Finite Group Databasebeta

← #13079941

Subgroups — #13079941

Order 1408.

398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623222C211yesmaximal, characteristic, complemented
2#10623079C211yesmaximal, characteristic, complemented
3C11×#478C211yesmaximal, characteristic, complemented
4#10622679C211yesmaximal, characteristic, complemented
5#10622629C211yesmaximal, characteristic, complemented
6#10622496C211yesmaximal, characteristic, complemented
7#10622488C211yesmaximal, characteristic, complemented
8#10622483C211yesmaximal, characteristic, complemented
9#10622477C211yesmaximal, characteristic, complemented
10#10622457C211yesmaximal, characteristic, complemented
11D11×C4⋊C8C211yesmaximal, characteristic, complemented
12#10622399C211yesmaximal, characteristic, complemented
13#10622391C211yesmaximal, characteristic, complemented
14#10622388C211yesmaximal, characteristic, complemented
15#10622375C211yesmaximal, characteristic, complemented
16C2×#4339—21no—
17C11×#125C2211yescharacteristic
18C4×D4×C11C2211yescharacteristic
19#66993C2211yescharacteristic
20#66991C2211yescharacteristic
21C2×#4324C2211yescharacteristic
22C2×#4323C2211yescharacteristic
23C4×C22⋊D11—21no—
24C2×D88C2211yescharacteristic
25C2×#4314C2211yescharacteristic
26C2×C8×D11C2211yescharacteristic
27C2×C8×D11C2211yescharacteristic
28#66951—21no—
29#66950C2211yescharacteristic
30#66948C2211yescharacteristic
31#66948C2211yescharacteristic
32#66947—21no—
33#66946—21no—
34#66946C2211yescharacteristic
35#66945—21no—
36#66941C2211yescharacteristic
37#66940C2211yescharacteristic
38#66938—21no—
39#66937—21no—
40#66928C2211yescharacteristic
41C4×D44C2211yescharacteristic
42C42×D11C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×#106C2211yescharacteristic
45C11×C4⋊C8C2211yescharacteristic
46C11×#102C2211yescharacteristic
47C11×#102C2211yescharacteristic
48#66885C2211yescharacteristic
49#66880C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52#66874C2211yescharacteristic
53#66873C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C2×C22⋊D11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64#4339—44no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44C2311yescharacteristic
68C2×D44C2311yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11D411yescharacteristic
72C2×C4×D11D411yescharacteristic
73C2×C4×D11C2311yescharacteristic
74C2×Dic22—21no—
75C2×Dic22C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4—21no—
79C11×C4⋊C4—21no—
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C42×C11C2311yescharacteristic
85C22⋊Dic11—21no—
86#4324—41no—
87#4323—41no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
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—
95C4⋊Dic11—21no—
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11D411yescharacteristic
101C4×Dic11D411yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105D88—41no—
106#4314—41no—
107C8×D11—41no—
108C8×D11—41no—
109#3247—111nomaximal, Sylow
110C23×C11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C22×D11C2×D411yescharacteristic
114D4×C11—21no—
115D4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—42no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2×D411yescharacteristic
122C2×C4×C11C2411yescharacteristic
123C22⋊D11—42no—
124C22⋊D11—42no—
125C22⋊D11—42no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131D44—21no—
132D44—21no—
133D44—21no—
134D44—21no—
135D44—42no—
136D44—42no—
137C4×D11—22no—
138C4×D11—21no—
139C4×D11—21no—
140C4×D11—22no—
141C4×D11—42no—
142C4×D11—42no—
143Dic22—21no—
144Dic22—21no—
145Dic22—42no—
146C8×C11—21no—
147C8×C11—21no—
148C11⋊C8—21no—
149C11⋊C8—21no—
150#532—111no—
151#529—111no—
152#478—111no—
153#478D1111yescharacteristic, complemented
154#477—111no—
155#476—111no—
156#466—111no—
157#466—111no—
158#465—111no—
159#465—111no—
160#463—111no—
161#463—111no—
162#460—111no—
163#459—111no—
164C2×C4⋊C8—111no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11C22×D411yescharacteristic
169C2×D11—21no—
