Finite Group Databasebeta

← #14908120

Subgroups — #14908120

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622760C211yesmaximal, characteristic, complemented
2C2×#10622807C211yesmaximal, characteristic, complemented
3#13077493C211yesmaximal, characteristic, complemented
4#13070675C212yesmaximal, complemented
5#13070668C212yesmaximal, complemented
6#13070653C212yesmaximal, complemented
7#13070648C212yesmaximal, complemented
8#13070375C211yesmaximal, characteristic, complemented
9#13070328C211yesmaximal, characteristic, complemented
10C2×#10622200C211yesmaximal, characteristic, complemented
11C11×#3155C211yesmaximal, characteristic, complemented
12C2×C11×AGL(1,ℤ/8)—21no—
13C2×C11×#135C2211yescharacteristic
14C22×C11×D8C2211yescharacteristic
15C11×#535—21no—
16C2×#66957C2211yescharacteristic
17#10623054—21no—
18C11×#496—22no—
19C11×#495C2212yes—
20C11×#493C2212yes—
21C11×#405C2211yescharacteristic
22#10622807—24no—
23C2×#66893C2211yescharacteristic, complemented
24C2×#66892C2211yescharacteristic, complemented
25C2×#66891C2212yes—
26C2×#66891C2211yescharacteristic, complemented
27#10622760—24no—
28C2×#66890C2212yes—
29C2×#66890C2211yescharacteristic, complemented
30#10622746—21no—
31C2×#66882C2211yescharacteristic
32C2×#66876C2211yescharacteristic
33C22×C11⋊C16C2211yescharacteristic
34#10622323—22no—
35C4×Dic44C2212yescomplemented
36C4×D88C2212yescomplemented
37#10622202C2212yescomplemented
38#10622200C2212yes—
39#10622200C2212yes—
40#10622200C2212yescomplemented
41C4⋊(C11⋊C16)C2212yescomplemented
42C4⋊(C11⋊C16)C2212yescomplemented
43C2×C11×#41—21no—
44C22×D4×C11—21no—
45C2×#4339—21no—
46C11×AGL(1,ℤ/8)—44no—
47C11×#135—22no—
48C11×#135—22no—
49C2×C11×Q16C2311yescharacteristic
50C2×C11×SD16—22no—
51C2×C11×SD16—21no—
52C2×C11×D8—22no—
53C2×C11×D8—22no—
54C2×C11×D8—21no—
55C2×C11×D8—22no—
56C2×C11×D8C2311yescharacteristic
57C2×C11×D8C2312yes—
58C2×C11×M16D411yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×#127—22no—
61C11×#124—22no—
62C11×#121—41no—
63C11×#121—41no—
64C11×#120—42no—
65C11×#117D411yescharacteristic
66C2×C4⋊Dic11—21no—
67C2×Dic44C2311yescharacteristic
68#66957—22no—
69#66957D414yescomplemented
70C2×D88C2311yescharacteristic
71C2×#4314—21no—
72#66945—41no—
73C4⋊C4×D11—41no—
74(C22⋊D11)⋊C4—42no—
75C4×D44—22no—
76C4×Dic22—22no—
77C11×#97D412yes—
78C4×C8×C11C2312yes—
79#66893—22no—
80#66892—22no—
81#66891—24no—
82#66891—22no—
83#66890—24no—
84#66890—22no—
85#66885—22no—
86#66882—21no—
87#66882C2312yes—
88#66880—22no—
89#66876—22no—
90C2×C11⋊C16—22no—
91C2×C11⋊C16C2312yes—
92C2×C11⋊C16C2311yescharacteristic
93C2×C11⋊C16C2311yescharacteristic
94#33589—111nomaximal, Sylow
95C24×C11—41no—
96C11×#41—42no—
97C11×#41—42no—
98C2×Q8×C11—21no—
99C2×D4×C11—22no—
100C2×D4×C11—21no—
101C2×D4×C11—41no—
102C2×D4×C11—42no—
103C2×D4×C11—41no—
104C2×D4×C11—42no—
105C2×D4×C11—42no—
106C2×D4×C11—42no—
107C22×C4×C11—41no—
108C22×C4×C11C2×D411yescharacteristic
109C2×C22⋊D11—41no—
110C22×Dic11—41no—
111#4339—24no—
112#4339—42no—
113C2×D44—21no—
114C2×C4×D11—41no—
115C2×C4×D11—42no—
116C2×Dic22—21no—
117C11×Q16—21no—
118C11×Q16—21no—
119C11×SD16—44no—
120C11×SD16—42no—
121C11×D8—22no—
122C11×D8—21no—
123C11×D8—22no—
124C11×D8—21no—
125C11×D8—44no—
126C11×D8—42no—
127C11×M16—22no—
128C2×C8×C11C2×D412yes—
129C2×C8×C11C2×D412yes—
130C2×C8×C11C2×D411yescharacteristic
131C2×C8×C11#4112yes—
132C2×C8×C11C2411yescharacteristic
133C11×C4⋊C4D811yescharacteristic
