Finite Group Databasebeta

← #13081079

Subgroups — #13081079

Order 1408.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623145C211yesmaximal, characteristic, complemented
2#10623038C211yesmaximal, characteristic, complemented
3C11×#481C211yesmaximal, characteristic, complemented
4#10622652C211yesmaximal, characteristic, complemented
5#10622577C211yesmaximal, characteristic, complemented
6#10622484C211yesmaximal, characteristic, complemented
7#10622476C211yesmaximal, characteristic, complemented
8D11×#106C211yesmaximal, characteristic, complemented
9#10622469C211yesmaximal, characteristic, complemented
10#10622398C211yesmaximal, characteristic, complemented
11#10622388C211yesmaximal, characteristic, complemented
12#10622387C211yesmaximal, characteristic, complemented
13#10622374C211yesmaximal, characteristic, complemented
14#10622350C211yesmaximal, characteristic, complemented
15#10622341C211yesmaximal, characteristic, complemented
16C2×#4339—21no—
17C11×#121C2211yescharacteristic
18C2×C11×C4⋊C4C2211yescharacteristic
19#66991—21no—
20#66991C2211yescharacteristic
21#66988—21no—
22D4×Dic11C2211yescharacteristic
23C2×#4323C2211yescharacteristic
24#66983C2211yescharacteristic
25#66982—21no—
26C4×C22⋊D11C2211yescharacteristic
27#66979C2211yescharacteristic
28C2×#4318C2211yescharacteristic
29C2×C8×D11C2211yescharacteristic
30#66949—21no—
31#66948C2211yescharacteristic
32#66947—21no—
33#66946C2211yescharacteristic
34C4⋊C4×D11C2211yescharacteristic
35C4⋊C4×D11C2211yescharacteristic
36#66943C2211yescharacteristic
37#66941C2211yescharacteristic
38(C22⋊D11)⋊C4—21no—
39#66932—21no—
40C11×#106C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#102C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66896C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66882C2211yescharacteristic
50#66881C2211yescharacteristic
51#66879C2211yescharacteristic
52Dic11⋊C8C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11—21no—
62C22×C4×C11C2311yescharacteristic
63C2×C22⋊D11—21no—
64C2×C22⋊D11—21no—
65C2×C22⋊D11D411yescharacteristic
66C22×Dic11—21no—
67#4339—44no—
68C2×D44—21no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×C4×D11C2311yescharacteristic
74C2×Dic22—21no—
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C4⋊C4—21no—
78C11×C4⋊C4C2311yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C22⋊C4—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11D411yescharacteristic
86#4323—22no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4D411yescharacteristic
91C4⋊Dic11—21no—
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94C4⋊Dic11C2311yescharacteristic
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4D411yescharacteristic
100C4×Dic11—21no—
101C4×Dic11C2311yescharacteristic
102#4318—22no—
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C8×D11—22no—
106#3345—111nomaximal, Sylow
107C23×C11—21no—
108C23×C11C2×D411yescharacteristic
109C22×D11—21no—
110C22×D11C2×D411yescharacteristic
111D4×C11—21no—
112D4×C11—21no—
113D4×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—42no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C22⋊D11—22no—
123C22⋊D11—42no—
124C22⋊D11—42no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—81no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131C2×Dic11C2×D411yescharacteristic
132D44—21no—
133D44—21no—
134D44—42no—
135C4×D11—21no—
136C4×D11—21no—
137C4×D11—42no—
138C4×D11—42no—
139C4×D11—81no—
140Dic22—42no—
141C8×C11—21no—
142C8×C11—21no—
143C11⋊C8—21no—
144C11⋊C8#4112yescomplemented
145#553—111no—
146#547—111no—
147#501—111no—
148#482—111no—
149#481—111no—
150#481D1111yescharacteristic, complemented
151#480—111no—
152#478—111no—
153#476—111no—
154#469—111no—
155#466—111no—
156#442—111no—
157#435—111no—
158#428—111no—
159C2×#106—111no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—21no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11C22×D411yescharacteristic
167C2×D11—21no—
