Finite Group Databasebeta

← #13079450

Subgroups — #13079450

Order 1408.

414 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×C22⋊Q8C211yesmaximal, characteristic, complemented
2#10623055C211yesmaximal, characteristic
3C11×#485C211yesmaximal, characteristic, complemented
4#10622660C211yesmaximal, characteristic, complemented
5#10622609C211yesmaximal, characteristic, complemented
6#10622499C211yesmaximal, characteristic, complemented
7#10622497C211yesmaximal, characteristic, complemented
8#10622481C211yesmaximal, characteristic, complemented
9#10622476C211yesmaximal, characteristic, complemented
10#10622429C211yesmaximal, characteristic, complemented
11#10622425C211yesmaximal, characteristic, complemented
12#10622421C211yesmaximal, characteristic, complemented
13#10622419C211yesmaximal, characteristic, complemented
14#10622346C211yesmaximal, characteristic, complemented
15#10622339C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20C11×#117C2211yescharacteristic
21#66999C2211yescharacteristic
22C2×#4326C2211yescharacteristic, complemented
23C2×#4325C2211yescharacteristic, complemented
24#66977C2211yescharacteristic
25C2×Dic44C2211yescharacteristic, complemented
26C2×#4314C2211yescharacteristic, complemented
27C2×#4313C2211yescharacteristic
28C2×#4313C2211yescharacteristic
29#66950C2211yescharacteristic
30#66950C2211yescharacteristic
31#66950C2211yescharacteristic
32#66949—21no—
33#66948C2211yescharacteristic
34#66948C2211yescharacteristic
35C4⋊C4×D11—21no—
36C4⋊C4×D11C2211yescharacteristic
37#66939—21no—
38#66935—21no—
39C22⋊C4×D11—21no—
40#66931—21no—
41C4×D44—21no—
42C4×D44—21no—
43C11×#107C2211yescharacteristic, complemented
44C11×#106C2211yescharacteristic, complemented
45C11×#103C2211yescharacteristic, complemented
46C11×#103C2211yescharacteristic, 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×Q8×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C22×Dic11D411yescharacteristic
64Q8×D11—41no—
65Q8×D11—41no—
66#4339—41no—
67#4339—41no—
68C2×D44—21no—
69C2×D44—21no—
70C2×D44C2311yescharacteristic
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11—41no—
75C2×C4×D11—41no—
76C2×C4×D11D411yescharacteristic
77C2×C4×D11D411yescharacteristic
78C2×C4×D11C2311yescharacteristic
79C2×C4×D11C2311yescharacteristic
80C2×Dic22—21no—
81C2×Dic22C2311yescharacteristic
82C2×Dic22C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C11×C4⋊C4—21no—
86C11×C4⋊C4C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C22⋊C4—21no—
90C11×C22⋊C4—21no—
91C42×C11—21no—
92C22⋊Dic11—21no—
93#4326—41no—
94#4325—41no—
95(C2×D11)⋊C4—21no—
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—
101C4⋊Dic11—21no—
102C4⋊Dic11—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11C2311yescharacteristic
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107Dic11⋊C4—21no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110Dic44—41no—
111#4314—41no—
112#4313—41no—
113#4313—41no—
114#3196—111nomaximal, Sylow
115C23×C11C2×D411yescharacteristic
116C22×D11—22no—
117C22×D11—21no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11C2×D411yescharacteristic
121C22×D11C2×D411yescharacteristic
122Q8×C11—21no—
123Q8×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—21no—
126C2×C4×C11—21no—
127C2×C4×C11—21no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—42no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—41no—
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139D44—21no—
140D44—21no—
141D44—42no—
142D44—42no—
143C4×D11—21no—
144C4×D11—21no—
145C4×D11—21no—
146C4×D11—21no—
147C4×D11—41no—
148C4×D11—41no—
149C4×D11—42no—
150C4×D11—42no—
151C4×D11—42no—
152Dic22—21no—
153Dic22—21no—
154Dic22—21no—
155Dic22—21no—
156Dic22—42no—
157C8×C11—21no—
158C8×C11—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161#525—111no—
162C2×C22⋊Q8—111no—
163#485—111no—
164#485D1111yescharacteristic, complemented
165#484—111no—
166#481—111no—
167#470—111no—
168#470—111no—
169#468—111no—
170#468—111no—
171#452—111no—
172#452—111no—
173#451—111no—
174#448—111no—
175#407—111no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—21no—
179C22×C11C22×D411yescharacteristic
180C2×D11—21no—
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—44no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C2×D11#13712yes—
190C4×C11—21no—
191C4×C11—41no—
192C4×C11—41no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11H(5,𝔽2)11yescharacteristic
196C4×C11H(5,𝔽2)11yescharacteristic
197Dic11—21no—
198Dic11—21no—
199Dic11—41no—
200Dic11—41no—
201Dic11—41no—
202C2×#41—111no—
203C22×Q8—111no—
204C23×C4—111no—
