Finite Group Databasebeta

← #14738951

Subgroups — #14738951

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#13079536C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic, complemented
3C2×#10622628C211yesmaximal, characteristic, complemented
4#13068053C214yesmaximal, complemented
5#13067971C214yesmaximal, complemented
6#13067391C211yesmaximal, characteristic, complemented
7#13067283C211yesmaximal, characteristic, complemented
8#13067263C211yesmaximal, characteristic, complemented
9C11×#2972C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66985—21no—
12C22×#4323—21no—
13#10623008C2211yescharacteristic
14C2×#66927C2211yescharacteristic
15C8×D4×C11—22no—
16C8×D4×C11C2214yescomplemented
17C11×#431C2211yescharacteristic
18C11×#431C2211yescharacteristic
19C2×C11×C22⋊C8—22no—
20#10622632C2212yescomplemented
21#10622629—22no—
22#10622628—22no—
23#10622628C2214yes—
24#10622628C2212yescomplemented
25#10622579—21no—
26C2×#66873—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622456—22no—
30#10622345—22no—
31#10622308C2212yescomplemented
32#10622307C2212yescomplemented
33#10622124C2212yescomplemented
34#10622123C2214yescomplemented
35#10622123C2212yescomplemented
36#10622096C2214yescomplemented
37C22×D4×C11D411yescharacteristic
38C23×C4×C11—21no—
39C2×#4339—21no—
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—21no—
43C22×C8×C11—24no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11D412yes—
47C4×D4×C11C2312yes—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×#4324—22no—
52#66985—44no—
53C2×#4323—24no—
54C2×#4323—22no—
55C2×#4323—44no—
56#66983—21no—
57#66983—21no—
58C2×#4318—21no—
59C22×C11⋊C8—21no—
60C2×D88—24no—
61#66928—21no—
62#66927—21no—
63#66927—21no—
64#66927—21no—
65#66927C2312yes—
66#66927C2311yescharacteristic
67C4×D44—21no—
68C4×D44—21no—
69#66922C2311yescharacteristic
70C11×C4⋊C8D412yes—
71C11×C4⋊C8C2312yes—
72C11×C22⋊C8—21no—
73C11×C22⋊C8—24no—
74C11×C22⋊C8D412yes—
75C4×C8×C11—21no—
76C4×C8×C11C2312yes—
77#66885—24no—
78#66874—22no—
79#66873—24no—
80#66873—22no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)C2312yes—
84C4⋊(C11⋊C8)C2312yes—
85#19386—111nomaximal, Sylow
86C24×C11—21no—
87C23×D11—41no—
88C2×D4×C11—21no—
89C2×D4×C11—22no—
90C2×D4×C11D814yescomplemented
91C2×D4×C11C2×D412yes—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—82no—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C2×C22⋊D11—41no—
100#4339—42no—
101#4339—42no—
102C2×D44—22no—
103C2×D44—21no—
104C2×D44—22no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—22no—
108C2×D44—41no—
109C2×D44—41no—
110C2×D44—41no—
111C2×D44—42no—
112C2×D44—42no—
113C2×D44—82no—
114C2×D44—82no—
115C2×C4×D11—41no—
116C2×Dic22—21no—
117C2×C8×C11—22no—
118C2×C8×C11—84no—
119C2×C8×C11C2×D414yes—
120C11×C4⋊C4—21no—
121C11×C4⋊C4C2×D412yes—
122C11×C22⋊C4—22no—
123C11×C22⋊C4—22no—
124C42×C11C2×D411yescharacteristic
125C42×C11C2×D411yescharacteristic
126C42×C11#4111yescharacteristic
127C42×C11C2411yescharacteristic
128#4324—44no—
129#4323—48no—
130#4323—44no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135#4318—42no—
136C2×C11⋊C8—22no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—42no—
139D88—84no—
