Finite Group Databasebeta

← #14908513

Subgroups — #14908513

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×#10622809C211yesmaximal, characteristic
3#13070790C214yesmaximal, complemented
4#13070785C214yesmaximal, complemented
5#13070389C211yesmaximal, characteristic, complemented
6#13070388C211yesmaximal, characteristic, complemented
7C2×#10622149C211yesmaximal, characteristic, complemented
8#13070352C211yesmaximal, characteristic
9C11×#2145C211yesmaximal, characteristic
10C2×C11×#135C2211yescharacteristic
11C2×#67001—21no—
12#10623048—21no—
13C2×C11×M32C2211yescharacteristic
14C11×#427C2211yescharacteristic
15C2×#66901—21no—
16#10622809—21no—
17#10622809—21no—
18#10622809C2212yes—
19#10622809C2212yes—
20C2×#66883C2211yescharacteristic
21#10622719C2211yescharacteristic
22C2×C8×Dic11C2211yescharacteristic
23C2×#66876C2211yescharacteristic
24#10622611—21no—
25#10622491—21no—
26#10622487—21no—
27#10622471C2212yescomplemented
28#10622468C2212yescomplemented
29C11×#360C2214yes—
30#10622204C2214yes—
31#10622151C2214yescomplemented
32#10622149C2212yescomplemented
33#10622149C2212yescomplemented
34#10622125C2214yescomplemented
35C2×C11×#41—21no—
36C11×#135—21no—
37C11×#135—21no—
38C11×#135Q812yescomplemented
39C11×#135C2312yes—
40C2×C11×Q16Q811yescharacteristic, complemented
41C2×C11×SD16—21no—
42C2×C11×D8Q811yescharacteristic, complemented
43C22×C8×C11C2311yescharacteristic
44C11×#117—21no—
45#67001—22no—
46#67001—22no—
47#67001—41no—
48#67001—41no—
49#66979—21no—
50C2×C4×Dic11D411yescharacteristic
51C2×#4318—21no—
52C2×#4318—41no—
53C22×C11⋊C8—41no—
54C22×C11⋊C8D411yescharacteristic
55#66943—22no—
56#66941—22no—
57#66931—42no—
58C4×Dic22—42no—
59C11×M32—21no—
60C11×M32C2312yes—
61C2×C11×C16—21no—
62C11×#107—21no—
63C11×#106C2312yes—
64#66901—22no—
65#66901—22no—
66#66883—21no—
67#66883C2312yes—
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
80C11×#41—22no—
81C11×#41—22no—
82C11×#41—41no—
83C11×#41—41no—
84C2×Q8×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11C2×D411yescharacteristic
89C22×Dic11—21no—
90C2×Dic22—42no—
91C11×Q16—21no—
92C11×Q16C2×Q812yes—
93C11×SD16—22no—
94C11×SD16—22no—
95C11×D8—21no—
96C11×D8C2×Q812yes—
97C2×C8×C11C2×D411yescharacteristic
98C2×C8×C11C2×Q811yescharacteristic
99C2×C8×C11C2×Q811yescharacteristic
100C2×C8×C11#4111yescharacteristic
101C2×C8×C11#4111yescharacteristic
102C2×C8×C11C2411yescharacteristic
103C11×C4⋊C4—22no—
104C11×C22⋊C4—41no—
105C42×C11—41no—
106C22⋊Dic11—41no—
107C4⋊Dic11—22no—
108C4⋊Dic11—42no—
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111C4×Dic11—21no—
112C4×Dic11—41no—
113C4×Dic11C2×D411yescharacteristic
114C4×Dic11C2×D411yescharacteristic
115#4318—22no—
116#4318—42no—
117#4318—42no—
118#4318—41no—
119C2×C11⋊C8—42no—
120C2×C11⋊C8—42no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8SD1611yescharacteristic
123C2×C11⋊C8SD1611yescharacteristic
124C2×C11⋊C8SD1611yescharacteristic
125C2×C11⋊C8SD1611yescharacteristic
126C2×C11⋊C8C2×D411yescharacteristic
127C2×C11⋊C8C2×D411yescharacteristic
128C11×C16—22no—
129C11⋊C16—22no—
130#3160—111no—
131C2×#443—111no—
132#2231—114no—
133#2230—114no—
134#2155—111no—
135#2155—111no—
136C2×#364—111no—
137#2145—111no—
138#2145D1111yescharacteristic
139C23×C11—41no—
140C23×C11AGL(1,ℤ/8)11yescharacteristic
141Q8×C11—22no—
142Q8×C11—41no—
143D4×C11—22no—
144D4×C11—42no—
145D4×C11—42no—
146D4×C11—41no—
147C2×C4×C11—41no—
148C2×C4×C11—42no—
149C2×C4×C11—42no—
150C2×C4×C11—42no—
151C2×C4×C11C22⋊Q811yescharacteristic
152C2×C4×C11C22⋊Q811yescharacteristic
153C2×C4×C11C2×SD1611yescharacteristic
154C2×C4×C11C2×SD1611yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C11C22×D411yescharacteristic
157C2×Dic11—21no—
158C2×Dic11—21no—
159C2×Dic11—42no—
160C2×Dic11—42no—
161Dic22—84no—
162C8×C11C22⋊Q811yescharacteristic
163C8×C11C22⋊Q811yescharacteristic
164C8×C11C22×Q811yescharacteristic
165C8×C11C2×#4111yescharacteristic
166C11⋊C8—42no—
