Finite Group Databasebeta

← #15753844

Subgroups — #15753844

Order 3328.

444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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#13117391C211yesmaximal, characteristic
2#13114584C212yesmaximal
3C2×#11718057C212yesmaximal
4#13112717C211yesmaximal, characteristic
5C13×#1295C211yesmaximal, characteristic
6C2×#88124C2211yescharacteristic
7C2×C13×#97C2212yes—
8C13×#382C2211yescharacteristic
9C4⋊C4×Dic13C412yes—
10#11718634C412yes—
11C42×Dic13C2211yescharacteristic
12C2×#88043C2212yes—
13#11718313—22no—
14#11718310—22no—
15#11718142—22no—
16#11718142—22no—
17#11718057C418yescomplemented
18C22×C8×C13—22no—
19C2×C13×C4⋊C4C2×C412yes—
20C2×C42×C13C2311yescharacteristic
21C2×C4⋊Dic13C2×C412yes—
22C2×#6101—22no—
23C2×#6101—22no—
24C2×C4×Dic13—22no—
25C2×C4×Dic13C2×C411yescharacteristic
26C2×C4×Dic13C2×C411yescharacteristic
27C2×C4×Dic13D412yes—
28C2×C4×Dic13D412yes—
29C22×#1055—22no—
30#88124—21no—
31#88124—21no—
32#88124C2×C414yes—
33C13×#97—22no—
34C13×#97C2×C414yes—
35C13×#95—22no—
36#88071—22no—
37#88071—22no—
38#88043—22no—
39#88043C2×C414yes—
40#8225—131nomaximal, Sylow
41C22×C4×C13—22no—
42C22×C4×C13C22×C411yescharacteristic
43C22×C4×C13C2×D412yes—
44C22×Dic13—22no—
45C22×Dic13C22⋊C411yescharacteristic
46C22×Dic13C22⋊C412yes—
47C22×Dic13C22⋊C411yescharacteristic
48C2×C8×C13—24no—
49C2×C8×C13—42no—
50C2×C8×C13—42no—
51C13×C4⋊C4—42no—
52C42×C13C22×C412yes—
53C42×C13#4111yescharacteristic
54C42×C13#4111yescharacteristic
55C4⋊Dic13—22no—
56C4⋊Dic13C4214yes—
57#6101—24no—
58#6101—24no—
59#6101—44no—
60C4×Dic13—22no—
61C4×Dic13—41no—
62C4×Dic13—42no—
63C4×Dic13—42no—
64C4×Dic13—44no—
65C2×#1055—24no—
66C2×#1055—42no—
67C2×#1055—42no—
68C4×#125—131no—
69#1745—132no—
70C2×#330—132no—
71#1295—131no—
72#1295D1311yescharacteristic
73C23×C13C2×C22⋊C411yescharacteristic
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13—22no—
78C2×C4×C13—42no—
79C2×C4×C13—42no—
80C2×C4×C13—42no—
81C2×C4×C13C2×C4211yescharacteristic
82C2×C4×C13#11711yescharacteristic
83C2×C4×C13C4×D412yes—
84C2×C4×C13C4×D412yes—
85C2×Dic13—22no—
86C2×Dic13—24no—
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—42no—
93C2×Dic13—42no—
94C2×Dic13#10112yes—
95C8×C13—44no—
96#1055—44no—
97C2×#125—131no—
98C2×#97—132no—
99C2×#97C2×D1312yes—
100#389—132no—
101#387—262no—
102#382C2×D1311yescharacteristic
103C4×C4⋊C4—132no—
104C4×C4⋊C4—262no—
105C43—131no—
106#336—262no—
107#336—262no—
108#330—138no—
109C22×C13C4×C22⋊C411yescharacteristic
110C22×C13C2×#10111yescharacteristic
111C22×C13#41311yescharacteristic
112C22×C13#42112yes—
113C22×C13#42112yes—
114C4×C13—21no—
115C4×C13—21no—
116C4×C13—22no—
117C4×C13—22no—
118C4×C13—82no—
119Dic13—22no—
120Dic13—41no—
121Dic13—44no—
122Dic13—42no—
123C22×C8—22no—
124C22×C8—262no—
125#125—134no—
126#125—261no—
127#125—261no—
128C2×C4⋊C4—132no—
129C2×C4⋊C4—262no—
130C2×C4⋊C4—262no—
131C2×C4⋊C4C4×D1312yes—
132C2×C42—131no—
133C2×C42—131no—
134C2×C42—132no—
135C2×C42—132no—
136C2×C42—262no—
137C2×C42C22×D1311yescharacteristic
138#97—22no—
139#97—134no—
140#97—262no—
141#97C4×D1314yes—
142#95—22no—
143#95—262no—
144#95—262no—
145C2×C13#153411yescharacteristic
146C2×C13#153512yes—
147C2×C13#153711yescharacteristic
148C2×C13C4×#10111yescharacteristic
149C2×C13#175912yes—
150C22×C4—22no—
151C22×C4—131no—
152C22×C4—131no—
153C22×C4—132no—
154C22×C4—262no—
155C22×C4C2×C4×D1311yescharacteristic
156C22×C4D4×D1312yes—
157C2×C8—24no—
158C2×C8—42no—
159C2×C8—42no—
160C2×C8—264no—
161C2×C8—522no—
162C2×C8—522no—
163C4⋊C4—42no—
164C4⋊C4—134no—
165C4⋊C4—264no—
166C4⋊C4—262no—
167C4⋊C4—264no—
168C4⋊C4—524no—
169C42—262no—
170C42—521no—
171C42—522no—
172C42—522no—
173C42—524no—
174C42C2×C4×D1312yes—
175C42#612911yescharacteristic
176C42#613111yescharacteristic
177C13#822511yescharacteristic, complemented, Sylow
178C23C22⋊C4×D1311yescharacteristic
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—132no—
187C2×C4—262no—
188C2×C4—262no—
189C2×C4—261no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—262no—
193C2×C4—264no—
194C2×C4—522no—
195C2×C4—522no—
196C2×C4C42×D1311yescharacteristic
197C2×C4#8813512yes—
198C2×C4#8814611yescharacteristic
199C2×C4#8814712yes—
200C8—44no—
201C8—524no—
202C22#1171832711yescharacteristic
203C22#1171840611yescharacteristic
204C22D13×#10111yescharacteristic
205C22#1171848212yes—
206C22#1171848212yes—
207C4—21no—
208C4—21no—
209C4—22no—
210C4—22no—
211C4—82no—
212C4—262no—
213C4—524no—
214C4—522no—
215C4—521no—
216C2#1311346111yescharacteristic
217C2#1311346412yes—
218C2#1311347211yescharacteristic
219C2#1311463111yescharacteristic
220C2#1311464512yes—
subgroupG/H
centerC23C22⋊C4×D13
commutatorC2×C4×C13C2×C42
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1295D13
hypocenterC13#8225
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
17. #11718057C4semidirect
177. C13#8225semidirect

Maximal subgroups

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

subgroupindex
#131173912
#131145842
C2×#117180572
#131127172
C13×#12952
#822513