Finite Group Databasebeta

← #13079471

Subgroups — #13079471

Order 1408.

422 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623160C211yesmaximal, characteristic, complemented
2#10623138C211yesmaximal, characteristic, complemented
3C11×#465C211yesmaximal, characteristic, complemented
4#10622785C211yesmaximal, characteristic, complemented
5#10622782C211yesmaximal, characteristic, complemented
6#10622728C211yesmaximal, characteristic, complemented
7#10622723C211yesmaximal, characteristic, complemented
8#10622662C211yesmaximal, characteristic, complemented
9#10622652C211yesmaximal, characteristic, complemented
10#10622479C211yesmaximal, characteristic, complemented
11#10622476C211yesmaximal, characteristic, complemented
12#10622427C211yesmaximal, characteristic, complemented
13#10622424C211yesmaximal, characteristic, complemented
14#10622387C211yesmaximal, characteristic, complemented
15#10622386C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic, complemented
17C2×D4×D11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C22×C8×C11C2211yescharacteristic, complemented
21C11×C22⋊Q8C2211yescharacteristic, complemented
22C11×#121C2211yescharacteristic
23#66999C2211yescharacteristic
24C2×#4325C2211yescharacteristic
25#66993—21no—
26#66991C2211yescharacteristic
27#66990—21no—
28C2×#4323C2211yescharacteristic
29#66983C2211yescharacteristic
30#66983C2211yescharacteristic, complemented
31C2×#4318C2211yescharacteristic, complemented
32C2×D88C2211yescharacteristic
33#66949—21no—
34#66948—21no—
35#66948C2211yescharacteristic
36#66948C2211yescharacteristic
37#66945C2211yescharacteristic
38C4⋊C4×D11C2211yescharacteristic, complemented
39#66938—21no—
40#66937—21no—
41#66937—21no—
42#66935—21no—
43C11×#106C2211yescharacteristic, complemented
44C11×#103C2211yescharacteristic, complemented
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic, complemented
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53(C2×D11)⋊C8C2211yescharacteristic, complemented
54#66882C2211yescharacteristic, complemented
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11—21no—
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11D411yescharacteristic
69C2×C22⋊D11D411yescharacteristic
70#4343—41no—
71#4343—41no—
72D4×D11—41no—
73D4×D11—41no—
74#4339—41no—
75#4339—41no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44D411yescharacteristic
80C2×D44C2311yescharacteristic
81C2×D44C2311yescharacteristic
82C2×C4×D11—21no—
83C2×C4×D11—21no—
84C2×C4×D11C2311yescharacteristic
85C2×C4×D11C2311yescharacteristic
86C2×Dic22D411yescharacteristic
87C11×SD16—41no—
88C2×C8×C11—41no—
89C2×C8×C11C2311yescharacteristic
90C2×C8×C11C2311yescharacteristic
91C11×C4⋊C4—21no—
92C11×C4⋊C4C2311yescharacteristic
93C11×C4⋊C4C2311yescharacteristic
94C11×C22⋊C4—21no—
95C11×C22⋊C4—21no—
96C22⋊Dic11—21no—
97#4325—41no—
98#4323—41no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105C4⋊Dic11C2311yescharacteristic
106C4⋊Dic11C2311yescharacteristic
107Dic11⋊C4—21no—
108Dic11⋊C4—21no—
109C4×Dic11—21no—
110#4318—41no—
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113D88—41no—
114#3198—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C22×D11—21no—
118C22×D11—21no—
119C22×D11—42no—
120C22×D11—81no—
121C22×D11—81no—
122C22×D11C2×D411yescharacteristic
123C22×D11C2×D411yescharacteristic
124Q8×C11—21no—
125Q8×C11—21no—
126D4×C11—21no—
127D4×C11—21no—
128D4×C11—81no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11C2×D411yescharacteristic
135C2×C4×C11C2411yescharacteristic
136C22⋊D11—41no—
137C22⋊D11—41no—
138C22⋊D11—42no—
139C22⋊D11—81no—
140C22⋊D11—81no—
141C22⋊D11—81no—
142C2×Dic11—21no—
143C2×Dic11—21no—
144C2×Dic11C2×D411yescharacteristic
145C2×Dic11C2×D411yescharacteristic
146D44—21no—
147D44—21no—
148D44—21no—
149D44—21no—
150D44—41no—
151D44—42no—
152D44—81no—
153D44—81no—
154C4×D11—21no—
155C4×D11—21no—
156C4×D11—21no—
157C4×D11—21no—
158C4×D11—42no—
159C4×D11—81no—
160Dic22—41no—
161C8×C11—21no—
162C8×C11—21no—
163C11⋊C8—21no—
164C11⋊C8—21no—
165#537—111no—
166#535—111no—
167#485—111no—
168#482—111no—
169#481—111no—
170#480—111no—
171#469—111no—
172#468—111no—
173#466—111no—
174#465D1111yescharacteristic, complemented
175#450—111no—
