no—
108#376C2×D1311yescharacteristic
109#327—262no—
110#327—262no—
111C22×C13—22no—
112C22×C13—81no—
113C22×C13—82no—
114C22×C13#39311yescharacteristic
115C22×C13#44912yes—
116C4×C13—22no—
117C4×C13—22no—
118C4×C13—82no—
119C4×C13—81no—
120C4×C13#47812yes—
121C4×C13#48811yescharacteristic
122C4×C13#49011yescharacteristic
123Dic13—44no—
124Dic13—82no—
125C2×#41—21no—
126C2×M16—21no—
127C4⋊Q8Dic2611yescharacteristic
128#127Dic2611yescharacteristic
129#124—21no—
130#121—22no—
131C4×D4—22no—
132C2×C4⋊C4—262no—
133C2×C4⋊C4—262no—
134C2×C4⋊C4—262no—
135C2×C42—262no—
136C2×C42C22⋊D1312yes—
137C2×C42C22×D1311yescharacteristic
138C4⋊C8—22no—
139C4⋊C8—262no—
140#104—44no—
141C22⋊C8—262no—
142C4×C8—262no—
143#95—22no—
144#95—132no—
145#95—132no—
146#95—262no—
147#95—262no—
148C2×C13—22no—
149C2×C13—161no—
150C2×C13#202511yescharacteristic
151C2×C13#203112yes—
152#41—42no—
153#41—42no—
154C2×Q8—21no—
155C2×D4—22no—
156C2×D4—21no—
157C2×D4—41no—
158C22×C4—22no—
159C22×C4—41no—
160C22×C4—262no—
161C22×C4—262no—
162C22×C4D4×D1312yes—
163C22×C4C2×C22⋊D1311yescharacteristic
164M16—42no—
165C2×C8—41no—
166C2×C8—522no—
167C4⋊C4—22no—
168C4⋊C4—524no—
169C4⋊C4—524no—
170C4⋊C4—524no—
171C22⋊C4—42no—
172C42—22no—
173C42—22no—
174C42—522no—
175C42—522no—
176C42C2×Dic2611yescharacteristic
177C42#612711yescharacteristic
178C42#612912yes—
179C13#1037211yescharacteristic, complemented, Sylow
180C23—41no—
181C23#8819111yescharacteristic
182Q8—42no—
183D4—42no—
184D4—82no—
185D4—82no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—41no—
191C2×C4—81no—
192C2×C4—81no—
193C2×C4—264no—
194C2×C4—522no—
195C2×C4—522no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4—522no—
199C2×C4#8813212yes—
200C2×C4#8813912yes—
201C2×C4#8817811yescharacteristic
202C2×C4#8818612yes—
203C2×C4#8819011yescharacteristic
204C2×C4#8820412yes—
205C8—81no—
206C8—1042no—
207C22—22no—
208C22—81no—
209C22—82no—
210C22#1171860811yescharacteristic
211C22#1171869812yes—
212C4—22no—
213C4—22no—
214C4—82no—
215C4—81no—
216C4—524no—
217C4—1042no—
218C4#1171867012yes—
219C4#1171871711yescharacteristic
220C4#1171873211yescharacteristic
221C2—22no—
222C2—161no—
223C2#1311598211yescharacteristic
224C2#1311600612yes—
subgroupG/H
centerC2×C4#88190
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1963C2
socleC22×C13#393
prime radicalC13×#532C22
hypercenter#1963D13
hypocenterC13#10372
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
1. #13118141C2semidirect
3. #13112737C2semidirect
4. #13112665C2semidirect
179. C13#10372semidirect

Maximal subgroups

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

subgroupindex
#131181412
#131133312
#131127372
#131126652
C13×#19632
#1037213