Finite Group Databasebeta

← #14738933

Subgroups — #14738933

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079559C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic, complemented
3C2×#10622628C211yesmaximal, characteristic
4#13068025C214yesmaximal, complemented
5#13067957C214yesmaximal, complemented
6#13067387C211yesmaximal, characteristic, complemented
7#13067283C211yesmaximal, characteristic, complemented
8#13067271C211yesmaximal, characteristic, complemented
9C11×#2972C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4323—21no—
12C2×#66927C2211yescharacteristic
13#10623001C2211yescharacteristic
14C8×D4×C11—22no—
15C8×D4×C11C2214yescomplemented
16C11×#431C2211yescharacteristic
17C11×#431C2211yescharacteristic
18C2×C11×C22⋊C8—22no—
19#10622828—21no—
20#10622628—22no—
21#10622628C2214yes—
22#10622622—22no—
23#10622621C2212yescomplemented
24#10622620C2212yescomplemented
25C2×#66873—21no—
26#10622577—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622461—22no—
30#10622344—22no—
31#10622307C2212yescomplemented
32#10622306C2212yescomplemented
33#10622123C2214yescomplemented
34#10622120C2212yescomplemented
35#10622119C2212yescomplemented
36#10622095C2214yescomplemented
37C22×D4×C11D411yescharacteristic
38C23×C4×C11—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—21no—
42C22×C8×C11—24no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11D412yes—
46C4×D4×C11C2312yes—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C42×C11C2311yescharacteristic
50C2×#4323—24no—
51C2×#4323—44no—
52#66979—21no—
53#66977—21no—
54#66977—21no—
55C2×#4318—21no—
56C22×C11⋊C8—21no—
57C2×#4314—24no—
58#66927—21no—
59#66927—21no—
60#66927—21no—
61#66927C2312yes—
62#66923—21no—
63#66922C2311yescharacteristic
64#66922C2311yescharacteristic
65C4×Dic22—21no—
66C4×Dic22—21no—
67C11×C4⋊C8D412yes—
68C11×C4⋊C8C2312yes—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—24no—
71C11×C22⋊C8D412yes—
72C4×C8×C11—21no—
73C4×C8×C11C2312yes—
74#66896—22no—
75#66896—22no—
76#66885—24no—
77#66873—24no—
78#66872—22no—
79#66871—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)C2312yes—
83C4⋊(C11⋊C8)C2312yes—
84#19384—111nomaximal, Sylow
85C24×C11—21no—
86C23×D11—41no—
87C2×D4×C11—21no—
88C2×D4×C11—22no—
89C2×D4×C11SD1614yescomplemented
90C2×D4×C11C2×D412yes—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—82no—
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C2×D44—22no—
99C2×D44—22no—
100C2×D44—22no—
101C2×D44—41no—
102C2×D44—41no—
103C2×D44—41no—
104C2×D44—42no—
105C2×D44—42no—
106C2×D44—82no—
107C2×D44—82no—
108C2×Dic22—21no—
109C2×Dic22—21no—
110C2×C8×C11—22no—
111C2×C8×C11—84no—
112C2×C8×C11C2×D414yes—
113C11×C4⋊C4—21no—
114C11×C4⋊C4C2×D412yes—
115C11×C22⋊C4—22no—
116C11×C22⋊C4—22no—
117C42×C11C2×D411yescharacteristic
118C42×C11C2×D411yescharacteristic
119C42×C11#4111yescharacteristic
120C42×C11C2411yescharacteristic
121C22⋊Dic11—41no—
122#4323—48no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127Dic11⋊C4—41no—
128Dic11⋊C4—41no—
129C4×Dic11—41no—
130#4318—42no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—42no—
134#4314—84no—
135#3208—111no—