140#3205—111no—
141#3036—111no—
142C2×#459—111no—
143#2972D1111yescharacteristic, complemented
144#1681—114no—
145#1667—114no—
146#1571—111no—
147#1545—111no—
148#1540—111no—
149C23×C11—22no—
150C23×C11—24no—
151C23×C11—81no—
152C23×C11—81no—
153C23×C11#12111yescharacteristic
154C22×D11—41no—
155C22×D11—42no—
156C22×D11—82no—
157C22×D11—82no—
158C22×D11—82no—
159D4×C11—22no—
160D4×C11—24no—
161D4×C11C2×D814yes—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—41no—
165C2×C4×C11—44no—
166C2×C4×C11—82no—
167C2×C4×C11—81no—
168C2×C4×C11#12111yescharacteristic
169C2×C4×C11#12111yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11C2×D812yes—
172C2×C4×C11#13512yes—
173C2×C4×C11C22×D411yescharacteristic
174C2×C4×C11C22×D411yescharacteristic
175C2×C4×C11C2×#4111yescharacteristic
176C22⋊D11—82no—
177C2×Dic11—41no—
178D44—42no—
179D44—41no—
180D44—42no—
181D44—41no—
182D44—42no—
183D44—44no—
184D44—81no—
185D44—82no—
186D44—82no—
187D44—82no—
188D44—82no—
189C4×D11—82no—
190Dic22—41no—
191Dic22—41no—
192C8×C11—24no—
193C8×C11—42no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C2×AGL(1,ℤ/8)—221no—
197C22×D8—221no—
198#532—111no—
199C2×#127—111no—
200C2×C4×D4C2×D1111yescharacteristic
201#493—112no—
202#486—112no—
203#463—222no—
204#461—112no—
205#459—112no—
206#459—114no—
207#459—222no—
208#459—222no—
209#447—222no—
210C8×D4—22no—
211C8×D4C2×D1114yescomplemented
212#431C2×D1111yescharacteristic
213#431C2×D1111yescharacteristic
214#423—111no—
215C2×C4⋊C8—111no—
216#417—221no—
217C2×#102—221no—
218C2×C22⋊C8—22no—
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#46612yes—
230C22×C11C2×#12111yescharacteristic
231C2×D11—82no—
232C2×D11—81no—
233C2×D11—82no—
234C2×D11—81no—
235C2×D11—82no—
236C2×D11—81no—
237C2×D11—164no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—42no—
242C4×C11#46612yes—
243C4×C11C22×D811yescharacteristic
244C4×C11C2×#13511yescharacteristic
245C4×C11#57612yes—
246Dic11—81no—
247C2×#41—221no—
248C22×D4—221no—
249C22×D4—221no—
250C22×D4—221no—
251C22×D4D4411yescharacteristic
252C23×C4—21no—
253AGL(1,ℤ/8)—444no—
254C2×SD16—222no—
255C2×D8—224no—
256C2×D8—222no—
257C2×D8—224no—
258C2×D8—444no—
259C2×M16—221no—
260C22×C8—24no—
261C22×C8—221no—
262C4⋊Q8—111no—
263#127—112no—
264#127—111no—
265#127—221no—
266#127—221no—
267#127—221no—
268#124—221no—
269#121—221no—
270#121—221no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—221no—
274C4×D4—221no—
275C4×D4D4412yes—
276C4×D4C22×D1112yes—
277C2×C4⋊C4D4411yescharacteristic
278C2×C22⋊C4—21no—
279C2×C42C22×D1111yescharacteristic
280C4⋊C8—112no—
281C4⋊C8—112no—
282C4⋊C8—221no—
283C4⋊C8—221no—
284C4⋊C8C22⋊D1112yes—
285C4⋊C8C22×D1112yes—
286#103—222no—
287#102—224no—
288#102—224no—
289#102—222no—
290C22⋊C8—21no—
291C22⋊C8—24no—
292C22⋊C8C22⋊D1112yes—
293C4×C8—21no—
294C4×C8C22×D1112yes—
295C2×C11—22no—
296C2×C11—44no—
297C2×C11#304111yescharacteristic
298C2×C11C2×#46611yescharacteristic
299C2×C11#306811yescharacteristic
300D11—161no—
301D11—162no—
302C24—21no—
303C24—441no—
304#41—442no—
305#41—442no—
306C2×Q8—221no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—221no—
310C2×D4—222no—
311C2×D4—221no—
312C2×D4—222no—
313C2×D4—222no—
