Finite Group Databasebeta

← #14908515

Subgroups — #14908515

Order 2816.

524 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079128C211yesmaximal, characteristic, complemented
2C2×#10622508C211yesmaximal, characteristic
3#13070791C214yesmaximal, complemented
4#13070786C214yesmaximal, complemented
5#13070390C211yesmaximal, characteristic, complemented
6C2×#10622149C211yesmaximal, characteristic, complemented
7#13070353C211yesmaximal, characteristic
8#13070351C211yesmaximal, characteristic
9C11×#2155C211yesmaximal, characteristic, complemented
10C2×#66960—21no—
11C2×#66957C2211yescharacteristic
12#10623048—21no—
13C2×C11×M32C2211yescharacteristic
14C2×C11×#108C2211yescharacteristic
15C11×#427C2211yescharacteristic
16C2×#66889—21no—
17#10622719C2211yescharacteristic
18C2×C8×Dic11C2211yescharacteristic
19C2×#66876C2211yescharacteristic
20#10622611—21no—
21#10622508—21no—
22#10622508—21no—
23#10622508C2212yes—
24#10622508C2212yes—
25#10622491—21no—
26#10622487—21no—
27#10622471C2212yescomplemented
28#10622468C2212yescomplemented
29C11×#365C2214yescomplemented
30#10622156C2214yes—
31#10622149C2212yescomplemented
32#10622149C2212yescomplemented
33#10622132C2214yescomplemented
34#10622126C2214yes—
35C2×#4339—21no—
36C2×C11×M16—21no—
37C22×C8×C11C2311yescharacteristic
38C11×#117—21no—
39#66979—21no—
40C2×C4×Dic11D411yescharacteristic
41C22×C11⋊C8D411yescharacteristic
42#66960—22no—
43#66960—22no—
44#66960—41no—
45#66960—41no—
46C2×Dic44Q811yescharacteristic, complemented
47#66957—21no—
48#66957—21no—
49#66957Q812yescomplemented
50#66957C2312yes—
51C2×D88Q811yescharacteristic, complemented
52C2×#4314—21no—
53C2×#4313—41no—
54C2×C8×D11—41no—
55#66943—22no—
56#66941—22no—
57#66931—42no—
58C4×Dic22—42no—
59C11×M32—21no—
60C11×M32C2312yes—
61C2×C11×C16—21no—
62C11×#108—21no—
63C11×#108C2312yes—
64C11×#107—21no—
65C11×#106C2312yes—
66#66889—22no—
67#66889—22no—
68#66882—21no—
69#66881C2312yes—
70C8×Dic11D411yescharacteristic
71C8×Dic11D411yescharacteristic
72C8×Dic11C2311yescharacteristic
73C8×Dic11C2311yescharacteristic
74#66876—21no—
75#66876C2312yes—
76C2×C11⋊C16—21no—
77#66872—22no—
78#66871—22no—
79#33637—111nomaximal, Sylow
80C22×C4×C11C2×D411yescharacteristic
81C2×C22⋊D11—41no—
82C22×Dic11—21no—
83#4339—22no—
84#4339—22no—
85#4339—41no—
86#4339—41no—
87C2×D44—21no—
88C2×C4×D11—41no—
89C2×Dic22—21no—
90C2×Dic22—42no—
91C11×M16—22no—
92C11×M16—41no—
93C2×C8×C11—41no—
94C2×C8×C11C2×D411yescharacteristic
95C2×C8×C11C2×Q811yescharacteristic
96C2×C8×C11C2×Q811yescharacteristic
97C2×C8×C11#4111yescharacteristic
98C2×C8×C11#4111yescharacteristic
99C2×C8×C11C2411yescharacteristic
100C11×C4⋊C4—22no—
101C11×C22⋊C4—41no—
102C42×C11—41no—
103C22⋊Dic11—41no—
104C4⋊Dic11—22no—
105C4⋊Dic11—42no—
106Dic11⋊C4—42no—
107Dic11⋊C4—42no—
108C4×Dic11—21no—
109C4×Dic11—41no—
110C4×Dic11C2×D411yescharacteristic
111C4×Dic11C2×D411yescharacteristic
112C2×C11⋊C8SD1611yescharacteristic
113C2×C11⋊C8SD1611yescharacteristic
114C2×C11⋊C8SD1611yescharacteristic
115C2×C11⋊C8SD1611yescharacteristic
