Finite Group Databasebeta

← #15760713

Subgroups — #15760713

Order 3328.

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

normal subgroups only

This group has 576 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#13119144C211yesmaximal, characteristic
2#13114923C212yesmaximal, complemented
3#13114824C211yesmaximal, characteristic
4#13112704C212yesmaximal, complemented
5C13×#2973C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88189—21no—
8C22×C4⋊Dic13C2211yescharacteristic
9C13×#435—24no—
10C13×#432—21no—
11C13×#407—21no—
12C2×C13×C22⋊C8C2212yes—
13C2×#88074—21no—
14#11718873—21no—
15#11718873C2212yes—
16#11718873C2211yescharacteristic
17#11718644C412yescomplemented
18#11718614C412yescomplemented
19#11718604—21no—
20#11718589—21no—
21#11718143—24no—
22#11718118—21no—
23C22×D4×C13D411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13C2311yescharacteristic
26C23×Dic13—21no—
27C2×C13×M16—22no—
28C22×C8×C13D414yes—
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4C2×C411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13D411yescharacteristic
35C2×C22⋊Dic13—22no—
36C2×C22⋊Dic13—21no—
37C2×C22⋊Dic13—22no—
38#88189—44no—
39C2×C4⋊Dic13—22no—
40C2×C4⋊Dic13—22no—
41C2×C4⋊Dic13—21no—
42C2×C4⋊Dic13—21no—
43C2×C4⋊Dic13—22no—
44C2×C4⋊Dic13C2×C412yes—
45C2×#6101—22no—
46C13×C4⋊C8—22no—
47C13×C22⋊C8—22no—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—22no—
50C13×#97—22no—
51#88074—42no—
52#88071—22no—
53#88071—22no—
54#88071—22no—
55#88071C2×C412yes—
56#9474—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C24×C13C2×D411yescharacteristic
59C2×D4×C13—22no—
60C2×D4×C13—21no—
61C2×D4×C13—22no—
62C2×D4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—42no—
66C22×C4×C13—42no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D412yes—
72C22×C4×C13C2×D411yescharacteristic
73C22×C4×C13#4112yes—
74C22×Dic13—22no—
75C22×Dic13—22no—
76C22×Dic13—42no—
77C22×Dic13—42no—
78C22×Dic13—41no—
79C22×Dic13—41no—
80C22×Dic13—42no—
81C13×M16—82no—
82C2×C8×C13—24no—
83C2×C8×C13—44no—
84C13×C4⋊C4—22no—
85C13×C22⋊C4—22no—
86C13×C22⋊C4—22no—
87C42×C13—21no—
88C42×C13—21no—
89C22⋊Dic13—44no—
90C22⋊Dic13—42no—
91C22⋊Dic13—42no—
92C22⋊Dic13—42no—
93C4⋊Dic13—24no—
94C4⋊Dic13—42no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97C4⋊Dic13—44no—
98#6101—44no—
99#2973D1311yescharacteristic
100#2486—131no—
101#1823—132no—
102#1799—131no—
103#1289—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13C2×C22⋊C411yescharacteristic
112C23×C13#12112yes—
113C23×C13AGL(1,ℤ/8)11yescharacteristic
114C23×C13AGL(1,ℤ/8)12yes—
115C23×C13#13711yescharacteristic
116D4×C13—42no—
117D4×C13—42no—
118C2×C4×C13—24no—
119C2×C4×C13—22no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—41no—
126C2×C4×C13—42no—
127C2×C4×C13—42no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—81no—
131C2×C4×C13C4×D412yes—
132C2×C4×C13#12011yescharacteristic
133C2×C4×C13#12311yescharacteristic
134C2×Dic13—42no—
135C2×Dic13—42no—
136C2×Dic13—42no—
137C2×Dic13—42no—
138C2×Dic13—42no—
139C2×Dic13—42no—
140C2×Dic13—82no—
141C2×Dic13—82no—
142C2×Dic13—82no—
143C2×Dic13—82no—
144C2×Dic13—82no—
145C8×C13—44no—
146C2×#123—261no—
147C2×C4×D4C2×D1311yescharacteristic
148C22×C4⋊C4—131no—
149#435—24no—
150#432—21no—
151C2×#99—261no—
152#407—21no—
153C2×C22⋊C8C2×D1312yes—
154#398—132no—
155#397—132no—
156#389—261no—
157#381—261no—
158#380—131no—
159#380—132no—
160#380—261no—
161#342—261no—
162#340—264no—
163C22×C13—21no—
164C22×C13—22no—
165C22×C13—21no—
166C22×C13—22no—
167C22×C13—42no—
168C22×C13—41no—
169C22×C13—41no—
170C22×C13—42no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—81no—
