Finite Group Databasebeta

← #15762701

Subgroups — #15762701

Order 3328.

578 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718731C211yesmaximal, characteristic
2#13115796C211yesmaximal, characteristic, complemented
3#13115643C211yesmaximal, characteristic
4#13115638C211yesmaximal, characteristic, complemented
5#13114992C211yesmaximal, characteristic, complemented
6C2×#11718046C211yesmaximal, characteristic, complemented
7C13×#1957C211yesmaximal, characteristic
8C2×C13×#127C2211yescharacteristic
9C2×#88123C2211yescharacteristic
10C2×C13×#102—22no—
11C2×C4×C8×C13C2211yescharacteristic
12C13×#384C2211yescharacteristic
13C2×#88072—22no—
14C2×#88072—22no—
15C2×#88056—22no—
16#11718731—22no—
17#11718731C414yescomplemented
18C2×#88048—22no—
19#11718596C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21C2×C4×#1055C2211yescharacteristic
22#11718121—22no—
23#11718046—22no—
24C22×D4×C13—21no—
25C22×D4×C13—21no—
26C22×D4×C13—21no—
27C22×Dic26—21no—
28C22×C8×C13D412yes—
29C13×#127—21no—
30C13×#127—21no—
31C13×#127—21no—
32C13×#127C2×C412yes—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—21no—
35C2×C13×C4⋊C4—21no—
36C2×C42×C13C2311yescharacteristic
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13—21no—
40C2×C4⋊Dic13—21no—
41C2×C4⋊Dic13—21no—
42C22×#1055D412yes—
43C22×#1055D412yes—
44#88123—21no—
45#88123—21no—
46#88123—21no—
47#88123C2×C412yes—
48C13×#102—44no—
49C4×C8×C13—21no—
50C4×C8×C13—21no—
51#88072—28no—
52#88072—44no—
53#88056—44no—
54#88048—44no—
55C4×#1055—21no—
56C4×#1055—21no—
57C4×#1055C2×C412yes—
58C4×#1055D412yes—
59#9827—131nomaximal, Sylow
60C24×C13—41no—
61C2×D4×C13—22no—
62C2×D4×C13—22no—
63C2×D4×C13—22no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
66C2×D4×C13—41no—
67C2×D4×C13—42no—
68C2×D4×C13—42no—
69C2×D4×C13—42no—
70C2×D4×C13—42no—
71C2×D4×C13—42no—
72C2×D4×C13—42no—
73C22×C4×C13—41no—
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×Dic13—41no—
78C22×Dic13—41no—
79C2×Dic26—22no—
80C2×Dic26—42no—
81C2×Dic26—42no—
82C2×Dic26—41no—
83C2×C8×C13—22no—
84C2×C8×C13—22no—
85C2×C8×C13—22no—
86C13×C4⋊C4—42no—
87C13×C4⋊C4—42no—
88C13×C4⋊C4—42no—
89C42×C13C22×C411yescharacteristic
90C42×C13C2×D411yescharacteristic
91C42×C13#4111yescharacteristic
92C42×C13#4111yescharacteristic
93C4⋊Dic13—22no—
94C4⋊Dic13—22no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97C4⋊Dic13—42no—
98C4⋊Dic13—42no—
99C4⋊Dic13—42no—
100C2×#1055—22no—
101C2×#1055—22no—
102C2×#1055—22no—
103C2×#1055—22no—
104C2×#1055C22⋊C414yes—
105C2×#1055SD1614yes—
106C2×#486—131no—
107#1990—131no—
108#1957—131no—
109#1957D1311yescharacteristic
110#1956—131no—
111#1844—131no—
112C2×#322—131no—
113C23×C13—42no—
114C23×C13—81no—
115C23×C13—81no—
116C23×C13—81no—
117C23×C13—81no—
118C23×C13—81no—
119C23×C13—81no—
120C23×C13#12711yescharacteristic
121D4×C13—44no—
122D4×C13—44no—
123D4×C13—44no—
124D4×C13—82no—
125D4×C13—82no—
126D4×C13—82no—
127C2×C4×C13—81no—
128C2×C4×C13—81no—
129C2×C4×C13—81no—
130C2×C4×C13C2×C22⋊C411yescharacteristic
131C2×C4×C13C4×D411yescharacteristic
132C2×C4×C13C4×D411yescharacteristic
133C2×C4×C13#12111yescharacteristic
134C2×C4×C13#12111yescharacteristic
135C2×C4×C13#12411yescharacteristic
136C2×C4×C13C2×SD1612yes—
137C2×C4×C13#13512yes—
138C2×C4×C13AGL(1,ℤ/8)12yes—
139C2×C4×C13AGL(1,ℤ/8)12yes—
140C2×C4×C13AGL(1,ℤ/8)12yes—
141C2×C4×C13#13712yes—
142C2×Dic13—42no—
143C2×Dic13—81no—
144C2×Dic13—81no—
145C2×Dic13—81no—
146C2×Dic13—81no—
147C2×Dic13—81no—
148Dic26—44no—
149Dic26—82no—
150C8×C13—42no—
151#1055—24no—
152#1055—24no—
153C2×C4⋊Q8—131no—
154C2×#127C2×D1311yescharacteristic
155#486—134no—
156#486—262no—
157C2×#106—262no—
158C2×#103—262no—
159C2×#102—22no—
160C2×#102—262no—
161C2×#102—262no—
162C2×C4×C8—131no—
163C2×C4×C8—131no—
164C2×C4×C8C2×D1311yescharacteristic
165#384—131no—
166#384C2×D1311yescharacteristic
167#340—262no—
168#322—262no—
169C22×C13—82no—
170C22×C13—82no—
171C22×C13—82no—
172C22×C13—161no—
173C22×C13—161no—
174C22×C13—161no—
175C22×C13—161no—
176C22×C13#39011yescharacteristic
177C22×C13#49211yescharacteristic
178C22×C13#49511yescharacteristic
179C22×C13#49611yescharacteristic