136#3077—111no—
137C2×#459—111no—
138#2972D1111yescharacteristic, complemented
139#1677—114no—
140#1665—114no—
141#1570—111no—
142#1545—111no—
143#1542—111no—
144C23×C11—22no—
145C23×C11—24no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11#12111yescharacteristic
149C22×D11—42no—
150C22×D11—82no—
151C22×D11—82no—
152C22×D11—82no—
153D4×C11—22no—
154D4×C11—24no—
155D4×C11C2×SD1614yes—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—41no—
159C2×C4×C11—44no—
160C2×C4×C11—82no—
161C2×C4×C11—81no—
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12111yescharacteristic
164C2×C4×C11#12111yescharacteristic
165C2×C4×C11C2×SD1612yes—
166C2×C4×C11#13512yes—
167C2×C4×C11C22×D411yescharacteristic
168C2×C4×C11C22×D411yescharacteristic
169C2×C4×C11C2×#4111yescharacteristic
170C2×Dic11—41no—
171C2×Dic11—41no—
172D44—42no—
173D44—42no—
174D44—44no—
175D44—82no—
176D44—82no—
177D44—82no—
178D44—82no—
179Dic22—42no—
180Dic22—81no—
181C8×C11—24no—
182C8×C11—42no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C22×D8—221no—
186#533—111no—
187C2×#127—111no—
188C2×C4×D4C2×D1111yescharacteristic
189#492—112no—
190#486—112no—
191#478—222no—
192#476—112no—
193#474—112no—
194#460—222no—
195#459—114no—
196#459—222no—
197#450—222no—
198C8×D4—22no—
199C8×D4C2×D1114yescomplemented
200#431C2×D1111yescharacteristic
201#431C2×D1111yescharacteristic
202#428—221no—
203#423—111no—
204C2×C4⋊C8—111no—
205#418—221no—
206C2×#102—221no—
207C2×C22⋊C8—22no—
208#334—114no—
209#333—112no—
210#332—112no—
211#331—114no—
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—24no—
215C22×C11—42no—
216C22×C11—42no—
217C22×C11—84no—
218C22×C11#46512yes—
219C22×C11C2×#12111yescharacteristic
220C2×D11—82no—
221C2×D11—82no—
222C2×D11—82no—
223C2×D11—164no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11—42no—
228C4×C11#46512yes—
229C4×C11C22×SD1611yescharacteristic
230C4×C11C2×#13511yescharacteristic
231C4×C11#57612yes—
232Dic11—81no—
233Dic11—81no—
234C22×D4—221no—
235C22×D4—221no—
236C22×D4—221no—
237C22×D4D4411yescharacteristic
238C23×C4—21no—
239C2×SD16—224no—
240C2×D8—224no—
241C2×D8—444no—
242C2×M16—221no—
243C22×C8—24no—
244C22×C8—221no—
245C4⋊Q8—111no—
246C4⋊Q8—111no—
247#127—112no—
248#127—221no—
249#127—221no—
250#127—221no—
251#125—221no—
252C22⋊Q8—221no—
253C22⋊Q8—221no—
254C4×Q8—221no—
255C4×Q8—221no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4D4412yes—
259C4×D4C22×D1112yes—
260#117—221no—
261C2×C4⋊C4D4411yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C22×D1111yescharacteristic
264#107—222no—
265#106—222no—
266C4⋊C8—112no—
267C4⋊C8—112no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270C4⋊C8C22⋊D1112yes—
271C4⋊C8C22×D1112yes—
272#102—222no—
273#102—222no—
274#102—224no—
275#102—224no—
276C22⋊C8—21no—
277C22⋊C8—24no—
278C22⋊C8C22⋊D1112yes—
279C4×C8—21no—
280C4×C8C22×D1112yes—
281C2×C11—22no—
282C2×C11—44no—
283C2×C11#304111yescharacteristic
284C2×C11C2×#46511yescharacteristic
285C2×C11#306811yescharacteristic
286D11—162no—
287C24—21no—
288C24—441no—
289C2×Q8—221no—
290C2×Q8—221no—
291C2×D4—22no—
292C2×D4—21no—
293C2×D4—222no—
294C2×D4—222no—
295C2×D4—222no—
