Finite Group Databasebeta

← #14907232

Subgroups — #14907232

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081750C211yesmaximal, characteristic
2#13077501C211yesmaximal, characteristic, complemented
3#13070514C214yesmaximal, complemented
4#13070507C214yesmaximal, complemented
5C2×#10622132C211yesmaximal, characteristic, complemented
6#13070363C211yesmaximal, characteristic, complemented
7C2×#10622204C211yesmaximal, characteristic, complemented
8#13070221C211yesmaximal, characteristic, complemented
9C11×#2957C211yesmaximal, characteristic, complemented
10C2×C11×#135C2211yescharacteristic
11C11×#568—21no—
12C2×#66957C2211yescharacteristic
13#10623054—21no—
14C11×#444C2214yes—
15C11×#443—22no—
16C2×C11×#108C2211yescharacteristic
17C11×#421—21no—
18C11×#405C2211yescharacteristic
19#10622808C2212yes—
20#10622807C414yescomplemented
21#10622806C2212yes—
22#10622792C412yescomplemented
23#10622760C412yescomplemented
24#10622746—21no—
25C2×#66881C2211yescharacteristic
26C2×#66876C2211yescharacteristic
27C2×#66876C2211yescharacteristic
28#10622329C2212yescomplemented
29#10622324C2212yescomplemented
30C4×#4314—22no—
31#10622204C2214yes—
32#10622134C2212yescomplemented
33#10622133C2212yescomplemented
34#10622132C2214yescomplemented
35#10622104C2214yescomplemented
36C2×C11×#41—21no—
37C2×#4339—21no—
38C11×#135—21no—
39C11×#135—21no—
40C11×#135C2×C412yescomplemented
41C11×#135C2312yes—
42C2×C11×Q16C2×C411yescharacteristic, complemented
43C2×C11×SD16—21no—
44C2×C11×D8C2×C411yescharacteristic, complemented
45C11×#131—24no—
46C11×#131—42no—
47C2×C11×M16—21no—
48C2×C11×M16—42no—
49C2×C11×M16D411yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C11×#117D411yescharacteristic
52C2×C4⋊Dic11—21no—
53C2×Dic44C2311yescharacteristic
54#66957—21no—
55#66957—21no—
56#66957C2×C412yes—
57#66957C2×C412yes—
58C2×D88C2311yescharacteristic
59C2×#4314—21no—
60#66945—41no—
61C4⋊C4×D11—41no—
62(C22⋊D11)⋊C4—42no—
63C4×D44—22no—
64C4×Dic22—22no—
65C11×#108—21no—
66C11×#108C2312yes—
67C11×#104—24no—
68C11×#97C2312yes—
69C4×C8×C11D412yes—
70#66893C2×C414yescomplemented
71#66892C2×C414yescomplemented
72#66891C2×C414yescomplemented
73#66890C2×C414yescomplemented
74#66885—22no—
75#66881—21no—
76#66881C2312yes—
77#66880—22no—
78#66876—21no—
79#66876C2×C412yescomplemented
80#66876C2312yes—
81#66876C2312yes—
82C2×C11⋊C16—21no—
83C2×C11⋊C16C2×C412yescomplemented
84#33469—111nomaximal, Sylow
85C11×#41—22no—
86C11×#41—22no—
87C11×#41—41no—
88C11×#41—41no—
89C2×Q8×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11C2×D411yescharacteristic
94C2×C22⋊D11—41no—
95C22×Dic11—41no—
96#4339—22no—
97#4339—22no—
98#4339—41no—
99#4339—41no—
100C2×D44—21no—
101C2×C4×D11—42no—
102C2×C4×D11—41no—
103C2×Dic22—21no—
104C11×Q16—21no—
105C11×Q16C22×C412yes—
106C11×SD16—22no—
107C11×SD16—22no—
108C11×D8—21no—
109C11×D8C22×C412yes—
110C11×M16—21no—
111C11×M16—21no—
112C11×M16—22no—
113C11×M16—44no—
114C11×M16—41no—
115C2×C8×C11—44no—
116C2×C8×C11—41no—
117C2×C8×C11C22×C411yescharacteristic
118C2×C8×C11C22×C411yescharacteristic
119C2×C8×C11C2×D412yes—
120C2×C8×C11C2×D411yescharacteristic
121C2×C8×C11#4111yescharacteristic
122C2×C8×C11#4111yescharacteristic
123C2×C8×C11C2411yescharacteristic
124C11×C4⋊C4—21no—
125C11×C22⋊C4—21no—
126C42×C11C2×D412yes—
127(C2×D11)⋊C4—42no—
128C4⋊Dic11—22no—
129C4⋊Dic11—41no—
130Dic11⋊C4—42no—
131C4×Dic11—42no—
132Dic44—21no—
133Dic44C22×C412yes—
134D88—21no—
135D88C22×C412yes—
136#4314—22no—
137#4314—22no—
138C11⋊C16—22no—
139C11⋊C16C22×C414yes—
140#3414—111no—
141#2957D1111yescharacteristic, complemented
142#2952—111no—
143AGL(1,ℤ/16)—114no—
144#2180—114no—
145C2×#365—111no—
146#2148—111no—
147C2×#360—111no—
148#2110—111no—
149C23×C11—41no—
150C23×C11AGL(1,ℤ/8)11yescharacteristic
151C22×D11—41no—
152Q8×C11—22no—
153Q8×C11—41no—
154D4×C11—22no—
155D4×C11—42no—
156D4×C11—42no—
157D4×C11—41no—
158C2×C4×C11—22no—
159C2×C4×C11—41no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11C4×D411yescharacteristic
163C2×C4×C11C4×D411yescharacteristic
164C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C11C22×D411yescharacteristic
168C22⋊D11—42no—
169C22⋊D11—42no—
170C2×Dic11—41no—
171C2×Dic11—42no—
172C2×Dic11—161no—
173D44—22no—
174D44—41no—
175C4×D11—42no—
176C4×D11—42no—
177C4×D11—162no—
178Dic22—22no—
179Dic22—41no—
180C8×C11—22no—
181C8×C11—42no—
182C8×C11C4×D411yescharacteristic
183C8×C11C4×D411yescharacteristic
184C8×C11C23×C411yescharacteristic
185C8×C11C2×#4111yescharacteristic