180C22×C13#49611yescharacteristic
181C22×C13#49611yescharacteristic
182C22×C13#49711yescharacteristic
183C4×C13—161no—
184C4×C13#41712yes—
185C4×C13C4×SD1612yes—
186C4×C13#44212yes—
187C4×C13#46512yes—
188C4×C13#46912yes—
189C4×C13#48912yes—
190Dic13—82no—
191Dic13—161no—
192C22×Q8—261no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4—21no—
196C22×C8—132no—
197C22×C8—132no—
198C22×C8C22⋊D1312yes—
199C4⋊Q8—132no—
200C4⋊Q8—261no—
201C4⋊Q8—261no—
202C4⋊Q8—261no—
203#127—21no—
204#127—21no—
205#127—21no—
206#127C4×D1312yes—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—261no—
211C2×C4⋊C4—261no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C42C22×D1311yescharacteristic
216#106—524no—
217#103—524no—
218#102—44no—
219#102—268no—
220#102—524no—
221C4×C8—21no—
222C4×C8—21no—
223C4×C8—132no—
224C4×C8—132no—
225C4×C8—261no—
226C4×C8—261no—
227C2×C13—162no—
228C2×C13#171411yescharacteristic
229C2×C13#171511yescharacteristic
230C2×C13#171711yescharacteristic
231C2×C13#172011yescharacteristic
232C2×C13#195911yescharacteristic
233C2×C13#196811yescharacteristic
234C2×C13#197211yescharacteristic
235C24—41no—
236C2×Q8—262no—
237C2×Q8—521no—
238C2×Q8—522no—
239C2×Q8—522no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—22no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—42no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—42no—
250C2×D4—41no—
251C2×D4—42no—
252C22×C4—41no—
253C22×C4—521no—
254C22×C4—521no—
255C22×C4D4×D1311yescharacteristic
256C22×C4D4×D1311yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—22no—
261C2×C8—134no—
262C2×C8—134no—
263C2×C8—262no—
264C2×C8—262no—
265C2×C8—262no—
266C2×C8—262no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—262no—
271C4⋊C4—262no—
272C4⋊C4—521no—
273C4⋊C4—521no—
274C4⋊C4—522no—
275C4⋊C4—522no—
276C4⋊C4—522no—
277C42C2×C4×D1311yescharacteristic
278C42#612711yescharacteristic
279C42D4×D1311yescharacteristic
280C42#612911yescharacteristic
281C13#982711yescharacteristic, complemented, Sylow
282C23—42no—
283C23—81no—
284C23—81no—
285C23—81no—
286C23—81no—
287C23—81no—
288C23—81no—
289C23#8819411yescharacteristic
290Q8—524no—
291Q8—1042no—
292D4—44no—
293D4—44no—
294D4—44no—
295D4—82no—
296D4—82no—
297D4—82no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—522no—
302C2×C4—1041no—
303C2×C4—1041no—
304C2×C4—1041no—
305C2×C4—1041no—
306C2×C4—1041no—
307C2×C4C22⋊C4×D1311yescharacteristic
308C2×C4#8813511yescharacteristic
309C2×C4#8813811yescharacteristic
310C2×C4#8813911yescharacteristic
311C2×C4#8816512yes—
312C2×C4#8816612yes—
313C2×C4SD16×D1312yes—
314C2×C4#8816912yes—
315C2×C4C4×C22⋊D1311yescharacteristic
316C2×C4#8818612yes—
317C2×C4#8819311yescharacteristic
318C2×C4#8820312yes—
319C8—42no—
320C8—264no—
321C8—264no—
322C22—82no—
323C22—82no—
324C22—82no—
325C22—161no—
326C22—161no—
327C22—161no—
328C22—161no—
329C22#1171861811yescharacteristic
330C22#1171871911yescharacteristic
331C22#1171873511yescharacteristic
332C22#1171881511yescharacteristic
333C22#1171881611yescharacteristic
334C22#1171882811yescharacteristic
335C22#1171883611yescharacteristic
336C4—161no—
337C4—1042no—
338C4—2081no—
339C4#1171841912yes—
340C4#1171842612yes—
341C4#1171843212yes—
342C4#1171843912yes—
343C4#1171867512yes—
344C4#1171870012yes—
345C2—162no—
346C2#1311445611yescharacteristic
347C2#1311446611yescharacteristic
348C2#1311447411yescharacteristic
349C2#1311449511yescharacteristic
350C2#1311565111yescharacteristic
351C2#1311569111yescharacteristic
352C2#1311571111yescharacteristic
subgroupG/H
centerC23#88194
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1957C2
socleC23×C13#127
prime radicalC2×C13×#127C22
cosocleC2×C42×C13C23
hypercenter#1957D13
hypocenterC13#9827
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. #13115796C2semidirect
4. #13115638C2semidirect
5. #13114992C2semidirect
6. C2×#11718046C2semidirect
17. #11718731C4semidirect
281. C13#9827semidirect

Maximal subgroups

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

subgroupindex
C2×#117187312
#131157962
#131156432
#131156382
#131149922
C2×#117180462
C13×#19572
#982713