Finite Group Databasebeta

← #14911489

Subgroups — #14911489

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#13081590C211yesmaximal, characteristic, complemented
2#13081485C211yesmaximal, characteristic, complemented
3#13070856C212yesmaximal, complemented
4#13070841C211yesmaximal, characteristic, complemented
5#13070772C212yesmaximal, complemented
6#13070652C211yesmaximal, characteristic, complemented
7#13070650C212yesmaximal, complemented
8#13070521C211yesmaximal, characteristic, complemented
9#13070491C212yesmaximal, complemented
10C4×#66890C211yesmaximal, characteristic, complemented
11C11×#2226C211yesmaximal, characteristic, complemented
12#10623261—21no—
13#10623084—21no—
14C11×#500C2211yescharacteristic
15C4×C11×D8C2211yescharacteristic
16#10622764C2212yes—
17C2×#66890C2211yescharacteristic
18#10622697—21no—
19#10622628—21no—
20C2×D176C2212yes—
21#10622504—22no—
22#10622491C2212yes—
23#10622485C2212yes—
24#10622485C2212yes—
25#10622399—22no—
26#10622308C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#367C2212yes—
30C11×C4⋊C16C2211yescharacteristic
31C11×#357C2212yes—
32#10622200C2211yescharacteristic
33#10622147C2212yes—
34#10622140C2212yes—
35Dic11⋊C16C2212yes—
36#10622129C2212yes—
37#10622129C2212yes—
38#10622129C2211yescharacteristic
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4339—41no—
42C2×C11×D8C2311yescharacteristic
43C11×C4⋊Q8—21no—
44C4×D4×C11—21no—
45#66999—42no—
46#66993—22no—
47C2×#4323—22no—
48#66983—41no—
49C2×D88—21no—
50C2×D88C2312yes—
51C2×D88C2311yescharacteristic
52#66950—41no—
53#66946—22no—
54#66946—22no—
55C4⋊C4×D11—41no—
56#66943—22no—
57#66937—42no—
58#66927—21no—
59C4×D44—21no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2312yes—
62C11×#107—21no—
63C11×#107C2312yes—
64C11×#107C2311yescharacteristic
65C11×#102—21no—
66C4×C8×C11C2311yescharacteristic
67#66890—22no—
68#66885—21no—
69#66882C2311yescharacteristic
70Dic11⋊C8D412yes—
71C8×Dic11C2312yes—
72C2×C11⋊C16C2311yescharacteristic
73C2×C11⋊C16C2311yescharacteristic
74#66873—22no—
75#66873—22no—
76#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78D176—24no—
79#33933—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—21no—
82C22×C4×C11—41no—
83C2×C22⋊D11—42no—
84C2×C22⋊D11—42no—
85#4339—84no—
86C2×D44—21no—
87C2×D44—22no—
88C2×D44—41no—
89C2×D44—41no—
90C2×C4×D11—42no—
91C2×C4×D11—42no—
92C2×C4×D11—41no—
93C2×Dic22D811yescharacteristic
94C11×D8—21no—
95C11×D8—21no—
96C2×C8×C11C2×D411yescharacteristic
97C2×C8×C11C2411yescharacteristic
98C11×C4⋊C4—22no—
99C11×C4⋊C4—21no—
100C11×C4⋊C4—41no—
101C11×C22⋊C4—41no—
102C42×C11C2×D411yescharacteristic
103#4323—82no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—42no—
106(C2×D11)⋊C4—41no—
107C4⋊Dic11—21no—
108C4⋊Dic11—42no—
109C4⋊Dic11D811yescharacteristic
110Dic11⋊C4—42no—
111Dic11⋊C4D812yes—
112C4×Dic11C2×D412yes—
113C2×C11⋊C8C2×D412yes—
114D88—22no—
115D88—21no—
116D88—22no—
117D88—81no—
118D88#4112yescomplemented
119C11×C16—22no—
120C11⋊C16—21no—
121C11⋊C16—21no—
122#3391—111no—
123#3380—111no—
124#2244—112no—
125#2240—111no—
126#2228—112no—
127#2226D1111yescharacteristic, complemented
128#2206—111no—
129#2206—112no—
130#2183—111no—
131#2177—112no—
132C4×D16—111no—
133C23×C11—41no—
134C22×D11—41no—
135C22×D11—42no—
136Q8×C11—161no—
137D4×C11—41no—
138D4×C11—41no—
139C2×C4×C11—42no—
140C2×C4×C11—41no—
141C2×C4×C11—82no—
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C22×D411yescharacteristic
145C22⋊D11—84no—
146C22⋊D11—162no—
147C2×Dic11—41no—
148C2×Dic11C2×D812yes—
149C2×Dic11C2×D812yes—
150D44—22no—
151D44—42no—
152D44—41no—
153D44—42no—
154D44—82no—
155D44—161no—
156C4×D11—84no—
157C4×D11—82no—
158C4×D11—162no—
159Dic22—22no—
160C8×C11—21no—
161C8×C11C2×#4111yescharacteristic
162C8×C112−1+411yescharacteristic
163C11⋊C8—22no—
164#554—221no—
165#550—221no—
166C2×D16—111no—
167C2×D16—112no—
168#500C2×D1111yescharacteristic
169#499—112no—
170#493—112no—
171#493—111no—
172#478—222no—
173#476—221no—
174#459—222no—
175#459—221no—
176C8×Q8—111no—
