Finite Group Databasebeta

← #13081661

Subgroups — #13081661

Order 1408.

418 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623249C211yesmaximal, characteristic, complemented
2#10623090C211yesmaximal, characteristic, complemented
3C11×#459C211yesmaximal, characteristic, complemented
4#10622767C211yesmaximal, characteristic, complemented
5#10622766C211yesmaximal, characteristic, complemented
6#10622764C211yesmaximal, characteristic, complemented
7#10622763C211yesmaximal, characteristic, complemented
8#10622687C211yesmaximal, characteristic, complemented
9#10622627C211yesmaximal, characteristic, complemented
10#10622457C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622399C211yesmaximal, characteristic, complemented
13#10622398C211yesmaximal, characteristic, complemented
14#10622375C211yesmaximal, characteristic, complemented
15#10622371C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C2×C11×D8C2211yescharacteristic
18C2×C11×D8C2211yescharacteristic
19C11×#127C2211yescharacteristic
20C4×D4×C11C2211yescharacteristic
21#66993C2211yescharacteristic
22#66993C2211yescharacteristic
23#66993C2211yescharacteristic
24#66992—21no—
25#66992—21no—
26#66991—21no—
27#66989C2211yescharacteristic
28D4×Dic11C2211yescharacteristic
29D4×Dic11C2211yescharacteristic
30C2×#4324C2211yescharacteristic
31C2×#4324C2211yescharacteristic
32C2×#4323C2211yescharacteristic
33C2×#4323C2211yescharacteristic
34C2×#4323C2211yescharacteristic
35#66982—21no—
36C4×C22⋊D11—21no—
37C2×D88C2211yescharacteristic
38C2×#4314C2211yescharacteristic
39#66946C2211yescharacteristic
40#66940C2211yescharacteristic
41#66938—21no—
42#66936—21no—
43#66928C2211yescharacteristic
44C4×D44C2211yescharacteristic
45C4×Dic22C2211yescharacteristic
46C11×C4⋊C8C2211yescharacteristic
47C11×#102C2211yescharacteristic
48C11×#102C2211yescharacteristic
49#66896C2211yescharacteristic
50#66885C2211yescharacteristic
51#66880C2211yescharacteristic
52#66879C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66873C2211yescharacteristic
57#66872C2211yescharacteristic
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—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73#4341—44no—
74C2×D44C2311yescharacteristic
75C2×D44C2311yescharacteristic
76C2×C4×D11—21no—
77C2×C4×D11—21no—
78C2×Dic22D411yescharacteristic
79C2×Dic22C2311yescharacteristic
80C11×D8—41no—
81C11×D8—41no—
82C2×C8×C11C2311yescharacteristic
83C2×C8×C11C2311yescharacteristic
84C11×C4⋊C4C2311yescharacteristic
85C11×C22⋊C4—21no—
86C42×C11C2311yescharacteristic
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89C22⋊Dic11—21no—
90C22⋊Dic11—21no—
91#4324—22no—
92#4324—41no—
93#4323—22no—
94#4323—22no—
95#4323—41no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100C4⋊Dic11D411yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4—21no—
103Dic11⋊C4D411yescharacteristic
104Dic11⋊C4D411yescharacteristic
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110D88—41no—
111#4314—41no—
112#3399—111nomaximal, Sylow
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—21no—
116C22×D11—21no—
117C22×D11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—21no—
124D4×C11—42no—
125D4×C11—81no—
126C2×C4×C11—21no—
127C2×C4×C11—81no—
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C22⋊D11—42no—
132C22⋊D11—42no—
133C22⋊D11—42no—
134C22⋊D11—81no—
135C22⋊D11—81no—
136C22⋊D11—81no—
137C2×Dic11—21no—
138C2×Dic11—21no—
139C2×Dic11—42no—
140C2×Dic11—42no—
141C2×Dic11C2×D411yescharacteristic
142C2×Dic11C2×D411yescharacteristic
143C2×Dic11C2×D411yescharacteristic
144C2×Dic11C2×D411yescharacteristic
145D44—21no—
146D44—21no—
147D44—21no—
148D44—21no—
149C4×D11—42no—
150C4×D11—81no—
151Dic22—22no—
152Dic22—21no—
153Dic22—21no—
154C8×C11—21no—
155C8×C11—21no—
156C11⋊C8—21no—
157C11⋊C8#4112yescomplemented
158#559—111no—
159#550—111no—
160#496—111no—
161#496—111no—
162#493—111no—
163#463—111no—
164#463—111no—
165#460—111no—
166#459—111no—
167#459—111no—
168#459D1111yescharacteristic, complemented
169#446—111no—
170#442—111no—
171#442—111no—
172C4×SD16—111no—
173C22×C11—41no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11C22×D411yescharacteristic
183C2×D11—41no—
184C2×D11—41no—
185C2×D11—41no—
186C2×D11—41no—
187C2×D11—41no—
188C2×D11—41no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—41no—