116C2×C11⋊C8C2×D411yescharacteristic
117C2×C11⋊C8C2×D411yescharacteristic
118Dic44—21no—
119Dic44C2×Q812yes—
120D88—21no—
121D88C2×Q812yes—
122#4314—22no—
123#4314—22no—
124#4313—42no—
125#4313—42no—
126C8×D11—42no—
127C8×D11—42no—
128C11×C16—22no—
129C11⋊C16—22no—
130#3160—111no—
131C2×#443—111no—
132#2231—114no—
133#2230—114no—
134#2155—111no—
135#2155D1111yescharacteristic, complemented
136C2×#364—111no—
137#2145—111no—
138#2145—111no—
139C23×C11AGL(1,ℤ/8)11yescharacteristic
140C22×D11—41no—
141C2×C4×C11—42no—
142C2×C4×C11C22⋊Q811yescharacteristic
143C2×C4×C11C22⋊Q811yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11C2×SD1611yescharacteristic
146C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C11C22×D411yescharacteristic
148C22⋊D11—42no—
149C22⋊D11—42no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—42no—
153C2×Dic11—41no—
154C2×Dic11—42no—
155D44—22no—
156D44—41no—
157C4×D11—42no—
158C4×D11—42no—
159Dic22—22no—
160Dic22—41no—
161Dic22—84no—
162C8×C11—42no—
163C8×C11C22⋊Q811yescharacteristic
164C8×C11C22⋊Q811yescharacteristic
165C8×C11C22×Q811yescharacteristic
166C8×C11C2×#4111yescharacteristic
167C11⋊C8C2×SD1611yescharacteristic
168C11⋊C8C2×SD1611yescharacteristic
169C11⋊C8C2×SD1611yescharacteristic
170C11⋊C8C2×SD1611yescharacteristic
171C2×#135—111no—
172C2×#131—221no—
173#533—221no—
174C2×M32—111no—
175C2×M32C2×D1111yescharacteristic
176#500—221no—
177#499—112no—
178#499—221no—
179#498—112no—
180#443—112no—
181#443—112no—
182#443—221no—
183#443—221no—
184C2×#108C2×D1111yescharacteristic
185#427—111no—
186#427—221no—
187#427C2×D1111yescharacteristic
188C2×#104—221no—
189C2×C4×C8—111no—
190#365—114no—
191#365C2×D1114yescomplemented
192#364—112no—
193#364—112no—
194#360—114no—
195#360—114no—
196C22×C11—41no—
197C22×C11#47611yescharacteristic
198C22×C11#47611yescharacteristic
199C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
200C2×D11—42no—
201C2×D11—82no—
202C4×C11—82no—
203C4×C11#47611yescharacteristic
204C4×C11#47611yescharacteristic
205C4×C11C2×C22⋊Q811yescharacteristic
206C4×C11C22×SD1611yescharacteristic
207Dic11—22no—
208Dic11—41no—
209Dic11—42no—
210Dic11—82no—
211C2×#41—221no—
212#135—112no—
213#135—112no—
214#135—221no—
215#135—221no—
216C2×Q16—111no—
217C2×SD16—221no—
218C2×D8—111no—
219#131—222no—
220#131—222no—
221#131—441no—
222#131—441no—
223C2×M16—21no—
224C2×M16—441no—
225C22×C8—111no—
226C22×C8—441no—
227C22×C8C22×D1111yescharacteristic
228C4⋊Q8—222no—
229#125—222no—
230C22⋊Q8—442no—
231C4×Q8—442no—
232#117—21no—
233#117—221no—
234C2×C42—111no—
235M32—21no—
236M32—112no—
237M32—221no—
238M32C22×D1112yes—
239C2×C16—21no—
240C2×C16—221no—
241#108—21no—
242#108C22×D1112yes—
243#107—21no—
244#107—222no—
245#107—221no—
246#106—112no—
247#106—222no—
248#106C22×D1112yes—
249#104—222no—
250#104—222no—
251C4×C8—111no—
252C4×C8—111no—
253C4×C8—111no—
254C4×C8—111no—
255C2×C11—21no—
256C2×C11—21no—
257C2×C11—21no—
258C2×C11C2×#47611yescharacteristic
259D11—82no—
260#41—222no—
261#41—222no—
262#41—441no—
