Finite Group Databasebeta

← #13081160

Subgroups — #13081160

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
1#10623263C211yesmaximal, characteristic, complemented
2#10623226C211yesmaximal, characteristic
3C11×#501C211yesmaximal, characteristic, complemented
4#10622697C211yesmaximal, characteristic, complemented
5#10622676C211yesmaximal, characteristic, complemented
6#10622501C211yesmaximal, characteristic, complemented
7#10622499C211yesmaximal, characteristic, complemented
8#10622498C211yesmaximal, characteristic, complemented
9#10622493C211yesmaximal, characteristic, complemented
10#10622479C211yesmaximal, characteristic, complemented
11#10622477C211yesmaximal, characteristic, complemented
12#10622475C211yesmaximal, characteristic, complemented
13#10622474C211yesmaximal, characteristic, complemented
14#10622323C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#125C2211yescharacteristic
18#67000—21no—
19Q8×Dic11—21no—
20C2×#4314C2211yescharacteristic
21C2×#4313C2211yescharacteristic
22C2×C8×D11C2211yescharacteristic
23#66951—21no—
24#66951—21no—
25#66951—21no—
26#66950C2211yescharacteristic
27#66950C2211yescharacteristic
28#66948—21no—
29#66948C2211yescharacteristic
30#66948C2211yescharacteristic
31#66947—21no—
32#66946—21no—
33#66945C2211yescharacteristic
34#66945C2211yescharacteristic
35#66945C2211yescharacteristic
36C4⋊C4×D11C2211yescharacteristic
37C4×D44C2211yescharacteristic
38C4×D44C2211yescharacteristic
39C4×Dic22C2211yescharacteristic
40C11×#107C2211yescharacteristic
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#106C2211yescharacteristic
44C11×#97C2211yescharacteristic
45#66885C2211yescharacteristic
46(C2×D11)⋊C8C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48#66882C2211yescharacteristic
49#66880C2211yescharacteristic
50#66874C2211yescharacteristic
51#66874C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×D44—21no—
61C2×D44—21no—
62C2×D44D411yescharacteristic
63C2×D44C2311yescharacteristic
64C2×C4×D11—21no—
65C2×C4×D11—21no—
66C2×C4×D11C2311yescharacteristic
67C2×C4×D11C2311yescharacteristic
68C2×Dic22C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C2×C8×C11C2311yescharacteristic
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4—21no—
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C11×C4⋊C4C2311yescharacteristic
78C42×C11C2311yescharacteristic
79(C2×D11)⋊C4—21no—
80(C2×D11)⋊C4—21no—
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
88(C2×D11)⋊C4D411yescharacteristic
89C4⋊Dic11—21no—
90C4⋊Dic11—21no—
91C4⋊Dic11D411yescharacteristic
92C4⋊Dic11C2311yescharacteristic
93C4⋊Dic11C2311yescharacteristic
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#4314—22no—
103#4313—22no—
104C8×D11—22no—
105#3350—111nomaximal, Sylow
106C22×D11—21no—
107C22×D11C2×D411yescharacteristic
108C22×D11C2×D411yescharacteristic
109Q8×C11—42no—
110C2×C4×C11—21no—
111C2×C4×C11—21no—
112C2×C4×C11—21no—
113C2×C4×C11—21no—
114C2×C4×C11C2×D411yescharacteristic
115C2×C4×C11C2×D411yescharacteristic
116C2×C4×C11C2411yescharacteristic
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11C2×D411yescharacteristic
121C2×Dic11C2×D411yescharacteristic
122D44—21no—
123D44—21no—
124D44—41no—
125D44—42no—
126D44—81no—
127C4×D11—21no—
128C4×D11—21no—
129C4×D11—21no—
130C4×D11—21no—
131C4×D11—81no—
132C4×D11—81no—
133Dic22—21no—
134Dic22—21no—
135C8×C11—21no—
136C8×C11#4112yes—
137C11⋊C8—21no—
138C11⋊C8—21no—
139#556—111no—
140#553—111no—
141#501D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
155C2×D11—21no—
156C2×D11—21no—
157C2×D11—21no—
