Finite Group Databasebeta

← #13079460

Subgroups — #13079460

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#10623158C211yesmaximal, characteristic, complemented
2#10623055C211yesmaximal, characteristic, complemented
3C11×#485C211yesmaximal, characteristic, complemented
4#10622660C211yesmaximal, characteristic, complemented
5#10622616C211yesmaximal, characteristic, complemented
6#10622499C211yesmaximal, characteristic, complemented
7#10622498C211yesmaximal, characteristic, complemented
8#10622480C211yesmaximal, characteristic, complemented
9#10622478C211yesmaximal, characteristic, complemented
10#10622429C211yesmaximal, characteristic, complemented
11#10622425C211yesmaximal, characteristic, complemented
12#10622424C211yesmaximal, characteristic, complemented
13#10622423C211yesmaximal, characteristic, complemented
14#10622347C211yesmaximal, characteristic, complemented
15#10622339C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C22×C4×D11C2211yescharacteristic
19C11×C22⋊Q8C2211yescharacteristic
20C11×#117C2211yescharacteristic
21#66999C2211yescharacteristic
22C2×#4326C2211yescharacteristic, complemented
23C2×#4325C2211yescharacteristic, complemented
24#66983C2211yescharacteristic
25C2×D88C2211yescharacteristic, complemented
26C2×#4314C2211yescharacteristic, complemented
27C2×#4313C2211yescharacteristic
28C2×#4313C2211yescharacteristic
29#66950C2211yescharacteristic
30#66950C2211yescharacteristic
31#66948C2211yescharacteristic
32#66948C2211yescharacteristic
33#66948C2211yescharacteristic
34#66947—21no—
35#66946—21no—
36#66945C2211yescharacteristic
37#66939—21no—
38#66935—21no—
39#66935—21no—
40(C22⋊D11)⋊C4—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#66873C2211yescharacteristic, complemented
55#66873C2211yescharacteristic, complemented
56#66873C2211yescharacteristic, complemented
57#66872C2211yescharacteristic, complemented
58#66871C2211yescharacteristic, complemented
59C23×D11D411yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C22×Dic11D411yescharacteristic
65#4343—41no—
66#4343—41no—
67#4339—41no—
68#4339—41no—
69C2×D44—21no—
70C2×D44—21no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44C2311yescharacteristic
74C2×D44C2311yescharacteristic
75C2×C4×D11—21no—
76C2×C4×D11—21no—
77C2×C4×D11—41no—
78C2×C4×D11—41no—
79C2×C4×D11D411yescharacteristic
80C2×C4×D11D411yescharacteristic
81C2×C4×D11C2311yescharacteristic
82C2×C4×D11C2311yescharacteristic
83C2×Dic22C2311yescharacteristic
84C2×C8×C11C2311yescharacteristic
85C2×C8×C11C2311yescharacteristic
86C11×C4⋊C4—21no—
87C11×C4⋊C4C2311yescharacteristic
88C11×C4⋊C4C2311yescharacteristic
89C11×C4⋊C4C2311yescharacteristic
90C11×C22⋊C4—21no—
91C11×C22⋊C4—21no—
92C42×C11—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—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103C4⋊Dic11—21no—
104C4⋊Dic11—21no—
105C4⋊Dic11C2311yescharacteristic
106Dic11⋊C4—21no—
107C4×Dic11—21no—
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110D88—41no—
111#4314—41no—
112#4313—41no—
113#4313—41no—
114#3197—111nomaximal, Sylow
115C23×C11C2×D411yescharacteristic
116C22×D11—21no—
117C22×D11—21no—
118C22×D11—41no—
119C22×D11—41no—
120C22×D11—41no—
121C22×D11C2×D411yescharacteristic
122C22×D11C2×D411yescharacteristic
123Q8×C11—21no—
124Q8×C11—21no—
125C2×C4×C11—21no—
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—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—41no—
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140D44—21no—
141D44—21no—
142D44—21no—
143D44—21no—
144D44—42no—
145D44—42no—
146D44—42no—
147D44—42no—
148C4×D11—21no—
149C4×D11—21no—
150C4×D11—21no—
151C4×D11—21no—
152C4×D11—41no—
153C4×D11—41no—
154C4×D11—42no—
155C4×D11—42no—
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#485D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
