Finite Group Databasebeta

← #14909110

Subgroups — #14909110

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079102C211yesmaximal, characteristic
2#13070859C212yesmaximal, complemented
3#13070855C212yesmaximal, complemented
4#13070850C212yesmaximal, complemented
5#13070841C212yesmaximal, complemented
6#13070331C211yesmaximal, characteristic, complemented
7#13070326C211yesmaximal, characteristic, complemented
8#13070321C211yesmaximal, characteristic, complemented
9C2×#10622129C211yesmaximal, characteristic, complemented
10#13070213C211yesmaximal, characteristic, complemented
11C11×#3164C211yesmaximal, characteristic, complemented
12C11×#544—21no—
13C2×#66961—21no—
14C2×#66957C2211yescharacteristic
15C22×D88C2211yescharacteristic
16#10623056—21no—
17C11×#501—22no—
18C11×#500C2212yescomplemented
19C11×#499C2212yescomplemented
20C11×#428—21no—
21C11×#427C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C11×#405C2211yescharacteristic
24C2×#66876C2211yescharacteristic
25C22×C11⋊C16C2211yescharacteristic
26#10622325—22no—
27#10622309C2212yes—
28#10622308C2212yes—
29#10622130C2211yescharacteristic, complemented
30#10622130C2212yescomplemented
31#10622130C2211yescharacteristic, complemented
32#10622129C2212yes—
33#10622129C2212yes—
34#10622129C2212yes—
35#10622129C2212yes—
36#10622129C2211yescharacteristic, complemented
37#10622129C2212yescomplemented
38#10622129C2211yescharacteristic, complemented
39#10622099C2212yescomplemented
40C4×C11⋊C16C2212yescomplemented
41C2×#4339—21no—
42C22×D44—21no—
43C2×C11×M16D411yescharacteristic
44C22×C8×C11C2311yescharacteristic
45C11×C4⋊Q8—22no—
46C11×C4⋊Q8—41no—
47C11×#125—22no—
48C11×#125—41no—
49C11×C22⋊Q8—42no—
50C11×#117—21no—
51C11×#117D411yescharacteristic
52C2×C11×C4⋊C4—21no—
53#66961—44no—
54C2×Dic44C2311yescharacteristic
55#66957—22no—
56#66957—22no—
57C2×D88—22no—
58C2×D88—22no—
59C2×D88—21no—
60C2×D88—22no—
61C2×D88C2312yes—
62C2×D88C2311yescharacteristic
63C2×#4314—21no—
64C2×#4314—22no—
65#66948—41no—
66#66948—41no—
67#66935—42no—
68#66928—22no—
69#66927—22no—
70C11×#107—22no—
71C11×#107—21no—
72C11×#107C2311yescharacteristic
73C11×#107C2312yes—
74C11×#107C2311yescharacteristic
75C11×#106—22no—
76C11×#106—21no—
77C11×#97D412yes—
78C4×C8×C11C2312yes—
79#66876—22no—
80C2×C11⋊C16—22no—
81C2×C11⋊C16C2311yescharacteristic
82C2×C11⋊C16C2312yes—
83C2×C11⋊C16C2311yescharacteristic
84#33702—111nomaximal, Sylow
85C23×D11—41no—
86C2×Q8×C11—42no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C2×C22⋊D11—41no—
90#4339—42no—
91#4339—42no—
92C2×D44—21no—
93C2×D44—22no—
94C2×D44—42no—
95C2×D44—41no—
96C2×D44—42no—
97C2×D44—42no—
98C2×D44—42no—
99C2×C4×D11—41no—
100C2×Dic22—21no—
101C11×M16SD1614yes—
102C2×C8×C11C2×D411yescharacteristic
103C2×C8×C11C2×D412yes—
104C2×C8×C11#4112yes—
105C2×C8×C11#4112yes—
106C2×C8×C11C2411yescharacteristic
107C11×C4⋊C4—21no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—21no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—42no—
112C11×C4⋊C4—42no—
113C11×C4⋊C4—42no—
114C11×C4⋊C4D811yescharacteristic
115C11×C4⋊C4D811yescharacteristic
116C11×C22⋊C4—41no—
