Finite Group Databasebeta

← #15767420

Subgroups — #15767420

Order 3328.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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#13115005C211yesmaximal, characteristic
3#13114970C212yesmaximal
4#13112718C212yesmaximal
5C13×#1295C211yesmaximal, characteristic
6C2×C13×#97C2212yes—
7C13×#382C2211yescharacteristic
8#11718647—21no—
9#11718640—21no—
10C2×#88048—21no—
11C2×#88047—21no—
12#11718597C2212yes—
13#11718596C2211yescharacteristic
14C2×#88043C2211yescharacteristic
15#11718321—22no—
16#11718317—22no—
17#11718143—22no—
18#11718143—22no—
19C22×Dic26—21no—
20C22×C8×C13—22no—
21C2×C13×C4⋊C4D411yescharacteristic
22C2×C13×C4⋊C4D411yescharacteristic
23C2×C42×C13C2311yescharacteristic
24C2×C4⋊Dic13—21no—
25C2×C4⋊Dic13—22no—
26C2×C4⋊Dic13—21no—
27C2×C4⋊Dic13D412yes—
28C2×C4⋊Dic13D412yes—
29C2×#6101—22no—
30C22×#1055—21no—
31C13×#97—22no—
32C13×#97Q814yescomplemented
33C13×#95—22no—
34#88071—22no—
35#88071—21no—
36#88071—21no—
37#88071—22no—
38#88071—22no—
39#88048—42no—
40#88047—42no—
41#88043—21no—
42#88043Q812yescomplemented
43#10584—131nomaximal, Sylow
44C22×C4×C13—21no—
45C22×C4×C13—21no—
46C22×C4×C13C2×D411yescharacteristic
47C22×C4×C13C2×D412yes—
48C22×Dic13—22no—
49C22×Dic13—22no—
50C22×Dic13—41no—
51C2×Dic26—81no—
52C2×Dic26—82no—
53C2×C8×C13—24no—
54C2×C8×C13—42no—
55C2×C8×C13—42no—
56C13×C4⋊C4—41no—
57C13×C4⋊C4—41no—
58C42×C13C2×Q812yes—
59C42×C13C2×Q811yescharacteristic
60C42×C13#4111yescharacteristic
61C4⋊Dic13—42no—
62C4⋊Dic13—42no—
63C4⋊Dic13—44no—
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66C4⋊Dic13—81no—
67#6101—82no—
68C2×#1055—22no—
69C2×#1055—22no—
70C2×#1055—22no—
71#2844—131no—
72#1847—131no—
73#1836—132no—
74#1295—132no—
75#1295D1311yescharacteristic
76C23×C13#12011yescharacteristic
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—21no—
81C2×C4×C13—41no—
82C2×C4×C13—41no—
83C2×C4×C13—42no—
84C2×C4×C13—42no—
85C2×C4×C13C22⋊Q812yes—
86C2×C4×C13C22⋊Q811yescharacteristic
87C2×C4×C13C4⋊Q811yescharacteristic
88C2×C4×C13C4⋊Q812yes—
89C2×Dic13—42no—
90C2×Dic13—42no—
91C2×Dic13—42no—
92C2×Dic13—42no—
93C2×Dic13—42no—
94C2×Dic13—42no—
95C2×Dic13—81no—
96C2×Dic13—82no—
97Dic26—84no—
98C8×C13—44no—
99#1055—24no—
100C2×#107—261no—
101C2×#106—261no—
102C2×#97—131no—
103C2×#97C2×D1312yes—
104#400—262no—
105#400—261no—
106#395—262no—
107#395—261no—
108#384—131no—
109#382—132no—
110#382C2×D1311yescharacteristic
111#340—262no—
112#340—262no—
113C22×C13#39511yescharacteristic
114C22×C13#45311yescharacteristic
115C22×C13#45412yes—
116C22×C13#45512yes—
117C22×C13#45611yescharacteristic
118C4×C13—21no—
119C4×C13—21no—
120C4×C13—22no—
121C4×C13—22no—
122C4×C13—81no—
123C4×C13—81no—
124Dic13—82no—
125Dic13—82no—
126Dic13—161no—
127C22×Q8—261no—
128C22×C8—22no—
129C22×C8—261no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—132no—
132C2×C4⋊C4—261no—
133C2×C4⋊C4—262no—
134C2×C4⋊C4—262no—
135C2×C4⋊C4—261no—
136C2×C4⋊C4D5211yescharacteristic
137C2×C4⋊C4D5211yescharacteristic
138C2×C42C22×D1311yescharacteristic
139#107—522no—
140#106—522no—
141#97—22no—
142#97—132no—
143#97—261no—
144#97Dic2614yescomplemented
145#95—22no—
146#95—262no—
147#95—261no—
148#95—261no—
149#95—262no—
150#95—262no—
151C2×C13#165711yescharacteristic
152C2×C13#165911yescharacteristic
153C2×C13#166412yes—
154C2×C13#206011yescharacteristic
155C2×C13#206112yes—
156C2×Q8—1041no—
157C2×Q8—1042no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—262no—
161C22×C4—262no—
162C22×C4—521no—
163C22×C4C2×D5211yescharacteristic
164C22×C4D4×D1312yes—
165C2×C8—24no—
166C2×C8—42no—
167C2×C8—42no—
168C2×C8—262no—
169C2×C8—262no—
170C2×C8—262no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—522no—
174C4⋊C4—522no—
175C4⋊C4—521no—
176C4⋊C4—521no—
177C4⋊C4—524no—
178C4⋊C4—1042no—
179C4⋊C4—1041no—
180C42C2×Dic2612yes—
181C42#612911yescharacteristic
182C42Q8×D1311yescharacteristic
183C13#1058411yescharacteristic, complemented, Sylow
184C23#8813611yescharacteristic
185Q8—1044no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—522no—
195C2×C4—522no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4—1041no—
201C2×C4—1042no—
202C2×C4#8812311yescharacteristic
203C2×C4#8813212yes—
204C2×C4#8814212yes—
205C2×C4#8815111yescharacteristic
206C8—44no—
207C8—264no—
208C22#1171831711yescharacteristic
209C22#1171840811yescharacteristic
210C22#1171841311yescharacteristic
211C22#1171848612yes—
212C22#1171848812yes—
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—1042no—
220C4—1042no—
221C4—2081no—
222C2#1311413511yescharacteristic
223C2#1311414311yescharacteristic
224C2#1311417212yes—
225C2#1311618211yescharacteristic
226C2#1311618512yes—
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socle, prime radicalC23×C13#120
hypercenter#1295D13
hypocenterC13#10584
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
32. C13×#97Q8semidirect
42. #88043Q8semidirect
144. #97Dic26semidirect
183. C13#10584semidirect

Maximal subgroups

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

subgroupindex
#131231082
#131150052
#131149702
#131127182
C13×#12952
#1058413