Finite Group Databasebeta

← #15765210

Subgroups — #15765210

Order 3328.

466 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 103 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#13125980C212yesmaximal
2#13125360C211yesmaximal, characteristic
3#13113399C212yesmaximal
4#13112681C211yesmaximal, characteristic
5C13×#1960C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7#11719175C2212yes—
8C2×C13×#103—22no—
9C2×C13×#97C2211yescharacteristic
10C13×#382C2211yescharacteristic
11#11718767—22no—
12#11718755—24no—
13#11718754—22no—
14#11718740—22no—
15#11718632—24no—
16#11718586C2212yes—
17#11718363—22no—
18#11718363—22no—
19#11718044—24no—
20C22×Q8×C13—21no—
21C22×C8×C13D412yes—
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—21no—
24C13×C4⋊Q8D412yes—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—21no—
27C2×C42×C13C2311yescharacteristic
28#88180—22no—
29#88178—22no—
30#88178—22no—
31#88124—22no—
32#88123D412yes—
33#88123D412yes—
34C4×Dic26—22no—
35C4×Dic26—22no—
36C13×#103—44no—
37C13×#97—22no—
38C13×#95—22no—
39C22⋊#1055D414yes—
40#88058—24no—
41#88057—22no—
42#88057—22no—
43#88050—28no—
44#88048—28no—
45C4⋊#1055—22no—
46C4×#1055—22no—
47#10227—131nomaximal, Sylow
48C2×Q8×C13—22no—
49C2×Q8×C13—41no—
50C2×Q8×C13—42no—
51C2×Q8×C13—42no—
52C22×C4×C13—41no—
53C22×C4×C13—41no—
54C22×C4×C13C2×D412yes—
55C22×C4×C13C2×D411yescharacteristic
56C2×Dic26—22no—
57C2×Dic26—22no—
58C2×C8×C13—22no—
59C2×C8×C13—22no—
60C2×C8×C13SD1614yes—
61C13×C4⋊C4—24no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—42no—
64C42×C13C2×D411yescharacteristic
65C42×C13C2×D412yes—
66C42×C13#4111yescharacteristic
67C22⋊Dic13—42no—
68C4⋊Dic13—22no—
69C4⋊Dic13—22no—
70C4⋊Dic13—22no—
71C4⋊Dic13—22no—
72#6101—42no—
73#6101—42no—
74C4×Dic13—42no—
75C2×#1055—24no—
76#3229—132no—
77#3162—131no—
78#1960D1311yescharacteristic
79#1518—132no—
80#1281—131no—
81C23×C13#12711yescharacteristic
82Q8×C13—44no—
83Q8×C13—82no—
84C2×C4×C13—42no—
85C2×C4×C13—42no—
86C2×C4×C13—81no—
87C2×C4×C13—81no—
88C2×C4×C13—82no—
89C2×C4×C13—81no—
90C2×C4×C13#12012yes—
91C2×C4×C13#12011yescharacteristic
92C2×C4×C13#12112yes—
93C2×C4×C13#12111yescharacteristic
94C2×C4×C13C2×SD1612yes—
95C2×C4×C13#13712yes—
96C2×Dic13—42no—
97C2×Dic13—42no—
98Dic26—44no—
99Dic26—82no—
100C8×C13—24no—
101#1055—44no—
102#533—132no—
103C2×C4⋊Q8C2×D1311yescharacteristic
104#501—262no—
105#501—262no—
106#498—262no—
107#487—262no—
108#483—264no—
109#475—264no—
110#431—132no—
111#427—262no—
112C2×#103—22no—
113C2×#97C2×D1311yescharacteristic
114#382C2×D1311yescharacteristic
115#328—264no—
116C22×C13—22no—
117C22×C13#39211yescharacteristic
118C22×C13#49211yescharacteristic
119C22×C13#49711yescharacteristic
120C4×C13—22no—
121C4×C13—22no—
122C4×C13—82no—
123C4×C13—161no—
124C4×C13#44812yes—
125C4×C13#46112yes—
126Dic13—82no—
127Dic13—82no—
128C22×Q8—21no—
129C22×C8C22⋊D1312yes—
130C4⋊Q8—21no—
131C4⋊Q8—22no—
132C4⋊Q8—132no—
133C4⋊Q8—132no—
134C4⋊Q8D5212yes—
135#125—262no—
136C22⋊Q8—262no—
137C22⋊Q8—262no—
138C4×Q8—262no—
139C4×Q8—262no—
140#117—262no—
141C2×C4⋊C4—22no—
142C2×C4⋊C4—21no—
143C2×C42C22×D1311yescharacteristic
144#107—264no—
145#106—268no—
146#106—262no—
147#106—262no—
148C4⋊C8—262no—
149#103—44no—
150#103—268no—
151C22⋊C8—134no—
152#97—22no—
153C4×C8—262no—
154#95—22no—
155C2×C13—21no—
156C2×C13—21no—
157C2×C13#200912yes—
158C2×C13#201311yescharacteristic
159C2×Q8—22no—
160C2×Q8—41no—
161C2×Q8—42no—
162C2×Q8—42no—
163C2×Q8—262no—
164C2×Q8—262no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4D4×D1312yes—
168C22×C4C2×C22⋊D1311yescharacteristic
169C2×C8—22no—
170C2×C8—22no—
171C2×C8—264no—
172C2×C8#610514yes—
173C4⋊C4—24no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—262no—
180C4⋊C4—522no—
181C4⋊C4—522no—
182C22⋊C4—522no—
183C42—522no—
184C42C2×D5211yescharacteristic
185C42#612711yescharacteristic
186C42D4×D1312yes—
187C13#1022711yescharacteristic, complemented, Sylow
188C23#8819411yescharacteristic
189Q8—44no—
190Q8—82no—
191Q8—524no—
192Q8—1042no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4—81no—
199C2×C4—522no—
200C2×C4—522no—
201C2×C4#8813612yes—
202C2×C4#8813812yes—
203C2×C4#8818411yescharacteristic
204C2×C4C2×#610512yes—
205C2×C4#8819111yescharacteristic
206C2×C4#8820512yes—
207C8—24no—
208C8—524no—
209C22—22no—
210C22#1171862111yescharacteristic
211C22#1171872111yescharacteristic
212C22#1171873711yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—161no—
217C4—1042no—
218C4—1042no—
219C4#1171868012yes—
220C4#1171870112yes—
221C2—21no—
222C2—21no—
223C2#1311589812yes—
224C2#1311591811yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1960C2
socleC22×C13#392
prime radicalC23×C13#127
hypercenter#1960D13
hypocenterC13#10227
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
187. C13#10227semidirect

Maximal subgroups

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

subgroupindex
#131259802
#131253602
#131133992
#131126812
C13×#19602
#1022713