Finite Group Databasebeta

← #15832137

Subgroups — #15832137

Order 3328.

572 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123953C212yesmaximal
2#13113625C212yesmaximal, complemented
3#13113621C212yesmaximal, complemented
4#13113616C212yesmaximal, complemented
5#13113611C212yesmaximal, complemented
6#13113603C212yesmaximal, complemented
7#13113599C211yesmaximal, characteristic, complemented
8#13113595C211yesmaximal, characteristic, complemented
9C13×#2922C211yesmaximal, characteristic
10C4×C13×#41C2211yescharacteristic
11C13×#433C414yes—
12C13×#431C2212yes—
13C13×#431C2212yes—
14C13×#424C412yes—
15C13×#408C412yes—
16C4×C13×M16C2211yescharacteristic
17C2×C4×C8×C13C2211yescharacteristic
18#11718685—22no—
19#11718673—22no—
20#11718672—22no—
21#11718672—22no—
22#11718587C2212yes—
23#11718587C2212yes—
24#11718586C2212yes—
25#11718585C2212yes—
26#11718585C2212yes—
27C2×C4⋊#1055C2212yes—
28#11718050C2212yes—
29#11718050C2212yes—
30#11718050C2211yescharacteristic
31#11718050C2212yes—
32#11718050C2211yescharacteristic
33#11718050C2211yescharacteristic
34#11718050C2211yescharacteristic
35#11718049C2212yes—
36#11718049C2212yes—
37#11718049C2212yes—
38C2×C13×#41C2×C411yescharacteristic
39C2×C13×M16C2×C412yes—
40C22×C8×C13C2×C412yes—
41C4×Q8×C13D411yescharacteristic
42C4×Q8×C13Q811yescharacteristic
43C4×D4×C13D411yescharacteristic
44C4×D4×C13D412yes—
45C4×D4×C13Q811yescharacteristic
46C4×D4×C13Q812yes—
47C13×#117C2×C411yescharacteristic
48C13×#117C2×C412yes—
49C2×C42×C13C2311yescharacteristic
50C2×C42×C13C2312yes—
51C2×#6099—22no—
52C2×#6099—22no—
53C22×#1055—22no—
54C13×C4⋊C8C2×C414yes—
55C13×C4⋊C8C2×C414yes—
56C13×C22⋊C8C2×C414yes—
57C13×C22⋊C8C2×C414yes—
58C13×#97C2×C412yes—
59C4×C8×C13C2×C412yes—
60C4×C8×C13C2311yescharacteristic
61C4×C8×C13C2311yescharacteristic
62C4×C8×C13C2312yes—
63C22⋊#1055—22no—
64C22⋊#1055—22no—
65C22⋊#1055—22no—
66C4⋊#1055—22no—
67C4⋊#1055—22no—
68C4⋊#1055—22no—
69C4⋊#1055C2312yes—
70C4⋊#1055C2312yes—
71C4⋊#1055C2312yes—
72C4⋊#1055C2312yes—
73#88043—22no—
74#88043—22no—
75C4×#1055—22no—
76#17825—131nomaximal, Sylow
77C13×#41—42no—
78C2×Q8×C13C4⋊C411yescharacteristic
79C2×D4×C13C4⋊C411yescharacteristic
80C2×D4×C13C4⋊C412yes—
81C22×C4×C13C22×C412yes—
82C22×C4×C13C22×C411yescharacteristic
83C22×C4×C13C2×D412yes—
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×Q811yescharacteristic
86C22×C4×C13C2×Q812yes—
87C13×M16—42no—
88C2×C8×C13—42no—
89C2×C8×C13C22×C412yes—
90C2×C8×C13C22×C412yes—
91C2×C8×C13C22×C414yes—
92C13×C4⋊C4C4⋊C411yescharacteristic
93C13×C4⋊C4C4⋊C412yes—
94C13×C4⋊C4C4⋊C411yescharacteristic
95C13×C4⋊C4C4⋊C412yes—
96C13×C22⋊C4C4⋊C412yes—
97C13×C22⋊C4C4⋊C412yes—
98C13×C22⋊C4C4⋊C412yes—
99C42×C13C22×C411yescharacteristic
100C42×C13C22×C412yes—
101C42×C13C2×D412yes—
102C42×C13C2×D411yescharacteristic
