Finite Group Databasebeta

← #14909360

Subgroups — #14909360

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#13079203C211yesmaximal, characteristic, complemented
2#13079183C211yesmaximal, characteristic
3#13070899C211yesmaximal, characteristic, complemented
4#13070888C211yesmaximal, characteristic, complemented
5#13070862C211yesmaximal, characteristic, complemented
6#13070728C212yesmaximal
7#13070723C212yesmaximal, complemented
8#13070472C212yesmaximal, complemented
9#13070471C212yesmaximal, complemented
10#13070209C211yesmaximal, characteristic, complemented
11C11×#2243C211yesmaximal, characteristic, complemented
12#10623259—21no—
13#10623211—21no—
14C11×#500C2211yescharacteristic
15C11×#495C2211yescharacteristic
16#10622801C2211yescharacteristic
17Q16×Dic11C2211yescharacteristic
18C2×#66893C2212yes—
19#10622784—21no—
20SD16×Dic11—21no—
21#10622770C2211yescharacteristic
22D8×Dic11C2211yescharacteristic
23C2×#66891C2212yes—
24#10622706—21no—
25#10622669—21no—
26C2×#66862C2212yes—
27#10622500—21no—
28#10622500C2212yes—
29#10622486—21no—
30#10622486C2212yes—
31#10622312C2211yescharacteristic
32C4×C8×D11C2211yescharacteristic
33#10622296C2211yescharacteristic
34C11×#358C2212yes—
35C11×#357C2212yes—
36C11×#346C2211yescharacteristic
37#10622141C2212yes—
38#10622141C2212yes—
39C16×Dic11C2212yes—
40#10622128C2212yes—
41#10622127C2212yes—
42#10622099C2211yescharacteristic
43C2×C11×Q16C2311yescharacteristic
44C2×C11×SD16—21no—
45C2×C11×D8C2311yescharacteristic
46C11×C4⋊Q8—21no—
47C11×#124—21no—
48#66999—21no—
49#66999—41no—
50Q8×Dic11—21no—
51Q8×Dic11—41no—
52#66991—21no—
53D4×Dic11—21no—
54C2×Dic44—21no—
55C2×Dic44C2312yes—
56C2×C8×D11D411yescharacteristic
57C2×C8×D11C2311yescharacteristic
58#66950—22no—
59#66945—41no—
60#66943—41no—
61#66940—22no—
62#66936—41no—
63(C22⋊D11)⋊C4—41no—
64#66932—41no—
65#66930—41no—
66C42×D11D411yescharacteristic
67#66923—21no—
68#66922—21no—
69C2×C11×C16C2312yes—
70C11×#107—21no—
71C11×#107C2312yes—
72C4×C8×C11C2311yescharacteristic
73#66899—21no—
74#66899—21no—
75#66896—21no—
76#66896—21no—
77#66893—24no—
78#66891—24no—
79#66882C2311yescharacteristic
80#66882C2311yescharacteristic
81#66881—21no—
82C8×Dic11D411yescharacteristic
83C8×Dic11C2311yescharacteristic
84C2×C11⋊C16C2312yes—
85#66874—22no—
86#66874—22no—
87C4×C11⋊C8D411yescharacteristic
88#66862—24no—
89#33738—111nomaximal, Sylow
90C2×Q8×C11—21no—
91C2×Q8×C11—41no—
92C2×D4×C11—21no—
93C2×C22⋊D11—41no—
94C22×Dic11—41no—
95C2×C4×D11D811yescharacteristic
96C2×C4×D11D811yescharacteristic
97C2×C4×D11C2×D411yescharacteristic
98C2×Dic22—22no—
99C11×Q16—22no—
100C11×SD16—42no—
101C11×D8—22no—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2411yescharacteristic
104C11×C4⋊C4—22no—
105C11×C4⋊C4—41no—
106C11×C22⋊C4—41no—
107C11×C22⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C22⋊Dic11—41no—
110C22⋊Dic11—41no—
111(C2×D11)⋊C4—41no—
112(C2×D11)⋊C4—42no—
