Finite Group Databasebeta

← #13081050

Subgroups — #13081050

Order 1408.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C11×#547C211yesmaximal, characteristic
2#10623072C211yesmaximal, characteristic, complemented
3#10622704C211yesmaximal, characteristic, complemented
4#10622693C211yesmaximal, characteristic, complemented
5#10622655C211yesmaximal, characteristic, complemented
6#10622654C211yesmaximal, characteristic, complemented
7#10622648C211yesmaximal, characteristic, complemented
8#10622646C211yesmaximal, characteristic, complemented
9#10622631C211yesmaximal, characteristic, complemented
10#10622624C211yesmaximal, characteristic, complemented
11#10622622C211yesmaximal, characteristic, complemented
12#10622584C211yesmaximal, characteristic, complemented
13#10622583C211yesmaximal, characteristic, complemented
14#10622577C211yesmaximal, characteristic, complemented
15C2×#66871C211yesmaximal, characteristic, complemented
16C2×C11×#41—21no—
17C11×C4⋊Q8C2211yescharacteristic
18C11×#123—21no—
19C11×#123—21no—
20C11×C22⋊Q8—21no—
21C11×#121C2211yescharacteristic
22C11×#121C2211yescharacteristic
23C4×D4×C11C2211yescharacteristic
24C4×D4×C11C2211yescharacteristic
25C2×C11×C4⋊C4C2211yescharacteristic
26C2×C11×C4⋊C4C2211yescharacteristic
27#66988—21no—
28C2×#4324C2211yescharacteristic
29#66979C2211yescharacteristic
30C2×C4⋊Dic11C2211yescharacteristic
31#66977C2211yescharacteristic
32#66977C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66942—21no—
36#66932—21no—
37#66930—21no—
38#66923C2211yescharacteristic
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#66871C2211yescharacteristic
52#66871C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C11×#41—44no—
60C2×Q8×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11—21no—
63C2×D4×C11D411yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2311yescharacteristic
69C22×C4×C11C2311yescharacteristic
70C22×Dic11—21no—
71C2×Dic22C2311yescharacteristic
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4D411yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C11×C4⋊C4C2311yescharacteristic
79C11×C22⋊C4—21no—
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C11×C22⋊C4D411yescharacteristic
83C11×C22⋊C4D411yescharacteristic
84C42×C11C2311yescharacteristic
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—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100#4318—22no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#3343—111nomaximal, Sylow
107C23×C11—21no—
108C23×C11C2×D411yescharacteristic
109C23×C11C2×D411yescharacteristic
110Q8×C11—42no—
111D4×C11—22no—
112D4×C11—21no—
113D4×C11—21no—
114D4×C11—42no—
115D4×C11—42no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—42no—
124C2×C4×C11—42no—
125C2×C4×C11—42no—
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2×D411yescharacteristic
129C2×C4×C11C2×D411yescharacteristic
130C2×C4×C11C2411yescharacteristic
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—21no—
134C2×Dic11—21no—
135C2×Dic11—42no—
136Dic22—21no—
137Dic22—21no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140C11⋊C8—21no—
141C11⋊C8#4112yescomplemented
142#552—111no—
143#547D1111yescharacteristic
144#501—111no—
145#484—111no—
146#483—111no—
147#482—111no—
148#480—111no—
149#478—111no—
150#477—111no—
151#468—111no—
152#465—111no—
153#440—111no—
154#435—111no—
155#428—111no—
156C2×#107—111no—
157C22×C11—21no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—21no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—41no—
165C22×C11AGL(1,ℤ/8)12yes—
166C22×C11C22×D411yescharacteristic
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11C2×#4111yescharacteristic
175C4×C112−1+411yescharacteristic
