Finite Group Databasebeta

← #14738935

Subgroups — #14738935

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#13079554C211yesmaximal, characteristic, complemented
2C2×#10622628C211yesmaximal, characteristic
3#13077640C211yesmaximal, characteristic, complemented
4#13068027C214yesmaximal, complemented
5#13067959C214yesmaximal, complemented
6#13067388C211yesmaximal, characteristic, complemented
7#13067285C211yesmaximal, characteristic, complemented
8#13067273C211yesmaximal, characteristic, complemented
9C11×#3077C211yesmaximal, characteristic, complemented
10C11×#533C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C22×#4323—21no—
13C2×#66927C2211yescharacteristic
14C11×#478—22no—
15C11×#476C2212yescomplemented
16C11×#474C2212yescomplemented
17C11×#428—21no—
18C11×#423C2211yescharacteristic
19C11×#418—21no—
20C2×C22⋊(C11⋊C8)—22no—
21#10622701C2212yescomplemented
22#10622698C2212yescomplemented
23#10622659—22no—
24#10622640—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#10622184C2212yescomplemented
35#10622123C2214yescomplemented
36#10622118C2214yescomplemented
37C22×D4×C11D411yescharacteristic
38C23×C4×C11—21no—
39C22×D44—21no—
40C22×D44—21no—
41C22×D44—21no—
42C2×C11×M16—21no—
43C11×C4⋊Q8C2311yescharacteristic
44C11×C4⋊Q8C2311yescharacteristic
45C11×#125—21no—
46C11×C22⋊Q8—21no—
47C11×C22⋊Q8—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11D412yes—
53C4×D4×C11C2312yes—
54C11×#117—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C2×#4325—24no—
59C2×#4323—24no—
60C2×#4323—44no—
61C22×C11⋊C8—21no—
62C22×C11⋊C8—24no—
63#66927—21no—
64#66927—21no—
65#66927—21no—
66#66927C2312yes—
67C11×#107—22no—
68C11×#106—22no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8C2312yes—
71C11×#102—22no—
72C11×#102—22no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—24no—
75C22⋊(C11⋊C8)D412yes—
76#66873—24no—
77#66873—24no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)D412yes—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4×C11⋊C8—21no—
83C4×C11⋊C8C2312yes—
84#19384—111nomaximal, Sylow
85C24×C11—21no—
86C23×D11—41no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—22no—
91C2×D4×C11SD1614yescomplemented
92C2×D4×C11C2×D412yes—
93C22×C4×C11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—82no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11#4111yescharacteristic
100C2×D44—22no—
101C2×D44—22no—
102C2×D44—22no—
103C2×D44—41no—
104C2×D44—41no—
105C2×D44—41no—
106C2×D44—42no—
107C2×D44—42no—
108C2×D44—82no—
109C2×D44—82no—
110C11×M16—42no—
111C2×C8×C11—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—21no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—21no—
116C11×C4⋊C4—21no—
117C11×C4⋊C4—41no—
118C11×C4⋊C4—41no—
119C11×C4⋊C4C2×D412yes—
120C11×C22⋊C4—22no—
121C11×C22⋊C4—22no—
122C11×C22⋊C4—41no—
123C42×C11—41no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128#4325—84no—
129#4323—48no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—42no—
133C2×C11⋊C8—84no—
134C2×C11⋊C8C2×D414yes—
135#3208—111no—
136#3077D1111yescharacteristic, complemented
137C2×#459—111no—
138#2972—111no—
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—
153Q8×C11—42no—
154Q8×C11—81no—
155D4×C11—22no—
156D4×C11—24no—
157D4×C11C2×SD1614yes—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—44no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—82no—
165C2×C4×C11—81no—
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11C2×SD1612yes—
170C2×C4×C11#13512yes—
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C22×D411yescharacteristic
173C2×C4×C11C2×#4111yescharacteristic
174D44—42no—
175D44—42no—
176D44—44no—
177D44—82no—
178D44—82no—
179D44—82no—
180D44—82no—
181C8×C11—42no—
182C11⋊C8—24no—
183C11⋊C8—42no—
184C11⋊C8—42no—
185C22×D8—221no—
186#533C2×D1111yescharacteristic
187C2×#127—111no—
188C2×C4×D4C2×D1111yescharacteristic
189#492—112no—
190#486—112no—
191#478—22no—
192#476C2×D1112yescomplemented
193#474C2×D1112yescomplemented
194#460—222no—
195#459—114no—
196#459—222no—
197#450—222no—
198C8×D4—114no—
199C8×D4—222no—
200#431—111no—
201#431—111no—
202#428—21no—
203#423C2×D1111yescharacteristic
204C2×C4⋊C8—111no—
205#418—21no—
