Finite Group Databasebeta

← #15760287

Subgroups — #15760287

Order 3328.

506 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 131 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#13123917C211yesmaximal, 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—
11Q8×#1055—24no—
12#11718644C414yes—
13#11718635—21no—
14C4×C4⋊Dic13C2211yescharacteristic
15#11718589—22no—
16#11718586—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—42no—
30#88198—42no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13C2×C412yes—
34C2×#6101—24no—
35C2×C4×Dic13—21no—
36#88123—22no—
37#88123—22no—
38C13×C4⋊C8—22no—
39C13×C4⋊C8—22no—
40C13×#101—42no—
41#88071—24no—
42#88071C2×C412yes—
43C22⋊#1055—22no—
44C4⋊#1055—24no—
45C4⋊#1055D414yes—
46C4×#1055—24no—
47C4×#1055—22no—
48#9394—131nomaximal, Sylow
49C2×Q8×C13—22no—
50C2×Q8×C13—22no—
51C2×Q8×C13D812yes—
52C2×Q8×C13SD1612yes—
53C22×C4×C13C22⋊C412yes—
54C22×C4×C13C22⋊C412yes—
55C22×C4×C13C22×C411yescharacteristic
56C22×C4×C13C2×D411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C22×Dic13—22no—
59C22×Dic13—22no—
60C2×Dic26—42no—
61C2×Dic26—41no—
62C2×Dic26—41no—
63C2×Dic26—42no—
64C13×M16—42no—
65C13×M16—42no—
66C2×C8×C13—42no—
67C13×C4⋊C4—24no—
68C13×C4⋊C4—22no—
69C42×C13—22no—
70C42×C13—22no—
71C42×C13C2×D412yes—
72C42×C13#4112yes—
73C4⋊Dic13—24no—
74C4⋊Dic13—24no—
75C4⋊Dic13—41no—
76C4⋊Dic13—41no—
77#6101—48no—
78C4×Dic13—41no—
79C4×Dic13—41no—
80C2×#1055—24no—
81#2982—131no—
82#2546—131no—
83#1801D1311yescharacteristic
84#1546—132no—
85#1303—132no—
86C23×C13C2×C22⋊C411yescharacteristic
87Q8×C13—24no—
88Q8×C13—24no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—41no—
94C2×C4×C13—42no—
95C2×C4×C13#10214yes—
96C2×C4×C13C4×D412yes—
97C2×C4×C13#12011yescharacteristic
98C2×C4×C13#12112yes—
99C2×C4×C13#12311yescharacteristic
100C2×C4×C13C2×D811yescharacteristic
101C2×C4×C13C2×SD1611yescharacteristic
102C2×C4×C13#13512yes—
103C2×Dic13—24no—
104C2×Dic13—42no—
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13—42no—
109Dic26—82no—
110Dic26—82no—
111C8×C13—82no—
112#1055—44no—
113C2×C4⋊Q8—131no—
114C2×C4⋊Q8—261no—
115C2×C4×Q8C2×D1311yescharacteristic
116C8×Q8—264no—
117#431—132no—
118#431—262no—
119#423C2×D1312yes—
120C2×#101—21no—
121#398—134no—
122#391—261no—
123#389—262no—
124C4×C4⋊C4—131no—
125#343—21no—
126#332—264no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13#38611yescharacteristic
130C22×C13C2×#10211yescharacteristic
131C22×C13#41611yescharacteristic
132C4×C13—21no—
133C4×C13—24no—
134C4×C13—22no—
135C4×C13—42no—
136C4×C13#45612yes—
137C4×C13#46512yes—
138C4×C13#46612yes—
139Dic13—44no—
140Dic13—82no—
141C22×Q8—261no—
142C22×Q8C22⋊D1311yescharacteristic
143C2×M16—22no—
144C4⋊Q8—262no—
145C4⋊Q8—262no—
146C4⋊Q8—522no—
147C4⋊Q8—522no—
148C4×Q8—22no—
149C4×Q8—22no—
150C2×C4⋊C4—132no—
151C2×C4⋊C4—261no—
152C2×C4⋊C4—264no—
153C2×C4⋊C4—261no—
154C2×C4⋊C4C4×D1312yes—
155C2×C4⋊C4C22⋊D1311yescharacteristic
156C2×C42—261no—
157C2×C42D5212yes—
158C2×C42C22×D1311yescharacteristic
159C4⋊C8—22no—
160C4⋊C8—22no—
161C4⋊C8—134no—
162C4⋊C8—264no—
163#101—42no—
164C22⋊C8—262no—
165C4×C8—264no—
166C4×C8—262no—
167#95—132no—
168#95—264no—
169C2×C13—21no—
170C2×C13—21no—
171C2×C13#188611yescharacteristic
172C2×C13#189311yescharacteristic
173C2×C13#191511yescharacteristic
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—521no—
177C2×Q8—522no—
178C2×Q8—521no—
179C2×Q8—522no—
180C2×Q8#610412yes—
181C2×Q8#610612yes—
182C22×C4—262no—
183C22×C4—262no—
184C22×C4#610312yes—
185C22×C4#610312yes—
186C22×C4C2×C4×D1311yescharacteristic
187C22×C4C2×D5211yescharacteristic
188C22×C4C2×C22⋊D1311yescharacteristic
189M16—42no—
190M16—42no—
191C2×C8—42no—
192C2×C8—264no—
193C4⋊C4—24no—
194C4⋊C4—22no—
195C4⋊C4—264no—
196C4⋊C4—264no—
197C4⋊C4—521no—
198C4⋊C4—521no—
199C4⋊C4—528no—
200C42—22no—
201C42—22no—
202C42—521no—
203C42—521no—
204C42D4×D1312yes—
205C42#612912yes—
206C13#939411yescharacteristic, complemented, Sylow
207C23C2×#610311yescharacteristic
208Q8—24no—
209Q8—24no—
210Q8—1042no—
211Q8—1042no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—41no—
217C2×C4—42no—
218C2×C4—264no—
219C2×C4—522no—
220C2×C4—522no—
221C2×C4—522no—
222C2×C4—522no—
223C2×C4—522no—
224C2×C4#8804914yes—
225C2×C4#8813512yes—
226C2×C4#8813611yescharacteristic
227C2×C4#8814011yescharacteristic
228C2×C4C2×#610411yescharacteristic
229C2×C4#8819312yes—
230C2×C4C2×#610611yescharacteristic
231C2×C4#8820412yes—
232C8—82no—
233C8—524no—
234C22—21no—
235C22—21no—
236C22#1171861911yescharacteristic
237C22C2×#8804911yescharacteristic
238C22#1171866311yescharacteristic
239C4—21no—
240C4—24no—
241C4—22no—
242C4—42no—
243C4—524no—
244C4—1042no—
245C4#1171841312yes—
246C4#1171869912yes—
247C4#1171870912yes—
248C2—21no—
249C2—21no—
250C2#1311522711yescharacteristic
251C2#1311526211yescharacteristic
252C2#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#9394
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
206. C13#9394semidirect

Maximal subgroups

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

subgroupindex
#131239172
#131198212
#131135092
#131127372
C13×#18012
#939413