Finite Group Databasebeta

← #14911494

Subgroups — #14911494

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#13081481C211yesmaximal, characteristic, complemented
3#13070856C212yesmaximal, complemented
4#13070839C211yesmaximal, characteristic, complemented
5#13070775C212yesmaximal, complemented
6#13070764C211yesmaximal, characteristic, complemented
7#13070649C212yesmaximal, complemented
8#13070521C211yesmaximal, characteristic, complemented
9#13070492C212yesmaximal, complemented
10C4×#66890C211yesmaximal, characteristic, complemented
11C11×#2206C211yesmaximal, characteristic, complemented
12#10623249—21no—
13#10623074—21no—
14C2×C11×D16C2212yes—
15C11×#493C2211yescharacteristic
16C4×C11×D8C2211yescharacteristic
17#10622764C2212yes—
18#10622763—22no—
19D8×Dic11C2212yes—
20D8×Dic11C2212yes—
21C2×#66890C2211yescharacteristic
22#10622685—21no—
23#10622621—21no—
24#10622491C2212yes—
25#10622379—22no—
26C4×D88C2211yescharacteristic
27#10622295C2211yescharacteristic
28C8×Dic22C2211yescharacteristic
29C11×C4⋊C16C2211yescharacteristic
30C11×#357C2212yes—
31#10622200C2212yes—
32#10622200C2212yes—
33#10622200C2211yescharacteristic
34#10622147C2212yes—
35#10622143C2212yes—
36#10622140C2212yes—
37Dic11⋊C16C2212yes—
38#10622129C2211yescharacteristic
39#10622127C2211yescharacteristic
40C4×C11⋊C16C2211yescharacteristic
41C2×#4341—41no—
42C2×C11×D8—21no—
43C2×C11×D8C2312yes—
44C2×C11×D8C2311yescharacteristic
45C11×#127—21no—
46C4×D4×C11—21no—
47#66993—22no—
48#66992—42no—
49#66991—41no—
50D4×Dic11—22no—
51D4×Dic11—22no—
52C2×#4323—22no—
53C2×C4⋊Dic11—41no—
54#66977—41no—
55C2×D88C2311yescharacteristic
56#66943—22no—
57#66931—42no—
58C4×D44—21no—
59#66922—21no—
60C4×Dic22D411yescharacteristic
61C11×D16—24no—
62C2×C11×C16C2312yes—
63C11×#107C2311yescharacteristic
64C11×#102—21no—
65C4×C8×C11C2311yescharacteristic
66#66896—22no—
67#66896—22no—
68#66890—22no—
69#66885—21no—
70#66882—21no—
71#66882C2312yes—
72#66882C2311yescharacteristic
73Dic11⋊C8D412yes—
74C8×Dic11C2312yes—
75C2×C11⋊C16C2311yescharacteristic
76C2×C11⋊C16C2311yescharacteristic
77#66872—22no—
78C4⋊(C11⋊C8)D411yescharacteristic
79#33933—111nomaximal, Sylow
80C2×D4×C11—21no—
81C2×D4×C11—22no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C22×C4×C11—41no—
85C2×C22⋊D11—42no—
86C2×C22⋊D11—42no—
87C22×Dic11—42no—
88C22×Dic11—42no—
89#4341—84no—
90C2×D44—21no—
91C2×C4×D11—41no—
92C2×Dic22—41no—
93C2×Dic22D811yescharacteristic
94C11×D8—21no—
95C11×D8—22no—
96C11×D8—22no—
97C11×D8—81no—
98C11×D8#4112yescomplemented
99C2×C8×C11C2×D411yescharacteristic
100C2×C8×C11C2411yescharacteristic
101C11×C4⋊C4—21no—
102C11×C22⋊C4—41no—
103C42×C11C2×D411yescharacteristic
104C22⋊Dic11—42no—
105C22⋊Dic11—42no—
106#4323—82no—
107(C2×D11)⋊C4—41no—
108C4⋊Dic11—22no—
109C4⋊Dic11—21no—
110C4⋊Dic11—42no—
111C4⋊Dic11—41no—
112C4⋊Dic11D811yescharacteristic
113Dic11⋊C4—42no—
114Dic11⋊C4D812yes—
115C4×Dic11C2×D412yes—
116C2×C11⋊C8C2×D412yes—
117D88—21no—
118D88—21no—
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#2226—111no—
128#2206—112no—
129#2206D1111yescharacteristic, complemented
130#2183—111no—
131#2177—112no—
132C4×D16—111no—
133C23×C11—41no—
134C23×C11—42no—
135C22×D11—41no—
136D4×C11—22no—
137D4×C11—42no—
138D4×C11—41no—
139D4×C11—42no—
140D4×C11—82no—
141D4×C11—161no—
142C2×C4×C11—41no—
143C2×C4×C11—82no—
144C2×C4×C11C2×D811yescharacteristic
145C2×C4×C11C2×D811yescharacteristic
146C2×C4×C11C22×D411yescharacteristic
147C22⋊D11—84no—
148C22⋊D11—162no—
149C2×Dic11—42no—
150C2×Dic11—41no—
151C2×Dic11—84no—
152C2×Dic11—162no—
153C2×Dic11C2×D812yes—
154C2×Dic11C2×D812yes—
155D44—41no—
156D44—41no—
157C4×D11—82no—
158Dic22—22no—
159Dic22—161no—
160C8×C11—21no—
161C8×C11C2×#4111yescharacteristic
162C8×C112−1+411yescharacteristic
163C11⋊C8—22no—
