Finite Group Databasebeta

← #13081022

Subgroups — #13081022

Order 1408.

352 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
1#10623172C211yesmaximal, characteristic, complemented
2#10623063C211yesmaximal, characteristic
3C11×#485C211yesmaximal, characteristic, complemented
4#10622661C211yesmaximal, characteristic, complemented
5#10622611C211yesmaximal, characteristic, complemented
6#10622503C211yesmaximal, characteristic, complemented
7#10622493C211yesmaximal, characteristic, complemented
8#10622479C211yesmaximal, characteristic, complemented
9#10622468C211yesmaximal, characteristic, complemented
10#10622428C211yesmaximal, characteristic, complemented
11#10622420C211yesmaximal, characteristic, complemented
12#10622407C211yesmaximal, characteristic, complemented
13#10622401C211yesmaximal, characteristic, complemented
14#10622350C211yesmaximal, characteristic, complemented
15(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
16C11×C22⋊Q8C2211yescharacteristic
17C11×#117C2211yescharacteristic
18#66999C2211yescharacteristic
19Q8×Dic11C2211yescharacteristic
20C2×#4325C2211yescharacteristic
21#66983C2211yescharacteristic
22C4×C22⋊D11C2211yescharacteristic
23#66979C2211yescharacteristic
24C22×C11⋊C8C2211yescharacteristic
25C2×C8×D11C2211yescharacteristic
26#66951—21no—
27#66948C2211yescharacteristic
28#66946C2211yescharacteristic
29#66945C2211yescharacteristic
30#66945C2211yescharacteristic
31#66941C2211yescharacteristic
32#66941C2211yescharacteristic
33#66940—21no—
34#66938—21no—
35#66938—21no—
36#66937—21no—
37#66932—21no—
38#66928—21no—
39#66925—21no—
40C11×#107C2211yescharacteristic
41C11×#106C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×#103C2211yescharacteristic
44C11×C22⋊C8C2211yescharacteristic
45#66899C2211yescharacteristic
46#66885C2211yescharacteristic
47#66885C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66882C2211yescharacteristic
50#66881C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11—21no—
62C2×C22⋊D11D411yescharacteristic
63C2×D44—21no—
64C2×D44C2311yescharacteristic
65C2×C4×D11—21no—
66C2×C4×D11C2311yescharacteristic
67C2×Dic22—21no—
68C2×Dic22—21no—
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C22⋊C4—21no—
76C11×C22⋊C4—21no—
77C42×C11—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11D411yescharacteristic
80#4325—22no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4—21no—
83(C2×D11)⋊C4—21no—
84(C2×D11)⋊C4—21no—
85(C2×D11)⋊C4—21no—
86(C2×D11)⋊C4—21no—
87(C2×D11)⋊C4D411yescharacteristic
88C4⋊Dic11—21no—
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
91C4⋊Dic11C2311yescharacteristic
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4D411yescharacteristic
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11C2311yescharacteristic
101C2×C11⋊C8—22no—
102C2×C11⋊C8C2311yescharacteristic
103C2×C11⋊C8C2311yescharacteristic
104C8×D11—22no—
105#3340—111nomaximal, Sylow
106C23×C11C2×D411yescharacteristic
107C22×D11—21no—
108C22×D11C2×D411yescharacteristic
109Q8×C11—21no—
110Q8×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11C2×D411yescharacteristic
118C2×C4×C11C2411yescharacteristic
119C22⋊D11—22no—
120C22⋊D11—81no—
121C2×Dic11—21no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11C2×D411yescharacteristic
125C2×Dic11C2×D411yescharacteristic
126C2×Dic11C2×D411yescharacteristic
127D44—21no—
128D44—21no—
129D44—81no—
130C4×D11—21no—
131C4×D11—21no—
132C4×D11—42no—
133Dic22—42no—
134Dic22—81no—
135C8×C11—21no—
136C8×C11—21no—
137C11⋊C8—21no—
138C11⋊C8#4112yes—
139#556—111no—
140#555—111no—
141#498—111no—
142#485—111no—
143#485D1111yescharacteristic, complemented
144#482—111no—
145#482—111no—
146#477—111no—
147#474—111no—
148#465—111no—
149#465—111no—
150C4×SD16—111no—
151C8×D4—111no—
152#427—111no—
153#427—111no—
154C22×C11—21no—
155C22×C11—21no—
156C22×C11—21no—
157C22×C11C22×D411yescharacteristic
158C2×D11—21no—
159C2×D11—21no—
