Finite Group Databasebeta

← #13079484

Subgroups — #13079484

Order 1408.

410 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#10623159C211yesmaximal, characteristic, complemented
2#10623138C211yesmaximal, characteristic
3C11×#468C211yesmaximal, characteristic, complemented
4#10622783C211yesmaximal, characteristic, complemented
5#10622782C211yesmaximal, characteristic, complemented
6#10622747C211yesmaximal, characteristic, complemented
7#10622742C211yesmaximal, characteristic, complemented
8#10622661C211yesmaximal, characteristic, complemented
9#10622654C211yesmaximal, characteristic, complemented
10#10622501C211yesmaximal, characteristic, complemented
11#10622498C211yesmaximal, characteristic, complemented
12#10622427C211yesmaximal, characteristic, complemented
13#10622419C211yesmaximal, characteristic, complemented
14#10622397C211yesmaximal, characteristic, complemented
15#10622389C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic, complemented
17C2×D4×D11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C2×C11×M16C2211yescharacteristic, complemented
21C11×C22⋊Q8C2211yescharacteristic, complemented
22C11×#121C2211yescharacteristic
23#66999C2211yescharacteristic
24C2×#4325C2211yescharacteristic
25#66993—21no—
26#66991C2211yescharacteristic
27#66990—21no—
28C2×#4324C2211yescharacteristic
29#66983C2211yescharacteristic
30#66977C2211yescharacteristic, complemented
31C22×C11⋊C8C2211yescharacteristic, complemented
32C2×#4314C2211yescharacteristic
33#66950C2211yescharacteristic
34#66948C2211yescharacteristic
35#66947—21no—
36#66945C2211yescharacteristic
37#66945C2211yescharacteristic, complemented
38#66941—21no—
39#66938—21no—
40#66938—21no—
41#66936—21no—
42#66935—21no—
43C11×#107C2211yescharacteristic, complemented
44C11×#103C2211yescharacteristic, complemented
45C11×#102C2211yescharacteristic
46#66899C2211yescharacteristic, complemented
47#66896C2211yescharacteristic
48#66885C2211yescharacteristic
49(C2×D11)⋊C8C2211yescharacteristic
50(C2×D11)⋊C8C2211yescharacteristic
51(C2×D11)⋊C8C2211yescharacteristic, complemented
52(C2×D11)⋊C8C2211yescharacteristic, complemented
53#66882C2211yescharacteristic, complemented
54#66880C2211yescharacteristic, complemented
55#66874C2211yescharacteristic, complemented
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic, complemented
58#66872C2211yescharacteristic, 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⋊D11D411yescharacteristic
68C2×C22⋊D11D411yescharacteristic
69Q8×D11—41no—
70Q8×D11—41no—
71D4×D11—41no—
72D4×D11—41no—
73#4339—41no—
74#4339—41no—
75C2×D44—21no—
76C2×D44D411yescharacteristic
77C2×D44C2311yescharacteristic
78C2×C4×D11—21no—
79C2×C4×D11C2311yescharacteristic
80C2×C4×D11C2311yescharacteristic
81C2×Dic22—21no—
82C2×Dic22D411yescharacteristic
83C2×Dic22C2311yescharacteristic
84C11×SD16—41no—
85C11×M16—41no—
86C2×C8×C11C2311yescharacteristic
87C2×C8×C11C2311yescharacteristic
88C11×C4⋊C4—21no—
89C11×C4⋊C4C2311yescharacteristic
90C11×C4⋊C4C2311yescharacteristic
91C11×C22⋊C4—21no—
92C11×C22⋊C4—21no—
93C22⋊Dic11—21no—
94C22⋊Dic11—21no—
95#4325—41no—
96#4324—41no—
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—
102(C2×D11)⋊C4—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11C2311yescharacteristic
105C4⋊Dic11C2311yescharacteristic
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108C4×Dic11—21no—
109C4×Dic11—21no—
110C2×C11⋊C8—41no—
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113#4314—41no—
114#3200—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11C2×D411yescharacteristic
117C22×D11—21no—
118C22×D11—42no—
119C22×D11—81no—
120C22×D11—81no—
121C22×D11C2×D411yescharacteristic
122C22×D11C2×D411yescharacteristic
123Q8×C11—21no—
124Q8×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—81no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11C2×D411yescharacteristic
134C2×C4×C11C2411yescharacteristic
135C22⋊D11—41no—
136C22⋊D11—41no—
137C22⋊D11—42no—
138C22⋊D11—81no—
139C22⋊D11—81no—
140C2×Dic11—21no—
141C2×Dic11—21no—
142C2×Dic11—21no—
143C2×Dic11C2×D411yescharacteristic
144C2×Dic11C2×D411yescharacteristic
145D44—21no—
146D44—21no—
147D44—41no—
148D44—81no—
149C4×D11—21no—
150C4×D11—21no—
151C4×D11—21no—
152C4×D11—21no—
153C4×D11—42no—
154Dic22—21no—
155Dic22—21no—
156Dic22—41no—
157Dic22—42no—
158C8×C11—21no—
159C8×C11—21no—
160C11⋊C8—21no—
161C11⋊C8—21no—
162#536—111no—
163#535—111no—
164#485—111no—
165#485—111no—
166#482—111no—
167#482—111no—
168#468—111no—
169#468D1111yescharacteristic, complemented
170#465—111no—
