Finite Group Databasebeta

← #14911486

Subgroups — #14911486

Order 2816.

532 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#13081484C211yesmaximal, characteristic, complemented
2#13070857C212yesmaximal, complemented
3#13070839C211yesmaximal, characteristic, complemented
4#13070773C212yesmaximal, complemented
5#13070763C211yesmaximal, characteristic, complemented
6#13070648C212yesmaximal, complemented
7#13070648C211yesmaximal, characteristic, complemented
8#13070525C211yesmaximal, characteristic, complemented
9#13070490C212yesmaximal, complemented
10C4×#66890C211yesmaximal, characteristic, complemented
11C11×#3391C211yesmaximal, characteristic, complemented
12C11×#550—21no—
13#10623110—21no—
14C11×#493C2212yes—
15C11×#493C2211yescharacteristic
16C11×#459—21no—
17C11×#459—22no—
18C8×Q8×C11C2211yescharacteristic
19C4×C11×D8C2211yescharacteristic
20C4×C11×D8C2212yes—
21C2×#66890C2211yescharacteristic
22C2×#66890C2212yes—
23#10622460—22no—
24#10622455—21no—
25C4×D88C2211yescharacteristic
26C4×D88C2212yes—
27#10622296C2212yes—
28#10622295C2211yescharacteristic
29#10622200C2211yescharacteristic
30#10622200C2212yes—
31#10622200C2212yes—
32#10622200C2212yes—
33#10622200C2212yes—
34#10622129C2211yescharacteristic
35#10622128C2212yes—
36#10622127C2211yescharacteristic
37C4⋊(C11⋊C16)C2211yescharacteristic
38C4⋊(C11⋊C16)C2212yes—
39#10622099C2212yes—
40C4×C11⋊C16C2211yescharacteristic
41C2×C11×#41—41no—
42C2×C11×D8—22no—
43C2×C11×D8—21no—
44C2×C11×D8C2311yescharacteristic
45C2×C11×D8C2312yes—
46C11×#127—21no—
47C11×#127—22no—
48C11×#121—41no—
49C11×#121—42no—
50C4×Q8×C11D411yescharacteristic
51C4×D4×C11—21no—
52C4×D4×C11—22no—
53#66999—41no—
54C2×D88C2311yescharacteristic
55#66949—42no—
56C4⋊C4×D11—41no—
57C4×D44—21no—
58C4×D44—22no—
59#66923—22no—
60#66922—21no—
61C11×#107C2311yescharacteristic
62C11×C4⋊C8D411yescharacteristic
63C11×C4⋊C8D412yes—
64C11×#102—22no—
65C11×#102—21no—
66C4×C8×C11C2311yescharacteristic
67C4×C8×C11C2312yes—
68#66890—22no—
69#66890—24no—
70#66885—22no—
71#66885—21no—
72#66882—21no—
73#66882C2312yes—
74#66882C2311yescharacteristic
75#66881—22no—
76C2×C11⋊C16C2311yescharacteristic
77C2×C11⋊C16C2312yes—
78C2×C11⋊C16C2311yescharacteristic
79#33933—111nomaximal, Sylow
80C11×#41—84no—
81C2×Q8×C11D811yescharacteristic
82C2×D4×C11—22no—
83C2×D4×C11—21no—
84C2×D4×C11—42no—
85C2×D4×C11—41no—
86C2×D4×C11—42no—
87C2×D4×C11—41no—
88C22×C4×C11—42no—
89C22×C4×C11—41no—
90C2×D44—21no—
91C2×C4×D11—41no—
92C2×C4×D11—42no—
93C2×Dic22—41no—
94C11×D8—21no—
95C11×D8—22no—
96C11×D8—21no—
97C11×D8—22no—
98C11×D8—82no—
99C11×D8—81no—
100C2×C8×C11C2×D412yes—
101C2×C8×C11C2×D411yescharacteristic
102C2×C8×C11C2411yescharacteristic
103C11×C4⋊C4—21no—
104C11×C4⋊C4D811yescharacteristic
105C11×C4⋊C4D812yes—
