Finite Group Databasebeta

← #14738953

Subgroups — #14738953

Order 2816.

792 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#13079531C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic, complemented
3#13077640C211yesmaximal, characteristic, complemented
4#13068055C214yesmaximal, complemented
5#13067969C214yesmaximal, complemented
6#13067392C211yesmaximal, characteristic, complemented
7#13067285C211yesmaximal, characteristic, complemented
8#13067265C211yesmaximal, characteristic, complemented
9C11×#3036C211yesmaximal, characteristic, complemented
10C2×C11×AGL(1,ℤ/8)—21no—
11C11×#532C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C22×#4323—21no—
14C2×#66927C2211yescharacteristic
15C11×#463—22no—
16C11×#461C2212yescomplemented
17C11×#459C2212yescomplemented
18C11×#423C2211yescharacteristic
19C11×#417—21no—
20C2×C22⋊(C11⋊C8)—22no—
21#10622701C2212yescomplemented
22#10622686C2212yescomplemented
23#10622649—22no—
24#10622628—22no—
25#10622628—22no—
26#10622628C2214yes—
27D4×C11⋊C8—22no—
28D4×C11⋊C8C2214yescomplemented
29C2×#66873—21no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32C2×C4⋊(C11⋊C8)C2211yescharacteristic
33#10622185C2212yescomplemented
34#10622182C2212yescomplemented
35#10622123C2214yescomplemented
36#10622117C2214yescomplemented
37C2×C11×#41—21no—
38C22×D4×C11D411yescharacteristic
39C23×C4×C11—21no—
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—21no—
43C11×AGL(1,ℤ/8)—44no—
44C2×C11×SD16—22no—
45C2×C11×D8—22no—
46C2×C11×M16—21no—
47C11×C4⋊Q8C2311yescharacteristic
48C11×#127C2311yescharacteristic
49C11×#124—21no—
50C11×#121—21no—
51C11×#121—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C4×D4×C11—21no—
56C4×D4×C11D412yes—
57C4×D4×C11C2312yes—
58C2×C11×C4⋊C4D411yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C42×C11C2311yescharacteristic
61C2×#4323—24no—
62C2×#4323—24no—
63C2×#4323—44no—
64C22×C11⋊C8—21no—
65C22×C11⋊C8—24no—
66#66927—21no—
67#66927—21no—
68#66927—21no—
69#66927C2312yes—
70C11×C4⋊C8—21no—
71C11×C4⋊C8C2312yes—
72C11×#103—22no—
73C11×#102—22no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—24no—
76C22⋊(C11⋊C8)D412yes—
77#66873—24no—
78#66873—24no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)D412yes—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84C4×C11⋊C8C2312yes—
85#19386—111nomaximal, Sylow
86C24×C11—21no—
87C23×D11—41no—
88C11×#41—42no—
89C11×#41—42no—
90C2×Q8×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—22no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—41no—
97C2×D4×C11D814yescomplemented
98C2×D4×C11C2×D412yes—
99C22×C4×C11—21no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—41no—
103C22×C4×C11—82no—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C2×D44—22no—
108C2×D44—22no—
109C2×D44—22no—
110C2×D44—41no—
111C2×D44—41no—
112C2×D44—41no—
113C2×D44—42no—
114C2×D44—42no—
115C2×D44—82no—
116C2×D44—82no—
117C11×SD16—44no—
118C11×D8—44no—
119C11×M16—42no—
120C2×C8×C11—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4C2×D412yes—
125C11×C22⋊C4—22no—
126C11×C22⋊C4—22no—
127C11×C22⋊C4—41no—
128C11×C22⋊C4—41no—
129C42×C11C2×D411yescharacteristic
130C42×C11C2×D411yescharacteristic
131C42×C11#4111yescharacteristic
132C42×C11C2411yescharacteristic
133#4323—48no—
134#4323—84no—
135C2×C11⋊C8—22no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—42no—
