Finite Group Databasebeta

← #13080834

Subgroups — #13080834

Order 1408.

402 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623081C211yesmaximal, characteristic
2#10623072C211yesmaximal, characteristic, complemented
3C11×#436C211yesmaximal, characteristic, complemented
4#10622750C211yesmaximal, characteristic, complemented
5#10622747C211yesmaximal, characteristic, complemented
6#10622746C211yesmaximal, characteristic, complemented
7#10622744C211yesmaximal, characteristic, complemented
8#10622460C211yesmaximal, characteristic, complemented
9#10622458C211yesmaximal, characteristic, complemented
10#10622348C211yesmaximal, characteristic, complemented
11#10622346C211yesmaximal, characteristic, complemented
12#10622344C211yesmaximal, characteristic, complemented
13#10622336C211yesmaximal, characteristic, complemented
14#10622310C211yesmaximal, characteristic, complemented
15C4×#4314C211yesmaximal, characteristic, complemented
16C2×#4339C2211yescharacteristic
17C22×D44C2211yescharacteristic
18C2×C11×M16C2211yescharacteristic
19C2×C11×M16C2211yescharacteristic, complemented
20C4×D4×C11C2211yescharacteristic
21#66990—21no—
22#66988—21no—
23#66983C2211yescharacteristic
24#66979C2211yescharacteristic
25C2×C4⋊Dic11C2211yescharacteristic, complemented
26#66977C2211yescharacteristic
27#66977C2211yescharacteristic
28#66977C2211yescharacteristic, complemented
29C2×Dic44C2211yescharacteristic, complemented
30C2×#4314C2211yescharacteristic
31C2×#4314C2211yescharacteristic
32#66947—21no—
33#66942—21no—
34#66937—21no—
35C22⋊C4×D11—21no—
36#66932—21no—
37#66930—21no—
38#66928C2211yescharacteristic
39C4×D44C2211yescharacteristic
40#66923C2211yescharacteristic, complemented
41C4×Dic22C2211yescharacteristic, complemented
42C11×C4⋊C8C2211yescharacteristic, complemented
43C11×C22⋊C8C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic, complemented
45C4×C8×C11C2211yescharacteristic, complemented
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52#66882C2211yescharacteristic, complemented
53#66881C2211yescharacteristic, complemented
54#66881C2211yescharacteristic, complemented
55#66880C2211yescharacteristic, complemented
56#66880C2211yescharacteristic, complemented
57#66880C2211yescharacteristic, complemented
58#66880C2211yescharacteristic, complemented
59C23×D11—21no—
60C2×D4×C11D411yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C22×Dic11—21no—
66#4339—22no—
67#4339—41no—
68C2×D44—22no—
69C2×D44—21no—
70C2×D44—41no—
71C2×D44C2311yescharacteristic
72C2×D44C2311yescharacteristic
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×Dic22C2311yescharacteristic
76C2×Dic22C2311yescharacteristic
77C11×M16—41no—
78C11×M16—41no—
79C2×C8×C11C2311yescharacteristic
80C2×C8×C11C2311yescharacteristic
81C2×C8×C11C2311yescharacteristic
82C2×C8×C11C2311yescharacteristic
83C11×C4⋊C4D411yescharacteristic
84C11×C22⋊C4D411yescharacteristic
85C11×C22⋊C4D411yescharacteristic
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100Dic11⋊C4—21no—
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103Dic11⋊C4—21no—
104Dic11⋊C4—21no—
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C4×Dic11—21no—
108Dic44—41no—
109#4314—22no—
110#4314—41no—
111#3323—111nomaximal, Sylow
112C23×C11C2×D411yescharacteristic
113C23×C11C2×D411yescharacteristic
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—81no—
119D4×C11—41no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2411yescharacteristic
129C22⋊D11—42no—
130C22⋊D11—81no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136C2×Dic11—21no—
137C2×Dic11—42no—
138D44—21no—
139D44—21no—
140D44—21no—
141D44—42no—
142D44#4112yes—
143C4×D11—42no—
144C4×D11—81no—
145Dic22—21no—
146Dic22—21no—
147Dic22—21no—
148Dic22—21no—
149C8×C11—21no—
150C8×C11—21no—
151C8×C11—21no—
152C8×C11—21no—
153#552—111no—
154#546—111no—
155#488—111no—
156#485—111no—
157#481—111no—
158#478—111no—
159#470—111no—
160#468—111no—
161#464—111no—
162#452—111no—
163#450—111no—
164C4×SD16—111no—
165#436D1111yescharacteristic, complemented
166#418—111no—
167#417—111no—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—21no—
173C22×C11—21no—
174C22×C11C22×D411yescharacteristic
175C2×D11—22no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—84no—
182C4×C11—21no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11C2×#4111yescharacteristic
187C4×C11H(5,𝔽2)11yescharacteristic
188Dic11—41no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192Dic11—41no—
193Dic11—41no—