176Dic11—41no—
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180C2×#41—21no—
181C2×SD16—111no—
182C2×M16—111no—
183C22×C8—111no—
184C4⋊Q8C2×D1111yescharacteristic
185#126—221no—
186#125—111no—
187#125—221no—
188#123—21no—
189#123—21no—
190#123—221no—
191C22⋊Q8—21no—
192C22⋊Q8—111no—
193C22⋊Q8—111no—
194#121C2×D1111yescharacteristic
195#121C2×D1111yescharacteristic
196C4×Q8—111no—
197C4×D4C2×D1111yescharacteristic
198C4×D4C2×D1111yescharacteristic
199#117—111no—
200#117—221no—
201C2×C4⋊C4—111no—
202C2×C4⋊C4C2×D1111yescharacteristic
203C2×C4⋊C4C2×D1111yescharacteristic
204#107—111no—
205#107—111no—
206#107—111no—
207#107—111no—
208#107—111no—
209#107—111no—
210#106—111no—
211#106—111no—
212#106—111no—
213C4⋊C8—111no—
214#103—111no—
215#103—111no—
216#103—111no—
217#102—111no—
218#102—111no—
219#102—111no—
220C22⋊C8—111no—
221C22⋊C8—111no—
222#97—111no—
223C2×C11—22no—
224C2×C11—41no—
225C2×C11—81no—
226C2×C11#54711yescharacteristic
227C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
228C2×C11#57811yescharacteristic
229#41—44no—
230C2×Q8—21no—
231C2×Q8—111no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4C22⋊D1111yescharacteristic
235C2×D4C22×D1111yescharacteristic
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—221no—
240C22×C4C22×D1111yescharacteristic
241C22×C4C22×D1111yescharacteristic
242SD16—222no—
243M16—222no—
244C2×C8—111no—
245C2×C8—111no—
246C2×C8—111no—
247C2×C8—111no—
248C2×C8—222no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—111no—
253C4⋊C4—111no—
254C4⋊C4—111no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4—221no—
258C4⋊C4—221no—
259C4⋊C4—221no—
260C4⋊C4—221no—
261C4⋊C4C22⋊D1111yescharacteristic
262C4⋊C4C22×D1111yescharacteristic
263C4⋊C4C22×D1111yescharacteristic
264C4⋊C4C22×D1111yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—221no—
269C22⋊C4—221no—
270C22⋊C4—221no—
271C22⋊C4C22⋊D1111yescharacteristic
272C22⋊C4C22⋊D1111yescharacteristic
273C42—221no—
274C42—221no—
275C42C22×D1111yescharacteristic
276C11#334311yescharacteristic, complemented, Sylow
277C23—21no—
278C23C2×C22⋊D1111yescharacteristic
279C23C2×C22⋊D1111yescharacteristic
280Q8—42no—
281Q8—221no—
282Q8—221no—
283D4—22no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—442no—
303C2×C4C2×C22⋊D1111yescharacteristic
304C2×C4C2×C22⋊D1111yescharacteristic
305C2×C4C2×C22⋊D1111yescharacteristic
306C2×C4C2×C22⋊D1111yescharacteristic
307C2×C4C23×D1111yescharacteristic
308C8—112no—
309C8—221no—
310C8—221no—
311C8—221no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#6698512yes—
321C22C22×C22⋊D1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—441no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4#41×D1111yescharacteristic
334C4#6704311yescharacteristic
335C2—22no—
336C2—41no—
337C2—81no—
338C2C2×#6698511yescharacteristic
339C2#1062335511yescharacteristic
340C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#547C2
socleC22×C11C22×D4
hypercenter#547D11
hypocenterC11#3343
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
2. #10623072C2semidirect
3. #10622704C2semidirect
4. #10622693C2semidirect
5. #10622655C2semidirect
6. #10622654C2semidirect
7. #10622648C2semidirect
8. #10622646C2semidirect
9. #10622631C2semidirect
10. #10622624C2semidirect
11. #10622622C2semidirect
12. #10622584C2semidirect
13. #10622583C2semidirect
14. #10622577C2semidirect
15. C2×#66871C2semidirect
141. C11⋊C8#41semidirect
276. C11#3343semidirect

Maximal subgroups

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

subgroupindex
C11×#5472
#106230722
#106227042
#106226932
#106226552
#106226542
#106226482
#106226462
#106226312
#106226242
#106226222
#106225842
#106225832
#106225772
C2×#668712
#334311