Finite Group Databasebeta

← #13081056

Subgroups — #13081056

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×#552C211yesmaximal, characteristic, complemented
2#10623086C211yesmaximal, characteristic
3#10622679C211yesmaximal, characteristic, complemented
4#10622678C211yesmaximal, characteristic, complemented
5#10622662C211yesmaximal, characteristic, complemented
6#10622661C211yesmaximal, characteristic, complemented
7#10622657C211yesmaximal, characteristic, complemented
8#10622656C211yesmaximal, characteristic, complemented
9#10622639C211yesmaximal, characteristic, complemented
10#10622634C211yesmaximal, characteristic, complemented
11#10622624C211yesmaximal, characteristic, complemented
12#10622616C211yesmaximal, characteristic, complemented
13#10622608C211yesmaximal, characteristic, complemented
14#10622580C211yesmaximal, characteristic, complemented
15C2×#66871C211yesmaximal, characteristic, complemented
16C2×#4341—21no—
17C11×#126—21no—
18C11×#125—21no—
19C11×#125C2211yescharacteristic
20C11×#123—21no—
21C11×C22⋊Q8C2211yescharacteristic
22C11×C22⋊Q8C2211yescharacteristic
23C4×Q8×C11C2211yescharacteristic
24C4×D4×C11C2211yescharacteristic
25C11×#117—21no—
26C11×#117C2211yescharacteristic
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×#4325C2211yescharacteristic
29#66983C2211yescharacteristic
30#66983C2211yescharacteristic
31C2×C4⋊Dic11C2211yescharacteristic
32C2×C4⋊Dic11C2211yescharacteristic
33C2×#4318C2211yescharacteristic
34C22×C11⋊C8C2211yescharacteristic
35#66950—21no—
36#66939—21no—
37#66939—21no—
38C4×D44C2211yescharacteristic
39#66922C2211yescharacteristic
40#66899C2211yescharacteristic
41#66899C2211yescharacteristic
42#66899C2211yescharacteristic
43C22⋊(C11⋊C8)C2211yescharacteristic
44C22⋊(C11⋊C8)C2211yescharacteristic
45#66873C2211yescharacteristic
46#66873C2211yescharacteristic
47#66873C2211yescharacteristic
48#66872C2211yescharacteristic
49#66872C2211yescharacteristic
50#66872C2211yescharacteristic
51#66871C2211yescharacteristic
52#66871C2211yescharacteristic
53#66871C2211yescharacteristic
54#66871C2211yescharacteristic
55#66871C2211yescharacteristic
56#66871C2211yescharacteristic
57C4⋊(C11⋊C8)C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11D411yescharacteristic
61C22×C4×C11—21no—
62C22×C4×C11C2311yescharacteristic
63C22×C4×C11C2311yescharacteristic
64C2×C22⋊D11—21no—
65C2×C22⋊D11—21no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68#4341—44no—
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×Dic22—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4—21no—
75C11×C4⋊C4—21no—
76C11×C4⋊C4—21no—
77C11×C4⋊C4—21no—
78C11×C4⋊C4D411yescharacteristic
79C11×C4⋊C4C2311yescharacteristic
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C22⋊C4—21no—
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C11×C22⋊C4D411yescharacteristic
86C11×C22⋊C4D411yescharacteristic
87C42×C11—21no—
88C42×C11—21no—
89C42×C11C2311yescharacteristic
90#4325—22no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11C2311yescharacteristic
98C4⋊Dic11C2311yescharacteristic
99C4⋊Dic11C2311yescharacteristic
100#4318—22no—
101C2×C11⋊C8—22no—
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#3343—111nomaximal, Sylow
107C23×C11C2×D411yescharacteristic
108C23×C11C2×D411yescharacteristic
109C22×D11—21no—
110Q8×C11—21no—
111Q8×C11—21no—
112D4×C11—22no—
113C2×C4×C11—21no—
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—42no—
122C2×C4×C11C2×D411yescharacteristic
123C2×C4×C11C2×D411yescharacteristic
124C2×C4×C11C2×D411yescharacteristic
