Finite Group Databasebeta

← #15766560

Subgroups — #15766560

Order 3328.

376 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 95 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×#11718755C211yesmaximal, characteristic
2#13114829C211yesmaximal, characteristic
3#13113612C211yesmaximal, characteristic
4#13113521C211yesmaximal, characteristic
5#13113232C211yesmaximal, characteristic
6#13112732C211yesmaximal, characteristic
7C13×#1548C211yesmaximal, characteristic
8C2×C13×C4⋊Q8C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×#88064—21no—
13#11718755—22no—
14#11718755—22no—
15C2×#88050—21no—
16C2×#88048—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C13×#333—22no—
21#11718146—21no—
22#11718139—22no—
23#11718071—22no—
24#11718048—22no—
25C22×Q8×C13—21no—
26C22×Dic26D411yescharacteristic
27C2×C13×M16—21no—
28C13×C4⋊Q8—21no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8D412yes—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C42×C13C2311yescharacteristic
35C2×C4⋊Dic13D411yescharacteristic
36C2×#6101—21no—
37C2×C4×Dic13—21no—
38C2×#6099—21no—
39C22×#1055—21no—
40C4×Dic26—21no—
41C4×Dic26—21no—
42C4×Dic26—21no—
43C4×Dic26—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C13×C22⋊C8—21no—
48C4×C8×C13—21no—
49C22⋊#1055—21no—
50#88064—42no—
51#88050—24no—
52#88048—24no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055—21no—
56C4⋊#1055D412yes—
57C4⋊#1055D412yes—
58C4×#1055—21no—
59#10451—131nomaximal, Sylow
60C2×Q8×C13—22no—
61C2×Q8×C13—41no—
62C2×Q8×C13—82no—
63C22×C4×C13—41no—
64C22×C4×C13C2×D411yescharacteristic
65C22×C4×C13#4111yescharacteristic
66C22×C4×C13#4111yescharacteristic
67C22×Dic13—21no—
68C22×Dic13—21no—
69C2×Dic26—21no—
70C2×Dic26—21no—
71C2×Dic26—21no—
72C2×Dic26—21no—
73C2×Dic26—21no—
74C2×Dic26Q1612yes—
75C13×M16—41no—
76C13×M16—41no—
77C2×C8×C13—41no—
78C2×C8×C13—41no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—22no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C42×C13C2×D411yescharacteristic
84C42×C13C2×D411yescharacteristic
85C42×C13C2×D411yescharacteristic
86C42×C13#4111yescharacteristic
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89#6101—41no—
90#6101—41no—
91C4×Dic13—41no—
92C4×Dic13—41no—
93#6099—41no—
94#6099—41no—
95C2×#1055—22no—
96C2×#1055—22no—
97C2×#1055—41no—
98C2×#1055—41no—
99C2×#1055—41no—
100C2×#475—131no—
101#1801—131no—
102#1571—131no—
103#1549—131no—
104#1548D1311yescharacteristic
105#1479—131no—
106#1301—131no—
107C23×C13#12311yescharacteristic
108Q8×C13—82no—
109Q8×C13—82no—
110C2×C4×C13—22no—
111C2×C4×C13—41no—
112C2×C4×C13—42no—
113C2×C4×C13—82no—
114C2×C4×C13#12011yescharacteristic
115C2×C4×C13#12111yescharacteristic
116C2×C4×C13#12111yescharacteristic
117C2×C4×C13#12111yescharacteristic
118C2×C4×C13#12311yescharacteristic
119C2×C4×C13#12411yescharacteristic
120C2×C4×C13C2×Q1611yescharacteristic
121C2×C4×C13#13511yescharacteristic
122C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C13#13711yescharacteristic
124C2×Dic13—22no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—81no—
129Dic26—22no—
130Dic26—22no—
131Dic26—41no—
132Dic26—41no—
133C8×C13—81no—
134C8×C13—81no—
135#1055—42no—
136#1055—42no—
137#1055—81no—
138C2×C4⋊Q8C2×D1311yescharacteristic
139C2×C4×Q8—131no—
140#475—262no—
141#475—262no—
142#431—131no—
143#431C2×D1311yescharacteristic
144C2×#106—261no—
145#423—131no—
146#423C2×D1311yescharacteristic
147C2×C4⋊C8—131no—
148C2×#103—261no—
149C2×#101—261no—
150#343—261no—
151#335—262no—
152#333—22no—