103C42×C13C2×Q811yescharacteristic
104C42×C13C2×Q812yes—
105C42×C13C2411yescharacteristic
106#6099—82no—
107#6099—82no—
108C2×#1055—22no—
109C2×#1055—22no—
110C2×#1055—22no—
111C2×#1055—22no—
112C2×#1055—82no—
113#2989—132no—
114#2922D1311yescharacteristic
115#1574—132no—
116#1573—132no—
117#1572—132no—
118#1571—132no—
119#1569—132no—
120#1568—131no—
121#1567—131no—
122C23×C13C2×C4⋊C412yes—
123C23×C13C2×C4⋊C411yescharacteristic
124Q8×C13—41no—
125D4×C13—41no—
126D4×C13—42no—
127C2×C4×C13—22no—
128C2×C4×C13—24no—
129C2×C4×C13—22no—
130C2×C4×C13—21no—
131C2×C4×C13—22no—
132C2×C4×C13—21no—
133C2×C4×C13—41no—
134C2×C4×C13—42no—
135C2×C4×C13C2×C4⋊C411yescharacteristic
136C2×C4×C13C2×C4⋊C412yes—
137C2×C4×C13C2×C4⋊C411yescharacteristic
138C2×C4×C13C2×C4⋊C412yes—
139C2×C4×C13C2×C4⋊C412yes—
140C2×C4×C13C2×C4⋊C411yescharacteristic
141C2×C4×C13C23×C411yescharacteristic
142C2×C4×C13C22×D411yescharacteristic
143C2×C4×C13C22×Q811yescharacteristic
144C8×C13—22no—
145C8×C13—22no—
146C8×C13—24no—
147#1055—42no—
148#1055—42no—
149#1055—42no—
150#1055—42no—
151C4×#41C2×D1311yescharacteristic
152#446—262no—
153#436—262no—
154#435—262no—
155#435—262no—
156#433Dic1314yes—
157#432—132no—
158#432—132no—
159#431—132no—
160#431C2×D1312yes—
161#431C2×D1312yes—
162#424Dic1312yes—
163#423—132no—
164#423—132no—
165C2×C4⋊C8—132no—
166#408Dic1312yes—
167C4×M16C2×D1311yescharacteristic
168C2×C4×C8C2×D1311yescharacteristic
169#335—132no—
170#335—131no—
171#335—131no—
172#335—131no—
173#335—131no—
174#335—132no—
175#335—132no—
176#334—132no—
177#334—132no—
178#334—132no—
179C22×C13—21no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—21no—
183C22×C13—22no—
184C22×C13—21no—
185C22×C13C22×C4⋊C411yescharacteristic
186C4×C13—21no—
187C4×C13—22no—
188C4×C13—22no—
189C4×C13—21no—
190C4×C13—21no—
191C4×C13—21no—
192C4×C13—22no—
193C4×C13#56812yes—
194C4×C13#57611yescharacteristic
195C4×C13#57811yescharacteristic
196C2×#41C2×Dic1311yescharacteristic
197C2×M16—262no—
198C2×M16—262no—
199C2×M16C2×Dic1312yes—
200C22×C8—262no—
201C22×C8C2×Dic1312yes—
202C4×Q8Dic2611yescharacteristic
203C4×Q8D5211yescharacteristic
204C4×D4Dic2611yescharacteristic
205C4×D4Dic2612yes—
206C4×D4D5211yescharacteristic
207C4×D4D5212yes—
208#117C2×Dic1311yescharacteristic
209#117C2×Dic1312yes—
210C2×C42C22×D1311yescharacteristic
211C2×C42C22×D1312yes—
212C4⋊C8—132no—
213C4⋊C8—132no—
214C4⋊C8—132no—
215C4⋊C8—132no—
216C4⋊C8—262no—
217C4⋊C8—262no—
218C4⋊C8—262no—
219C4⋊C8C2×Dic1314yes—
220C4⋊C8C2×Dic1314yes—
221C22⋊C8—262no—
222C22⋊C8—262no—
223C22⋊C8—262no—
224C22⋊C8C2×Dic1314yes—
225C22⋊C8C2×Dic1314yes—
226#97—262no—
227#97—262no—
228#97C2×Dic1312yes—
229C4×C8—262no—
230C4×C8C2×Dic1312yes—
231C4×C8C22×D1311yescharacteristic
232C4×C8C22×D1312yes—
233C4×C8C22×D1311yescharacteristic
