Finite Group Databasebeta

← #14739322

Subgroups — #14739322

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×#10622620C211yesmaximal, characteristic, complemented
3#13078080C211yesmaximal, characteristic
4#13068163C214yesmaximal, complemented
5#13068081C214yesmaximal, complemented
6#13067391C211yesmaximal, characteristic, complemented
7#13067300C211yesmaximal, characteristic, complemented
8#13067263C211yesmaximal, characteristic, complemented
9C11×#2975C211yesmaximal, characteristic, complemented
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66985—21no—
12#10623008C2211yescharacteristic
13C2×#66922C2211yescharacteristic
14C11×#436—22no—
15C11×#436C2214yes—
16C11×#431C2211yescharacteristic
17C11×#431C2211yescharacteristic
18C11×#407—22no—
19C2×#66896—21no—
20#10622632C2212yes—
21#10622629—22no—
22#10622628C2212yes—
23#10622620—22no—
24#10622620C2214yes—
25#10622579—21no—
26C2×#66871—21no—
27#10622537C2211yescharacteristic
28C2×C4⋊(C11⋊C8)C2211yescharacteristic
29#10622454—22no—
30#10622351—22no—
31#10622306C2212yescomplemented
32#10622294C2212yescomplemented
33#10622124C2212yescomplemented
34#10622123C2212yescomplemented
35#10622120C2214yescomplemented
36#10622096C2214yescomplemented
37C22×D4×C11D411yescharacteristic
38C23×C4×C11—21no—
39C2×#4339—21no—
40C22×Dic22—21no—
41C2×C11×M16—24no—
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11D412yes—
45C4×D4×C11C2312yes—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C22⋊C4—21no—
48C2×C42×C11C2311yescharacteristic
49C2×#4324—22no—
50#66985—44no—
51C2×#4323—22no—
52#66983—21no—
53#66983—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×#4318—21no—
57C22×C11⋊C8—21no—
58C2×#4314—24no—
59#66928—21no—
60#66927C2311yescharacteristic
61C4×D44—21no—
62C4×D44—21no—
63#66922—21no—
64#66922—21no—
65#66922—21no—
66#66922C2312yes—
67#66922C2311yescharacteristic
68C11×C4⋊C8D412yes—
69C11×C4⋊C8C2312yes—
70C11×C22⋊C8—21no—
71C11×C22⋊C8—24no—
72C11×C22⋊C8D412yes—
73C4×C8×C11—21no—
74C4×C8×C11C2312yes—
75#66896—24no—
76#66880—24no—
77#66874—22no—
78#66873—22no—
79#66871—24no—
80C4⋊(C11⋊C8)—21no—
81C4⋊(C11⋊C8)—21no—
82C4⋊(C11⋊C8)C2312yes—
83C4⋊(C11⋊C8)C2312yes—
84#19421—111nomaximal, Sylow
85C24×C11—21no—
86C2×D4×C11—21no—
87C2×D4×C11—22no—
88C2×D4×C11—22no—
89C2×D4×C11C2×D412yes—
90C22×C4×C11—21no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—82no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C2×C22⋊D11—41no—
98C22×Dic11—41no—
99#4339—42no—
100#4339—42no—
101C2×D44—21no—
102C2×D44—21no—
103C2×D44—21no—
104C2×C4×D11—41no—
105C2×Dic22—21no—
106C2×Dic22—22no—
107C2×Dic22—41no—
108C2×Dic22—82no—
109C11×M16—84no—
110C2×C8×C11—22no—
111C2×C8×C11C2×D414yes—
112C11×C4⋊C4—21no—
113C11×C4⋊C4C2×D412yes—
114C11×C22⋊C4—22no—
115C11×C22⋊C4—22no—
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120#4324—44no—
121#4323—44no—
122(C2×D11)⋊C4—41no—
123(C2×D11)⋊C4—41no—
124C4⋊Dic11—22no—
125C4⋊Dic11—21no—
126C4⋊Dic11—22no—
