Finite Group Databasebeta

← #14739318

Subgroups — #14739318

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
1C2×#10622700C211yesmaximal, characteristic, complemented
2#13078076C211yesmaximal, characteristic
3#13077656C211yesmaximal, characteristic, complemented
4#13068160C214yesmaximal, complemented
5#13068078C214yesmaximal, complemented
6#13067391C211yesmaximal, characteristic, complemented
7#13067301C211yesmaximal, characteristic, complemented
8#13067265C211yesmaximal, characteristic, complemented
9C11×#3206C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67002—21no—
13C2×C4×D44C2211yescharacteristic
14C11×#492C2212yescomplemented
15C11×#487C2212yescomplemented
16C11×#461—22no—
17C11×#448—22no—
18C11×#431C2211yescharacteristic
19#10622845—21no—
20#10622700—22no—
21#10622700C2214yes—
22#10622696C2212yes—
23#10622685C2212yes—
24#10622670—22no—
25C2×#66873—21no—
26C2×#66871—21no—
27#10622538C2211yescharacteristic
28#10622537C2211yescharacteristic
29C2×C4⋊(C11⋊C8)C2211yescharacteristic
30#10622451—22no—
31#10622339—22no—
32#10622301C2214yes—
33#10622185C2212yescomplemented
34#10622185C2214yescomplemented
35#10622182C2212yescomplemented
36#10622096C2214yescomplemented
37C2×C11×#41—21no—
38C22×Q8×C11—21no—
39C22×D44D411yescharacteristic
40C22×C4×D11—21no—
41C2×C11×SD16—24no—
42C11×C4⋊Q8—21no—
43C11×C4⋊Q8—21no—
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8C2312yes—
46C11×C4⋊Q8C2311yescharacteristic
47C11×#127C2311yescharacteristic
48C11×#124—21no—
49C11×#121—21no—
50C11×#121—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56#67002—44no—
57C2×#4325—22no—
58C2×#4323—22no—
59C2×(C2×D11)⋊C4—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×#4318—21no—
62C22×C11⋊C8—21no—
63C2×#4313—24no—
64C4×D44—21no—
65C4×D44—21no—
66C4×D44D412yes—
67C4×D44C2312yes—
68C11×C4⋊C8D412yes—
69C11×#103—24no—
70C11×C22⋊C8D412yes—
71C4×C8×C11C2312yes—
72#66899—22no—
73#66896—22no—
74C22⋊(C11⋊C8)—21no—
75(C2×D11)⋊C8—24no—
76#66873—24no—
77#66871—24no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)—21no—
80C4⋊(C11⋊C8)C2312yes—
81C4⋊(C11⋊C8)C2312yes—
82C4⋊(C11⋊C8)C2312yes—
83C4×C11⋊C8—21no—
84#19421—111nomaximal, Sylow
85C23×D11—21no—
86C11×#41—42no—
87C11×#41—42no—
88C2×Q8×C11—21no—
89C2×Q8×C11—22no—
90C2×Q8×C11—41no—
91C2×Q8×C11—82no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11#4111yescharacteristic
101C22×Dic11—21no—
102C2×D44—21no—
103C2×D44—22no—
104C2×D44—22no—
105C2×D44C2×D412yes—
106C2×C4×D11—22no—
107C2×C4×D11—22no—
108C2×C4×D11—82no—
109C11×SD16—84no—
110C2×C8×C11C2×D414yes—
111C11×C4⋊C4—22no—
112C11×C4⋊C4—21no—
113C11×C4⋊C4—22no—
114C11×C4⋊C4—21no—
115C11×C4⋊C4—41no—
116C11×C4⋊C4—41no—
117C11×C22⋊C4—41no—
118C11×C22⋊C4—41no—
119C42×C11C2×D411yescharacteristic
120C42×C11C2×D411yescharacteristic
121C42×C11#4111yescharacteristic
122C42×C11C2411yescharacteristic
123#4325—44no—
124#4323—44no—
125(C2×D11)⋊C4—22no—
126(C2×D11)⋊C4—22no—
127C4⋊Dic11—21no—
128C4⋊Dic11C2×D412yes—
129#4318—42no—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8—22no—
