Finite Group Databasebeta

← #15765998

Subgroups — #15765998

Order 3328.

476 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 89 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#13123111C211yesmaximal, characteristic, complemented
2#13115660C212yesmaximal
3#13115659C211yesmaximal, characteristic
4#13112718C212yesmaximal, complemented
5C13×#1295C211yesmaximal, characteristic, complemented
6C2×#88128C2211yescharacteristic
7C2×C13×#97C2212yes—
8C13×#382C2211yescharacteristic
9C2×#88061—22no—
10C2×#88061—22no—
11#11718645—22no—
12C2×#88049—22no—
13#11718597C2212yes—
14C2×#88043C2211yescharacteristic
15#11718322—22no—
16#11718318—22no—
17C22×D52—22no—
18C22×D52—21no—
19C22×C8×C13—22no—
20C2×C13×C4⋊C4D412yes—
21C2×C42×C13C2311yescharacteristic
22C2×C4⋊Dic13—22no—
23C2×C4⋊Dic13D412yes—
24C2×C4⋊Dic13D412yes—
25C2×#6101—22no—
26C2×#6101—22no—
27C22×#1055—21no—
28#88128—22no—
29#88128—21no—
30#88128Q812yes—
31C13×#97—22no—
32C13×#97—22no—
33C13×#95—22no—
34#88071—22no—
35#88071—22no—
36#88071—22no—
37#88061—44no—
38#88061—44no—
39#88049—44no—
40#88043—22no—
41#10360—131nomaximal, Sylow
42C23×D13—41no—
43C22×C4×C13—22no—
44C22×C4×C13C2×D411yescharacteristic
45C22×C4×C13C2×D412yes—
46C22×Dic13—22no—
47C22×Dic13—22no—
48C2×D52—24no—
49C2×D52—22no—
50C2×D52—42no—
51C2×D52—42no—
52C2×D52—42no—
53C2×D52—42no—
54C2×D52—42no—
55C2×D52—42no—
56C2×D52—41no—
57C2×D52—42no—
58C2×C8×C13—24no—
59C2×C8×C13—42no—
60C2×C8×C13—42no—
61C13×C4⋊C4—42no—
62C42×C13C2×Q811yescharacteristic
63C42×C13#4112yes—
64C42×C13#4111yescharacteristic
65C4⋊Dic13—42no—
66C4⋊Dic13—42no—
67C4⋊Dic13—82no—
68#6101—82no—
69#6101—82no—
70C2×#1055—22no—
71C2×#1055—41no—
72C2×#1055—41no—
73#2845—131no—
74#1961—132no—
75#1961—131no—
76#1295—132no—
77#1295D1311yescharacteristic, complemented
78C23×C13#12011yescharacteristic
79C22×D13—42no—
80C22×D13—81no—
81C22×D13—82no—
82C22×D13—81no—
83C22×D13—82no—
84C2×C4×C13—21no—
85C2×C4×C13—22no—
86C2×C4×C13—21no—
87C2×C4×C13—22no—
88C2×C4×C13—42no—
89C2×C4×C13—42no—
90C2×C4×C13—42no—
91C2×C4×C13C22⋊Q812yes—
92C2×C4×C13C22⋊Q811yescharacteristic
93C2×C4×C13#12411yescharacteristic
94C2×C4×C13#12412yes—
95C2×Dic13—42no—
96C2×Dic13—42no—
97C2×Dic13—42no—
98C2×Dic13—42no—
99C2×Dic13—42no—
100C2×Dic13—42no—
101D52—44no—
102D52—44no—
103D52—44no—
104D52—82no—
105D52—82no—
106D52—82no—
107C8×C13—44no—
108#1055—42no—
109C2×#127—131no—
110C2×#102—262no—
111C2×#102—262no—
112C2×#102—262no—
113C2×#97—131no—
114C2×#97C2×D1312yes—
115#398—262no—
116#398—262no—
117#398—262no—
118#382—132no—
119#382C2×D1311yescharacteristic
120C22×C13#39311yescharacteristic
121C22×C13#45311yescharacteristic
122C22×C13#45312yes—
123C22×C13#45411yescharacteristic
124C22×C13#45412yes—
125C2×D13—84no—
126C2×D13—82no—
127C2×D13—162no—
