Finite Group Databasebeta

← #14739323

Subgroups — #14739323

Order 2816.

684 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079543C211yesmaximal, characteristic, complemented
2C2×#10622459C211yesmaximal, characteristic, complemented
3#13078082C211yesmaximal, characteristic
4#13077656C211yesmaximal, characteristic, complemented
5#13068164C214yesmaximal, complemented
6#13068082C214yesmaximal, complemented
7#13067302C211yesmaximal, characteristic, complemented
8#13067266C211yesmaximal, characteristic, complemented
9C11×#1571C211yesmaximal, characteristic, complemented
10C2×#66961—21no—
11#10623008C2211yescharacteristic
12C2×C4×D44C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#431C2211yescharacteristic
15C11×#423C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17#10622746—21no—
18C2×#66885—21no—
19C2×#66882—21no—
20#10622538C2211yescharacteristic
21#10622459—22no—
22#10622459C2214yes—
23#10622457—22no—
24#10622456C2212yes—
25#10622454—22no—
26#10622454C2212yes—
27#10622451—22no—
28#10622351—22no—
29#10622339—22no—
30#10622306C2212yescomplemented
31#10622301C2214yes—
32#10622294C2212yescomplemented
33C11×#335C2214yescomplemented
34#10622124C2214yescomplemented
35#10622123C2212yescomplemented
36#10622120C2212yescomplemented
37C2×#4339—21no—
38C22×D44D411yescharacteristic
39C22×C4×D11—21no—
40C22×Dic22—21no—
41C2×C11×M16—21no—
42C22×C8×C11—21no—
43C2×C42×C11C2311yescharacteristic
44#66983—21no—
45#66983—21no—
46C2×(C2×D11)⋊C4—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11—21no—
49C2×C4⋊Dic11D411yescharacteristic
50#66961—44no—
51C2×D88—22no—
52C2×#4314—22no—
53C2×#4314—24no—
54C2×#4313—24no—
55#66928—21no—
56#66927C2311yescharacteristic
57C4×D44—21no—
58C4×D44—21no—
59C4×D44—21no—
60C4×D44—21no—
61C4×D44D412yes—
62C4×D44C2312yes—
63#66922—21no—
64#66922—21no—
65#66922—21no—
66#66922C2312yes—
67#66922C2311yescharacteristic
68C11×C4⋊C8—21no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8D412yes—
71C11×C4⋊C8C2312yes—
72C11×C4⋊C8C2312yes—
73C11×C22⋊C8D412yes—
74C4×C8×C11C2312yes—
75C22⋊(C11⋊C8)—21no—
76#66885—24no—
77#66885—22no—
78(C2×D11)⋊C8—24no—
79#66882—24no—
80#66880—24no—
81#66880—22no—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84#19421—111nomaximal, Sylow
85C23×D11—21no—
86C22×C4×C11C2×D411yescharacteristic
87C22×C4×C11C2×D411yescharacteristic
88C22×C4×C11#4111yescharacteristic
89C2×C22⋊D11—41no—
90C22×Dic11—21no—
91C22×Dic11—41no—
92#4339—42no—
93#4339—42no—
94C2×D44—21no—
95C2×D44—22no—
96C2×D44—22no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44C2×D412yes—
101C2×C4×D11—22no—
102C2×C4×D11—22no—
103C2×C4×D11—41no—
104C2×C4×D11—82no—
105C2×Dic22—22no—
106C2×Dic22—21no—
107C2×Dic22—41no—
108C2×Dic22—82no—
109C11×M16—42no—
110C2×C8×C11—22no—
111C2×C8×C11—22no—
112C2×C8×C11—42no—
113C2×C8×C11C2×D414yes—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11#4111yescharacteristic
117C42×C11C2411yescharacteristic
118(C2×D11)⋊C4—22no—
119(C2×D11)⋊C4—22no—
120(C2×D11)⋊C4—41no—
121(C2×D11)⋊C4—41no—
122C4⋊Dic11—21no—
123C4⋊Dic11—21no—
124C4⋊Dic11—22no—
125C4⋊Dic11—22no—
126C4⋊Dic11—21no—