176#449—111no—
177#449—111no—
178#447—111no—
179#408—111no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—41no—
184C22×C11—41no—
185C22×C11—41no—
186C22×C11C22×D411yescharacteristic
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—21no—
191C2×D11—21no—
192C2×D11—21no—
193C2×D11—41no—
194C2×D11—41no—
195C2×D11—41no—
196C2×D11—41no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—84no—
200C4×C11—21no—
201C4×C11—41no—
202C4×C11—41no—
203C4×C11—41no—
204C4×C11H(5,𝔽2)11yescharacteristic
205C4×C11H(5,𝔽2)11yescharacteristic
206Dic11—21no—
207Dic11—21no—
208Dic11—41no—
209Dic11—41no—
210C2×#41—111no—
211C2×#41—111no—
212C22×D4—111no—
213C2×SD16—111no—
214C2×SD16C2×D1111yescharacteristic
215C2×D8—111no—
216C2×D8—111no—
217C2×M16—111no—
218C22×C8C2×D1111yescharacteristic, complemented
219#127—221no—
220#124—221no—
221C22⋊Q8—111no—
222C22⋊Q8—221no—
223C22⋊Q8C2×D1111yescharacteristic, complemented
224#121—111no—
225#121—111no—
226#121—111no—
227#121—111no—
228#121—111no—
229#121—221no—
230#121—221no—
231#121—221no—
232#121C2×D1111yescharacteristic
233#120—221no—
234#120—221no—
235#117—111no—
236C2×C4⋊C4—111no—
237#107—111no—
238#107—111no—
239#106—111no—
240#106C2×D1111yescharacteristic, complemented
241#103—111no—
242#103C2×D1111yescharacteristic, complemented
243#102—111no—
244#102—111no—
245#102—111no—
246#102—111no—
247#102—111no—
248#102C2×D1111yescharacteristic
249C22⋊C8—111no—
250C22⋊C8—111no—
251C22⋊C8—111no—
252C22⋊C8—111no—
253C2×C11—41no—
254C2×C11—81no—
255C2×C11#53411yescharacteristic
256C2×C11#57611yescharacteristic
257C2×C11#57711yescharacteristic
258D11—41no—
259D11—41no—
260D11—81no—
261D11—81no—
262C24—221no—
263#41—441no—
264#41—441no—
265#41—441no—
266#41—441no—
267C2×Q8—111no—
268C2×Q8C22×D1111yescharacteristic
269C2×D4—21no—
270C2×D4—111no—
271C2×D4—111no—
272C2×D4—111no—
273C2×D4—111no—
274C2×D4—111no—
275C2×D4—221no—
276C2×D4—221no—
277C2×D4—221no—
278C2×D4—221no—
279C2×D4—221no—
280C2×D4—221no—
281C2×D4—221no—
282C2×D4—441no—
283C2×D4—441no—
284C2×D4C22×D1111yescharacteristic
285C22×C4—111no—
286C22×C4—111no—
287C22×C4—221no—
288C22×C4—221no—
289C22×C4C22×D1111yescharacteristic
290SD16—41no—
291SD16—441no—
292D8—441no—
293D8—441no—
294M16—441no—
295C2×C8—41no—
296C2×C8—111no—
297C2×C8—111no—
298C2×C8C22×D1111yescharacteristic
299C2×C8C22×D1111yescharacteristic
300C4⋊C4—21no—
301C4⋊C4—111no—
302C4⋊C4—111no—
303C4⋊C4—221no—
304C4⋊C4—221no—
305C4⋊C4C22×D1111yescharacteristic
306C4⋊C4C22×D1111yescharacteristic
307C22⋊C4—21no—
308C22⋊C4—21no—
309C22⋊C4—221no—
310C22⋊C4—221no—
311C22⋊C4—221no—
312C22⋊C4—221no—
313C22⋊C4—221no—
314C22⋊C4—221no—
315C22⋊C4—221no—
316C42—221no—
317C11#319811yescharacteristic, complemented, Sylow
318C23—21no—
319C23—111no—
320C23—111no—
321C23—221no—
322C23—221no—
323C23—442no—
324C23—881no—
325C23—881no—
326C23D4×D1111yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—441no—
330D4—21no—
331D4—21no—
332D4—81no—
333D4—221no—
334D4—221no—
335D4—221no—
336D4—221no—
337D4—441no—
338D4—442no—
339D4—441no—
340D4—441no—
341D4—442no—
342D4—881no—
343D4—881no—
344D4—881no—
345D4—881no—
346D4—881no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—111no—
353C2×C4—111no—
354C2×C4—221no—
355C2×C4—221no—
356C2×C4—221no—
357C2×C4—221no—
358C2×C4—221no—
359C2×C4—221no—
360C2×C4—442no—
361C2×C4—881no—
362C2×C4D4×D1111yescharacteristic
363C2×C4C23×D1111yescharacteristic
364C8—21no—
365C8—21no—
366C8—221no—
367C8—221no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—221no—
375C22—221no—
376C22—221no—
377C22—221no—
378C22—221no—
379C22—221no—
380C22—441no—
381C22—441no—
382C22—441no—
383C22—441no—
384C22—441no—
385C22—441no—
386C22—884no—
387C22C2×D4×D1111yescharacteristic
388C4—21no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—221no—
393C4—221no—
394C4—441no—
395C4—441no—
396C4#6703711yescharacteristic
397C4#6704211yescharacteristic
398C2—41no—
399C2—81no—
400C2—441no—
401C2—441no—
402C2—881no—
403C2—881no—
404C2#1062313611yescharacteristic
405C2#1062329311yescharacteristic
406C2#1062330011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#465C2
socleC22×C11C22×D4
hypercenter#465D11
hypocenterC11#3198
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #465

