Finite Group Databasebeta

← #13079885

Subgroups — #13079885

Order 1408.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623260C211yesmaximal, characteristic
2#10623228C211yesmaximal, characteristic
3C11×#501C211yesmaximal, characteristic, complemented
4#10622706C211yesmaximal, characteristic, complemented
5#10622677C211yesmaximal, characteristic, complemented
6#10622501C211yesmaximal, characteristic
7#10622497C211yesmaximal, characteristic
8#10622490C211yesmaximal, characteristic, complemented
9#10622488C211yesmaximal, characteristic, complemented
10#10622480C211yesmaximal, characteristic
11#10622475C211yesmaximal, characteristic
12#10622470C211yesmaximal, characteristic, complemented
13#10622467C211yesmaximal, characteristic, complemented
14#10622322C211yesmaximal, characteristic
15#10622316C211yesmaximal, characteristic, complemented
16C11×C4⋊Q8C2211yescharacteristic
17C11×#125C2211yescharacteristic
18#66999—21no—
19#66997—21no—
20#66951—21no—
21#66951—21no—
22#66950C2211yescharacteristic
23#66950C2211yescharacteristic
24#66949—21no—
25#66945C2211yescharacteristic
26C4⋊C4×D11C2211yescharacteristic
27#66943—21no—
28#66943—21no—
29#66943C2211yescharacteristic
30#66942—21no—
31#66941C2211yescharacteristic
32#66940C2211yescharacteristic
33#66940C2211yescharacteristic
34#66925C2211yescharacteristic
35#66923C2211yescharacteristic
36#66922C2211yescharacteristic
37C11×#107C2211yescharacteristic
38C11×#107C2211yescharacteristic
39C11×#106C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C11×#97C2211yescharacteristic
42(C2×D11)⋊C8C2211yescharacteristic
43(C2×D11)⋊C8C2211yescharacteristic
44#66880C2211yescharacteristic
45#66880C2211yescharacteristic
46#66880C2211yescharacteristic
47#66880C2211yescharacteristic
48Dic11⋊C8C2211yescharacteristic
49Dic11⋊C8C2211yescharacteristic
50#66874C2211yescharacteristic
51#66874C2211yescharacteristic
52#66874C2211yescharacteristic
53#66874C2211yescharacteristic
54#66872C2211yescharacteristic
55#66872C2211yescharacteristic
56#66871C2211yescharacteristic
57#66871C2211yescharacteristic
58C4×C11⋊C8C2211yescharacteristic
59C2×Q8×C11—21no—
60C2×C4×D11—21no—
61C2×C4×D11C2311yescharacteristic
62C2×Dic22—21no—
63C2×Dic22C2311yescharacteristic
64C2×Dic22C2311yescharacteristic
65C2×C8×C11C2311yescharacteristic
66C2×C8×C11C2311yescharacteristic
67C11×C4⋊C4—21no—
68C11×C4⋊C4—21no—
69C11×C4⋊C4—21no—
70C11×C4⋊C4C2311yescharacteristic
71C11×C4⋊C4C2311yescharacteristic
72C11×C4⋊C4C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C42×C11C2311yescharacteristic
75(C2×D11)⋊C4—21no—
76(C2×D11)⋊C4—21no—
77(C2×D11)⋊C4—21no—
78(C2×D11)⋊C4D411yescharacteristic
79(C2×D11)⋊C4D411yescharacteristic
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11—21no—
84C4⋊Dic11—21no—
85C4⋊Dic11C2311yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87Dic11⋊C4—21no—
88Dic11⋊C4—21no—
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4D411yescharacteristic
95Dic11⋊C4D411yescharacteristic
96C4×Dic11—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11C2311yescharacteristic
100C2×C11⋊C8C2311yescharacteristic
101C2×C11⋊C8C2311yescharacteristic
102#3242—111nomaximal, Sylow
103C22×D11C2×D411yescharacteristic
104Q8×C11—81no—
105C2×C4×C11—21no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11—21no—
109C2×C4×C11C2×D411yescharacteristic
110C2×C4×C11C2×D411yescharacteristic
111C2×C4×C11C2411yescharacteristic
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11C2×D411yescharacteristic
117C2×Dic11C2×D411yescharacteristic
118C2×Dic11C2×D411yescharacteristic
