Finite Group Databasebeta

← #15762714

Subgroups — #15762714

Order 3328.

610 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13115798C211yesmaximal, characteristic, complemented
2#13115798C211yesmaximal, characteristic, complemented
3#13115643C211yesmaximal, characteristic
4#13115643C211yesmaximal, characteristic
5#13114964C211yesmaximal, characteristic, complemented
6C2×#11718046C211yesmaximal, characteristic, complemented
7C2×C13×#492C211yesmaximal, characteristic
8C22×C13×SD16—22no—
9C2×C13×C4⋊Q8C2211yescharacteristic
10C2×C13×#127C2211yescharacteristic
11C13×#492—22no—
12C13×#492C414yescomplemented
13C2×C4×C8×C13C2211yescharacteristic
14C2×#88072—22no—
15C2×#88072—22no—
16#11718596C2211yescharacteristic
17#11718596C2211yescharacteristic
18C2×C4×#1055C2211yescharacteristic
19C2×C4×#1055C2211yescharacteristic
20#11718143—22no—
21#11718121—22no—
22#11718121—22no—
23#11718046—22no—
24C22×Q8×C13—21no—
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×D4×C13—21no—
28C2×C13×SD16—28no—
29C2×C13×SD16—44no—
30C2×C13×SD16—44no—
31C22×C8×C13D412yes—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8—21no—
34C13×C4⋊Q8—21no—
35C13×C4⋊Q8C2×C412yes—
36C13×#127—21no—
37C13×#127—21no—
38C13×#127—21no—
39C13×#127C2×C412yes—
40C2×C13×C4⋊C4—21no—
41C2×C13×C4⋊C4—21no—
42C2×C42×C13C2311yescharacteristic
43C2×C4⋊Dic13—21no—
44C2×C4⋊Dic13—21no—
45C2×C4⋊Dic13—21no—
46C2×C4⋊Dic13—21no—
47C2×C4⋊Dic13—21no—
48C2×C4⋊Dic13—21no—
49C22×#1055D412yes—
50C22×#1055D412yes—
51C4×C8×C13C2×C412yes—
52C4×C8×C13D412yes—
53#88072—44no—
54#88072—44no—
55C4×#1055—21no—
56C4×#1055—21no—
57C4×#1055—21no—
58C4×#1055—21no—
59#9829—131nomaximal, Sylow
60C24×C13—41no—
61C2×Q8×C13—22no—
62C2×Q8×C13—41no—
63C2×Q8×C13—42no—
64C2×Q8×C13—42no—
65C2×D4×C13—22no—
66C2×D4×C13—22no—
67C2×D4×C13—22no—
68C2×D4×C13—41no—
69C2×D4×C13—41no—
70C2×D4×C13—41no—
71C2×D4×C13—42no—
72C2×D4×C13—42no—
73C2×D4×C13—42no—
74C2×D4×C13—42no—
75C2×D4×C13—42no—
76C2×D4×C13—42no—
77C22×C4×C13—41no—
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C22×Dic13—41no—
82C22×Dic13—41no—
83C13×SD16—416no—
84C2×C8×C13—22no—
85C2×C8×C13—22no—
86C2×C8×C13C22⋊C414yes—
87C13×C4⋊C4—22no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C42×C13C22×C411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13#4111yescharacteristic
94C42×C13#4111yescharacteristic
95C4⋊Dic13—42no—
96C4⋊Dic13—42no—
97C4⋊Dic13—42no—
98C4⋊Dic13—42no—
99C4⋊Dic13—42no—
100C4⋊Dic13—42no—
101C2×#1055—22no—
102C2×#1055—22no—
103C2×#1055—22no—
104C2×#1055—22no—
105C2×#1055—22no—
106C2×#1055SD1614yescomplemented
107C2×#492D1311yescharacteristic
108#1990—131no—
109#1990—131no—
110#1957—131no—
111#1957—131no—
112#1834—131no—
113C2×#322—131no—
114C23×C13—42no—
115C23×C13—81no—
116C23×C13—81no—
117C23×C13—81no—
118C23×C13—81no—
119C23×C13—81no—
120C23×C13—81no—
121C23×C13#12711yescharacteristic
122Q8×C13—44no—
123Q8×C13—82no—
124D4×C13—44no—
125D4×C13—44no—
126D4×C13—44no—
127D4×C13—82no—
128D4×C13—82no—
129D4×C13—82no—
130C2×C4×C13—42no—
131C2×C4×C13—81no—
132C2×C4×C13—81no—
133C2×C4×C13C2×C22⋊C411yescharacteristic
134C2×C4×C13C4×D411yescharacteristic
135C2×C4×C13C4×D411yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13#12111yescharacteristic
138C2×C4×C13#12411yescharacteristic
139C2×C4×C13C2×SD1612yes—
140C2×C4×C13#13512yes—
141C2×C4×C13AGL(1,ℤ/8)12yes—
142C2×C4×C13AGL(1,ℤ/8)12yes—
143C2×C4×C13AGL(1,ℤ/8)12yes—
144C2×C4×C13#13712yes—
145C2×Dic13—81no—
146C2×Dic13—81no—
147C2×Dic13—81no—
148C2×Dic13—81no—
149C2×Dic13—81no—
150C2×Dic13—81no—
151C8×C13—24no—
152#1055—24no—
153#1055—42no—
154C22×SD16—22no—
155C2×C4⋊Q8C2×D1311yescharacteristic
156C2×#127C2×D1311yescharacteristic
157#492—22no—
158#492Dic1314yescomplemented
159C2×#102—262no—
160C2×#102—262no—
161C2×C4×C8—131no—
162C2×C4×C8—131no—
163C2×C4×C8C2×D1311yescharacteristic
164#384—131no—
165#384—131no—
166#340—262no—
167#340—262no—
168#340—262no—
169#322—262no—
170C22×C13—82no—
171C22×C13—82no—
172C22×C13—82no—
173C22×C13—161no—
174C22×C13—161no—
175C22×C13—161no—
176C22×C13—161no—
177C22×C13#39011yescharacteristic
178C22×C13#49211yescharacteristic
179C22×C13#49511yescharacteristic
180C22×C13#49611yescharacteristic
