Finite Group Databasebeta

← #13079663

Subgroups — #13079663

Order 1408.

420 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623205C211yesmaximal, characteristic, complemented
2#10623093C211yesmaximal, characteristic, complemented
3C11×#463C211yesmaximal, characteristic, complemented
4#10622789C211yesmaximal, characteristic, complemented
5#10622785C211yesmaximal, characteristic, complemented
6#10622769C211yesmaximal, characteristic, complemented
7#10622764C211yesmaximal, characteristic, complemented
8#10622670C211yesmaximal, characteristic, complemented
9#10622628C211yesmaximal, characteristic, complemented
10#10622456C211yesmaximal, characteristic, complemented
11#10622453C211yesmaximal, characteristic, complemented
12#10622424C211yesmaximal, characteristic, complemented
13#10622413C211yesmaximal, characteristic, complemented
14#10622386C211yesmaximal, characteristic, complemented
15#10622377C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×C11×SD16C2211yescharacteristic, complemented
19C2×C11×D8C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C4×D4×C11C2211yescharacteristic, complemented
22#67000C2211yescharacteristic
23C2×#4325C2211yescharacteristic, complemented
24#66993C2211yescharacteristic
25#66993C2211yescharacteristic, complemented
26#66991C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28C2×#4323C2211yescharacteristic
29C2×#4323C2211yescharacteristic, complemented
30#66983—21no—
31#66982—21no—
32C2×D88C2211yescharacteristic
33C2×D88C2211yescharacteristic, complemented
34#66948C2211yescharacteristic
35#66943C2211yescharacteristic, complemented
36#66937—21no—
37#66937—21no—
38#66937—21no—
39#66936—21no—
40#66935—21no—
41#66935—21no—
42#66927C2211yescharacteristic
43C4×D44C2211yescharacteristic, complemented
44#66925C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic, complemented
46C11×#103C2211yescharacteristic, complemented
47C11×#102C2211yescharacteristic
48#66899C2211yescharacteristic, complemented
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic, complemented
52(C2×D11)⋊C8C2211yescharacteristic
53(C2×D11)⋊C8C2211yescharacteristic
54#66879C2211yescharacteristic, complemented
55C8×Dic11C2211yescharacteristic, complemented
56#66873C2211yescharacteristic
57#66873C2211yescharacteristic, complemented
58C4⋊(C11⋊C8)C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70#4343—41no—
71#4343—41no—
72D4×D11—41no—
73D4×D11—41no—
74C2×D44—21no—
75C2×D44—21no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44C2311yescharacteristic
79C2×D44C2311yescharacteristic
80C2×D44C2311yescharacteristic
81C2×C4×D11—21no—
82C2×C4×D11—21no—
83C2×C4×D11C2311yescharacteristic
84C11×SD16—41no—
85C11×D8—41no—
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C22⋊C4—21no—
90C11×C22⋊C4—21no—
91C11×C22⋊C4—21no—
92C42×C11C2311yescharacteristic
93C22⋊Dic11—21no—
94#4325—41no—
95#4323—41no—
96#4323—41no—
97#4323—41no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4D411yescharacteristic
103(C2×D11)⋊C4D411yescharacteristic
104C4⋊Dic11—21no—
105C4⋊Dic11C2311yescharacteristic
106Dic11⋊C4—21no—
107Dic11⋊C4D411yescharacteristic
108Dic11⋊C4D411yescharacteristic
109C4×Dic11C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112D88—41no—
113D88—41no—
114#3220—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—21no—
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—21no—
120C22×D11—42no—
121C22×D11—81no—
122C22×D11—81no—
123C22×D11C2×D411yescharacteristic
124Q8×C11—21no—
125Q8×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—21no—
129D4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—81no—
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2411yescharacteristic
136C22⋊D11—42no—
137C22⋊D11—81no—
138C22⋊D11—81no—
139C22⋊D11—81no—
140C22⋊D11—81no—
141C22⋊D11—81no—
142C2×Dic11—21no—
143C2×Dic11C2×D411yescharacteristic
144C2×Dic11C2×D411yescharacteristic
145C2×Dic11C2×D411yescharacteristic
146D44—21no—
147D44—21no—
148D44—21no—
149D44—21no—
150D44—21no—
151D44—21no—
152D44—42no—
153D44—81no—
154D44—81no—
155D44—81no—
156C4×D11—21no—
157C4×D11—21no—
158C4×D11—42no—
159C4×D11—81no—
160C8×C11—21no—
161C8×C11—21no—
162C11⋊C8—21no—
163C11⋊C8—21no—
164#540—111no—
165#535—111no—
166#496—111no—
167#493—111no—
168#490—111no—
169#488—111no—
170#463—111no—
171#463D1111yescharacteristic, complemented
172#459—111no—
173#459—111no—
174#449—111no—
175#449—111no—
176#447—111no—
177#447—111no—
178#433—111no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11C22×D411yescharacteristic
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—84no—
199C4×C11—21no—
200C4×C11—21no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11H(5,𝔽2)11yescharacteristic
