Finite Group Databasebeta

← #15867790

Subgroups — #15867790

Order 3328.

914 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117243C211yesmaximal, characteristic
2C4×#88180C211yesmaximal, characteristic
3#13115600C212yesmaximal, complemented
4#13115595C212yesmaximal, complemented
5#13115037C214yesmaximal
6C4×#88058C212yesmaximal, complemented
7C4×#88057C212yesmaximal, complemented
8C2×C13×#431C211yesmaximal, characteristic
9C22×C42×C13C2211yescharacteristic
10C2×#88180—21no—
11C2×#88180C2212yes—
12C13×#431C418yescomplemented
13C2×C13×C4⋊C8C2211yescharacteristic
14C2×C13×C4⋊C8C2211yescharacteristic
15C2×C13×C22⋊C8C2212yes—
16C2×C4×C8×C13C2212yes—
17#11718873—21no—
18#11718873C2212yes—
19C4×C22⋊Dic13—21no—
20C4×C22⋊Dic13—21no—
21C2×#88058C2214yes—
22C2×#88057C2214yes—
23#11718597—21no—
24#11718596C2212yes—
25C4×C4⋊Dic13—21no—
26C4×C4⋊Dic13C2212yes—
27C4×C4⋊Dic13C2211yescharacteristic
28C4×C4⋊Dic13C2211yescharacteristic
29C4×C4⋊Dic13C2212yes—
30#11718593—21no—
31C42×Dic13—21no—
32#11718143C2214yes—
33#11718143C2214yes—
34C23×C4×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C22×C8×C13C2312yes—
38C22×C8×C13C2312yes—
39C2×C42×C13C2×C414yes—
40C2×C42×C13D411yescharacteristic
41C2×C42×C13D411yescharacteristic
42C2×C42×C13Q814yes—
43C2×C42×C13C2311yescharacteristic
44C2×C42×C13C2311yescharacteristic
45C2×C22⋊Dic13—22no—
46C2×C22⋊Dic13—22no—
47#88180—24no—
48#88180—24no—
49#88180—44no—
50C2×C4⋊Dic13—22no—
51C2×C4⋊Dic13—22no—
52C2×C4⋊Dic13C2314yes—
53C2×C4⋊Dic13C2312yes—
54C2×C4⋊Dic13C2312yes—
55C2×C4×Dic13—22no—
56C2×C4×Dic13—22no—
57C2×C4×Dic13—22no—
58C2×C4×Dic13—21no—
59C2×C4×Dic13—21no—
60C13×C4⋊C8C2×C414yes—
61C13×C4⋊C8C2×C414yes—
62C13×C22⋊C8C2×C418yes—
63C4×C8×C13C2×C418yes—
64#88071—21no—
65#88071—21no—
66#88071—22no—
67#88071—22no—
68#88071—22no—
69#88058—28no—
70#88057—28no—
71#21362—131nomaximal, Sylow
72C24×C13C2×D411yescharacteristic
73C22×C4×C13—24no—
74C22×C4×C13—22no—
75C22×C4×C13—22no—
76C22×C4×C13—22no—
77C22×C4×C13—22no—
78C22×C4×C13C4⋊C414yes—
79C22×C4×C13C4⋊C414yes—
80C22×C4×C13C22×C412yes—
81C22×C4×C13C2×D411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×D411yescharacteristic
84C22×C4×C13C2×D411yescharacteristic
85C22×C4×C13C2×D411yescharacteristic
86C22×C4×C13C2×Q812yes—
87C22×C4×C13C2411yescharacteristic
88C22×Dic13—22no—
89C22×Dic13—22no—
90C22×Dic13—24no—
91C2×C8×C13—24no—
92C2×C8×C13—24no—
93C2×C8×C13C22×C414yes—
94C2×C8×C13C22×C414yes—
95C42×C13C4⋊C414yes—
96C42×C13C4⋊C414yes—
97C42×C13C22×C412yes—
98C42×C13C22×C412yes—
99C42×C13C2×Q812yes—
100C42×C13C2×Q812yes—
101C22⋊Dic13—28no—
102C22⋊Dic13—44no—
103C4⋊Dic13—22no—
104C4⋊Dic13—22no—
105C4⋊Dic13—24no—
106C4⋊Dic13—24no—
107C4⋊Dic13—44no—
108C4⋊Dic13—44no—
109C4⋊Dic13#4114yes—
110C4⋊Dic13#4114yes—
111C4×Dic13—28no—
112C4×Dic13—44no—
113C4×Dic13—42no—
114C4×Dic13—44no—
115C4×Dic13—42no—
116C2×#431D1311yescharacteristic
117#2285—131no—
118C4×#117—131no—
119#1948—132no—
