Finite Group Databasebeta

← #15758998

Subgroups — #15758998

Order 3328.

578 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 119 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#13117439C211yesmaximal, characteristic, complemented
2#13113404C212yesmaximal
3C2×#11718120C211yesmaximal, characteristic, complemented
4#13112703C212yesmaximal, complemented
5C13×#2618C211yesmaximal, characteristic
6C2×C13×#123—21no—
7C2×C13×#121C2211yescharacteristic
8C22×C13×C4⋊C4C2211yescharacteristic
9C13×#398C412yescomplemented
10C13×#396—22no—
11C13×#394C412yescomplemented
12C13×#386—21no—
13C13×#380C2211yescharacteristic
14#11718873C2212yes—
15#11718872—21no—
16C4×C22⋊Dic13—21no—
17C2×C22⋊#1055C2212yes—
18#11718642—24no—
19#11718129—24no—
20#11718120—22no—
21C22×D4×C13—21no—
22C22×D4×C13C2×C411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C13×#123—44no—
27C13×#121—22no—
28C13×#121—22no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C412yes—
35C2×C13×C4⋊C4D412yes—
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—22no—
40C2×C22⋊Dic13—22no—
41C2×C4⋊Dic13—22no—
42C2×C4×Dic13—22no—
43C22×#1055—22no—
44C13×#95—22no—
45C13×#95C2×C412yes—
46#88071—22no—
47#88071—24no—
48#88071D414yes—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51#9206—131nomaximal, Sylow
52C24×C13—21no—
53C24×C13C2×D411yescharacteristic
54C2×D4×C13—22no—
55C2×D4×C13—41no—
56C2×D4×C13—41no—
57C2×D4×C13—42no—
58C2×D4×C13—42no—
59C2×D4×C13—81no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—22no—
68C22×C4×C13—81no—
69C22×C4×C13—81no—
70C22×C4×C13C22⋊C412yes—
71C22×C4×C13C22⋊C412yes—
72C22×C4×C13C22×C411yescharacteristic
73C22×C4×C13C2×D412yes—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13#4112yes—
76C22×Dic13—24no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—24no—
79C13×C4⋊C4—22no—
80C13×C4⋊C4—44no—
81C13×C4⋊C4—81no—
82C13×C22⋊C4—44no—
83C13×C22⋊C4—42no—
84C13×C22⋊C4—42no—
85C13×C22⋊C4—82no—
86C22⋊Dic13—42no—
87C22⋊Dic13—42no—
88C4⋊Dic13—82no—
89C4×Dic13—82no—
90C2×#1055—42no—
91C2×#1055—82no—
92#2618D1311yescharacteristic
93#2313—131no—
94#1519—132no—
95C2×#324—131no—
96#1289—132no—
97C23×C13—41no—
98C23×C13—41no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13—41no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13C2×C22⋊C411yescharacteristic
105C23×C13#12011yescharacteristic
106C23×C13#12311yescharacteristic
107C23×C13#13512yes—
108C23×C13AGL(1,ℤ/8)12yes—
109D4×C13—82no—
110D4×C13—82no—
111D4×C13—82no—
112C2×C4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13—22no—
115C2×C4×C13—22no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—41no—
130C2×C4×C13—81no—
131C2×C4×C13C4×D412yes—
132C2×C4×C13#12112yes—
133C2×Dic13—44no—
134C2×Dic13—44no—
135C2×Dic13—44no—
136#1055—82no—
137C2×#123—21no—
138C2×#121C2×D1311yescharacteristic
139C22×C4⋊C4C2×D1311yescharacteristic
140C2×C22⋊C8—132no—
141#398Dic1312yescomplemented
142#396—22no—
143#394Dic1312yescomplemented
144#387—264no—
145#386—21no—
146#381—261no—
147#380—132no—
148#380C2×D1311yescharacteristic
149C4×C22⋊C4—261no—
150#327—264no—
151#324—262no—
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—82no—
161C22×C13—82no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13—81no—
165C22×C13#38611yescharacteristic
166C22×C13#41611yescharacteristic
