Finite Group Databasebeta

← #14738941

Subgroups — #14738941

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079541C211yesmaximal, characteristic, complemented
2C2×#10622700C211yesmaximal, characteristic, complemented
3#13078082C211yesmaximal, characteristic
4#13077639C211yesmaximal, characteristic, complemented
5#13068038C214yesmaximal, complemented
6#13067960C214yesmaximal, complemented
7#13067388C211yesmaximal, characteristic, complemented
8#13067263C211yesmaximal, characteristic, complemented
9C11×#1549C211yesmaximal, characteristic, complemented
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66961—21no—
12#10623008C2211yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16#10622840—22no—
17#10622746—21no—
18#10622700—22no—
19#10622700C2214yes—
20#10622698C2212yescomplemented
21#10622696—22no—
22#10622694C2212yescomplemented
23C2×#66873—21no—
24C2×#66871—21no—
25#10622538C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622457—22no—
28#10622456C2212yes—
29#10622454C2212yes—
30#10622447C2214yes—
31D11×C22⋊C8—22no—
32C8×D44—22no—
33C11×#332C2214yescomplemented
34#10622124C2212yescomplemented
35#10622123C2212yescomplemented
36#10622118C2214yescomplemented
37C22×Q8×C11—21no—
38C2×#4339—21no—
39C22×D44D411yescharacteristic
40C22×C4×D11—21no—
41C2×C11×M16—21no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8C2312yes—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4325—24no—
50#66983—21no—
51#66983—21no—
52C2×(C2×D11)⋊C4—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C22×C11⋊C8—21no—
55#66961—44no—
56C2×D88—22no—
57C2×#4314—22no—
58C2×C8×D11—24no—
59#66928—21no—
60#66927C2311yescharacteristic
61C4×D44—21no—
62C4×D44—21no—
63C4×D44—21no—
64C4×D44—21no—
65C4×D44D412yes—
66C4×D44C2312yes—
67#66922C2311yescharacteristic
68C11×C4⋊C8—21no—
69C11×C4⋊C8C2312yes—
70C11×C4⋊C8C2312yes—
71C11×C22⋊C8—21no—
72C4×C8×C11—21no—
73#66899—24no—
74C22⋊(C11⋊C8)D412yes—
75#66885—22no—
76(C2×D11)⋊C8—24no—
77#66880—22no—
78#66873—24no—
79#66871—24no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8C2312yes—
84#19385—111nomaximal, Sylow
85C23×D11—21no—
86C2×Q8×C11—22no—
87C2×Q8×C11—41no—
88C2×Q8×C11—82no—
89C22×C4×C11—41no—
90C22×C4×C11C2×D411yescharacteristic
91C22×C4×C11C2×D411yescharacteristic
92C22×C4×C11#4111yescharacteristic
93C2×C22⋊D11—41no—
94C22×Dic11—21no—
95#4339—42no—
96#4339—42no—
97C2×D44—21no—
98C2×D44—22no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44—21no—
102C2×D44SD1614yescomplemented
103C2×D44C2×D412yes—
104C2×C4×D11—22no—
105C2×C4×D11—22no—
106C2×C4×D11—41no—
107C2×C4×D11—82no—
108C2×Dic22—21no—
109C11×M16—42no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C11×C4⋊C4—22no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—41no—
115C11×C4⋊C4—41no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120#4325—84no—
121(C2×D11)⋊C4—22no—
122(C2×D11)⋊C4—22no—
123(C2×D11)⋊C4—41no—
124(C2×D11)⋊C4—41no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11—21no—
128C4⋊Dic11C2×D412yes—
129C2×C11⋊C8—22no—
130C2×C11⋊C8—42no—
131C2×C11⋊C8C2×D414yes—
132D88—44no—
133#4314—44no—
134C8×D11—84no—
135#3206—111no—
136C2×#474—111no—
137#3036—111no—
138#2972—111no—
139#1679—114no—
140#1665—114no—
141#1570—111no—
142#1549D1111yescharacteristic, complemented
143#1540—111no—
144C23×C11#12111yescharacteristic
145C22×D11—22no—
146C22×D11—24no—
147C22×D11—41no—
148C22×D11—81no—
149C22×D11—81no—
150Q8×C11—44no—
151Q8×C11—82no—
152C2×C4×C11—22no—
153C2×C4×C11—41no—
154C2×C4×C11—42no—
155C2×C4×C11—82no—
156C2×C4×C11#12111yescharacteristic
157C2×C4×C11#12111yescharacteristic
158C2×C4×C11#12111yescharacteristic
159C2×C4×C11C2×SD1612yes—
160C2×C4×C11#13512yes—
161C2×C4×C11C22×D411yescharacteristic
162C2×C4×C11C22×D411yescharacteristic
163C2×C4×C11C2×#4111yescharacteristic
164C22⋊D11—82no—
165C2×Dic11—22no—
166C2×Dic11—41no—
167C2×Dic11—81no—
168D44—22no—
169D44—24no—
170D44—41no—
171D44—41no—
172D44—42no—
173D44—81no—
174D44C2×SD1614yes—
175C4×D11—44no—
176C4×D11—82no—
177C4×D11—82no—
178Dic22—41no—
179Dic22—41no—
180C8×C11—42no—
181C8×C11—42no—
182C11⋊C8—24no—
183C11⋊C8—42no—
184C2×AGL(1,ℤ/8)—221no—
185#532—111no—
186C2×C4⋊Q8C2×D1111yescharacteristic
187C2×C4×D4—111no—
188#492—112no—
189#487—112no—
190#474—114no—
191#474—222no—
192#463—222no—
193#461—112no—
194#461—222no—
195#459—112no—
196#448—222no—
197C8×D4—114no—
198C8×D4—222no—
199#431—111no—
200#431C2×D1111yescharacteristic
201C2×#107—221no—
202#423C2×D1111yescharacteristic
203C2×C4⋊C8—111no—
204#417—221no—
205C2×#102—221no—
