Finite Group Databasebeta

← #13078893

Subgroups — #13078893

Order 1408.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#520C211yesmaximal, characteristic, complemented
2#10623065C211yesmaximal, characteristic, complemented
3#10622852C211yesmaximal, characteristic, complemented
4#10622851C211yesmaximal, characteristic
5#10622643C211yesmaximal, characteristic, complemented
6#10622641C211yesmaximal, characteristic, complemented
7C4×#4325C211yesmaximal, characteristic, complemented
8#10622633C211yesmaximal, characteristic, complemented
9C4×#4324C211yesmaximal, characteristic, complemented
10#10622629C211yesmaximal, characteristic, complemented
11#10622627C211yesmaximal, characteristic, complemented
12#10622621C211yesmaximal, characteristic, complemented
13#10622613C211yesmaximal, characteristic, complemented
14#10622584C211yesmaximal, characteristic, complemented
15#10622581C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C4×Q8×C11C2211yescharacteristic
18C4×Q8×C11C2211yescharacteristic
19C4×D4×C11—21no—
20C4×D4×C11—21no—
21C4×D4×C11C2211yescharacteristic
22C4×D4×C11C2211yescharacteristic
23C11×#117—21no—
24C11×#117C2211yescharacteristic
25C2×C11×C4⋊C4—21no—
26C2×C11×C4⋊C4C2211yescharacteristic
27C2×#4326C2211yescharacteristic
28C2×#4325C2211yescharacteristic
29C2×#4324C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66983C2211yescharacteristic
32#66977C2211yescharacteristic
33#66951—21no—
34#66949—21no—
35#66938—21no—
36#66936—21no—
37#66928C2211yescharacteristic
38C4×D44C2211yescharacteristic
39#66922C2211yescharacteristic
40C4×Dic22C2211yescharacteristic
41#66899C2211yescharacteristic
42#66899C2211yescharacteristic
43#66896C2211yescharacteristic
44#66896C2211yescharacteristic
45C22⋊(C11⋊C8)C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic
47#66874C2211yescharacteristic
48#66874C2211yescharacteristic
49#66873C2211yescharacteristic
50#66873C2211yescharacteristic
51#66872C2211yescharacteristic
52#66872C2211yescharacteristic
53#66872C2211yescharacteristic
54#66872C2211yescharacteristic
55C4⋊(C11⋊C8)C2211yescharacteristic
56C4⋊(C11⋊C8)C2211yescharacteristic
57#66867C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C11×#41—22no—
60C11×#41—22no—
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11—21no—
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2311yescharacteristic
69C2×C22⋊D11—21no—
70C2×D44C2311yescharacteristic
71C2×C4×D11—21no—
72C2×Dic22—21no—
73C2×Dic22C2311yescharacteristic
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4D411yescharacteristic
78C11×C4⋊C4D411yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C22⋊C4—21no—
82C11×C22⋊C4—21no—
83C11×C22⋊C4D411yescharacteristic
84C11×C22⋊C4D411yescharacteristic
85C42×C11—21no—
86C42×C11—21no—
87C42×C11C2311yescharacteristic
88C42×C11C2311yescharacteristic
89C22⋊Dic11—21no—
90#4326—22no—
91#4325—22no—
92#4324—22no—
93#4323—22no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11C2311yescharacteristic
100C4⋊Dic11C2311yescharacteristic
101Dic11⋊C4—21no—
102Dic11⋊C4—21no—
103C4×Dic11—21no—
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106C2×C11⋊C8C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108#3125—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111C22×D11—21no—
112Q8×C11—21no—
113Q8×C11#4112yes—
114D4×C11—24no—
115D4×C11—21no—
116D4×C11#4112yes—
117C2×C4×C11—24no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11—81no—
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2411yescharacteristic
132C22⋊D11—81no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—21no—
136D44—21no—
137D44—21no—
138C4×D11—81no—
139Dic22—21no—
140Dic22—21no—
141Dic22—81no—
142C11⋊C8—21no—
143C11⋊C8—21no—
144C11⋊C8—21no—
145C11⋊C8—21no—
146#542—111no—
147#520D1111yescharacteristic, complemented
148#483—111no—
149#481—111no—
150#476—111no—
151#475—111no—
152#464—111no—
153#463—111no—
154#452—111no—
155#449—111no—
156#442—111no—
157#441—111no—
158C4×SD16—111no—
159C4×SD16—111no—
160#433—111no—
161C22×C11—21no—
162C22×C11—22no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11C22×D411yescharacteristic