181C2×D11—21no—
182C2×D11—21no—
183C2×D11—21no—
184C2×D11—21no—
185C2×D11—21no—
186C2×D11—21no—
187C2×D11—44no—
188C2×D11—41no—
189C2×D11—41no—
190C2×D11—41no—
191C2×D11—41no—
192C2×D11—41no—
193C2×D11—41no—
194C4×C11—21no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—41no—
199C4×C11H(5,𝔽2)11yescharacteristic
200C4×C11H(5,𝔽2)11yescharacteristic
201Dic11—21no—
202Dic11—21no—
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⋊Q8C2×D1111yescharacteristic
220#121—111no—
221#121—111no—
222#121—111no—
223#121—111no—
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#103C2×D1111yescharacteristic, complemented
239#103C2×D1111yescharacteristic, complemented
240#102—111no—
241#102—111no—
242#102—111no—
243#102—111no—
244C22⋊C8—111no—
245C22⋊C8—111no—
246C22⋊C8—111no—
247C22⋊C8C2×D1111yescharacteristic
248C2×C11—41no—
249C2×C11#53411yescharacteristic
250C2×C11#57511yescharacteristic
251C2×C11#57511yescharacteristic
252D11—41no—
253D11—41no—
254D11—81no—
255D11—81no—
256C24—111no—
257#41—441no—
258#41—441no—
259#41—441no—
260#41—441no—
261C2×Q8—111no—
262C2×Q8C22×D1111yescharacteristic
263C2×D4—111no—
264C2×D4—111no—
265C2×D4—221no—
266C2×D4—221no—
267C2×D4—221no—
268C2×D4—221no—
269C2×D4—221no—
270C2×D4—221no—
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—21no—
292C4⋊C4—111no—
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—111no—
313C23—111no—
314C23—221no—
315C23—221no—
316C23—441no—
317C23—441no—
318C23—441no—
319C23D4×D1111yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—221no—
323Q8—221no—
324D4—221no—
325D4—221no—
326D4—221no—
327D4—221no—
328D4—442no—
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—21no—
340C2×C4—111no—
341C2×C4—111no—
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—442no—
352C2×C4—441no—
353C2×C4D4×D1111yescharacteristic
354C2×C4C23×D1111yescharacteristic
355C8—21no—
356C8—21no—
357C8—221no—
358C8—221no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—221no—
363C22—221no—
364C22—221no—
365C22—221no—
366C22—221no—
367C22—221no—
368C22—444no—
369C22—441no—
370C22—441no—
371C22—441no—
372C22—441no—
373C22—441no—
374C22—441no—
375C22C2×D4×D1111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—221no—
382C4—221no—
383C4—441no—
384C4—441no—
385C4#6704211yescharacteristic
386C4#6704211yescharacteristic
387C2—41no—
388C2—441no—
389C2—441no—
390C2—881no—
391C2—881no—
392C2#1062318411yescharacteristic
393C2#1062329911yescharacteristic
394C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
hypercenter#485D11
hypocenterC11#3197
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. #10623158C2semidirect
2. #10623055C2semidirect
3. C11×#485C2semidirect
4. #10622660C2semidirect
5. #10622616C2semidirect
6. #10622499C2semidirect
7. #10622498C2semidirect
8. #10622480C2semidirect
9. #10622478C2semidirect
10. #10622429C2semidirect
11. #10622425C2semidirect
12. #10622424C2semidirect
13. #10622423C2semidirect
14. #10622347C2semidirect
15. #10622339C2semidirect
22. C2×#4326C22semidirect
23. C2×#4325C22semidirect
25. C2×D88C22semidirect
26. C2×#4314C22semidirect
43. C11×#107C22semidirect
44. C11×#106C22semidirect
45. C11×#103C22semidirect
46. C11×#103C22semidirect
49. #66885C22semidirect
52. #66880C22semidirect
53. #66874C22semidirect
54. #66873C22semidirect
55. #66873C22semidirect
56. #66873C22semidirect
57. #66872C22semidirect
58. #66871C22semidirect
165. #485D11semidirect
233. #107C2×D11semidirect
235. #106C2×D11semidirect
238. #103C2×D11semidirect
239. #103C2×D11semidirect
311. C11#3197semidirect

Maximal subgroups

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

subgroupindex
#106231582
#106230552
C11×#4852
#106226602
#106226162
#106224992
#106224982
#106224802
#106224782
#106224292
#106224252
#106224242
#106224232
#106223472
#106223392
#319711