Finite Group Databasebeta

← #14909358

Subgroups — #14909358

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079202C211yesmaximal, characteristic, complemented
2#13070903C211yesmaximal, characteristic, complemented
3#13070888C211yesmaximal, characteristic, complemented
4#13070863C211yesmaximal, characteristic, complemented
5#13070852C211yesmaximal, characteristic, complemented
6#13070727C212yesmaximal
7#13070722C212yesmaximal, complemented
8C4×#66893C212yesmaximal, complemented
9C4×#66891C212yesmaximal, complemented
10C4×#66876C211yesmaximal, characteristic, complemented
11C11×#3168C211yesmaximal, characteristic
12C11×#529—21no—
13#10623001—21no—
14C11×#499C2211yescharacteristic
15C11×#495C2211yescharacteristic
16C11×#488—21no—
17C11×#467C2211yescharacteristic
18C11×#466C2211yescharacteristic
19C11×#465—21no—
20C4×C11×Q16C2211yescharacteristic
21C4×C11×SD16—21no—
22C4×C11×D8C2211yescharacteristic
23C2×C4×C8×C11C2211yescharacteristic
24C2×#66893C2212yes—
25C2×#66891C2212yes—
26#10622729—21no—
27#10622729C2212yes—
28C2×#66876C2212yes—
29#10622312C2211yescharacteristic
30C4×Dic44—21no—
31C4×Dic44C2212yes—
32#10622295C2211yescharacteristic
33#10622294—21no—
34#10622202C2212yes—
35#10622200C2212yes—
36#10622130C2212yes—
37#10622130C2212yes—
38#10622128C2212yes—
39#10622127C2212yes—
40#10622099C2211yescharacteristic
41#10622099C2211yescharacteristic
42C4×C11⋊C16C2212yes—
43C2×C11×Q16C2311yescharacteristic
44C2×C11×SD16—21no—
45C2×C11×D8C2311yescharacteristic
46C22×C8×C11D411yescharacteristic
47C22×C8×C11C2311yescharacteristic
48C11×#126—41no—
49C11×#125—21no—
50C11×#124—21no—
51C11×#123—41no—
52C11×C22⋊Q8—21no—
53C11×#121—21no—
54C4×Q8×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11—41no—
57C11×#117—41no—
58C2×C42×C11D411yescharacteristic
59#66979—41no—
60#66977—22no—
61#66977—41no—
62C2×Dic44—21no—
63C2×Dic44C2312yes—
64#66923—41no—
65#66922—21no—
66#66922—21no—
67C4×Dic22—22no—
68C4×Dic22—41no—
69C11×#107C2311yescharacteristic
70C11×#107C2311yescharacteristic
71C11×#106—21no—
72C11×#103—21no—
73C11×#103—21no—
74C11×#102—21no—
75C11×#102—21no—
76C4×C8×C11D411yescharacteristic
77C4×C8×C11D411yescharacteristic
78C4×C8×C11C2311yescharacteristic
79C4×C8×C11C2311yescharacteristic
80#66893—24no—
81#66891—24no—
82#66882—21no—
83#66882C2312yes—
84#66880—22no—
85#66880—22no—
86#66876—24no—
87C2×C11⋊C16C2312yes—
88C2×C11⋊C16C2312yes—
89#33738—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11D811yescharacteristic
95C22×C4×C11D811yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C2×Dic22—22no—
98C2×Dic22—41no—
99C11×Q16—22no—
100C11×SD16—42no—
101C11×D8—22no—
102C2×C8×C11—22no—
103C2×C8×C11—22no—
104C2×C8×C11C2×D411yescharacteristic
105C2×C8×C11C2×D411yescharacteristic
106C2×C8×C11C2×D411yescharacteristic
107C2×C8×C11C2411yescharacteristic
108C11×C4⋊C4—21no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C4⋊C4—41no—
114C11×C22⋊C4—41no—
115C11×C22⋊C4—41no—
116C11×C22⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11—41no—
120C42×C11D811yescharacteristic
121C42×C11D811yescharacteristic
122C42×C11C2×D411yescharacteristic
123C42×C11C2×D411yescharacteristic
124C22⋊Dic11—42no—
125C4⋊Dic11—22no—
126C4⋊Dic11—41no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129Dic11⋊C4—42no—
130Dic11⋊C4—42no—
131C4×Dic11—42no—
132Dic44—22no—
133Dic44—22no—
134Dic44—42no—
135C11⋊C16—22no—
136C11⋊C16#4114yes—
137#3170—111no—
138#3168D1111yescharacteristic
139#2255—111no—
140#2251—111no—
141#2245—111no—
142#2243—111no—
143#2220—112no—
144#2219—112no—
145C4×Q32—112no—
146C4×SD32—112no—
147C4×M32—111no—
148C23×C11—41no—
149C23×C11C2×D811yescharacteristic
150Q8×C11—41no—
151Q8×C11—41no—
152D4×C11—41no—
153D4×C11—41no—
154D4×C11—82no—
155C2×C4×C11—21no—
156C2×C4×C11—21no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—41no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—82no—
163C2×C4×C11C2×D811yescharacteristic
164C2×C4×C11C2×D811yescharacteristic
165C2×C4×C11C2×D811yescharacteristic
166C2×C4×C11C2×D811yescharacteristic
167C2×C4×C11C2×D811yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×Dic11—42no—
170C2×Dic11—42no—
171Dic22—42no—
172Dic22—42no—
173Dic22—82no—
174C8×C11—21no—
175C8×C11—21no—
176C8×C11#13512yes—
177C8×C11C2×#4112yes—
178#533—221no—
179#529—21no—
180C2×Q32—112no—
181C2×SD32—112no—
182C2×M32—112no—
183#500—111no—
184#499C2×D1111yescharacteristic