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C4×C11—21no—
172C4×C11—22no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—41no—
178C4×C11—41no—
179C4×C11C2×#4111yescharacteristic
180C4×C11C2×#4111yescharacteristic
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184C2×#41C2×D1111yescharacteristic
185C2×Q16—111no—
186C2×SD16—111no—
187C2×SD16—111no—
188C2×D8—111no—
189C4⋊Q8—111no—
190#126—221no—
191#124—111no—
192#124—221no—
193#123—221no—
194C22⋊Q8—111no—
195C22⋊Q8—221no—
196#121—111no—
197C4×Q8—111no—
198C4×Q8C2×D1111yescharacteristic
199C4×Q8C2×D1111yescharacteristic
200C4×D4—21no—
201C4×D4—21no—
202C4×D4—111no—
203C4×D4C2×D1111yescharacteristic
204C4×D4C2×D1111yescharacteristic
205#117—21no—
206#117C2×D1111yescharacteristic
207C2×C4⋊C4—21no—
208C2×C4⋊C4C2×D1111yescharacteristic
209#106—111no—
210#106—111no—
211#106—111no—
212#106—111no—
213C4⋊C8—111no—
214C4⋊C8—111no—
215#103—111no—
216#103—111no—
217#103—111no—
218#103—111no—
219#102—111no—
220#102—111no—
221#102—111no—
222#102—111no—
223C22⋊C8—111no—
224C22⋊C8—111no—
225#97—111no—
226C4×C8—111no—
227C2×C11—41no—
228C2×C11—42no—
229C2×C11#52511yescharacteristic
230C2×C11#57711yescharacteristic
231C2×C11#57711yescharacteristic
232D11—81no—
233#41—22no—
234#41—22no—
235C2×Q8—111no—
236C2×Q8—221no—
237C2×Q8C22×D1111yescharacteristic
238C2×D4—21no—
239C2×D4—111no—
240C2×D4—221no—
241C2×D4C22×D1111yescharacteristic
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—221no—
247C22×C4C22×D1111yescharacteristic
248Q16—222no—
249SD16—222no—
250SD16—222no—
251D8—222no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8—111no—
255C2×C8—111no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—221no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4C22⋊D1111yescharacteristic
265C4⋊C4C22⋊D1111yescharacteristic
266C4⋊C4C22×D1111yescharacteristic
267C4⋊C4C22×D1111yescharacteristic
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—221no—
271C22⋊C4—221no—
272C22⋊C4—221no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4C22⋊D1111yescharacteristic
276C22⋊C4C22⋊D1111yescharacteristic
277C42—21no—
278C42—21no—
279C42—221no—
280C42C22×D1111yescharacteristic
281C42C22×D1111yescharacteristic
282C11#312511yescharacteristic, complemented, Sylow
283C23—21no—
284C23—221no—
285C23C2×C22⋊D1111yescharacteristic
286Q8—21no—
287Q8—221no—
288Q8—221no—
289Q8—881no—
290Q8#433912yes—
291D4—24no—
292D4—21no—
293D4—221no—
294D4—221no—
295D4—881no—
296D4#433912yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—881no—
310C2×C4C2×C22⋊D1111yescharacteristic
311C2×C4C2×C22⋊D1111yescharacteristic
312C2×C4C2×C22⋊D1111yescharacteristic
313C2×C4C2×C22⋊D1111yescharacteristic
314C2×C4C2×C22⋊D1111yescharacteristic
315C2×C4C23×D1111yescharacteristic
316C8—221no—
317C8—221no—
318C8—221no—
319C8—221no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—441no—
327C22—441no—
328C22—441no—
329C22C22×C22⋊D1111yescharacteristic
330C4—21no—
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—41no—
337C4—41no—
338C4—441no—
339C4—441no—
340C4—441no—
341C4C2×#433911yescharacteristic
342C4C2×#433911yescharacteristic
343C2—41no—
344C2—42no—
345C2—881no—
346C2#1062332211yescharacteristic
347C2#1062336711yescharacteristic
348C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#520C2
socleC22×C11C22×D4
prime radical#10622851C2
hypercenter#520D11
hypocenterC11#3125
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. C11×#520C2semidirect
2. #10623065C2semidirect
3. #10622852C2semidirect
5. #10622643C2semidirect
6. #10622641C2semidirect
7. C4×#4325C2semidirect
8. #10622633C2semidirect
9. C4×#4324C2semidirect
10. #10622629C2semidirect
11. #10622627C2semidirect
12. #10622621C2semidirect
13. #10622613C2semidirect
14. #10622584C2semidirect
15. #10622581C2semidirect
147. #520D11semidirect
282. C11#3125semidirect

Maximal subgroups

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

subgroupindex
C11×#5202
#106230652
#106228522
#106228512
#106226432
#106226412
C4×#43252
#106226332
C4×#43242
#106226292
#106226272
#106226212
#106226132
#106225842
#106225812
#312511