Finite Group Databasebeta

← #13079913

Subgroups — #13079913

Order 1408.

320 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623220C211yesmaximal, characteristic, complemented
2#10623092C211yesmaximal, characteristic
3C11×#478C211yesmaximal, characteristic, complemented
4#10622676C211yesmaximal, characteristic, complemented
5#10622621C211yesmaximal, characteristic, complemented
6#10622501C211yesmaximal, characteristic, complemented
7#10622489C211yesmaximal, characteristic, complemented
8#10622475C211yesmaximal, characteristic, complemented
9#10622468C211yesmaximal, characteristic, complemented
10#10622464C211yesmaximal, characteristic, complemented
11#10622453C211yesmaximal, characteristic, complemented
12#10622392C211yesmaximal, characteristic
13#10622390C211yesmaximal, characteristic
14#10622381C211yesmaximal, characteristic, complemented
15#10622378C211yesmaximal, characteristic, complemented
16C11×#125C2211yescharacteristic
17C4×D4×C11C2211yescharacteristic
18#66991C2211yescharacteristic
19#66989C2211yescharacteristic
20#66982—21no—
21#66977—21no—
22#66950—21no—
23#66950C2211yescharacteristic
24#66949—21no—
25#66945C2211yescharacteristic
26C4⋊C4×D11C2211yescharacteristic
27#66943C2211yescharacteristic
28#66942—21no—
29#66941—21no—
30#66941C2211yescharacteristic
31#66941C2211yescharacteristic
32#66938—21no—
33#66932—21no—
34#66925C2211yescharacteristic
35#66922C2211yescharacteristic
36C4×Dic22C2211yescharacteristic
37C11×#107C2211yescharacteristic
38C11×#106C2211yescharacteristic
39C11×C4⋊C8C2211yescharacteristic
40C11×#102C2211yescharacteristic
41C11×#102C2211yescharacteristic
42#66896C2211yescharacteristic
43#66896C2211yescharacteristic
44(C2×D11)⋊C8C2211yescharacteristic
45(C2×D11)⋊C8C2211yescharacteristic
46#66881C2211yescharacteristic
47#66881C2211yescharacteristic
48#66880C2211yescharacteristic
49#66880C2211yescharacteristic
50#66879C2211yescharacteristic
51C8×Dic11C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66871C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×D4×C11C2311yescharacteristic
60C22×C4×C11—21no—
61C2×C22⋊D11—21no—
62C2×C4×D11—21no—
63C2×C4×D11C2311yescharacteristic
64C2×Dic22—21no—
65C2×Dic22—21no—
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C22⋊C4—21no—
76C42×C11C2311yescharacteristic
77C22⋊Dic11—21no—
78C22⋊Dic11—21no—
79C22⋊Dic11—21no—
80(C2×D11)⋊C4—21no—
81(C2×D11)⋊C4—21no—
82(C2×D11)⋊C4D411yescharacteristic
83(C2×D11)⋊C4D411yescharacteristic
84C4⋊Dic11—21no—
85C4⋊Dic11—21no—
86C4⋊Dic11—21no—
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4D411yescharacteristic
96Dic11⋊C4D411yescharacteristic
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3244—111nomaximal, Sylow
103C23×C11—21no—
104C22×D11C2×D411yescharacteristic
105D4×C11—21no—
106D4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11—81no—
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2×D411yescharacteristic
113C2×C4×C11C2411yescharacteristic
114C22⋊D11—81no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11C2×D411yescharacteristic
120C2×Dic11C2×D411yescharacteristic
121C2×Dic11C2×D411yescharacteristic
122C4×D11—21no—
123C4×D11—21no—
124C4×D11—81no—
125Dic22—21no—
126Dic22—21no—
127Dic22—81no—
128Dic22—81no—
129Dic22—81no—
130C8×C11—21no—
131C8×C11—21no—
132C11⋊C8—21no—
133C11⋊C8—21no—
134#544—111no—
135#542—111no—
136#501—111no—
137#498—111no—
138#489—111no—
139#488—111no—
140#485—111no—
141#483—111no—
142#482—111no—
143#481—111no—
144#479—111no—
145#478D1111yescharacteristic, complemented
146#476—111no—
147#475—111no—
148#433—111no—
149C22×C11—41no—
150C22×C11—41no—
151C22×C11—41no—
152C22×C11C22×D411yescharacteristic
153C2×D11—21no—
