Finite Group Databasebeta

← #14745237

Subgroups — #14745237

Order 2816.

724 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13080852C212yesmaximal, complemented
2D8×D44C211yesmaximal, characteristic, complemented
3#13068209C211yesmaximal, characteristic, complemented
4#13068151C212yesmaximal, complemented
5#13068012C211yesmaximal, characteristic, complemented
6#13067971C211yesmaximal, characteristic, complemented
7#13067731C212yesmaximal, complemented
8#13067699C212yesmaximal, complemented
9#13067501C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11C11×#3341C211yesmaximal, characteristic, complemented
12C11×#555C2212yescomplemented
13C2×D8×D11—21no—
14D4×D44C2212yes—
15C11×#500C2211yescharacteristic, complemented
16C11×#482—22no—
17C11×#476C2212yescomplemented
18C11×#466—21no—
19C4×C11×D8C2211yescharacteristic
20C8×D4×C11C2211yescharacteristic, complemented
21C11×#427—21no—
22#10622701C2212yescomplemented
23#10622698C2212yescomplemented
24#10622697C2212yes—
25#10622652—22no—
26#10622649—22no—
27#10622628C2212yes—
28#10622628C2212yescomplemented
29C4×#4323C2211yescharacteristic
30#10622625C2212yescomplemented
31#10622616—22no—
32#10622614—22no—
33#10622496—21no—
34#10622386—22no—
35#10622308C2211yescharacteristic
36C8×D44C2211yescharacteristic
37#10622184C2212yescomplemented
38D4⋊(C11⋊C8)C2211yescharacteristic, complemented
39D4⋊(C11⋊C8)C2212yescomplemented
40#10622123C2212yescomplemented
41#10622121C2211yescharacteristic
42#10622117C2211yescharacteristic, complemented
43#10622096C2211yescharacteristic, complemented
44C8×C11⋊C8C2211yescharacteristic, complemented
45C2×D4×D11—22no—
46C22×D44—22no—
47C2×C11×D8D411yescharacteristic
48C22×C8×C11—21no—
49C11×C4⋊Q8C2312yes—
50C11×#124—42no—
51C11×#121—22no—
52C11×#121—22no—
53C4×D4×C11C2312yes—
54C4×D4×C11C2311yescharacteristic
55C11×#117—22no—
56C11×#117—22no—
57C2×#4325—42no—
58C2×#4323—22no—
59C2×#4323—22no—
60C2×#4323D411yescharacteristic
61#66983—22no—
62C2×#4318—22no—
63D8×D11—44no—
64C2×D88—21no—
65C2×D88—21no—
66C2×C8×D11—21no—
67#66948—22no—
68#66935—42no—
69#66927C2312yes—
70C4×D44C2311yescharacteristic
71C11×#107—21no—
72C11×#107—21no—
73C11×#107D411yescharacteristic
74C11×#106—22no—
75C11×C4⋊C8C2311yescharacteristic
76C11×#102—22no—
77C11×#102D412yes—
78C11×C22⋊C8—21no—
79C4×C8×C11C2311yescharacteristic
80#66896D411yescharacteristic
81C22⋊(C11⋊C8)—22no—
82(C2×D11)⋊C8—21no—
83#66873—22no—
84#66873—22no—
85#66873—22no—
86#66873—22no—
87#66873—22no—
88#66873D411yescharacteristic
89#66872—22no—
90#66871D411yescharacteristic
91C4⋊(C11⋊C8)C2311yescharacteristic
92C4⋊(C11⋊C8)C2312yes—
93C4×C11⋊C8C2311yescharacteristic
94C4×C11⋊C8C2311yescharacteristic
95#19898—111nomaximal, Sylow
96C23×D11—42no—
97C2×Q8×C11—22no—
98C2×D4×C11—42no—
99C2×D4×C11C2×D411yescharacteristic
100C2×D4×C11C2×D412yes—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C2×C22⋊D11—42no—
104D4×D11—44no—
105D4×D11—82no—
106C2×D44—22no—
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—42no—
110C2×D44—44no—
111C2×D44—82no—
112C2×D44C2×D411yescharacteristic
113C2×C4×D11—21no—
114C11×D8—22no—
115C2×C8×C11—21no—
116C2×C8×C11—42no—
117C2×C8×C11C2×D411yescharacteristic
118C2×C8×C11C2×D411yescharacteristic
119C11×C4⋊C4—22no—
120C11×C4⋊C4—22no—
121C11×C4⋊C4C2×D411yescharacteristic
122C11×C4⋊C4C2×D412yes—
123C11×C22⋊C4—22no—
124C11×C22⋊C4—21no—
125C11×C22⋊C4—42no—
126C11×C22⋊C4—42no—
127C42×C11—42no—
128C42×C11C2411yescharacteristic
129#4325—84no—
130#4323—22no—
131#4323—44no—
132#4323—82no—
133(C2×D11)⋊C4—21no—
134(C2×D11)⋊C4—42no—
135C4⋊Dic11C2×D411yescharacteristic
136#4318—82no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—21no—
139C2×C11⋊C8—21no—
140C2×C11⋊C8C2×D411yescharacteristic
141C2×C11⋊C8C2×D411yescharacteristic
142D88—42no—
143D88—81no—
144C8×D11—42no—
145#3341D1111yescharacteristic, complemented
146#3325—112no—
147D4×D8—111no—
148#1706—111no—
149#1697—112no—
150#1675—111no—
151#1667—111no—
152#1629—112no—
153#1624—112no—
154#1589—111no—
155C8×D8—111no—
156C23×C11—21no—
157C23×C11—22no—
158C22×D11—21no—
159C22×D11—42no—
160C22×D11—84no—
161C22×D11—84no—
162C22×D11—162no—
163Q8×C11—82no—
164D4×C11—21no—
165D4×C11—22no—
166D4×C11—21no—
167D4×C11—22no—
168D4×C11—162no—
169C2×C4×C11—22no—
170C2×C4×C11—21no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—42no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11C22×D411yescharacteristic
177C2×C4×C11C22×D411yescharacteristic
178C2×C4×C11H(5,𝔽2)11yescharacteristic
179C22⋊D11—84no—
180C2×Dic11—21no—
181D44—21no—
182D44—42no—
183D44—42no—
184D44—42no—
185D44—42no—
186D44—82no—
187D44—84no—
188D44#13512yes—
189C4×D11—41no—
