Finite Group Databasebeta

← #13081405

Subgroups — #13081405

Order 1408.

384 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623258C211yesmaximal, characteristic, complemented
2#10623212C211yesmaximal, characteristic, complemented
3C11×#489C211yesmaximal, characteristic, complemented
4#10622697C211yesmaximal, characteristic, complemented
5#10622670C211yesmaximal, characteristic, complemented
6#10622432C211yesmaximal, characteristic, complemented
7#10622408C211yesmaximal, characteristic, complemented
8#10622404C211yesmaximal, characteristic, complemented
9#10622401C211yesmaximal, characteristic, complemented
10#10622399C211yesmaximal, characteristic
11#10622398C211yesmaximal, characteristic, complemented
12#10622374C211yesmaximal, characteristic, complemented
13#10622373C211yesmaximal, characteristic, complemented
14#10622324C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×Q8×D11—21no—
17C11×C4⋊Q8C2211yescharacteristic
18C11×#124C2211yescharacteristic
19#67000C2211yescharacteristic
20#66999—21no—
21Q8×Dic11C2211yescharacteristic
22C2×#4325C2211yescharacteristic
23#66993C2211yescharacteristic
24D4×Dic11C2211yescharacteristic
25C2×#4323C2211yescharacteristic
26C2×D88C2211yescharacteristic
27#66949—21no—
28#66949—21no—
29#66946C2211yescharacteristic
30#66946C2211yescharacteristic
31#66941C2211yescharacteristic
32#66941C2211yescharacteristic
33#66939—21no—
34#66938—21no—
35#66936—21no—
36(C22⋊D11)⋊C4—21no—
37C4×D44C2211yescharacteristic
38C4×D44C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#103C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66899C2211yescharacteristic
46#66896C2211yescharacteristic
47#66885C2211yescharacteristic
48#66885C2211yescharacteristic
49#66881C2211yescharacteristic
50#66879C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53C8×Dic11C2211yescharacteristic
54#66873C2211yescharacteristic
55#66873C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65Q8×D11—44no—
66C2×D44C2311yescharacteristic
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×Dic22—21no—
73C2×Dic22—21no—
74C2×Dic22D411yescharacteristic
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C42×C11C2311yescharacteristic
83C22⋊Dic11—21no—
84#4325—22no—
85#4323—22no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11D411yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4D411yescharacteristic
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102C4×Dic11C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105D88—22no—
106#3373—111nomaximal, Sylow
107C23×C11—21no—
108C22×D11—21no—
109C22×D11—21no—
110Q8×C11—21no—
111Q8×C11—21no—
112Q8×C11—42no—
113D4×C11—21no—
114D4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11C2×D411yescharacteristic
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C22⋊D11—42no—
122C22⋊D11—81no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—81no—
126C2×Dic11C2×D411yescharacteristic
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130D44—21no—
131D44—21no—
132D44—21no—
133D44#4112yes—
134C4×D11—42no—
135C4×D11—42no—
136C4×D11—42no—
137C4×D11—81no—
138Dic22—22no—
139Dic22—42no—
140Dic22—42no—
141C8×C11—21no—
142C8×C11—21no—
143C11⋊C8—21no—
144C11⋊C8—21no—
145#559—111no—
146D4×Q8—111no—
147#489—111no—
148#489D1111yescharacteristic, complemented
149#486—111no—
150#476—111no—
151#476—111no—
152#475—111no—
153#463—111no—
154#463—111no—
155#459—111no—
156#446—111no—
157#442—111no—
158#442—111no—
159C4×SD16—111no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11C22×D411yescharacteristic
164C2×D11—22no—
165C2×D11—41no—
166C2×D11—41no—
167C2×D11—41no—
168C2×D11—41no—
169C2×D11—41no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11C2×#4111yescharacteristic
176C4×C112−1+411yescharacteristic
177Dic11—21no—
