Finite Group Databasebeta

← #15758995

Subgroups — #15758995

Order 3328.

578 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 111 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#13120578C211yesmaximal, characteristic
2#13117439C211yesmaximal, characteristic, complemented
3#13113405C212yesmaximal
4#13112704C212yesmaximal, complemented
5C2×C13×#324C211yesmaximal, characteristic, complemented
6C22×C13×C4⋊C4C2211yescharacteristic
7C2×#88184C2211yescharacteristic
8C2×#88183—21no—
9C2×C13×C22⋊C8C2212yes—
10#11718874—21no—
11#11718873C2211yescharacteristic
12#11718873C2212yes—
13#11718872—21no—
14C4×C22⋊Dic13—21no—
15#11718655—22no—
16#11718652C412yescomplemented
17#11718644C412yescomplemented
18#11718642—24no—
19C13×#324—22no—
20#11718062—24no—
21C23×C4×C13D411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13C2311yescharacteristic
24C22×C22⋊D13—21no—
25C22×D52C2×C411yescharacteristic
26C22×C8×C13—22no—
27C2×C13×C4⋊C4—22no—
28C2×C13×C4⋊C4—22no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C13×C4⋊C4D412yes—
31C2×C22⋊Dic13—21no—
32C2×C22⋊Dic13—22no—
33#88184—22no—
34#88184—22no—
35#88183—44no—
36C2×#6103—22no—
37C2×#6103—21no—
38C2×#6103—22no—
39C2×C4⋊Dic13—22no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13C2×C411yescharacteristic
42C2×#6101—22no—
43C2×C4×Dic13—22no—
44C13×C22⋊C8—22no—
45C13×C22⋊C8—22no—
46#88071—22no—
47#88071—24no—
48#88071—22no—
49#88071C2×C412yes—
50#88071D414yes—
51#9206—131nomaximal, Sylow
52C24×C13C2×D411yescharacteristic
53C23×D13—21no—
54C22×C4×C13—21no—
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—21no—
60C22×C4×C13—81no—
61C22×C4×C13—81no—
62C22×C4×C13C22⋊C412yes—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13C22×C411yescharacteristic
65C22×C4×C13C2×D412yes—
66C22×C4×C13C2×D411yescharacteristic
67C22×C4×C13#4112yes—
68C2×C22⋊D13—41no—
69C2×C22⋊D13—41no—
70C2×C22⋊D13—42no—
71C2×C22⋊D13—42no—
72C22×Dic13—21no—
73C22×Dic13—22no—
74C22×Dic13—24no—
75C2×D52—22no—
76C2×D52—81no—
77C2×C8×C13—42no—
78C2×C8×C13—82no—
79C13×C4⋊C4—24no—
80C13×C4⋊C4—24no—
81C22⋊Dic13—42no—
82C22⋊Dic13—42no—
83C22⋊Dic13—42no—
84#6103—44no—
85#6103—42no—
86#6103—82no—
87C4⋊Dic13—22no—
88C4⋊Dic13—82no—
89C4⋊Dic13—81no—
90#6101—44no—
91C4×Dic13—82no—
92#2618—131no—
93#2313—131no—
94#1519—132no—
95C2×#324D1311yescharacteristic, complemented
96#1289—132no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13C2×C22⋊C411yescharacteristic
100C23×C13#12011yescharacteristic
101C23×C13#12311yescharacteristic
102C23×C13#13512yes—
103C23×C13AGL(1,ℤ/8)12yes—
104C22×D13—42no—
105C22×D13—42no—
106C22×D13—41no—
107C22×D13—41no—
108C22×D13—41no—
109C2×C4×C13—22no—
110C2×C4×C13—22no—
111C2×C4×C13—22no—
112C2×C4×C13—22no—
113C2×C4×C13—41no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—81no—
122C2×C4×C13C4×D412yes—
123C2×C4×C13#12112yes—
124C22⋊D13—82no—
125C22⋊D13—82no—
126C2×Dic13—44no—
127C2×Dic13—42no—
128C2×Dic13—44no—
129C2×Dic13—42no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—42no—
134C2×Dic13—44no—
135D52—82no—
136C8×C13—82no—
137C2×#123—261no—
138C2×#121—131no—
139C22×C4⋊C4C2×D1311yescharacteristic
140C2×C22⋊C8C2×D1312yes—
141#398—132no—
142#396—262no—
143#394—132no—
144#387—264no—
145#386—261no—
146#381—261no—
147#380—131no—
148#380—132no—
149C4×C22⋊C4—261no—
150#327—264no—
151#324—22no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13#38611yescharacteristic
161C22×C13#41611yescharacteristic