120#1947—132no—
121#1854—134no—
122C4×#107—132no—
123C4×#106—132no—
124C23×C13—22no—
125C23×C13—22no—
126C23×C13—21no—
127C23×C13—21no—
128C23×C13C2×C4⋊C412yes—
129C23×C13C22×D411yescharacteristic
130C2×C4×C13—22no—
131C2×C4×C13—22no—
132C2×C4×C13—21no—
133C2×C4×C13—21no—
134C2×C4×C13—22no—
135C2×C4×C13—22no—
136C2×C4×C13—24no—
137C2×C4×C13—28no—
138C2×C4×C13—28no—
139C2×C4×C13C2×C4⋊C412yes—
140C2×C4×C13C2×C4⋊C412yes—
141C2×C4×C13C2×C4⋊C412yes—
142C2×C4×C13C2×C4⋊C412yes—
143C2×C4×C13C2×C4⋊C412yes—
144C2×C4×C13#13514yes—
145C2×C4×C13AGL(1,ℤ/8)12yes—
146C2×C4×C13#13712yes—
147C2×C4×C13C23×C411yescharacteristic
148C2×C4×C13C22×Q811yescharacteristic
149C2×C4×C13C2×#4112yes—
150C2×C4×C13C2×#4112yes—
151C2×Dic13—24no—
152C2×Dic13—24no—
153C2×Dic13—42no—
154C2×Dic13—42no—
155C2×Dic13—42no—
156C2×Dic13—42no—
157C2×Dic13—44no—
158C2×Dic13—44no—
159C2×Dic13—44no—
160C8×C13—24no—
161C8×C13—24no—
162C2×#117—132no—
163C2×#117—261no—
164C22×C42C2×D1311yescharacteristic
165#431Dic1318yescomplemented
166C2×#107—134no—
167C2×#106—134no—
168C2×C4⋊C8C2×D1311yescharacteristic
169C2×C4⋊C8C2×D1311yescharacteristic
170C2×C22⋊C8C2×D1312yes—
171C2×C4×C8C2×D1312yes—
172#384—132no—
173#382—261no—
174#380—132no—
175#380—261no—
176C4×C4⋊C4—132no—
177C4×C4⋊C4—131no—
178C4×C4⋊C4—131no—
179C4×C4⋊C4—132no—
180C4×C4⋊C4—261no—
181C4×C22⋊C4—261no—
182C4×C22⋊C4—261no—
183#376—261no—
184C43—261no—
185#340—134no—
186#340—134no—
187C22×C13—22no—
188C22×C13—22no—
189C22×C13—22no—
190C22×C13—42no—
191C22×C13—42no—
192C22×C13C22×C4⋊C411yescharacteristic
193C22×C13#52512yes—
194C22×C13C2×#13512yes—
195C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
196C22×C13C2×#13711yescharacteristic
197C4×C13—22no—
198C4×C13—22no—
199C4×C13—22no—
200C4×C13#42714yes—
201C4×C13#42814yes—
202C4×C13C4×#4111yescharacteristic
203C4×C13C4×#4111yescharacteristic
204C4×C13#53312yes—
205Dic13—44no—
206Dic13—44no—
207Dic13—84no—
208C23×C4D5211yescharacteristic
209C23×C4D5211yescharacteristic
210C23×C4C22×D1311yescharacteristic
211C22×C8C22×D1312yes—
212C22×C8C22×D1312yes—
213#117—264no—
214#117—264no—
215#117—524no—
216C2×C4⋊C4—132no—
217C2×C4⋊C4—132no—
218C2×C4⋊C4—134no—
219C2×C4⋊C4—262no—
220C2×C4⋊C4—262no—
221C2×C22⋊C4—262no—
222C2×C22⋊C4—262no—
223C2×C42—262no—
224C2×C42—262no—
225C2×C42—262no—
226C2×C42—261no—
227C2×C42—261no—
228C2×C42Dic2614yes—
229C2×C42D5211yescharacteristic
230C2×C42D5211yescharacteristic
231C2×C42C2×Dic1314yes—
232C2×C42C22×D1311yescharacteristic
233C2×C42C22×D1311yescharacteristic
234#107—268no—
235#106—268no—
236C4⋊C8C2×Dic1314yes—
237C4⋊C8C2×Dic1314yes—
238C22⋊C8C2×Dic1318yes—
239C4×C8C2×Dic1318yes—
240#95—261no—
241#95—261no—
242#95—262no—
243#95—262no—
244#95—262no—
245C2×C13—42no—
246C2×C13#229611yescharacteristic
247C2×C13C2×#42711yescharacteristic
248C2×C13C2×#42811yescharacteristic
249C2×C13#310612yes—
250C2×C13#310712yes—
251C24C2×D5211yescharacteristic
