Finite Group Databasebeta

← #14738932

Subgroups — #14738932

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#13079557C211yesmaximal, characteristic, complemented
2#13078415C211yesmaximal, characteristic, complemented
3C2×#10622685C211yesmaximal, characteristic
4#13077639C211yesmaximal, characteristic, complemented
5#13068024C214yesmaximal, complemented
6#13067956C214yesmaximal, complemented
7#13067388C211yesmaximal, characteristic, complemented
8#13067271C211yesmaximal, characteristic, complemented
9C11×#1545C211yesmaximal, characteristic, complemented
10C2×C11×#127C2211yescharacteristic
11C22×#4323—21no—
12C2×C4×D44C2211yescharacteristic
13#10623001C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16#10622831—22no—
17C2×#66896—21no—
18#10622744—21no—
19#10622734—21no—
20#10622689C2212yescomplemented
21#10622688—22no—
22#10622685—22no—
23#10622685C2214yes—
24#10622683C2212yescomplemented
25#10622538C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622460—22no—
28#10622459C2212yescomplemented
29#10622455C2212yescomplemented
30#10622447C2214yescomplemented
31D11×C22⋊C8—22no—
32C8×D44—22no—
33C11×#331C2214yescomplemented
34#10622120C2212yescomplemented
35#10622119C2212yescomplemented
36#10622118C2214yescomplemented
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D44D411yescharacteristic
41C22×C4×D11—21no—
42C2×C11×M16—21no—
43C11×#127—21no—
44C11×#127—21no—
45C11×#127—21no—
46C11×#127C2312yes—
47C2×C42×C11C2311yescharacteristic
48C2×#4324—24no—
49C2×#4323—24no—
50C2×#4323—44no—
51C2×(C2×D11)⋊C4—21no—
52#66979—21no—
53C2×C4⋊Dic11D411yescharacteristic
54#66977—21no—
55#66977—21no—
56C22×C11⋊C8—21no—
57C2×C8×D11—24no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44D412yes—
61C4×D44C2312yes—
62#66923—21no—
63#66922C2311yescharacteristic
64#66922C2311yescharacteristic
65C4×Dic22—21no—
66C4×Dic22—21no—
67C11×C4⋊C8—21no—
68C11×C4⋊C8C2312yes—
69C11×C4⋊C8C2312yes—
70C11×C22⋊C8—21no—
71C4×C8×C11—21no—
72#66896—24no—
73#66896—24no—
74C22⋊(C11⋊C8)D412yes—
75#66885—22no—
76#66885—22no—
77(C2×D11)⋊C8—24no—
78#66882—22no—
79#66881—22no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)D412yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8C2312yes—
84#19384—111nomaximal, Sylow
85C24×C11—41no—
86C23×D11—21no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11—22no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—42no—
94C2×D4×C11—42no—
95C2×D4×C11—82no—
96C2×D4×C11—82no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C22×Dic11—21no—
101C2×D44—21no—
102C2×D44—22no—
103C2×D44SD1614yescomplemented
104C2×D44C2×D412yes—
105C2×C4×D11—22no—
106C2×C4×D11—22no—
107C2×C4×D11—82no—
108C2×Dic22—21no—
109C2×Dic22—21no—
110C11×M16—42no—
111C2×C8×C11—22no—
112C2×C8×C11—22no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11#4111yescharacteristic
116C42×C11C2411yescharacteristic
117C22⋊Dic11—41no—
118#4324—84no—
119#4323—48no—
120(C2×D11)⋊C4—22no—
121(C2×D11)⋊C4—22no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—21no—