106C11×C22⋊C4—42no—
107C11×C22⋊C4—41no—
108C42×C11C2×D411yescharacteristic
109C42×C11C2×D412yes—
110(C2×D11)⋊C4—41no—
111(C2×D11)⋊C4—42no—
112C4⋊Dic11—21no—
113C4⋊Dic11—22no—
114C4⋊Dic11—41no—
115Dic11⋊C4—42no—
116Dic11⋊C4—42no—
117D88—21no—
118D88#4112yescomplemented
119C11⋊C16—21no—
120C11⋊C16—22no—
121C11⋊C16—21no—
122#3391D1111yescharacteristic, complemented
123#3380—111no—
124#2244—112no—
125#2240—111no—
126#2228—112no—
127#2226—111no—
128#2206—112no—
129#2206—111no—
130#2183—111no—
131#2177—112no—
132C4×D16—111no—
133C23×C11—42no—
134C23×C11—41no—
135C22×D11—41no—
136Q8×C11—22no—
137D4×C11—41no—
138D4×C11—42no—
139D4×C11—41no—
140D4×C11—42no—
141D4×C11—84no—
142D4×C11—82no—
143D4×C11—161no—
144D4×C11—162no—
145C2×C4×C11—41no—
146C2×C4×C11—84no—
147C2×C4×C11—82no—
148C2×C4×C11C2×D812yes—
149C2×C4×C11C2×D812yes—
150C2×C4×C11C2×D811yescharacteristic
151C2×C4×C11C2×D811yescharacteristic
152C2×C4×C11C22×D411yescharacteristic
153C2×Dic11—41no—
154C2×Dic11—42no—
155D44—22no—
156D44—41no—
157C4×D11—82no—
158C4×D11—162no—
159Dic22—161no—
160C8×C11—22no—
161C8×C11—21no—
162C8×C11C2×#4111yescharacteristic
163C8×C112−1+411yescharacteristic
164#554—221no—
165#550—21no—
166C2×D16—111no—
167C2×D16—112no—
168#500—111no—
169#499—112no—
170#493C2×D1111yescharacteristic
171#493C2×D1112yes—
172#478—222no—
173#476—221no—
174#459—21no—
175#459—22no—
176C8×Q8C2×D1111yescharacteristic
177C4×D8—111no—
178C4×D8—112no—
179C4×D8C2×D1111yescharacteristic
180C4×D8C2×D1112yes—
181#367—112no—
182#366—111no—
183C4⋊C16—111no—
184C4⋊C16—112no—
185#357—111no—
186#357—112no—
187#357—112no—
188#357—112no—
189#357—112no—
190#357—111no—
191#346—112no—
192C4×C16—111no—
193C22×C11—82no—
194C22×C11—81no—
195C22×C11—82no—
196C22×C11—81no—
197C22×C11—82no—
198C22×C11—81no—
199C22×C11C22×D811yescharacteristic
200C2×D11—42no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—22no—
204C4×C11—21no—
205C4×C11—22no—
206C4×C11—81no—
207C4×C11#50912yes—
208C4×C11#54811yescharacteristic
209C4×C11#57711yescharacteristic
210Dic11—81no—
211Dic11—82no—
212C2×#41—41no—
213C2×D8—22no—
214C2×D8—21no—
215C2×D8—111no—
216C2×D8C22×D1111yescharacteristic
217C2×D8C22×D1112yes—
218C4⋊Q8—221no—
219#127—22no—
220#127—21no—
221#125—222no—
222C22⋊Q8—441no—
223C22⋊Q8—442no—
224#121—41no—
225#121—42no—
226C4×Q8C22⋊D1111yescharacteristic
227C4×D4—22no—
228C4×D4—21no—
229C4×D4—221no—
230C4×D4—222no—
231C2×C4⋊C4—441no—
232D16—222no—
233D16—224no—
234C2×C16—111no—
235C2×C16—111no—
236C2×C16—112no—
237#107—111no—
238#107—112no—
239#107—221no—
240#107C22×D1111yescharacteristic
241#106—222no—
242C4⋊C8C22⋊D1111yescharacteristic
243C4⋊C8C22⋊D1112yes—
244#102—22no—
245#102—21no—
246#102—222no—
247#102—221no—
248C4×C8C22×D1111yescharacteristic
249C4×C8C22×D1112yes—
250C2×C11—162no—
