Finite Group Databasebeta

← #14739328

Subgroups — #14739328

Order 2816.

768 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#13079534C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic, complemented
3#13077657C211yesmaximal, characteristic, complemented
4#13068175C214yesmaximal, complemented
5#13068093C214yesmaximal, complemented
6#13067386C211yesmaximal, characteristic, complemented
7#13067284C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic, complemented
9C2×C11×#459C211yesmaximal, characteristic, complemented
10C22×C11×D8—21no—
11C2×C11×#127C2211yescharacteristic
12C2×C4×D4×C11C2211yescharacteristic
13C2×#66985—21no—
14#10623008C2211yescharacteristic
15C11×#459—22no—
16C11×#459C2214yes—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102—21no—
19#10622830—22no—
20#10622820—22no—
21#10622686C2212yescomplemented
22#10622685—22no—
23#10622683C2212yescomplemented
24#10622632C2212yescomplemented
25#10622629—22no—
26#10622628C2212yescomplemented
27#10622625—22no—
28#10622625C2214yescomplemented
29#10622579—21no—
30#10622538C2211yescharacteristic
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622182C2214yescomplemented
34#10622123C2212yescomplemented
35#10622120C2212yescomplemented
36#10622118C2214yescomplemented
37C22×D4×C11—21no—
38C22×D4×C11—21no—
39C22×D4×C11—21no—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11—21no—
42C2×#4339—21no—
43C2×C11×D8—24no—
44C2×C11×D8—44no—
45C22×C8×C11—21no—
46C11×#127—21no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127C2312yes—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11D412yes—
53C4×D4×C11C2312yes—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57C2×#4324—22no—
58#66985—44no—
59C2×#4323—22no—
60C2×#4323—24no—
61#66983—21no—
62#66983—21no—
63C2×#4318—21no—
64C2×#4318—24no—
65#66928—21no—
66#66927C2311yescharacteristic
67C4×D44—21no—
68C4×D44—21no—
69#66922C2311yescharacteristic
70C11×C4⋊C8—21no—
71C11×C4⋊C8C2312yes—
72C11×#102—24no—
73#66896—24no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—24no—
76C22⋊(C11⋊C8)D412yes—
77#66874—22no—
78#66873—22no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)D412yes—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84C4×C11⋊C8C2312yes—
85#19422—111nomaximal, Sylow
86C24×C11—21no—
87C24×C11—41no—
88C2×D4×C11—21no—
89C2×D4×C11—22no—
90C2×D4×C11—22no—
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—42no—
98C2×D4×C11—42no—
99C2×D4×C11—82no—
100C2×D4×C11—82no—
101C2×D4×C11C2×D412yes—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—82no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C2×C22⋊D11—41no—
110#4339—42no—
111#4339—42no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×C4×D11—41no—
116C2×Dic22—21no—
117C11×D8—48no—
118C2×C8×C11—22no—
119C2×C8×C11—42no—
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—44no—
130#4323—84no—
131(C2×D11)⋊C4—41no—
132(C2×D11)⋊C4—41no—
133C4⋊Dic11—21no—
134C4⋊Dic11—21no—
135#4318—42no—
136#4318—84no—
137C2×C11⋊C8—22no—
138C2×C11⋊C8—22no—
139C2×C11⋊C8C2×D414yes—
140#3205—111no—
141#3036—111no—
142C2×#459D1111yescharacteristic, complemented