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2411yescharacteristic
127C22⋊D11—42no—
128C22⋊D11—42no—
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—42no—
133C2×Dic11—42no—
134D44—21no—
135D44—21no—
136C4×D11—42no—
137Dic22—42no—
138C11⋊C8—21no—
139C11⋊C8—21no—
140C11⋊C8—21no—
141C11⋊C8#4112yescomplemented
142#552D1111yescharacteristic, complemented
143#547—111no—
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×C11AGL(1,ℤ/8)12yes—
163C22×C11C22×D411yescharacteristic
164C2×D11—41no—
165C2×D11—41no—
166C2×D11—41no—
167C4×C11—21no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—21no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11C2×#4111yescharacteristic
176C4×C112−1+411yescharacteristic
177Dic11—41no—
178Dic11—41no—
179Dic11—41no—
180C2×#41—221no—
181C2×SD16—111no—
182C2×M16—111no—
183C22×C8—111no—
184C4⋊Q8—111no—
185#126—21no—
186#125—21no—
187#125C2×D1111yescharacteristic
188#123—21no—
189#123—221no—
190#123—221no—
191C22⋊Q8—221no—
192C22⋊Q8C2×D1111yescharacteristic
193C22⋊Q8C2×D1111yescharacteristic
194#121—111no—
195#121—111no—
196C4×Q8C2×D1111yescharacteristic
197C4×D4—111no—
198C4×D4C2×D1111yescharacteristic
199#117—21no—
200#117C2×D1111yescharacteristic
201C2×C4⋊C4—111no—
202C2×C4⋊C4—111no—
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#54711yescharacteristic
226C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
227C2×C11#57811yescharacteristic
228D11—81no—
229#41—444no—
230C2×Q8—221no—
231C2×Q8C22×D1111yescharacteristic
232C2×D4—111no—
233C2×D4—221no—
234C2×D4—221no—
235C2×D4C22⋊D1111yescharacteristic
236C22×C4—21no—
237C22×C4—221no—
238C22×C4—221no—
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—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—111no—
256C4⋊C4—111no—
257C4⋊C4—111no—
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—21no—
274C42—21no—
275C42C22×D1111yescharacteristic
276C11#334311yescharacteristic, complemented, Sylow
277C23—221no—
278C23C2×C22⋊D1111yescharacteristic
279C23C2×C22⋊D1111yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—442no—
283D4—22no—
284D4—221no—
285D4—221no—
286D4—442no—
287D4—442no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—221no—
300C2×C4—442no—
301C2×C4—442no—
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—441no—
318C22—441no—
319C22—441no—
320C22#6700212yes—
321C22C22×C22⋊D1111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—441no—
331C4—441no—
332C4—441no—
333C4#41×D1111yescharacteristic
334C4#6704311yescharacteristic
335C2—22no—
336C2—41no—
337C2—881no—
338C2C2×#6700211yescharacteristic
339C2#1062335511yescharacteristic
340C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#552C2
socleC22×C11C22×D4
prime radical#10623086C2
hypercenter#552D11
hypocenterC11#3343
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. C11×#552C2semidirect
3. #10622679C2semidirect
4. #10622678C2semidirect
5. #10622662C2semidirect
6. #10622661C2semidirect
7. #10622657C2semidirect
8. #10622656C2semidirect
9. #10622639C2semidirect
10. #10622634C2semidirect
11. #10622624C2semidirect
12. #10622616C2semidirect
13. #10622608C2semidirect
14. #10622580C2semidirect
15. C2×#66871C2semidirect
141. C11⋊C8#41semidirect
142. #552D11semidirect
276. C11#3343semidirect

Maximal subgroups

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

subgroupindex
C11×#5522
#106230862
#106226792
#106226782
#106226622
#106226612
#106226572
#106226562
#106226392
#106226342
#106226242
#106226162
#106226082
#106225802
C2×#668712
#334311