Finite Group Databasebeta

← #15765992

Subgroups — #15765992

Order 3328.

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

normal subgroups only

This group has 400 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#13123108C211yesmaximal, characteristic
2#13115810C212yesmaximal
3#13112718C212yesmaximal
4#13112717C211yesmaximal, characteristic
5C13×#1960C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×#103—21no—
8C2×C13×#103—21no—
9C2×C13×#97C2211yescharacteristic
10C13×#382C2211yescharacteristic
11#11718647—21no—
12#11718640—21no—
13#11718597C2212yes—
14C2×#88043C2212yes—
15#11718321—22no—
16#11718317—22no—
17#11718121—22no—
18#11718121—22no—
19C22×Q8×C13—21no—
20C22×Dic26—21no—
21C22×C8×C13—21no—
22C13×C4⋊Q8—22no—
23C13×C4⋊Q8—21no—
24C13×C4⋊Q8Q812yescomplemented
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C42×C13C2311yescharacteristic
29C2×C4⋊Dic13—21no—
30C2×C4⋊Dic13D412yes—
31C2×C4⋊Dic13D412yes—
32C2×#6101—22no—
33C22×#1055—22no—
34C13×#103—42no—
35C13×#103—42no—
36C13×#97—22no—
37C13×#95—22no—
38#88071—22no—
39#88071—21no—
40#88071—21no—
41#88071—22no—
42#88071—22no—
43#88043—22no—
44#88043—22no—
45#10359—131nomaximal, Sylow
46C2×Q8×C13—22no—
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C2×Q8×C13—41no—
50C2×Q8×C13—41no—
51C2×Q8×C13—41no—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—41no—
55C22×C4×C13C2×D412yes—
56C22×C4×C13C2×D411yescharacteristic
57C22×Dic13—22no—
58C22×Dic13—22no—
59C2×Dic26—81no—
60C2×Dic26—82no—
61C2×C8×C13—22no—
62C2×C8×C13—41no—
63C2×C8×C13—41no—
64C13×C4⋊C4—24no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—41no—
67C13×C4⋊C4—42no—
68C42×C13C2×Q811yescharacteristic
69C42×C13#4111yescharacteristic
70C42×C13#4112yes—
71C4⋊Dic13—42no—
72C4⋊Dic13—42no—
73C4⋊Dic13—81no—
74#6101—82no—
75C2×#1055—24no—
76C2×#1055—42no—
77C2×#1055—42no—
78#2844—131no—
79#1993—132no—
80#1960D1311yescharacteristic
81#1295—132no—
82#1295—131no—
83C23×C13#12011yescharacteristic
84Q8×C13—42no—
85Q8×C13—42no—
86Q8×C13—81no—
87Q8×C13—81no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—42no—
93C2×C4×C13—41no—
94C2×C4×C13—41no—
95C2×C4×C13—42no—
96C2×C4×C13—42no—
97C2×C4×C13—81no—
98C2×C4×C13—81no—
99C2×C4×C13C22⋊Q812yes—
100C2×C4×C13C22⋊Q811yescharacteristic
101C2×C4×C13#12412yes—
102C2×C4×C13#12411yescharacteristic
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109Dic26—84no—
110C8×C13—42no—
111#1055—44no—
112C2×C4⋊Q8C2×D1311yescharacteristic
113C2×#103—21no—
114C2×#103—21no—
115C2×#97—132no—
116C2×#97C2×D1311yescharacteristic
117#400—262no—
118#400—261no—
119#395—262no—
120#395—261no—
121#382—132no—
122#382C2×D1311yescharacteristic
123#340—262no—
124#340—262no—
125C22×C13#39311yescharacteristic
126C22×C13#45311yescharacteristic
127C22×C13#45411yescharacteristic
128C22×C13#45512yes—
129C22×C13#45612yes—
130C4×C13—21no—
131C4×C13—21no—
132C4×C13—22no—
133C4×C13—22no—
134C4×C13—81no—
135C4×C13—81no—
136C4×C13—82no—
137Dic13—82no—
138Dic13—82no—
139C22×Q8—21no—
140C22×Q8—261no—
141C22×C8—21no—
142C22×C8—262no—
143C4⋊Q8—21no—
144C4⋊Q8—22no—
145C4⋊Q8Dic2612yescomplemented
146C2×C4⋊C4—22no—
147C2×C4⋊C4—132no—
148C2×C4⋊C4—132no—
149C2×C4⋊C4—262no—
150C2×C4⋊C4—261no—
151C2×C4⋊C4C22⋊D1311yescharacteristic
152C2×C4⋊C4C22⋊D1311yescharacteristic
153C2×C42C22×D1311yescharacteristic
154#103—42no—
155#103—42no—
156#97—22no—
157#97—262no—
158#97—262no—
159#95—22no—
160#95—262no—
161#95—261no—
162#95—261no—
163#95—262no—
164#95—262no—
165C2×C13#165911yescharacteristic
166C2×C13#166011yescharacteristic
167C2×C13#166412yes—
168C2×C13#202711yescharacteristic
169C2×C13#202812yes—
170C2×Q8—22no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—1041no—
177C2×Q8—1042no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—41no—
181C22×C4—262no—
182C22×C4—262no—
183C22×C4D4×D1312yes—
184C22×C4C2×C22⋊D1311yescharacteristic
185C2×C8—22no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—264no—
189C2×C8—522no—
190C2×C8—522no—
191C4⋊C4—24no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—522no—
196C4⋊C4—522no—
197C4⋊C4—1042no—
198C4⋊C4—1041no—
199C42C2×Dic2611yescharacteristic
200C42#612711yescharacteristic
201C42#612912yes—
202C13#1035911yescharacteristic, complemented, Sylow
203C23#8819111yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—81no—
207Q8—81no—
208Q8—1044no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—522no—
221C2×C4—522no—
222C2×C4—522no—
223C2×C4—522no—
224C2×C4—522no—
225C2×C4—522no—
226C2×C4#8813212yes—
227C2×C4#8813912yes—
228C2×C4#8817811yescharacteristic
229C2×C4#8819011yescharacteristic
230C8—42no—
231C8—524no—
232C22#1171860811yescharacteristic
233C22#1171872311yescharacteristic
234C22#1171873811yescharacteristic
235C22#1171886312yes—
236C22#1171886612yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—81no—
243C4—82no—
244C4—1042no—
245C4—1042no—
246C2#1311414011yescharacteristic
247C2#1311414511yescharacteristic
248C2#1311416712yes—
249C2#1311599211yescharacteristic
250C2#1311599512yes—
subgroupG/H
centerC23#88191
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1960C2
socle, prime radicalC23×C13#120
hypercenter#1960D13
hypocenterC13#10359
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
24. C13×C4⋊Q8Q8semidirect
145. C4⋊Q8Dic26semidirect
202. C13#10359semidirect

Maximal subgroups

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

subgroupindex
#131231082
#131158102
#131127182
#131127172
C13×#19602
#1035913