Finite Group Databasebeta

← #15765949

Subgroups — #15765949

Order 3328.

416 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 123 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#13120078C211yesmaximal, characteristic
2#13115785C212yesmaximal
3#13112719C211yesmaximal, characteristic
4#13112676C212yesmaximal
5C13×#1956C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×#103—22no—
8C2×C4×C8×C13C2211yescharacteristic
9C13×#384C2211yescharacteristic
10#11718647—22no—
11#11718646—22no—
12#11718638—22no—
13C4×C4⋊Dic13C2212yes—
14C2×C4⋊#1055C2212yes—
15#11718121—22no—
16#11718121—22no—
17C22×Q8×C13—21no—
18C22×C8×C13—21no—
19C13×C4⋊Q8—22no—
20C13×C4⋊Q8—21no—
21C13×C4⋊Q8Q812yes—
22C2×C13×C4⋊C4—22no—
23C2×C13×C4⋊C4—22no—
24C2×C13×C4⋊C4D412yes—
25C2×C42×C13C2311yescharacteristic
26C2×C4⋊Dic13—22no—
27C2×C4⋊Dic13D412yes—
28C2×C4⋊Dic13D412yes—
29C2×C4×Dic13—22no—
30C22×#1055—22no—
31C13×#103—44no—
32C4×C8×C13—22no—
33#88071—22no—
34#88071—24no—
35#88071—22no—
36C4⋊#1055—22no—
37C4⋊#1055—22no—
38#10352—131nomaximal, Sylow
39C2×Q8×C13—22no—
40C2×Q8×C13—42no—
41C2×Q8×C13—42no—
42C2×Q8×C13—41no—
43C22×C4×C13—22no—
44C22×C4×C13—41no—
45C22×C4×C13C2×D412yes—
46C22×C4×C13C2×D411yescharacteristic
47C22×Dic13—22no—
48C22×Dic13—22no—
49C2×C8×C13—22no—
50C2×C8×C13—41no—
51C2×C8×C13—41no—
52C13×C4⋊C4—24no—
53C13×C4⋊C4—42no—
54C13×C4⋊C4—42no—
55C13×C4⋊C4—42no—
56C13×C4⋊C4—42no—
57C42×C13C2×Q811yescharacteristic
58C42×C13#4111yescharacteristic
59C42×C13#4112yes—
60C4⋊Dic13—22no—
61C4⋊Dic13—22no—
62C4⋊Dic13—22no—
63C4⋊Dic13—22no—
64C4⋊Dic13—82no—
65C4×Dic13—42no—
66C4×Dic13—42no—
67C2×#1055—42no—
68C2×#1055—42no—
69C2×#1055—42no—
70#2571—131no—
71#1987—132no—
72#1956D1311yescharacteristic
73#1296—131no—
74#1279—132no—
75C23×C13#12011yescharacteristic
76Q8×C13—44no—
77Q8×C13—82no—
78C2×C4×C13—21no—
79C2×C4×C13—21no—
80C2×C4×C13—42no—
81C2×C4×C13—44no—
82C2×C4×C13—42no—
83C2×C4×C13—81no—
84C2×C4×C13—81no—
85C2×C4×C13C22⋊Q811yescharacteristic
86C2×C4×C13C22⋊Q812yes—
87C2×C4×C13#12411yescharacteristic
88C2×C4×C13#12412yes—
89C2×C4×C13#13512yes—
90C2×C4×C13#13512yes—
91C2×C4×C13#13712yes—
92C2×C4×C13#13712yes—
93C2×Dic13—42no—
94C2×Dic13—42no—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C8×C13—42no—
100#1055—82no—
101C2×C4⋊Q8C2×D1311yescharacteristic
102C2×C4⋊C8—132no—
103C2×#103—22no—
104C2×C4×C8C2×D1311yescharacteristic
105#400—262no—
106#389—262no—
107#384C2×D1311yescharacteristic
108#382—262no—
109C4×C4⋊C4—132no—
110#340—262no—
111#340—262no—
112C22×C13#39311yescharacteristic
113C22×C13#45212yes—
114C22×C13#45212yes—
115C22×C13#45311yescharacteristic
116C22×C13#45411yescharacteristic
117C4×C13—21no—
118C4×C13—21no—
119C4×C13—82no—
120C4×C13—82no—
121C4×C13#47912yes—
122C4×C13#47912yes—
123C4×C13#48812yes—
124C4×C13#49112yes—
125Dic13—82no—
126Dic13—82no—
127C22×Q8—21no—
128C22×C8—21no—
129C22×C8—262no—
130C4⋊Q8—21no—
131C4⋊Q8—22no—
132C4⋊Q8Dic2612yes—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—132no—
136C2×C4⋊C4—132no—
137C2×C4⋊C4—262no—
138C2×C4⋊C4C22⋊D1312yes—
139C2×C42—262no—
140C2×C42C22×D1311yescharacteristic
141C4⋊C8—262no—
142C4⋊C8—262no—
143#103—44no—
144C4×C8—22no—
145#95—262no—
146#95—264no—
147#95—262no—
148C2×C13#163011yescharacteristic
149C2×C13#163411yescharacteristic
150C2×C13#163812yes—
151C2×C13#202612yes—
152C2×C13#202711yescharacteristic
153C2×Q8—22no—
154C2×Q8—42no—
155C2×Q8—42no—
156C2×Q8—41no—
157C22×C4—22no—
158C22×C4—41no—
159C22×C4—262no—
160C22×C4—262no—
161C22×C4D4×D1312yes—
162C22×C4C2×C22⋊D1311yescharacteristic
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—522no—
167C2×C8—522no—
168C2×C8—522no—
169C4⋊C4—24no—
170C4⋊C4—42no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—262no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—262no—
178C4⋊C4—1042no—
179C42—522no—
180C42—522no—
181C42C2×Dic2611yescharacteristic
182C42#612711yescharacteristic
183C42#612912yes—
184C13#1035211yescharacteristic, complemented, Sylow
185C23#8819111yescharacteristic
186Q8—44no—
187Q8—82no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—42no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4—522no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4—522no—
199C2×C4—522no—
200C2×C4—522no—
201C2×C4#8813212yes—
202C2×C4#8813912yes—
203C2×C4#8816912yes—
204C2×C4#8817012yes—
205C2×C4#8817212yes—
206C2×C4#8817312yes—
207C2×C4#8817811yescharacteristic
208C2×C4#8819011yescharacteristic
209C8—42no—
210C8—1042no—
211C22#1171860811yescharacteristic
212C22#1171872311yescharacteristic
213C22#1171873811yescharacteristic
214C22#1171883412yes—
215C22#1171884812yes—
216C4—21no—
217C4—21no—
218C4—82no—
219C4—82no—
220C4—1042no—
221C4—1042no—
222C4#1171845712yes—
223C4#1171845812yes—
224C4#1171846012yes—
225C4#1171846112yes—
226C2#1311395511yescharacteristic
227C2#1311397911yescharacteristic
228C2#1311400512yes—
229C2#1311598512yes—
230C2#1311599211yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1956C2
socle, prime radicalC23×C13#120
hypercenter#1956D13
hypocenterC13#10352
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

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

NH ≅ G/Ntype
184. C13#10352semidirect

Maximal subgroups

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

subgroupindex
#131200782
#131157852
#131127192
#131126762
C13×#19562
#1035213