117C11×C22⋊C4D812yes—
118C42×C11—41no—
119C42×C11C2×D412yes—
120(C2×D11)⋊C4—42no—
121(C2×D11)⋊C4—42no—
122Dic44—21no—
123Dic44—21no—
124D88—22no—
125D88—22no—
126D88—21no—
127D88—21no—
128D88—42no—
129D88—44no—
130#4314—42no—
131#4314—44no—
132C11⋊C16—21no—
133C11⋊C16—21no—
134C11⋊C16—22no—
135#3164D1111yescharacteristic, complemented
136#3155—111no—
137#2244—112no—
138#2243—112no—
139#2242—112no—
140#2240—112no—
141#2140—111no—
142#2139—111no—
143#2138—111no—
144C2×#357—111no—
145#2108—111no—
146C23×C11C2×D811yescharacteristic
147C22×D11—42no—
148C22×D11—41no—
149C22×D11—82no—
150C22×D11—161no—
151C22×D11—161no—
152Q8×C11—162no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—42no—
156C2×C4×C11—161no—
157C2×C4×C11#12412yes—
158C2×C4×C11C2×D812yes—
159C2×C4×C11C2×D812yes—
160C2×C4×C11C2×D811yescharacteristic
161C2×C4×C11C2×SD1612yes—
162C2×C4×C11C22×D411yescharacteristic
163C22⋊D11—82no—
164C2×Dic11—41no—
165D44—41no—
166D44—42no—
167D44—42no—
168D44—41no—
169D44—82no—
170D44—162no—
171D44—162no—
172C4×D11—82no—
173Dic22—41no—
174Dic22—41no—
175C8×C11#12412yes—
176C8×C11C2×SD1614yes—
177C8×C11C2×#4111yescharacteristic
178C8×C11C2×#4111yescharacteristic
179C2×AGL(1,ℤ/8)—221no—
180C2×#135—111no—
181C22×D8—111no—
182#544—21no—
183#535—221no—
184C2×M32—111no—
185C22×C16—111no—
186#501—22no—
187#500C2×D1112yescomplemented
188#499C2×D1112yescomplemented
189#496—222no—
190#495—112no—
191#493—112no—
192#428—21no—
193#427C2×D1111yescharacteristic
194C2×#107C2×D1111yescharacteristic
195#405C2×D1111yescharacteristic
196#358—111no—
197#358—111no—
198#358—112no—
199#357—112no—
200#357—112no—
201#357—111no—
202#357—111no—
203#357—112no—
204#357—112no—
205#357—112no—
206#346—112no—
207C4×C16—112no—
208C22×C11—21no—
209C22×C11—21no—
210C22×C11#48612yes—
211C22×C11C22×D811yescharacteristic
212C2×D11—82no—
213C2×D11—81no—
214C2×D11—82no—
215C2×D11—81no—
216C2×D11—82no—
217C2×D11—81no—
218C2×D11—164no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—82no—
222C4×C11—81no—
223C4×C11—81no—
224C4×C11#48612yes—
225C4×C11C2×#12411yescharacteristic
226C4×C11C22×SD1611yescharacteristic
227Dic11—81no—
228C2×#41—221no—
229C22×D4—221no—
230AGL(1,ℤ/8)—444no—
231#135—222no—
232#135—222no—
233C2×Q16—111no—
234C2×SD16—221no—
235C2×SD16—222no—
236C2×D8—112no—
237C2×D8—111no—
238C2×D8—222no—
239C2×D8—222no—
240C2×D8—221no—
241C2×D8—222no—
242C2×M16C22⋊D1111yescharacteristic
243C22×C8C22×D1111yescharacteristic
244C4⋊Q8—22no—
245C4⋊Q8—41no—
246#127—222no—
247#125—22no—
248#125—41no—
249#124—222no—
250C22⋊Q8—42no—
251#121—441no—
252#121—441no—
253#120—442no—
254#117—21no—
255#117C22⋊D1111yescharacteristic
256C2×C4⋊C4—21no—
257M32—222no—
258C2×C16—111no—
259C2×C16—112no—
260C2×C16—111no—
261C2×C16—222no—
262#107—21no—
263#107—22no—
264#107C22×D1112yes—
265#107C22×D1111yescharacteristic
266#107C22×D1111yescharacteristic
267#106—21no—
268#106—22no—
269#97C22⋊D1112yes—
270C4×C8C22×D1112yes—
271C2×C11—22no—
272C2×C11C2×#48611yescharacteristic
273C2×C11#341511yescharacteristic
274C2×C11#341611yescharacteristic
275D11—161no—
276D11—162no—
277C24—441no—
278#41—442no—