185#495C2×D1111yescharacteristic
186#494—111no—
187#488—21no—
188#487—221no—
189#467—112no—
190#467—221no—
191#467C2×D1111yescharacteristic
192#466C2×D1111yescharacteristic
193#465—21no—
194C4×Q16—112no—
195C4×Q16—221no—
196C4×Q16C2×D1111yescharacteristic
197C4×SD16—21no—
198C4×D8C2×D1111yescharacteristic
199C2×C4×C8C2×D1111yescharacteristic
200#367—112no—
201#366—112no—
202#358—112no—
203#358—112no—
204#358—112no—
205#357—112no—
206#346—111no—
207#346—111no—
208C4×C16—112no—
209C22×C11—21no—
210C22×C11—21no—
211C22×C11—21no—
212C22×C11—81no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11C22×D811yescharacteristic
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—21no—
219C4×C11—21no—
220C4×C11—81no—
221C4×C11—81no—
222C4×C11—81no—
223C4×C11#51012yes—
224C4×C11#53211yescharacteristic
225C4×C11C2×#13511yescharacteristic
226Dic11—82no—
227Dic11—82no—
228C2×Q16—112no—
229C2×Q16—221no—
230C2×Q16C22×D1111yescharacteristic
231C2×SD16—21no—
232C2×D8C22×D1111yescharacteristic
233C22×C8C22⋊D1111yescharacteristic
234C22×C8C22×D1111yescharacteristic
235C4⋊Q8—221no—
236C4⋊Q8—221no—
237#126—41no—
238#125—21no—
239#125—441no—
240#124—21no—
241#123—41no—
242C22⋊Q8—21no—
243C22⋊Q8—222no—
244C22⋊Q8—441no—
245#121—21no—
246C4×Q8—21no—
247C4×Q8—222no—
248C4×Q8—441no—
249C4×D4—21no—
250C4×D4—41no—
251#117—41no—
252#117—441no—
253C2×C42C22⋊D1111yescharacteristic
254Q32—224no—
255SD32—224no—
256M32—224no—
257C2×C16—112no—
258C2×C16—112no—
259#107—112no—
260#107—221no—
261#107C22×D1111yescharacteristic
262#107C22×D1111yescharacteristic
263#106—21no—
264#103—21no—
265#103—21no—
266#103—222no—
267#103—222no—
268#102—21no—
269#102—21no—
270C4×C8C22⋊D1111yescharacteristic
271C4×C8C22⋊D1111yescharacteristic
272C4×C8C22×D1111yescharacteristic
273C4×C8C22×D1111yescharacteristic
274C2×C11—41no—
275C2×C11—161no—
276C2×C11#316911yescharacteristic
277C2×C11C2×#51011yescharacteristic
278C2×C11#341411yescharacteristic
279C2×Q8—21no—
280C2×Q8—222no—
281C2×Q8—441no—
282C2×D4—21no—
283C2×D4—41no—
284C22×C4—41no—
285C22×C4#432311yescharacteristic
286C22×C4#432311yescharacteristic
287C22×C4C2×C22⋊D1111yescharacteristic
288Q16—22no—
289Q16—222no—
290Q16—222no—
291Q16—442no—
292SD16—42no—
293D8—22no—
294C2×C8—22no—
295C2×C8—22no—
296C2×C8C2×C22⋊D1111yescharacteristic
297C2×C8C2×C22⋊D1111yescharacteristic
298C2×C8C2×C22⋊D1111yescharacteristic
299C2×C8C23×D1111yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—222no—
307C4⋊C4—441no—
308C4⋊C4—441no—
309C4⋊C4—442no—
310C4⋊C4—442no—
311C4⋊C4—441no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—442no—
318C42—41no—
319C42—442no—
320C42#432311yescharacteristic
321C42#432311yescharacteristic
322C42C2×C22⋊D1111yescharacteristic
323C42C2×C22⋊D1111yescharacteristic
324C16—114no—
325C16—222no—
326C11#3373811yescharacteristic, complemented, Sylow
327C23—41no—
328C23C2×#432311yescharacteristic
329Q8—41no—
330Q8—41no—
331Q8—442no—
332Q8—442no—
333Q8—882no—
334D4—41no—
335D4—41no—
336D4—82no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4C2×#432311yescharacteristic
348C2×C4C2×#432311yescharacteristic
349C2×C4C2×#432311yescharacteristic
350C2×C4C2×#432311yescharacteristic
351C2×C4C2×#432311yescharacteristic
352C2×C4C22×C22⋊D1111yescharacteristic
353C8—21no—
354C8—21no—
355C8#6700312yes—
356C8#41×D1112yes—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22C22×#432311yescharacteristic
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—81no—
369C4—81no—
370C4—81no—
371C4—882no—
372C4—882no—
373C4#1062280812yes—
374C4C2×#6700311yescharacteristic
375C4#1062336311yescharacteristic
376C2—41no—
377C2—161no—
378C2#1307919111yescharacteristic
379C2C2×#1062280811yescharacteristic
380C2#1308175011yescharacteristic
subgroupG/H
centerC2×C4C2×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3168C2
socleC22×C11C22×D8
prime radicalC11×#466C22
hypercenter#3168D11
hypocenterC11#33738
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13079202C2semidirect
2. #13070903C2semidirect
3. #13070888C2semidirect
4. #13070863C2semidirect
5. #13070852C2semidirect
7. #13070722C2semidirect
8. C4×#66893C2semidirect
9. C4×#66891C2semidirect
10. C4×#66876C2semidirect
326. C11#33738semidirect

Maximal subgroups

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

subgroupindex
#130792022
#130709032
#130708882
#130708632
#130708522
#130707272
#130707222
C4×#668932
C4×#668912
C4×#668762
C11×#31682
#3373811