Finite Group Databasebeta

← #15760312

Subgroups — #15760312

Order 3328.

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

normal subgroups only

This group has 514 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#13123877C211yesmaximal, characteristic
2#13120009C211yesmaximal, characteristic
3#13113518C212yesmaximal, complemented
4#13112737C212yesmaximal, complemented
5C13×#1800C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88123C2211yescharacteristic
8C13×#423C2212yes—
9C2×C13×#100—21no—
10#11718882—21no—
11#11718873—22no—
12#11718868—22no—
13#11718673—24no—
14#11718638—21no—
15#11718608C414yes—
16C4×C4⋊Dic13C2211yescharacteristic
17#11718586C2212yes—
18C13×#343—21no—
19#11718073—24no—
20C22×D4×C13D411yescharacteristic
21C23×C4×C13D412yes—
22C22×Dic26C2×C412yes—
23C2×C13×M16—22no—
24C4×D4×C13—22no—
25C4×D4×C13—22no—
26C2×C13×C4⋊C4D411yescharacteristic
27C2×C13×C22⋊C4C2×C412yes—
28C2×C42×C13C2311yescharacteristic
29C2×C22⋊Dic13—24no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13—21no—
33C2×C4×Dic13—21no—
34C2×#6099—24no—
35#88123—22no—
36#88123—22no—
37C13×C4⋊C8—22no—
38C13×C4⋊C8—22no—
39C13×#100—42no—
40#88071—24no—
41#88071C2×C412yes—
42C22⋊#1055—24no—
43C22⋊#1055—22no—
44C4⋊#1055D414yes—
45C4×#1055—22no—
46#9399—131nomaximal, Sylow
47C24×C13C22⋊C412yes—
48C2×D4×C13—22no—
49C2×D4×C13—21no—
50C2×D4×C13—21no—
51C2×D4×C13—22no—
52C22×C4×C13—22no—
53C22×C4×C13—22no—
54C22×C4×C13—44no—
55C22×C4×C13C22⋊C412yes—
56C22×C4×C13C22×C411yescharacteristic
57C22×C4×C13C2×D411yescharacteristic
58C22×C4×C13C2×D411yescharacteristic
59C22×Dic13—22no—
60C22×Dic13—22no—
61C2×Dic26—24no—
62C2×Dic26—82no—
63C13×M16—42no—
64C13×M16—42no—
65C2×C8×C13—42no—
66C13×C4⋊C4—22no—
67C13×C22⋊C4—24no—
68C42×C13C2×D412yes—
69C42×C13#4112yes—
70C22⋊Dic13—84no—
71C4⋊Dic13—42no—
72C4⋊Dic13—41no—
73C4⋊Dic13—42no—
74C4⋊Dic13—41no—
75C4×Dic13—41no—
76C4×Dic13—41no—
77#6099—84no—
78C2×#1055—24no—
79#2975—131no—
80#2563—131no—
81#1800D1311yescharacteristic
82#1548—132no—
83#1303—132no—
84C23×C13—22no—
85C23×C13—22no—
86C23×C13—22no—
87C23×C13—42no—
88C23×C13—42no—
89C23×C13C2×C22⋊C411yescharacteristic
90D4×C13—42no—
91D4×C13—42no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—41no—
95C2×C4×C13—44no—
96C2×C4×C13—42no—
97C2×C4×C13—82no—
98C2×C4×C13C4×D412yes—
99C2×C4×C13#12011yescharacteristic
100C2×C4×C13#12112yes—
101C2×C4×C13#12311yescharacteristic
102C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
103C2×C4×C13#13712yes—
104C2×C4×C13#13711yescharacteristic
105C2×Dic13—42no—
106C2×Dic13—42no—
107C2×Dic13—44no—
108C2×Dic13—42no—
109C2×Dic13—42no—
110Dic26—84no—
111C8×C13—82no—
112#1055—44no—
113C2×C4⋊Q8—131no—
114C2×C4×D4C2×D1311yescharacteristic
115#436—264no—
116#431—132no—
117#423C2×D1312yes—
118C2×#100—21no—
119#407—262no—
120#393—134no—
121#390—261no—
122#382—261no—
123#380—262no—
124C4×C4⋊C4—131no—
125#343—21no—
126#333—264no—
127C22×C13—21no—
128C22×C13—21no—
129C22×C13—44no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—82no—