160C2×D11—21no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C4×C11—21no—
165C4×C11—41no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11C2×#4111yescharacteristic
170C4×C112−1+411yescharacteristic
171Dic11—21no—
172Dic11—21no—
173Dic11—41no—
174Dic11—41no—
175Dic11—41no—
176Dic11#13512yes—
177C2×SD16—111no—
178C22×C8—111no—
179C22×C8—111no—
180C4⋊Q8—111no—
181C4⋊Q8—111no—
182#126—221no—
183#126—221no—
184#124—221no—
185#124—221no—
186#124—221no—
187C22⋊Q8—111no—
188C22⋊Q8C2×D1111yescharacteristic
189#121—111no—
190#121—111no—
191#121—221no—
192C4×Q8—111no—
193C4×Q8—221no—
194C4×D4—111no—
195C4×D4—111no—
196#117—111no—
197#117—111no—
198#117—111no—
199#117—221no—
200#117C2×D1111yescharacteristic
201#107—111no—
202#107—111no—
203#107—111no—
204#107C2×D1111yescharacteristic
205#106—111no—
206#106—111no—
207#106—111no—
208#106—111no—
209#106C2×D1111yescharacteristic
210C4⋊C8—111no—
211#103—111no—
212#103C2×D1111yescharacteristic
213#103C2×D1111yescharacteristic
214#102—111no—
215#102—111no—
216#102—111no—
217C22⋊C8—111no—
218C22⋊C8C2×D1111yescharacteristic
219C4×C8—111no—
220C2×C11—41no—
221C2×C11#54711yescharacteristic
222C2×C11C2×#13511yescharacteristic
223C2×C11#57711yescharacteristic
224D11—41no—
225D11—81no—
226C2×Q8—221no—
227C2×Q8—221no—
228C2×Q8C22×D1111yescharacteristic
229C2×D4—111no—
230C2×D4—111no—
231C2×D4—221no—
232C2×D4—221no—
233C22×C4—111no—
234C22×C4—221no—
235C22×C4C22×D1111yescharacteristic
236SD16—222no—
237C2×C8—111no—
238C2×C8—111no—
239C2×C8—222no—
240C2×C8—222no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—111no—
245C4⋊C4—111no—
246C4⋊C4—111no—
247C4⋊C4—111no—
248C4⋊C4—221no—
249C4⋊C4—221no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4C22×D1111yescharacteristic
253C4⋊C4C22×D1111yescharacteristic
254C4⋊C4C22×D1111yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—111no—
258C22⋊C4—111no—
259C22⋊C4—221no—
260C22⋊C4—221no—
261C22⋊C4—221no—
262C22⋊C4—221no—
263C22⋊C4—221no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C42—21no—
267C42—111no—
268C42—221no—
269C42—221no—
270C42—221no—
271C42—221no—
272C11#334011yescharacteristic, complemented, Sylow
273C23—111no—
274C23—221no—
275C23D4×D1111yescharacteristic
276Q8—21no—
277Q8—21no—
278Q8—442no—
279Q8—881no—
280D4—222no—
281D4—221no—
282D4—221no—
283D4—881no—
284D4—881no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—111no—
292C2×C4—111no—
293C2×C4—111no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—221no—
298C2×C4—221no—
299C2×C4—442no—
300C2×C4D4×D1111yescharacteristic
301C2×C4C23×D1111yescharacteristic
302C8—21no—
303C8—21no—
304C8—112no—
305C8—221no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—221no—
310C22—221no—
311C22—221no—
312C22—441no—
313C22—441no—
314C22—441no—
315C22C2×D4×D1111yescharacteristic
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—112no—
322C4—221no—
323C4—221no—
324C4—441no—
325C4—441no—
326C4—441no—
327C4#41×D1111yescharacteristic
328C4#6704311yescharacteristic
329C2—41no—
330C2—441no—
331C2—881no—
332C2#1062318611yescharacteristic
333C2D11×#13511yescharacteristic
334C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radical#10623063C2
hypercenter#485D11
hypocenterC11#3340
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
1. #10623172C2semidirect
3. C11×#485C2semidirect
4. #10622661C2semidirect
5. #10622611C2semidirect
6. #10622503C2semidirect
7. #10622493C2semidirect
8. #10622479C2semidirect
9. #10622468C2semidirect
10. #10622428C2semidirect
11. #10622420C2semidirect
12. #10622407C2semidirect
13. #10622401C2semidirect
14. #10622350C2semidirect
15. (C22⋊D11)⋊C8C2semidirect
143. #485D11semidirect
272. C11#3340semidirect

Maximal subgroups

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

subgroupindex
#106231722
#106230632
C11×#4852
#106226612
#106226112
#106225032
#106224932
#106224792
#106224682
#106224282
#106224202
#106224072
#106224012
#106223502
(C22⋊D11)⋊C82
#334011