186C2×#135—111no—
187C2×#135C2×D1111yescharacteristic
188#568—21no—
189#520—221no—
190#510—112no—
191#510—112no—
192#509—112no—
193#509—112no—
194#508—114no—
195C2×M32—111no—
196C2×M32—111no—
197#444C2×D1114yes—
198#443—22no—
199#442—112no—
200#441—112no—
201C4×SD16—222no—
202C2×#108C2×D1111yescharacteristic
203C2×#106—111no—
204#421—21no—
205#417—221no—
206#405C2×D1111yescharacteristic
207#365—114no—
208#362—112no—
209#361—112no—
210#360—114no—
211#347—114no—
212C22×C11—41no—
213C22×C11—42no—
214C22×C11—161no—
215C22×C11#44211yescharacteristic
216C22×C11#44211yescharacteristic
217C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
218C2×D11—42no—
219C2×D11—81no—
220C2×D11—81no—
221C4×C11—42no—
222C4×C11—42no—
223C4×C11#44211yescharacteristic
224C4×C11#44211yescharacteristic
225C4×C11C2×C4×D411yescharacteristic
226C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
227Dic11—42no—
228Dic11—82no—
229C2×#41—21no—
230C2×#41—221no—
231#135—21no—
232#135—21no—
233#135—112no—
234#135—112no—
235#135—221no—
236#135—221no—
237#135C4×D1112yescomplemented
238#135C22×D1112yes—
239C2×Q16—111no—
240C2×Q16C4×D1111yescharacteristic, complemented
241C2×SD16—21no—
242C2×SD16—221no—
243C2×D8—111no—
244C2×D8C4×D1111yescharacteristic, complemented
245#131—24no—
246#131—42no—
247C2×M16—21no—
248C2×M16—42no—
249C2×M16C22⋊D1111yescharacteristic
250C22×C8C22×D1111yescharacteristic
251C4×Q8—222no—
252C4×D4—222no—
253C4×D4—442no—
254#117—441no—
255#117C22⋊D1111yescharacteristic
256C2×C4⋊C4—221no—
257C2×C4⋊C4—441no—
258Q32—114no—
259SD32—114no—
260SD32—114no—
261D16—114no—
262M32—112no—
263M32—112no—
264M32—112no—
265M32—221no—
266C2×C16—112no—
267C2×C16—221no—
268#108—21no—
269#108C22×D1112yes—
270#106—112no—
271#106—221no—
272#104—24no—
273#103—222no—
274#102—222no—
275#97C22×D1112yes—
276C4×C8C22⋊D1112yes—
277C2×C11—21no—
278C2×C11—21no—
279C2×C11—21no—
280C2×C11—82no—
281C2×C11C2×#44211yescharacteristic
282D11—82no—
283#41—22no—
284#41—22no—
285#41—41no—
286#41—41no—
287#41—222no—
288#41—222no—
289#41—441no—
290#41—441no—
291C2×Q8—21no—
292C2×Q8—221no—
293C2×D4—21no—
294C2×D4—41no—
295C2×D4—221no—
296C2×D4—441no—
297C22×C4—41no—
298C22×C4—442no—
299C22×C4—441no—
300C22×C4—441no—
301C22×C4C2×C22⋊D1111yescharacteristic
302Q16—21no—
303Q16—112no—
304Q16—221no—
305Q16C2×C4×D1112yes—
306SD16—22no—
307SD16—22no—
308SD16—222no—
309SD16—222no—
310D8—21no—
311D8—112no—
312D8—221no—
313D8C2×C4×D1112yes—
314M16—21no—
315M16—21no—
316M16—22no—
317M16—44no—
318M16—41no—
319C2×C8—44no—
320C2×C8—41no—
321C2×C8C2×C4×D1111yescharacteristic
322C2×C8C2×C4×D1111yescharacteristic
323C2×C8#433911yescharacteristic
324C2×C8#433911yescharacteristic
325C2×C8C2×C22⋊D1112yes—
326C2×C8C2×C22⋊D1111yescharacteristic
327C2×C8C23×D1111yescharacteristic
328C4⋊C4—21no—
329C4⋊C4—222no—
330C4⋊C4—442no—
331C4⋊C4—441no—
332C22⋊C4—21no—
333C22⋊C4—442no—
334C42—442no—
335C42C2×C22⋊D1112yes—
336C16—114no—
337C16—222no—
338C11#3346911yescharacteristic, complemented, Sylow
339C23—41no—
340C23—441no—
341C23#6700211yescharacteristic
342Q8—22no—
343Q8—41no—
344Q8—222no—
345Q8—441no—
346D4—22no—
347D4—42no—
348D4—42no—
349D4—41no—
350D4—222no—
351D4—442no—
352D4—442no—
353D4—441no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—441no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—1762no—
363C2×C4—1761no—
364C2×C4C4×C22⋊D1111yescharacteristic
365C2×C4C4×C22⋊D1111yescharacteristic
366C2×C4#6698511yescharacteristic
367C2×C4#6698511yescharacteristic
368C2×C4#6700211yescharacteristic
369C2×C4C22×C22⋊D1111yescharacteristic
370C8—22no—
371C8—42no—
372C8C4×C22⋊D1111yescharacteristic
373C8C4×C22⋊D1111yescharacteristic
374C8C22×C4×D1111yescharacteristic
375C8C2×#433911yescharacteristic
376C22—41no—
377C22—42no—
378C22—161no—
379C22—442no—
380C22—881no—
381C22—881no—
382C22#1062262711yescharacteristic
383C22#1062262711yescharacteristic
384C22C2×#6700211yescharacteristic
385C4—42no—
386C4—42no—
387C4—442no—
388C4—882no—
389C4#1062262711yescharacteristic
390C4#1062262711yescharacteristic
391C4C2×C4×C22⋊D1111yescharacteristic
392C4C2×#6698511yescharacteristic
393C2—21no—
394C2—21no—
395C2—21no—
396C2—82no—
397C2—882no—
398C2C2×#1062262711yescharacteristic
subgroupG/H
centerC2C2×#10622627
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC11×#2957C2
socleC2×C11C2×#442
prime radical#13081750C2
cosocleC2×C8×C11C24
hypercenter#2957D11
hypocenterC11#33469
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ #405 ◁ #2957