192C4×C11C2×#4111yescharacteristic
193C4×C11H(5,𝔽2)11yescharacteristic
194Dic11—21no—
195Dic11—21no—
196Dic11—21no—
197Dic11—41no—
198Dic11—41no—
199Dic11AGL(1,ℤ/8)12yes—
200C2×#41—221no—
201C2×SD16—111no—
202C2×SD16—111no—
203C2×SD16—111no—
204C2×D8—111no—
205C2×D8—111no—
206C2×D8—111no—
207C2×D8—111no—
208C2×D8C2×D1111yescharacteristic
209C2×D8C2×D1111yescharacteristic
210#127—111no—
211#127—111no—
212#127—111no—
213#127C2×D1111yescharacteristic
214#124—111no—
215#124—111no—
216#124—221no—
217#123—221no—
218#123—221no—
219#121—221no—
220#121—221no—
221#121—221no—
222C4×Q8—111no—
223C4×Q8—111no—
224C4×D4—111no—
225C4×D4—111no—
226C4×D4—111no—
227C4×D4—111no—
228C4×D4—221no—
229C4×D4C2×D1111yescharacteristic
230#106—111no—
231C4⋊C8—111no—
232C4⋊C8—111no—
233C4⋊C8C2×D1111yescharacteristic
234#103—111no—
235#102—111no—
236#102—111no—
237#102—111no—
238#102C2×D1111yescharacteristic
239#102C2×D1111yescharacteristic
240#97—111no—
241#97—111no—
242C4×C8—111no—
243C2×C11—81no—
244C2×C11—81no—
245C2×C11—81no—
246C2×C11#55011yescharacteristic
247C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
248C2×C11#57611yescharacteristic
249D11—81no—
250D11—81no—
251#41—444no—
252C2×Q8—111no—
253C2×Q8—111no—
254C2×D4—21no—
255C2×D4—21no—
256C2×D4—111no—
257C2×D4—111no—
258C2×D4—221no—
259C2×D4—221no—
260C2×D4—221no—
261C2×D4—221no—
262C2×D4—221no—
263C2×D4—221no—
264C2×D4C22×D1111yescharacteristic
265C2×D4C22×D1111yescharacteristic
266C2×D4C22×D1111yescharacteristic
267C22×C4—21no—
268C22×C4—221no—
269C22×C4—221no—
270C22×C4—221no—
271C22×C4—221no—
272SD16—222no—
273SD16—441no—
274SD16—441no—
275D8—41no—
276D8—41no—
277D8—222no—
278D8—222no—
279D8—441no—
280D8—441no—
281C2×C8—111no—
282C2×C8—111no—
283C2×C8C22×D1111yescharacteristic
284C2×C8C22×D1111yescharacteristic
285C4⋊C4—111no—
286C4⋊C4—111no—
287C4⋊C4—111no—
288C4⋊C4—111no—
289C4⋊C4—221no—
290C4⋊C4C22×D1111yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—221no—
293C22⋊C4—221no—
294C22⋊C4—221no—
295C22⋊C4—221no—
296C22⋊C4—221no—
297C22⋊C4—221no—
298C22⋊C4—221no—
299C22⋊C4—221no—
300C42—111no—
301C42—111no—
302C42—221no—
303C42C22×D1111yescharacteristic
304C11#339911yescharacteristic, complemented, Sylow
305C23—21no—
306C23—21no—
307C23—21no—
308C23—221no—
309C23—221no—
310Q8—222no—
311Q8—221no—
312Q8—221no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—21no—
317D4—21no—
318D4—21no—
319D4—42no—
320D4—81no—
321D4—221no—
322D4—221no—
323D4—221no—
324D4—221no—
325D4—442no—
326D4—442no—
327D4—442no—
328D4—881no—
329D4—881no—
330D4—881no—
331C2×C4—21no—
332C2×C4—81no—
333C2×C4—111no—
334C2×C4—111no—
335C2×C4—111no—
336C2×C4—111no—
337C2×C4—221no—
338C2×C4—221no—
339C2×C4—442no—
340C2×C4—442no—
341C2×C4—442no—
342C2×C4—881no—
343C2×C4D4×D1111yescharacteristic
344C2×C4D4×D1111yescharacteristic
345C2×C4C23×D1111yescharacteristic
346C8—21no—
347C8—21no—
348C8—112no—
349C8—221no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—441no—
360C22—441no—
361C22—441no—
362C22—441no—
363C22—441no—
364C22—441no—
365C22C2×D4×D1111yescharacteristic
366C4—21no—
367C4—21no—
368C4—41no—
369C4—112no—
370C4—221no—
371C4—221no—
372C4—221no—
373C4—441no—
374C4—441no—
375C4#6703711yescharacteristic
376C4#41×D1111yescharacteristic
377C2—81no—
378C2—81no—
379C2—81no—
380C2—881no—
381C2—881no—
382C2#1062313011yescharacteristic
383C2#1062328811yescharacteristic
384C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#459C2
socleC22×C11C22×D4
hypercenter#459D11
hypocenterC11#3399
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. #10623249C2semidirect
2. #10623090C2semidirect
3. C11×#459C2semidirect
4. #10622767C2semidirect
5. #10622766C2semidirect
6. #10622764C2semidirect
7. #10622763C2semidirect
8. #10622687C2semidirect
9. #10622627C2semidirect
10. #10622457C2semidirect
11. #10622441C2semidirect
12. #10622399C2semidirect
13. #10622398C2semidirect
14. #10622375C2semidirect
15. #10622371C2semidirect
157. C11⋊C8#41semidirect
168. #459D11semidirect
304. C11#3399semidirect

Maximal subgroups

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

subgroupindex
#106232492
#106230902
C11×#4592
#106227672
#106227662
#106227642
#106227632
#106226872
#106226272
#106224572
#106224412
#106223992
#106223982
#106223752
#106223712
#339911