164#554—221no—
165#550—221no—
166C2×D16—111no—
167C2×D16C2×D1112yes—
168#500—111no—
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×D8C2×D1111yescharacteristic
181#367—112no—
182#366—111no—
183C4⋊C16—112no—
184C4⋊C16C2×D1111yescharacteristic
185#357—111no—
186#357—112no—
187#357—112no—
188#357—112no—
189#357—111no—
190#357C2×D1112yes—
191#346—112no—
192C4×C16—111no—
193C22×C11—42no—
194C22×C11—81no—
195C22×C11—81no—
196C22×C11—82no—
197C22×C11—82no—
198C22×C11—82no—
199C22×C11C22×D811yescharacteristic
200C2×D11—81no—
201C2×D11—81no—
202C2×D11—81no—
203C4×C11—21no—
204C4×C11—81no—
205C4×C11#50912yes—
206C4×C11#54811yescharacteristic
207C4×C11#57711yescharacteristic
208Dic11—22no—
209Dic11—22no—
210Dic11—81no—
211Dic11—82no—
212C2×#41—441no—
213C2×D8—21no—
214C2×D8—111no—
215C2×D8—222no—
216C2×D8C22×D1112yes—
217C2×D8C22×D1111yescharacteristic
218C4⋊Q8—221no—
219#127—21no—
220#127—222no—
221#125—222no—
222C22⋊Q8—442no—
223C22⋊Q8—441no—
224#121—441no—
225#121—442no—
226C4×Q8—111no—
227C4×D4—21no—
228C4×D4—222no—
229C4×D4—222no—
230C4×D4—221no—
231C2×C4⋊C4—441no—
232D16—24no—
233D16—222no—
234C2×C16—111no—
235C2×C16—111no—
236C2×C16C22×D1112yes—
237#107—112no—
238#107—111no—
239#107—221no—
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—82no—
251C2×C11—162no—
252C2×C11#335811yescharacteristic
253C2×C11C2×#50911yescharacteristic
254C2×C11#341511yescharacteristic
255D11—161no—
256#41—884no—
257C2×Q8—111no—
258C2×Q8—441no—
259C2×D4—21no—
260C2×D4—22no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4—221no—
264C2×D4—442no—
265C2×D4—442no—
266C22×C4—41no—
267C22×C4—442no—
268C22×C4—442no—
269C22×C4—441no—
270D8—22no—
271D8—21no—
272D8—22no—
273D8—81no—
274D8—221no—
275D8—221no—
276D8—882no—
277D8#434112yescomplemented
278C2×C8—112no—
279C2×C8D4×D1111yescharacteristic
280C2×C8C23×D1111yescharacteristic
281C4⋊C4—21no—
282C4⋊C4—111no—
283C4⋊C4—112no—
284C4⋊C4—221no—
285C4⋊C4—222no—
286C4⋊C4—442no—
287C4⋊C4—442no—
288C4⋊C4—441no—
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—42no—
301C23—441no—
302Q8—222no—
303Q8—1761no—
304D4—22no—
305D4—41no—
306D4—42no—
307D4—42no—
308D4—82no—
309D4—161no—
310D4—441no—
311D4—441no—
312D4—884no—
313D4—1762no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4—112no—
317C2×C4—112no—
318C2×C4—441no—
319C2×C4—442no—
320C2×C4—884no—
321C2×C4—882no—
322C2×C4—1762no—
323C2×C4D8×D1111yescharacteristic
324C2×C4D8×D1111yescharacteristic
325C2×C4C2×D4×D1111yescharacteristic
326C8—21no—
327C8—222no—
328C8C2×#434111yescharacteristic
329C8#6704311yescharacteristic
330C22—42no—
331C22—81no—
332C22—81no—
333C22—82no—
334C22—82no—
335C22—82no—
336C22—881no—
337C22—881no—
338C22—881no—
339C22C2×D8×D1111yescharacteristic
340C4—21no—
341C4—81no—
342C4—222no—
343C4—222no—
344C4—881no—
345C4—882no—
346C4#1062252412yes—
347C4#1062312911yescharacteristic
348C4#1062330611yescharacteristic
349C2—82no—
350C2—162no—
351C2—1761no—
352C2#1308124611yescharacteristic
353C2C2×#1062252411yescharacteristic
354C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2206C2
socleC22×C11C22×D8
hypercenter#2206D11
hypocenterC11#33933
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #13081589C2semidirect
2. #13081481C2semidirect
3. #13070856C2semidirect
4. #13070839C2semidirect
5. #13070775C2semidirect
6. #13070764C2semidirect
7. #13070649C2semidirect
8. #13070521C2semidirect
9. #13070492C2semidirect
10. C4×#66890C2semidirect
11. C11×#2206C2semidirect
98. C11×D8#41semidirect
129. #2206D11semidirect
277. D8#4341semidirect
298. C11#33933semidirect

Maximal subgroups

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

subgroupindex
#130815892
#130814812
#130708562
#130708392
#130707752
#130707642
#130706492
#130705212
#130704922
C4×#668902
C11×#22062
#3393311