127C4⋊Dic11—41no—
128C4⋊Dic11—41no—
129C4⋊Dic11C2×D412yes—
130C2×C11⋊C8—22no—
131D88—44no—
132#4314—44no—
133#4314—84no—
134#4313—84no—
135#3206—111no—
136C2×#474—111no—
137#3036—111no—
138#2975—111no—
139#1699—114no—
140#1685—114no—
141#1571D1111yescharacteristic, complemented
142#1549—111no—
143#1540—111no—
144C23×C11#12111yescharacteristic
145C22×D11—22no—
146C22×D11—42no—
147C22×D11—41no—
148C22×D11—81no—
149C22×D11—81no—
150C2×C4×C11—22no—
151C2×C4×C11—41no—
152C2×C4×C11#12111yescharacteristic
153C2×C4×C11#12111yescharacteristic
154C2×C4×C11#12111yescharacteristic
155C2×C4×C11AGL(1,ℤ/8)12yes—
156C2×C4×C11#13712yes—
157C2×C4×C11C22×D411yescharacteristic
158C2×C4×C11C22×D411yescharacteristic
159C2×C4×C11C2×#4111yescharacteristic
160C22⋊D11—82no—
161C2×Dic11—22no—
162C2×Dic11—42no—
163C2×Dic11—41no—
164C2×Dic11—81no—
165C2×Dic11—82no—
166D44—22no—
167D44—22no—
168D44—41no—
169D44—41no—
170D44—42no—
171D44—42no—
172D44—81no—
173C4×D11—44no—
174C4×D11—82no—
175C4×D11—82no—
176Dic22—41no—
177Dic22—41no—
178Dic22—44no—
179Dic22—82no—
180C8×C11—24no—
181C8×C11—42no—
182C8×C11—42no—
183C11⋊C8—42no—
184C2×AGL(1,ℤ/8)—221no—
185#532—111no—
186C2×C4⋊Q8—111no—
187C2×C4×D4—111no—
188#492—112no—
189#487—112no—
190#474—114no—
191#474—222no—
192#463—222no—
193#461—112no—
194#461—222no—
195#459—112no—
196#448—222no—
197#436—114no—
198#436—222no—
199#431—111no—
200#431C2×D1111yescharacteristic
201C2×#107—221no—
202#423C2×D1111yescharacteristic
203C2×C4⋊C8C2×D1111yescharacteristic
204#417—221no—
205C2×#102—221no—
206#407—222no—
207#335C2×D1114yescomplemented
208#332—112no—
209#332—114no—
210#331—112no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11#46812yes—
214C22×C11C2×#12111yescharacteristic
215C2×D11—42no—
216C2×D11—42no—
217C2×D11—42no—
218C2×D11—84no—
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11#46812yes—
226C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C4×C11C2×#13711yescharacteristic
228C4×C11#57612yes—
229Dic11—42no—
230Dic11—82no—
231Dic11—81no—
232C2×#41—221no—
233C22×Q8—221no—
234C22×D4—111no—
235C23×C4—221no—
236AGL(1,ℤ/8)—444no—
237C2×SD16—222no—
238C2×SD16—224no—
239C2×D8—222no—
240C2×M16—21no—
241C2×M16—224no—
242C22×C8—21no—
243C4⋊Q8—112no—
244C4⋊Q8—111no—
245C4⋊Q8—221no—
246C4⋊Q8—221no—
247C4⋊Q8—221no—
248#127—111no—
249#124—221no—
250#121—221no—
251#121—221no—
252C4×D4—112no—
253C4×D4—112no—
254C4×D4—221no—
255C4×D4—221no—
256C4×D4—221no—
257C4×D4—221no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C22⋊C4—221no—
262C2×C42C22×D1111yescharacteristic
263#107—224no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—112no—
267C4⋊C8D4412yes—
268C4⋊C8C22×D1112yes—
269C4⋊C8C22×D1112yes—
270#103—222no—
271#103—224no—
272#102—222no—
273#102—224no—
274C22⋊C8—221no—
275C22⋊C8—224no—
276C22⋊C8D4412yes—
277C4×C8—221no—
278C4×C8C22×D1112yes—
279C2×C11—22no—
280C2×C11#304111yescharacteristic
281C2×C11C2×#46811yescharacteristic
282C2×C11#306911yescharacteristic
283D11—82no—
284D11—161no—
285C24—221no—
286#41—442no—
287#41—442no—
288C2×Q8—222no—
289C2×Q8—221no—
290C2×Q8—441no—
291C2×Q8—882no—
292C2×D4—112no—
