Finite Group Databasebeta

← #13079453

Subgroups — #13079453

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
1C11×#525C211yesmaximal, characteristic, complemented
2#10623322C211yesmaximal, characteristic, complemented
3#10622852C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic, complemented
5#10622820C211yesmaximal, characteristic, complemented
6#10622665C211yesmaximal, characteristic, complemented
7#10622662C211yesmaximal, characteristic, complemented
8#10622660C211yesmaximal, characteristic, complemented
9#10622658C211yesmaximal, characteristic, complemented
10#10622655C211yesmaximal, characteristic, complemented
11#10622652C211yesmaximal, characteristic, complemented
12#10622650C211yesmaximal, characteristic, complemented
13#10622648C211yesmaximal, characteristic, complemented
14#10622616C211yesmaximal, characteristic, complemented
15#10622609C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C23×C4×C11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C11×#123—21no—
20C11×C22⋊Q8C2211yescharacteristic
21C11×C22⋊Q8C2211yescharacteristic
22C11×#121C2211yescharacteristic
23C11×#121C2211yescharacteristic
24C11×#120—21no—
25C4×D4×C11—21no—
26C4×D4×C11—21no—
27C11×#117C2211yescharacteristic
28#67006—21no—
29C2×#4326C2211yescharacteristic, complemented
30C2×#4325C2211yescharacteristic, complemented
31C2×#4324C2211yescharacteristic, complemented
32C2×#4323C2211yescharacteristic, complemented
33#66983C2211yescharacteristic
34#66983C2211yescharacteristic
35#66982—21no—
36C4×C22⋊D11—21no—
37C4×C22⋊D11—21no—
38#66979C2211yescharacteristic
39#66977C2211yescharacteristic
40#66977C2211yescharacteristic
41C2×#4318C2211yescharacteristic
42C2×#4318C2211yescharacteristic
43#66899C2211yescharacteristic, complemented
44#66899C2211yescharacteristic, complemented
45#66896C2211yescharacteristic, complemented
46#66896C2211yescharacteristic, complemented
47C22⋊(C11⋊C8)C2211yescharacteristic
48C22⋊(C11⋊C8)C2211yescharacteristic
49C22⋊(C11⋊C8)C2211yescharacteristic
50C22⋊(C11⋊C8)C2211yescharacteristic
51#66874C2211yescharacteristic, complemented
52#66874C2211yescharacteristic, complemented
53#66873C2211yescharacteristic, complemented
54#66873C2211yescharacteristic, complemented
55#66872C2211yescharacteristic, complemented
56#66872C2211yescharacteristic, complemented
57#66871C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C24×C11D411yescharacteristic
60C11×#41—41no—
61C11×#41—41no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11—21no—
65C2×D4×C11—21no—
66C2×D4×C11C2311yescharacteristic
67C22×C4×C11—21no—
68C22×C4×C11—41no—
69C22×C4×C11—41no—
70C22×C4×C11D411yescharacteristic
71C22×C4×C11D411yescharacteristic
72C22×C4×C11D411yescharacteristic
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C2×C22⋊D11—21no—
77C2×C22⋊D11—21no—
78C2×C22⋊D11—21no—
79#4339—41no—
80#4339—41no—
81C2×D44C2311yescharacteristic
82C2×C4×D11—21no—
83C2×Dic22C2311yescharacteristic
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4C2311yescharacteristic
87C11×C4⋊C4C2311yescharacteristic
88C11×C22⋊C4—21no—
89C11×C22⋊C4—21no—
90C11×C22⋊C4—21no—
91C11×C22⋊C4—21no—
92C11×C22⋊C4—21no—
93C42×C11—21no—
94C22⋊Dic11—21no—
95C22⋊Dic11—21no—
96C22⋊Dic11—21no—
97#4326—41no—
98#4325—41no—
99#4324—41no—
100#4323—41no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103C4⋊Dic11C2311yescharacteristic
104C4⋊Dic11C2311yescharacteristic
105Dic11⋊C4—21no—
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108#4318—41no—
109#4318—41no—
110C2×C11⋊C8C2311yescharacteristic
111C2×C11⋊C8C2311yescharacteristic
112C2×C11⋊C8C2311yescharacteristic
113C2×C11⋊C8C2311yescharacteristic
114#3197—111nomaximal, Sylow
115C23×C11—21no—
116C23×C11—41no—
117C23×C11—41no—
118C23×C11—41no—
119C23×C11C2×D411yescharacteristic
120C23×C11C2×D411yescharacteristic
121C23×C11C2×D411yescharacteristic
122C22×D11—21no—
123Q8×C11—21no—
124Q8×C11—21no—
125D4×C11—21no—
126D4×C11—21no—
127D4×C11—42no—
128D4×C11—42no—
129D4×C11—42no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—42no—
143C2×C4×C11C2×D411yescharacteristic
144C2×C4×C11C2×D411yescharacteristic
145C2×C4×C11C2×D411yescharacteristic
146C2×C4×C11C2411yescharacteristic
147C22⋊D11—42no—
148C22⋊D11—42no—
149C22⋊D11—42no—
150C2×Dic11—21no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153D44—21no—
154D44—21no—
155C4×D11—42no—
156Dic22—21no—
157Dic22—21no—
158C11⋊C8—21no—
159C11⋊C8—21no—
160C11⋊C8—21no—
161C11⋊C8—21no—
162#525—111no—
163#525D1111yescharacteristic, complemented
164#485—111no—
165#485—111no—
166#482—111no—
167#482—111no—
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—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—44no—
187C22×C11—41no—
188C22×C11—41no—