113C4⋊Dic11—21no—
114C4⋊Dic11—21no—
115C4⋊Dic11—41no—
116C4⋊Dic11—42no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119Dic11⋊C4—41no—
120Dic11⋊C4—42no—
121Dic11⋊C4—41no—
122Dic11⋊C4—41no—
123C4×Dic11—41no—
124C4×Dic11—42no—
125C4×Dic11D811yescharacteristic
126C4×Dic11D811yescharacteristic
127C4×Dic11C2×D411yescharacteristic
128C2×C11⋊C8C2×D411yescharacteristic
129C2×C11⋊C8C2×D411yescharacteristic
130Dic44—22no—
131Dic44—22no—
132Dic44—42no—
133C8×D11—22no—
134C8×D11—22no—
135C11×C16—22no—
136C11⋊C16#4114yes—
137#3170—111no—
138#3168—111no—
139#2255—111no—
140#2251—111no—
141#2245—111no—
142#2243D1111yescharacteristic, complemented
143#2220—112no—
144#2219—112no—
145C4×Q32—112no—
146C4×SD32—112no—
147C4×M32—111no—
148C23×C11—41no—
149C22×D11C2×D811yescharacteristic
150Q8×C11—41no—
151Q8×C11—41no—
152Q8×C11—82no—
153D4×C11—41no—
154D4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—42no—
157C2×C4×C11C2×D811yescharacteristic
158C2×C4×C11C2×D811yescharacteristic
159C2×C4×C11C22×D411yescharacteristic
160C22⋊D11—82no—
161C2×Dic11—41no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—82no—
165C2×Dic11C2×D811yescharacteristic
166C2×Dic11C2×D811yescharacteristic
167C2×Dic11C2×D811yescharacteristic
168C4×D11—21no—
169C4×D11—21no—
170C4×D11—22no—
171C4×D11—41no—
172Dic22—42no—
173Dic22—42no—
174C8×C11#13512yes—
175C8×C11C2×#4112yes—
176C11⋊C8—21no—
177C11⋊C8—21no—
178#533—221no—
179#529—221no—
180C2×Q32—112no—
181C2×SD32—112no—
182C2×M32—112no—
183#500C2×D1111yescharacteristic
184#499—111no—
185#495C2×D1111yescharacteristic
186#494—111no—
187#488—221no—
188#487—221no—
189#467—111no—
190#467—112no—
191#467—221no—
192#466—111no—
193#465—221no—
194C4×Q16—111no—
195C4×Q16—112no—
196C4×Q16—221no—
197C4×SD16—221no—
198C4×D8—111no—
199C2×C4×C8—111no—
200#367—112no—
201#366—112no—
202#358—112no—
203#358—112no—
204#358C2×D1112yes—
205#357C2×D1112yes—
206#346—111no—
207#346C2×D1111yescharacteristic
208C4×C16—112no—
209C22×C11—81no—
210C22×C11—81no—
211C22×C11—81no—
212C22×C11C22×D811yescharacteristic
213C2×D11—21no—
214C2×D11—21no—
215C2×D11—21no—
216C4×C11—21no—
217C4×C11—21no—
218C4×C11—82no—
219C4×C11—81no—
220C4×C11#53211yescharacteristic
221C4×C11C2×#13511yescharacteristic
222Dic11—21no—
223Dic11—21no—
224Dic11—81no—
225Dic11—81no—
226Dic11—82no—
227Dic11#51012yes—
228C2×Q16—112no—
229C2×Q16—221no—
230C2×Q16C22×D1111yescharacteristic
231C2×SD16—21no—
232C2×D8C22×D1111yescharacteristic
233C22×C8—111no—
234C22×C8—111no—
235C4⋊Q8—21no—
236C4⋊Q8—221no—
237#126—441no—
238#125—221no—
239#125—441no—
240#124—21no—
241#123—441no—
242C22⋊Q8—222no—
243C22⋊Q8—221no—
244C22⋊Q8—441no—
245#121—221no—
246C4×Q8—222no—
247C4×Q8—221no—
248C4×Q8—441no—
249C4×D4—221no—
250C4×D4—441no—
251#117—441no—
252#117—441no—
253C2×C42—111no—
254Q32—224no—
255SD32—224no—
256M32—224no—
257C2×C16—112no—
258C2×C16C22×D1112yes—
259#107—21no—
260#107—111no—
261#107—111no—