154C2×D11—21no—
155C2×D11—21no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C112−1+411yescharacteristic
162C4×C112−1+411yescharacteristic
163Dic11—21no—
164Dic11—21no—
165Dic11—21no—
166Dic11—41no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170C4⋊Q8—111no—
171C4⋊Q8—111no—
172C4⋊Q8—111no—
173C4⋊Q8—221no—
174#126—221no—
175#125—111no—
176#125—221no—
177#125C2×D1111yescharacteristic
178#124—111no—
179#124—221no—
180#123—221no—
181C22⋊Q8—111no—
182C22⋊Q8—221no—
183C22⋊Q8—221no—
184C22⋊Q8—221no—
185#121—111no—
186C4×Q8—111no—
187C4×D4C2×D1111yescharacteristic
188#117—111no—
189#117—111no—
190C2×C4⋊C4—111no—
191#107—111no—
192#107C2×D1111yescharacteristic
193#106—111no—
194#106—111no—
195#106—111no—
196#106—111no—
197#106—111no—
198#106C2×D1111yescharacteristic
199C4⋊C8—111no—
200C4⋊C8C2×D1111yescharacteristic
201#103—111no—
202#103—111no—
203#103—111no—
204#103—111no—
205#102—111no—
206#102—111no—
207#102C2×D1111yescharacteristic
208#102C2×D1111yescharacteristic
209C22⋊C8—111no—
210C22⋊C8—111no—
211#97—111no—
212C4×C8—111no—
213C2×C11—81no—
214C2×C11#53611yescharacteristic
215C2×C11#57711yescharacteristic
216C2×C11#57711yescharacteristic
217D11—41no—
218C2×Q8—111no—
219C2×Q8—221no—
220C2×Q8—221no—
221C2×Q8—221no—
222C2×D4—221no—
223C2×D4C22×D1111yescharacteristic
224C22×C4—21no—
225C22×C4—111no—
226C22×C4—221no—
227C2×C8—111no—
228C2×C8—111no—
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—111no—
234C4⋊C4—111no—
235C4⋊C4—111no—
236C4⋊C4—111no—
237C4⋊C4—111no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—221no—
246C4⋊C4C22×D1111yescharacteristic
247C4⋊C4C22×D1111yescharacteristic
248C4⋊C4C22×D1111yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—111no—
251C22⋊C4—111no—
252C22⋊C4—221no—
253C22⋊C4—221no—
254C22⋊C4—221no—
255C22⋊C4—221no—
256C22⋊C4—221no—
257C42—111no—
258C42—221no—
259C42—221no—
260C42C22×D1111yescharacteristic
261C11#324411yescharacteristic, complemented, Sylow
262C23—21no—
263C23—111no—
264Q8—221no—
265Q8—221no—
266Q8—881no—
267Q8—881no—
268Q8—881no—
269D4—21no—
270D4—21no—
271D4—881no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—81no—
276C2×C4—111no—
277C2×C4—111no—
278C2×C4—111no—
279C2×C4—221no—
280C2×C4—221no—
281C2×C4—221no—
282C2×C4—221no—
283C2×C4—221no—
284C2×C4—221no—
285C2×C4—881no—
286C2×C4D4×D1111yescharacteristic
287C2×C4D4×D1111yescharacteristic
288C2×C4C23×D1111yescharacteristic
289C8—21no—
290C8—21no—
291C8—221no—
292C8—221no—
293C22—41no—
294C22—41no—
295C22—41no—
296C22—221no—
297C22—221no—
298C22—221no—
299C22C2×D4×D1111yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—221no—
306C4—221no—
307C4—221no—
308C4—441no—
309C4—441no—
310C4—441no—
311C4—441no—
312C4#6704011yescharacteristic
313C4#6704311yescharacteristic
314C2—81no—
315C2—441no—
316C2#1062315911yescharacteristic
317C2#1062330111yescharacteristic
318C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#478C2
socleC22×C11C22×D4
prime radical#66991C22
hypercenter#478D11
hypocenterC11#3244
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #10623220C2semidirect
3. C11×#478C2semidirect
4. #10622676C2semidirect
5. #10622621C2semidirect
6. #10622501C2semidirect
7. #10622489C2semidirect
8. #10622475C2semidirect
9. #10622468C2semidirect
10. #10622464C2semidirect
11. #10622453C2semidirect
14. #10622381C2semidirect
15. #10622378C2semidirect
145. #478D11semidirect
261. C11#3244semidirect

Maximal subgroups

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

subgroupindex
#106232202
#106230922
C11×#4782
#106226762
#106226212
#106225012
#106224892
#106224752
#106224682
#106224642
#106224532
#106223922
#106223902
#106223812
#106223782
#324411