314C2×D4—221no—
315C2×D4—441no—
316C2×D4—442no—
317C2×D4—442no—
318C2×D4—441no—
319C2×D4—441no—
320C2×D4—441no—
321C2×D4—882no—
322C2×D4—882no—
323C2×D4D8814yescomplemented
324C2×D4C2×D4412yes—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—82no—
329C22×C4—441no—
330C22×C4C2×D4411yescharacteristic
331C22×C4#433911yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—444no—
334D8—448no—
335D8—444no—
336D8—884no—
337M16—442no—
338C2×C8—22no—
339C2×C8—84no—
340C2×C8—222no—
341C2×C8—222no—
342C2×C8—442no—
343C2×C8C2×C22⋊D1114yes—
344C4⋊C4—21no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4C2×D4412yes—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C42C2×D4411yescharacteristic
353C42#433911yescharacteristic
354C42C2×C22⋊D1111yescharacteristic
355C42C23×D1111yescharacteristic
356C11#1938611yescharacteristic, complemented, Sylow
357C23—22no—
358C23—24no—
359C23—81no—
360C23—81no—
361C23—441no—
362C23—442no—
363C23—882no—
364C23—882no—
365C23—882no—
366C23#6698311yescharacteristic
367Q8—441no—
368Q8—441no—
369D4—24no—
370D4—22no—
371D4—442no—
372D4—441no—
373D4—442no—
374D4—441no—
375D4—442no—
376D4—444no—
377D4—882no—
378D4—881no—
379D4—882no—
380D4—882no—
381D4—882no—
382D4—882no—
383D4C2×D8814yes—
384C2×C4—22no—
385C2×C4—22no—
386C2×C4—41no—
387C2×C4—44no—
388C2×C4—82no—
389C2×C4—81no—
390C2×C4—441no—
391C2×C4—882no—
392C2×C4C2×D8812yes—
393C2×C4#6695712yes—
394C2×C4#6698311yescharacteristic
395C2×C4#6698311yescharacteristic
396C2×C4#6698311yescharacteristic
397C2×C4C22×D4411yescharacteristic
398C2×C4C2×#433911yescharacteristic
399C2×C4C22×C22⋊D1111yescharacteristic
400C8—24no—
401C8—42no—
402C8—442no—
403C8—442no—
404C22—21no—
405C22—21no—
406C22—24no—
407C22—42no—
408C22—42no—
409C22—84no—
410C22—882no—
411C22—881no—
412C22—882no—
413C22—881no—
414C22—881no—
415C22—882no—
416C22—1764no—
417C22#1062272812yes—
418C22C2×#6698311yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—42no—
423C4—881no—
424C4#1062272812yes—
425C4C22×D8811yescharacteristic
426C4C2×#6695711yescharacteristic
427C4#1062336612yes—
428C2—22no—
429C2—44no—
430C2—1762no—
431C2—1761no—
432C2#1307811911yescharacteristic
433C2C2×#1062272811yescharacteristic
434C2#1307834411yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2972C2
socleC22×C11C2×#121
hypercenter#2972D11
hypocenterC11#19386
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. #13079536C2semidirect
2. #13078080C2semidirect
3. C2×#10622628C2semidirect
4. #13068053C2semidirect
5. #13067971C2semidirect
6. #13067391C2semidirect
7. #13067283C2semidirect
8. #13067263C2semidirect
9. C11×#2972C2semidirect
16. C8×D4×C11C22semidirect
20. #10622632C22semidirect
24. #10622628C22semidirect
31. #10622308C22semidirect
32. #10622307C22semidirect
33. #10622124C22semidirect
34. #10622123C22semidirect
35. #10622123C22semidirect
36. #10622096C22semidirect
90. C2×D4×C11D8semidirect
143. #2972D11semidirect
211. C8×D4C2×D11semidirect
323. C2×D4D88semidirect
356. C11#19386semidirect

Maximal subgroups

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

subgroupindex
#130795362
#130780802
C2×#106226282
#130680532
#130679712
#130673912
#130672832
#130672632
C11×#29722
#1938611