Finite Group Databasebeta

← #13081155

Subgroups — #13081155

Order 1408.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#553C211yesmaximal, characteristic
2#10623073C211yesmaximal, characteristic, complemented
3#10622678C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622655C211yesmaximal, characteristic, complemented
6#10622654C211yesmaximal, characteristic, complemented
7#10622648C211yesmaximal, characteristic, complemented
8#10622648C211yesmaximal, characteristic, complemented
9#10622631C211yesmaximal, characteristic, complemented
10#10622624C211yesmaximal, characteristic, complemented
11#10622621C211yesmaximal, characteristic, complemented
12#10622611C211yesmaximal, characteristic, complemented
13#10622609C211yesmaximal, characteristic, complemented
14#10622584C211yesmaximal, characteristic, complemented
15#10622577C211yesmaximal, characteristic, complemented
16C11×#126—21no—
17C11×#125C2211yescharacteristic
18C11×#123—21no—
19C11×#121—21no—
20C11×#121C2211yescharacteristic
21C11×#121C2211yescharacteristic
22C4×D4×C11—21no—
23C4×D4×C11C2211yescharacteristic
24C4×D4×C11C2211yescharacteristic
25C11×#117C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27#66989—21no—
28C2×#4324C2211yescharacteristic
29#66979C2211yescharacteristic
30#66979C2211yescharacteristic
31#66977C2211yescharacteristic
32#66977C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66940—21no—
36#66932—21no—
37#66932—21no—
38#66922C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40#66896C2211yescharacteristic
41#66896C2211yescharacteristic
42#66896C2211yescharacteristic
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66874C2211yescharacteristic
46#66874C2211yescharacteristic
47#66874C2211yescharacteristic
48#66872C2211yescharacteristic
49#66872C2211yescharacteristic
50#66872C2211yescharacteristic
51#66872C2211yescharacteristic
52#66872C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11—21no—
61C2×D4×C11D411yescharacteristic
62C2×D4×C11C2311yescharacteristic
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11C2311yescharacteristic
66C22×C4×C11C2311yescharacteristic
67C2×Dic22—21no—
68C2×Dic22C2311yescharacteristic
69C11×C4⋊C4—21no—
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4D411yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C22⋊C4—21no—
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C11×C22⋊C4—21no—
80C11×C22⋊C4D411yescharacteristic
81C11×C22⋊C4D411yescharacteristic
82C42×C11—21no—
83C42×C11C2311yescharacteristic
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88#4324—22no—
89C4⋊Dic11—21no—
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99#4318—22no—
100C2×C11⋊C8—22no—
101C2×C11⋊C8C2311yescharacteristic
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105#3350—111nomaximal, Sylow
106C23×C11—21no—
107C23×C11C2×D411yescharacteristic
108C23×C11C2×D411yescharacteristic
109D4×C11—21no—
110D4×C11—21no—
111D4×C11—41no—
112D4×C11—42no—
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—21no—
120C2×C4×C11—21no—
121C2×C4×C11—81no—
122C2×C4×C11—81no—
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C2×Dic11—21no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132Dic22—21no—
133Dic22—21no—
134Dic22—42no—
135C11⋊C8—21no—
136C11⋊C8—21no—
137C11⋊C8—21no—
138C11⋊C8#4112yes—
139#556—111no—
140#553D1111yescharacteristic
141#501—111no—
142#485—111no—
143#483—111no—
144#482—111no—
145#482—111no—
146#479—111no—
147#476—111no—
148#468—111no—
149#465—111no—
150#440—111no—
151#435—111no—
152#428—111no—
153#427—111no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11C22×D411yescharacteristic
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—21no—
167C4×C11—21no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11—41no—
171C4×C11C2×#4111yescharacteristic
172C4×C112−1+411yescharacteristic
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×SD16—111no—
178C2×M16—111no—
179C22×C8—111no—
180C4⋊Q8—111no—
181#126—21no—
182#126—221no—
183#126—221no—
184#125C2×D1111yescharacteristic
185#124—221no—
186#123—21no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189#121—21no—
190#121C2×D1111yescharacteristic
191#121C2×D1111yescharacteristic
192C4×Q8—111no—
193C4×Q8—221no—
194C4×D4—21no—
195C4×D4C2×D1111yescharacteristic
196C4×D4C2×D1111yescharacteristic
197#117—111no—
198#117—111no—
199#117C2×D1111yescharacteristic
200C2×C4⋊C4C2×D1111yescharacteristic
201#107—111no—
202#107—111no—
203#107—111no—
204#107—111no—
205#106—111no—
206#106—111no—
207#106—111no—
208#106—111no—
209#106—111no—
210C4⋊C8—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#102—111no—
215#102—111no—
216#102—111no—
217C22⋊C8—111no—
218C22⋊C8—111no—
219#97—111no—
220C2×C11—41no—
221C2×C11—41no—
222C2×C11—81no—
223C2×C11#54711yescharacteristic
224C2×C11#57511yescharacteristic
225C2×C11#57711yescharacteristic
226C2×Q8—111no—
227C2×Q8—221no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4C22⋊D1111yescharacteristic
231C2×D4C22×D1111yescharacteristic
232C22×C4—21no—
233C22×C4—21no—
234C22×C4C22×D1111yescharacteristic
235C22×C4C22×D1111yescharacteristic
236SD16—222no—
237M16—222no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—111no—
241C2×C8—111no—
242C2×C8—222no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4C22⋊D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C4⋊C4C22×D1111yescharacteristic
256C4⋊C4C22×D1111yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4C22⋊D1111yescharacteristic
266C22⋊C4C22⋊D1111yescharacteristic
267C42—21no—
268C42—221no—
269C42—221no—
270C42—221no—
271C42C22×D1111yescharacteristic
272C11#335011yescharacteristic, complemented, Sylow
273C23—21no—
274C23C2×C22⋊D1111yescharacteristic
275C23C2×C22⋊D1111yescharacteristic
276Q8—221no—
277Q8—221no—
278Q8—442no—
279D4—21no—
280D4—21no—
281D4—41no—
282D4—42no—
283D4—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4C2×C22⋊D1111yescharacteristic
298C2×C4C2×C22⋊D1111yescharacteristic
299C2×C4C2×C22⋊D1111yescharacteristic
300C2×C4C2×C22⋊D1111yescharacteristic
301C2×C4C23×D1111yescharacteristic
302C8—112no—
303C8—221no—
304C8—221no—
305C8—221no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—41no—
313C22—41no—
314C22—41no—
315C22C22×C22⋊D1111yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—441no—
324C4—441no—
325C4—441no—
326C4—441no—
327C4#41×D1111yescharacteristic
328C4#6704311yescharacteristic
329C2—41no—
330C2—41no—
331C2—81no—
332C2#1062335311yescharacteristic
333C2#1062335511yescharacteristic
334C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#553C2
socleC22×C11C22×D4
hypercenter#553D11
hypocenterC11#3350
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
2. #10623073C2semidirect
3. #10622678C2semidirect
4. #10622676C2semidirect
5. #10622655C2semidirect
6. #10622654C2semidirect
7. #10622648C2semidirect
8. #10622648C2semidirect
9. #10622631C2semidirect
10. #10622624C2semidirect
11. #10622621C2semidirect
12. #10622611C2semidirect
13. #10622609C2semidirect
14. #10622584C2semidirect
15. #10622577C2semidirect
272. C11#3350semidirect

Maximal subgroups

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

subgroupindex
C11×#5532
#106230732
#106226782
#106226762
#106226552
#106226542
#106226482
#106226312
#106226242
#106226212
#106226112
#106226092
#106225842
#106225772
#335011