167C22×C13#41811yescharacteristic
168C22×C13#44912yes—
169C22×C13#48212yes—
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—42no—
173C4×C13—42no—
174C4×C13—82no—
175C4×C13—81no—
176Dic13—84no—
177C22×D4—21no—
178C22×D4C2×Dic1311yescharacteristic
179C23×C4C22⋊D1311yescharacteristic
180C23×C4C22⋊D1311yescharacteristic
181C23×C4C22×D1311yescharacteristic
182C22×C8—262no—
183#123—44no—
184#121—22no—
185#121—22no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—262no—
191C2×C4⋊C4C2×Dic1311yescharacteristic
192C2×C4⋊C4C2×Dic1312yes—
193C2×C4⋊C4C22⋊D1312yes—
194C2×C22⋊C4—21no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—21no—
197C2×C22⋊C4—22no—
198C2×C22⋊C4—262no—
199C2×C42—262no—
200C22⋊C8—262no—
201C22⋊C8—262no—
202#95—22no—
203#95—134no—
204#95—262no—
205#95—264no—
206#95C2×Dic1312yes—
207C2×C13—22no—
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—22no—
211C2×C13—161no—
212C2×C13#187511yescharacteristic
213C2×C13#191211yescharacteristic
214C2×C13#191311yescharacteristic
215C24—21no—
216C24C2×C22⋊D1311yescharacteristic
217C2×D4—22no—
218C2×D4—42no—
219C2×D4—41no—
220C2×D4—41no—
221C2×D4—42no—
222C2×D4—81no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—81no—
232C22×C4—81no—
233C22×C4—264no—
234C22×C4C22⋊Dic1312yes—
235C22×C4C22⋊Dic1312yes—
236C22×C4D4×D1312yes—
237C22×C4#612912yes—
238C22×C4C22×Dic1311yescharacteristic
239C22×C4C2×C22⋊D1311yescharacteristic
240C2×C8—522no—
241C2×C8—1042no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—22no—
245C4⋊C4—44no—
246C4⋊C4—81no—
247C4⋊C4—1042no—
248C22⋊C4—44no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—82no—
252C22⋊C4—522no—
253C22⋊C4—522no—
254C42—1042no—
255C13#920611yescharacteristic, complemented, Sylow
256C23—41no—
257C23—41no—
258C23—42no—
259C23—42no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23#8818612yes—
264C23#8818911yescharacteristic
265C23#8819111yescharacteristic
266C23#8820412yes—
267C23C2×C22⋊Dic1311yescharacteristic
268D4—82no—
269D4—82no—
270D4—82no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—81no—
290C2×C4—524no—
291C2×C4—524no—
292C2×C4—524no—
293C2×C4D4×Dic1312yes—
294C2×C4#8819312yes—
295C8—1042no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—42no—
304C22—82no—
305C22—82no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#1171869612yes—
310C22#1171869812yes—
311C22#1171887611yescharacteristic
312C22#1171888111yescharacteristic
313C22#1171889411yescharacteristic
314C4—22no—
315C4—22no—
316C4—42no—
317C4—42no—
318C4—82no—
319C4—81no—
320C4—1044no—
321C2—21no—
322C2—22no—
323C2—21no—
324C2—22no—
325C2—161no—
326C2#1311515911yescharacteristic
327C2#1311537411yescharacteristic
328C2#1311537911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2618C2
socleC22×C13#386
prime radicalC2×C13×#121C22
cosocleC23×C4×C13C23
hypercenter#2618D13
hypocenterC13#9206
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
1. #13117439C2semidirect
3. C2×#11718120C2semidirect
4. #13112703C2semidirect
9. C13×#398C4semidirect
11. C13×#394C4semidirect
141. #398Dic13semidirect
143. #394Dic13semidirect
255. C13#9206semidirect

Maximal subgroups

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

subgroupindex
#131174392
#131134042
C2×#117181202
#131127032
C13×#26182
#920613