Finite Group Databasebeta

← #15760327

Subgroups — #15760327

Order 3328.

486 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 115 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#13123921C211yesmaximal, characteristic
2#13119821C211yesmaximal, characteristic
3#13113509C212yesmaximal
4#13112737C212yesmaximal
5C13×#1801C211yesmaximal, characteristic
6C2×C4×Q8×C13C2211yescharacteristic
7C2×#88198—21no—
8C2×#88123C2211yescharacteristic
9C13×#423C2212yes—
10C2×C13×#101—21no—
11#11718685—24no—
12#11718644C414yes—
13#11718635—21no—
14C4×C4⋊Dic13C2211yescharacteristic
15#11718589—22no—
16#11718587—22no—
17#11718586C2212yes—
18C13×#343—21no—
19#11718074—24no—
20C22×Q8×C13D411yescharacteristic
21C22×Dic26—21no—
22C2×C13×M16—22no—
23C4×Q8×C13—22no—
24C4×Q8×C13—22no—
25C2×C13×C4⋊C4C2×C412yes—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C42×C13D412yes—
28C2×C42×C13C2311yescharacteristic
29#88198—44no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C412yes—
33C2×#6101—24no—
34C2×C4×Dic13—21no—
35#88123—22no—
36#88123—22no—
37C13×C4⋊C8—22no—
38C13×C4⋊C8—22no—
39C13×#101—42no—
40#88071—24no—
41#88071C2×C412yes—
42C22⋊#1055—22no—
43C4⋊#1055—24no—
44C4⋊#1055D414yes—
45#88043—24no—
46C4×#1055—22no—
47#9402—131nomaximal, Sylow
48C2×Q8×C13—22no—
49C2×Q8×C13—21no—
50C2×Q8×C13—22no—
51C2×Q8×C13—21no—
52C22×C4×C13C22⋊C412yes—
53C22×C4×C13C22⋊C412yes—
54C22×C4×C13C22×C411yescharacteristic
55C22×C4×C13C2×D411yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C22×Dic13—22no—
58C22×Dic13—22no—
59C2×Dic26—42no—
60C2×Dic26—42no—
61C2×Dic26—41no—
62C2×Dic26—41no—
63C13×M16—42no—
64C13×M16—42no—
65C2×C8×C13—42no—
66C13×C4⋊C4—24no—
67C13×C4⋊C4—22no—
68C42×C13—22no—
69C42×C13—22no—
70C42×C13C2×D412yes—
71C42×C13#4112yes—
72C4⋊Dic13—24no—
73C4⋊Dic13—24no—
74C4⋊Dic13—41no—
75C4⋊Dic13—41no—
76#6101—48no—
77C4×Dic13—42no—
78C2×#1055—24no—
79#2983—131no—
80#2546—131no—
81#1801D1311yescharacteristic
82#1546—132no—
83#1303—132no—
84C23×C13C2×C22⋊C411yescharacteristic
85Q8×C13—42no—
86Q8×C13—42no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—41no—
93C2×C4×C13—42no—
94C2×C4×C13C4×D412yes—
95C2×C4×C13#12011yescharacteristic
96C2×C4×C13#12112yes—
97C2×C4×C13#12311yescharacteristic
98C2×C4×C13AGL(1,ℤ/8)12yes—
99C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
100C2×C4×C13#13711yescharacteristic
101C2×Dic13—24no—
102C2×Dic13—42no—
103C2×Dic13—42no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107Dic26—82no—
108Dic26—82no—
109C8×C13—82no—
110#1055—44no—
111C2×C4⋊Q8—131no—
112C2×C4⋊Q8—261no—
113C2×C4×Q8C2×D1311yescharacteristic
114#446—264no—
115#432—262no—
116#431—132no—
117#423C2×D1312yes—
118C2×#101—21no—
119#398—134no—
120#391—261no—
121#389—262no—
122C4×C4⋊C4—131no—
123#343—21no—
124#332—264no—
125C22×C13—21no—