171#465—111no—
172#450—111no—
173#450—111no—
174#448—111no—
175#448—111no—
176#408—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—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—84no—
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—
206C22×Q8—111no—
207C22×D4—111no—
208C2×SD16—111no—
209C2×SD16—111no—
210C2×SD16—111no—
211C2×SD16C2×D1111yescharacteristic
212C2×M16C2×D1111yescharacteristic, complemented
213C22×C8—111no—
214C4⋊Q8—221no—
215#127—221no—
216#124—221no—
217#124—221no—
218#123—221no—
219#123—221no—
220C22⋊Q8—111no—
221C22⋊Q8—111no—
222C22⋊Q8—111no—
223C22⋊Q8C2×D1111yescharacteristic, complemented
224#121—111no—
225#121—111no—
226#121—111no—
227#121C2×D1111yescharacteristic
228#120—221no—
229#120—221no—
230#117—111no—
231#117—111no—
232#107—111no—
233#107C2×D1111yescharacteristic, complemented
234#106—111no—
235#106—111no—
236#103—111no—
237#103—111no—
238#103—111no—
239#103C2×D1111yescharacteristic, complemented
240#102—111no—
241#102—111no—
242#102—111no—
243#102C2×D1111yescharacteristic
244C22⋊C8—111no—
245C22⋊C8—111no—
246C22⋊C8—111no—
247C22⋊C8—111no—
248C2×C11—41no—
249C2×C11—81no—
250C2×C11#53411yescharacteristic
251C2×C11#57711yescharacteristic
252C2×C11#57711yescharacteristic
253D11—41no—
254D11—41no—
255D11—81no—
256C24—221no—
257#41—441no—
258#41—441no—
259C2×Q8—111no—
260C2×Q8—111no—
261C2×Q8—221no—
262C2×Q8—441no—
263C2×Q8—441no—
264C2×Q8C22×D1111yescharacteristic
265C2×D4—21no—
266C2×D4—111no—
267C2×D4—111no—
268C2×D4—111no—
269C2×D4—111no—
270C2×D4—221no—
271C2×D4—221no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—441no—
275C2×D4—441no—
276C2×D4C22×D1111yescharacteristic
277C22×C4—111no—
278C22×C4—111no—
279C22×C4—221no—
280C22×C4C22×D1111yescharacteristic
281SD16—41no—
282SD16—441no—
283SD16—441no—
284SD16—441no—
285M16—41no—
286C2×C8—111no—
287C2×C8—111no—
288C2×C8—441no—
289C2×C8C22×D1111yescharacteristic
290C2×C8C22×D1111yescharacteristic
291C4⋊C4—21no—
292C4⋊C4—111no—
293C4⋊C4—111no—
294C4⋊C4—221no—
295C4⋊C4—221no—
296C4⋊C4—221no—
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—221no—
310C42—221no—
311C11#320011yescharacteristic, complemented, Sylow
312C23—21no—
313C23—111no—
314C23—111no—
315C23—221no—
316C23—442no—
317C23—881no—
318C23—881no—
319C23D4×D1111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—221no—
323Q8—221no—
324Q8—441no—
325Q8—442no—
326D4—21no—
327D4—21no—
328D4—81no—
329D4—221no—
330D4—221no—
331D4—441no—
332D4—441no—
333D4—441no—
334D4—442no—
335D4—881no—
336D4—881no—
337D4—881no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—111no—
344C2×C4—111no—
345C2×C4—221no—
346C2×C4—221no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—221no—
351C2×C4—221no—
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—441no—
372C22—441no—
373C22—441no—
374C22—884no—
375C22C2×D4×D1111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—221no—
381C4—221no—
382C4—441no—
383C4—441no—
384C4—441no—
385C4#6703711yescharacteristic
386C4#6704211yescharacteristic
387C2—41no—
388C2—81no—
389C2—441no—
390C2—441no—
391C2—881no—
392C2#1062313611yescharacteristic
393C2#1062330611yescharacteristic
394C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#468C2
socleC22×C11C22×D4
prime radical#10623138C2
hypercenter#468D11
hypocenterC11#3200
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #10623159C2semidirect
3. C11×#468C2semidirect
4. #10622783C2semidirect
5. #10622782C2semidirect
6. #10622747C2semidirect
7. #10622742C2semidirect
8. #10622661C2semidirect
9. #10622654C2semidirect
10. #10622501C2semidirect
11. #10622498C2semidirect
12. #10622427C2semidirect
13. #10622419C2semidirect
14. #10622397C2semidirect
15. #10622389C2semidirect
16. C2×Q8×D11C22semidirect
20. C2×C11×M16C22semidirect
21. C11×C22⋊Q8C22semidirect
30. #66977C22semidirect
31. C22×C11⋊C8C22semidirect
37. #66945C22semidirect
43. C11×#107C22semidirect
44. C11×#103C22semidirect
46. #66899C22semidirect
51. (C2×D11)⋊C8C22semidirect
52. (C2×D11)⋊C8C22semidirect
53. #66882C22semidirect
54. #66880C22semidirect
55. #66874C22semidirect
57. #66872C22semidirect
58. #66872C22semidirect
169. #468D11semidirect
212. C2×M16C2×D11semidirect
223. C22⋊Q8C2×D11semidirect
233. #107C2×D11semidirect
239. #103C2×D11semidirect
311. C11#3200semidirect

Maximal subgroups

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

subgroupindex
#106231592
#106231382
C11×#4682
#106227832
#106227822
#106227472
#106227422
#106226612
#106226542
#106225012
#106224982
#106224272
#106224192
#106223972
#106223892
#320011