158C2×D11—21no—
159C2×D11—21no—
160C2×D11—21no—
161C2×D11—41no—
162C2×D11—41no—
163C2×D11—41no—
164C4×C11—21no—
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11—41no—
170C4×C11C2×#4111yescharacteristic
171C4×C112−1+411yescharacteristic
172Dic11—21no—
173Dic11—21no—
174Dic11—41no—
175Dic11—41no—
176Dic11—41no—
177C2×SD16—111no—
178C2×M16—111no—
179C22×C8—111no—
180C4⋊Q8C2×D1111yescharacteristic
181#126—221no—
182#126—221no—
183#126—221no—
184#125C2×D1111yescharacteristic
185#124—221no—
186#123—221no—
187C22⋊Q8—111no—
188C22⋊Q8—111no—
189#121—111no—
190#121—111no—
191#121—221no—
192C4×Q8—111no—
193C4×Q8—221no—
194C4×D4—111no—
195C4×D4—111no—
196C4×D4—221no—
197#117—111no—
198#117—111no—
199#117—111no—
200C2×C4⋊C4—111no—
201#107—111no—
202#107—111no—
203#107C2×D1111yescharacteristic
204#107C2×D1111yescharacteristic
205#106—111no—
206#106—111no—
207#106—111no—
208#106C2×D1111yescharacteristic
209#106C2×D1111yescharacteristic
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#97C2×D1111yescharacteristic
220C2×C11#54711yescharacteristic
221C2×C11#57511yescharacteristic
222C2×C11#57711yescharacteristic
223D11—41no—
224D11—41no—
225D11—81no—
226C2×Q8—21no—
227C2×Q8—111no—
228C2×D4—111no—
229C2×D4—111no—
230C2×D4—221no—
231C2×D4—221no—
232C22×C4—111no—
233C22×C4—111no—
234C22×C4—221no—
235C22×C4—221no—
236SD16—222no—
237M16—222no—
238C2×C8—111no—
239C2×C8—111no—
240C2×C8—222no—
241C2×C8C22×D1111yescharacteristic
242C2×C8C22×D1111yescharacteristic
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—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—
266C22⋊C4—221no—
267C42—221no—
268C42—221no—
269C42—221no—
270C42—221no—
271C42C22×D1111yescharacteristic
272C11#335011yescharacteristic, complemented, Sylow
273C23—111no—
274C23—111no—
275C23—221no—
276Q8—42no—
277Q8—221no—
278Q8—221no—
279D4—221no—
280D4—221no—
281D4—441no—
282D4—442no—
283D4—881no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—111no—
289C2×C4—111no—
290C2×C4—221no—
291C2×C4—221no—
292C2×C4—221no—
293C2×C4—221no—
294C2×C4—221no—
295C2×C4—221no—
296C2×C4—221no—
297C2×C4—881no—
298C2×C4—881no—
299C2×C4D4×D1111yescharacteristic
300C2×C4D4×D1111yescharacteristic
301C2×C4C23×D1111yescharacteristic
302C8—21no—
303C8—221no—
304C8—221no—
305C8#434312yes—
306C22—221no—
307C22—221no—
308C22—221no—
309C22—221no—
310C22—221no—
311C22—221no—
312C22—441no—
313C22—441no—
314C22—441no—
315C22C2×D4×D1111yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—221no—
323C4—221no—
324C4—441no—
325C4—441no—
326C4—441no—
327C4C2×#434311yescharacteristic
328C4#6704011yescharacteristic
329C2—441no—
330C2—441no—
331C2—881no—
332C2#1062325711yescharacteristic
333C2#1062330411yescharacteristic
334C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#501C2
socleC22×C11C22×D4
prime radical#10623226C2
hypercenter#501D11
hypocenterC11#3350
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #10623263C2semidirect
3. C11×#501C2semidirect
4. #10622697C2semidirect
5. #10622676C2semidirect
6. #10622501C2semidirect
7. #10622499C2semidirect
8. #10622498C2semidirect
9. #10622493C2semidirect
10. #10622479C2semidirect
11. #10622477C2semidirect
12. #10622475C2semidirect
13. #10622474C2semidirect
14. #10622323C2semidirect
15. #10622319C2semidirect
141. #501D11semidirect
272. C11#3350semidirect

Maximal subgroups

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

subgroupindex
#106232632
#106232262
C11×#5012
#106226972
#106226762
#106225012
#106224992
#106224982
#106224932
#106224792
#106224772
#106224752
#106224742
#106223232
#106223192
#335011