134C11×C4⋊C4D811yescharacteristic
135C11×C22⋊C4—42no—
136C11×C22⋊C4—42no—
137C11×C22⋊C4D812yes—
138C42×C11C2×D412yes—
139(C2×D11)⋊C4—42no—
140C4⋊Dic11—22no—
141C4⋊Dic11—41no—
142Dic11⋊C4—42no—
143C4×Dic11—42no—
144Dic44—21no—
145Dic44C2×D412yes—
146D88—21no—
147D88C2×D412yes—
148#4314—24no—
149C11⋊C16—21no—
150C11⋊C16—21no—
151C11⋊C16—22no—
152C2×#509—111no—
153C2×#508—111no—
154#3155D1111yescharacteristic, complemented
155#2951—111no—
156#2211—112no—
157#2210—112no—
158#2207—112no—
159#2206—112no—
160#2151—111no—
161#2139—111no—
162C2×#357—111no—
163C23×C11—42no—
164C23×C11—41no—
165C23×C11—82no—
166C23×C11—161no—
167C23×C11—161no—
168C23×C11C2×D811yescharacteristic
169C22×D11—41no—
170Q8×C11—41no—
171Q8×C11—41no—
172D4×C11—42no—
173D4×C11—41no—
174D4×C11—41no—
175D4×C11—42no—
176D4×C11—82no—
177D4×C11—82no—
178D4×C11—162no—
179D4×C11—162no—
180C2×C4×C11—41no—
181C2×C4×C11—82no—
182C2×C4×C11#12112yes—
183C2×C4×C11C2×D812yes—
184C2×C4×C11C2×D812yes—
185C2×C4×C11C2×D811yescharacteristic
186C2×C4×C11AGL(1,ℤ/8)12yes—
187C2×C4×C11C22×D411yescharacteristic
188C22⋊D11—44no—
189C2×Dic11—41no—
190C2×Dic11—42no—
191C2×Dic11—161no—
192D44—22no—
193D44—41no—
194C4×D11—44no—
195C4×D11—162no—
196Dic22—22no—
197Dic22—41no—
198C8×C11—22no—
199C8×C11#12112yes—
200C8×C11C22×D411yescharacteristic
201C8×C11C2×#4111yescharacteristic
202C2×AGL(1,ℤ/8)—21no—
203C2×#135—111no—
204C2×#135C2×D1111yescharacteristic
205C22×D8C2×D1111yescharacteristic
206#535—21no—
207#520—221no—
208#509—224no—
209#508—224no—
210C2×Q32—111no—
211C2×SD32—111no—
212C2×SD32—112no—
213C2×SD32—111no—
214C2×D16—112no—
215C2×D16—111no—
216C2×M32—111no—
217C22×C16—111no—
218#496—22no—
219#495C2×D1112yes—
220#493C2×D1112yes—
221#440—222no—
222C4×Q16—112no—
223C4×D8—112no—
224C2×#107—111no—
225#417—221no—
226#405C2×D1111yescharacteristic
227C4⋊C16—112no—
228C4⋊C16—112no—
229#358—112no—
230#357—112no—
231#357—112no—
232#357—112no—
233C22×C11—21no—
234C22×C11—21no—
235C22×C11—81no—
236C22×C11—82no—
237C22×C11—81no—
238C22×C11—82no—
239C22×C11—81no—
240C22×C11—82no—
241C22×C11—164no—
242C22×C11#45912yes—
243C22×C11C22×D811yescharacteristic
244C2×D11—42no—
245C2×D11—81no—
246C2×D11—81no—
247C4×C11—22no—
248C4×C11—22no—
249C4×C11—81no—
250C4×C11#45912yes—
251C4×C11C2×#12111yescharacteristic
252C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
253Dic11—42no—
254Dic11—82no—
255C2×#41—21no—
256C2×#41—221no—
257C22×D4—21no—
258AGL(1,ℤ/8)—44no—
259#135—22no—
260#135—22no—
261#135—114no—
262#135—222no—
263C2×Q16—111no—
264C2×Q16C22×D1111yescharacteristic
265C2×SD16—21no—
266C2×SD16—22no—
267C2×SD16—221no—
268C2×D8—22no—
269C2×D8—22no—
270C2×D8—21no—
271C2×D8—22no—
272C2×D8—111no—
273C2×D8C22×D1112yes—
274C2×D8C22×D1111yescharacteristic
275C2×M16C22⋊D1111yescharacteristic
276C22×C8C22×D1111yescharacteristic
277#127—22no—
278#124—22no—
279#121—41no—
280#121—41no—
281#120—42no—
282C4×Q8—222no—
283C4×D4—222no—
284C4×D4—442no—
285#117—441no—
286#117C22⋊D1111yescharacteristic
287C2×C4⋊C4—221no—
288C2×C4⋊C4—441no—
289Q32—222no—
290SD32—222no—
291SD32—224no—
292SD32—222no—
293D16—222no—
294D16—224no—
295M32—222no—
296C2×C16—111no—
297C2×C16—111no—
298C2×C16—112no—
299C2×C16—222no—
300#107—112no—
301#107—221no—
302#103—222no—
303#102—222no—
304#97C22⋊D1112yes—
305C4×C8C22×D1112yes—
306C2×C11—22no—
307C2×C11—161no—
308C2×C11—162no—
309C2×C11C2×#45911yescharacteristic
310C2×C11#341511yescharacteristic
311C2×C11#341611yescharacteristic
