Finite Group Databasebeta

← #72254554

Subgroups — #72254554

Order 7040.

892 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72254551C214yesmaximal, complemented
2#72249026C211yesmaximal, characteristic, complemented
3C11⋊C5×#486C211yesmaximal, characteristic, complemented
4#72249021C211yesmaximal, characteristic, complemented
5C4×#4313⋊C5C211yesmaximal, characteristic, complemented
6#72248922C211yesmaximal, characteristic, complemented
7#72248920C211yesmaximal, characteristic, complemented
8#72248919C211yesmaximal, characteristic, complemented
9#72248717C214yesmaximal, complemented
10C2×#4343⋊C5—21no—
11C2×#4341⋊C5—21no—
12C4⋊Q8×C11⋊C5C2211yescharacteristic
13#127×C11⋊C5C2211yescharacteristic
14#67000⋊C5—21no—
15#66991⋊C5—21no—
16#66991⋊C5C2212yes—
17C2×#4323⋊C5C2214yes—
18#66989⋊C5—21no—
19D4×Dic11⋊C5—21no—
20D4×Dic11⋊C5C2212yes—
21C2×#4313⋊C5C2212yes—
22#66948⋊C5—21no—
23#66948⋊C5C2212yes—
24#66946⋊C5—21no—
25#66946⋊C5C2212yes—
26#66927⋊C5C2211yescharacteristic
27C42×AGL(1,𝔽11)C2211yescharacteristic
28#66922⋊C5C2211yescharacteristic
29#102×C11⋊C5C2214yes—
30C4×C8×C11⋊C5C2211yescharacteristic
31#66885⋊C5C2214yes—
32#66879⋊C5C2212yes—
33#66872⋊C5C2214yes—
34C4×(C11⋊C5)⋊C8C2211yescharacteristic
35#13079353C511yesmaximal, characteristic, complemented, Hall
36C2×Q8×C11⋊C5—21no—
37C2×D4×C11⋊C5—21no—
38C2×D4×C11⋊C5—21no—
39C2×D4×C11⋊C5C2312yes—
40C2×C22⋊AGL(1,𝔽11)—22no—
41C22×Dic11⋊C5—22no—
42#4343⋊C5—44no—
43#4341⋊C5—44no—
44C2×C4⋊AGL(1,𝔽11)—22no—
45C2×C4⋊AGL(1,𝔽11)—21no—
46C2×C4⋊AGL(1,𝔽11)—21no—
47C2×C4⋊AGL(1,𝔽11)C2312yes—
48C2×C4×AGL(1,𝔽11)—22no—
49C2×C4×AGL(1,𝔽11)D411yescharacteristic
50C2×C4×AGL(1,𝔽11)D411yescharacteristic
51C2×C4×AGL(1,𝔽11)C2311yescharacteristic
52C2×(C11⋊C5)⋊Q8—21no—
53C2×C8×C11⋊C5C2312yes—
54C4⋊C4×C11⋊C5—21no—
55C4⋊C4×C11⋊C5C2312yes—
56C42×C11⋊C5C2311yescharacteristic
57C22⋊(Dic11⋊C5)—22no—
58C22⋊(Dic11⋊C5)—22no—
59#4323⋊C5—28no—
60((C2×D11)⋊C4)⋊C5—22no—
61((C2×D11)⋊C4)⋊C5—22no—
62C4⋊(Dic11⋊C5)—21no—
63C4⋊(Dic11⋊C5)C2312yes—
64C4×Dic11⋊C5D411yescharacteristic
65C4×Dic11⋊C5D411yescharacteristic
66C4×Dic11⋊C5C2311yescharacteristic
67C2×(C11⋊C5)⋊C8C2312yes—
68#4313⋊C5—24no—
69#10623256C2×C511yescharacteristic, complemented
70#10623247C2×C511yescharacteristic, complemented
71C11×#486C2×C511yescharacteristic, complemented
72#10622692C2×C511yescharacteristic, complemented
73#10622686C2×C511yescharacteristic, complemented
