Finite Group Databasebeta

← #13081699

Subgroups — #13081699

Order 1408.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623244C211yesmaximal, characteristic, complemented
2#10623090C211yesmaximal, characteristic, complemented
3C11×#459C211yesmaximal, characteristic, complemented
4#10622768C211yesmaximal, characteristic, complemented
5#10622767C211yesmaximal, characteristic, complemented
6#10622766C211yesmaximal, characteristic, complemented
7#10622763C211yesmaximal, characteristic, complemented
8#10622687C211yesmaximal, characteristic, complemented
9#10622631C211yesmaximal, characteristic, complemented
10#10622458C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622400C211yesmaximal, characteristic, complemented
13#10622380C211yesmaximal, characteristic, complemented
14#10622370C211yesmaximal, characteristic, complemented
15#10622369C211yesmaximal, characteristic, complemented
16C2×C11×D8C2211yescharacteristic
17C2×C11×D8C2211yescharacteristic
18C11×#127C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#66993C2211yescharacteristic
21#66989—21no—
22#66989C2211yescharacteristic
23#66989C2211yescharacteristic
24#66989C2211yescharacteristic
25#66988—21no—
26#66988—21no—
27D4×Dic11—21no—
28D4×Dic11C2211yescharacteristic
29D4×Dic11C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31C2×#4324C2211yescharacteristic
32C2×#4324C2211yescharacteristic
33C2×#4323C2211yescharacteristic
34C2×#4323C2211yescharacteristic
35#66982—21no—
36C4×C22⋊D11—21no—
37C2×Dic44C2211yescharacteristic
38C2×#4314C2211yescharacteristic
39#66946C2211yescharacteristic
40#66940C2211yescharacteristic
41#66938—21no—
42#66936—21no—
43#66928C2211yescharacteristic
44C4×Dic22C2211yescharacteristic
45C4×Dic22C2211yescharacteristic
46C11×C4⋊C8C2211yescharacteristic
47C11×#102C2211yescharacteristic
48C11×#102C2211yescharacteristic
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51#66880C2211yescharacteristic
52#66879C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66874C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68C22×Dic11—21no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×Dic22D411yescharacteristic
72C2×Dic22C2311yescharacteristic
73C2×Dic22C2311yescharacteristic
74C11×D8—41no—
75C11×D8—41no—
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C42×C11C2311yescharacteristic
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89#4324—22no—
90#4324—22no—
91#4324—41no—
92#4323—22no—
93#4323—41no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97C4⋊Dic11D411yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4D411yescharacteristic
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11C2311yescharacteristic
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109Dic44—41no—
110#4314—41no—
111#3403—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115C22×D11—21no—
116D4×C11—21no—
117D4×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—42no—
123D4×C11—81no—
124C2×C4×C11—21no—
125C2×C4×C11—81no—
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—81no—
135C2×Dic11—81no—
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140D44—21no—
141D44—21no—
142C4×D11—81no—
143Dic22—21no—
144Dic22—21no—
145Dic22—21no—
146Dic22—21no—
147Dic22—41no—
148C8×C11—21no—
149C8×C11—21no—
150C11⋊C8—21no—
151C11⋊C8#4112yes—
152#559—111no—
153#559—111no—
154#496—111no—
155#496—111no—
156#495—111no—
157#464—111no—
158#464—111no—
159#463—111no—
160#463—111no—
161#459—111no—
162#459D1111yescharacteristic, complemented
163#446—111no—
164#440—111no—
165#440—111no—
166C4×D8—111no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11C22×D411yescharacteristic
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—41no—
183C4×C11C2×#4111yescharacteristic
184C4×C11H(5,𝔽2)11yescharacteristic
