Finite Group Databasebeta

← #13081637

Subgroups — #13081637

Order 1408.

406 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623099C211yesmaximal, characteristic, complemented
2#10623084C211yesmaximal, characteristic, complemented
3C11×#440C211yesmaximal, characteristic, complemented
4#10622789C211yesmaximal, characteristic, complemented
5#10622788C211yesmaximal, characteristic, complemented
6#10622640C211yesmaximal, characteristic, complemented
7#10622629C211yesmaximal, characteristic, complemented
8#10622502C211yesmaximal, characteristic, complemented
9#10622485C211yesmaximal, characteristic, complemented
10#10622432C211yesmaximal, characteristic, complemented
11#10622431C211yesmaximal, characteristic, complemented
12#10622399C211yesmaximal, characteristic, complemented
13#10622375C211yesmaximal, characteristic, complemented
14#10622325C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×#4339—21no—
17C2×C11×SD16C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#67000C2211yescharacteristic
21#66997C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23C2×#4325C2211yescharacteristic
24#66993C2211yescharacteristic
25#66993C2211yescharacteristic
26C2×#4324C2211yescharacteristic
27C2×#4323C2211yescharacteristic
28#66983—21no—
29C2×D88C2211yescharacteristic
30C2×D88C2211yescharacteristic
31C2×#4314C2211yescharacteristic
32C2×#4314C2211yescharacteristic
33#66951—21no—
34#66949—21no—
35#66946C2211yescharacteristic
36#66946C2211yescharacteristic
37#66946C2211yescharacteristic
38#66940C2211yescharacteristic
39#66937—21no—
40#66937—21no—
41#66929—21no—
42#66928C2211yescharacteristic
43#66927C2211yescharacteristic
44#66925—21no—
45C4×Dic22C2211yescharacteristic
46C11×#107C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#102C2211yescharacteristic
49C11×#97C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66874C2211yescharacteristic
55#66873C2211yescharacteristic
56#66873C2211yescharacteristic
57#66873C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66#4339—44no—
67C2×D44—21no—
68C2×D44—21no—
69C2×D44C2311yescharacteristic
70C2×D44C2311yescharacteristic
71C2×D44C2311yescharacteristic
72C2×C4×D11—21no—
73C2×C4×D11—21no—
74C2×C4×D11—21no—
75C2×Dic22D411yescharacteristic
76C2×Dic22C2311yescharacteristic
77C11×SD16—22no—
78C2×C8×C11C2311yescharacteristic
79C2×C8×C11C2311yescharacteristic
80C11×C4⋊C4—21no—
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C42×C11—21no—
85C42×C11C2311yescharacteristic
86#4325—41no—
87#4325—41no—
88#4324—41no—
89#4323—41no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97C4⋊Dic11D411yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4D411yescharacteristic
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11C2311yescharacteristic
105C4×Dic11C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108D88—22no—
109D88—41no—
110#4314—22no—
111#4314—41no—
112#3397—111nomaximal, Sylow
113C23×C11—21no—
114C22×D11—21no—
115C22×D11—21no—
116C22×D11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119D4×C11—21no—
120D4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—42no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—42no—
129C22⋊D11—42no—
130C22⋊D11—81no—
131C22⋊D11—81no—
132C2×Dic11—21no—
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136C2×Dic11C2×D411yescharacteristic
137D44—21no—
138D44—21no—
139D44—21no—
140D44—21no—
141D44—21no—
142D44—21no—
143D44—42no—
144D44—81no—
145C4×D11—42no—
146C4×D11—42no—
147C4×D11—42no—
148Dic22—22no—
149Dic22—21no—
150Dic22—21no—
151C8×C11—21no—
152C8×C11#4112yescomplemented
153C11⋊C8—21no—
154C11⋊C8—21no—
155#556—111no—
156#550—111no—
157#496—111no—
158#496—111no—
159#492—111no—
160#463—111no—
161#463—111no—
162#461—111no—
163#460—111no—
164#460—111no—
165#459—111no—
166#446—111no—
167#440—111no—
168#440D1111yescharacteristic, complemented
169C4×D8—111no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11C22×D411yescharacteristic
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C2×D11—41no—
181C2×D11—41no—
182C2×D11—41no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—41no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11C2×#4111yescharacteristic