74#10622398C2×C514yescomplemented
75#10622395C2×C514yescomplemented
76#10622307C2×C511yescharacteristic, complemented
77C4×#4313C2×C511yescharacteristic, complemented
78C5×#3184—111nomaximal, Hall
79C23×C11⋊C5—22no—
80C22×AGL(1,𝔽11)—22no—
81C22×AGL(1,𝔽11)C2×D411yescharacteristic
82Q8×C11⋊C5—42no—
83D4×C11⋊C5—24no—
84D4×C11⋊C5—42no—
85D4×C11⋊C5—42no—
86C2×C4×C11⋊C5—22no—
87C2×C4×C11⋊C5C2×D411yescharacteristic
88C2×C4×C11⋊C5C2×D411yescharacteristic
89C2×C4×C11⋊C5C2411yescharacteristic
90C22⋊AGL(1,𝔽11)—44no—
91C2×Dic11⋊C5—22no—
92C2×Dic11⋊C5—44no—
93C2×Dic11⋊C5C2×D411yescharacteristic
94C2×Dic11⋊C5C2×D411yescharacteristic
95C2×Dic11⋊C5C2×D411yescharacteristic
96C4⋊AGL(1,𝔽11)—24no—
97C4⋊AGL(1,𝔽11)—44no—
98C4⋊AGL(1,𝔽11)—42no—
99C4⋊AGL(1,𝔽11)—42no—
100C4×AGL(1,𝔽11)—22no—
101C4×AGL(1,𝔽11)—22no—
102C4×AGL(1,𝔽11)—22no—
103C4×AGL(1,𝔽11)—44no—
104(C11⋊C5)⋊Q8—42no—
105C8×C11⋊C5—22no—
106(C11⋊C5)⋊C8#4114yescomplemented
107C2×#4343—21no—
108C2×#4341—21no—
109C11×C4⋊Q8C22×C511yescharacteristic
110C11×#127C22×C511yescharacteristic
111#67000—21no—
112#66991—21no—
113#66991C22×C512yes—
114#66989—21no—
115D4×Dic11—21no—
116D4×Dic11C22×C512yes—
117C2×#4323C22×C514yes—
118C2×#4313C22×C512yes—
119#66948—21no—
120#66948C22×C512yes—
121#66946—21no—
122#66946C22×C512yes—
123#66927C22×C511yescharacteristic
124C42×D11C22×C511yescharacteristic
125#66922C22×C511yescharacteristic
126C11×#102C22×C514yes—
127C4×C8×C11C22×C511yescharacteristic
128#66885C22×C514yes—
129#66879C22×C512yes—
130#66872C22×C514yes—
131C4×C11⋊C8C22×C511yescharacteristic
132C5×#532—111no—
133C5×#532—111no—
134C5×#498—111no—
135C5×#493—111no—
136C5×#486—111no—
137C5×#486—221no—
138C5×#469—114no—
139C5×#442—114no—
140C4×C5×M16—111no—
141C22×C11⋊C5—42no—
142C22×C11⋊C5—42no—
143C22×C11⋊C5—42no—
144C22×C11⋊C5C22×D411yescharacteristic
145C2×AGL(1,𝔽11)—21no—
146C2×AGL(1,𝔽11)—21no—
147C2×AGL(1,𝔽11)—21no—
148C2×AGL(1,𝔽11)—42no—
149C2×AGL(1,𝔽11)—42no—
150C2×AGL(1,𝔽11)—42no—
151C4×C11⋊C5—42no—
152C4×C11⋊C5AGL(1,ℤ/8)12yes—
153C4×C11⋊C5AGL(1,ℤ/8)12yes—
154C4×C11⋊C5C2×#4112yes—
155Dic11⋊C5—21no—
156Dic11⋊C5—21no—
157Dic11⋊C5—21no—
158Dic11⋊C5—42no—
159C2×Q8×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11C23×C512yes—
163C2×C22⋊D11—22no—
164C22×Dic11—22no—
165#4343—44no—
166#4341—44no—
167C2×D44—22no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44C23×C512yes—
171C2×C4×D11—22no—
172C2×C4×D11C5×D411yescharacteristic