279#41—442no—
280C2×Q8—42no—
281C2×Q8—221no—
282C2×D4—222no—
283C2×D4—221no—
284C2×D4—441no—
285C2×D4—441no—
286C2×D4—442no—
287C2×D4—442no—
288C2×D4—442no—
289C2×D4—442no—
290C22×C4—41no—
291C22×C4—441no—
292C22×C4C2×C22⋊D1111yescharacteristic
293Q16—221no—
294Q16—221no—
295SD16—444no—
296SD16—442no—
297D8—222no—
298D8—222no—
299D8—221no—
300D8—221no—
301D8—444no—
302D8—442no—
303M16#432514yes—
304C2×C8#434312yes—
305C2×C8#434312yes—
306C2×C8C2×C22⋊D1112yes—
307C2×C8C2×C22⋊D1111yescharacteristic
308C2×C8C23×D1111yescharacteristic
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C4⋊C4—42no—
316C4⋊C4#432311yescharacteristic
317C4⋊C4#432311yescharacteristic
318C22⋊C4—41no—
319C22⋊C4—442no—
320C22⋊C4—442no—
321C22⋊C4#432312yes—
322C42—41no—
323C42C2×C22⋊D1112yes—
324C16—221no—
325C16—221no—
326C16—222no—
327C11#3370211yescharacteristic, complemented, Sylow
328C23—442no—
329C23—441no—
330C23—882no—
331C23—1761no—
332C23—1761no—
333C23C2×#432311yescharacteristic
334Q8—162no—
335Q8—441no—
336Q8—441no—
337D4—441no—
338D4—442no—
339D4—442no—
340D4—441no—
341D4—882no—
342D4—882no—
343D4—1762no—
344D4—1762no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—161no—
349C2×C4—441no—
350C2×C4—882no—
351C2×C4C2×#432312yes—
352C2×C4C2×#432312yes—
353C2×C4C2×#432311yescharacteristic
354C2×C4C2×#432512yes—
355C2×C4#6700012yes—
356C2×C4C22×C22⋊D1111yescharacteristic
357C8C2×#432514yes—
358C8#6700012yes—
359C8C2×#434311yescharacteristic
360C8C2×#434311yescharacteristic
361C22—21no—
362C22—21no—
363C22—881no—
364C22—882no—
365C22—881no—
366C22—882no—
367C22—881no—
368C22—882no—
369C22—1764no—
370C22#1062270112yes—
371C22C22×#432311yescharacteristic
372C4—22no—
373C4—22no—
374C4—82no—
375C4—81no—
376C4—81no—
377C4—881no—
378C4#1062270112yes—
379C4C22×#432511yescharacteristic
380C4C2×#6700011yescharacteristic
381C2—22no—
382C2—1762no—
383C2—1761no—
384C2C2×#1062270111yescharacteristic
385C2#1308175511yescharacteristic
386C2#1308176011yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3164C2
socleC22×C11C22×D8
prime radical#13079102C2
hypercenter#3164D11
hypocenterC11#33702
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3164

Complements

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

NH ≅ G/Ntype
2. #13070859C2semidirect
3. #13070855C2semidirect
4. #13070850C2semidirect
5. #13070841C2semidirect
6. #13070331C2semidirect
7. #13070326C2semidirect
8. #13070321C2semidirect
9. C2×#10622129C2semidirect
10. #13070213C2semidirect
11. C11×#3164C2semidirect
18. C11×#500C22semidirect
19. C11×#499C22semidirect
29. #10622130C22semidirect
30. #10622130C22semidirect
31. #10622130C22semidirect
36. #10622129C22semidirect
37. #10622129C22semidirect
38. #10622129C22semidirect
39. #10622099C22semidirect
40. C4×C11⋊C16C22semidirect
135. #3164D11semidirect
187. #500C2×D11semidirect
188. #499C2×D11semidirect
327. C11#33702semidirect

Maximal subgroups

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

subgroupindex
#130791022
#130708592
#130708552
#130708502
#130708412
#130703312
#130703262
#130703212
C2×#106221292
#130702132
C11×#31642
#3370211