Finite Group Databasebeta

← #13079310

Subgroups — #13079310

Order 1408.

410 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#10623111C211yesmaximal, characteristic, complemented
2#10623079C211yesmaximal, characteristic, complemented
3C11×#440C211yesmaximal, characteristic, complemented
4#10622789C211yesmaximal, characteristic, complemented
5#10622784C211yesmaximal, characteristic, complemented
6#10622639C211yesmaximal, characteristic, complemented
7#10622627C211yesmaximal, characteristic, complemented
8#10622496C211yesmaximal, characteristic, complemented
9#10622489C211yesmaximal, characteristic, complemented
10#10622420C211yesmaximal, characteristic, complemented
11#10622408C211yesmaximal, characteristic, complemented
12#10622388C211yesmaximal, characteristic, complemented
13#10622377C211yesmaximal, characteristic, complemented
14#10622324C211yesmaximal, characteristic, complemented
15D11×#97C211yesmaximal, characteristic, complemented
16C2×#4339—21no—
17C2×C11×SD16C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20#67000C2211yescharacteristic
21#66999C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23#66993C2211yescharacteristic
24#66991C2211yescharacteristic
25C2×#4323C2211yescharacteristic
26C4×C22⋊D11—21no—
27C2×D88C2211yescharacteristic
28C2×C8×D11C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66951—21no—
31#66948C2211yescharacteristic
32#66948C2211yescharacteristic
33#66947—21no—
34#66943C2211yescharacteristic
35#66941C2211yescharacteristic
36#66938—21no—
37#66937—21no—
38C4×D44—21no—
39C4×D44C2211yescharacteristic
40C4×D44C2211yescharacteristic
41#66925—21no—
42C42×D11C2211yescharacteristic
43C11×#107C2211yescharacteristic
44C11×#103C2211yescharacteristic
45C11×#102C2211yescharacteristic
46C11×#97C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66885C2211yescharacteristic
50#66885C2211yescharacteristic
51#66881C2211yescharacteristic
52#66879C2211yescharacteristic
53#66879C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65#4339—44no—
66C2×D44—21no—
67C2×D44—21no—
68C2×D44C2311yescharacteristic
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11D411yescharacteristic
73C2×C4×D11D411yescharacteristic
74C2×C4×D11C2311yescharacteristic
75C2×Dic22—21no—
76C11×SD16—22no—
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4—21no—
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C22⋊C4—21no—
83C42×C11—21no—
84C42×C11C2311yescharacteristic
85C22⋊Dic11—21no—
86#4325—22no—
87#4323—22no—
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
97C4⋊Dic11C2311yescharacteristic
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11D411yescharacteristic
102C4×Dic11D411yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106D88—22no—
107C8×D11—22no—
108C8×D11—22no—
109#3180—111nomaximal, Sylow
110C23×C11—21no—
111C22×D11—21no—
112C22×D11—21no—
113C22×D11C2×D411yescharacteristic
114Q8×C11—21no—
115Q8×C11—21no—
116D4×C11—21no—
117D4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—42no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2411yescharacteristic
125C22⋊D11—42no—
126C22⋊D11—42no—
127C22⋊D11—42no—
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132C2×Dic11C2×D411yescharacteristic
133D44—21no—
134D44—21no—
135D44—21no—
136D44—21no—
137D44—42no—
138D44—42no—
139C4×D11—22no—
140C4×D11—21no—
141C4×D11—21no—
142C4×D11—41no—
143C4×D11—42no—
144C4×D11—42no—
145Dic22—42no—
146C8×C11—21no—
147C8×C11#4112yescomplemented
148C11⋊C8—21no—
149C11⋊C8#4112yescomplemented
150#532—111no—
151#529—111no—
152#501—111no—
153#496—111no—
154#490—111no—
155#489—111no—
156#466—111no—
157#466—111no—
158#465—111no—
159#465—111no—
160#442—111no—
161#442—111no—
162#440—111no—
163#440D1111yescharacteristic, complemented
164C2×#97—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×C11C2×#4111yescharacteristic
184C4×C11C2×#4111yescharacteristic
185Dic11—21no—
186Dic11—21no—
187Dic11—21no—
188Dic11—41no—
189Dic11—41no—
190C2×#41—221no—
191C2×SD16—111no—
192C2×SD16C2×D1111yescharacteristic
193C2×D8—111no—
194C2×D8—111no—
195C22×C8—111no—
196C22×C8—111no—
197C4⋊Q8—111no—
198#127—111no—
199#126—221no—
200#125—111no—
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×Q8C2×D1111yescharacteristic
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#106—111no—
221#103—111no—
222#103C2×D1111yescharacteristic
223#102—111no—
224#102—111no—
225#102—111no—
226#102—111no—
227#102—111no—
228#102C2×D1111yescharacteristic
229#97—111no—
230#97—111no—
231#97—111no—
232#97C2×D1111yescharacteristic
233C2×C11—81no—
234C2×C11#53211yescharacteristic
235C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
236C2×C11#57511yescharacteristic
237D11—22no—
238D11—81no—
239D11—81no—
240#41—444no—
241C2×Q8—221no—
242C2×Q8C22×D1111yescharacteristic
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—22no—
258SD16—222no—
259D8—222no—
260D8—222no—
261C2×C8—111no—
262C2×C8—111no—
263C2×C8—222no—
264C2×C8—222no—
265C2×C8C22×D1111yescharacteristic
266C2×C8C22×D1111yescharacteristic
267C4⋊C4—21no—
268C4⋊C4—111no—
269C4⋊C4—111no—
270C4⋊C4—221no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—221no—
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—21no—
286C42—111no—
287C42—111no—
288C42—111no—
289C42C22×D1111yescharacteristic
290C11#318011yescharacteristic, complemented, Sylow
291C23—21no—
292C23—111no—
293C23—221no—
294C23—221no—
295Q8—21no—
296Q8—21no—
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—221no—
318C2×C4—221no—
319C2×C4—221no—
320C2×C4—221no—
321C2×C4—441no—
322C2×C4—442no—
323C2×C4—442no—
324C2×C4D4×D1111yescharacteristic
325C2×C4D4×D1111yescharacteristic
326C2×C4C23×D1111yescharacteristic
327C8—21no—
328C8—112no—
329C8—221no—
330C8#433912yescomplemented
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—221no—
350C4—221no—
351C4—221no—
352C4—441no—
353C4—441no—
354C4C2×#433911yescharacteristic
355C4#41×D1111yescharacteristic
356C2—81no—
357C2—222no—
358C2—881no—
359C2—881no—
360C2#1062307911yescharacteristic
361C2D11×AGL(1,ℤ/8)11yescharacteristic
362C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
hypercenter#440D11
hypocenterC11#3180
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. #10623111C2semidirect
2. #10623079C2semidirect
3. C11×#440C2semidirect
4. #10622789C2semidirect
5. #10622784C2semidirect
6. #10622639C2semidirect
7. #10622627C2semidirect
8. #10622496C2semidirect
9. #10622489C2semidirect
10. #10622420C2semidirect
11. #10622408C2semidirect
12. #10622388C2semidirect
13. #10622377C2semidirect
14. #10622324C2semidirect
15. D11×#97C2semidirect
147. C8×C11#41semidirect
149. C11⋊C8#41semidirect
163. #440D11semidirect
290. C11#3180semidirect
330. C8#4339semidirect

Maximal subgroups

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

subgroupindex
#106231112
#106230792
C11×#4402
#106227892
#106227842
#106226392
#106226272
#106224962
#106224892
#106224202
#106224082
#106223882
#106223772
#106223242
D11×#972
#318011