153#332—262no—
154Q8⋊C8—262no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13#39411yescharacteristic
158C22×C13#48411yescharacteristic
159C22×C13#48511yescharacteristic
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—82no—
164C4×C13#44911yescharacteristic
165C4×C13#45111yescharacteristic
166C4×C13#46711yescharacteristic
167C4×C13#46811yescharacteristic
168C4×C13#47112yes—
169Dic13—42no—
170Dic13—81no—
171C22×Q8—21no—
172C22×Q8—131no—
173C2×M16—21no—
174C2×M16—261no—
175C22×C8—261no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8C22⋊D1312yes—
180C4×Q8—261no—
181C4×Q8—261no—
182C4×Q8—261no—
183C4×Q8—261no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—131no—
187C2×C4⋊C4—261no—
188C2×C42—261no—
189C2×C42C22×D1311yescharacteristic
190#106—264no—
191C4⋊C8—21no—
192C4⋊C8—21no—
193C4⋊C8—21no—
194C4⋊C8—132no—
195C4⋊C8—132no—
196C4⋊C8—261no—
197C4⋊C8—261no—
198C4⋊C8—261no—
199#103—264no—
200#101—522no—
201C22⋊C8—21no—
202C22⋊C8—261no—
203C4×C8—21no—
204C4×C8—261no—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13#203611yescharacteristic
208C2×C13#204611yescharacteristic
209C2×C13#204911yescharacteristic
210C2×Q8—22no—
211C2×Q8—41no—
212C2×Q8—82no—
213C2×Q8—132no—
214C2×Q8—261no—
215C2×Q8—261no—
216C2×Q8—261no—
217C2×Q8—261no—
218C2×Q8—261no—
219C22×C4—41no—
220C22×C4—261no—
221C22×C4—261no—
222C22×C4#612711yescharacteristic
223C22×C4D4×D1311yescharacteristic
224C22×C4#612911yescharacteristic
225M16—41no—
226M16—41no—
227M16—521no—
228M16—521no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—262no—
232C2×C8—262no—
233C2×C8—521no—
234C2×C8—521no—
235C2×C8—521no—
236C4⋊C4—22no—
237C4⋊C4—22no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—521no—
243C4⋊C4—521no—
244C42—521no—
245C42—521no—
246C42#612711yescharacteristic
247C42D4×D1311yescharacteristic
248C42D4×D1311yescharacteristic
249C42C2×C22⋊D1311yescharacteristic
250C13#1045111yescharacteristic, complemented, Sylow
251C23#8813711yescharacteristic
252Q8—82no—
253Q8—82no—
254Q8—262no—
255Q8—262no—
256Q8—521no—
257Q8—521no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—262no—
263C2×C4—521no—
264C2×C4—521no—
265C2×C4—521no—
266C2×C4—1041no—
267C2×C4#8813811yescharacteristic
268C2×C4#8813811yescharacteristic
269C2×C4#8813911yescharacteristic
270C2×C4#8816811yescharacteristic
271C2×C4#8817011yescharacteristic
272C2×C4Q16×D1311yescharacteristic
273C2×C4#8817211yescharacteristic
274C2×C4#8818311yescharacteristic
275C2×C4#8819111yescharacteristic
276C2×C4#8819311yescharacteristic
277C8—81no—
278C8—81no—
279C8—522no—
280C8—522no—
281C8—1041no—
282C22—21no—
283C22—21no—
284C22#1171847011yescharacteristic
285C22#1171847611yescharacteristic
286C22#1171862011yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—82no—
291C4—522no—
292C4—1041no—
293C4#1171840912yes—
294C4#1171847311yescharacteristic
295C4#1171847411yescharacteristic
296C4#1171883311yescharacteristic
297C4#1171884711yescharacteristic
298C2—21no—
299C2—21no—
300C2#1311603711yescharacteristic
301C2#1311609711yescharacteristic
302C2#1311611411yescharacteristic
subgroupG/H
centerC22#11718620
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1548C2
socleC22×C13#394
prime radicalC23×C13#123
hypercenter#1548D13
hypocenterC13#10451
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
250. C13#10451semidirect

Maximal subgroups

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

subgroupindex
C2×#117187552
#131148292
#131136122
#131135212
#131132322
#131127322
C13×#15482
#1045113