190C4×D11—41no—
191C8×C11—21no—
192C8×C11—41no—
193C8×C11AGL(1,ℤ/8)12yes—
194C11⋊C8—22no—
195C11⋊C8—21no—
196C11⋊C8—21no—
197C11⋊C8—41no—
198C11⋊C8—42no—
199C22×D8—221no—
200#555C2×D1112yescomplemented
201D42—112no—
202#500C2×D1111yescharacteristic, complemented
203#493—111no—
204#492—112no—
205#486—112no—
206#482—22no—
207#482—222no—
208#476—112no—
209#476C2×D1112yescomplemented
210#469—222no—
211#466—21no—
212#466—221no—
213#459—112no—
214#459—112no—
215#447—222no—
216#447—222no—
217C4×D8—111no—
218C4×D8C2×D1111yescharacteristic
219#436—112no—
220C8×D4—111no—
221C8×D4C2×D1111yescharacteristic, complemented
222#427—21no—
223#418—222no—
224#335—111no—
225#335—111no—
226#333—112no—
227#331—112no—
228D4⋊C8—111no—
229D4⋊C8—112no—
230D4⋊C8—111no—
231C82—111no—
232C22×C11—41no—
233C22×C11—42no—
234C22×C11—42no—
235C22×C11—41no—
236C22×C11—41no—
237C22×C11—42no—
238C22×C11D4211yescharacteristic
239C2×D11—22no—
240C2×D11—41no—
241C2×D11—41no—
242C2×D11—82no—
243C2×D11—82no—
244C2×D11—82no—
245C2×D11—168no—
246C4×C11—21no—
247C4×C11—41no—
248C4×C11—42no—
249C4×C11—82no—
250C4×C11C2×#13511yescharacteristic
251C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
252C4×C11#57611yescharacteristic
253C4×C11#57711yescharacteristic
254Dic11—41no—
255C22×D4—222no—
256C22×D4—222no—
257C2×SD16—442no—
258C2×D8—111no—
259C2×D8—222no—
260C2×D8—222no—
261C2×D8—221no—
262C2×D8—221no—
263C2×D8—444no—
264C2×D8C22⋊D1111yescharacteristic
265C2×M16—222no—
266C22×C8—21no—
267C22×C8—221no—
268C4⋊Q8C22×D1112yes—
269#127—112no—
270#124—42no—
271#121—22no—
272#121—22no—
273#121—222no—
274#121—222no—
275#120—442no—
276C4×D4—111no—
277C4×D4C22×D1111yescharacteristic
278C4×D4C22×D1112yes—
279#117—22no—
280#117—22no—
281#107—21no—
282#107—21no—
283#107—111no—
284#107C22⋊D1111yescharacteristic
285#106—22no—
286#106—222no—
287C4⋊C8—112no—
288C4⋊C8—111no—
289C4⋊C8C22×D1111yescharacteristic
290#102—22no—
291#102—111no—
292#102—111no—
293#102—222no—
294#102—222no—
295#102—222no—
296#102—222no—
297#102—222no—
298#102C22⋊D1112yes—
299C22⋊C8—21no—
300C22⋊C8—222no—
301C22⋊C8—221no—
302C4×C8—111no—
303C4×C8—111no—
304C4×C8C22×D1111yescharacteristic
305C2×C11—82no—
306C2×C11—81no—
307C2×C11#327211yescharacteristic
308C2×C11#328011yescharacteristic
309C2×C11#329211yescharacteristic
310D11—42no—
311D11—162no—
312C24—442no—
313C2×Q8—22no—
314C2×D4—42no—
315C2×D4—111no—
316C2×D4—222no—
317C2×D4—222no—
318C2×D4—222no—
319C2×D4—442no—
320C2×D4—444no—
321C2×D4—442no—
322C2×D4—444no—
323C2×D4—882no—
324C2×D4—882no—
325C2×D4D4×D1111yescharacteristic
326C2×D4C2×C22⋊D1112yes—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—221no—
330SD16—884no—
331D8—22no—
332D8—222no—
333D8—444no—
334D8—442no—
335D8—881no—
336D8—882no—
337M16—882no—
338C2×C8—21no—
339C2×C8—42no—
340C2×C8—111no—
341C2×C8—111no—
342C2×C8—221no—
343C2×C8—222no—
344C2×C8—221no—
345C2×C8—442no—
346C2×C8C2×C22⋊D1111yescharacteristic
347C2×C8C2×C22⋊D1111yescharacteristic
348C4⋊C4—22no—
349C4⋊C4—22no—
350C4⋊C4—111no—
351C4⋊C4D4×D1111yescharacteristic
352C4⋊C4C2×C22⋊D1112yes—
353C22⋊C4—22no—
354C22⋊C4—21no—
355C22⋊C4—42no—
356C22⋊C4—42no—
357C22⋊C4—221no—
358C22⋊C4—442no—
359C42—42no—
360C42C23×D1111yescharacteristic
361C11#1989811yescharacteristic, complemented, Sylow
362C23—21no—
363C23—22no—
364C23—221no—
365C23—442no—
366C23—884no—
367C23—884no—
368C23—1762no—
369Q8—82no—
370D4—21no—
371D4—21no—
372D4—22no—
373D4—22no—
374D4—112no—
375D4—162no—
376D4—221no—
377D4—442no—
378D4—442no—
379D4—442no—
380D4—442no—
381D4—882no—
382D4—884no—
383D4—884no—
384C2×C4—21no—
385C2×C4—22no—
386C2×C4—42no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—42no—
391C2×C4—221no—
392C2×C4—441no—
393C2×C4—441no—
394C2×C4C2×D4×D1111yescharacteristic
395C2×C4#6703711yescharacteristic
396C2×C4C22×C22⋊D1111yescharacteristic
397C8—21no—
398C8—41no—
399C8—222no—
400C8—221no—
401C8—221no—
402C8—442no—
403C8—441no—
404C8#6700212yes—
405C22—41no—
406C22—42no—
407C22—41no—
408C22—42no—
409C22—42no—
410C22—41no—
411C22—222no—
412C22—441no—
413C22—441no—
414C22—882no—
415C22—882no—
416C22—882no—
417C22—1768no—
418C22D4×C22⋊D1111yescharacteristic
419C4—21no—
420C4—41no—
421C4—42no—
422C4—82no—
423C4—441no—
424C4D11×#13511yescharacteristic
425C4#1062330011yescharacteristic
426C4C2×#6700211yescharacteristic
427C4#1062336811yescharacteristic
428C2—82no—
429C2—81no—
430C2—442no—
431C2—1762no—
432C2#1308021611yescharacteristic
433C2#1308029511yescharacteristic
434C2#1308041311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3341C2
socleC22×C11D42
hypercenter#3341D11
hypocenterC11#19898
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #3341