Complements

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

NH ≅ G/Ntype
2. #13077501C2semidirect
3. #13070514C2semidirect
4. #13070507C2semidirect
5. C2×#10622132C2semidirect
6. #13070363C2semidirect
7. C2×#10622204C2semidirect
8. #13070221C2semidirect
9. C11×#2957C2semidirect
20. #10622807C4semidirect
22. #10622792C4semidirect
23. #10622760C4semidirect
28. #10622329C22semidirect
29. #10622324C22semidirect
32. #10622134C22semidirect
33. #10622133C22semidirect
34. #10622132C22semidirect
35. #10622104C22semidirect
40. C11×#135C2×C4semidirect
42. C2×C11×Q16C2×C4semidirect
44. C2×C11×D8C2×C4semidirect
70. #66893C2×C4semidirect
71. #66892C2×C4semidirect
72. #66891C2×C4semidirect
73. #66890C2×C4semidirect
79. #66876C2×C4semidirect
83. C2×C11⋊C16C2×C4semidirect
141. #2957D11semidirect
237. #135C4×D11semidirect
240. C2×Q16C4×D11semidirect
244. C2×D8C4×D11semidirect
338. C11#33469semidirect

Maximal subgroups

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

subgroupindex
#130817502
#130775012
#130705142
#130705072
C2×#106221322
#130703632
C2×#106222042
#130702212
C11×#29572
#3346911