263#41—441no—
264C2×Q8—221no—
265C2×Q8—442no—
266C2×D4—221no—
267C2×D4—441no—
268C22×C4—221no—
269C22×C4—441no—
270C22×C4D4×D1111yescharacteristic
271Q16—112no—
272Q16—221no—
273SD16—222no—
274SD16—222no—
275D8—112no—
276D8—221no—
277M16—22no—
278M16—41no—
279M16—442no—
280M16—442no—
281C2×C8—41no—
282C2×C8—111no—
283C2×C8—111no—
284C2×C8—111no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8—111no—
288C2×C8—442no—
289C2×C8—442no—
290C2×C8#433911yescharacteristic
291C2×C8#433911yescharacteristic
292C2×C8D4×D1111yescharacteristic
293C2×C8Q8×D1111yescharacteristic
294C2×C8Q8×D1111yescharacteristic
295C2×C8C23×D1111yescharacteristic
296C4⋊C4—22no—
297C4⋊C4—222no—
298C4⋊C4—442no—
299C4⋊C4—442no—
300C4⋊C4—442no—
301C22⋊C4—41no—
302C22⋊C4—441no—
303C42—41no—
304C42—111no—
305C42—111no—
306C42—221no—
307C42—441no—
308C16—22no—
309C16—222no—
310C11#3363711yescharacteristic, complemented, Sylow
311C23—441no—
312C23#6696711yescharacteristic
313Q8—222no—
314Q8—441no—
315Q8—884no—
316D4—222no—
317D4—442no—
318D4—442no—
319D4—441no—
320C2×C4—42no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—442no—
324C2×C4—441no—
325C2×C4—442no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4#6694911yescharacteristic
329C2×C4#6694911yescharacteristic
330C2×C4SD16×D1111yescharacteristic
331C2×C4SD16×D1111yescharacteristic
332C2×C4#6696711yescharacteristic
333C2×C4C2×D4×D1111yescharacteristic
334C8—42no—
335C8—111no—
336C8—111no—
337C8—111no—
338C8—111no—
339C8#6694911yescharacteristic
340C8#6694911yescharacteristic
341C8C2×#433911yescharacteristic
342C8C2×Q8×D1111yescharacteristic
343C22—41no—
344C22—442no—
345C22—882no—
346C22#1062248311yescharacteristic
347C22#1062248311yescharacteristic
348C22C2×#6696711yescharacteristic
349C4—82no—
350C4—222no—
351C4—441no—
352C4—442no—
353C4—882no—
354C4#1062248311yescharacteristic
355C4#1062248311yescharacteristic
356C4C2×#6694911yescharacteristic
357C4C2×SD16×D1111yescharacteristic
358C2—21no—
359C2—21no—
360C2—21no—
361C2—882no—
362C2C2×#1062248311yescharacteristic
subgroupG/H
centerC4#10622483
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2155C2
socleC2×C11C2×#476
prime radicalC2×#66957C22
hypercenter#2155D11
hypocenterC11#33637
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2155

Complements

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

NH ≅ G/Ntype
1. #13079128C2semidirect
3. #13070791C2semidirect
4. #13070786C2semidirect
5. #13070390C2semidirect
6. C2×#10622149C2semidirect
9. C11×#2155C2semidirect
27. #10622471C22semidirect
28. #10622468C22semidirect
29. C11×#365C22semidirect
31. #10622149C22semidirect
32. #10622149C22semidirect
33. #10622132C22semidirect
46. C2×Dic44Q8semidirect
49. #66957Q8semidirect
51. C2×D88Q8semidirect
135. #2155D11semidirect
191. #365C2×D11semidirect
310. C11#33637semidirect

Maximal subgroups

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

subgroupindex
#130791282
C2×#106225082
#130707912
#130707862
#130703902
C2×#106221492
#130703532
#130703512
C11×#21552
#3363711