Finite Group Databasebeta

← #15767416

Subgroups — #15767416

Order 3328.

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

normal subgroups only

This group has 406 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#13123108C211yesmaximal, characteristic
2#13115002C212yesmaximal
3#13112718C212yesmaximal
4#13112717C211yesmaximal, characteristic
5C13×#1847C211yesmaximal, characteristic
6C2×C13×#107—21no—
7C2×C13×#106—21no—
8C2×C13×#97C2211yescharacteristic
9C13×#384C2211yescharacteristic
10C13×#382C2211yescharacteristic
11#11718647—21no—
12#11718640—21no—
13C2×#88048—22no—
14C2×#88047—22no—
15#11718597C2212yes—
16C2×#88043C2212yes—
17#11718321—22no—
18#11718317—22no—
19C22×Dic26—21no—
20C22×C8×C13—21no—
21C2×C13×C4⋊C4—21no—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4D411yescharacteristic
24C2×C13×C4⋊C4D411yescharacteristic
25C2×C42×C13C2311yescharacteristic
26C2×C4⋊Dic13—21no—
27C2×C4⋊Dic13D412yes—
28C2×C4⋊Dic13D412yes—
29C2×#6101—22no—
30C22×#1055—22no—
31C13×#107—42no—
32C13×#106—42no—
33C13×#97—21no—
34C13×#97Q812yescomplemented
35C13×#95—22no—
36#88071—22no—
37#88071—21no—
38#88071—21no—
39#88071—22no—
40#88071—22no—
41#88048—44no—
42#88047—44no—
43#88043—22no—
44#88043Q814yescomplemented
45#10583—131nomaximal, Sylow
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—41no—
49C22×C4×C13C2×D412yes—
50C22×C4×C13C2×D411yescharacteristic
51C22×Dic13—22no—
52C22×Dic13—22no—
53C2×Dic26—82no—
54C2×Dic26—81no—
55C2×C8×C13—22no—
56C2×C8×C13—22no—
57C2×C8×C13—22no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—41no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C42×C13C2×Q811yescharacteristic
65C42×C13C2×Q812yes—
66C42×C13#4111yescharacteristic
67C4⋊Dic13—42no—
68C4⋊Dic13—42no—
69C4⋊Dic13—81no—
70#6101—82no—
71C2×#1055—24no—
72C2×#1055—24no—
73C2×#1055—24no—
74#2844—131no—
75#1847—132no—
76#1847D1311yescharacteristic
77#1295—132no—
78#1295—131no—
79C23×C13#12011yescharacteristic
80C2×C4×C13—22no—
81C2×C4×C13—21no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—42no—
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—42no—
88C2×C4×C13—81no—
89C2×C4×C13—82no—
90C2×C4×C13C22⋊Q812yes—
91C2×C4×C13C22⋊Q811yescharacteristic
92C2×C4×C13C4⋊Q812yes—
93C2×C4×C13C4⋊Q811yescharacteristic
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100Dic26—84no—
101C8×C13—24no—
102#1055—28no—
103C2×#107—21no—
104C2×#107—262no—
105C2×#106—21no—
106C2×#106—262no—
107C2×#97—132no—
108C2×#97C2×D1311yescharacteristic
109#400—262no—
110#400—261no—
111#395—262no—
112#395—261no—
113#384C2×D1311yescharacteristic
114#382—132no—
115#382C2×D1311yescharacteristic
116C22×C13#39511yescharacteristic
117C22×C13#45311yescharacteristic
118C22×C13#45312yes—
119C22×C13#45611yescharacteristic
120C22×C13#45612yes—
121C4×C13—22no—
122C4×C13—21no—
123C4×C13—22no—
124C4×C13—21no—
125C4×C13—81no—
126C4×C13—81no—
127C4×C13—161no—
128Dic13—82no—
129Dic13—82no—
130C22×Q8—261no—
131C22×C8—21no—
132C22×C8—262no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—262no—
138C2×C4⋊C4—261no—
139C2×C4⋊C4C22⋊D1311yescharacteristic
140C2×C4⋊C4C22⋊D1311yescharacteristic
141C2×C42C22×D1311yescharacteristic
142#107—42no—
143#107—524no—
144#106—42no—
145#106—524no—
146#97—21no—
147#97—134no—
148#97—262no—
149#97Dic2612yescomplemented
150#95—22no—
151#95—262no—
152#95—261no—
153#95—261no—
154#95—262no—
155#95—262no—
156C2×C13#165511yescharacteristic
157C2×C13#166011yescharacteristic
158C2×C13#166012yes—
159C2×C13#206012yes—
160C2×C13#206011yescharacteristic
161C2×Q8—1041no—
162C2×Q8—1042no—
163C22×C4—21no—
164C22×C4—21no—
165C22×C4—41no—
166C22×C4—262no—
167C22×C4—262no—
168C22×C4D4×D1312yes—
169C22×C4C2×C22⋊D1311yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—22no—
173C2×C8—264no—
174C2×C8—264no—
175C2×C8—264no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—42no—
180C4⋊C4—41no—
181C4⋊C4—42no—
182C4⋊C4—522no—
183C4⋊C4—522no—
184C4⋊C4—1042no—
185C4⋊C4—1041no—
186C42C2×Dic2611yescharacteristic
187C42#612711yescharacteristic
188C42Q8×D1312yes—
189C13#1058311yescharacteristic, complemented, Sylow
190C23#8819111yescharacteristic
191Q8—1044no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—81no—
201C2×C4—82no—
202C2×C4—522no—
203C2×C4—522no—
204C2×C4—522no—
205C2×C4—522no—
206C2×C4—522no—
207C2×C4—522no—
208C2×C4#8814212yes—
209C2×C4#8815012yes—
210C2×C4#8817811yescharacteristic
211C2×C4#8819811yescharacteristic
212C8—24no—
213C8—268no—
214C22#1171864011yescharacteristic
215C22#1171873811yescharacteristic
216C22#1171875611yescharacteristic
217C22#1171885912yes—
218C22#1171886612yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—81no—
224C4—81no—
225C4—161no—
226C4—1042no—
227C4—1042no—
228C2#1311412411yescharacteristic
229C2#1311414511yescharacteristic
230C2#1311414612yes—
231C2#1311617912yes—
232C2#1311618111yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1847C2
socle, prime radicalC23×C13#120
hypercenter#1847D13
hypocenterC13#10583
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
34. C13×#97Q8semidirect
44. #88043Q8semidirect
149. #97Dic26semidirect
189. C13#10583semidirect

Maximal subgroups

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

subgroupindex
#131231082
#131150022
#131127182
#131127172
C13×#18472
#1058313