162C22×C13#41811yescharacteristic
163C22×C13#44912yes—
164C22×C13#48212yes—
165C2×D13—82no—
166C2×D13—82no—
167C2×D13—81no—
168C2×D13—81no—
169C2×D13—81no—
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—42no—
173C4×C13—42no—
174Dic13—82no—
175Dic13—84no—
176Dic13—81no—
177C22×D4—131no—
178C22×D4—261no—
179C23×C4D5211yescharacteristic
180C23×C4D5211yescharacteristic
181C23×C4C22×D1311yescharacteristic
182C22×C8—22no—
183#123—524no—
184#121—262no—
185#121—262no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—262no—
190C2×C4⋊C4—262no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4C4×D1312yes—
193C2×C4⋊C4C22⋊D1312yes—
194C2×C22⋊C4—261no—
195C2×C22⋊C4—262no—
196C2×C22⋊C4—262no—
197C2×C22⋊C4—261no—
198C2×C22⋊C4—262no—
199C2×C42—262no—
200C22⋊C8—22no—
201C22⋊C8—22no—
202#95—132no—
203#95—134no—
204#95—262no—
205#95—264no—
206#95—262no—
207C2×C13—21no—
208C2×C13—22no—
209C2×C13—21no—
210C2×C13—22no—
211C2×C13#187511yescharacteristic
212C2×C13#191211yescharacteristic
213C2×C13#191311yescharacteristic
214D13—161no—
215C24—261no—
216C24C2×D5211yescharacteristic
217C2×D4—262no—
218C2×D4—521no—
219C2×D4—521no—
220C2×D4—522no—
221C2×D4—522no—
222C2×D4—1041no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—81no—
230C22×C4—81no—
231C22×C4—264no—
232C22×C4—262no—
233C22×C4—261no—
234C22×C4#610312yes—
235C22×C4#610312yes—
236C22×C4C2×C4×D1311yescharacteristic
237C22×C4D4×D1312yes—
238C22×C4#612912yes—
239C22×C4C2×C22⋊D1311yescharacteristic
240C2×C8—42no—
241C2×C8—82no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—262no—
245C4⋊C4—524no—
246C4⋊C4—1042no—
247C4⋊C4—1041no—
248C22⋊C4—524no—
249C22⋊C4—522no—
250C22⋊C4—522no—
251C22⋊C4—522no—
252C22⋊C4—522no—
253C22⋊C4—1042no—
254C42—1042no—
255C13#920611yescharacteristic, complemented, Sylow
256C23—41no—
257C23—41no—
258C23—522no—
259C23—522no—
260C23—521no—
261C23—521no—
262C23—521no—
263C23#8813611yescharacteristic
264C23#8814011yescharacteristic
265C23#8815812yes—
266C23#8816212yes—
267C23C2×#610311yescharacteristic
268D4—1042no—
269D4—1042no—
270D4—1042no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—81no—
284C2×C4—524no—
285C2×C4—522no—
286C2×C4—524no—
287C2×C4—522no—
288C2×C4—521no—
289C2×C4—522no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—524no—
293C2×C4#8813512yes—
294C2×C4#8819312yes—
295C8—82no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—42no—
304C22—1042no—
305C22—1042no—
306C22—1041no—
307C22—1041no—
308C22—1041no—
309C22#1171839512yes—
310C22#1171839812yes—
311C22#1171861911yescharacteristic
312C22#1171877411yescharacteristic
313C22#1171879211yescharacteristic
314C4—22no—
315C4—22no—
316C4—42no—
317C4—42no—
318C4—1042no—
319C4—1044no—
320C4—1041no—
321C2—21no—
322C2—22no—
323C2—21no—
324C2—22no—
325C2—2081no—
326C2#1311515611yescharacteristic
327C2#1311537111yescharacteristic
328C2#1311537611yescharacteristic
subgroupG/H
centerC22#11718619
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#324C2
socleC22×C13#386
prime radicalC2×#88184C22
cosocleC23×C4×C13C23
hypercenterC2×#324D13
hypocenterC13#9206
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #13117439C2semidirect
4. #13112704C2semidirect
5. C2×C13×#324C2semidirect
16. #11718652C4semidirect
17. #11718644C4semidirect
95. C2×#324D13semidirect
255. C13#9206semidirect

Maximal subgroups

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

subgroupindex
#131205782
#131174392
#131134052
#131127042
C2×C13×#3242
#920613