128C2×D13—161no—
129C2×D13—161no—
130C4×C13—21no—
131C4×C13—22no—
132C4×C13—22no—
133C4×C13—21no—
134C4×C13—82no—
135Dic13—82no—
136Dic13—82no—
137C22×D4—261no—
138C22×D4—262no—
139C22×C8—22no—
140C22×C8—261no—
141#127—132no—
142#127—262no—
143#127—261no—
144C2×C4⋊C4—132no—
145C2×C4⋊C4—132no—
146C2×C4⋊C4—262no—
147C2×C4⋊C4—262no—
148C2×C4⋊C4—262no—
149C2×C4⋊C4D5212yes—
150C2×C42C22×D1311yescharacteristic
151#102—524no—
152#102—524no—
153#102—524no—
154#97—22no—
155#97—22no—
156#97—262no—
157#95—22no—
158#95—262no—
159#95—262no—
160#95—262no—
161C2×C13#165612yes—
162C2×C13#165611yescharacteristic
163C2×C13#165811yescharacteristic
164C2×C13#202712yes—
165C2×C13#202711yescharacteristic
166D13—162no—
167C24—521no—
168C2×D4—264no—
169C2×D4—262no—
170C2×D4—522no—
171C2×D4—522no—
172C2×D4—522no—
173C2×D4—522no—
174C2×D4—522no—
175C2×D4—522no—
176C2×D4—521no—
177C2×D4—522no—
178C22×C4—22no—
179C22×C4—262no—
180C22×C4—262no—
181C22×C4C2×D5211yescharacteristic
182C22×C4D4×D1312yes—
183C2×C8—24no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—262no—
187C2×C8—521no—
188C2×C8—521no—
189C4⋊C4—42no—
190C4⋊C4—522no—
191C4⋊C4—522no—
192C4⋊C4—1042no—
193C4⋊C4—1042no—
194C4⋊C4—1042no—
195C42#612712yes—
196C42#612911yescharacteristic
197C42Q8×D1311yescharacteristic
198C13#1036011yescharacteristic, complemented, Sylow
199C23—522no—
200C23—1041no—
201C23—1041no—
202C23—1042no—
203C23—1042no—
204C23#8813611yescharacteristic
205D4—524no—
206D4—524no—
207D4—524no—
208D4—1042no—
209D4—1042no—
210D4—1042no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—522no—
219C2×C4—522no—
220C2×C4—522no—
221C2×C4—522no—
222C2×C4—522no—
223C2×C4—522no—
224C2×C4#8812911yescharacteristic
225C2×C4#8813912yes—
226C2×C4#8815012yes—
227C2×C4#8815111yescharacteristic
228C8—44no—
229C8—522no—
230C22—1044no—
231C22—1042no—
232C22—2082no—
233C22—2081no—
234C22—2081no—
235C22#1171833411yescharacteristic
236C22#1171840811yescharacteristic
237C22#1171841411yescharacteristic
238C22#1171848312yes—
239C22#1171848812yes—
240C4—22no—
241C4—22no—
242C4—21no—
243C4—21no—
244C4—82no—
245C4—1042no—
246C4—1042no—
247C2—2082no—
248C2#1311413012yes—
249C2#1311413111yescharacteristic
250C2#1311413911yescharacteristic
251C2#1311599112yes—
252C2#1311599311yescharacteristic
subgroupG/H
centerC23#88136
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1295C2
socleC23×C13#120
prime radicalC2×#88128C22
hypercenter#1295D13
hypocenterC13#10360
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
1. #13123111C2semidirect
4. #13112718C2semidirect
5. C13×#1295C2semidirect
77. #1295D13semidirect
198. C13#10360semidirect

Maximal subgroups

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

subgroupindex
#131231112
#131156602
#131156592
#131127182
C13×#12952
#1036013