173C2×C4×D11C5×D411yescharacteristic
174C2×C4×D11C23×C511yescharacteristic
175C2×Dic22—21no—
176C2×C8×C11C23×C512yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4C23×C512yes—
179C42×C11C23×C511yescharacteristic
180C22⋊Dic11—22no—
181C22⋊Dic11—22no—
182#4323—28no—
183(C2×D11)⋊C4—22no—
184(C2×D11)⋊C4—22no—
185C4⋊Dic11—21no—
186C4⋊Dic11C23×C512yes—
187C4×Dic11C5×D411yescharacteristic
188C4×Dic11C5×D411yescharacteristic
189C4×Dic11C23×C511yescharacteristic
190C2×C11⋊C8C23×C512yes—
191#4313—24no—
192C2×C5×#41—221no—
193C2×C5×#41—221no—
194C2×C5×D8—114no—
195C2×C5×M16—112no—
196C5×C4⋊Q8—111no—
197C5×C4⋊Q8—221no—
198C5×#127—111no—
199C5×#127—221no—
200C5×#124—221no—
201C5×#124—221no—
202C5×#121—112no—
203C5×#121—112no—
204C5×#121—221no—
205C5×#121—221no—
206C4×C5×D4—112no—
207C4×C5×D4—112no—
208C4×C5×D4—221no—
209C4×C5×D4—221no—
210C2×C42×C5—111no—
211C5×#106—114no—
212C5×#102—114no—
213C5×#102—224no—
214C5×#97—112no—
215C4×C5×C8—111no—
216C4×C5×C8—221no—
217#3184—111noSylow
218C2×C11⋊C5—82no—
219C2×C11⋊C5#53211yescharacteristic
220C2×C11⋊C5C2×AGL(1,ℤ/8)11yescharacteristic
221C2×C11⋊C5C2×AGL(1,ℤ/8)11yescharacteristic
222AGL(1,𝔽11)—41no—
223AGL(1,𝔽11)—82no—
224C23×C11—22no—
225C22×D11—22no—
226C22×D11C2×C5×D411yescharacteristic
227Q8×C11—42no—
228D4×C11—24no—
229D4×C11—42no—
230D4×C11—42no—
231C2×C4×C11—22no—
232C2×C4×C11C2×C5×D411yescharacteristic
233C2×C4×C11C2×C5×D411yescharacteristic
234C2×C4×C11C24×C511yescharacteristic
235C22⋊D11—44no—
236C2×Dic11—22no—
237C2×Dic11—44no—
238C2×Dic11C2×C5×D411yescharacteristic
239C2×Dic11C2×C5×D411yescharacteristic
240C2×Dic11C2×C5×D411yescharacteristic
241D44—24no—
242D44—44no—
243D44—42no—
244D44—42no—
245C4×D11—22no—
246C4×D11—22no—
247C4×D11—22no—
248C4×D11—44no—
249Dic22—42no—
250C8×C11—22no—
251C11⋊C8C5×#4114yescomplemented
252C5×#41—444no—
253C5×#41—444no—
254C2×C5×Q8—221no—
255C2×C5×Q8—441no—
256C2×C5×D4—112no—
257C2×C5×D4—222no—
258C2×C5×D4—221no—
259C2×C5×D4—221no—
260C2×C5×D4—222no—
261C2×C5×D4—222no—
262C2×C5×D4—441no—
263C2×C5×D4—441no—
264C22×C4×C5—111no—
265C22×C4×C5—111no—
266C22×C4×C5—111no—
267C22×C4×C5—222no—
268C22×C4×C5—222no—
269C5×D8—228no—
270C5×M16—224no—
271C2×C5×C8—112no—
272C2×C5×C8—222no—
273C5×C4⋊C4—112no—
274C5×C4⋊C4—221no—
275C5×C4⋊C4—222no—
276C5×C4⋊C4—441no—
277C5×C22⋊C4—222no—
278C5×C22⋊C4—222no—
279C5×C22⋊C4—222no—
280C5×C22⋊C4—222no—
281C42×C5—111no—
282C42×C5—111no—
283C42×C5—111no—