133C2×C11⋊C8—42no—
134#4313—84no—
135#3206D1111yescharacteristic, complemented
136C2×#474—111no—
137#3036—111no—
138#2975—111no—
139#1699—114no—
140#1685—114no—
141#1571—111no—
142#1549—111no—
143#1540—111no—
144C23×C11—41no—
145C23×C11#12111yescharacteristic
146C22×D11—22no—
147C22×D11—42no—
148C22×D11—81no—
149C22×D11—81no—
150Q8×C11—41no—
151Q8×C11—41no—
152Q8×C11—44no—
153Q8×C11—82no—
154D4×C11—41no—
155D4×C11—41no—
156D4×C11—42no—
157D4×C11—81no—
158D4×C11—82no—
159C2×C4×C11—22no—
160C2×C4×C11—41no—
161C2×C4×C11—41no—
162C2×C4×C11—42no—
163C2×C4×C11—82no—
164C2×C4×C11—82no—
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12111yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)12yes—
169C2×C4×C11#13712yes—
170C2×C4×C11C22×D411yescharacteristic
171C2×C4×C11C22×D411yescharacteristic
172C2×C4×C11C2×#4111yescharacteristic
173C2×Dic11—22no—
174C2×Dic11—81no—
175D44—22no—
176D44—22no—
177D44—42no—
178C4×D11—44no—
179C4×D11—82no—
180C8×C11—24no—
181C11⋊C8—42no—
182C11⋊C8—42no—
183C11⋊C8—42no—
184C2×AGL(1,ℤ/8)—221no—
185#532C2×D1111yescharacteristic
186C2×C4⋊Q8C2×D1111yescharacteristic
187C2×C4×D4—111no—
188#492C2×D1112yescomplemented
189#487C2×D1112yescomplemented
190#474—114no—
191#474—222no—
192#463—222no—
193#461—22no—
194#461—112no—
195#459—112no—
196#448—22no—
197#436—114no—
198#436—222no—
199#431—111no—
200#431C2×D1111yescharacteristic
201C2×#107—221no—
202#423—111no—
203C2×C4⋊C8—111no—
204#417—221no—
205C2×#102—221no—
206#407—222no—
207#335—114no—
208#332—112no—
209#332—114no—
210#331—112no—
211C22×C11—21no—
212C22×C11—21no—
213C22×C11—81no—
214C22×C11—81no—
215C22×C11—81no—
216C22×C11#46812yes—
217C22×C11C2×#12111yescharacteristic
218C2×D11—42no—
219C2×D11—42no—
220C2×D11—42no—
221C2×D11—84no—
222C4×C11—21no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—82no—
226C4×C11—81no—
227C4×C11#46812yes—
228C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
229C4×C11C2×#13711yescharacteristic
230C4×C11#57612yes—
231Dic11—42no—
232C2×#41—21no—
233C22×Q8—21no—
234C22×D4—111no—
235C23×C4—221no—
236AGL(1,ℤ/8)—444no—
237C2×SD16—24no—
238C2×SD16—222no—
239C2×D8—222no—
240C2×M16—221no—
241C2×M16—224no—
242C22×C8—221no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8C22×D1112yes—
247C4⋊Q8C22×D1111yescharacteristic
248#127C22×D1111yescharacteristic
249#124—21no—
250#121—21no—
251#121—21no—
252C4×D4—21no—
253C4×D4—21no—
254C4×D4—112no—
255C4×D4—112no—
256C4×D4—221no—
257C4×D4—221no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—111no—
261C2×C22⋊C4—221no—
262C2×C42C22×D1111yescharacteristic
263#107—224no—
264C4⋊C8—112no—
265C4⋊C8—112no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8C22⋊D1112yes—
270#103—24no—
271#103—222no—
272#102—224no—
273#102—222no—
274C22⋊C8—221no—
275C22⋊C8—224no—
276C22⋊C8C22⋊D1112yes—
277C4×C8—221no—
278C4×C8C22×D1112yes—
279C2×C11—22no—
280C2×C11—161no—
281C2×C11#304111yescharacteristic
282C2×C11C2×#46811yescharacteristic
283C2×C11#306911yescharacteristic