296C2×D4—442no—
297C2×D4—442no—
298C2×D4—441no—
299C2×D4—441no—
300C2×D4—441no—
301C2×D4—882no—
302C2×D4—882no—
303C2×D4#431414yescomplemented
304C2×D4C2×D4412yes—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—82no—
309C22×C4C2×D4411yescharacteristic
310C22×C4#433911yescharacteristic
311C22×C4C2×C22⋊D1111yescharacteristic
312SD16—884no—
313D8—448no—
314M16—442no—
315C2×C8—22no—
316C2×C8—84no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8—442no—
320C2×C8C2×C22⋊D1114yes—
321C4⋊C4—21no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—441no—
327C4⋊C4—441no—
328C4⋊C4C2×D4412yes—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—441no—
332C42—441no—
333C42C2×D4411yescharacteristic
334C42#433911yescharacteristic
335C42C2×C22⋊D1111yescharacteristic
336C42C23×D1111yescharacteristic
337C11#1938411yescharacteristic, complemented, Sylow
338C23—22no—
339C23—24no—
340C23—81no—
341C23—81no—
342C23—442no—
343C23—882no—
344C23—882no—
345C23—882no—
346C23#6698311yescharacteristic
347Q8—442no—
348Q8—881no—
349D4—24no—
350D4—22no—
351D4—442no—
352D4—442no—
353D4—444no—
354D4—882no—
355D4—882no—
356D4—882no—
357D4—882no—
358D4C2×#431414yes—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—44no—
363C2×C4—82no—
364C2×C4—81no—
365C2×C4—441no—
366C2×C4—441no—
367C2×C4C2×#431412yes—
368C2×C4#6695712yes—
369C2×C4#6698311yescharacteristic
370C2×C4#6698311yescharacteristic
371C2×C4#6698311yescharacteristic
372C2×C4C22×D4411yescharacteristic
373C2×C4C2×#433911yescharacteristic
374C2×C4C22×C22⋊D1111yescharacteristic
375C8—24no—
376C8—42no—
377C8—442no—
378C8—442no—
379C22—21no—
380C22—21no—
381C22—24no—
382C22—42no—
383C22—42no—
384C22—84no—
385C22—882no—
386C22—882no—
387C22—882no—
388C22—1764no—
389C22#1062272712yes—
390C22C2×#6698311yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—881no—
396C4—881no—
397C4#1062272712yes—
398C4C22×#431411yescharacteristic
399C4C2×#6695711yescharacteristic
400C4#1062336612yes—
401C2—22no—
402C2—44no—
403C2—1762no—
404C2#1307811911yescharacteristic
405C2C2×#1062272711yescharacteristic
406C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2972C2
socleC22×C11C2×#121
prime radicalC2×#10622628C2
hypercenter#2972D11
hypocenterC11#19384
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2972

Complements

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

NH ≅ G/Ntype
1. #13079559C2semidirect
2. #13078413C2semidirect
4. #13068025C2semidirect
5. #13067957C2semidirect
6. #13067387C2semidirect
7. #13067283C2semidirect
8. #13067271C2semidirect
9. C11×#2972C2semidirect
15. C8×D4×C11C22semidirect
23. #10622621C22semidirect
24. #10622620C22semidirect
31. #10622307C22semidirect
32. #10622306C22semidirect
33. #10622123C22semidirect
34. #10622120C22semidirect
35. #10622119C22semidirect
36. #10622095C22semidirect
89. C2×D4×C11SD16semidirect
138. #2972D11semidirect
199. C8×D4C2×D11semidirect
303. C2×D4#4314semidirect
337. C11#19384semidirect

Maximal subgroups

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

subgroupindex
#130795592
#130784132
C2×#106226282
#130680252
#130679572
#130673872
#130672832
#130672712
C11×#29722
#1938411