Finite Group Databasebeta

← #13079456

Subgroups — #13079456

Order 1408.

418 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623137C211yesmaximal, characteristic, complemented
2#10623055C211yesmaximal, characteristic, complemented
3C11×#482C211yesmaximal, characteristic, complemented
4#10622650C211yesmaximal, characteristic, complemented
5#10622609C211yesmaximal, characteristic, complemented
6#10622501C211yesmaximal, characteristic, complemented
7#10622499C211yesmaximal, characteristic, complemented
8#10622481C211yesmaximal, characteristic, complemented
9#10622479C211yesmaximal, characteristic, complemented
10#10622396C211yesmaximal, characteristic, complemented
11#10622395C211yesmaximal, characteristic, complemented
12#10622394C211yesmaximal, characteristic, complemented
13#10622393C211yesmaximal, characteristic, complemented
14#10622346C211yesmaximal, characteristic, complemented
15#10622339C211yesmaximal, characteristic, complemented
16C2×#4341C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C11×#121C2211yescharacteristic
20C11×#117C2211yescharacteristic
21#66991C2211yescharacteristic
22#66990—21no—
23D4×Dic11—21no—
24C2×#4324C2211yescharacteristic, complemented
25C2×#4323C2211yescharacteristic, complemented
26#66977C2211yescharacteristic
27C2×Dic44C2211yescharacteristic, complemented
28C2×#4314C2211yescharacteristic, complemented
29C2×#4313C2211yescharacteristic
30C2×#4313C2211yescharacteristic
31#66950C2211yescharacteristic
32#66950C2211yescharacteristic
33#66950C2211yescharacteristic
34#66948C2211yescharacteristic
35#66948C2211yescharacteristic
36#66945C2211yescharacteristic
37#66939—21no—
38#66936—21no—
39#66935—21no—
40(C22⋊D11)⋊C4—21no—
41C4×D44—21no—
42C4×D44—21no—
43C11×#107C2211yescharacteristic, complemented
44C11×#106C2211yescharacteristic, complemented
45C11×#102C2211yescharacteristic, complemented
46C11×#102C2211yescharacteristic, complemented
47C11×C22⋊C8C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49#66885C2211yescharacteristic, complemented
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic
52#66880C2211yescharacteristic, complemented
53#66874C2211yescharacteristic, complemented
54#66874C2211yescharacteristic, complemented
55#66874C2211yescharacteristic, complemented
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11D411yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67C22×Dic11D411yescharacteristic
68#4341—41no—
69#4341—41no—
70#4339—41no—
71#4339—41no—
72C2×D44—21no—
73C2×D44—21no—
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—41no—
77C2×C4×D11—41no—
78C2×C4×D11D411yescharacteristic
79C2×C4×D11D411yescharacteristic
80C2×C4×D11C2311yescharacteristic
81C2×C4×D11C2311yescharacteristic
82C2×Dic22C2311yescharacteristic
83C2×Dic22C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C2×C8×C11C2311yescharacteristic
86C11×C4⋊C4C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C22⋊C4—21no—
90C11×C22⋊C4—21no—
91C42×C11—21no—
92C22⋊Dic11—21no—
93C22⋊Dic11—21no—
94#4324—41no—
95#4323—41no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11C2311yescharacteristic
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110Dic44—41no—
111#4314—41no—
112#4313—41no—
113#4313—41no—
114#3197—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C22×D11—21no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11C2×D411yescharacteristic
122C22×D11C2×D411yescharacteristic
123D4×C11—21no—
124D4×C11—21no—
125D4×C11—42no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2411yescharacteristic
133C22⋊D11—42no—
134C22⋊D11—42no—
135C22⋊D11—42no—
136C2×Dic11—21no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—41no—
140C2×Dic11—42no—
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143D44—21no—
144D44—21no—
145D44—42no—
146D44—42no—
147C4×D11—21no—
148C4×D11—21no—
149C4×D11—21no—
150C4×D11—21no—
151C4×D11—41no—
152C4×D11—41no—
153C4×D11—42no—
154Dic22—21no—
155Dic22—21no—
156Dic22—21no—
157Dic22—21no—
158C8×C11—21no—
159C8×C11—21no—
160C11⋊C8—21no—
161C11⋊C8—21no—
162#525—111no—
163#525—111no—
164#485—111no—
165#485—111no—
166#482—111no—
167#482D1111yescharacteristic, complemented
168#470—111no—
169#469—111no—
170#468—111no—
171#468—111no—
172#452—111no—
173#452—111no—
174#449—111no—
175#449—111no—
176#407—111no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—41no—
183C22×C11C22×D411yescharacteristic
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—21no—
188C2×D11—21no—
189C2×D11—21no—
190C2×D11—44no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C4×C11—21no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11H(5,𝔽2)11yescharacteristic
