Finite Group Databasebeta

← #13079915

Subgroups — #13079915

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#10623264C211yesmaximal, characteristic
2#10623220C211yesmaximal, characteristic, complemented
3C11×#501C211yesmaximal, characteristic, complemented
4#10622692C211yesmaximal, characteristic, complemented
5#10622681C211yesmaximal, characteristic, complemented
6#10622504C211yesmaximal, characteristic, complemented
7#10622501C211yesmaximal, characteristic, complemented
8#10622498C211yesmaximal, characteristic
9#10622490C211yesmaximal, characteristic, complemented
10#10622483C211yesmaximal, characteristic, complemented
11#10622476C211yesmaximal, characteristic
12#10622475C211yesmaximal, characteristic, complemented
13#10622467C211yesmaximal, characteristic, complemented
14#10622327C211yesmaximal, characteristic, complemented
15#10622322C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#125C2211yescharacteristic
18#67000—21no—
19#66999—21no—
20#66951—21no—
21#66950—21no—
22#66950C2211yescharacteristic
23#66949—21no—
24#66948C2211yescharacteristic
25#66947—21no—
26#66946C2211yescharacteristic
27#66945C2211yescharacteristic
28C4⋊C4×D11C2211yescharacteristic
29#66943C2211yescharacteristic
30#66942—21no—
31#66941—21no—
32#66941C2211yescharacteristic
33#66940C2211yescharacteristic
34#66928C2211yescharacteristic
35#66925C2211yescharacteristic
36#66922C2211yescharacteristic
37C11×#107C2211yescharacteristic
38C11×#107C2211yescharacteristic
39C11×#106C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C11×#97C2211yescharacteristic
42#66885C2211yescharacteristic
43#66885C2211yescharacteristic
44(C2×D11)⋊C8C2211yescharacteristic
45(C2×D11)⋊C8C2211yescharacteristic
46#66880C2211yescharacteristic
47#66880C2211yescharacteristic
48Dic11⋊C8C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50#66874C2211yescharacteristic
51#66874C2211yescharacteristic
52#66873C2211yescharacteristic
53#66873C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×D44—21no—
61C2×D44C2311yescharacteristic
62C2×C4×D11—21no—
63C2×C4×D11—21no—
64C2×C4×D11C2311yescharacteristic
65C2×Dic22—21no—
66C2×Dic22—21no—
67C2×Dic22C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C2×C8×C11C2311yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4—21no—
72C11×C4⋊C4—21no—
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C4⋊C4C2311yescharacteristic
77C42×C11C2311yescharacteristic
78(C2×D11)⋊C4—21no—
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)⋊C4D411yescharacteristic
85(C2×D11)⋊C4D411yescharacteristic
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88C4⋊Dic11—21no—
89C4⋊Dic11C2311yescharacteristic
90C4⋊Dic11C2311yescharacteristic
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
103C22×D11—21no—
104C22×D11C2×D411yescharacteristic
105Q8×C11—81no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11—21no—
110C2×C4×C11C2×D411yescharacteristic
111C2×C4×C11C2×D411yescharacteristic
112C2×C4×C11C2411yescharacteristic
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11C2×D411yescharacteristic
117C2×Dic11C2×D411yescharacteristic
118C2×Dic11C2×D411yescharacteristic
119D44—21no—
120D44—21no—
121D44—81no—
122C4×D11—21no—
123C4×D11—21no—
124C4×D11—81no—
125C4×D11—81no—
126Dic22—21no—
127Dic22—21no—
128Dic22—81no—
129Dic22—81no—
130C8×C11—21no—
131C8×C11—21no—
132C11⋊C8—21no—
133C11⋊C8—21no—
134#544—111no—
135#542—111no—