189C4×C11H(5,𝔽2)11yescharacteristic
190Dic11—21no—
191Dic11—21no—
192Dic11—21no—
193Dic11—41no—
194Dic11AGL(1,ℤ/8)12yes—
195C2×#41—221no—
196C2×SD16—111no—
197C2×SD16—111no—
198C2×SD16—111no—
199C2×SD16—111no—
200C2×SD16—111no—
201C2×SD16C2×D1111yescharacteristic
202C2×D8—111no—
203C2×D8—111no—
204C2×D8—111no—
205C4⋊Q8—111no—
206#127—111no—
207#127—111no—
208#127—111no—
209#126—221no—
210#126—221no—
211#124—111no—
212#124—111no—
213C22⋊Q8—221no—
214#121—221no—
215#121—221no—
216#121—221no—
217C4×Q8—111no—
218C4×Q8—111no—
219C4×Q8C2×D1111yescharacteristic
220C4×D4—111no—
221C4×D4—111no—
222C4×D4—111no—
223C4×D4C2×D1111yescharacteristic
224#117—221no—
225#107C2×D1111yescharacteristic
226C4⋊C8—111no—
227C4⋊C8—111no—
228C4⋊C8—111no—
229#103—111no—
230#103C2×D1111yescharacteristic
231#102—111no—
232#102—111no—
233#102—111no—
234#102C2×D1111yescharacteristic
235#97—111no—
236#97C2×D1111yescharacteristic
237C4×C8—111no—
238C2×C11—81no—
239C2×C11#55011yescharacteristic
240C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
241C2×C11#57711yescharacteristic
242D11—81no—
243D11—81no—
244D11—81no—
245#41—444no—
246C2×Q8—111no—
247C2×Q8—111no—
248C2×Q8C22×D1111yescharacteristic
249C2×D4—111no—
250C2×D4—111no—
251C2×D4—111no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—221no—
256C2×D4—221no—
257C2×D4—221no—
258C2×D4C22×D1111yescharacteristic
259C22×C4—21no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—221no—
263SD16—22no—
264SD16—222no—
265SD16—441no—
266SD16—441no—
267SD16—441no—
268SD16—441no—
269D8—222no—
270D8—441no—
271D8—441no—
272C2×C8—111no—
273C2×C8—111no—
274C2×C8C22×D1111yescharacteristic
275C2×C8C22×D1111yescharacteristic
276C4⋊C4—21no—
277C4⋊C4—111no—
278C4⋊C4—111no—
279C4⋊C4—111no—
280C4⋊C4—221no—
281C4⋊C4—221no—
282C4⋊C4—221no—
283C4⋊C4C22×D1111yescharacteristic
284C4⋊C4C22×D1111yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C22⋊C4—221no—
290C22⋊C4—221no—
291C22⋊C4—221no—
292C22⋊C4—221no—
293C42—21no—
294C42—111no—
295C42—111no—
296C42—221no—
297C42C22×D1111yescharacteristic
298C11#339711yescharacteristic, complemented, Sylow
299C23—21no—
300C23—221no—
301C23—221no—
302C23—221no—
303Q8—21no—
304Q8—21no—
305Q8—222no—
306Q8—221no—
307Q8—221no—
308D4—21no—
309D4—21no—
310D4—221no—
311D4—221no—
312D4—221no—
313D4—221no—
314D4—221no—
315D4—221no—
316D4—442no—
317D4—442no—
318D4—442no—
319D4—881no—
320D4—881no—
321D4—881no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—42no—
326C2×C4—111no—
327C2×C4—111no—
328C2×C4—111no—
329C2×C4—111no—
330C2×C4—221no—
331C2×C4—442no—
332C2×C4—442no—
333C2×C4—442no—
334C2×C4D4×D1111yescharacteristic
335C2×C4D4×D1111yescharacteristic
336C2×C4C23×D1111yescharacteristic
337C8—21no—
338C8—221no—
339C8—221no—
340C8#433912yescomplemented
341C22—41no—
342C22—41no—
343C22—41no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22—441no—
348C22—441no—
349C22—441no—
350C22—441no—
351C22—441no—
352C22—441no—
353C22C2×D4×D1111yescharacteristic
354C4—21no—
355C4—21no—
356C4—41no—
357C4—41no—
358C4—41no—
359C4—112no—
360C4—221no—
361C4—221no—
362C4—221no—
363C4—441no—
364C4C2×#433911yescharacteristic
365C4#6704211yescharacteristic
366C2—81no—
367C2—881no—
368C2—881no—
369C2—881no—
370C2#1062308411yescharacteristic
371C2D11×AGL(1,ℤ/8)11yescharacteristic
372C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
hypercenter#440D11
hypocenterC11#3397
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #10623099C2semidirect
2. #10623084C2semidirect
3. C11×#440C2semidirect
4. #10622789C2semidirect
5. #10622788C2semidirect
6. #10622640C2semidirect
7. #10622629C2semidirect
8. #10622502C2semidirect
9. #10622485C2semidirect
10. #10622432C2semidirect
11. #10622431C2semidirect
12. #10622399C2semidirect
13. #10622375C2semidirect
14. #10622325C2semidirect
15. #10622314C2semidirect
152. C8×C11#41semidirect
168. #440D11semidirect
298. C11#3397semidirect
340. C8#4339semidirect

Maximal subgroups

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

subgroupindex
#106230992
#106230842
C11×#4402
#106227892
#106227882
#106226402
#106226292
#106225022
#106224852
#106224322
#106224312
#106223992
#106223752
#106223252
#106223142
#339711