199C4×C11H(5,𝔽2)11yescharacteristic
200Dic11—21no—
201Dic11—21no—
202Dic11—41no—
203Dic11—41no—
204Dic11—41no—
205C2×#41—111no—
206C2×#41—111no—
207C23×C4—111no—
208C2×Q16—111no—
209C2×SD16—111no—
210C2×SD16—111no—
211C2×D8—111no—
212C2×M16—111no—
213C2×M16—111no—
214#123—221no—
215#123—221no—
216C22⋊Q8—111no—
217C22⋊Q8—111no—
218C22⋊Q8—111no—
219C22⋊Q8—111no—
220#121—111no—
221#121—111no—
222#121—111no—
223#121C2×D1111yescharacteristic
224#120—221no—
225#120—221no—
226C4×D4—221no—
227C4×D4—221no—
228C4×D4—221no—
229C4×D4—221no—
230#117—111no—
231#117C2×D1111yescharacteristic
232#107—111no—
233#107C2×D1111yescharacteristic, complemented
234#106—111no—
235#106C2×D1111yescharacteristic, complemented
236#103—111no—
237#103—111no—
238#103—111no—
239#103—111no—
240#102—111no—
241#102—111no—
242#102C2×D1111yescharacteristic, complemented
243#102C2×D1111yescharacteristic, complemented
244C22⋊C8—111no—
245C22⋊C8—111no—
246C22⋊C8—111no—
247C22⋊C8C2×D1111yescharacteristic
248C2×C11—41no—
249C2×C11—81no—
250C2×C11#53411yescharacteristic
251C2×C11#57511yescharacteristic
252C2×C11#57511yescharacteristic
253D11—41no—
254D11—41no—
255D11—81no—
256C24—111no—
257#41—441no—
258#41—441no—
259#41—441no—
260#41—441no—
261C2×Q8—111no—
262C2×Q8—111no—
263C2×D4—21no—
264C2×D4—111no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4C22×D1111yescharacteristic
271C22×C4—111no—
272C22×C4—111no—
273C22×C4—111no—
274C22×C4—111no—
275C22×C4—111no—
276C22×C4—221no—
277C22×C4—221no—
278C22×C4—441no—
279C22×C4—441no—
280C22×C4C22×D1111yescharacteristic
281Q16—441no—
282SD16—441no—
283SD16—441no—
284D8—441no—
285M16—441no—
286M16—441no—
287C2×C8—111no—
288C2×C8—111no—
289C2×C8C22×D1111yescharacteristic
290C2×C8C22×D1111yescharacteristic
291C4⋊C4—111no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4C22×D1111yescharacteristic
297C4⋊C4C22×D1111yescharacteristic
298C4⋊C4C22×D1111yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C22⋊C4—221no—
307C22⋊C4—221no—
308C22⋊C4—221no—
309C42—21no—
310C42—221no—
311C11#319711yescharacteristic, complemented, Sylow
312C23—21no—
313C23—111no—
314C23—111no—
315C23—221no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23D4×D1111yescharacteristic
320Q8—221no—
321Q8—221no—
322Q8—221no—
323Q8—221no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—221no—
328D4—221no—
329D4—442no—
330D4—442no—
331D4—442no—
332D4—442no—
333D4—442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—111no—
340C2×C4—111no—
341C2×C4—221no—
342C2×C4—221no—
343C2×C4—221no—
344C2×C4—221no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—441no—
349C2×C4—441no—
350C2×C4—442no—
351C2×C4—441no—
352C2×C4—442no—
353C2×C4D4×D1111yescharacteristic
354C2×C4C23×D1111yescharacteristic
355C8—21no—
356C8—21no—
357C8—221no—
358C8—221no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—221no—
366C22—221no—
367C22—221no—
368C22—221no—
369C22—221no—
370C22—221no—
371C22—444no—
372C22—441no—
373C22—441no—
374C22—441no—
375C22C2×D4×D1111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—221no—
381C4—221no—
382C4—441no—
383C4—441no—
384C4—441no—
385C4#6704211yescharacteristic
386C4#6704211yescharacteristic
387C2—41no—
388C2—81no—
389C2—441no—
390C2—441no—
391C2—881no—
392C2#1062318411yescharacteristic
393C2#1062329911yescharacteristic
394C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#482C2
socleC22×C11C22×D4
hypercenter#482D11
hypocenterC11#3197
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #10623137C2semidirect
2. #10623055C2semidirect
3. C11×#482C2semidirect
4. #10622650C2semidirect
5. #10622609C2semidirect
6. #10622501C2semidirect
7. #10622499C2semidirect
8. #10622481C2semidirect
9. #10622479C2semidirect
10. #10622396C2semidirect
11. #10622395C2semidirect
12. #10622394C2semidirect
13. #10622393C2semidirect
14. #10622346C2semidirect
15. #10622339C2semidirect
24. C2×#4324C22semidirect
25. C2×#4323C22semidirect
27. C2×Dic44C22semidirect
28. C2×#4314C22semidirect
43. C11×#107C22semidirect
44. C11×#106C22semidirect
45. C11×#102C22semidirect
46. C11×#102C22semidirect
49. #66885C22semidirect
52. #66880C22semidirect
53. #66874C22semidirect
54. #66874C22semidirect
55. #66874C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
167. #482D11semidirect
233. #107C2×D11semidirect
235. #106C2×D11semidirect
242. #102C2×D11semidirect
243. #102C2×D11semidirect
311. C11#3197semidirect

Maximal subgroups

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

subgroupindex
#106231372
#106230552
C11×#4822
#106226502
#106226092
#106225012
#106224992
#106224812
#106224792
#106223962
#106223952
#106223942
#106223932
#106223462
#106223392
#319711