206C2×#102—221no—
207C2×C22⋊C8—222no—
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—81no—
229C4×C11—81no—
230C4×C11#46512yes—
231C4×C11C22×SD1611yescharacteristic
232C4×C11C2×#13511yescharacteristic
233C4×C11#57612yes—
234C22×D4—221no—
235C22×D4—221no—
236C22×D4—221no—
237C22×D4C22⋊D1111yescharacteristic
238C23×C4—21no—
239C2×SD16—224no—
240C2×D8—224no—
241C2×D8—444no—
242C2×M16—21no—
243C22×C8—224no—
244C22×C8—221no—
245C4⋊Q8C22×D1111yescharacteristic
246C4⋊Q8C22×D1111yescharacteristic
247#127—112no—
248#127—221no—
249#127—221no—
250#127—221no—
251#125—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C4×Q8—21no—
255C4×Q8—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4C22⋊D1112yes—
259C4×D4C22×D1112yes—
260#117—21no—
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C22×D1111yescharacteristic
264#107—22no—
265#106—22no—
266C4⋊C8—21no—
267C4⋊C8—112no—
268C4⋊C8—112no—
269C4⋊C8—112no—
270C4⋊C8—221no—
271C4⋊C8C22×D1112yes—
272#102—22no—
273#102—22no—
274#102—224no—
275#102—224no—
276C22⋊C8—112no—
277C22⋊C8—224no—
278C22⋊C8—221no—
279C4×C8—112no—
280C4×C8—221no—
281C2×C11—22no—
282C2×C11—44no—
283C2×C11#304111yescharacteristic
284C2×C11C2×#46511yescharacteristic
285C2×C11#306811yescharacteristic
286D11—162no—
287C24—21no—
288C24—441no—
289C2×Q8—21no—
290C2×Q8—21no—
291C2×D4—21no—
292C2×D4—22no—
293C2×D4—222no—
294C2×D4—222no—
295C2×D4—222no—
296C2×D4—441no—
297C2×D4—441no—
298C2×D4—441no—
299C2×D4—442no—
300C2×D4—442no—
301C2×D4—882no—
302C2×D4—882no—
303C2×D4#432514yescomplemented
304C2×D4C2×C22⋊D1112yes—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—82no—
309C22×C4D4×D1111yescharacteristic
310C22×C4#434111yescharacteristic
311C22×C4C2×C22⋊D1111yescharacteristic
312SD16—884no—
313D8—448no—
314M16—42no—
315C2×C8—22no—
316C2×C8—114no—
317C2×C8—222no—
318C2×C8—222no—
319C2×C8—442no—
320C2×C8—884no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—41no—
327C4⋊C4—41no—
328C4⋊C4C2×C22⋊D1112yes—
329C22⋊C4—22no—
330C22⋊C4—22no—
331C22⋊C4—41no—
332C42—41no—
333C42D4×D1111yescharacteristic
334C42#434111yescharacteristic
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#6699211yescharacteristic
347Q8—42no—
348Q8—81no—
349D4—22no—
350D4—24no—
351D4—444no—
352D4—442no—
353D4—442no—
354D4—882no—
355D4—882no—
356D4—882no—
357D4—882no—
358D4C2×#432514yes—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—41no—
362C2×C4—44no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—82no—
366C2×C4—81no—
367C2×C4#6699211yescharacteristic
368C2×C4#6699211yescharacteristic
369C2×C4#6699211yescharacteristic
370C2×C4C2×#432512yes—
371C2×C4#6700312yes—
372C2×C4C2×D4×D1111yescharacteristic
373C2×C4C2×#434111yescharacteristic
374C2×C4C22×C22⋊D1111yescharacteristic
375C8—42no—
376C8—224no—
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#1062266112yes—
390C22C2×#6699211yescharacteristic
391C4—21no—
392C4—21no—
393C4—21no—
394C4—42no—
395C4—81no—
396C4—81no—
397C4#1062266112yes—
398C4#1062330512yes—
399C4C22×#432511yescharacteristic
400C4C2×#6700311yescharacteristic
401C2—22no—
402C2—44no—
403C2—1762no—
404C2#1307812111yescharacteristic
405C2C2×#1062266111yescharacteristic
406C2#1307834611yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3077C2
socleC22×C11C2×#121
prime radicalC2×#10622628C2
hypercenter#3077D11
hypocenterC11#19384
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #13079554C2semidirect
3. #13077640C2semidirect
4. #13068027C2semidirect
5. #13067959C2semidirect
6. #13067388C2semidirect
7. #13067285C2semidirect
8. #13067273C2semidirect
9. C11×#3077C2semidirect
15. C11×#476C22semidirect
16. C11×#474C22semidirect
21. #10622701C22semidirect
22. #10622698C22semidirect
28. D4×C11⋊C8C22semidirect
33. #10622185C22semidirect
34. #10622184C22semidirect
35. #10622123C22semidirect
36. #10622118C22semidirect
91. C2×D4×C11SD16semidirect
136. #3077D11semidirect
192. #476C2×D11semidirect
193. #474C2×D11semidirect
303. C2×D4#4325semidirect
337. C11#19384semidirect

Maximal subgroups

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

subgroupindex
#130795542
C2×#106226282
#130776402
#130680272
#130679592
#130673882
#130672852
#130672732
C11×#30772
#1938411