Finite Group Databasebeta

← #15757866

Subgroups — #15757866

Order 3328.

416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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#13125181C211yesmaximal, characteristic
2#13123907C211yesmaximal, characteristic
3#13113310C212yesmaximal, complemented
4#13112736C212yesmaximal, complemented
5C13×#1543C211yesmaximal, characteristic
6C13×#532C2211yescharacteristic
7#11719175C2211yescharacteristic
8C13×#431C2212yes—
9#11718895—22no—
10#11718894—22no—
11#11718743—21no—
12#11718732—21no—
13#11718716C414yes—
14#11718672—24no—
15#11718587C2212yes—
16C2×#88043C2211yescharacteristic
17C13×#333—21no—
18C13×#331—21no—
19#11718048—24no—
20C2×C13×#41D412yes—
21C13×C4⋊Q8D411yescharacteristic
22C13×#127D411yescharacteristic
23C13×#124C2×C412yes—
24C13×#121—22no—
25C4×D4×C13—22no—
26C2×C42×C13C2311yescharacteristic
27#88180—21no—
28#88178—22no—
29C2×#6099—22no—
30C22×#1055—21no—
31C22×#1055—22no—
32#88124—21no—
33#88123C2×C412yes—
34C4×Dic26—22no—
35C13×C4⋊C8—22no—
36C13×C22⋊C8—22no—
37C4×C8×C13—22no—
38#88075—24no—
39#88072—24no—
40C22⋊#1055—24no—
41C22⋊#1055—22no—
42C4⋊#1055D414yes—
43#88043—22no—
44#88043—21no—
45#88043C2×C412yes—
46#9005—131nomaximal, Sylow
47C13×#41—42no—
48C13×#41—42no—
49C2×Q8×C13C22⋊C412yes—
50C2×D4×C13—22no—
51C2×D4×C13—22no—
52C2×D4×C13C22⋊C412yes—
53C22×C4×C13—22no—
54C22×C4×C13C2×D411yescharacteristic
55C22×C4×C13#4112yes—
56C2×Dic26—22no—
57C2×C8×C13—42no—
58C13×C4⋊C4—22no—
59C13×C22⋊C4—24no—
60C42×C13C22×C411yescharacteristic
61C42×C13C2×D412yes—
62C42×C13C2×D411yescharacteristic
63C22⋊Dic13—41no—
64C4⋊Dic13—22no—
65C4⋊Dic13—22no—
66#6101—42no—
67C4×Dic13—41no—
68#6099—82no—
69C2×#1055—22no—
70C2×#1055—24no—
71C2×#1055—42no—
72C2×#1055—82no—
73#3135—131no—
74#2980—131no—
75#1543D1311yescharacteristic
76#1497—132no—
77#1302—132no—
78C23×C13—22no—
79C23×C13#12311yescharacteristic
80Q8×C13—42no—
81D4×C13—42no—
82D4×C13—82no—
83D4×C13—82no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—42no—
87C2×C4×C13—42no—
88C2×C4×C13—42no—
89C2×C4×C13C2×C22⋊C411yescharacteristic
90C2×C4×C13C4×D412yes—
91C2×C4×C13#12011yescharacteristic
92C2×C4×C13#12112yes—
93C2×Dic13—42no—
94Dic26—44no—
95C8×C13—82no—
96#1055—42no—
97#1055—44no—
98#533—131no—
99#532C2×D1311yescharacteristic
100#491—261no—
101#490—261no—
102#489—134no—
103#435—264no—
104#432—132no—
105#431C2×D1312yes—
106#416—262no—
107#408—262no—
108C2×#97—131no—
109#333—21no—
110#331—21no—
111Q8⋊C8—264no—
112C22×C13—22no—
113C22×C13—21no—
114C22×C13—44no—
115C22×C13—42no—
116C22×C13#38611yescharacteristic
117C4×C13—22no—
118C4×C13—22no—
119C4×C13—21no—
120C4×C13—42no—
121C4×C13#45512yes—
122Dic13—82no—
123C2×#41D5212yes—
124C2×M16—262no—
125C22×C8—261no—
126C22×C8—262no—
127C4⋊Q8—132no—
128C4⋊Q8C22⋊D1311yescharacteristic
129#127C22⋊D1311yescharacteristic
130#125—261no—
131#124C4×D1312yes—
132C22⋊Q8—262no—
133#121—22no—
134C4×Q8—262no—
135C4×D4—22no—
136#117—261no—
137C2×C42C22×D1311yescharacteristic
138C4⋊C8—22no—
139C4⋊C8—134no—
140#103—264no—
141#102—264no—
142C22⋊C8—22no—
143C22⋊C8—264no—
144C22⋊C8—262no—
145#97—132no—
146#97—262no—
147#97—261no—
148C4×C8—22no—
149C2×C13—41no—
150C2×C13—82no—
151C2×C13#188112yes—
152C2×C13#188511yescharacteristic
153#41—42no—
154#41—42no—
155C2×Q8—262no—
156C2×Q8#610312yes—
157C2×D4—22no—
158C2×D4—22no—
159C2×D4#610312yes—
160C22×C4—22no—
161C22×C4C2×D5211yescharacteristic
162C22×C4#612912yes—
163M16—1042no—
164C2×C8—42no—
165C2×C8—264no—
166C2×C8—262no—
167C2×C8—522no—
168C2×C8—1042no—
169C4⋊C4—22no—
170C4⋊C4—262no—
171C4⋊C4—262no—
172C4⋊C4—522no—
173C22⋊C4—24no—
174C22⋊C4—521no—
175C42—521no—
176C42C2×C4×D1311yescharacteristic
177C42D4×D1312yes—
178C42C2×C22⋊D1311yescharacteristic
179C13#900511yescharacteristic, complemented, Sylow
180C23—22no—
181C23#8814011yescharacteristic
182Q8—42no—
183Q8—524no—
184D4—42no—
185D4—82no—
186D4—82no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—522no—
193C2×C4#8813512yes—
194C2×C4#8813611yescharacteristic
195C2×C4C2×#610311yescharacteristic
196C2×C4#8819312yes—
197C8—82no—
198C8—522no—
199C8—524no—
200C22—22no—
201C22—21no—
202C22—44no—
203C22—42no—
204C22#1171861911yescharacteristic
205C4—22no—
206C4—22no—
207C4—21no—
208C4—42no—
209C4—1042no—
210C4#1171840712yes—
211C2—41no—
212C2—82no—
213C2#1311519612yes—
214C2#1311522211yescharacteristic
subgroupG/H
centerC2×C4#88136
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1543C2
socleC22×C13#386
prime radicalC13×#532C22
cosocleC2×C42×C13C23
hypercenter#1543D13
hypocenterC13#9005
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1543

Complements

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

NH ≅ G/Ntype
3. #13113310C2semidirect
4. #13112736C2semidirect
179. C13#9005semidirect

Maximal subgroups

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

subgroupindex
#131251812
#131239072
#131133102
#131127362
C13×#15432
#900513