204C4×C11H(5,𝔽2)11yescharacteristic
205Dic11—21no—
206Dic11—21no—
207Dic11—21no—
208Dic11—41no—
209C2×#41—111no—
210C22×D4—111no—
211C2×SD16—111no—
212C2×SD16C2×D1111yescharacteristic, complemented
213C2×D8—111no—
214C2×D8—111no—
215C2×D8—111no—
216C2×D8—111no—
217C2×D8—111no—
218C2×D8C2×D1111yescharacteristic
219#127—111no—
220#127—111no—
221#127—111no—
222#125—111no—
223#124—111no—
224#124C2×D1111yescharacteristic
225#123—221no—
226#123—221no—
227#121—111no—
228#121—111no—
229#121—221no—
230#121—221no—
231#121—221no—
232#121—221no—
233#120—221no—
234#120—221no—
235C4×D4—111no—
236C4×D4C2×D1111yescharacteristic, complemented
237#117—111no—
238C4⋊C8—111no—
239C4⋊C8C2×D1111yescharacteristic, complemented
240#103—111no—
241#103C2×D1111yescharacteristic, complemented
242#102—111no—
243#102—111no—
244#102—111no—
245#102—111no—
246#102—111no—
247#102C2×D1111yescharacteristic
248C22⋊C8—111no—
249C22⋊C8—111no—
250#97—111no—
251C4×C8—111no—
252C2×C11—81no—
253C2×C11—81no—
254C2×C11#53511yescharacteristic
255C2×C11#57611yescharacteristic
256C2×C11#57611yescharacteristic
257D11—41no—
258D11—81no—
259D11—81no—
260D11—81no—
261C24—221no—
262#41—441no—
263#41—441no—
264C2×Q8C22×D1111yescharacteristic
265C2×D4—111no—
266C2×D4—111no—
267C2×D4—111no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—441no—
279C2×D4—441no—
280C2×D4C22×D1111yescharacteristic
281C2×D4C22×D1111yescharacteristic
282C22×C4—21no—
283C22×C4—111no—
284C22×C4—221no—
285C22×C4—221no—
286SD16—41no—
287SD16—441no—
288D8—41no—
289D8—441no—
290D8—441no—
291D8—441no—
292D8—441no—
293D8—441no—
294C2×C8—111no—
295C2×C8—111no—
296C2×C8C22×D1111yescharacteristic
297C2×C8C22×D1111yescharacteristic
298C4⋊C4—111no—
299C4⋊C4—111no—
300C4⋊C4—111no—
301C4⋊C4—221no—
302C4⋊C4—221no—
303C4⋊C4C22×D1111yescharacteristic
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—111no—
308C22⋊C4—111no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C42—111no—
315C42C22×D1111yescharacteristic
316C11#322011yescharacteristic, complemented, Sylow
317C23—21no—
318C23—21no—
319C23—111no—
320C23—221no—
321C23—221no—
322C23—221no—
323C23—442no—
324C23—881no—
325C23—881no—
326Q8—21no—
327Q8—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—221no—
333D4—221no—
334D4—221no—
335D4—221no—
336D4—221no—
337D4—221no—
338D4—442no—
339D4—442no—
340D4—881no—
341D4—881no—
342D4—881no—
343D4—881no—
344D4—881no—
345D4—881no—
346D4—881no—
347D4—881no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—81no—
351C2×C4—111no—
352C2×C4—111no—
353C2×C4—111no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—442no—
358C2×C4—881no—
359C2×C4D4×D1111yescharacteristic
360C2×C4D4×D1111yescharacteristic
361C2×C4C23×D1111yescharacteristic
362C8—21no—
363C8—21no—
364C8—221no—
365C8—221no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—221no—
373C22—221no—
374C22—221no—
375C22—441no—
376C22—441no—
377C22—441no—
378C22—441no—
379C22—441no—
380C22—441no—
381C22—441no—
382C22—441no—
383C22—441no—
384C22—884no—
385C22C2×D4×D1111yescharacteristic
386C4—21no—
387C4—21no—
388C4—41no—
389C4—41no—
390C4—221no—
391C4—221no—
392C4—221no—
393C4—441no—
394C4#6703711yescharacteristic
395C4#6704211yescharacteristic
396C2—81no—
397C2—81no—
398C2—441no—
399C2—881no—
400C2—881no—
401C2—881no—
402C2#1062313811yescharacteristic
403C2#1062330011yescharacteristic
404C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
hypercenter#463D11
hypocenterC11#3220
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. #10623205C2semidirect
2. #10623093C2semidirect
3. C11×#463C2semidirect
4. #10622789C2semidirect
5. #10622785C2semidirect
6. #10622769C2semidirect
7. #10622764C2semidirect
8. #10622670C2semidirect
9. #10622628C2semidirect
10. #10622456C2semidirect
11. #10622453C2semidirect
12. #10622424C2semidirect
13. #10622413C2semidirect
14. #10622386C2semidirect
15. #10622377C2semidirect
18. C2×C11×SD16C22semidirect
21. C4×D4×C11C22semidirect
23. C2×#4325C22semidirect
25. #66993C22semidirect
29. C2×#4323C22semidirect
33. C2×D88C22semidirect
35. #66943C22semidirect
43. C4×D44C22semidirect
45. C11×C4⋊C8C22semidirect
46. C11×#103C22semidirect
48. #66899C22semidirect
51. #66885C22semidirect
54. #66879C22semidirect
55. C8×Dic11C22semidirect
57. #66873C22semidirect
58. C4⋊(C11⋊C8)C22semidirect
171. #463D11semidirect
212. C2×SD16C2×D11semidirect
236. C4×D4C2×D11semidirect
239. C4⋊C8C2×D11semidirect
241. #103C2×D11semidirect
316. C11#3220semidirect

Maximal subgroups

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

subgroupindex
#106232052
#106230932
C11×#4632
#106227892
#106227852
#106227692
#106227642
#106226702
#106226282
#106224562
#106224532
#106224242
#106224132
#106223862
#106223772
#322011