Finite Group Databasebeta

← #14911495

Subgroups — #14911495

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#13081589C211yesmaximal, characteristic, complemented
2#13081485C211yesmaximal, characteristic, complemented
3#13070856C212yesmaximal, complemented
4#13070771C212yesmaximal, complemented
5#13070760C211yesmaximal, characteristic, complemented
6#13070650C212yesmaximal, complemented
7#13070648C211yesmaximal, characteristic, complemented
8#13070524C211yesmaximal, characteristic, complemented
9#13070489C212yesmaximal, complemented
10C4×D176C211yesmaximal, characteristic, complemented
11C11×#2240C211yesmaximal, characteristic, complemented
12#10623261—21no—
13#10623249—21no—
14C11×#500C2211yescharacteristic
15C11×#493C2211yescharacteristic
16#10622764C2212yes—
17#10622763—22no—
18D8×Dic11C2212yes—
19C2×#66890C2212yes—
20#10622697—21no—
21#10622685—21no—
22C2×D176C2211yescharacteristic
23#10622504—22no—
24#10622491C2212yes—
25#10622485C2212yes—
26C4×D88C2211yescharacteristic
27C4×D88C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×#357C2212yes—
30C11×#357C2212yes—
31C4×C11×C16C2211yescharacteristic
32#10622200C2212yes—
33#10622147C2211yescharacteristic
34#10622147C2211yescharacteristic
35#10622142C2211yescharacteristic
36#10622140C2212yes—
37Dic11⋊C16C2212yes—
38#10622129C2212yes—
39#10622128C2212yes—
40C4⋊(C11⋊C16)C2211yescharacteristic
41C2×#4341—41no—
42C2×C11×D8—21no—
43C2×C11×D8C2312yes—
44C11×C4⋊Q8—21no—
45C11×#127—21no—
46#66999—42no—
47#66993—22no—
48#66992—42no—
49#66991—41no—
50D4×Dic11—22no—
51C2×#4323—22no—
52C2×D88C2311yescharacteristic
53C2×D88C2311yescharacteristic
54#66950—41no—
55#66946—22no—
56C4⋊C4×D11—41no—
57#66943—22no—
58C4×D44—21no—
59C4×D44—21no—
60C4×Dic22D411yescharacteristic
61C2×C11×C16C2311yescharacteristic
62C2×C11×C16C2311yescharacteristic
63C11×#107—21no—
64C11×#107C2312yes—
65C4×C8×C11C2311yescharacteristic
66#66896—22no—
67#66890—24no—
68#66885—21no—
69#66885—21no—
70#66882C2311yescharacteristic
71#66882C2311yescharacteristic
72Dic11⋊C8D412yes—
73C8×Dic11C2312yes—
74C2×C11⋊C16C2312yes—
75#66873—22no—
76#66872—22no—
77C4⋊(C11⋊C8)D411yescharacteristic
78D176—22no—
79#33933—111nomaximal, Sylow
80C2×Q8×C11—41no—
81C2×D4×C11—22no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×C22⋊D11—42no—
85C2×C22⋊D11—42no—
86C22×Dic11—42no—
87#4341—84no—
88C2×D44—21no—
89C2×D44—21no—
90C2×C4×D11—42no—
91C2×C4×D11—41no—
92C2×C4×D11—41no—
93C2×Dic22D811yescharacteristic
94C11×D8—22no—
95C11×D8—22no—
96C11×D8—81no—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2411yescharacteristic
99C11×C4⋊C4—22no—
100C11×C4⋊C4—41no—
101C42×C11C2×D411yescharacteristic
102C22⋊Dic11—42no—
103#4323—82no—
104(C2×D11)⋊C4—42no—
105(C2×D11)⋊C4—41no—
106(C2×D11)⋊C4—41no—
107C4⋊Dic11—21no—
108C4⋊Dic11—21no—
109C4⋊Dic11—42no—
110C4⋊Dic11D811yescharacteristic
111Dic11⋊C4—42no—
112Dic11⋊C4D812yes—
113C4×Dic11C2×D412yes—
114C2×C11⋊C8C2×D412yes—
115D88—21no—
116D88—21no—
117D88—21no—
118D88#4112yescomplemented
119C11×C16—21no—
120C11×C16—21no—
121C11⋊C16—22no—
122#3391—111no—
123#3380—111no—
124#2244—112no—
125#2240D1111yescharacteristic, complemented
126#2228—112no—
127#2226—111no—
128#2206—111no—
129#2206—112no—
130#2183—111no—
131#2177—112no—
132C4×D16—111no—
133C23×C11—42no—
134C22×D11—41no—
135C22×D11—41no—
136Q8×C11—161no—
137D4×C11—42no—
138D4×C11—42no—
139D4×C11—82no—
140D4×C11—161no—
141C2×C4×C11—42no—
142C2×C4×C11C2×D811yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C22×D411yescharacteristic
145C22⋊D11—84no—
146C22⋊D11—162no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—84no—
150C2×Dic11C2×D812yes—
151C2×Dic11C2×D812yes—
152D44—22no—
153D44—41no—
154D44—41no—
155D44—41no—
156C4×D11—82no—
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—112no—
167C2×D16—111no—
168#500C2×D1111yescharacteristic
169#499—112no—
170#493—112no—
171#493C2×D1111yescharacteristic
172#478—222no—
173#476—221no—
174#459—221no—
175#459—222no—
176C8×Q8—111no—
177C4×D8—112no—