284C42×C5—221no—
285#532—111no—
286#532—111no—
287#498—111no—
288#493—111no—
289#486—111no—
290#486AGL(1,𝔽11)11yescharacteristic, complemented
291#469—114no—
292#442—114no—
293C4×M16—111no—
294C11⋊C5#318411yescharacteristic, complemented, Hall
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11C22×C5×D411yescharacteristic
299C2×D11—21no—
300C2×D11—21no—
301C2×D11—21no—
302C2×D11—42no—
303C2×D11—42no—
304C2×D11—42no—
305C4×C11—42no—
306C4×C11C5×AGL(1,ℤ/8)12yes—
307C4×C11C5×AGL(1,ℤ/8)12yes—
308C4×C11C2×C5×#4112yes—
309Dic11—21no—
310Dic11—21no—
311Dic11—21no—
312Dic11—42no—
313C23×C5—111no—
314C23×C5—222no—
315C23×C5—442no—
316C5×Q8—442no—
317C5×Q8—882no—
318C5×D4—224no—
319C5×D4—444no—
320C5×D4—442no—
321C5×D4—442no—
322C5×D4—444no—
323C5×D4—444no—
324C5×D4—882no—
325C5×D4—882no—
326C2×C4×C5—111no—
327C2×C4×C5—111no—
328C2×C4×C5—111no—
329C2×C4×C5—222no—
330C2×C4×C5—222no—
331C2×C4×C5—222no—
332C2×C4×C5—222no—
333C2×C4×C5—221no—
334C2×C4×C5—221no—
335C2×C4×C5—221no—
336C2×C4×C5—442no—
337C2×C4×C5—444no—
338C2×C4×C5—444no—
339C5×C8—114no—
340C5×C8—442no—
341C2×#41—221no—
342C2×#41—221no—
343C2×D8—114no—
344C2×M16—112no—
345C4⋊Q8—111no—
346C4⋊Q8C2×AGL(1,𝔽11)11yescharacteristic
347#127—111no—
348#127C2×AGL(1,𝔽11)11yescharacteristic
349#124—221no—
350#124—221no—
351#121—112no—
352#121—112no—
353#121—221no—
354#121—221no—
355C4×D4—112no—
356C4×D4—112no—
357C4×D4—221no—
358C4×D4—221no—
359C2×C42—111no—
360#106—114no—
361#102—114no—
362#102C2×AGL(1,𝔽11)14yes—
363#97—112no—
364C4×C8—111no—
365C4×C8C2×AGL(1,𝔽11)11yescharacteristic
366C2×C11—82no—
367C2×C11C5×#53211yescharacteristic
368C2×C11C2×C5×AGL(1,ℤ/8)11yescharacteristic
369C2×C11C2×C5×AGL(1,ℤ/8)11yescharacteristic
370D11—41no—
371D11—82no—
372C22×C5—221no—
373C22×C5—221no—
374C22×C5—221no—
375C22×C5—221no—
376C22×C5—442no—
377C22×C5—442no—
378C22×C5—442no—
379C22×C5—882no—
380C22×C5—882no—
381C22×C5—882no—
382C4×C5—221no—
383C4×C5—221no—
384C4×C5—221no—
385C4×C5—222no—
386C4×C5—222no—
387C4×C5—222no—
388C4×C5—442no—
389C4×C5—882no—
390#41—444no—
391#41—444no—
392C2×Q8—21no—
393C2×Q8—221no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—112no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—221no—
400C2×D4—221no—
401C2×D4C22×AGL(1,𝔽11)12yes—
402C22×C4—111no—
403C22×C4—111no—
404C22×C4—111no—
405C22×C4—222no—
406C22×C4—222no—
407D8—228no—
408M16—224no—
409C2×C8—112no—
410C2×C8C22×AGL(1,𝔽11)12yes—