284D11—82no—
285C24—221no—
286#41—42no—
287#41—42no—
288C2×Q8—21no—
289C2×Q8—22no—
290C2×Q8—41no—
291C2×Q8—82no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—41no—
296C2×D4—112no—
297C2×D4—222no—
298C2×D4—222no—
299C2×D4—221no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4—221no—
303C22×C4—222no—
304C22×C4—222no—
305C22×C4—882no—
306C22×C4D4×D1111yescharacteristic
307C22×C4#434111yescharacteristic
308C22×C4C2×C22⋊D1111yescharacteristic
309SD16—84no—
310SD16—444no—
311D8—444no—
312M16—442no—
313M16—884no—
314C2×C8—222no—
315C2×C8—222no—
316C2×C8—222no—
317C2×C8—442no—
318C2×C8C2×C22⋊D1114yes—
319C4⋊C4—22no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—112no—
326C4⋊C4—221no—
327C22⋊C4—41no—
328C22⋊C4—41no—
329C22⋊C4—222no—
330C22⋊C4—222no—
331C42D4×D1111yescharacteristic
332C42#434111yescharacteristic
333C42C2×C22⋊D1111yescharacteristic
334C42C23×D1111yescharacteristic
335C11#1942111yescharacteristic, complemented, Sylow
336C23—41no—
337C23—222no—
338C23—442no—
339C23—881no—
340C23—881no—
341C23#6699111yescharacteristic
342Q8—41no—
343Q8—41no—
344Q8—44no—
345Q8—82no—
346D4—41no—
347D4—41no—
348D4—42no—
349D4—81no—
350D4—82no—
351D4—222no—
352D4—222no—
353D4—442no—
354C2×C4—22no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—42no—
358C2×C4—82no—
359C2×C4—82no—
360C2×C4—222no—
361C2×C4—444no—
362C2×C4—882no—
363C2×C4—881no—
364C2×C4#6696712yes—
365C2×C4#6696812yes—
366C2×C4#6699111yescharacteristic
367C2×C4#6699111yescharacteristic
368C2×C4#6699111yescharacteristic
369C2×C4C2×D4×D1111yescharacteristic
370C2×C4C2×#434111yescharacteristic
371C2×C4C22×C22⋊D1111yescharacteristic
372C8—24no—
373C8—442no—
374C8—442no—
375C8—442no—
376C22—21no—
377C22—21no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—442no—
382C22—442no—
383C22—442no—
384C22—884no—
385C22#1062278712yes—
386C22C2×#6699111yescharacteristic
387C4—21no—
388C4—21no—
389C4—21no—
390C4—82no—
391C4—81no—
392C4—442no—
393C4#1062278712yes—
394C4C2×#6696711yescharacteristic
395C4C2×#6696811yescharacteristic
396C4#1062336612yes—
397C2—22no—
398C2—161no—
399C2—882no—
400C2#1307811511yescharacteristic
401C2C2×#1062278711yescharacteristic
402C2#1307834911yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC11×#3206C2
socleC22×C11C2×#121
prime radical#13078076C2
hypercenter#3206D11
hypocenterC11#19421
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
1. C2×#10622700C2semidirect
3. #13077656C2semidirect
4. #13068160C2semidirect
5. #13068078C2semidirect
6. #13067391C2semidirect
7. #13067301C2semidirect
8. #13067265C2semidirect
9. C11×#3206C2semidirect
14. C11×#492C22semidirect
15. C11×#487C22semidirect
33. #10622185C22semidirect
34. #10622185C22semidirect
35. #10622182C22semidirect
36. #10622096C22semidirect
135. #3206D11semidirect
188. #492C2×D11semidirect
189. #487C2×D11semidirect
335. C11#19421semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
#130780762
#130776562
#130681602
#130680782
#130673912
#130673012
#130672652
C11×#32062
#1942111