185Dic11—21no—
186Dic11—21no—
187Dic11—21no—
188Dic11—21no—
189Dic11—41no—
190Dic11—41no—
191Dic11—41no—
192C2×Q16—111no—
193C2×SD16—111no—
194C2×SD16—111no—
195C2×SD16—111no—
196C2×SD16—111no—
197C2×D8—111no—
198C2×D8—111no—
199C2×D8C2×D1111yescharacteristic
200C2×D8C2×D1111yescharacteristic
201#127—111no—
202#127C2×D1111yescharacteristic
203#124—111no—
204#124—111no—
205#124—111no—
206#124—111no—
207#124—221no—
208#124—221no—
209#123—221no—
210#123—221no—
211#123—221no—
212#123—221no—
213C4×Q8—111no—
214C4×Q8—111no—
215C4×Q8—111no—
216C4×D4—111no—
217C4×D4—111no—
218C4×D4—111no—
219C4×D4—221no—
220C4×D4—221no—
221C4×D4C2×D1111yescharacteristic
222#107—111no—
223C4⋊C8—111no—
224C4⋊C8—111no—
225C4⋊C8C2×D1111yescharacteristic
226#103—111no—
227#103—111no—
228#102—111no—
229#102—111no—
230#102C2×D1111yescharacteristic
231#102C2×D1111yescharacteristic
232#97—111no—
233#97—111no—
234C4×C8—111no—
235C2×C11—81no—
236C2×C11—81no—
237C2×C11—81no—
238C2×C11#55011yescharacteristic
239C2×C11#57511yescharacteristic
240C2×C11#57611yescharacteristic
241D11—81no—
242C2×Q8—111no—
243C2×Q8—111no—
244C2×Q8—111no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—111no—
248C2×D4—221no—
249C2×D4—221no—
250C2×D4C22×D1111yescharacteristic
251C2×D4C22×D1111yescharacteristic
252C2×D4C22×D1111yescharacteristic
253C22×C4—21no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257Q16—441no—
258SD16—222no—
259SD16—222no—
260SD16—441no—
261SD16—441no—
262D8—41no—
263D8—41no—
264D8—222no—
265D8—441no—
266C2×C8—111no—
267C2×C8—111no—
268C2×C8C22×D1111yescharacteristic
269C2×C8C22×D1111yescharacteristic
270C4⋊C4—111no—
271C4⋊C4—111no—
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4C22×D1111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C42—111no—
290C42—111no—
291C42—221no—
292C42—221no—
293C42C22×D1111yescharacteristic
294C11#340311yescharacteristic, complemented, Sylow
295C23—21no—
296C23—21no—
297C23—21no—
298C23—221no—
299Q8—221no—
300Q8—221no—
301Q8—221no—
302Q8—221no—
303Q8—441no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—81no—
312D4—221no—
313D4—221no—
314D4—442no—
315D4—881no—
316C2×C4—21no—
317C2×C4—81no—
318C2×C4—111no—
319C2×C4—111no—
320C2×C4—111no—
321C2×C4—111no—
322C2×C4—221no—
323C2×C4—221no—
324C2×C4—221no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4—881no—
328C2×C4D4×D1111yescharacteristic
329C2×C4D4×D1111yescharacteristic
330C2×C4C23×D1111yescharacteristic
331C8—21no—
332C8—21no—
333C8—112no—
334C8—221no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22C2×D4×D1111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—221no—
352C4—221no—
353C4—221no—
354C4—221no—
355C4—441no—
356C4—441no—
357C4—441no—
358C4#6703711yescharacteristic
359C4#41×D1111yescharacteristic
360C2—81no—
361C2—81no—
362C2—81no—
363C2—881no—
364C2#1062313011yescharacteristic
365C2#1062328811yescharacteristic
366C2#1062330411yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#459C2
socleC22×C11C22×D4
hypercenter#459D11
hypocenterC11#3403
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #10623244C2semidirect
2. #10623090C2semidirect
3. C11×#459C2semidirect
4. #10622768C2semidirect
5. #10622767C2semidirect
6. #10622766C2semidirect
7. #10622763C2semidirect
8. #10622687C2semidirect
9. #10622631C2semidirect
10. #10622458C2semidirect
11. #10622441C2semidirect
12. #10622400C2semidirect
13. #10622380C2semidirect
14. #10622370C2semidirect
15. #10622369C2semidirect
162. #459D11semidirect
294. C11#3403semidirect

Maximal subgroups

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

subgroupindex
#106232442
#106230902
C11×#4592
#106227682
#106227672
#106227662
#106227632
#106226872
#106226312
#106224582
#106224412
#106224002
#106223802
#106223702
#106223692
#340311