127C4⋊Dic11—21no—
128C4⋊Dic11—41no—
129C4⋊Dic11—41no—
130#4318—42no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—42no—
134#4314—84no—
135#3206—111no—
136C2×#474—111no—
137#3036—111no—
138#2975D1111yescharacteristic, complemented
139#1699—114no—
140#1685—114no—
141#1571—111no—
142#1549—111no—
143#1540—111no—
144C23×C11—22no—
145C23×C11—42no—
146C23×C11—81no—
147C23×C11—81no—
148C23×C11#12111yescharacteristic
149C22×D11—41no—
150D4×C11—22no—
151D4×C11—22no—
152D4×C11—42no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—41no—
156C2×C4×C11—44no—
157C2×C4×C11—82no—
158C2×C4×C11—81no—
159C2×C4×C11#12111yescharacteristic
160C2×C4×C11#12111yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11AGL(1,ℤ/8)12yes—
163C2×C4×C11#13712yes—
164C2×C4×C11C22×D411yescharacteristic
165C2×C4×C11C22×D411yescharacteristic
166C2×C4×C11C2×#4111yescharacteristic
167C22⋊D11—82no—
168C2×Dic11—42no—
169C2×Dic11—41no—
170C2×Dic11—82no—
171D44—41no—
172D44—41no—
173D44—42no—
174D44—81no—
175C4×D11—82no—
176Dic22—41no—
177Dic22—41no—
178Dic22—44no—
179Dic22—82no—
180C8×C11—24no—
181C8×C11—42no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C2×AGL(1,ℤ/8)—221no—
185#532—111no—
186C2×C4⋊Q8—111no—
187C2×C4×D4C2×D1111yescharacteristic
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—22no—
198#436C2×D1114yes—
199#431C2×D1111yescharacteristic
200#431C2×D1111yescharacteristic
201C2×#107—221no—
202#423—111no—
203C2×C4⋊C8—111no—
204#417—221no—
205C2×#102—221no—
206#407—22no—
207#335—114no—
208#332—112no—
209#332—114no—
210#331—112no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—42no—
214C22×C11—42no—
215C22×C11—42no—
216C22×C11—84no—
217C22×C11#46812yes—
218C22×C11C2×#12111yescharacteristic
219C2×D11—81no—
220C2×D11—81no—
221C2×D11—81no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—42no—
226C4×C11#46812yes—
227C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
228C4×C11C2×#13711yescharacteristic
229C4×C11#57612yes—
230Dic11—82no—
231Dic11—81no—
232C2×#41—221no—
233C22×Q8—221no—
234C22×D4D4411yescharacteristic
235C23×C4—21no—
236AGL(1,ℤ/8)—444no—
237C2×SD16—222no—
238C2×SD16—224no—
239C2×D8—222no—
240C2×M16—24no—
241C2×M16—221no—
242C22×C8—221no—
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—21no—
253C4×D4—21no—
254C4×D4—221no—
255C4×D4—221no—
256C4×D4D4412yes—
257C4×D4C22×D1112yes—
258C2×C4⋊C4—221no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4D4411yescharacteristic
261C2×C22⋊C4—21no—
262C2×C42C22×D1111yescharacteristic
263#107—224no—
264C4⋊C8—112no—
265C4⋊C8—112no—
266C4⋊C8—221no—
267C4⋊C8—221no—
268C4⋊C8C22⋊D1112yes—
269C4⋊C8C22×D1112yes—
270#103—224no—
271#103—222no—
272#102—224no—
273#102—222no—
274C22⋊C8—21no—
275C22⋊C8—24no—
276C22⋊C8C22⋊D1112yes—
277C4×C8—21no—
278C4×C8C22×D1112yes—
279C2×C11—22no—
280C2×C11—82no—
281C2×C11#304111yescharacteristic
282C2×C11C2×#46811yescharacteristic
283C2×C11#306911yescharacteristic
284D11—161no—
285C24—21no—
286#41—442no—
287#41—442no—
