Finite Group Databasebeta

← #15772932

Subgroups — #15772932

Order 3328.

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

normal subgroups only

This group has 354 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#13125415C211yesmaximal, characteristic
2#13116639C211yesmaximal, characteristic, complemented
3#13112802C214yesmaximal, complemented
4C2×C13×#334C211yesmaximal, characteristic, complemented
5#11719182—21no—
6C2×C13×C4⋊C8—21no—
7C2×C4×C8×C13C2211yescharacteristic
8#11718776—21no—
9#11718776C412yes—
10#11718356C411yescharacteristic
11#11718355—21no—
12C4×D104—21no—
13C4×D104C2212yes—
14#11718343C411yescharacteristic
15C13×#334—21no—
16C13×#334C2212yes—
17C22⋊#6090—21no—
18C4⋊#6090—21no—
19#11718053C2212yes—
20C2×#6127—41no—
21C22×C8×C13—41no—
22C22×C8×C13C2×C411yescharacteristic
23C22×C8×C13D411yescharacteristic
24C2×C42×C13D411yescharacteristic
25#88184—22no—
26#88184—41no—
27C2×D104—21no—
28C2×D104C2×C412yes—
29#88129—41no—
30#88128—21no—
31C4×D52—22no—
32C4×D52—41no—
33#88123—21no—
34C13×C4⋊C8—22no—
35C13×C4⋊C8—41no—
36C4×C8×C13C2×C411yescharacteristic
37C4×C8×C13D411yescharacteristic
38C4×C8×C13D411yescharacteristic
39C4×C8×C13C2311yescharacteristic
40#88061—22no—
41#88061—22no—
42#88058—21no—
43#88058C2×C412yes—
44C2×#6090—22no—
45#11654—131nomaximal, Sylow
46C22×C4×C13C22⋊C411yescharacteristic
47C22×C4×C13D811yescharacteristic
48C22×C4×C13SD1611yescharacteristic
49C2×C22⋊D13—42no—
50#6127—84no—
51C2×D52—22no—
52C2×D52—41no—
53C2×D52—41no—
54C2×C4×D13—42no—
55C2×Dic26—41no—
56C2×C8×C13—22no—
57C2×C8×C13—41no—
58C2×C8×C13—42no—
59C2×C8×C13—82no—
60C2×C8×C13C22⋊C411yescharacteristic
61C2×C8×C13C22⋊C411yescharacteristic
62C2×C8×C13C22×C411yescharacteristic
63C2×C8×C13C2×D411yescharacteristic
64C42×C13C22⋊C411yescharacteristic
65C42×C13D811yescharacteristic
66C42×C13SD1611yescharacteristic
67C42×C13C2×D411yescharacteristic
68#6103—42no—
69#6103—42no—
70C4⋊Dic13—22no—
71C4⋊Dic13—41no—
72D104—24no—
73D104—42no—
74#6090—42no—
75#3169—131no—
76#2163—131no—
77C2×#334D1311yescharacteristic, complemented
78#1333—134no—
79C23×C13#10211yescharacteristic
80C22×D13—42no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—21no—
84C2×C4×C13—21no—
85C2×C4×C13#10211yescharacteristic
86C2×C4×C13#10211yescharacteristic
87C2×C4×C13#10211yescharacteristic
88C2×C4×C13C2×C22⋊C411yescharacteristic
89C2×C4×C13C2×D811yescharacteristic
90C2×C4×C13C2×SD1611yescharacteristic
91C22⋊D13—84no—
92C2×Dic13—42no—
93D52—42no—
94D52—42no—
95D52—82no—
96D52—82no—
97C4×D13—84no—
98Dic26—82no—
99C8×C13—21no—
100C8×C13—21no—
101C8×C13—21no—
102C8×C13—82no—
103C8×C13#13112yes—
104#532—261no—
105#500—131no—
106#493—131no—
107#486—261no—
108#466—132no—
109#466—261no—
110C4×D8—132no—
111C4×D8—261no—
112C2×C4⋊C8—21no—
113C2×C4×C8C2×D1311yescharacteristic
114C4⋊C16—261no—
115C22⋊C16—261no—
116#346—132no—
117#334—21no—
118#334C2×D1312yes—
119C22×C13—21no—
120C22×C13—21no—
121C22×C13#36112yes—
122C22×C13C2×#10211yescharacteristic
123C2×D13—82no—
124C2×D13—82no—
125C2×D13—82no—
126C4×C13—21no—