205C2×Q16—111no—
206C2×Q16—111no—
207C2×SD16—111no—
208C2×SD16—111no—
209C2×M16—111no—
210C2×M16—111no—
211#123—221no—
212C22⋊Q8—111no—
213C22⋊Q8—111no—
214C22⋊Q8—111no—
215C22⋊Q8—111no—
216C22⋊Q8—111no—
217C22⋊Q8—221no—
218C22⋊Q8—221no—
219C22⋊Q8C2×D1111yescharacteristic
220#121—111no—
221#121—111no—
222#120—221no—
223C4×D4—221no—
224C4×D4—221no—
225#117C2×D1111yescharacteristic
226C2×C4⋊C4—111no—
227C2×C4⋊C4—221no—
228C2×C22⋊C4—221no—
229#107—111no—
230#107C2×D1111yescharacteristic, complemented
231#106—111no—
232#106C2×D1111yescharacteristic, complemented
233#103—111no—
234#103—111no—
235#103—111no—
236#103—111no—
237#103C2×D1111yescharacteristic, complemented
238#103C2×D1111yescharacteristic, complemented
239#102—111no—
240#102—111no—
241C22⋊C8—111no—
242C22⋊C8—111no—
243C22⋊C8—111no—
244C22⋊C8C2×D1111yescharacteristic
245C2×C11—41no—
246C2×C11#53411yescharacteristic
247C2×C11C2×#13711yescharacteristic
248C2×C11#57511yescharacteristic
249D11—22no—
250D11—41no—
251D11—81no—
252C24—111no—
253#41—441no—
254#41—441no—
255C2×Q8—111no—
256C2×Q8—111no—
257C2×Q8—221no—
258C2×Q8—441no—
259C2×Q8—441no—
260C2×Q8C22×D1111yescharacteristic
261C2×D4—111no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4—221no—
265C22×C4—111no—
266C22×C4—111no—
267C22×C4—111no—
268C22×C4—111no—
269C22×C4—111no—
270C22×C4—221no—
271C22×C4—221no—
272C22×C4—221no—
273C22×C4—441no—
274C22×C4—441no—
275C22×C4C22×D1111yescharacteristic
276Q16—441no—
277Q16—441no—
278SD16—441no—
279SD16—441no—
280M16—441no—
281M16—441no—
282C2×C8—111no—
283C2×C8—111no—
284C2×C8C22×D1111yescharacteristic
285C2×C8C22×D1111yescharacteristic
286C4⋊C4—21no—
287C4⋊C4—111no—
288C4⋊C4—221no—
289C4⋊C4—221no—
290C4⋊C4—221no—
291C4⋊C4—221no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4C22×D1111yescharacteristic
295C4⋊C4C22×D1111yescharacteristic
296C4⋊C4C22×D1111yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—221no—
300C22⋊C4—221no—
301C22⋊C4—221no—
302C22⋊C4—221no—
303C22⋊C4—221no—
304C22⋊C4—221no—
305C22⋊C4—221no—
306C42—21no—
307C11#319611yescharacteristic, complemented, Sylow
308C23—111no—
309C23—111no—
310C23—222no—
311C23—221no—
312C23—441no—
313C23—441no—
314C23D4×D1111yescharacteristic
315Q8—21no—
316Q8—21no—
317Q8—221no—
318Q8—221no—
319Q8—221no—
320Q8—221no—
321Q8—442no—
322D4—221no—
323D4—221no—
324D4—442no—
325D4—442no—
326D4—442no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—111no—
334C2×C4—111no—
335C2×C4—221no—
336C2×C4—221no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—221no—
340C2×C4—221no—
341C2×C4—221no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—442no—
345C2×C4—442no—
346C2×C4—442no—
347C2×C4—441no—
348C2×C4D4×D1111yescharacteristic
349C2×C4C23×D1111yescharacteristic
350C8—21no—
351C8—21no—
352C8—221no—
353C8—221no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—112no—
358C22—221no—
359C22—221no—
360C22—221no—
361C22—221no—
362C22—221no—
363C22—444no—
364C22—441no—
365C22—441no—
366C22—441no—
367C22C2×D4×D1111yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—221no—
374C4—221no—
375C4—441no—
376C4—441no—
377C4—441no—
378C4#6704211yescharacteristic
379C4#6704211yescharacteristic
380C2—41no—
381C2—222no—
382C2—441no—
383C2—881no—
384C2#1062318411yescharacteristic
385C2#1062329911yescharacteristic
386C2D11×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radical#10623055C2
hypercenter#485D11
hypocenterC11#3196
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. D11×C22⋊Q8C2semidirect
3. C11×#485C2semidirect
4. #10622660C2semidirect
5. #10622609C2semidirect
6. #10622499C2semidirect
7. #10622497C2semidirect
8. #10622481C2semidirect
9. #10622476C2semidirect
10. #10622429C2semidirect
11. #10622425C2semidirect
12. #10622421C2semidirect
13. #10622419C2semidirect
14. #10622346C2semidirect
15. #10622339C2semidirect
22. C2×#4326C22semidirect
23. C2×#4325C22semidirect
25. C2×Dic44C22semidirect
26. C2×#4314C22semidirect
43. C11×#107C22semidirect
44. C11×#106C22semidirect
45. C11×#103C22semidirect
46. C11×#103C22semidirect
49. #66885C22semidirect
52. #66880C22semidirect
53. #66874C22semidirect
54. #66874C22semidirect
55. #66874C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
164. #485D11semidirect
230. #107C2×D11semidirect
232. #106C2×D11semidirect
237. #103C2×D11semidirect
238. #103C2×D11semidirect
307. C11#3196semidirect

Maximal subgroups

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

subgroupindex
D11×C22⋊Q82
#106230552
C11×#4852
#106226602
#106226092
#106224992
#106224972
#106224812
#106224762
#106224292
#106224252
#106224212
#106224192
#106223462
#106223392
#319611