194C2×#41—111no—
195C22×D4—111no—
196C2×Q16—111no—
197C2×SD16—111no—
198C2×SD16—111no—
199C2×M16C2×D1111yescharacteristic
200C2×M16C2×D1111yescharacteristic, complemented
201#126—221no—
202#125—111no—
203#125—221no—
204#124—111no—
205#123—221no—
206#123—221no—
207C22⋊Q8—111no—
208C22⋊Q8—111no—
209C22⋊Q8—111no—
210#121—111no—
211#121—221no—
212#120—221no—
213C4×Q8—111no—
214C4×D4—111no—
215C4×D4C2×D1111yescharacteristic
216#117—111no—
217#117—221no—
218C2×C4⋊C4—111no—
219C2×C22⋊C4—221no—
220#107—111no—
221#106—111no—
222#106—111no—
223C4⋊C8C2×D1111yescharacteristic, complemented
224#103—111no—
225#103—111no—
226#103—111no—
227#103—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102—111no—
232#102—111no—
233#102—111no—
234C22⋊C8C2×D1111yescharacteristic
235C22⋊C8C2×D1111yescharacteristic, complemented
236C4×C8C2×D1111yescharacteristic, complemented
237C2×C11—41no—
238C2×C11—41no—
239C2×C11#54611yescharacteristic
240C2×C11#57511yescharacteristic
241C2×C11#57711yescharacteristic
242D11—42no—
243D11—81no—
244C24—221no—
245#41—222no—
246#41—441no—
247C2×Q8—111no—
248C2×Q8—111no—
249C2×D4—111no—
250C2×D4—111no—
251C2×D4—222no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—441no—
256C2×D4D4411yescharacteristic
257C22×C4—221no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4C22×D1111yescharacteristic
261C22×C4C22×D1111yescharacteristic
262Q16—441no—
263SD16—222no—
264SD16—441no—
265M16—41no—
266M16—41no—
267C2×C8C22×D1111yescharacteristic
268C2×C8C22×D1111yescharacteristic
269C2×C8C22×D1111yescharacteristic
270C2×C8C22×D1111yescharacteristic
271C4⋊C4—111no—
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—221no—
279C4⋊C4—221no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4D4411yescharacteristic
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4D4411yescharacteristic
292C22⋊C4D4411yescharacteristic
293C42—221no—
294C42—221no—
295C42C22×D1111yescharacteristic
296C11#332311yescharacteristic, complemented, Sylow
297C23—221no—
298C23—221no—
299C23—442no—
300C23—442no—
301C23—881no—
302C23C2×D4411yescharacteristic
303C23C2×D4411yescharacteristic
304Q8—221no—
305Q8—221no—
306Q8—221no—
307Q8—221no—
308D4—41no—
309D4—112no—
310D4—221no—
311D4—221no—
312D4—221no—
313D4—442no—
314D4—442no—
315D4—881no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—221no—
326C2×C4—442no—
327C2×C4—442no—
328C2×C4—881no—
329C2×C4C2×D4411yescharacteristic
330C2×C4C2×D4411yescharacteristic
331C2×C4C2×D4411yescharacteristic
332C2×C4C2×D4411yescharacteristic
333C2×C4C23×D1111yescharacteristic
334C8—21no—
335C8—21no—
336C8—21no—
337C8—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—222no—
345C22—441no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22—441no—
350C22—884no—
351C22C22×D4411yescharacteristic
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—441no—
357C4—441no—
358C4—441no—
359C4—441no—
360C4—441no—
361C4—441no—
362C4#6703711yescharacteristic
363C4#41×D1111yescharacteristic
364C2—41no—
365C2—41no—
366C2—442no—
367C2—881no—
368C2#1062308511yescharacteristic
369C2#1062327911yescharacteristic
370C2#1062328211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#436C2
socleC22×C11C22×D4
prime radical#10623081C2
hypercenter#436D11
hypocenterC11#3323
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
2. #10623072C2semidirect
3. C11×#436C2semidirect
4. #10622750C2semidirect
5. #10622747C2semidirect
6. #10622746C2semidirect
7. #10622744C2semidirect
8. #10622460C2semidirect
9. #10622458C2semidirect
10. #10622348C2semidirect
11. #10622346C2semidirect
12. #10622344C2semidirect
13. #10622336C2semidirect
14. #10622310C2semidirect
15. C4×#4314C2semidirect
19. C2×C11×M16C22semidirect
25. C2×C4⋊Dic11C22semidirect
28. #66977C22semidirect
29. C2×Dic44C22semidirect
40. #66923C22semidirect
41. C4×Dic22C22semidirect
42. C11×C4⋊C8C22semidirect
44. C11×C22⋊C8C22semidirect
45. C4×C8×C11C22semidirect
52. #66882C22semidirect
53. #66881C22semidirect
54. #66881C22semidirect
55. #66880C22semidirect
56. #66880C22semidirect
57. #66880C22semidirect
58. #66880C22semidirect
165. #436D11semidirect
200. C2×M16C2×D11semidirect
223. C4⋊C8C2×D11semidirect
235. C22⋊C8C2×D11semidirect
236. C4×C8C2×D11semidirect
296. C11#3323semidirect

Maximal subgroups

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

subgroupindex
#106230812
#106230722
C11×#4362
#106227502
#106227472
#106227462
#106227442
#106224602
#106224582
#106223482
#106223462
#106223442
#106223362
#106223102
C4×#43142
#332311