Finite Group Databasebeta

← #15760599

Subgroups — #15760599

Order 3328.

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

normal subgroups only

This group has 518 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#13123865C211yesmaximal, characteristic
2#13113562C212yesmaximal, complemented
3#13113177C211yesmaximal, characteristic
4#13112692C212yesmaximal, complemented
5C13×#2547C211yesmaximal, characteristic
6C2×C13×C4⋊Q8C2211yescharacteristic
7C2×C13×#124C412yes—
8C2×C4×D4×C13C2211yescharacteristic
9C13×#397—21no—
10C13×#397—21no—
11C13×#391C412yes—
12C13×#380—21no—
13C13×#380—21no—
14C4×C13×C4⋊C4C2211yescharacteristic
15#11718868—21no—
16C2×C22⋊#1055—21no—
17#11718672—24no—
18#11718587C2212yes—
19#11718587C2212yes—
20#11718138—24no—
21#11718117—21no—
22#11718117—21no—
23C22×Q8×C13C2×C412yes—
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C4⋊Q8—22no—
28C13×C4⋊Q8—22no—
29C13×#124—44no—
30C4×D4×C13—22no—
31C4×D4×C13—22no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4—22no—
38C2×C13×C22⋊C4D411yescharacteristic
39C2×C13×C22⋊C4D411yescharacteristic
40C2×C42×C13C2×C412yes—
41C2×C42×C13C2311yescharacteristic
42C2×#6099—22no—
43C22×#1055—22no—
44C13×#95—22no—
45C13×#95—22no—
46C13×#95—21no—
47C22⋊#1055—22no—
48C22⋊#1055—22no—
49C22⋊#1055—22no—
50C22⋊#1055—22no—
51C4⋊#1055—22no—
52C4⋊#1055D414yes—
53#88043—22no—
54#88043—22no—
55#9451—131nomaximal, Sylow
56C24×C13C22⋊C411yescharacteristic
57C24×C13C22⋊C411yescharacteristic
58C2×Q8×C13—24no—
59C2×Q8×C13—42no—
60C2×Q8×C13—42no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—41no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—22no—
69C22×C4×C13—22no—
70C22×C4×C13—42no—
71C22×C4×C13—42no—
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22×C411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C13×C4⋊C4—22no—
78C13×C4⋊C4—42no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—41no—
82C13×C22⋊C4—22no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—44no—
85C13×C22⋊C4—44no—
86C42×C13—42no—
87C42×C13C2×D412yes—
88C42×C13#4112yes—
89#6099—82no—
90C2×#1055—24no—
91C2×#1055—42no—
92C2×#1055—82no—
93#2973—131no—
94#2547D1311yescharacteristic
95#1558—132no—
96#1466—131no—
97#1285—132no—
98C23×C13—21no—
99C23×C13—21no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13#10012yes—
108C23×C13C2×C22⋊C411yescharacteristic
109Q8×C13—84no—
110D4×C13—44no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—22no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—42no—
118C2×C4×C13—42no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—42no—
122C2×C4×C13—42no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13—42no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13C4×D412yes—
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12112yes—
132C2×C4×C13#12311yescharacteristic
133#1055—44no—
134#1055—82no—
135C2×C4⋊Q8C2×D1311yescharacteristic
136C2×#124Dic1312yes—
137C2×C4×D4C2×D1311yescharacteristic
138#435—264no—
139#432—132no—
140#432—132no—
141#407—261no—
142C2×C22⋊C8—261no—
143#397—21no—
144#397—21no—
145#391Dic1312yes—
146#380—21no—
147#380—21no—
148C4×C4⋊C4C2×D1311yescharacteristic
149#333—264no—
150#323—261no—
151#323—261no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—22no—
155C22×C13—42no—
156C22×C13—42no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13#38611yescharacteristic
165C22×C13C2×#10011yescharacteristic
166C22×C13#41311yescharacteristic
167C4×C13—21no—
168C4×C13—22no—
169C4×C13—22no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—82no—
173C4×C13—82no—
174C4×C13#45512yes—
175C22×Q8C2×Dic1312yes—
176C22×D4C2×Dic1311yescharacteristic
177C23×C4C22⋊D1311yescharacteristic
178C23×C4C22⋊D1311yescharacteristic
179C2×M16—262no—
180C22×C8—262no—
181C4⋊Q8—22no—
182C4⋊Q8—22no—
183#124—44no—
184C4×D4—22no—
185C4×D4—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4C2×Dic1311yescharacteristic
190C2×C22⋊C4—22no—
191C2×C22⋊C4—22no—
192C2×C22⋊C4C22⋊D1311yescharacteristic
193C2×C22⋊C4C22⋊D1311yescharacteristic
194C2×C42C2×Dic1312yes—
195C2×C42C22×D1311yescharacteristic
196C4⋊C8—134no—
197C4⋊C8—262no—
198C22⋊C8—262no—
199C22⋊C8—262no—
200C22⋊C8—262no—
201C22⋊C8—262no—
202#97—262no—
203#97—262no—
204#95—22no—
205#95—22no—
206#95—21no—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—42no—
210C2×C13—81no—
211C2×C13#188511yescharacteristic
212C2×C13#190011yescharacteristic
213C2×C13#190911yescharacteristic
214C24C22⋊Dic1311yescharacteristic
215C24C22⋊Dic1311yescharacteristic
216C2×Q8—24no—
217C2×Q8—42no—
218C2×Q8—42no—
219C2×D4—22no—
220C2×D4—22no—
221C2×D4—41no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—42no—
229C22×C4—42no—
230C22×C4C22⋊Dic1311yescharacteristic
231C22×C4C22⋊Dic1311yescharacteristic
232C22×C4C22×Dic1311yescharacteristic
233C22×C4C2×C22⋊D1311yescharacteristic
234C22×C4C2×C22⋊D1311yescharacteristic
235M16—1042no—
236C2×C8—264no—
237C2×C8—522no—
238C2×C8—1042no—
239C4⋊C4—22no—
240C4⋊C4—42no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C22⋊C4—22no—
245C22⋊C4—22no—
246C22⋊C4—44no—
247C22⋊C4—44no—
248C42—42no—
249C42D4×D1312yes—
250C42#612912yes—
251C13#945111yescharacteristic, complemented, Sylow
252C23—21no—
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23#8807312yes—
262C23C2×C22⋊Dic1311yescharacteristic
263Q8—84no—
264D4—44no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4D4×Dic1312yes—
284C2×C4#8818911yescharacteristic
285C2×C4#8819111yescharacteristic
286C2×C4#8819312yes—
287C8—524no—
288C8—1042no—
289C22—21no—
290C22—21no—
291C22—22no—
292C22—42no—
293C22—42no—
294C22—41no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22—81no—
301C22C2×#8807311yescharacteristic
302C22#1171888111yescharacteristic
303C22#1171889811yescharacteristic
304C4—21no—
305C4—22no—
306C4—22no—
307C4—41no—
308C4—41no—
309C4—82no—
310C4—82no—
311C4#1171872212yes—
312C2—21no—
313C2—21no—
314C2—42no—
315C2—81no—
316C2#1311522511yescharacteristic
317C2#1311530011yescharacteristic
318C2#1311535911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2547C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2547D13
hypocenterC13#9451
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2547

Complements

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

NH ≅ G/Ntype
2. #13113562C2semidirect
4. #13112692C2semidirect
251. C13#9451semidirect

Maximal subgroups

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

subgroupindex
#131238652
#131135622
#131131772
#131126922
C13×#25472
#945113