Complements

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

NH ≅ G/Ntype
1. #13080852C2semidirect
2. D8×D44C2semidirect
3. #13068209C2semidirect
4. #13068151C2semidirect
5. #13068012C2semidirect
6. #13067971C2semidirect
7. #13067731C2semidirect
8. #13067699C2semidirect
9. #13067501C2semidirect
10. C8×#4323C2semidirect
11. C11×#3341C2semidirect
12. C11×#555C22semidirect
15. C11×#500C22semidirect
17. C11×#476C22semidirect
20. C8×D4×C11C22semidirect
22. #10622701C22semidirect
23. #10622698C22semidirect
28. #10622628C22semidirect
30. #10622625C22semidirect
37. #10622184C22semidirect
38. D4⋊(C11⋊C8)C22semidirect
39. D4⋊(C11⋊C8)C22semidirect
40. #10622123C22semidirect
42. #10622117C22semidirect
43. #10622096C22semidirect
44. C8×C11⋊C8C22semidirect
145. #3341D11semidirect
200. #555C2×D11semidirect
202. #500C2×D11semidirect
209. #476C2×D11semidirect
221. C8×D4C2×D11semidirect
361. C11#19898semidirect

Maximal subgroups

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

subgroupindex
#130808522
D8×D442
#130682092
#130681512
#130680122
#130679712
#130677312
#130676992
#130675012
C8×#43232
C11×#33412
#1989811