252C22×C4—24no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—262no—
258C22×C4—262no—
259C22×C4—264no—
260C22×C4C4⋊Dic1314yes—
261C22×C4C4⋊Dic1314yes—
262C22×C4C2×Dic2612yes—
263C22×C4C2×D5211yescharacteristic
264C22×C4C2×D5211yescharacteristic
265C22×C4C2×D5211yescharacteristic
266C22×C4C2×D5211yescharacteristic
267C22×C4C2×D5211yescharacteristic
268C22×C4C22×Dic1312yes—
269C22×C4C23×D1311yescharacteristic
270C2×C8—24no—
271C2×C8—24no—
272C2×C8C22×Dic1314yes—
273C2×C8C22×Dic1314yes—
274C4⋊C4—134no—
275C4⋊C4—134no—
276C4⋊C4—262no—
277C4⋊C4—262no—
278C4⋊C4—264no—
279C4⋊C4—264no—
280C4⋊C4—524no—
281C4⋊C4—524no—
282C22⋊C4—268no—
283C22⋊C4—524no—
284C42—268no—
285C42—524no—
286C42—524no—
287C42—522no—
288C42—522no—
289C42C4⋊Dic1314yes—
290C42C4⋊Dic1314yes—
291C42C2×Dic2612yes—
292C42C2×Dic2612yes—
293C42C22×Dic1312yes—
294C42C22×Dic1312yes—
295C13#2136211yescharacteristic, complemented, Sylow
296C23—22no—
297C23—21no—
298C23—21no—
299C23—22no—
300C23C2×C4⋊Dic1312yes—
301C23C22×D5211yescharacteristic
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—22no—
306C2×C4—24no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—28no—
310C2×C4—28no—
311C2×C4—264no—
312C2×C4—264no—
313C2×C4—522no—
314C2×C4—522no—
315C2×C4—522no—
316C2×C4—522no—
317C2×C4—524no—
318C2×C4—524no—
319C2×C4—524no—
320C2×C4#8815814yes—
321C2×C4#8816212yes—
322C2×C4#8816312yes—
323C2×C4C2×C4⋊Dic1312yes—
324C2×C4C2×C4⋊Dic1312yes—
325C2×C4C2×C4⋊Dic1312yes—
326C2×C4C2×C4⋊Dic1312yes—
327C2×C4C2×C4⋊Dic1312yes—
328C2×C4C22×Dic2611yescharacteristic
329C2×C4#41×D1312yes—
330C2×C4#41×D1312yes—
331C2×C4C23×Dic1311yescharacteristic
332C8—24no—
333C8—24no—
334C22—22no—
335C22—22no—
336C22—22no—
337C22—42no—
338C22—42no—
339C22#1171922912yes—
340C22C2×#8815812yes—
341C22C2×#8816211yescharacteristic
342C22C2×#8816311yescharacteristic
343C22C22×C4⋊Dic1311yescharacteristic
344C4—22no—
345C4—22no—
346C4—22no—
347C4—524no—
348C4—524no—
349C4—1044no—
350C4#1171876714yes—
351C4#1171878214yes—
352C4#1171922212yes—
353C4#41×Dic1311yescharacteristic
354C4#41×Dic1311yescharacteristic
355C2—42no—
356C2#1311732011yescharacteristic
357C2C2×#1171876711yescharacteristic
358C2C2×#1171878211yescharacteristic
359C2#1312489712yes—
360C2#1312490812yes—
subgroupG/H
centerC22×C4C2×D52
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#431C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
cosocleC22×C4×C13C24
hypercenterC2×#431D13
hypocenterC13#21362
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×#431

Complements

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

NH ≅ G/Ntype
3. #13115600C2semidirect
4. #13115595C2semidirect
6. C4×#88058C2semidirect
7. C4×#88057C2semidirect
12. C13×#431C4semidirect
165. #431Dic13semidirect
295. C13#21362semidirect

Maximal subgroups

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

subgroupindex
#131172432
C4×#881802
#131156002
#131155952
#131150372
C4×#880582
C4×#880572
C2×C13×#4312
#2136213