138C2×C11⋊C8—84no—
139C2×C11⋊C8C2×D414yes—
140#3205—111no—
141#3036D1111yescharacteristic, complemented
142C2×#459—111no—
143#2972—111no—
144#1681—114no—
145#1667—114no—
146#1571—111no—
147#1545—111no—
148#1540—111no—
149C23×C11—22no—
150C23×C11—24no—
151C23×C11—41no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11#12111yescharacteristic
155C22×D11—42no—
156C22×D11—82no—
157C22×D11—82no—
158C22×D11—82no—
159Q8×C11—41no—
160Q8×C11—41no—
161D4×C11—22no—
162D4×C11—24no—
163D4×C11—41no—
164D4×C11—41no—
165D4×C11—42no—
166D4×C11—81no—
167D4×C11—82no—
168D4×C11C2×D814yes—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—44no—
173C2×C4×C11—41no—
174C2×C4×C11—82no—
175C2×C4×C11—81no—
176C2×C4×C11—82no—
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11#12111yescharacteristic
179C2×C4×C11#12111yescharacteristic
180C2×C4×C11C2×D812yes—
181C2×C4×C11#13512yes—
182C2×C4×C11C22×D411yescharacteristic
183C2×C4×C11C22×D411yescharacteristic
184C2×C4×C11C2×#4111yescharacteristic
185D44—42no—
186D44—42no—
187D44—44no—
188D44—82no—
189D44—82no—
190D44—82no—
191D44—82no—
192C8×C11—42no—
193C11⋊C8—24no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C2×AGL(1,ℤ/8)—21no—
197C22×D8—221no—
198#532C2×D1111yescharacteristic
199C2×#127—111no—
200C2×C4×D4C2×D1111yescharacteristic
201#493—112no—
202#486—112no—
203#463—22no—
204#461C2×D1112yescomplemented
205#459—114no—
206#459—222no—
207#459—222no—
208#459C2×D1112yescomplemented
209#447—222no—
210C8×D4—114no—
211C8×D4—222no—
212#431—111no—
213#431—111no—
214#423C2×D1111yescharacteristic
215C2×C4⋊C8—111no—
216#417—21no—
217C2×#102—221no—
218C2×C22⋊C8—222no—
219#335—114no—
220#332—112no—
221#331—112no—
222#331—114no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—24no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11—84no—
229C22×C11—81no—
230C22×C11—81no—
231C22×C11—81no—
232C22×C11#46612yes—
233C22×C11C2×#12111yescharacteristic
234C2×D11—82no—
235C2×D11—82no—
236C2×D11—82no—
237C2×D11—164no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—42no—
242C4×C11—81no—
243C4×C11#46612yes—
244C4×C11C22×D811yescharacteristic
245C4×C11C2×#13511yescharacteristic
246C4×C11#57612yes—
247C2×#41—21no—
248C22×D4—221no—
249C22×D4—221no—
250C22×D4—221no—
251C22×D4C22⋊D1111yescharacteristic
252C23×C4—21no—
253AGL(1,ℤ/8)—44no—
254C2×SD16—22no—
255C2×D8—22no—
256C2×D8—224no—
257C2×D8—224no—
258C2×D8—444no—
259C2×M16—21no—
260C22×C8—224no—
261C22×C8—221no—
262C4⋊Q8C22×D1111yescharacteristic
263#127—112no—
264#127—221no—
265#127—221no—
266#127—221no—
267#127C22×D1111yescharacteristic
268#124—21no—
269#121—21no—
270#121—21no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—21no—
274C4×D4—21no—
275C4×D4C22⋊D1112yes—
276C4×D4C22×D1112yes—
277C2×C4⋊C4C22⋊D1111yescharacteristic
278C2×C22⋊C4—21no—
279C2×C42C22×D1111yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—112no—
282C4⋊C8—112no—
283C4⋊C8—112no—
284C4⋊C8—221no—
285C4⋊C8C22×D1112yes—
286#103—22no—
287#102—22no—
288#102—224no—
289#102—224no—
290C22⋊C8—112no—
291C22⋊C8—224no—
292C22⋊C8—221no—
293C4×C8—112no—
294C4×C8—221no—
295C2×C11—22no—
296C2×C11—44no—
297C2×C11—161no—
298C2×C11#304111yescharacteristic
299C2×C11C2×#46611yescharacteristic
300C2×C11#306811yescharacteristic
301D11—162no—
302C24—21no—
303C24—441no—
304#41—42no—