178Dic11—21no—
179Dic11—21no—
180Dic11—41no—
181Dic11—41no—
182Dic11AGL(1,ℤ/8)12yes—
183C22×Q8—221no—
184C2×SD16—111no—
185C2×D8—111no—
186C2×D8—111no—
187C4⋊Q8—111no—
188C4⋊Q8—111no—
189C4⋊Q8C2×D1111yescharacteristic
190#127—111no—
191#124—111no—
192#124—221no—
193#124C2×D1111yescharacteristic
194#123—221no—
195#123—221no—
196C22⋊Q8—221no—
197C22⋊Q8—221no—
198C22⋊Q8—221no—
199C4×Q8—111no—
200C4×Q8—111no—
201C4×D4—111no—
202C4×D4—111no—
203C4×D4—111no—
204C4×D4—111no—
205C4×D4—111no—
206C4×D4—221no—
207#106—111no—
208#106—111no—
209#106—111no—
210C4⋊C8—111no—
211C4⋊C8—111no—
212C4⋊C8—111no—
213#103—111no—
214#103C2×D1111yescharacteristic
215#103C2×D1111yescharacteristic
216#102—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220#102—111no—
221#102C2×D1111yescharacteristic
222#102C2×D1111yescharacteristic
223#97—111no—
224#97C2×D1111yescharacteristic
225C4×C8—111no—
226C2×C11—81no—
227C2×C11#54811yescharacteristic
228C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
229C2×C11#57711yescharacteristic
230D11—42no—
231D11—81no—
232C2×Q8—21no—
233C2×Q8—111no—
234C2×Q8—221no—
235C2×Q8—221no—
236C2×Q8—444no—
237C2×Q8C22×D1111yescharacteristic
238C2×D4—111no—
239C2×D4—111no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4C22×D1111yescharacteristic
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248SD16—222no—
249D8—222no—
250D8—222no—
251C2×C8—111no—
252C2×C8—111no—
253C2×C8C22×D1111yescharacteristic
254C2×C8C22×D1111yescharacteristic
255C4⋊C4—21no—
256C4⋊C4—111no—
257C4⋊C4—111no—
258C4⋊C4—111no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4C22×D1111yescharacteristic
265C4⋊C4C22×D1111yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C42—111no—
276C42—111no—
277C42—221no—
278C42C22×D1111yescharacteristic
279C11#337311yescharacteristic, complemented, Sylow
280C23—21no—
281C23—221no—
282C23—221no—
283Q8—21no—
284Q8—21no—
285Q8—42no—
286Q8—222no—
287Q8—442no—
288Q8—442no—
289D4—21no—
290D4—21no—
291D4—112no—
292D4—221no—
293D4—221no—
294D4—221no—
295D4—442no—
296D4—881no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—111no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—111no—
304C2×C4—221no—
305C2×C4—221no—
306C2×C4—442no—
307C2×C4—442no—
308C2×C4—442no—
309C2×C4—881no—
310C2×C4—881no—
311C2×C4D4×D1111yescharacteristic
312C2×C4D4×D1111yescharacteristic
313C2×C4C23×D1111yescharacteristic
314C8—21no—
315C8—21no—
316C8—221no—
317C8—221no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—222no—
322C22—441no—
323C22—441no—
324C22—441no—
325C22—441no—
326C22—441no—
327C22C2×D4×D1111yescharacteristic
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—112no—
334C4—221no—
335C4—221no—
336C4—221no—
337C4—441no—
338C4—441no—
339C4#41×D1111yescharacteristic
340C4#6704311yescharacteristic
341C2—81no—
342C2—442no—
343C2—881no—
344C2#1062320811yescharacteristic
345C2D11×AGL(1,ℤ/8)11yescharacteristic
346C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#489C2
socleC22×C11C22×D4
prime radical#10622399C2
hypercenter#489D11
hypocenterC11#3373
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #10623258C2semidirect
2. #10623212C2semidirect
3. C11×#489C2semidirect
4. #10622697C2semidirect
5. #10622670C2semidirect
6. #10622432C2semidirect
7. #10622408C2semidirect
8. #10622404C2semidirect
9. #10622401C2semidirect
11. #10622398C2semidirect
12. #10622374C2semidirect
13. #10622373C2semidirect
14. #10622324C2semidirect
15. #10622314C2semidirect
148. #489D11semidirect
279. C11#3373semidirect

Maximal subgroups

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

subgroupindex
#106232582
#106232122
C11×#4892
#106226972
#106226702
#106224322
#106224082
#106224042
#106224012
#106223992
#106223982
#106223742
#106223732
#106223242
#106223142
#337311