Finite Group Databasebeta

← #13081682

Subgroups — #13081682

Order 1408.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#556C211yesmaximal, characteristic, complemented
2#10623116C211yesmaximal, characteristic, complemented
3#10622699C211yesmaximal, characteristic, complemented
4#10622696C211yesmaximal, characteristic, complemented
5#10622672C211yesmaximal, characteristic, complemented
6#10622671C211yesmaximal, characteristic
7#10622670C211yesmaximal, characteristic, complemented
8#10622667C211yesmaximal, characteristic, complemented
9#10622643C211yesmaximal, characteristic, complemented
10#10622641C211yesmaximal, characteristic, complemented
11#10622640C211yesmaximal, characteristic, complemented
12C4×#4325C211yesmaximal, characteristic, complemented
13#10622637C211yesmaximal, characteristic, complemented
14#10622629C211yesmaximal, characteristic, complemented
15#10622627C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#126—21no—
18C11×#126—21no—
19C11×#124C2211yescharacteristic
20C11×#124C2211yescharacteristic
21C11×C22⋊Q8—21no—
22C4×Q8×C11C2211yescharacteristic
23C4×Q8×C11C2211yescharacteristic
24C4×Q8×C11C2211yescharacteristic
25C4×D4×C11C2211yescharacteristic
26C11×#117—21no—
27#67000—21no—
28C2×#4326C2211yescharacteristic
29C2×#4326C2211yescharacteristic
30C2×#4325C2211yescharacteristic
31C2×#4325C2211yescharacteristic
32C2×#4325C2211yescharacteristic
33C2×#4325C2211yescharacteristic
34C2×#4324C2211yescharacteristic
35C2×#4323C2211yescharacteristic
36C2×#4323C2211yescharacteristic
37#66947—21no—
38#66947—21no—
39#66946—21no—
40#66928C2211yescharacteristic
41#66928C2211yescharacteristic
42#66927C2211yescharacteristic
43C4×D44C2211yescharacteristic
44C4×D44C2211yescharacteristic
45C4×Dic22C2211yescharacteristic
46#66899C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66874C2211yescharacteristic
50#66873C2211yescharacteristic
51#66873C2211yescharacteristic
52#66872C2211yescharacteristic
53C4⋊(C11⋊C8)C2211yescharacteristic
54C4⋊(C11⋊C8)C2211yescharacteristic
55C4⋊(C11⋊C8)C2211yescharacteristic
56#66867C2211yescharacteristic
57#66867C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11D411yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×Q8×C11C2311yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C2×D44—21no—
65C2×D44—21no—
66C2×D44C2311yescharacteristic
67C2×D44C2311yescharacteristic
68C2×C4×D11—21no—
69C2×C4×D11—21no—
70C2×Dic22C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4D411yescharacteristic
76C11×C4⋊C4D411yescharacteristic
77C11×C4⋊C4D411yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C11×C22⋊C4—21no—
83C11×C22⋊C4—21no—
84C42×C11—21no—
85C42×C11—21no—
86C42×C11C2311yescharacteristic
87C42×C11C2311yescharacteristic
88C42×C11C2311yescharacteristic
89#4326—22no—
90#4326—41no—
91#4325—22no—
92#4325—41no—
93#4325—41no—
94#4325—41no—
95#4324—41no—
96#4323—22no—
97#4323—41no—
98(C2×D11)⋊C4—21no—
99(C2×D11)⋊C4—21no—
100(C2×D11)⋊C4—21no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104C4⋊Dic11C2311yescharacteristic
105Dic11⋊C4—21no—
106C4×Dic11—21no—
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110C2×C11⋊C8C2311yescharacteristic
111#3401—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11—21no—
114C22×D11—21no—
115Q8×C11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—41no—
120D4×C11—21no—
121D4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11—42no—
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2×D411yescharacteristic
131C2×C4×C11C2×D411yescharacteristic
132C2×C4×C11C2411yescharacteristic
133C2×Dic11—21no—
134C2×Dic11—21no—
135D44—21no—
136D44—21no—
137D44—21no—
138D44—21no—
139D44—42no—
140D44—81no—
141C4×D11—81no—
142C4×D11—81no—
143Dic22—21no—
144Dic22—21no—
145C11⋊C8—21no—
146C11⋊C8—21no—
147C11⋊C8—21no—
148C11⋊C8#4112yes—
149#559—111no—
150#556D1111yescharacteristic, complemented
151#497—111no—
152#496—111no—
153#495—111no—
154#464—111no—
155#464—111no—
156#463—111no—
157#463—111no—
158#461—111no—
159#460—111no—
160#446—111no—
161#442—111no—
162#441—111no—
163C4×SD16—111no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11C22×D411yescharacteristic