293C2×D4—221no—
294C2×D4—222no—
295C2×D4—222no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—221no—
299C2×D4—441no—
300C22×C4—221no—
301C22×C4—222no—
302C22×C4—222no—
303C22×C4—441no—
304C22×C4—441no—
305C22×C4—882no—
306C22×C4C2×D4411yescharacteristic
307C22×C4D4×D1111yescharacteristic
308C22×C4#434311yescharacteristic
309SD16—444no—
310SD16—884no—
311D8—444no—
312M16—42no—
313M16—884no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—42no—
317C2×C8—222no—
318C2×C8C2×D4414yes—
319C4⋊C4—112no—
320C4⋊C4—221no—
321C4⋊C4—221no—
322C4⋊C4—222no—
323C4⋊C4—222no—
324C4⋊C4—221no—
325C4⋊C4—441no—
326C4⋊C4—441no—
327C22⋊C4—222no—
328C22⋊C4—222no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C42C2×D4411yescharacteristic
332C42D4×D1111yescharacteristic
333C42#434311yescharacteristic
334C42C23×D1111yescharacteristic
335C11#1942111yescharacteristic, complemented, Sylow
336C23—222no—
337C23—442no—
338C23—441no—
339C23—881no—
340C23—881no—
341C23#6694811yescharacteristic
342Q8—444no—
343Q8—441no—
344Q8—441no—
345Q8—882no—
346D4—222no—
347D4—222no—
348D4—442no—
349D4—442no—
350D4—441no—
351D4—441no—
352D4—881no—
353D4—882no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—222no—
357C2×C4—444no—
358C2×C4—441no—
359C2×C4—442no—
360C2×C4—882no—
361C2×C4—881no—
362C2×C4—882no—
363C2×C4—882no—
364C2×C4#6694811yescharacteristic
365C2×C4#6694811yescharacteristic
366C2×C4#6694811yescharacteristic
367C2×C4#6696412yes—
368C2×C4#6697112yes—
369C2×C4C22×D4411yescharacteristic
370C2×C4C2×D4×D1111yescharacteristic
371C2×C4C2×#434311yescharacteristic
372C8—24no—
373C8—42no—
374C8—42no—
375C8—442no—
376C22—21no—
377C22—21no—
378C22—442no—
379C22—442no—
380C22—442no—
381C22—884no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22#1062249912yes—
386C22C2×#6694811yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—442no—
391C4—882no—
392C4—881no—
393C4#1062249912yes—
394C4#1062328312yes—
395C4C2×#6696411yescharacteristic
396C4C2×#6697111yescharacteristic
397C2—22no—
398C2—882no—
399C2—1761no—
400C2#1307812011yescharacteristic
401C2C2×#1062249911yescharacteristic
402C2#1307835411yescharacteristic
subgroupG/H
centerC22C2×#66948
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#1571C2
socleC22×C11C2×#121
prime radical#13078082C2
hypercenter#1571D11
hypocenterC11#19421
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1571

Complements

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

NH ≅ G/Ntype
1. #13079543C2semidirect
2. C2×#10622459C2semidirect
4. #13077656C2semidirect
5. #13068164C2semidirect
6. #13068082C2semidirect
7. #13067302C2semidirect
8. #13067266C2semidirect
9. C11×#1571C2semidirect
30. #10622306C22semidirect
32. #10622294C22semidirect
33. C11×#335C22semidirect
34. #10622124C22semidirect
35. #10622123C22semidirect
36. #10622120C22semidirect
141. #1571D11semidirect
207. #335C2×D11semidirect
335. C11#19421semidirect

Maximal subgroups

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

subgroupindex
#130795432
C2×#106224592
#130780822
#130776562
#130681642
#130680822
#130673022
#130672662
C11×#15712
#1942111