126C22×C13—21no—
127C22×C13#38611yescharacteristic
128C22×C13#41711yescharacteristic
129C22×C13#41811yescharacteristic
130C4×C13—21no—
131C4×C13—22no—
132C4×C13—42no—
133C4×C13—42no—
134C4×C13#45612yes—
135C4×C13#46812yes—
136C4×C13#46912yes—
137Dic13—44no—
138Dic13—82no—
139C22×Q8—261no—
140C22×Q8C22⋊D1311yescharacteristic
141C2×M16—22no—
142C4⋊Q8—262no—
143C4⋊Q8—262no—
144C4⋊Q8—524no—
145C4×Q8—22no—
146C4×Q8—22no—
147C2×C4⋊C4—132no—
148C2×C4⋊C4—261no—
149C2×C4⋊C4—264no—
150C2×C4⋊C4—261no—
151C2×C4⋊C4C4×D1312yes—
152C2×C4⋊C4C22⋊D1311yescharacteristic
153C2×C42—261no—
154C2×C42D5212yes—
155C2×C42C22×D1311yescharacteristic
156C4⋊C8—22no—
157C4⋊C8—22no—
158C4⋊C8—134no—
159C4⋊C8—264no—
160#101—42no—
161C22⋊C8—262no—
162#97—264no—
163C4×C8—262no—
164#95—132no—
165#95—264no—
166C2×C13—21no—
167C2×C13—21no—
168C2×C13#188611yescharacteristic
169C2×C13#189511yescharacteristic
170C2×C13#191511yescharacteristic
171C2×Q8—21no—
172C2×Q8—22no—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—521no—
176C2×Q8—522no—
177C2×Q8—521no—
178C2×Q8—522no—
179C22×C4—262no—
180C22×C4—262no—
181C22×C4#610312yes—
182C22×C4#610312yes—
183C22×C4C2×C4×D1311yescharacteristic
184C22×C4C2×D5211yescharacteristic
185C22×C4C2×C22⋊D1311yescharacteristic
186M16—42no—
187M16—42no—
188C2×C8—42no—
189C2×C8—264no—
190C4⋊C4—24no—
191C4⋊C4—22no—
192C4⋊C4—264no—
193C4⋊C4—264no—
194C4⋊C4—528no—
195C4⋊C4—521no—
196C4⋊C4—521no—
197C42—22no—
198C42—22no—
199C42—522no—
200C42D4×D1312yes—
201C42#612912yes—
202C13#940211yescharacteristic, complemented, Sylow
203C23C2×#610311yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—1042no—
207Q8—1042no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—264no—
216C2×C4—522no—
217C2×C4—522no—
218C2×C4—522no—
219C2×C4—522no—
220C2×C4—522no—
221C2×C4#8813512yes—
222C2×C4#8813611yescharacteristic
223C2×C4#8814011yescharacteristic
224C2×C4#8818611yescharacteristic
225C2×C4#8819312yes—
226C2×C4#8819611yescharacteristic
227C2×C4#8820312yes—
228C8—82no—
229C8—524no—
230C22—21no—
231C22—21no—
232C22#1171861911yescharacteristic
233C22#1171862711yescharacteristic
234C22#1171866211yescharacteristic
235C4—21no—
236C4—22no—
237C4—42no—
238C4—42no—
239C4—524no—
240C4—1042no—
241C4#1171841312yes—
242C4#1171870012yes—
243C4#1171871012yes—
244C2—21no—
245C2—21no—
246C2#1311522711yescharacteristic
247C2#1311527211yescharacteristic
248C2#1311538611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1801C2
socleC22×C13#386
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1801D13
hypocenterC13#9402
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
202. C13#9402semidirect

Maximal subgroups

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

subgroupindex
#131239212
#131198212
#131135092
#131127372
C13×#18012
#940213