168C2×D11—21no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11AGL(1,ℤ/8)12yes—
173C4×C11—21no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11C2×#4111yescharacteristic
178C4×C112−1+411yescharacteristic
179Dic11—21no—
180Dic11—21no—
181Dic11—21no—
182Dic11—41no—
183Dic11—41no—
184Dic11—41no—
185C2×#41—221no—
186C2×D8—111no—
187C2×M16—111no—
188C22×C8—111no—
189C4⋊Q8—111no—
190#126—221no—
191#125—111no—
192#123—221no—
193#123—221no—
194#123—221no—
195C22⋊Q8—221no—
196#121—111no—
197#121—111no—
198#121—111no—
199#121—221no—
200#121C2×D1111yescharacteristic
201C4×D4—111no—
202C4×D4—111no—
203C4×D4—111no—
204C4×D4—221no—
205#117—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208C2×C4⋊C4C2×D1111yescharacteristic
209#107—111no—
210#107—111no—
211#107—111no—
212#106—111no—
213#106—111no—
214#106—111no—
215#106—111no—
216#106C2×D1111yescharacteristic
217#106C2×D1111yescharacteristic
218C4⋊C8—111no—
219#102—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223#102C2×D1111yescharacteristic
224#102C2×D1111yescharacteristic
225C22⋊C8—111no—
226C22⋊C8C2×D1111yescharacteristic
227#97—111no—
228C2×C11—41no—
229C2×C11—81no—
230C2×C11#54711yescharacteristic
231C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
232C2×C11#57711yescharacteristic
233D11—22no—
234D11—81no—
235#41—444no—
236C2×Q8—221no—
237C2×D4—21no—
238C2×D4—111no—
239C2×D4—111no—
240C2×D4—221no—
241C2×D4—221no—
242C2×D4—221no—
243C2×D4C22×D1111yescharacteristic
244C22×C4—21no—
245C22×C4—111no—
246C22×C4—221no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4C22×D1111yescharacteristic
251D8—222no—
252M16—222no—
253C2×C8—111no—
254C2×C8—111no—
255C2×C8—222no—
256C2×C8C22×D1111yescharacteristic
257C2×C8C22×D1111yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4C22×D1111yescharacteristic
269C4⋊C4C22×D1111yescharacteristic
270C4⋊C4C22×D1111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—111no—
273C22⋊C4—111no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C42—111no—
281C42—221no—
282C11#334511yescharacteristic, complemented, Sylow
283C23—21no—
284C23—111no—
285C23—221no—
286C23D4×D1111yescharacteristic
287Q8—442no—
288D4—21no—
289D4—21no—
290D4—81no—
291D4—222no—
292D4—221no—
293D4—221no—
294D4—442no—
295D4—442no—
296D4—442no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—111no—
304C2×C4—111no—
305C2×C4—111no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—442no—
312C2×C4—442no—
313C2×C4—881no—
314C2×C4—881no—
315C2×C4D4×D1111yescharacteristic
316C2×C4C23×D1111yescharacteristic
317C8—21no—
318C8—21no—
319C8—112no—
320C8—221no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—112no—
328C22—221no—
329C22—221no—
330C22—441no—
331C22—441no—
332C22—441no—
333C22C2×D4×D1111yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—221no—
339C4—221no—
340C4—221no—
341C4—441no—
342C4—441no—
343C4—441no—
344C4#41×D1111yescharacteristic
345C4#6704311yescharacteristic
346C2—41no—
347C2—81no—
348C2—222no—
349C2—881no—
350C2#1062318611yescharacteristic
351C2#1062329311yescharacteristic
352C2D11×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#481C2
socleC22×C11C22×D4
hypercenter#481D11
hypocenterC11#3345
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #10623145C2semidirect
2. #10623038C2semidirect
3. C11×#481C2semidirect
4. #10622652C2semidirect
5. #10622577C2semidirect
6. #10622484C2semidirect
7. #10622476C2semidirect
8. D11×#106C2semidirect
9. #10622469C2semidirect
10. #10622398C2semidirect
11. #10622388C2semidirect
12. #10622387C2semidirect
13. #10622374C2semidirect
14. #10622350C2semidirect
15. #10622341C2semidirect
144. C11⋊C8#41semidirect
150. #481D11semidirect
282. C11#3345semidirect

Maximal subgroups

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

subgroupindex
#106231452
#106230382
C11×#4812
#106226522
#106225772
#106224842
#106224762
D11×#1062
#106224692
#106223982
#106223882
#106223872
#106223742
#106223502
#106223412
#334511