206C2×C22⋊C8—222no—
207#334—114no—
208#332—112no—
209#332C2×D1114yescomplemented
210#331—112no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11#46512yes—
214C22×C11C2×#12111yescharacteristic
215C2×D11—24no—
216C2×D11—42no—
217C2×D11—42no—
218C2×D11—84no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—82no—
226C4×C11#46512yes—
227C4×C11C22×SD1611yescharacteristic
228C4×C11C2×#13511yescharacteristic
229C4×C11#57612yes—
230Dic11—42no—
231Dic11—81no—
232C2×#41—221no—
233C22×Q8—21no—
234C22×D4—111no—
235C23×C4—221no—
236AGL(1,ℤ/8)—444no—
237C2×SD16—222no—
238C2×SD16—224no—
239C2×D8—222no—
240C2×M16—21no—
241C22×C8—224no—
242C22×C8—221no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—111no—
247C4⋊Q8C22×D1112yes—
248#127—111no—
249#124—221no—
250#121—221no—
251#121—221no—
252C4×D4—112no—
253C4×D4—112no—
254C4×D4—221no—
255C4×D4—221no—
256C4×D4—221no—
257C4×D4—221no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—111no—
261C2×C22⋊C4—221no—
262C2×C42C22×D1111yescharacteristic
263#107—224no—
264C4⋊C8—21no—
265C4⋊C8—112no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8C22×D1112yes—
269C4⋊C8C22×D1112yes—
270#103—222no—
271#103—224no—
272#102—224no—
273#102—222no—
274C22⋊C8—21no—
275C22⋊C8—112no—
276C22⋊C8—224no—
277C4×C8—21no—
278C4×C8—112no—
279C2×C11—22no—
280C2×C11#304111yescharacteristic
281C2×C11C2×#46511yescharacteristic
282C2×C11#306911yescharacteristic
283D11—44no—
284D11—161no—
285C24—221no—
286#41—442no—
287#41—442no—
288C2×Q8—22no—
289C2×Q8—41no—
290C2×Q8—82no—
291C2×Q8—221no—
292C2×D4—114no—
293C2×D4—112no—
294C2×D4—221no—
295C2×D4—222no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—441no—
300C22×C4—41no—
301C22×C4—221no—
302C22×C4—222no—
303C22×C4—222no—
304C22×C4—441no—
305C22×C4—882no—
306C22×C4#433911yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4D4×D1111yescharacteristic
309SD16—444no—
310SD16—884no—
311D8—444no—
312M16—42no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—114no—
316C2×C8—222no—
317C2×C8—442no—
318C2×C8—884no—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—112no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—221no—
327C22⋊C4—222no—
328C22⋊C4—222no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C42#433911yescharacteristic
332C42D4×D1111yescharacteristic
333C42D4×D1111yescharacteristic
334C42C23×D1111yescharacteristic
335C11#1938511yescharacteristic, complemented, Sylow
336C23—222no—
337C23—224no—
338C23—441no—
339C23—881no—
340C23—881no—
341C23#6693711yescharacteristic
342Q8—44no—
343Q8—82no—
344Q8—441no—
345Q8—441no—
346D4—114no—
347D4—222no—
348D4—224no—
349D4—441no—
350D4—441no—
351D4—442no—
352D4—881no—
353D4—882no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—82no—
358C2×C4—222no—
359C2×C4—444no—
360C2×C4—441no—
361C2×C4—882no—
362C2×C4—881no—
363C2×C4—882no—
364C2×C4#6693711yescharacteristic
365C2×C4#6693711yescharacteristic
366C2×C4#6693711yescharacteristic
367C2×C4SD16×D1112yes—
368C2×C4#6697212yes—
369C2×C4C2×#433911yescharacteristic
370C2×C4C2×D4×D1111yescharacteristic
371C2×C4C2×D4×D1111yescharacteristic
372C8—42no—
373C8—42no—
374C8—224no—
375C8—442no—
376C22—21no—
377C22—21no—
378C22—224no—
379C22—442no—
380C22—442no—
381C22—884no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22#1062242012yes—
386C22C2×#6693711yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—82no—
391C4—442no—
392C4—881no—
393C4#1062242012yes—
394C4C2×SD16×D1111yescharacteristic
395C4C2×#6697211yescharacteristic
396C4#1062330512yes—
397C2—22no—
398C2—444no—
399C2—1761no—
400C2#1307811811yescharacteristic
401C2C2×#1062242011yescharacteristic
402C2#1307835211yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1549C2
socleC22×C11C2×#121
prime radical#13078082C2
hypercenter#1549D11
hypocenterC11#19385
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
1. #13079541C2semidirect
2. C2×#10622700C2semidirect
4. #13077639C2semidirect
5. #13068038C2semidirect
6. #13067960C2semidirect
7. #13067388C2semidirect
8. #13067263C2semidirect
9. C11×#1549C2semidirect
20. #10622698C22semidirect
22. #10622694C22semidirect
33. C11×#332C22semidirect
34. #10622124C22semidirect
35. #10622123C22semidirect
36. #10622118C22semidirect
102. C2×D44SD16semidirect
142. #1549D11semidirect
209. #332C2×D11semidirect
335. C11#19385semidirect

Maximal subgroups

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

subgroupindex
#130795412
C2×#106227002
#130780822
#130776392
#130680382
#130679602
#130673882
#130672632
C11×#15492
#1938511