143#2975—111no—
144#1701—114no—
145#1687—114no—
146#1570—111no—
147#1545—111no—
148#1540—111no—
149C23×C11—22no—
150C23×C11—42no—
151C23×C11—42no—
152C23×C11—81no—
153C23×C11—81no—
154C23×C11—82no—
155C23×C11—82no—
156C23×C11—82no—
157C23×C11#12111yescharacteristic
158C22×D11—41no—
159D4×C11—22no—
160D4×C11—22no—
161D4×C11—42no—
162D4×C11—42no—
163D4×C11—44no—
164D4×C11—42no—
165D4×C11—82no—
166D4×C11—82no—
167D4×C11—82no—
168D4×C11—82no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—41no—
172C2×C4×C11—44no—
173C2×C4×C11—82no—
174C2×C4×C11—81no—
175C2×C4×C11#12111yescharacteristic
176C2×C4×C11#12111yescharacteristic
177C2×C4×C11#12111yescharacteristic
178C2×C4×C11AGL(1,ℤ/8)12yes—
179C2×C4×C11AGL(1,ℤ/8)12yes—
180C2×C4×C11C22×D411yescharacteristic
181C2×C4×C11C22×D411yescharacteristic
182C2×C4×C11C2×#4111yescharacteristic
183C22⋊D11—82no—
184C2×Dic11—41no—
185D44—41no—
186D44—41no—
187D44—42no—
188D44—81no—
189C4×D11—82no—
190Dic22—41no—
191Dic22—41no—
192C8×C11—42no—
193C11⋊C8—24no—
194C11⋊C8—42no—
195C11⋊C8—42no—
196C2×AGL(1,ℤ/8)—221no—
197C22×D8—21no—
198#532—111no—
199C2×#127C2×D1111yescharacteristic
200C2×C4×D4C2×D1111yescharacteristic
201#493—112no—
202#486—112no—
203#463—222no—
204#461—112no—
205#459—22no—
206#459—112no—
207#459—222no—
208#459C2×D1114yes—
209#447—222no—
210#436—114no—
211#436—222no—
212#431—111no—
213#431—111no—
214#423—111no—
215C2×C4⋊C8C2×D1111yescharacteristic
216#417—221no—
217C2×#102—21no—
218#407—222no—
219#334—114no—
220#332—112no—
221#331—114no—
222#331—112no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—42no—
226C22×C11—42no—
227C22×C11—42no—
228C22×C11—84no—
229C22×C11—82no—
230C22×C11—82no—
231C22×C11—82no—
232C22×C11—164no—
233C22×C11#46912yes—
234C22×C11C2×#12111yescharacteristic
235C2×D11—81no—
236C2×D11—81no—
237C2×D11—81no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—21no—
241C4×C11—42no—
242C4×C11#46912yes—
243C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
244C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
245C4×C11#57612yes—
246Dic11—81no—
247C2×#41—221no—
248C22×D4—21no—
249C22×D4—21no—
250C22×D4—21no—
251C22×D4C22⋊D1111yescharacteristic
252C23×C4—21no—
253AGL(1,ℤ/8)—444no—
254C2×SD16—222no—
255C2×D8—24no—
256C2×D8—44no—
257C2×D8—224no—
258C2×D8—222no—
259C2×M16—224no—
260C2×M16—221no—
261C22×C8—21no—
262C4⋊Q8—111no—
263#127—21no—
264#127—21no—
265#127—21no—
266#127—111no—
267#127C22×D1112yes—
268#124—221no—
269#121—221no—
270#121—221no—
271C4×D4—21no—
272C4×D4—21no—
273C4×D4—221no—
274C4×D4—221no—
275C4×D4C22⋊D1112yes—
276C4×D4C22×D1112yes—
277C2×C4⋊C4C22⋊D1111yescharacteristic
278C2×C22⋊C4—21no—
279C2×C42C22×D1111yescharacteristic
280C4⋊C8—21no—
281C4⋊C8—112no—
282C4⋊C8—112no—
283C4⋊C8—112no—
284C4⋊C8—221no—
285C4⋊C8C22×D1112yes—
286#103—222no—
287#102—24no—
288#102—224no—
289#102—222no—
290C22⋊C8—112no—
291C22⋊C8—224no—
292C22⋊C8—221no—
293C4×C8—112no—
294C4×C8—221no—
295C2×C11—22no—
296C2×C11—82no—
297C2×C11—162no—
298C2×C11#304111yescharacteristic
299C2×C11C2×#46911yescharacteristic
300C2×C11#306811yescharacteristic
301D11—161no—
302C24—21no—
303C24—41no—
