Finite Group Databasebeta

← #15778088

Subgroups — #15778088

Order 3328.

564 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 113 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#13117546C211yesmaximal, characteristic
2C2×#11718065C212yesmaximal
3#99×Dic13C212yesmaximal
4#13112961C211yesmaximal, characteristic
5C13×#1393C211yesmaximal, characteristic
6C2×#88190C2211yescharacteristic
7C2×D4×Dic13C2211yescharacteristic
8C2×#88141C411yescharacteristic, complemented
9C2×C13×#99C2212yes—
10C13×#390C2211yescharacteristic
11C2×#88074C2212yes—
12#11718637C411yescharacteristic, complemented
13#11718607—22no—
14#11718606—22no—
15C22⋊C4×Dic13—22no—
16#11718593C411yescharacteristic, complemented
17#11718590C411yescharacteristic, complemented
18#11718119—22no—
19#11718065C418yescomplemented
20C22×D4×C13C2311yescharacteristic
21C23×Dic13D412yes—
22C22×Dic26C2×C411yescharacteristic
23C2×C13×C4⋊C4C2×C411yescharacteristic
24C2×C13×C22⋊C4—22no—
25C2×C13×C22⋊C4—22no—
26C2×C42×C13C2×C411yescharacteristic
27C2×C22⋊Dic13—22no—
28C2×C22⋊Dic13—22no—
29C2×C22⋊Dic13D412yes—
30#88190—21no—
31#88190—21no—
32#88190C2×C414yes—
33D4×Dic13—42no—
34C2×C4⋊Dic13C2×C411yescharacteristic
35C2×#6101—21no—
36C2×#6101—22no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13—42no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13C2×C411yescharacteristic
41#88141—42no—
42C13×#99—22no—
43C13×#99C2×C414yes—
44#88074—22no—
45#88074C2×C414yes—
46#88071—22no—
47#88071—21no—
48#88071—21no—
49#88071—42no—
50#12627—131nomaximal, Sylow
51C24×C13C2×D412yes—
52C2×D4×C13—41no—
53C2×D4×C13—41no—
54C2×D4×C13C22×C412yes—
55C2×D4×C13#4111yescharacteristic
56C2×D4×C13#4111yescharacteristic
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—42no—
60C22×C4×C13C22×C411yescharacteristic
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13—22no—
64C22×Dic13—22no—
65C22×Dic13—42no—
66C22×Dic13—82no—
67C22×Dic13C22⋊C411yescharacteristic
68C22×Dic13C22⋊C412yes—
69C22×Dic13C22⋊C411yescharacteristic
70C2×Dic26—21no—
71C2×Dic26—41no—
72C2×Dic26—41no—
73C2×Dic26C4212yescomplemented
74C13×C4⋊C4—41no—
75C13×C22⋊C4—24no—
76C13×C22⋊C4—42no—
77C13×C22⋊C4—82no—
78C42×C13—41no—
79C22⋊Dic13—24no—
80C22⋊Dic13—24no—
81C22⋊Dic13—24no—
82C22⋊Dic13—42no—
83C22⋊Dic13—42no—
84C4⋊Dic13—41no—
85#6101—42no—
86#6101—82no—
87C4×Dic13—21no—
88C4×Dic13—22no—
89C4×Dic13—42no—
90C4×Dic13—84no—
91C4×Dic13C4212yescomplemented
92#2326—131no—
93C2×#354—132no—
94C4×#99—132no—
95#1393—131no—
96#1393D1311yescharacteristic
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—42no—
100C23×C13—42no—
101C23×C13C2×C22⋊C411yescharacteristic
102C23×C13C4×D412yes—
103C23×C13C4×D412yes—
104D4×C13—42no—
105D4×C13—41no—
106D4×C13—41no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—42no—
110C2×C4×C13—44no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—82no—
116C2×C4×C13—82no—
117C2×C4×C13C2×C4211yescharacteristic
118C2×C4×C13#11711yescharacteristic
119C2×Dic13—22no—
120C2×Dic13—22no—
121C2×Dic13—21no—
122C2×Dic13—22no—
123C2×Dic13—41no—
124C2×Dic13—44no—
125C2×Dic13—41no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—42no—
130C2×Dic13—41no—
131C2×Dic13—44no—
132C2×Dic13—82no—
133C2×Dic13—82no—
134C2×Dic13—82no—
135C2×Dic13#9912yes—
136Dic26—42no—
137Dic26—42no—
138C2×#124—131no—
139C2×C4×Q8—131no—
140C2×C4×D4—131no—
141C2×#99—132no—
142C2×#99C2×D1312yes—
143#391—131no—
144#390C2×D1311yescharacteristic
145#388—262no—
146#385—262no—
147#384—131no—
148C4×C22⋊C4—262no—
149#376—131no—
150#354—138no—
151#342—262no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—22no—
155C22×C13—22no—
156C22×C13—42no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—82no—