177C4×D8—112no—
178C4×D8—112no—
179C4×D8—111no—
180C4×D8C2×D1111yescharacteristic
181#367C2×D1112yes—
182#366—111no—
183C4⋊C16—112no—
184C4⋊C16C2×D1111yescharacteristic
185#357—111no—
186#357—112no—
187#357—111no—
188#357—112no—
189#357—112no—
190#357C2×D1112yes—
191#346—112no—
192C4×C16—111no—
193C22×C11—81no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11C22×D811yescharacteristic
197C2×D11—42no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—82no—
201C2×D11—82no—
202C2×D11—82no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11—82no—
206C4×C11#50912yes—
207C4×C11#54811yescharacteristic
208C4×C11#57711yescharacteristic
209Dic11—22no—
210Dic11—22no—
211Dic11—81no—
212C2×#41—441no—
213C2×D8—111no—
214C2×D8—112no—
215C2×D8—222no—
216C2×D8—221no—
217C2×D8C22×D1111yescharacteristic
218C4⋊Q8—21no—
219#127—222no—
220#127—221no—
221#125—222no—
222C22⋊Q8—441no—
223C22⋊Q8—442no—
224#121—442no—
225#121—441no—
226C4×Q8—111no—
227C4×D4—21no—
228C4×D4—222no—
229C4×D4—222no—
230C4×D4—221no—
231C2×C4⋊C4—441no—
232D16—224no—
233D16—222no—
234C2×C16—111no—
235C2×C16—111no—
236C2×C16C22×D1112yes—
237#107—21no—
238#107—111no—
239#107C22×D1112yes—
240#107C22×D1111yescharacteristic
241#106—222no—
242C4⋊C8—112no—
243C4⋊C8—111no—
244#102—21no—
245#102—222no—
246#102—222no—
247#102—221no—
248C4×C8—112no—
249C4×C8C22×D1111yescharacteristic
250C2×C11—161no—
251C2×C11#335811yescharacteristic
252C2×C11C2×#50911yescharacteristic
253C2×C11#341511yescharacteristic
254D11—82no—
255D11—162no—
256#41—884no—
257C2×Q8—41no—
258C2×Q8—111no—
259C2×D4—21no—
260C2×D4—221no—
261C2×D4—222no—
262C2×D4—442no—
263C2×D4—442no—
264C2×D4—441no—
265C2×D4—441no—
266C22×C4—41no—
267C22×C4—442no—
268C22×C4—442no—
269C22×C4—441no—
270D8—21no—
271D8—21no—
272D8—112no—
273D8—221no—
274D8—222no—
275D8—222no—
276D8—881no—
277D8—882no—
278C2×C8—112no—
279C2×C8D4×D1111yescharacteristic
280C2×C8C23×D1111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—22no—
283C4⋊C4—41no—
284C4⋊C4—111no—
285C4⋊C4—112no—
286C4⋊C4—221no—
287C4⋊C4—442no—
288C4⋊C4—442no—
289C22⋊C4—41no—
290C22⋊C4—442no—
291C22⋊C4—442no—
292C22⋊C4—441no—
293C42—112no—
294C42D4×D1111yescharacteristic
295C16—22no—
296C16—221no—
297C16—221no—
298C11#3393311yescharacteristic, complemented, Sylow
299C23—41no—
300C23—441no—
301C23—442no—
302Q8—161no—
303Q8—222no—
304D4—41no—
305D4—41no—
306D4—222no—
307D4—441no—
308D4—442no—
309D4—442no—
310D4—884no—
311D4—882no—
312D4—1761no—
313D4—1762no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—82no—
317C2×C4—112no—
318C2×C4—112no—
319C2×C4—441no—
320C2×C4—884no—
321C2×C4—882no—
322C2×C4—1762no—
323C2×C4D8×D1111yescharacteristic
324C2×C4D8×D1111yescharacteristic
325C2×C4C2×D4×D1111yescharacteristic
326C8—21no—
327C8—222no—
328C8#6704011yescharacteristic
329C8#41×D1111yescharacteristic
330C22—81no—
331C22—81no—
332C22—81no—
333C22—442no—
334C22—881no—
335C22—881no—
336C22—882no—
337C22—882no—
338C22—882no—
339C22C2×D8×D1111yescharacteristic
340C4—21no—
341C4—81no—
342C4—82no—
343C4—222no—
344C4—222no—
345C4—881no—
346C4#1062252712yes—
347C4#1062316411yescharacteristic
348C4#1062330911yescharacteristic
349C2—161no—
350C2—882no—
351C2—1762no—
352C2#1308125011yescharacteristic
353C2C2×#1062252711yescharacteristic
354C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2226C2
socleC22×C11C22×D8
hypercenter#2226D11
hypocenterC11#33933
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. #13081590C2semidirect
2. #13081485C2semidirect
3. #13070856C2semidirect
4. #13070841C2semidirect
5. #13070772C2semidirect
6. #13070652C2semidirect
7. #13070650C2semidirect
8. #13070521C2semidirect
9. #13070491C2semidirect
10. C4×#66890C2semidirect
11. C11×#2226C2semidirect
118. D88#41semidirect
127. #2226D11semidirect
298. C11#33933semidirect

Maximal subgroups

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

subgroupindex
#130815902
#130814852
#130708562
#130708412
#130707722
#130706522
#130706502
#130705212
#130704912
C4×#668902
C11×#22262
#3393311