134C22×C13#38611yescharacteristic
135C22×C13#41711yescharacteristic
136C22×C13#41911yescharacteristic
137C4×C13—21no—
138C4×C13—22no—
139C4×C13—42no—
140C4×C13#45512yes—
141C4×C13#46812yes—
142C4×C13#47012yes—
143Dic13—82no—
144Dic13—82no—
145C22×Q8—132no—
146C22×D4C22⋊D1311yescharacteristic
147C23×C4D5212yes—
148C2×M16—22no—
149C2×M16—264no—
150C4⋊Q8—262no—
151C4⋊Q8—262no—
152C4×D4—22no—
153C4×D4—22no—
154C2×C4⋊C4—261no—
155C2×C4⋊C4—261no—
156C2×C4⋊C4—261no—
157C2×C4⋊C4C22⋊D1311yescharacteristic
158C2×C22⋊C4—264no—
159C2×C22⋊C4C4×D1312yes—
160C2×C42—261no—
161C2×C42C22×D1311yescharacteristic
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—134no—
165#100—42no—
166C22⋊C8—264no—
167C22⋊C8—262no—
168C4×C8—262no—
169#95—132no—
170#95—264no—
171C2×C13—21no—
172C2×C13—21no—
173C2×C13—82no—
174C2×C13#188511yescharacteristic
175C2×C13#189411yescharacteristic
176C2×C13#191411yescharacteristic
177C24#610312yes—
178C2×Q8—264no—
179C2×Q8—1042no—
180C2×D4—21no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—22no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4—44no—
187C22×C4—262no—
188C22×C4—262no—
189C22×C4#610312yes—
190C22×C4C2×C4×D1311yescharacteristic
191C22×C4C2×D5211yescharacteristic
192C22×C4C2×C22⋊D1311yescharacteristic
193M16—42no—
194M16—42no—
195M16—1044no—
196C2×C8—42no—
197C2×C8—264no—
198C4⋊C4—22no—
199C4⋊C4—522no—
200C4⋊C4—521no—
201C4⋊C4—521no—
202C4⋊C4—522no—
203C22⋊C4—24no—
204C22⋊C4—1044no—
205C42—521no—
206C42—521no—
207C42D4×D1312yes—
208C42#612912yes—
209C13#939911yescharacteristic, complemented, Sylow
210C23—22no—
211C23—22no—
212C23—22no—
213C23—42no—
214C23—42no—
215C23C2×#610311yescharacteristic
216Q8—1044no—
217D4—42no—
218D4—42no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—41no—
222C2×C4—44no—
223C2×C4—42no—
224C2×C4—82no—
225C2×C4—522no—
226C2×C4—524no—
227C2×C4—522no—
228C2×C4—522no—
229C2×C4—522no—
230C2×C4#8813512yes—
231C2×C4#8813611yescharacteristic
232C2×C4#8814011yescharacteristic
233C2×C4#8818611yescharacteristic
234C2×C4#8819312yes—
235C2×C4#8819611yescharacteristic
236C2×C4#8820512yes—
237C8—82no—
238C8—524no—
239C22—21no—
240C22—21no—
241C22—44no—
242C22—42no—
243C22—42no—
244C22—42no—
245C22—82no—
246C22#1171861911yescharacteristic
247C22#1171862711yescharacteristic
248C22#1171866511yescharacteristic
249C4—21no—
250C4—22no—
251C4—42no—
252C4—1042no—
253C4—1042no—
254C4#1171840712yes—
255C4#1171870312yes—
256C4#1171871312yes—
257C2—21no—
258C2—21no—
259C2—82no—
260C2#1311522211yescharacteristic
261C2#1311526711yescharacteristic
262C2#1311538111yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1800C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC2×C42×C13C23
hypercenter#1800D13
hypocenterC13#9399
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
3. #13113518C2semidirect
4. #13112737C2semidirect
209. C13#9399semidirect

Maximal subgroups

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

subgroupindex
#131238772
#131200092
#131135182
#131127372
C13×#18002
#939913