304#41—442no—
305#41—442no—
306C2×Q8—221no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—42no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—42no—
318C2×D4—82no—
319C2×D4—82no—
320C2×D4—221no—
321C2×D4—221no—
322C2×D4—221no—
323C2×D4—441no—
324C2×D4C2×C22⋊D1112yes—
325C22×C4—21no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—82no—
329C22×C4—441no—
330C22×C4D4×D1111yescharacteristic
331C22×C4#434111yescharacteristic
332C22×C4C2×C22⋊D1111yescharacteristic
333SD16—444no—
334D8—48no—
335D8—444no—
336D8—884no—
337M16—442no—
338M16—884no—
339C2×C8—22no—
340C2×C8—42no—
341C2×C8—114no—
342C2×C8—222no—
343C2×C8—222no—
344C4⋊C4—21no—
345C4⋊C4—221no—
346C4⋊C4—221no—
347C4⋊C4C2×C22⋊D1112yes—
348C22⋊C4—22no—
349C22⋊C4—22no—
350C22⋊C4—441no—
351C22⋊C4—441no—
352C42D4×D1111yescharacteristic
353C42#434111yescharacteristic
354C42C2×C22⋊D1111yescharacteristic
355C42C23×D1111yescharacteristic
356C11#1942211yescharacteristic, complemented, Sylow
357C23—22no—
358C23—42no—
359C23—42no—
360C23—81no—
361C23—81no—
362C23—82no—
363C23—82no—
364C23—82no—
365C23—441no—
366C23#6699211yescharacteristic
367Q8—441no—
368Q8—441no—
369D4—22no—
370D4—22no—
371D4—44no—
372D4—42no—
373D4—42no—
374D4—42no—
375D4—82no—
376D4—82no—
377D4—82no—
378D4—82no—
379D4—442no—
380D4—441no—
381D4—441no—
382D4—881no—
383D4—882no—
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×C4#6698512yes—
393C2×C4#6699211yescharacteristic
394C2×C4#6699211yescharacteristic
395C2×C4#6699211yescharacteristic
396C2×C4#6700212yes—
397C2×C4C2×D4×D1111yescharacteristic
398C2×C4C2×#434111yescharacteristic
399C2×C4C22×C22⋊D1111yescharacteristic
400C8—42no—
401C8—224no—
402C8—442no—
403C8—442no—
404C22—21no—
405C22—21no—
406C22—42no—
407C22—42no—
408C22—42no—
409C22—84no—
410C22—82no—
411C22—82no—
412C22—82no—
413C22—164no—
414C22—881no—
415C22—881no—
416C22—881no—
417C22#1062265212yes—
418C22C2×#6699211yescharacteristic
419C4—21no—
420C4—21no—
421C4—21no—
422C4—42no—
423C4—881no—
424C4#1062265212yes—
425C4#1062328812yes—
426C4C2×#6698511yescharacteristic
427C4C2×#6700211yescharacteristic
428C2—22no—
429C2—82no—
430C2—162no—
431C2—1761no—
432C2#1307811611yescharacteristic
433C2C2×#1062265211yescharacteristic
434C2#1307834111yescharacteristic
subgroupG/H
centerC22C2×#66992
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#459C2
socleC22×C11C2×#121
hypercenterC2×#459D11
hypocenterC11#19422
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #13079534C2semidirect
2. #13078080C2semidirect
3. #13077657C2semidirect
4. #13068175C2semidirect
5. #13068093C2semidirect
6. #13067386C2semidirect
7. #13067284C2semidirect
8. #13067266C2semidirect
9. C2×C11×#459C2semidirect
21. #10622686C22semidirect
23. #10622683C22semidirect
24. #10622632C22semidirect
26. #10622628C22semidirect
28. #10622625C22semidirect
33. #10622182C22semidirect
34. #10622123C22semidirect
35. #10622120C22semidirect
36. #10622118C22semidirect
142. C2×#459D11semidirect
356. C11#19422semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130780802
#130776572
#130681752
#130680932
#130673862
#130672842
#130672662
C2×C11×#4592
#1942211