175C22×C13#38611yescharacteristic
176C22×C13#41711yescharacteristic
177C22×C13#41811yescharacteristic
178C22×C13#46812yes—
179C22×C13#46912yes—
180C4×C13—21no—
181C4×C13—22no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—41no—
185C4×C13#45812yes—
186Dic13—82no—
187Dic13—82no—
188Dic13—162no—
189C22×D4D5211yescharacteristic
190C23×C4—261no—
191C23×C4C22⋊D1311yescharacteristic
192C23×C4C22×D1311yescharacteristic
193C2×M16—22no—
194C22×C8C22⋊D1314yes—
195#123—524no—
196C4×D4—22no—
197C4×D4—22no—
198C2×C4⋊C4—132no—
199C2×C4⋊C4—262no—
200C2×C4⋊C4—262no—
201C2×C4⋊C4—262no—
202C2×C4⋊C4—261no—
203C2×C4⋊C4—261no—
204C2×C4⋊C4—262no—
205C2×C4⋊C4C4×D1311yescharacteristic
206C2×C22⋊C4—262no—
207C2×C22⋊C4—261no—
208C2×C22⋊C4—262no—
209C2×C22⋊C4C4×D1311yescharacteristic
210C2×C22⋊C4D5211yescharacteristic
211C2×C42C22⋊D1311yescharacteristic
212C4⋊C8—22no—
213#99—522no—
214C22⋊C8—22no—
215C22⋊C8—22no—
216C22⋊C8—22no—
217#97—22no—
218#95—132no—
219#95—262no—
220#95—262no—
221#95—262no—
222C2×C13—21no—
223C2×C13—22no—
224C2×C13—21no—
225C2×C13—22no—
226C2×C13—81no—
227C2×C13#189011yescharacteristic
228C2×C13#189511yescharacteristic
229C2×C13#190911yescharacteristic
230C24#610311yescharacteristic
231C24C2×D5211yescharacteristic
232C2×D4—21no—
233C2×D4—22no—
234C2×D4—21no—
235C2×D4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4—262no—
241C22×C4—262no—
242C22×C4—522no—
243C22×C4—521no—
244C22×C4—521no—
245C22×C4—522no—
246C22×C4—522no—
247C22×C4#610311yescharacteristic
248C22×C4#610311yescharacteristic
249C22×C4#610311yescharacteristic
250C22×C4C2×C4×D1311yescharacteristic
251C22×C4#612712yes—
252C22×C4C2×C22⋊D1312yes—
253C22×C4C2×C22⋊D1311yescharacteristic
254M16—82no—
255C2×C8—24no—
256C2×C8—44no—
257C4⋊C4—22no—
258C4⋊C4—264no—
259C4⋊C4—524no—
260C4⋊C4—522no—
261C4⋊C4—524no—
262C4⋊C4—521no—
263C4⋊C4—521no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—524no—
267C22⋊C4—522no—
268C22⋊C4—522no—
269C22⋊C4—522no—
270C42—21no—
271C42—21no—
272C13#947411yescharacteristic, complemented, Sylow
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23#8816212yes—
281C23#8816211yescharacteristic
282C23#8816311yescharacteristic
283C23C2×#610311yescharacteristic
284C23#8818412yes—
285D4—42no—
286D4—42no—
287C2×C4—24no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4—522no—
303C2×C4—522no—
304C2×C4—522no—
305C2×C4—522no—
306C2×C4—1042no—
307C2×C4—1042no—
308C2×C4—1042no—
309C2×C4—1042no—
310C2×C4—1042no—
311C2×C4C4×C22⋊D1312yes—
312C2×C4#8818311yescharacteristic
313C2×C4#8820711yescharacteristic
314C8—44no—
315C22—21no—
316C22—22no—
317C22—21no—
318C22—22no—
319C22—42no—
320C22—41no—
321C22—41no—
322C22—42no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—81no—
327C22#1171879211yescharacteristic
328C22#1171879411yescharacteristic
329C22#1171879512yes—
330C22#1171879612yes—
331C22#1171887411yescharacteristic
332C4—21no—
333C4—22no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—1042no—
338C4—1042no—
339C4—2082no—
340C4#1171890412yes—
341C2—21no—
342C2—22no—
343C2—21no—
344C2—22no—
345C2—81no—
346C2#1311524911yescharacteristic
347C2#1311527411yescharacteristic
348C2#1311535811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#2973C2
socleC22×C13#386
prime radicalC22×D4×C13D4
cosocleC23×C4×C13C23
hypercenter#2973D13
hypocenterC13#9474
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13114923C2semidirect
4. #13112704C2semidirect
17. #11718644C4semidirect
18. #11718614C4semidirect
272. C13#9474semidirect

Maximal subgroups

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

subgroupindex
#131191442
#131149232
#131148242
#131127042
C13×#29732
#947413