234C2×C13—41no—
235C2×C13—42no—
236C2×C13#290511yescharacteristic
237C2×C13#291311yescharacteristic
238C2×C13#291611yescharacteristic
239#41—42no—
240C2×Q8C4⋊Dic1311yescharacteristic
241C2×D4C4⋊Dic1311yescharacteristic
242C2×D4C4⋊Dic1312yes—
243C22×C4C2×Dic2611yescharacteristic
244C22×C4C2×Dic2612yes—
245C22×C4C2×D5212yes—
246C22×C4C2×D5211yescharacteristic
247C22×C4C22×Dic1312yes—
248C22×C4C22×Dic1311yescharacteristic
249M16—42no—
250M16—1042no—
251M16—1042no—
252C2×C8—42no—
253C2×C8—262no—
254C2×C8—262no—
255C2×C8—262no—
256C2×C8—262no—
257C2×C8—1042no—
258C2×C8C22×Dic1312yes—
259C2×C8C22×Dic1312yes—
260C2×C8C22×Dic1314yes—
261C4⋊C4C4⋊Dic1311yescharacteristic
262C4⋊C4C4⋊Dic1312yes—
263C4⋊C4C4⋊Dic1311yescharacteristic
264C4⋊C4C4⋊Dic1312yes—
265C22⋊C4C4⋊Dic1312yes—
266C22⋊C4C4⋊Dic1312yes—
267C22⋊C4C4⋊Dic1312yes—
268C42C2×Dic2611yescharacteristic
269C42C2×Dic2612yes—
270C42C2×D5212yes—
271C42C2×D5211yescharacteristic
272C42C22×Dic1311yescharacteristic
273C42C22×Dic1312yes—
274C42C23×D1311yescharacteristic
275C13#1782511yescharacteristic, complemented, Sylow
276C23C2×C4⋊Dic1312yes—
277C23C2×C4⋊Dic1311yescharacteristic
278Q8—41no—
279D4—41no—
280D4—42no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—41no—
288C2×C4—42no—
289C2×C4C2×C4⋊Dic1312yes—
290C2×C4C2×C4⋊Dic1311yescharacteristic
291C2×C4C2×C4⋊Dic1311yescharacteristic
292C2×C4C2×C4⋊Dic1312yes—
293C2×C4C2×C4⋊Dic1312yes—
294C2×C4C2×C4⋊Dic1311yescharacteristic
295C2×C4C22×Dic2611yescharacteristic
296C2×C4C22×D5211yescharacteristic
297C2×C4C23×Dic1311yescharacteristic
298C8—22no—
299C8—22no—
300C8—24no—
301C8—522no—
302C8—522no—
303C8—522no—
304C8—522no—
305C22—21no—
306C22—22no—
307C22—22no—
308C22—21no—
309C22—22no—
310C22—21no—
311C22C22×C4⋊Dic1311yescharacteristic
312C4—21no—
313C4—22no—
314C4—22no—
315C4—21no—
316C4—21no—
317C4—22no—
318C4—21no—
319C4#1171945711yescharacteristic
320C4#1171945811yescharacteristic
321C4#1171952412yes—
322C2—41no—
323C2—42no—
324C2#1312340011yescharacteristic
325C2#1312343611yescharacteristic
326C2#1312344711yescharacteristic
subgroupG/H
centerC2×C4C22×D52
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2922C2
socleC22×C13C22×C4⋊C4
prime radicalC2×C13×#41C2×C4
cosocleC42×C13C24
hypercenter#2922D13
hypocenterC13#17825
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2922

Complements

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

NH ≅ G/Ntype
2. #13113625C2semidirect
3. #13113621C2semidirect
4. #13113616C2semidirect
5. #13113611C2semidirect
6. #13113603C2semidirect
7. #13113599C2semidirect
8. #13113595C2semidirect
275. C13#17825semidirect

Maximal subgroups

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

subgroupindex
#131239532
#131136252
#131136212
#131136162
#131136112
#131136032
#131135992
#131135952
C13×#29222
#1782513