125C4⋊Dic11—21no—
126C4⋊Dic11—21no—
127C4⋊Dic11C2×D412yes—
128Dic11⋊C4—41no—
129Dic11⋊C4—41no—
130C4×Dic11—41no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—42no—
133C2×C11⋊C8C2×D414yes—
134C8×D11—84no—
135#3208—111no—
136#3077—111no—
137C2×#459—111no—
138#2972—111no—
139#1677—114no—
140#1665—114no—
141#1570—111no—
142#1545D1111yescharacteristic, complemented
143#1542—111no—
144C23×C11—42no—
145C23×C11—82no—
146C23×C11—82no—
147C23×C11—82no—
148C23×C11#12111yescharacteristic
149C22×D11—22no—
150C22×D11—24no—
151C22×D11—81no—
152C22×D11—81no—
153D4×C11—42no—
154D4×C11—42no—
155D4×C11—44no—
156D4×C11—82no—
157D4×C11—82no—
158D4×C11—82no—
159D4×C11—82no—
160C2×C4×C11—22no—
161C2×C4×C11—41no—
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—22no—
171C2×Dic11—41no—
172C2×Dic11—41no—
173C2×Dic11—81no—
174D44—22no—
175D44—24no—
176D44C2×SD1614yes—
177C4×D11—44no—
178C4×D11—82no—
179Dic22—42no—
180Dic22—81no—
181C8×C11—42no—
182C8×C11—42no—
183C11⋊C8—24no—
184C11⋊C8—42no—
185C22×D8—221no—
186#533—111no—
187C2×#127C2×D1111yescharacteristic
188C2×C4×D4—111no—
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—114no—
199C8×D4—222no—
200#431—111no—
201#431C2×D1111yescharacteristic
202#428—221no—
203#423C2×D1111yescharacteristic
204C2×C4⋊C8—111no—
205#418—221no—
206C2×#102—221no—
207C2×C22⋊C8—222no—
208#334—114no—
209#333—112no—
210#332—112no—
211#331C2×D1114yescomplemented
212C22×C11—21no—
213C22×C11—21no—
214C22×C11—82no—
215C22×C11—82no—
216C22×C11—82no—
217C22×C11—164no—
218C22×C11#46512yes—
219C22×C11C2×#12111yescharacteristic
220C2×D11—24no—
221C2×D11—42no—
222C2×D11—42no—
223C2×D11—84no—
224C4×C11—21no—
225C4×C11—21no—
226C4×C11—21no—
227C4×C11#46512yes—
228C4×C11C22×SD1611yescharacteristic
229C4×C11C2×#13511yescharacteristic
230C4×C11#57612yes—
231Dic11—42no—
232Dic11—81no—
233Dic11—81no—
234C22×D4—21no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—111no—
238C23×C4—221no—
239C2×SD16—224no—
240C2×D8—224no—
241C2×D8—444no—
242C2×M16—21no—
243C22×C8—224no—
244C22×C8—221no—
245C4⋊Q8—111no—
246C4⋊Q8—111no—
247#127—21no—
248#127—21no—
249#127—21no—
250#127C22×D1112yes—
251#125—221no—
252C22⋊Q8—221no—
253C22⋊Q8—221no—
254C4×Q8—221no—
255C4×Q8—221no—
256C4×D4—112no—
257C4×D4—112no—
258C4×D4—221no—
259C4×D4—221no—
260#117—221no—
261C2×C4⋊C4—111no—
262C2×C22⋊C4—221no—
263C2×C42C22×D1111yescharacteristic
264#107—222no—
265#106—222no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8—112no—
269C4⋊C8—221no—
270C4⋊C8C22×D1112yes—
271C4⋊C8C22×D1112yes—
272#102—224no—
273#102—222no—
274#102—222no—
275#102—224no—
276C22⋊C8—21no—
277C22⋊C8—112no—
278C22⋊C8—224no—
279C4×C8—21no—
280C4×C8—112no—
281C2×C11—22no—
282C2×C11—162no—
283C2×C11#304111yescharacteristic
284C2×C11C2×#46511yescharacteristic
285C2×C11#306811yescharacteristic
286D11—44no—
287C24—41no—
288C24—221no—
289C2×Q8—221no—
290C2×Q8—221no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—82no—
300C2×D4—82no—
301C2×D4—114no—
302C2×D4—112no—
303C2×D4—221no—
304C2×D4—222no—
305C22×C4—221no—