305#41—42no—
306C2×Q8—21no—
307C2×D4—21no—
308C2×D4—22no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—41no—
313C2×D4—222no—
314C2×D4—222no—
315C2×D4—222no—
316C2×D4—442no—
317C2×D4—441no—
318C2×D4—441no—
319C2×D4—441no—
320C2×D4—442no—
321C2×D4—882no—
322C2×D4—882no—
323C2×D4#432314yescomplemented
324C2×D4C2×C22⋊D1112yes—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—41no—
329C22×C4—82no—
330C22×C4D4×D1111yescharacteristic
331C22×C4#434111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—44no—
334D8—44no—
335D8—448no—
336D8—884no—
337M16—42no—
338C2×C8—22no—
339C2×C8—114no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—442no—
343C2×C8—884no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4C2×C22⋊D1112yes—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—41no—
351C22⋊C4—41no—
352C42D4×D1111yescharacteristic
353C42#434111yescharacteristic
354C42C2×C22⋊D1111yescharacteristic
355C42C23×D1111yescharacteristic
356C11#1938611yescharacteristic, complemented, Sylow
357C23—22no—
358C23—24no—
359C23—41no—
360C23—81no—
361C23—81no—
362C23—442no—
363C23—882no—
364C23—882no—
365C23—882no—
366C23#6699211yescharacteristic
367Q8—41no—
368Q8—41no—
369D4—22no—
370D4—24no—
371D4—42no—
372D4—41no—
373D4—41no—
374D4—81no—
375D4—82no—
376D4—444no—
377D4—442no—
378D4—442no—
379D4—882no—
380D4—882no—
381D4—882no—
382D4—882no—
383D4C2×#432314yes—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—41no—
389C2×C4—82no—
390C2×C4—81no—
391C2×C4—82no—
392C2×C4C2×#432312yes—
393C2×C4#6699211yescharacteristic
394C2×C4#6699211yescharacteristic
395C2×C4#6699211yescharacteristic
396C2×C4#6700312yes—
397C2×C4C2×D4×D1111yescharacteristic
398C2×C4C2×#434111yescharacteristic
399C2×C4C22×C22⋊D1111yescharacteristic
400C8—42no—
401C8—224no—
402C8—442no—
403C8—442no—
404C22—21no—
405C22—21no—
406C22—24no—
407C22—42no—
408C22—42no—
409C22—84no—
410C22—81no—
411C22—81no—
412C22—81no—
413C22—882no—
414C22—882no—
415C22—882no—
416C22—1764no—
417C22#1062265112yes—
418C22C2×#6699211yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—42no—
423C4—81no—
424C4#1062265112yes—
425C4#1062330512yes—
426C4C22×#432311yescharacteristic
427C4C2×#6700311yescharacteristic
428C2—22no—
429C2—44no—
430C2—161no—
431C2—1762no—
432C2#1307812111yescharacteristic
433C2C2×#1062265111yescharacteristic
434C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3036C2
socleC22×C11C2×#121
hypercenter#3036D11
hypocenterC11#19386
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079531C2semidirect
2. C2×#10622628C2semidirect
3. #13077640C2semidirect
4. #13068055C2semidirect
5. #13067969C2semidirect
6. #13067392C2semidirect
7. #13067285C2semidirect
8. #13067265C2semidirect
9. C11×#3036C2semidirect
16. C11×#461C22semidirect
17. C11×#459C22semidirect
21. #10622701C22semidirect
22. #10622686C22semidirect
28. D4×C11⋊C8C22semidirect
33. #10622185C22semidirect
34. #10622182C22semidirect
35. #10622123C22semidirect
36. #10622117C22semidirect
97. C2×D4×C11D8semidirect
141. #3036D11semidirect
204. #461C2×D11semidirect
208. #459C2×D11semidirect
323. C2×D4#4323semidirect
356. C11#19386semidirect

Maximal subgroups

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

subgroupindex
#130795312
C2×#106226282
#130776402
#130680552
#130679692
#130673922
#130672852
#130672652
C11×#30362
#1938611