178C4×D8—112no—
179C4×D8—111no—
180C4×D8—111no—
181#367—112no—
182#366—111no—
183C4⋊C16—112no—
184C4⋊C16—111no—
185#357—112no—
186#357—111no—
187#357—111no—
188#357—112no—
189#357C2×D1112yes—
190#357C2×D1112yes—
191#346—112no—
192C4×C16C2×D1111yescharacteristic
193C22×C11—82no—
194C22×C11—82no—
195C22×C11—82no—
196C22×C11C22×D811yescharacteristic
197C2×D11—42no—
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—82no—
205C4×C11#50912yes—
206C4×C11#54811yescharacteristic
207C4×C11#57711yescharacteristic
208Dic11—22no—
209Dic11—22no—
210Dic11—81no—
211Dic11—81no—
212C2×#41—441no—
213C2×D8—21no—
214C2×D8—111no—
215C2×D8—111no—
216C2×D8—222no—
217C2×D8C22×D1112yes—
218C4⋊Q8—21no—
219#127—21no—
220#127—222no—
221#125—222no—
222C22⋊Q8—441no—
223C22⋊Q8—442no—
224#121—441no—
225#121—442no—
226C4×Q8—111no—
227C4×D4—222no—
228C4×D4—222no—
229C4×D4—221no—
230C4×D4—221no—
231C2×C4⋊C4—441no—
232D16—222no—
233D16—224no—
234C2×C16—112no—
235C2×C16C22×D1111yescharacteristic
236C2×C16C22×D1111yescharacteristic
237#107—21no—
238#107—111no—
239#107—111no—
240#107C22×D1112yes—
241#106—222no—
242C4⋊C8—112no—
243C4⋊C8—111no—
244#102—222no—
245#102—222no—
246#102—221no—
247#102—221no—
248C4×C8—112no—
249C4×C8C22×D1111yescharacteristic
250C2×C11—162no—
251C2×C11#335811yescharacteristic
252C2×C11C2×#50911yescharacteristic
253C2×C11#341511yescharacteristic
254D11—82no—
255D11—161no—
256#41—884no—
257C2×Q8—41no—
258C2×Q8—111no—
259C2×D4—22no—
260C2×D4—41no—
261C2×D4—41no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—442no—
265C2×D4—442no—
266C22×C4—442no—
267C22×C4—442no—
268C22×C4—441no—
269C22×C4—441no—
270D8—22no—
271D8—22no—
272D8—81no—
273D8—112no—
274D8—221no—
275D8—221no—
276D8—221no—
277D8—882no—
278C2×C8—112no—
279C2×C8D4×D1111yescharacteristic
280C2×C8C23×D1111yescharacteristic
281C4⋊C4—22no—
282C4⋊C4—41no—
283C4⋊C4—111no—
284C4⋊C4—112no—
285C4⋊C4—221no—
286C4⋊C4—221no—
287C4⋊C4—442no—
288C4⋊C4—442no—
289C22⋊C4—442no—
290C22⋊C4—442no—
291C22⋊C4—441no—
292C22⋊C4—441no—
293C42—112no—
294C42D4×D1111yescharacteristic
295C16—21no—
296C16—21no—
297C16—222no—
298C11#3393311yescharacteristic, complemented, Sylow
299C23—42no—
300C23—441no—
301C23—441no—
302Q8—161no—
303Q8—222no—
304D4—42no—
305D4—42no—
306D4—82no—
307D4—161no—
308D4—222no—
309D4—441no—
310D4—441no—
311D4—441no—
312D4—884no—
313D4—1762no—
314C2×C4—42no—
315C2×C4—112no—
316C2×C4—112no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—884no—
320C2×C4—882no—
321C2×C4—882no—
322C2×C4—1762no—
323C2×C4D8×D1111yescharacteristic
324C2×C4D8×D1111yescharacteristic
325C2×C4C2×D4×D1111yescharacteristic
326C8—21no—
327C8—222no—
328C8#41×D1111yescharacteristic
329C8#6704311yescharacteristic
330C22—82no—
331C22—82no—
332C22—82no—
333C22—442no—
334C22—881no—
335C22—881no—
336C22—881no—
337C22—881no—
338C22—881no—
339C22C2×D8×D1111yescharacteristic
340C4—21no—
341C4—82no—
342C4—222no—
343C4—222no—
344C4—881no—
345C4—881no—
346C4#1062252712yes—
347C4#1062320811yescharacteristic
348C4#1062329311yescharacteristic
349C2—162no—
350C2—882no—
351C2—1761no—
352C2#1308124811yescharacteristic
353C2C2×#1062252711yescharacteristic
354C2#1308175311yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2240C2
socleC22×C11C22×D8
hypercenter#2240D11
hypocenterC11#33933
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2240

Complements

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

NH ≅ G/Ntype
1. #13081589C2semidirect
2. #13081485C2semidirect
3. #13070856C2semidirect
4. #13070771C2semidirect
5. #13070760C2semidirect
6. #13070650C2semidirect
7. #13070648C2semidirect
8. #13070524C2semidirect
9. #13070489C2semidirect
10. C4×D176C2semidirect
11. C11×#2240C2semidirect
118. D88#41semidirect
125. #2240D11semidirect
298. C11#33933semidirect

Maximal subgroups

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

subgroupindex
#130815892
#130814852
#130708562
#130707712
#130707602
#130706502
#130706482
#130705242
#130704892
C4×D1762
C11×#22402
#3393311