Complements

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

NH ≅ G/Ntype
1. #10623160C2semidirect
2. #10623138C2semidirect
3. C11×#465C2semidirect
4. #10622785C2semidirect
5. #10622782C2semidirect
6. #10622728C2semidirect
7. #10622723C2semidirect
8. #10622662C2semidirect
9. #10622652C2semidirect
10. #10622479C2semidirect
11. #10622476C2semidirect
12. #10622427C2semidirect
13. #10622424C2semidirect
14. #10622387C2semidirect
15. #10622386C2semidirect
16. C2×#4343C22semidirect
20. C22×C8×C11C22semidirect
21. C11×C22⋊Q8C22semidirect
30. #66983C22semidirect
31. C2×#4318C22semidirect
38. C4⋊C4×D11C22semidirect
43. C11×#106C22semidirect
44. C11×#103C22semidirect
46. #66899C22semidirect
49. #66885C22semidirect
52. (C2×D11)⋊C8C22semidirect
53. (C2×D11)⋊C8C22semidirect
54. #66882C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
174. #465D11semidirect
218. C22×C8C2×D11semidirect
223. C22⋊Q8C2×D11semidirect
240. #106C2×D11semidirect
242. #103C2×D11semidirect
317. C11#3198semidirect

Maximal subgroups

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

subgroupindex
#106231602
#106231382
C11×#4652
#106227852
#106227822
#106227282
#106227232
#106226622
#106226522
#106224792
#106224762
#106224272
#106224242
#106223872
#106223862
#319811