Finite Group Databasebeta

← #15766054

Subgroups — #15766054

Order 3328.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#13115668C211yesmaximal, characteristic
2#13113330C212yesmaximal
3#13112739C212yesmaximal, complemented
4#13112665C211yesmaximal, characteristic, complemented
5C13×#2402C211yesmaximal, characteristic, complemented
6#11719182C2211yescharacteristic
7C13×#400—22no—
8C13×#398—22no—
9C4×C13×C4⋊C4—22no—
10C4×C13×C4⋊C4C2212yes—
11C13×#376C2211yescharacteristic
12C2×#88045—22no—
13#11718586C2212yes—
14#11718585C2211yescharacteristic
15#11718043—22no—
16#11718043—22no—
17C2×#6127—21no—
18C2×C13×C4⋊C4—22no—
19C2×C13×C4⋊C4—22no—
20C2×C13×C4⋊C4—22no—
21C2×C42×C13—22no—
22C2×C42×C13D412yes—
23C2×C42×C13C2311yescharacteristic
24#88184—22no—
25C2×#6099—21no—
26#88129—21no—
27#88128Q811yescharacteristic
28C4×D52—22no—
29#88123Q811yescharacteristic
30C13×#95—22no—
31C13×#95—22no—
32C13×#95—22no—
33C13×#95D412yes—
34C13×#95D412yes—
35C22⋊#1055—22no—
36#88045—44no—
37C4⋊#1055—22no—
38C4⋊#1055—22no—
39C4×#1055—22no—
40#10372—131nomaximal, Sylow
41C22×C4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—22no—
44C22×C4×C13C2×D412yes—
45C22×C4×C13C2×D411yescharacteristic
46C2×C22⋊D13—41no—
47#6127—42no—
48#6127—42no—
49C2×D52—21no—
50C2×D52—22no—
51C2×C4×D13—41no—
52C2×Dic26—21no—
53C13×C4⋊C4—44no—
54C13×C4⋊C4—44no—
55C13×C4⋊C4—44no—
56C42×C13—22no—
57C42×C13—22no—
58C42×C13—42no—
59C42×C13—42no—
60C42×C13C2×Q811yescharacteristic
61C42×C13#4112yes—
62C42×C13#4111yescharacteristic
63#6103—42no—
64C4⋊Dic13—22no—
65#6099—42no—
66C2×#1055—42no—
67C2×#1055—41no—
68#2402D1311yescharacteristic, complemented
69#1963—131no—
70#1502—132no—
71#1303—132no—
72#1274—131no—
73C23×C13#12011yescharacteristic
74C22×D13—41no—
75C2×C4×C13—24no—
76C2×C4×C13—42no—
77C2×C4×C13—42no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13—42no—
82C2×C4×C13—42no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13C22⋊Q812yes—
86C2×C4×C13C22⋊Q811yescharacteristic
87C2×C4×C13#12412yes—
88C2×C4×C13#12411yescharacteristic
89C2×C4×C13#13512yes—
90C2×C4×C13AGL(1,ℤ/8)12yes—
91C22⋊D13—82no—
92C2×Dic13—41no—
93D52—42no—
94D52—82no—
95C4×D13—81no—
96C4×D13—81no—
97Dic26—42no—
98#1055—82no—
99#1055—81no—
100#532—131no—
101#431—132no—
102#423—131no—
103C2×#104—262no—
104#400—22no—
105#398—22no—
106C4×C4⋊C4—22no—
107C4×C4⋊C4C2×D1312yes—
108#376C2×D1311yescharacteristic
109#327—262no—
110#327—262no—
111C22×C13—22no—
112C22×C13#39311yescharacteristic
113C22×C13#44912yes—
114C2×D13—81no—
115C2×D13—82no—
116C4×C13—22no—
117C4×C13—22no—
118C4×C13—44no—
119C4×C13—82no—
120C4×C13—82no—
121C4×C13#47812yes—
122C4×C13#48811yescharacteristic
123C4×C13#49011yescharacteristic
124Dic13—81no—
125C2×#41—261no—
126C2×M16—261no—
127C4⋊Q8—131no—
128#127—131no—
129#124—261no—
130#121—262no—
131C4×D4—262no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C42—22no—
136C2×C42C22⋊D1312yes—
137C2×C42C22×D1311yescharacteristic
138C4⋊C8—262no—
139C4⋊C8—262no—
140#104—524no—
141C22⋊C8—262no—
142C4×C8—262no—
143#95—22no—
144#95—22no—
145#95—22no—
146#95C22⋊D1312yes—
147#95C22⋊D1312yes—
148C2×C13—22no—
149C2×C13#202511yescharacteristic
150C2×C13#203112yes—
151D13—161no—
152#41—522no—
153#41—522no—
154C2×Q8—261no—
155C2×D4—261no—
156C2×D4—262no—
157C2×D4—521no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—521no—
162C22×C4C2×C22⋊D1312yes—
163C22×C4C2×C22⋊D1311yescharacteristic
164M16—522no—
165C2×C8—522no—
166C2×C8—521no—
167C4⋊C4—44no—
168C4⋊C4—44no—
169C4⋊C4—44no—
170C4⋊C4—262no—
171C22⋊C4—522no—
172C42—22no—
173C42—22no—
174C42—42no—
175C42—42no—
176C42Q8×D1311yescharacteristic
177C42#613111yescharacteristic
178C42#613112yes—
179C13#1037211yescharacteristic, complemented, Sylow
180C23—521no—
181C23#8820711yescharacteristic
182Q8—522no—
183D4—522no—
184D4—1042no—
185D4—1042no—
186C2×C4—24no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—521no—
197C2×C4—1041no—
198C2×C4—1041no—
199C2×C4#8820012yes—
200C2×C4#8820011yescharacteristic
201C2×C4#8820112yes—
202C2×C4#8820111yescharacteristic
203C2×C4#8820312yes—
204C2×C4#8820412yes—
205C8—1042no—
206C8—1041no—
207C22—22no—
208C22—1041no—
209C22—1042no—
210C22#1171889211yescharacteristic
211C22#1171889912yes—
212C4—22no—
213C4—22no—
214C4—44no—
215C4—82no—
216C4—82no—
217C4—1041no—
218C4#1171872712yes—
219C4#1171872811yescharacteristic
220C4#1171872911yescharacteristic
221C2—22no—
222C2—2081no—
223C2#1311597911yescharacteristic
224C2#1311600512yes—
subgroupG/H
centerC2×C4#88201
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#2402C2
socleC22×C13#393
prime radical#11719182C22
hypercenter#2402D13
hypocenterC13#10372
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2402

Complements

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

NH ≅ G/Ntype
3. #13112739C2semidirect
4. #13112665C2semidirect
5. C13×#2402C2semidirect
68. #2402D13semidirect
179. C13#10372semidirect

Maximal subgroups

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

subgroupindex
#131156682
#131133302
#131127392
#131126652
C13×#24022
#1037213