170C2×D11—21no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11AGL(1,ℤ/8)12yes—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11H(5,𝔽2)11yescharacteristic
184C4×C112−1+411yescharacteristic
185Dic11—21no—
186Dic11—21no—
187Dic11—41no—
188Dic11—41no—
189Dic11#13512yes—
190C2×#41—221no—
191C2×SD16—111no—
192C2×SD16—111no—
193C2×D8—111no—
194C2×D8—111no—
195C22×C8—111no—
196C22×C8—111no—
197C4⋊Q8—111no—
198#127—111no—
199#126—221no—
200#125C2×D1111yescharacteristic
201#124—111no—
202#124—221no—
203#123—221no—
204C22⋊Q8—111no—
205#121—111no—
206#121—111no—
207#121—111no—
208#121—221no—
209C4×Q8—111no—
210C4×D4—111no—
211C4×D4—111no—
212C4×D4—221no—
213C4×D4—221no—
214C4×D4C2×D1111yescharacteristic
215#117—221no—
216C2×C42—111no—
217#107—111no—
218#107C2×D1111yescharacteristic
219#106—111no—
220#106C2×D1111yescharacteristic
221C4⋊C8—111no—
222C4⋊C8—111no—
223C4⋊C8—111no—
224C4⋊C8C2×D1111yescharacteristic
225#103—111no—
226#103—111no—
227#102—111no—
228#102—111no—
229#102—111no—
230#102—111no—
231#102C2×D1111yescharacteristic
232#102C2×D1111yescharacteristic
233C2×C11—81no—
234C2×C11#53711yescharacteristic
235C2×C11C2×#13511yescharacteristic
236C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
237D11—22no—
238D11—81no—
239D11—81no—
240#41—444no—
241C2×Q8—111no—
242C2×Q8—221no—
243C2×D4—111no—
244C2×D4—111no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4—221no—
248C2×D4—221no—
249C2×D4—221no—
250C2×D4C22×D1111yescharacteristic
251C22×C4—21no—
252C22×C4—111no—
253C22×C4—111no—
254C22×C4—111no—
255C22×C4—221no—
256C22×C4—221no—
257SD16—441no—
258SD16—441no—
259D8—441no—
260D8—441no—
261C2×C8—111no—
262C2×C8—111no—
263C2×C8—441no—
264C2×C8—441no—
265C2×C8C22×D1111yescharacteristic
266C2×C8C22×D1111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—111no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4C22×D1111yescharacteristic
274C4⋊C4C22×D1111yescharacteristic
275C4⋊C4C22×D1111yescharacteristic
276C22⋊C4—21no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C42—111no—
286C42—111no—
287C42—111no—
288C42—221no—
289C42C22×D1111yescharacteristic
290C11#324711yescharacteristic, complemented, Sylow
291C23—21no—
292C23—111no—
293C23—221no—
294C23—221no—
295Q8—221no—
296Q8—221no—
297Q8—442no—
298D4—21no—
299D4—21no—
300D4—221no—
301D4—221no—
302D4—221no—
303D4—221no—
304D4—442no—
305D4—442no—
306D4—442no—
307D4—442no—
308D4—442no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—111no—
314C2×C4—111no—
315C2×C4—111no—
316C2×C4—222no—
317C2×C4—222no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—221no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4D4×D1111yescharacteristic
325C2×C4D4×D1111yescharacteristic
326C2×C4C23×D1111yescharacteristic
327C8—21no—
328C8—21no—
329C8—221no—
330C8—221no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—112no—
335C22—221no—
336C22—221no—
337C22—441no—
338C22—441no—
339C22—441no—
340C22—441no—
341C22—441no—
342C22—441no—
343C22C2×D4×D1111yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—112no—
350C4—221no—
351C4—221no—
352C4—441no—
353C4—441no—
354C4#6704011yescharacteristic
355C4#6704211yescharacteristic
356C2—81no—
357C2—222no—
358C2—881no—
359C2—881no—
360C2#1062316011yescharacteristic
361C2D11×#13511yescharacteristic
362C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#478C2
socleC22×C11C22×D4
hypercenter#478D11
hypocenterC11#3247
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10623222C2semidirect
2. #10623079C2semidirect
3. C11×#478C2semidirect
4. #10622679C2semidirect
5. #10622629C2semidirect
6. #10622496C2semidirect
7. #10622488C2semidirect
8. #10622483C2semidirect
9. #10622477C2semidirect
10. #10622457C2semidirect
11. D11×C4⋊C8C2semidirect
12. #10622399C2semidirect
13. #10622391C2semidirect
14. #10622388C2semidirect
15. #10622375C2semidirect
153. #478D11semidirect
290. C11#3247semidirect

Maximal subgroups

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

subgroupindex
#106232222
#106230792
C11×#4782
#106226792
#106226292
#106224962
#106224882
#106224832
#106224772
#106224572
D11×C4⋊C82
#106223992
#106223912
#106223882
#106223752
#324711