411C4⋊C4—21no—
412C4⋊C4—112no—
413C4⋊C4—221no—
414C4⋊C4C22×AGL(1,𝔽11)12yes—
415C22⋊C4—222no—
416C22⋊C4—222no—
417C22⋊C4—222no—
418C22⋊C4—222no—
419C42—111no—
420C42—111no—
421C42—111no—
422C42C22×AGL(1,𝔽11)11yescharacteristic
423C11C5×#318411yescharacteristic, complemented, Sylow
424C2×C5—221no—
425C2×C5—221no—
426C2×C5—221no—
427C2×C5—441no—
428C2×C5—882no—
429C2×C5—1762no—
430C23—22no—
431C23—111no—
432C23—222no—
433Q8—42no—
434Q8—442no—
435D4—24no—
436D4—42no—
437D4—42no—
438D4—224no—
439D4—444no—
440D4—444no—
441D4—442no—
442D4—442no—
443C2×C4—22no—
444C2×C4—111no—
445C2×C4—111no—
446C2×C4—111no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—444no—
452C2×C4—444no—
453C2×C4D4×AGL(1,𝔽11)11yescharacteristic
454C2×C4D4×AGL(1,𝔽11)11yescharacteristic
455C2×C4C23×AGL(1,𝔽11)11yescharacteristic
456C8—22no—
457C8—114no—
458C5—221noSylow
459C22—42no—
460C22—42no—
461C22—42no—
462C22—221no—
463C22—221no—
464C22—221no—
465C22—442no—
466C22—442no—
467C22—442no—
468C22C2×D4×AGL(1,𝔽11)11yescharacteristic
469C4—42no—
470C4—221no—
471C4—221no—
472C4—221no—
473C4—442no—
474C4#66964⋊C512yes—
475C4#66967⋊C512yes—
476C4#41×AGL(1,𝔽11)12yes—
477C2—82no—
478C2—441no—
479C2—882no—
480C2C2×#66964⋊C511yescharacteristic
481C2C2×#66967⋊C511yescharacteristic
482C2#7224892411yescharacteristic
subgroupG/H
centerC22C2×D4×AGL(1,𝔽11)
commutator, cosocleC2×C4×C11C24×C5
FrattiniC2×C4C23×AGL(1,𝔽11)
FittingC11×#486C2×C5
socleC22×C11C22×C5×D4
hypercenter#486AGL(1,𝔽11)
hypocenterC11C5×#3184
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #72254551C2semidirect
2. #72249026C2semidirect
3. C11⋊C5×#486C2semidirect
4. #72249021C2semidirect
5. C4×#4313⋊C5C2semidirect
6. #72248922C2semidirect
7. #72248920C2semidirect
8. #72248919C2semidirect
9. #72248717C2semidirect
35. #13079353C5semidirect
69. #10623256C2×C5semidirect
70. #10623247C2×C5semidirect
71. C11×#486C2×C5semidirect
72. #10622692C2×C5semidirect
73. #10622686C2×C5semidirect
74. #10622398C2×C5semidirect
75. #10622395C2×C5semidirect
76. #10622307C2×C5semidirect
77. C4×#4313C2×C5semidirect
106. (C11⋊C5)⋊C8#41semidirect
251. C11⋊C8C5×#41semidirect
290. #486AGL(1,𝔽11)semidirect
294. C11⋊C5#3184semidirect
423. C11C5×#3184semidirect

Maximal subgroups

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

subgroupindex
#722545512
#722490262
C11⋊C5×#4862
#722490212
C4×#4313⋊C52
#722489222
#722489202
#722489192
#722487172
#130793535
C5×#318411