168C2×D11—41no—
169C2×D11—41no—
170C2×D11—41no—
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—21no—
177C4×C11—21no—
178C4×C11—21no—
179C4×C11—21no—
180C4×C11—41no—
181C4×C11—41no—
182C4×C11—41no—
183C4×C11C2×#4111yescharacteristic
184C4×C11H(5,𝔽2)11yescharacteristic
185Dic11—41no—
186Dic11—41no—
187C2×Q16—111no—
188C2×Q16—111no—
189C2×SD16—111no—
190C2×SD16—111no—
191C2×SD16—111no—
192C2×SD16—111no—
193C2×SD16—111no—
194C2×D8—111no—
195C2×D8—111no—
196C4⋊Q8C2×D1111yescharacteristic
197#127—111no—
198#126—21no—
199#126—21no—
200#124—111no—
201#124—111no—
202#124—221no—
203#124C2×D1111yescharacteristic
204#124C2×D1111yescharacteristic
205#123—221no—
206#123—221no—
207C22⋊Q8—21no—
208C4×Q8—111no—
209C4×Q8C2×D1111yescharacteristic
210C4×Q8C2×D1111yescharacteristic
211C4×Q8C2×D1111yescharacteristic
212C4×D4—111no—
213C4×D4—111no—
214C4×D4—221no—
215C4×D4C2×D1111yescharacteristic
216#117—21no—
217#106—111no—
218C4⋊C8—111no—
219C4⋊C8—111no—
220C4⋊C8—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#102—111no—
225#102—111no—
226#102—111no—
227#97—111no—
228#97—111no—
229C4×C8—111no—
230C2×C11—81no—
231C2×C11#55011yescharacteristic
232C2×C11#57511yescharacteristic
233C2×C11#57711yescharacteristic
234D11—81no—
235D11—81no—
236C2×Q8—111no—
237C2×Q8C22⋊D1111yescharacteristic
238C2×Q8C22×D1111yescharacteristic
239C2×Q8C22×D1111yescharacteristic
240C2×D4—111no—
241C2×D4—111no—
242C2×D4—221no—
243C2×D4—221no—
244C2×D4C22×D1111yescharacteristic
245C22×C4—21no—
246C22×C4—221no—
247C22×C4—221no—
248Q16—222no—
249Q16—441no—
250SD16—222no—
251SD16—441no—
252SD16—441no—
253SD16—441no—
254SD16—441no—
255D8—222no—
256D8—441no—
257C2×C8—111no—
258C2×C8—111no—
259C2×C8—111no—
260C2×C8—111no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—111no—
266C4⋊C4—221no—
267C4⋊C4C22⋊D1111yescharacteristic
268C4⋊C4C22⋊D1111yescharacteristic
269C4⋊C4C22⋊D1111yescharacteristic
270C4⋊C4C22×D1111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C42—21no—
283C42—21no—
284C42—221no—
285C42C22×D1111yescharacteristic
286C42C22×D1111yescharacteristic
287C42C22×D1111yescharacteristic
288C11#340111yescharacteristic, complemented, Sylow
289C23—21no—
290C23—221no—
291C23—221no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—41no—
297Q8—221no—
298Q8—221no—
299D4—21no—
300D4—21no—
301D4—221no—
302D4—221no—
303D4—221no—
304D4—221no—
305D4—442no—
306D4—881no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—221no—
312C2×C4—221no—
313C2×C4—881no—
314C2×C4—881no—
315C2×C4C2×C22⋊D1111yescharacteristic
316C2×C4C2×C22⋊D1111yescharacteristic
317C2×C4C2×C22⋊D1111yescharacteristic
318C2×C4C2×C22⋊D1111yescharacteristic
319C2×C4C2×C22⋊D1111yescharacteristic
320C2×C4C2×C22⋊D1111yescharacteristic
321C2×C4C23×D1111yescharacteristic
322C8—112no—
323C8—221no—
324C8—221no—
325C8—221no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—441no—
330C22—441no—
331C22—441no—
332C22—441no—
333C22—441no—
334C22—441no—
335C22C22×C22⋊D1111yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—441no—
346C4—441no—
347C4#41×D1111yescharacteristic
348C4#6704211yescharacteristic
349C2—81no—
350C2—881no—
351C2—881no—
352C2#1062335311yescharacteristic
353C2#1062336511yescharacteristic
354C2#1062336811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#556C2
socleC22×C11C22×D4
prime radical#10622671C2
hypercenter#556D11
hypocenterC11#3401
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. C11×#556C2semidirect
2. #10623116C2semidirect
3. #10622699C2semidirect
4. #10622696C2semidirect
5. #10622672C2semidirect
7. #10622670C2semidirect
8. #10622667C2semidirect
9. #10622643C2semidirect
10. #10622641C2semidirect
11. #10622640C2semidirect
12. C4×#4325C2semidirect
13. #10622637C2semidirect
14. #10622629C2semidirect
15. #10622627C2semidirect
150. #556D11semidirect
288. C11#3401semidirect

Maximal subgroups

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

subgroupindex
C11×#5562
#106231162
#106226992
#106226962
#106226722
#106226712
#106226702
#106226672
#106226432
#106226412
#106226402
C4×#43252
#106226372
#106226292
#106226272
#340111