136#501D1111yescharacteristic, complemented
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#478—111no—
146#476—111no—
147#475—111no—
148#433—111no—
149C22×C11C22×D411yescharacteristic
150C2×D11—21no—
151C2×D11—21no—
152C2×D11—21no—
153C2×D11—41no—
154C2×D11—41no—
155C2×D11—41no—
156C4×C11—21no—
157C4×C11—21no—
158C4×C11—41no—
159C4×C11—41no—
160C4×C11—41no—
161C4×C11—41no—
162C4×C112−1+411yescharacteristic
163C4×C112−1+411yescharacteristic
164Dic11—21no—
165Dic11—21no—
166Dic11—21no—
167Dic11—41no—
168Dic11—41no—
169Dic11—41no—
170C4⋊Q8—111no—
171C4⋊Q8—111no—
172C4⋊Q8—221no—
173C4⋊Q8C2×D1111yescharacteristic
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×D4—111no—
188#117—111no—
189#117—111no—
190C2×C4⋊C4—111no—
191#107C2×D1111yescharacteristic
192#107C2×D1111yescharacteristic
193#106—111no—
194#106—111no—
195#106—111no—
196#106—111no—
197#106C2×D1111yescharacteristic
198#106C2×D1111yescharacteristic
199C4⋊C8—111no—
200C4⋊C8—111no—
201#103—111no—
202#103—111no—
203#103—111no—
204#103—111no—
205#102—111no—
206#102—111no—
207#102—111no—
208#102—111no—
209C22⋊C8—111no—
210C22⋊C8—111no—
211#97C2×D1111yescharacteristic
212C4×C8—111no—
213C2×C11#53611yescharacteristic
214C2×C11#57711yescharacteristic
215C2×C11#57711yescharacteristic
216D11—41no—
217D11—81no—
218C2×Q8—21no—
219C2×Q8—111no—
220C2×Q8—221no—
221C2×Q8—221no—
222C2×D4—111no—
223C2×D4—221no—
224C22×C4—111no—
225C22×C4—221no—
226C22×C4—221no—
227C2×C8—111no—
228C2×C8—111no—
229C2×C8C22×D1111yescharacteristic
230C2×C8C22×D1111yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
246C4⋊C4C22×D1111yescharacteristic
247C4⋊C4C22×D1111yescharacteristic
248C4⋊C4C22×D1111yescharacteristic
249C22⋊C4—111no—
250C22⋊C4—111no—
251C22⋊C4—221no—
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—111no—
263C23—221no—
264Q8—81no—
265Q8—221no—
266Q8—221no—
267Q8—881no—
268Q8—881no—
269D4—221no—
270D4—221no—
271D4—881no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
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—881no—
285C2×C4—881no—
286C2×C4D4×D1111yescharacteristic
287C2×C4D4×D1111yescharacteristic
288C2×C4C23×D1111yescharacteristic
289C8—21no—
290C8—21no—
291C8—221no—
292C8—221no—
293C22—221no—
294C22—221no—
295C22—221no—
296C22—441no—
297C22—441no—
298C22—441no—
299C22C2×D4×D1111yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—221no—
307C4—221no—
308C4—221no—
309C4—441no—
310C4—441no—
311C4—441no—
312C4#6704011yescharacteristic
313C4#6704011yescharacteristic
314C2—441no—
315C2—881no—
316C2#1062325511yescharacteristic
317C2#1062330611yescharacteristic
318C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#501C2
socleC22×C11C22×D4
prime radical#66948C22
hypercenter#501D11
hypocenterC11#3244
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
2. #10623220C2semidirect
3. C11×#501C2semidirect
4. #10622692C2semidirect
5. #10622681C2semidirect
6. #10622504C2semidirect
7. #10622501C2semidirect
9. #10622490C2semidirect
10. #10622483C2semidirect
12. #10622475C2semidirect
13. #10622467C2semidirect
14. #10622327C2semidirect
15. #10622322C2semidirect
136. #501D11semidirect
261. C11#3244semidirect

Maximal subgroups

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

subgroupindex
#106232642
#106232202
C11×#5012
#106226922
#106226812
#106225042
#106225012
#106224982
#106224902
#106224832
#106224762
#106224752
#106224672
#106223272
#106223222
#324411