167C11⋊C8C2×SD1611yescharacteristic
168C11⋊C8C2×SD1611yescharacteristic
169C11⋊C8C2×SD1611yescharacteristic
170C11⋊C8C2×SD1611yescharacteristic
171C2×#135C2×D1111yescharacteristic
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×#108—111no—
185#427—111no—
186#427—221no—
187#427C2×D1111yescharacteristic
188C2×#104—221no—
189C2×C4×C8—111no—
190#365—114no—
191#365—114no—
192#364—112no—
193#364—112no—
194#360—114no—
195#360C2×D1114yes—
196C22×C11—41no—
197C22×C11—42no—
198C22×C11—82no—
199C22×C11#47611yescharacteristic
200C22×C11#47611yescharacteristic
201C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
202C4×C11—42no—
203C4×C11—82no—
204C4×C11#47611yescharacteristic
205C4×C11#47611yescharacteristic
206C4×C11C2×C22⋊Q811yescharacteristic
207C4×C11C22×SD1611yescharacteristic
208Dic11—22no—
209Dic11—41no—
210Dic11—82no—
211C2×#41—21no—
212#135—21no—
213#135—21no—
214#135Dic2212yescomplemented
215#135C22×D1112yes—
216C2×Q16Dic2211yescharacteristic, complemented
217C2×SD16—21no—
218C2×D8Dic2211yescharacteristic, complemented
219#131—222no—
220#131—222no—
221#131—441no—
222#131—441no—
223C2×M16—221no—
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—112no—
242#108—221no—
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×C11—82no—
259C2×C11C2×#47611yescharacteristic
260#41—22no—
261#41—22no—
262#41—41no—
263#41—41no—
264C2×Q8—21no—
265C2×Q8—442no—
266C2×D4—21no—
267C2×D4—41no—
268C22×C4—41no—
269C22×C4—221no—
270C22×C4D4×D1111yescharacteristic
271Q16—21no—
272Q16C2×Dic2212yes—
273SD16—22no—
274SD16—22no—
275D8—21no—
276D8C2×Dic2212yes—
277M16—222no—
278M16—442no—
279M16—442no—
280M16—441no—
281C2×C8—111no—
282C2×C8—111no—
283C2×C8—111no—
284C2×C8—111no—
285C2×C8—111no—
286C2×C8—111no—
287C2×C8—442no—
288C2×C8—442no—
289C2×C8—441no—
290C2×C8C2×Dic2211yescharacteristic
291C2×C8C2×Dic2211yescharacteristic
292C2×C8D4×D1111yescharacteristic
293C2×C8#434111yescharacteristic
294C2×C8#434111yescharacteristic
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—41no—
312C23#6696411yescharacteristic
313Q8—22no—
314Q8—41no—
315Q8—884no—
316D4—22no—
317D4—42no—
318D4—42no—
319D4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4#6693111yescharacteristic
329C2×C4#6693111yescharacteristic
330C2×C4#6696411yescharacteristic
331C2×C4SD16×D1111yescharacteristic
332C2×C4SD16×D1111yescharacteristic
333C2×C4C2×D4×D1111yescharacteristic
334C8—111no—
335C8—111no—
336C8—111no—
337C8—111no—
338C8—442no—
339C8#6693111yescharacteristic
340C8#6693111yescharacteristic
341C8C22×Dic2211yescharacteristic
342C8C2×#434111yescharacteristic
343C22—41no—
344C22—42no—
345C22—82no—
346C22#1062237411yescharacteristic
347C22#1062237411yescharacteristic
348C22C2×#6696411yescharacteristic
349C4—42no—
350C4—82no—
351C4—222no—
352C4—441no—
353C4—882no—
354C4#1062237411yescharacteristic
355C4#1062237411yescharacteristic
356C4C2×#6693111yescharacteristic
357C4C2×SD16×D1111yescharacteristic
358C2—21no—
359C2—21no—
360C2—21no—
361C2—82no—
362C2C2×#1062237411yescharacteristic
subgroupG/H
centerC4#10622374
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2145C2
socleC2×C11C2×#476
prime radicalC2×C11×#135C22
hypercenter#2145D11
hypocenterC11#33637
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2145

Complements

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

NH ≅ G/Ntype
1. #13079128C2semidirect
3. #13070790C2semidirect
4. #13070785C2semidirect
5. #13070389C2semidirect
6. #13070388C2semidirect
7. C2×#10622149C2semidirect
27. #10622471C22semidirect
28. #10622468C22semidirect
31. #10622151C22semidirect
32. #10622149C22semidirect
33. #10622149C22semidirect
34. #10622125C22semidirect
38. C11×#135Q8semidirect
40. C2×C11×Q16Q8semidirect
42. C2×C11×D8Q8semidirect
214. #135Dic22semidirect
216. C2×Q16Dic22semidirect
218. C2×D8Dic22semidirect
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×#106228092
#130707902
#130707852
#130703892
#130703882
C2×#106221492
#130703522
C11×#21452
#3363711