181C22×C13#49611yescharacteristic
182C22×C13#49611yescharacteristic
183C22×C13#49711yescharacteristic
184C4×C13—82no—
185C4×C13#41812yes—
186C4×C13C4×SD1612yes—
187C4×C13#44012yes—
188C4×C13#46512yes—
189C4×C13#46812yes—
190C4×C13#49012yes—
191Dic13—161no—
192Dic13—161no—
193C22×Q8—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×D4—21no—
197C2×SD16—28no—
198C2×SD16—44no—
199C2×SD16—44no—
200C22×C8—132no—
201C22×C8—132no—
202C22×C8C22⋊D1312yes—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8C2×Dic1312yes—
207#127—21no—
208#127—21no—
209#127—21no—
210#127C2×Dic1312yes—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4—261no—
216C2×C4⋊C4—261no—
217C2×C4⋊C4—261no—
218C2×C4⋊C4—261no—
219C2×C42C22×D1311yescharacteristic
220#102—524no—
221#102—524no—
222C4×C8—261no—
223C4×C8—261no—
224C4×C8—261no—
225C4×C8—261no—
226C4×C8C2×Dic1312yes—
227C4×C8C22⋊D1312yes—
228C2×C13—162no—
229C2×C13#171411yescharacteristic
230C2×C13#171511yescharacteristic
231C2×C13#171711yescharacteristic
232C2×C13#171911yescharacteristic
233C2×C13#196111yescharacteristic
234C2×C13#196811yescharacteristic
235C2×C13#197311yescharacteristic
236C24—41no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—42no—
240C2×Q8—42no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—42no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C22×C4—41no—
254C22×C4—521no—
255C22×C4—521no—
256C22×C4D4×D1311yescharacteristic
257C22×C4D4×D1311yescharacteristic
258C22×C4C2×C22⋊D1311yescharacteristic
259SD16—416no—
260C2×C8—22no—
261C2×C8—22no—
262C2×C8—134no—
263C2×C8—262no—
264C2×C8—262no—
265C2×C8—262no—
266C2×C8—262no—
267C2×C8—262no—
268C2×C8C22⋊Dic1314yes—
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—522no—
274C4⋊C4—522no—
275C4⋊C4—522no—
276C4⋊C4—522no—
277C4⋊C4—522no—
278C4⋊C4—522no—
279C42#612911yescharacteristic
280C42#612911yescharacteristic
281C42C22×Dic1311yescharacteristic
282C42C2×C22⋊D1311yescharacteristic
283C13#982911yescharacteristic, complemented, Sylow
284C23—42no—
285C23—81no—
286C23—81no—
287C23—81no—
288C23—81no—
289C23—81no—
290C23—81no—
291C23#8819411yescharacteristic
292Q8—44no—
293Q8—82no—
294D4—44no—
295D4—44no—
296D4—44no—
297D4—82no—
298D4—82no—
299D4—82no—
300C2×C4—42no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—1041no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4—1041no—
307C2×C4—1041no—
308C2×C4—1041no—
309C2×C4SD16×D1312yes—
310C2×C4#8816812yes—
311C2×C4#8816912yes—
312C2×C4#8817012yes—
313C2×C4#8818612yes—
314C2×C4#8818612yes—
315C2×C4D4×Dic1311yescharacteristic
316C2×C4D4×Dic1311yescharacteristic
317C2×C4#8819011yescharacteristic
318C2×C4#8819211yescharacteristic
319C2×C4#8819211yescharacteristic
320C2×C4C2×C22⋊Dic1311yescharacteristic
321C8—24no—
322C8—264no—
323C8—522no—
324C22—82no—
325C22—82no—
326C22—82no—
327C22—161no—
328C22—161no—
329C22—161no—
330C22—161no—
331C22#1171873511yescharacteristic
332C22#1171873511yescharacteristic
333C22#1171882811yescharacteristic
334C22#1171882911yescharacteristic
335C22#1171883611yescharacteristic
336C22#1171883711yescharacteristic
337C22#1171888211yescharacteristic
338C4—82no—
339C4—2081no—
340C4—2081no—
341C4#1171873212yes—
342C4SD16×Dic1312yes—
343C4#1171882512yes—
344C4#1171883212yes—
345C4#1171883512yes—
346C4#1171887612yes—
347C2—162no—
348C2#1311445611yescharacteristic
349C2#1311446311yescharacteristic
350C2#1311447311yescharacteristic
351C2#1311448711yescharacteristic
352C2#1311566111yescharacteristic
353C2#1311569211yescharacteristic
354C2#1311571911yescharacteristic
subgroupG/H
centerC23#88194
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC2×C13×#492C2
socleC23×C13#127
prime radicalC2×C13×#127C22
cosocleC2×C42×C13C23
hypercenterC2×#492D13
hypocenterC13#9829
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. #13115798C2semidirect
2. #13115798C2semidirect
5. #13114964C2semidirect
6. C2×#11718046C2semidirect
12. C13×#492C4semidirect
106. C2×#1055SD16semidirect
158. #492Dic13semidirect
283. C13#9829semidirect

Maximal subgroups

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

subgroupindex
#131157982
#131156432
#131149642
C2×#117180462
C2×C13×#4922
#982913