Finite Group Databasebeta

← #15766555

Subgroups — #15766555

Order 3328.

376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#11718681C211yesmaximal, characteristic
2#13113608C211yesmaximal, characteristic
3#13113522C211yesmaximal, characteristic
4#13113518C211yesmaximal, characteristic
5#13113231C211yesmaximal, characteristic
6#13112731C211yesmaximal, characteristic
7C13×#1801C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C13×#423C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×C13×#101—21no—
13C2×#88075—21no—
14#11718681—22no—
15#11718681—22no—
16C2×#88048—21no—
17#11718586C2211yescharacteristic
18#11718586C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C13×#343—21no—
21Q8⋊#1055—22no—
22#11718078—22no—
23#11718073—22no—
24#11718072—22no—
25C22×Q8×C13D411yescharacteristic
26C22×Dic26—21no—
27C2×C13×M16—21no—
28C2×C13×M16—21no—
29C4×Q8×C13—21no—
30C4×Q8×C13—21no—
31C4×Q8×C13—21no—
32C4×Q8×C13—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4D411yescharacteristic
35C2×C42×C13—21no—
36C2×C42×C13C2311yescharacteristic
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C22×#1055—21no—
40#88123—21no—
41#88123—21no—
42#88123—21no—
43#88123D412yes—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×#101—42no—
49#88075—24no—
50C22⋊#1055—21no—
51C22⋊#1055—21no—
52#88048—24no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055D412yes—
56C4⋊#1055D412yes—
57C4×#1055—21no—
58C4×#1055—21no—
59#10450—131nomaximal, Sylow
60C2×Q8×C13—21no—
61C2×Q8×C13—21no—
62C2×Q8×C13—21no—
63C2×Q8×C13—21no—
64C2×Q8×C13—21no—
65C2×Q8×C13SD1612yes—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C2×D411yescharacteristic
69C22×C4×C13#4111yescharacteristic
70C22×C4×C13#4111yescharacteristic
71C22×Dic13—41no—
72C2×Dic26—22no—
73C2×Dic26—41no—
74C2×Dic26—82no—
75C13×M16—41no—
76C13×M16—41no—
77C13×M16—41no—
78C13×M16—41no—
79C2×C8×C13—41no—
80C2×C8×C13—41no—
81C13×C4⋊C4—21no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C42×C13—41no—
86C42×C13—41no—
87C42×C13C2×D411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13C2×D411yescharacteristic
90C42×C13#4111yescharacteristic
91C4⋊Dic13—22no—
92C4⋊Dic13—22no—
93C4⋊Dic13—41no—
94C4⋊Dic13—41no—
95C2×#1055—22no—
96C2×#1055—22no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#475—131no—
101#1801D1311yescharacteristic
102#1570—131no—
103#1549—131no—
104#1548—131no—
105#1479—131no—
106#1301—131no—
107C23×C13#12311yescharacteristic
108Q8×C13—22no—
109Q8×C13—22no—
110Q8×C13—41no—
111Q8×C13—41no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—81no—
119C2×C4×C13#12011yescharacteristic
120C2×C4×C13#12111yescharacteristic
121C2×C4×C13#12111yescharacteristic
122C2×C4×C13#12111yescharacteristic
123C2×C4×C13#12311yescharacteristic
124C2×C4×C13#12411yescharacteristic
125C2×C4×C13C2×SD1611yescharacteristic
126C2×C4×C13#13511yescharacteristic
127C2×C4×C13#13711yescharacteristic
128C2×C4×C13#13711yescharacteristic
129C2×Dic13—42no—
130C2×Dic13—82no—
131Dic26—82no—
132Dic26—82no—
133C8×C13—81no—
134C8×C13—81no—
135#1055—42no—
136#1055—42no—
137#1055—81no—
138C2×C4⋊Q8—131no—
139C2×C4×Q8C2×D1311yescharacteristic
140#475—262no—
141#475—262no—
142#431—131no—
143#431—131no—
144C2×#106—261no—
145#423C2×D1311yescharacteristic
146#423C2×D1311yescharacteristic
147C2×C4⋊C8—131no—
148C2×#103—261no—
149C2×#101—21no—
150#343—21no—
151#334—262no—
152#333—262no—
153#332—262no—