161C22×C13C4×C22⋊C411yescharacteristic
162C22×C13C2×#9911yescharacteristic
163C22×C13#41011yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—81no—
167C4×C13—84no—
168C4×C13—81no—
169Dic13—22no—
170Dic13—42no—
171Dic13—42no—
172Dic13—41no—
173Dic13—42no—
174Dic13—84no—
175C22×Q8—131no—
176C22×D4C22×D1311yescharacteristic
177C23×C4—132no—
178#124—134no—
179#124—261no—
180#124—261no—
181C4×Q8—522no—
182C4×D4—522no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—262no—
186C2×C4⋊C4C4×D1311yescharacteristic
187C2×C22⋊C4—22no—
188C2×C22⋊C4—22no—
189C2×C22⋊C4—132no—
190C2×C22⋊C4—262no—
191C2×C22⋊C4—262no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—261no—
195C2×C42—522no—
196C2×C42C4×D1311yescharacteristic
197#99—22no—
198#99—134no—
199#99—262no—
200#99C4×D1314yes—
201#95—261no—
202#95—261no—
203#95—262no—
204#95—522no—
205C2×C13—21no—
206C2×C13—21no—
207C2×C13—42no—
208C2×C13—42no—
209C2×C13C4×#9911yescharacteristic
210C2×C13#212711yescharacteristic
211C2×C13#212911yescharacteristic
212C24D4×D1312yes—
213C2×Q8—132no—
214C2×Q8—261no—
215C2×Q8—521no—
216C2×Q8—521no—
217C2×D4—41no—
218C2×D4—41no—
219C2×D4C2×C4×D1312yes—
220C2×D4#612911yescharacteristic
221C2×D4#613111yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—42no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—132no—
228C22×C4—262no—
229C22×C4—262no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4—522no—
233C22×C4—1042no—
234C22×C4C2×C4×D1311yescharacteristic
235C4⋊C4—41no—
236C4⋊C4—521no—
237C4⋊C4—522no—
238C4⋊C4—1042no—
239C22⋊C4—24no—
240C22⋊C4—42no—
241C22⋊C4—82no—
242C22⋊C4—264no—
243C22⋊C4—264no—
244C22⋊C4—264no—
245C22⋊C4—522no—
246C22⋊C4—522no—
247C42—41no—
248C42—132no—
249C42—262no—
250C42—261no—
251C42—522no—
252C42—1044no—
253C13#1262711yescharacteristic, complemented, Sylow
254C23—22no—
255C23—22no—
256C23—42no—
257C23—42no—
258C23C22⋊C4×D1311yescharacteristic
259C23#8813512yes—
260C23#8814712yes—
261Q8—522no—
262Q8—522no—
263D4—42no—
264D4—41no—
265D4—41no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—44no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—132no—
277C2×C4—261no—
278C2×C4—262no—
279C2×C4—262no—
280C2×C4—262no—
281C2×C4—521no—
282C2×C4—524no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—522no—
288C2×C4—521no—
289C2×C4—524no—
290C2×C4—1042no—
291C2×C4—1042no—
292C2×C4—1042no—
293C2×C4C42×D1311yescharacteristic
294C2×C4#8814611yescharacteristic
295C22—21no—
296C22—21no—
297C22—22no—
298C22—22no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—82no—
304C22#1171832711yescharacteristic
305C22#1171840111yescharacteristic
306C22D13×#9911yescharacteristic
307C4—21no—
308C4—21no—
309C4—81no—
310C4—84no—
311C4—81no—
312C4—262no—
313C4—522no—
314C4—522no—
315C4—521no—
316C4—522no—
317C4—1044no—
318C2—21no—
319C2—21no—
320C2—42no—
321C2—42no—
322C2#1311462311yescharacteristic
323C2#1311650211yescharacteristic
324C2#1311650911yescharacteristic
subgroupG/H
centerC22D13×#99
commutatorC2×C4×C13C2×C42
FrattiniC22×D4C22×D13
FittingC13×#1393C2
socleC22×C13C2×#99
prime radical, cosocleC22×D4×C13C23
hypercenter#1393D13
hypocenterC13#12627
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ #1393

Complements

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

NH ≅ G/Ntype
8. C2×#88141C4semidirect
12. #11718637C4semidirect
16. #11718593C4semidirect
17. #11718590C4semidirect
19. #11718065C4semidirect
73. C2×Dic26C42semidirect
91. C4×Dic13C42semidirect
253. C13#12627semidirect

Maximal subgroups

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

subgroupindex
#131175462
C2×#117180652
#99×Dic132
#131129612
C13×#13932
#1262713