Finite Group Databasebeta

← #15752118

Subgroups — #15752118

Order 3328.

398 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 87 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#13122829C211yesmaximal, characteristic
2#13116379C211yesmaximal, characteristic
3#13116246C212yesmaximal
4#13112661C212yesmaximal
5C13×#1272C211yesmaximal, characteristic
6C13×#391C2211yescharacteristic
7#11718891—21no—
8C2×#88075—21no—
9C2×#88056—22no—
10#11718640—21no—
11C2×#88048—21no—
12#11718596C2211yescharacteristic
13#11718590C2212yes—
14#11718317—22no—
15#11718307—22no—
16C13×#336C2212yes—
17#11718143—22no—
18#11718116C2211yescharacteristic
19C22×Q8×C13D411yescharacteristic
20C22×Dic26—21no—
21C22×Dic26D412yes—
22C22×C8×C13—22no—
23C2×C13×C4⋊C4D411yescharacteristic
24C2×C42×C13C2311yescharacteristic
25C2×C4⋊Dic13—22no—
26C2×C4⋊Dic13—21no—
27C2×C4⋊Dic13—21no—
28C2×C4⋊Dic13D412yes—
29C2×#6101—22no—
30C2×C4×Dic13—21no—
31C22×#1055—21no—
32C13×#95—22no—
33#88075—42no—
34#88071—21no—
35#88071—22no—
36#88071—22no—
37#88071—22no—
38#88056—44no—
39#88048—42no—
40#7812—131nomaximal, Sylow
41C2×Q8×C13—21no—
42C2×Q8×C13—41no—
43C2×Q8×C13—41no—
44C2×Q8×C13Q1612yes—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C2×D411yescharacteristic
48C22×C4×C13C2×D412yes—
49C22×Dic13—22no—
50C22×Dic13—22no—
51C22×Dic13—41no—
52C2×Dic26—22no—
53C2×Dic26—42no—
54C2×Dic26—42no—
55C2×Dic26—81no—
56C2×Dic26—82no—
57C2×Dic26SD1614yes—
58C2×C8×C13—42no—
59C2×C8×C13—42no—
60C2×C8×C13—42no—
61C13×C4⋊C4—41no—
62C42×C13—41no—
63C4⋊Dic13—42no—
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66C4⋊Dic13—42no—
67C4⋊Dic13—42no—
68C4⋊Dic13—81no—
69#6101—82no—
70C4×Dic13—81no—
71C2×#1055—22no—
72C2×#1055—41no—
73C2×#1055—41no—
74#2811—131no—
75#2096—131no—
76#2072—132no—
77#1272—132no—
78#1272D1311yescharacteristic
79C23×C13#12011yescharacteristic
80Q8×C13—42no—
81Q8×C13—81no—
82C2×C4×C13—21no—
83C2×C4×C13—22no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—22no—
87C2×C4×C13—41no—
88C2×C4×C13—41no—
89C2×C4×C13—41no—
90C2×C4×C13—42no—
91C2×C4×C13C2×SD1612yes—
92C2×C4×C13C2×Q1611yescharacteristic
93C2×C4×C13#13712yes—
94C2×C4×C13#13711yescharacteristic
95C2×Dic13—24no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101C2×Dic13—82no—
102C2×Dic13—81no—
103Dic26—44no—
104Dic26—82no—
105Dic26—84no—
106C8×C13—82no—
107#1055—42no—
108C2×#106—261no—
109C2×#103—262no—
110C2×#103—261no—
111#395—262no—
112#395—261no—
113#391—132no—
114#391—262no—
115#391—261no—
116#391C2×D1311yescharacteristic
117#384—131no—
118#340—262no—
119#336—131no—
120#336C2×D1312yes—
121C22×C13#44812yes—
122C22×C13#45111yescharacteristic
123C22×C13#45311yescharacteristic
124C22×C13#45512yes—
125C22×C13#45811yescharacteristic
126C4×C13—22no—
127C4×C13—22no—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13—42no—
131C4×C13—81no—
132Dic13—44no—
133Dic13—82no—
134Dic13—161no—
135C22×Q8—132no—
136C22×Q8—261no—
137C22×Q8D5211yescharacteristic
138C22×C8—22no—
139C22×C8—261no—
140C2×C4⋊C4—132no—
141C2×C4⋊C4—261no—
142C2×C4⋊C4—262no—
143C2×C4⋊C4—262no—
144C2×C4⋊C4—261no—
145C2×C4⋊C4D5211yescharacteristic
146C2×C42—261no—
147C2×C42C22×D1311yescharacteristic
148#106—522no—
149#103—524no—
150#103—522no—
151#95—22no—
152#95—262no—
153#95—261no—
154#95—262no—
155#95—262no—
156C2×C13#160812yes—
157C2×C13#161411yescharacteristic
158C2×C13#162311yescharacteristic
159C2×C13#164512yes—
160C2×C13#165911yescharacteristic
161C2×Q8—21no—
162C2×Q8—41no—
163C2×Q8—41no—
164C2×Q8—134no—
165C2×Q8—262no—
166C2×Q8—522no—
167C2×Q8—522no—
168C2×Q8—1041no—
169C2×Q8—1042no—
170C2×Q8Dic5212yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—262no—
174C22×C4—262no—
175C22×C4—521no—
176C22×C4C2×D5211yescharacteristic
177C22×C4D4×D1312yes—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—262no—
182C2×C8—521no—
183C2×C8—521no—
184C4⋊C4—41no—
185C4⋊C4—522no—
186C4⋊C4—521no—
187C4⋊C4—521no—
188C4⋊C4—522no—
189C4⋊C4—522no—
190C4⋊C4—1042no—
191C4⋊C4—1041no—
192C42—41no—
193C42—1041no—
194C13#781211yescharacteristic, complemented, Sylow
195C23#8813611yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—524no—
199Q8—1042no—
200Q8—1044no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—264no—
211C2×C4—522no—
212C2×C4—522no—
213C2×C4—522no—
214C2×C4—522no—
215C2×C4—522no—
216C2×C4—1041no—
217C2×C4—1042no—
218C2×C4C2×Dic5211yescharacteristic
219C2×C4#8816311yescharacteristic
220C2×C4SD16×D1312yes—
221C2×C4#8817212yes—
222C8—82no—
223C8—522no—
224C22#1171840011yescharacteristic
225C22#1171840311yescharacteristic
226C22#1171840811yescharacteristic
227C22#1171846712yes—
228C22#1171848612yes—
229C4—21no—
230C4—21no—
231C4—22no—
232C4—22no—
233C4—42no—
234C4—81no—
235C4—524no—
236C4—1042no—
237C4—2081no—
238C2#1311382812yes—
239C2#1311386311yescharacteristic
240C2#1311391511yescharacteristic
241C2#1311406012yes—
242C2#1311414311yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1272C2
socle, prime radicalC23×C13#120
hypercenter#1272D13
hypocenterC13#7812
LCSG ▷ C2×C42×C13 ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
194. C13#7812semidirect

Maximal subgroups

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

subgroupindex
#131228292
#131163792
#131162462
#131126612
C13×#12722
#781213