189C22×C11—41no—
190C22×C11C22×D411yescharacteristic
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C4×C11—21no—
195C4×C11—21no—
196C4×C11—21no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11—41no—
200C4×C11H(5,𝔽2)11yescharacteristic
201C4×C11H(5,𝔽2)11yescharacteristic
202Dic11—41no—
203Dic11—41no—
204Dic11—41no—
205C2×#41—111no—
206C2×#41C2×D1111yescharacteristic
207C23×C4C2×D1111yescharacteristic
208C2×Q16—111no—
209C2×SD16—111no—
210C2×SD16—111no—
211C2×D8—111no—
212C2×M16—111no—
213C2×M16—111no—
214#123—21no—
215#123—221no—
216C22⋊Q8—111no—
217C22⋊Q8—111no—
218C22⋊Q8C2×D1111yescharacteristic
219C22⋊Q8C2×D1111yescharacteristic
220#121—111no—
221#121—111no—
222#121C2×D1111yescharacteristic
223#121C2×D1111yescharacteristic
224#120—21no—
225#120—221no—
226C4×D4—21no—
227C4×D4—21no—
228C4×D4—221no—
229C4×D4—221no—
230#117—111no—
231#117C2×D1111yescharacteristic
232#107—111no—
233#107—111no—
234#106—111no—
235#106—111no—
236#103—111no—
237#103—111no—
238#103—111no—
239#103—111no—
240#102—111no—
241#102—111no—
242#102—111no—
243#102—111no—
244C22⋊C8—111no—
245C22⋊C8—111no—
246C22⋊C8—111no—
247C22⋊C8—111no—
248C2×C11—41no—
249C2×C11—41no—
250C2×C11—41no—
251C2×C11—81no—
252C2×C11#53411yescharacteristic
253C2×C11#57511yescharacteristic
254C2×C11#57511yescharacteristic
255D11—81no—
256C24C22⋊D1111yescharacteristic
257#41—41no—
258#41—41no—
259#41—441no—
260#41—441no—
261C2×Q8—111no—
262C2×Q8C22×D1111yescharacteristic
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—111no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4C22×D1111yescharacteristic
271C22×C4—21no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—221no—
275C22×C4C22⋊D1111yescharacteristic
276C22×C4C22⋊D1111yescharacteristic
277C22×C4C22⋊D1111yescharacteristic
278C22×C4C22×D1111yescharacteristic
279C22×C4C22×D1111yescharacteristic
280C22×C4C22×D1111yescharacteristic
281Q16—441no—
282SD16—441no—
283SD16—441no—
284D8—441no—
285M16—441no—
286M16—441no—
287C2×C8—111no—
288C2×C8—111no—
289C2×C8—111no—
290C2×C8—111no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—111no—
294C4⋊C4—111no—
295C4⋊C4—221no—
296C4⋊C4—221no—
297C4⋊C4C22×D1111yescharacteristic
298C4⋊C4C22×D1111yescharacteristic
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
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—41no—
314C23—41no—
315C23—41no—
316C23—221no—
317C23C2×C22⋊D1111yescharacteristic
318C23C2×C22⋊D1111yescharacteristic
319C23C2×C22⋊D1111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—221no—
323Q8—221no—
324D4—21no—
325D4—21no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—221no—
330D4—221no—
331D4—442no—
332D4—442no—
333D4—442no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—221no—
348C2×C4—221no—
349C2×C4—221no—
350C2×C4—442no—
351C2×C4C2×C22⋊D1111yescharacteristic
352C2×C4C2×C22⋊D1111yescharacteristic
353C2×C4C2×C22⋊D1111yescharacteristic
354C2×C4C23×D1111yescharacteristic
355C8—221no—
356C8—221no—
357C8—221no—
358C8—221no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—44no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—441no—
373C22—441no—
374C22—441no—
375C22C22×C22⋊D1111yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—441no—
383C4—441no—
384C4—441no—
385C4#6703711yescharacteristic
386C4#6703711yescharacteristic
387C2—41no—
388C2—41no—
389C2—41no—
390C2—81no—
391C2—881no—
392C2#1062333511yescharacteristic
393C2#1062335311yescharacteristic
394C2#1062335311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#525C2
socleC22×C11C22×D4
hypercenter#525D11
hypocenterC11#3197
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C11×#525C2semidirect
2. #10623322C2semidirect
3. #10622852C2semidirect
4. #10622851C2semidirect
5. #10622820C2semidirect
6. #10622665C2semidirect
7. #10622662C2semidirect
8. #10622660C2semidirect
9. #10622658C2semidirect
10. #10622655C2semidirect
11. #10622652C2semidirect
12. #10622650C2semidirect
13. #10622648C2semidirect
14. #10622616C2semidirect
15. #10622609C2semidirect
29. C2×#4326C22semidirect
30. C2×#4325C22semidirect
31. C2×#4324C22semidirect
32. C2×#4323C22semidirect
43. #66899C22semidirect
44. #66899C22semidirect
45. #66896C22semidirect
46. #66896C22semidirect
51. #66874C22semidirect
52. #66874C22semidirect
53. #66873C22semidirect
54. #66873C22semidirect
55. #66872C22semidirect
56. #66872C22semidirect
57. #66871C22semidirect
58. #66871C22semidirect
163. #525D11semidirect
311. C11#3197semidirect

Maximal subgroups

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

subgroupindex
C11×#5252
#106233222
#106228522
#106228512
#106228202
#106226652
#106226622
#106226602
#106226582
#106226552
#106226522
#106226502
#106226482
#106226162
#106226092
#319711