127C4×C13—21no—
128C4×C13—21no—
129C4×C13—21no—
130C4×C13#36012yes—
131C4×C13#40811yescharacteristic
132C4×C13#42111yescharacteristic
133Dic13—82no—
134C2×#41—521no—
135C2×D8—132no—
136C2×D8—261no—
137C22×C8—41no—
138C22×C8C4×D1311yescharacteristic
139C22×C8D5211yescharacteristic
140C4⋊Q8—261no—
141#127—261no—
142#124—521no—
143#121—262no—
144#121—521no—
145C4×D4—262no—
146C4×D4—521no—
147C2×C42C22⋊D1311yescharacteristic
148C2×C16—262no—
149#107—132no—
150#107—261no—
151C4⋊C8—22no—
152C4⋊C8—41no—
153#102—262no—
154#102—262no—
155C4×C8C4×D1311yescharacteristic
156C4×C8D5211yescharacteristic
157C4×C8C22⋊D1311yescharacteristic
158C4×C8C22×D1311yescharacteristic
159C2×C13—22no—
160C2×C13#148011yescharacteristic
161C2×C13C2×#36011yescharacteristic
162C2×C13C2×#36111yescharacteristic
163D13—162no—
164#41—1044no—
165C2×Q8—521no—
166C2×D4—262no—
167C2×D4—522no—
168C2×D4—521no—
169C2×D4—521no—
170C22×C4—522no—
171C22×C4#610311yescharacteristic
172C22×C4#610411yescharacteristic
173C22×C4#610611yescharacteristic
174D8—264no—
175D8—522no—
176C2×C8—22no—
177C2×C8—41no—
178C2×C8—42no—
179C2×C8—82no—
180C2×C8#610311yescharacteristic
181C2×C8#610311yescharacteristic
182C2×C8C2×C4×D1311yescharacteristic
183C2×C8C2×D5211yescharacteristic
184C4⋊C4—262no—
185C4⋊C4—521no—
186C22⋊C4—522no—
187C22⋊C4—522no—
188C42#610311yescharacteristic
189C42#610411yescharacteristic
190C42#610611yescharacteristic
191C42C2×C22⋊D1311yescharacteristic
192C16—522no—
193C13#1165411yescharacteristic, complemented, Sylow
194C23—522no—
195C23#8804911yescharacteristic
196Q8—1042no—
197D4—522no—
198D4—522no—
199D4—1042no—
200D4—1044no—
201D4—1042no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—522no—
207C2×C4—1044no—
208C2×C4#8804911yescharacteristic
209C2×C4#8804911yescharacteristic
210C2×C4#8804911yescharacteristic
211C2×C4C2×#610311yescharacteristic
212C2×C4C2×#610411yescharacteristic
213C2×C4C2×#610611yescharacteristic
214C8—21no—
215C8—21no—
216C8—21no—
217C8—82no—
218C8#8815512yes—
219C22—21no—
220C22—21no—
221C22—1042no—
222C22—1042no—
223C22—1042no—
224C22#1171808712yes—
225C22C2×#8804911yescharacteristic
226C4—21no—
227C4—21no—
228C4—21no—
229C4—21no—
230C4—1042no—
231C4#1171808012yes—
232C4#1171877111yescharacteristic
233C4#1171880011yescharacteristic
234C2—22no—
235C2—2082no—
236C2#1311323411yescharacteristic
237C2C2×#1171808011yescharacteristic
238C2C2×#1171808711yescharacteristic
subgroupG/H
centerC22C2×#88049
commutatorC2×C8×C13C22×C4
FrattiniC4×C8C22×D13
FittingC2×C13×#334C2
socleC22×C13C2×#102
prime radical#13125415C2
cosocleC4×C8×C13C23
hypercenterC2×#334D13
hypocenterC13#11654
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#334

Complements

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

NH ≅ G/Ntype
2. #13116639C2semidirect
3. #13112802C2semidirect
4. C2×C13×#334C2semidirect
77. C2×#334D13semidirect
193. C13#11654semidirect

Maximal subgroups

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

subgroupindex
#131254152
#131166392
#131128022
C2×C13×#3342
#1165413