262#107C22×D1112yes—
263#106—221no—
264#103—222no—
265#103—222no—
266#103—221no—
267#103—221no—
268#102—221no—
269#102—221no—
270C4×C8—111no—
271C4×C8—111no—
272C4×C8—111no—
273C4×C8C22×D1111yescharacteristic
274C2×C11—161no—
275C2×C11#316911yescharacteristic
276C2×C11C2×#51011yescharacteristic
277C2×C11#341411yescharacteristic
278D11—41no—
279C2×Q8—21no—
280C2×Q8—41no—
281C2×Q8—222no—
282C2×D4—21no—
283C2×D4—441no—
284C22×C4—111no—
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—441no—
288Q16—22no—
289Q16—222no—
290Q16—222no—
291Q16—442no—
292SD16—42no—
293D8—22no—
294C2×C8—111no—
295C2×C8—111no—
296C2×C8—222no—
297C2×C8—222no—
298C2×C8D4×D1111yescharacteristic
299C2×C8C23×D1111yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—221no—
303C4⋊C4—221no—
304C4⋊C4—441no—
305C4⋊C4—442no—
306C4⋊C4—441no—
307C4⋊C4—442no—
308C4⋊C4—441no—
309C4⋊C4—441no—
310C4⋊C4—441no—
311C4⋊C4—441no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—442no—
315C22⋊C4—441no—
316C22⋊C4—441no—
317C22⋊C4—441no—
318C42—111no—
319C42—111no—
320C42—111no—
321C42—441no—
322C42—442no—
323C42D4×D1111yescharacteristic
324C16—22no—
325C16—114no—
326C11#3373811yescharacteristic, complemented, Sylow
327C23—41no—
328C23—111no—
329Q8—41no—
330Q8—41no—
331Q8—82no—
332Q8—442no—
333Q8—442no—
334D4—41no—
335D4—41no—
336D4—882no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—111no—
340C2×C4—111no—
341C2×C4—111no—
342C2×C4—222no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—442no—
348C2×C4—441no—
349C2×C4—882no—
350C2×C4D8×D1111yescharacteristic
351C2×C4D8×D1111yescharacteristic
352C2×C4C2×D4×D1111yescharacteristic
353C8—221no—
354C8—221no—
355C8#6696912yes—
356C8#41×D1112yes—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—221no—
361C22—221no—
362C22—221no—
363C22C2×D8×D1111yescharacteristic
364C4—21no—
365C4—21no—
366C4—82no—
367C4—81no—
368C4—112no—
369C4—221no—
370C4—221no—
371C4—881no—
372C4—881no—
373C4—882no—
374C4#1062319911yescharacteristic
375C4C2×#6696911yescharacteristic
376C2—161no—
377C2—441no—
378C2#1307919411yescharacteristic
379C2D11×#51011yescharacteristic
380C2#1308174811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2243C2
socleC22×C11C22×D8
prime radical#10622770C22
hypercenter#2243D11
hypocenterC11#33738
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

Complements

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

NH ≅ G/Ntype
1. #13079203C2semidirect
3. #13070899C2semidirect
4. #13070888C2semidirect
5. #13070862C2semidirect
7. #13070723C2semidirect
8. #13070472C2semidirect
9. #13070471C2semidirect
10. #13070209C2semidirect
11. C11×#2243C2semidirect
142. #2243D11semidirect
326. C11#33738semidirect

Maximal subgroups

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

subgroupindex
#130792032
#130791832
#130708992
#130708882
#130708622
#130707282
#130707232
#130704722
#130704712
#130702092
C11×#22432
#3373811