288C2×Q8—221no—
289C2×Q8—222no—
290C2×Q8—441no—
291C2×Q8—882no—
292C2×D4—22no—
293C2×D4—22no—
294C2×D4—21no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—441no—
299C2×D4C2×D4412yes—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—82no—
304C22×C4—441no—
305C22×C4—441no—
306C22×C4C2×D4411yescharacteristic
307C22×C4#433911yescharacteristic
308C22×C4C2×C22⋊D1111yescharacteristic
309SD16—444no—
310SD16—884no—
311D8—444no—
312M16—84no—
313M16—442no—
314C2×C8—22no—
315C2×C8—222no—
316C2×C8—222no—
317C2×C8—442no—
318C2×C8C2×C22⋊D1114yes—
319C4⋊C4—21no—
320C4⋊C4—222no—
321C4⋊C4—222no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4—441no—
325C4⋊C4—441no—
326C4⋊C4C2×D4412yes—
327C22⋊C4—22no—
328C22⋊C4—22no—
329C22⋊C4—441no—
330C22⋊C4—441no—
331C42C2×D4411yescharacteristic
332C42#433911yescharacteristic
333C42C2×C22⋊D1111yescharacteristic
334C42C23×D1111yescharacteristic
335C11#1942111yescharacteristic, complemented, Sylow
336C23—22no—
337C23—42no—
338C23—81no—
339C23—81no—
340C23—441no—
341C23#6698311yescharacteristic
342Q8—441no—
343Q8—441no—
344Q8—444no—
345Q8—882no—
346D4—22no—
347D4—22no—
348D4—42no—
349D4—441no—
350D4—441no—
351D4—442no—
352D4—881no—
353D4—882no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—41no—
357C2×C4—44no—
358C2×C4—82no—
359C2×C4—81no—
360C2×C4—441no—
361C2×C4—442no—
362C2×C4—882no—
363C2×C4—882no—
364C2×C4#6696112yes—
365C2×C4#6696212yes—
366C2×C4#6698311yescharacteristic
367C2×C4#6698311yescharacteristic
368C2×C4#6698311yescharacteristic
369C2×C4C22×D4411yescharacteristic
370C2×C4C2×#433911yescharacteristic
371C2×C4C22×C22⋊D1111yescharacteristic
372C8—24no—
373C8—42no—
374C8—442no—
375C8—442no—
376C22—21no—
377C22—21no—
378C22—42no—
379C22—42no—
380C22—42no—
381C22—84no—
382C22—881no—
383C22—881no—
384C22—881no—
385C22#1062274712yes—
386C22C2×#6698311yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—42no—
391C4—882no—
392C4—881no—
393C4#1062274712yes—
394C4C2×#6696111yescharacteristic
395C4C2×#6696211yescharacteristic
396C4#1062336612yes—
397C2—22no—
398C2—82no—
399C2—1761no—
400C2#1307811911yescharacteristic
401C2C2×#1062274711yescharacteristic
402C2#1307835311yescharacteristic
subgroupG/H
centerC22C2×#66983
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#2975C2
socleC22×C11C2×#121
prime radical#13078080C2
hypercenter#2975D11
hypocenterC11#19421
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
1. #13079543C2semidirect
2. C2×#10622620C2semidirect
4. #13068163C2semidirect
5. #13068081C2semidirect
6. #13067391C2semidirect
7. #13067300C2semidirect
8. #13067263C2semidirect
9. C11×#2975C2semidirect
31. #10622306C22semidirect
32. #10622294C22semidirect
33. #10622124C22semidirect
34. #10622123C22semidirect
35. #10622120C22semidirect
36. #10622096C22semidirect
138. #2975D11semidirect
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×#106226202
#130780802
#130681632
#130680812
#130673912
#130673002
#130672632
C11×#29752
#1942111