Finite Group Databasebeta

← #15760756

Subgroups — #15760756

Order 3328.

542 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 127 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#13123860C211yesmaximal, characteristic
2#13120190C211yesmaximal, characteristic
3#13113264C212yesmaximal, complemented
4#13112696C212yesmaximal, complemented
5C13×#1800C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×C4×Dic26C2211yescharacteristic
8C13×#423C2212yes—
9C2×C13×#100—21no—
10#11718882—21no—
11#11718871—22no—
12C2×C22⋊#1055—22no—
13D4×#1055—24no—
14#11718634—21no—
15#11718610C412yes—
16#11718608C412yes—
17#11718597C2211yescharacteristic
18#11718586C2212yes—
19C13×#343—21no—
20#11718076—24no—
21C22×D4×C13D411yescharacteristic
22C23×C4×C13D412yes—
23C22×Dic26C2×C411yescharacteristic
24C2×C13×M16—22no—
25C4×D4×C13—22no—
26C4×D4×C13—22no—
27C2×C13×C4⋊C4D411yescharacteristic
28C2×C13×C22⋊C4C2×C412yes—
29C2×C42×C13C2311yescharacteristic
30C2×C22⋊Dic13—22no—
31C2×C22⋊Dic13—22no—
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13C2×C411yescharacteristic
34C2×#6101—21no—
35C2×#6101—22no—
36C2×C4×Dic13—21no—
37C22×#1055—24no—
38C4×Dic26—22no—
39C4×Dic26—22no—
40C13×C4⋊C8—22no—
41C13×C4⋊C8—22no—
42C13×#100—42no—
43#88071—22no—
44#88071—21no—
45#88071C2×C412yes—
46C22⋊#1055—24no—
47C22⋊#1055—22no—
48C4⋊#1055—22no—
49C4×#1055D414yes—
50#9483—131nomaximal, Sylow
51C24×C13C22⋊C412yes—
52C2×D4×C13—22no—
53C2×D4×C13—22no—
54C2×D4×C13SD1612yes—
55C2×D4×C13Q1612yes—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13—82no—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C22×C411yescharacteristic
61C22×C4×C13C2×D411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—22no—
65C22×Dic13—21no—
66C2×Dic26—22no—
67C2×Dic26—42no—
68C13×M16—42no—
69C13×M16—42no—
70C2×C8×C13—42no—
71C13×C4⋊C4—22no—
72C13×C22⋊C4—24no—
73C42×C13C2×D412yes—
74C42×C13#4112yes—
75C22⋊Dic13—44no—
76C22⋊Dic13—82no—
77C4⋊Dic13—22no—
78C4⋊Dic13—42no—
79#6101—41no—
80#6101—41no—
81#6101—82no—
82C4×Dic13—42no—
83C2×#1055—24no—
84C2×#1055—84no—
85#2972—131no—
86#2580—131no—
87#1800D1311yescharacteristic
88#1487—132no—
89#1286—132no—
90C23×C13—22no—
91C23×C13—22no—
92C23×C13—42no—
93C23×C13—42no—
94C23×C13#10314yes—
95C23×C13C2×C22⋊C411yescharacteristic
96D4×C13—24no—
97D4×C13—24no—
98C2×C4×C13—22no—
99C2×C4×C13—41no—
100C2×C4×C13—41no—
101C2×C4×C13—44no—
102C2×C4×C13—42no—
103C2×C4×C13—82no—
104C2×C4×C13C4×D412yes—
105C2×C4×C13#12011yescharacteristic
106C2×C4×C13#12112yes—
107C2×C4×C13#12311yescharacteristic
108C2×C4×C13C2×SD1611yescharacteristic
109C2×C4×C13C2×Q1611yescharacteristic
110C2×C4×C13#13512yes—
111C2×Dic13—22no—
112C2×Dic13—41no—
113C2×Dic13—41no—
114C2×Dic13—41no—
115C2×Dic13—42no—
116C2×Dic13—42no—
117C2×Dic13—41no—
118C2×Dic13—41no—
119C2×Dic13—42no—
120Dic26—24no—
121Dic26—42no—
122C8×C13—82no—
123#1055—44no—
124C2×C4×Q8—131no—
125C2×C4×D4C2×D1311yescharacteristic
126C8×D4—264no—
127#431—132no—
128#423C2×D1312yes—
129C2×#100—21no—
130C2×C22⋊C8—262no—
131#399—132no—
132#393—132no—
133#390—261no—
134#389—261no—
135#385—262no—
136#382—131no—
137#343—21no—
138Q8⋊C8—264no—
139C22×C13—21no—
140C22×C13—21no—
141C22×C13—24no—