154Q8⋊C8—262no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13#39411yescharacteristic
158C22×C13#48311yescharacteristic
159C22×C13#48511yescharacteristic
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—42no—
164C4×C13—81no—
165C4×C13#44811yescharacteristic
166C4×C13#45211yescharacteristic
167C4×C13#46511yescharacteristic
168C4×C13#47011yescharacteristic
169C4×C13#47112yes—
170Dic13—82no—
171C22×Q8—261no—
172C22×Q8C22⋊D1311yescharacteristic
173C2×M16—21no—
174C2×M16—21no—
175C22×C8—261no—
176C4⋊Q8—132no—
177C4⋊Q8—261no—
178C4⋊Q8—261no—
179C4⋊Q8—261no—
180C4×Q8—21no—
181C4×Q8—21no—
182C4×Q8—21no—
183C4×Q8—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4C22⋊D1311yescharacteristic
188C2×C42—21no—
189C2×C42C22×D1311yescharacteristic
190#106—264no—
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—21no—
194C4⋊C8—21no—
195C4⋊C8—132no—
196C4⋊C8—132no—
197C4⋊C8—261no—
198C4⋊C8—261no—
199#103—264no—
200#101—42no—
201C22⋊C8—261no—
202C22⋊C8—261no—
203C4×C8—261no—
204C4×C8—261no—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13#203511yescharacteristic
208C2×C13#204611yescharacteristic
209C2×C13#204911yescharacteristic
210C2×Q8—21no—
211C2×Q8—21no—
212C2×Q8—21no—
213C2×Q8—21no—
214C2×Q8—21no—
215C2×Q8—262no—
216C2×Q8—521no—
217C2×Q8—1042no—
218C2×Q8#610512yes—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—521no—
222C22×C4#612711yescharacteristic
223C22×C4#612711yescharacteristic
224C22×C4C2×C22⋊D1311yescharacteristic
225M16—41no—
226M16—41no—
227M16—41no—
228M16—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—262no—
232C2×C8—262no—
233C2×C8—521no—
234C2×C8—521no—
235C2×C8—521no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—262no—
241C4⋊C4—262no—
242C4⋊C4—521no—
243C4⋊C4—521no—
244C42—41no—
245C42—41no—
246C42D4×D1311yescharacteristic
247C42D4×D1311yescharacteristic
248C42D4×D1311yescharacteristic
249C42#612911yescharacteristic
250C13#1045011yescharacteristic, complemented, Sylow
251C23#8818311yescharacteristic
252Q8—22no—
253Q8—22no—
254Q8—41no—
255Q8—41no—
256Q8—1042no—
257Q8—1042no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—522no—
266C2×C4—1042no—
267C2×C4#8813711yescharacteristic
268C2×C4#8813811yescharacteristic
269C2×C4#8813811yescharacteristic
270C2×C4#8813911yescharacteristic
271C2×C4C2×#610511yescharacteristic
272C2×C4#8819111yescharacteristic
273C2×C4#8819311yescharacteristic
274C2×C4#8819611yescharacteristic
275C2×C4#8820411yescharacteristic
276C2×C4#8820511yescharacteristic
277C8—81no—
278C8—81no—
279C8—522no—
280C8—522no—
281C8—1041no—
282C22—21no—
283C22—21no—
284C22#1171862011yescharacteristic
285C22#1171863211yescharacteristic
286C22#1171865711yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—42no—
291C4—81no—
292C4—1042no—
293C4#1171841512yes—
294C4#1171870111yescharacteristic
295C4#1171870211yescharacteristic
296C4#1171870811yescharacteristic
297C4#1171871311yescharacteristic
298C2—21no—
299C2—21no—
300C2#1311603211yescharacteristic
301C2#1311609511yescharacteristic
302C2#1311611611yescharacteristic
subgroupG/H
centerC22#11718620
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1801C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenter#1801D13
hypocenterC13#10450
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
250. C13#10450semidirect

Maximal subgroups

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

subgroupindex
C2×#117186812
#131136082
#131135222
#131135182
#131132312
#131127312
C13×#18012
#1045013