Finite Group Databasebeta

← #15765997

Subgroups — #15765997

Order 3328.

476 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 91 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#13115661C212yesmaximal
3#13112718C212yesmaximal, complemented
4#13112717C211yesmaximal, characteristic, complemented
5C13×#1961C211yesmaximal, characteristic
6C2×C13×#127C2211yescharacteristic
7C2×C13×#102—22no—
8C2×C13×#97C2211yescharacteristic
9C13×#382C2211yescharacteristic
10C2×#88072—22no—
11C2×#88072—22no—
12#11718645—22no—
13#11718597C2212yes—
14C2×#88043C2212yes—
15#11718322—22no—
16#11718318—22no—
17C22×D4×C13—21no—
18C22×D4×C13—22no—
19C22×C8×C13—21no—
20C13×#127—21no—
21C13×#127—22no—
22C13×#127Q812yes—
23C2×C13×C4⋊C4D412yes—
24C2×C42×C13C2311yescharacteristic
25C2×C4⋊Dic13—22no—
26C2×C4⋊Dic13D412yes—
27C2×C4⋊Dic13D412yes—
28C2×#6101—22no—
29C2×#6101—22no—
30C22×#1055—22no—
31C13×#102—44no—
32C13×#97—22no—
33C13×#95—22no—
34#88072—44no—
35#88072—44no—
36#88071—22no—
37#88071—22no—
38#88071—22no—
39#88043—22no—
40#88043—22no—
41#10360—131nomaximal, Sylow
42C24×C13—41no—
43C2×D4×C13—24no—
44C2×D4×C13—22no—
45C2×D4×C13—42no—
46C2×D4×C13—42no—
47C2×D4×C13—42no—
48C2×D4×C13—42no—
49C2×D4×C13—42no—
50C2×D4×C13—42no—
51C2×D4×C13—42no—
52C2×D4×C13—41no—
53C22×C4×C13—22no—
54C22×C4×C13C2×D412yes—
55C22×C4×C13C2×D411yescharacteristic
56C22×Dic13—22no—
57C22×Dic13—22no—
58C2×C8×C13—22no—
59C2×C8×C13—41no—
60C2×C8×C13—41no—
61C13×C4⋊C4—42no—
62C42×C13C2×Q811yescharacteristic
63C42×C13#4111yescharacteristic
64C42×C13#4112yes—
65C4⋊Dic13—42no—
66C4⋊Dic13—42no—
67C4⋊Dic13—82no—
68#6101—82no—
69#6101—82no—
70C2×#1055—24no—
71C2×#1055—42no—
72C2×#1055—42no—
73#2845—131no—
74#1961—132no—
75#1961D1311yescharacteristic
76#1295—132no—
77#1295—131no—
78C23×C13—42no—
79C23×C13—81no—
80C23×C13—82no—
81C23×C13—81no—
82C23×C13—82no—
83C23×C13#12011yescharacteristic
84D4×C13—44no—
85D4×C13—44no—
86D4×C13—44no—
87D4×C13—82no—
88D4×C13—82no—
89D4×C13—82no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—42no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13C22⋊Q812yes—
98C2×C4×C13C22⋊Q811yescharacteristic
99C2×C4×C13#12412yes—
100C2×C4×C13#12411yescharacteristic
101C2×Dic13—42no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C8×C13—42no—
108#1055—44no—
109C2×#127C2×D1311yescharacteristic
110C2×#102—22no—
111C2×#102—262no—
112C2×#102—262no—
113C2×#97—132no—
114C2×#97C2×D1311yescharacteristic
115#398—262no—
116#398—262no—
117#398—262no—
118#382—132no—
119#382C2×D1311yescharacteristic
120C22×C13—84no—
121C22×C13—82no—
122C22×C13—162no—
123C22×C13—161no—
124C22×C13—161no—
125C22×C13#39311yescharacteristic
126C22×C13#45311yescharacteristic
127C22×C13#45312yes—
128C22×C13#45411yescharacteristic
129C22×C13#45412yes—
130C4×C13—22no—
131C4×C13—21no—
132C4×C13—22no—
133C4×C13—21no—
134C4×C13—82no—
135Dic13—82no—
136Dic13—82no—
137C22×D4—22no—
138C22×D4—21no—
139C22×C8—21no—
140C22×C8—262no—
141#127—21no—
142#127—22no—
143#127Dic2612yes—
144C2×C4⋊C4—132no—
145C2×C4⋊C4—132no—
146C2×C4⋊C4—262no—
147C2×C4⋊C4—262no—
148C2×C4⋊C4—262no—
149C2×C4⋊C4C22⋊D1312yes—
150C2×C42C22×D1311yescharacteristic
151#102—44no—
152#102—524no—
153#102—524no—
154#97—22no—
155#97—262no—
156#97—262no—
157#95—22no—
158#95—262no—
159#95—262no—
160#95—262no—
161C2×C13—162no—
162C2×C13#165612yes—
163C2×C13#165611yescharacteristic
164C2×C13#165811yescharacteristic
165C2×C13#202712yes—
166C2×C13#202711yescharacteristic
167C24—41no—
168C2×D4—24no—
169C2×D4—22no—
170C2×D4—42no—
171C2×D4—42no—
172C2×D4—42no—
173C2×D4—42no—
174C2×D4—42no—
175C2×D4—42no—
176C2×D4—42no—
177C2×D4—41no—
178C22×C4—22no—
179C22×C4—262no—
180C22×C4—262no—
181C22×C4D4×D1312yes—
182C22×C4C2×C22⋊D1311yescharacteristic
183C2×C8—22no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—264no—
187C2×C8—522no—
188C2×C8—522no—
189C4⋊C4—42no—
190C4⋊C4—522no—
191C4⋊C4—522no—
192C4⋊C4—1042no—
193C4⋊C4—1042no—
194C4⋊C4—1042no—
195C42C2×Dic2611yescharacteristic
196C42#612711yescharacteristic
197C42#612912yes—
198C13#1036011yescharacteristic, complemented, Sylow
199C23—42no—
200C23—81no—
201C23—81no—
202C23—82no—
203C23—82no—
204C23#8819111yescharacteristic
205D4—44no—
206D4—44no—
207D4—44no—
208D4—82no—
209D4—82no—
210D4—82no—
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#8813212yes—
225C2×C4#8813912yes—
226C2×C4#8817811yescharacteristic
227C2×C4#8819011yescharacteristic
228C8—42no—
229C8—524no—
230C22—84no—
231C22—82no—
232C22—162no—
233C22—161no—
234C22—161no—
235C22#1171860811yescharacteristic
236C22#1171872311yescharacteristic
237C22#1171873811yescharacteristic
238C22#1171885912yes—
239C22#1171886212yes—
240C4—22no—
241C4—22no—
242C4—21no—
243C4—21no—
244C4—82no—
245C4—1042no—
246C4—1042no—
247C2—162no—
248C2#1311412712yes—
249C2#1311412811yescharacteristic
250C2#1311413711yescharacteristic
251C2#1311599012yes—
252C2#1311599211yescharacteristic
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1961C2
socleC23×C13#120
prime radicalC2×C13×#127C22
hypercenter#1961D13
hypocenterC13#10360
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
1. #13123111C2semidirect
3. #13112718C2semidirect
4. #13112717C2semidirect
198. C13#10360semidirect

Maximal subgroups

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

subgroupindex
#131231112
#131156612
#131127182
#131127172
C13×#19612
#1036013