306C22×C4—222no—
307C22×C4—222no—
308C22×C4—882no—
309C22×C4#433911yescharacteristic
310C22×C4D4×D1111yescharacteristic
311C22×C4D4×D1111yescharacteristic
312SD16—884no—
313D8—448no—
314M16—42no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—114no—
318C2×C8—222no—
319C2×C8—442no—
320C2×C8—884no—
321C4⋊C4—112no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—221no—
325C4⋊C4—221no—
326C4⋊C4—221no—
327C4⋊C4—441no—
328C4⋊C4—441no—
329C22⋊C4—222no—
330C22⋊C4—222no—
331C22⋊C4—441no—
332C42—441no—
333C42#433911yescharacteristic
334C42D4×D1111yescharacteristic
335C42D4×D1111yescharacteristic
336C42C23×D1111yescharacteristic
337C11#1938411yescharacteristic, complemented, Sylow
338C23—42no—
339C23—82no—
340C23—82no—
341C23—82no—
342C23—222no—
343C23—224no—
344C23—881no—
345C23—881no—
346C23#6693711yescharacteristic
347Q8—442no—
348Q8—881no—
349D4—42no—
350D4—42no—
351D4—44no—
352D4—82no—
353D4—82no—
354D4—82no—
355D4—82no—
356D4—114no—
357D4—222no—
358D4—224no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—222no—
362C2×C4—444no—
363C2×C4—441no—
364C2×C4—441no—
365C2×C4—882no—
366C2×C4—881no—
367C2×C4#6693711yescharacteristic
368C2×C4#6693711yescharacteristic
369C2×C4#6693711yescharacteristic
370C2×C4#6696512yes—
371C2×C4SD16×D1112yes—
372C2×C4C2×#433911yescharacteristic
373C2×C4C2×D4×D1111yescharacteristic
374C2×C4C2×D4×D1111yescharacteristic
375C8—42no—
376C8—42no—
377C8—224no—
378C8—442no—
379C22—21no—
380C22—21no—
381C22—82no—
382C22—82no—
383C22—82no—
384C22—164no—
385C22—224no—
386C22—442no—
387C22—442no—
388C22—884no—
389C22#1062239112yes—
390C22C2×#6693711yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—442no—
395C4—881no—
396C4—881no—
397C4#1062239112yes—
398C4C2×#6696511yescharacteristic
399C4C2×SD16×D1111yescharacteristic
400C4#1062330512yes—
401C2—22no—
402C2—162no—
403C2—444no—
404C2#1307811811yescharacteristic
405C2C2×#1062239111yescharacteristic
406C2#1307834311yescharacteristic
subgroupG/H
centerC22C2×#66937
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1545C2
socleC22×C11C2×#121
prime radicalC2×#10622685C2
hypercenter#1545D11
hypocenterC11#19384
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1545

Complements

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

NH ≅ G/Ntype
1. #13079557C2semidirect
2. #13078415C2semidirect
4. #13077639C2semidirect
5. #13068024C2semidirect
6. #13067956C2semidirect
7. #13067388C2semidirect
8. #13067271C2semidirect
9. C11×#1545C2semidirect
20. #10622689C22semidirect
24. #10622683C22semidirect
28. #10622459C22semidirect
29. #10622455C22semidirect
30. #10622447C22semidirect
33. C11×#331C22semidirect
34. #10622120C22semidirect
35. #10622119C22semidirect
36. #10622118C22semidirect
103. C2×D44SD16semidirect
142. #1545D11semidirect
211. #331C2×D11semidirect
337. C11#19384semidirect

Maximal subgroups

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

subgroupindex
#130795572
#130784152
C2×#106226852
#130776392
#130680242
#130679562
#130673882
#130672712
C11×#15452
#1938411