312D11—82no—
313C24—41no—
314#41—42no—
315#41—42no—
316#41—224no—
317#41—442no—
318C2×Q8—21no—
319C2×Q8—221no—
320C2×D4—22no—
321C2×D4—21no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—42no—
325C2×D4—42no—
326C2×D4—42no—
327C2×D4—42no—
328C2×D4—221no—
329C2×D4—441no—
330C22×C4—41no—
331C22×C4—441no—
332C22×C4—441no—
333C22×C4—442no—
334C22×C4C2×C22⋊D1111yescharacteristic
335Q16—21no—
336Q16—21no—
337Q16—112no—
338Q16—221no—
339SD16—44no—
340SD16—42no—
341SD16—224no—
342D8—22no—
343D8—21no—
344D8—22no—
345D8—21no—
346D8—44no—
347D8—42no—
348D8—112no—
349D8—221no—
350M16—22no—
351C2×C8D4×D1112yes—
352C2×C8#434112yes—
353C2×C8C2×C22⋊D1112yes—
354C2×C8C2×C22⋊D1111yescharacteristic
355C2×C8C23×D1111yescharacteristic
356C4⋊C4—222no—
357C4⋊C4—441no—
358C4⋊C4—442no—
359C4⋊C4#432311yescharacteristic
360C4⋊C4#432311yescharacteristic
361C22⋊C4—42no—
362C22⋊C4—42no—
363C22⋊C4—442no—
364C22⋊C4#432312yes—
365C42—442no—
366C42C2×C22⋊D1112yes—
367C16—221no—
368C16—221no—
369C16—222no—
370C11#3358911yescharacteristic, complemented, Sylow
371C23—42no—
372C23—41no—
373C23—82no—
374C23—161no—
375C23—161no—
376C23—441no—
377C23C2×#432311yescharacteristic
378Q8—41no—
379Q8—41no—
380Q8—222no—
381Q8—441no—
382D4—41no—
383D4—42no—
384D4—42no—
385D4—41no—
386D4—82no—
387D4—82no—
388D4—162no—
389D4—162no—
390D4—222no—
391D4—444no—
392D4—441no—
393C2×C4—41no—
394C2×C4—82no—
395C2×C4—441no—
396C2×C4—444no—
397C2×C4—442no—
398C2×C4—1762no—
399C2×C4—1761no—
400C2×C4C2×#432312yes—
401C2×C4C2×#432312yes—
402C2×C4C2×#432311yescharacteristic
403C2×C4#6698512yes—
404C2×C4#6699112yes—
405C2×C4C22×C22⋊D1111yescharacteristic
406C8—22no—
407C8#6699112yes—
408C8C2×D4×D1111yescharacteristic
409C8C2×#434111yescharacteristic
410C22—21no—
411C22—21no—
412C22—81no—
413C22—82no—
414C22—81no—
415C22—82no—
416C22—81no—
417C22—82no—
418C22—164no—
419C22—442no—
420C22—881no—
421C22—881no—
422C22#1062268512yes—
423C22C22×#432311yescharacteristic
424C4—22no—
425C4—22no—
426C4—81no—
427C4—442no—
428C4—882no—
429C4#1062268512yes—
430C4C2×#6698511yescharacteristic
431C4C2×#6699111yescharacteristic
432C2—22no—
433C2—162no—
434C2—161no—
435C2—882no—
436C2C2×#1062268511yescharacteristic
437C2#1308175511yescharacteristic
438C2#1308176311yescharacteristic
subgroupG/H
centerC22C22×#4323
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#3155C2
socleC22×C11C22×D8
hypercenter#3155D11
hypocenterC11#33589
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #405 ◁ #3155

Complements

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

NH ≅ G/Ntype
1. C2×#10622760C2semidirect
2. C2×#10622807C2semidirect
3. #13077493C2semidirect
4. #13070675C2semidirect
5. #13070668C2semidirect
6. #13070653C2semidirect
7. #13070648C2semidirect
8. #13070375C2semidirect
9. #13070328C2semidirect
10. C2×#10622200C2semidirect
11. C11×#3155C2semidirect
23. C2×#66893C22semidirect
24. C2×#66892C22semidirect
26. C2×#66891C22semidirect
29. C2×#66890C22semidirect
35. C4×Dic44C22semidirect
36. C4×D88C22semidirect
37. #10622202C22semidirect
40. #10622200C22semidirect
41. C4⋊(C11⋊C16)C22semidirect
42. C4⋊(C11⋊C16)C22semidirect
69. #66957D4semidirect
154. #3155D11semidirect
370. C11#33589semidirect

Maximal subgroups

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

subgroupindex
C2×#106227602
C2×#106228072
#130774932
#130706752
#130706682
#130706532
#130706482
#130703752
#130703282
C2×#106222002
C11×#31552
#3358911