142C22×C13—44no—
143C22×C13—42no—
144C22×C13—42no—
145C22×C13—82no—
146C22×C13#38611yescharacteristic
147C22×C13C2×#10311yescharacteristic
148C22×C13#41611yescharacteristic
149C4×C13—22no—
150C4×C13—21no—
151C4×C13—21no—
152C4×C13—42no—
153C4×C13#46512yes—
154C4×C13#46712yes—
155Dic13—42no—
156Dic13—82no—
157Dic13—81no—
158C22×Q8—131no—
159C22×D4C22⋊D1311yescharacteristic
160C23×C4D5212yes—
161C2×M16—22no—
162C22×C8—264no—
163C4×Q8—262no—
164C4×Q8—262no—
165C4×D4—22no—
166C4×D4—22no—
167C2×C4⋊C4—131no—
168C2×C4⋊C4—261no—
169C2×C4⋊C4—261no—
170C2×C4⋊C4—262no—
171C2×C4⋊C4C22⋊D1311yescharacteristic
172C2×C22⋊C4—262no—
173C2×C22⋊C4—262no—
174C2×C22⋊C4C4×D1312yes—
175C2×C42—261no—
176C2×C42C22×D1311yescharacteristic
177C4⋊C8—22no—
178C4⋊C8—22no—
179C4⋊C8—262no—
180#100—42no—
181C22⋊C8—264no—
182C22⋊C8—262no—
183C4×C8—134no—
184#95—132no—
185#95—262no—
186#95—261no—
187C2×C13—21no—
188C2×C13—21no—
189C2×C13—44no—
190C2×C13#189111yescharacteristic
191C2×C13#189211yescharacteristic
192C2×C13#191111yescharacteristic
193C24#610312yes—
194C2×Q8—262no—
195C2×Q8—522no—
196C2×D4—22no—
197C2×D4—22no—
198C2×D4#610512yes—
199C2×D4#610712yes—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—82no—
203C22×C4—261no—
204C22×C4—262no—
205C22×C4—261no—
206C22×C4#610312yes—
207C22×C4C2×C4×D1311yescharacteristic
208C22×C4C2×D5211yescharacteristic
209C22×C4C2×C22⋊D1311yescharacteristic
210M16—42no—
211M16—42no—
212C2×C8—42no—
213C2×C8—264no—
214C2×C8—1044no—
215C4⋊C4—22no—
216C4⋊C4—262no—
217C4⋊C4—521no—
218C4⋊C4—521no—
219C4⋊C4—522no—
220C4⋊C4—1042no—
221C22⋊C4—24no—
222C22⋊C4—524no—
223C22⋊C4—1042no—
224C42—522no—
225C42D4×D1312yes—
226C42#612912yes—
227C13#948311yescharacteristic, complemented, Sylow
228C23—22no—
229C23—22no—
230C23—42no—
231C23—42no—
232C23#8805014yes—
233C23C2×#610311yescharacteristic
234Q8—264no—
235Q8—522no—
236D4—24no—
237D4—24no—
238C2×C4—22no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—44no—
242C2×C4—42no—
243C2×C4—82no—
244C2×C4—262no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4—522no—
248C2×C4—521no—
249C2×C4—522no—
250C2×C4—521no—
251C2×C4—522no—
252C2×C4—521no—
253C2×C4#8813512yes—
254C2×C4#8813611yescharacteristic
255C2×C4#8814011yescharacteristic
256C2×C4C2×#610511yescharacteristic
257C2×C4#8819312yes—
258C2×C4C2×#610711yescharacteristic
259C2×C4#8820412yes—
260C8—82no—
261C8—524no—
262C22—21no—
263C22—21no—
264C22—24no—
265C22—44no—
266C22—42no—
267C22—42no—
268C22—82no—
269C22#1171861911yescharacteristic
270C22C2×#8805011yescharacteristic
271C22#1171866311yescharacteristic
272C4—22no—
273C4—21no—
274C4—21no—
275C4—42no—
276C4—522no—
277C4—1042no—
278C4—1041no—
279C4#1171870212yes—
280C4#1171871212yes—
281C2—21no—
282C2—21no—
283C2—44no—
284C2#1311525211yescharacteristic
285C2#1311525711yescharacteristic
286C2#1311536611yescharacteristic
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#9483
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. #13113264C2semidirect
4. #13112696C2semidirect
227. C13#9483semidirect

Maximal subgroups

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

subgroupindex
#131238602
#131201902
#131132642
#131126962
C13×#18002
#948313