251C2×C11—161no—
252C2×C11#335811yescharacteristic
253C2×C11C2×#50911yescharacteristic
254C2×C11#341511yescharacteristic
255D11—82no—
256#41—84no—
257C2×Q8—441no—
258C2×Q8#432311yescharacteristic
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—42no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—221no—
266C22×C4—42no—
267C22×C4—41no—
268C22×C4—441no—
269C22×C4—442no—
270D8—21no—
271D8—22no—
272D8—21no—
273D8—22no—
274D8—82no—
275D8—81no—
276D8—112no—
277D8—221no—
278C2×C8C2×C22⋊D1112yes—
279C2×C8C2×C22⋊D1111yescharacteristic
280C2×C8C23×D1111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—221no—
283C4⋊C4—222no—
284C4⋊C4—442no—
285C4⋊C4—441no—
286C4⋊C4—442no—
287C4⋊C4#432311yescharacteristic
288C4⋊C4#432312yes—
289C22⋊C4—41no—
290C22⋊C4—42no—
291C22⋊C4—441no—
292C22⋊C4—442no—
293C42C2×C22⋊D1112yes—
294C42C2×C22⋊D1111yescharacteristic
295C16—221no—
296C16—222no—
297C16—221no—
298C11#3393311yescharacteristic, complemented, Sylow
299C23—42no—
300C23—41no—
301C23—441no—
302Q8—22no—
303Q8—1761no—
304D4—41no—
305D4—42no—
306D4—41no—
307D4—42no—
308D4—84no—
309D4—82no—
310D4—162no—
311D4—161no—
312D4—222no—
313D4—441no—
314C2×C4—41no—
315C2×C4—84no—
316C2×C4—82no—
317C2×C4—441no—
318C2×C4—442no—
319C2×C4—882no—
320C2×C4—1762no—
321C2×C4C2×#432311yescharacteristic
322C2×C4C2×#432312yes—
323C2×C4C2×#432312yes—
324C2×C4C2×#432311yescharacteristic
325C2×C4C22×C22⋊D1111yescharacteristic
326C8—22no—
327C8—21no—
328C8#41×D1111yescharacteristic
329C8#6704311yescharacteristic
330C22—82no—
331C22—81no—
332C22—81no—
333C22—82no—
334C22—82no—
335C22—81no—
336C22—442no—
337C22—881no—
338C22—881no—
339C22C22×#432311yescharacteristic
340C4—22no—
341C4—22no—
342C4—21no—
343C4—81no—
344C4—881no—
345C4—882no—
346C4#1062276012yes—
347C4#1062336211yescharacteristic
348C4#1062336711yescharacteristic
349C2—162no—
350C2—161no—
351C2—882no—
352C2#1308124711yescharacteristic
353C2C2×#1062276011yescharacteristic
354C2#1308175511yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3391C2
socleC22×C11C22×D8
hypercenter#3391D11
hypocenterC11#33933
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8 ◁ #3391

Complements

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

NH ≅ G/Ntype
1. #13081484C2semidirect
2. #13070857C2semidirect
3. #13070839C2semidirect
4. #13070773C2semidirect
5. #13070763C2semidirect
6. #13070648C2semidirect
7. #13070648C2semidirect
8. #13070525C2semidirect
9. #13070490C2semidirect
10. C4×#66890C2semidirect
11. C11×#3391C2semidirect
118. D88#41semidirect
122. #3391D11semidirect
298. C11#33933semidirect

Maximal subgroups

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

subgroupindex
#130814842
#130708572
#130708392
#130707732
#130707632
#130706482
#130705252
#130704902
C4×#668902
C11×#33912
#3393311