119C4×D11—21no—
120C4×D11—21no—
121C4×D11—81no—
122Dic22—21no—
123Dic22—21no—
124Dic22—21no—
125Dic22—21no—
126Dic22—81no—
127C8×C11—21no—
128C8×C11—21no—
129C11⋊C8—21no—
130C11⋊C8—21no—
131#544—111no—
132#541—111no—
133#501D1111yescharacteristic, complemented
134#499—111no—
135#491—111no—
136#487—111no—
137#485—111no—
138#485—111no—
139#484—111no—
140#483—111no—
141#479—111no—
142#479—111no—
143#477—111no—
144#475—111no—
145#433—111no—
146C22×C11C22×D411yescharacteristic
147C2×D11—21no—
148C2×D11—21no—
149C2×D11—21no—
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—41no—
153C4×C11—41no—
154C4×C11—41no—
155C4×C11—41no—
156C4×C112−1+411yescharacteristic
157C4×C112−1+411yescharacteristic
158Dic11—21no—
159Dic11—21no—
160Dic11—21no—
161Dic11—41no—
162Dic11—41no—
163Dic11—41no—
164Dic11—41no—
165C4⋊Q8—111no—
166C4⋊Q8—111no—
167C4⋊Q8—221no—
168C4⋊Q8C2×D1111yescharacteristic
169#126—221no—
170#126—221no—
171#125—111no—
172#125—111no—
173#125—221no—
174#125—221no—
175#125—221no—
176#125C2×D1111yescharacteristic
177C22⋊Q8—111no—
178C22⋊Q8—111no—
179C22⋊Q8—221no—
180C22⋊Q8—221no—
181C4×Q8—111no—
182C4×Q8—111no—
183#117—111no—
184#117—111no—
185C2×C4⋊C4—111no—
186#107—111no—
187#107—111no—
188#107C2×D1111yescharacteristic
189#107C2×D1111yescharacteristic
190#106—111no—
191#106—111no—
192#106C2×D1111yescharacteristic
193#106C2×D1111yescharacteristic
194C4⋊C8—111no—
195C4⋊C8—111no—
196#103—111no—
197#103—111no—
198#103—111no—
199#103—111no—
200#103—111no—
201#103—111no—
202#103—111no—
203#103—111no—
204C22⋊C8—111no—
205C22⋊C8—111no—
206#97C2×D1111yescharacteristic
207C4×C8—111no—
208C2×C11#53611yescharacteristic
209C2×C11#57711yescharacteristic
210C2×C11#57811yescharacteristic
211D11—41no—
212C2×Q8—21no—
213C2×Q8—111no—
214C2×Q8—111no—
215C2×Q8—221no—
216C22×C4—111no—
217C22×C4—221no—
218C2×C8—111no—
219C2×C8—111no—
220C2×C8C22×D1111yescharacteristic
221C2×C8C22×D1111yescharacteristic
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—21no—
225C4⋊C4—111no—
226C4⋊C4—111no—
227C4⋊C4—111no—
228C4⋊C4—111no—
229C4⋊C4—221no—
230C4⋊C4—221no—
231C4⋊C4—221no—
232C4⋊C4—221no—
233C4⋊C4—221no—
234C4⋊C4—221no—
235C4⋊C4—221no—
236C4⋊C4—221no—
237C4⋊C4—221no—
238C4⋊C4—221no—
239C4⋊C4—221no—
240C4⋊C4—221no—
241C4⋊C4C22×D1111yescharacteristic
242C4⋊C4C22×D1111yescharacteristic
243C4⋊C4C22×D1111yescharacteristic
244C4⋊C4C22×D1111yescharacteristic
245C22⋊C4—111no—
246C22⋊C4—111no—
247C22⋊C4—221no—
248C22⋊C4—221no—
249C22⋊C4—221no—
250C42—111no—
251C42—221no—
252C42—221no—
253C42—221no—
254C42C22×D1111yescharacteristic
255C11#324211yescharacteristic, complemented, Sylow
256C23—111no—
257Q8—81no—
258Q8—221no—
259Q8—221no—
260Q8—221no—
261Q8—221no—
262Q8—881no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—111no—
268C2×C4—111no—
269C2×C4—111no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—221no—
273C2×C4—221no—
274C2×C4—221no—
275C2×C4—221no—
276C2×C4—881no—
277C2×C4D4×D1111yescharacteristic
278C2×C4D4×D1111yescharacteristic
279C2×C4C23×D1111yescharacteristic
280C8—21no—
281C8—21no—
282C8—221no—
283C8—221no—
284C22—221no—
285C22—221no—
286C22—221no—
287C22C2×D4×D1111yescharacteristic
288C4—21no—
289C4—21no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—221no—
295C4—221no—
296C4—221no—
297C4—441no—
298C4—441no—
299C4—441no—
300C4—441no—
301C4#6704011yescharacteristic
302C4#6704011yescharacteristic
303C2—441no—
304C2#1062325511yescharacteristic
305C2#1062330611yescharacteristic
306C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#501C2
socleC22×C11C22×D4
prime radicalC22×D11C2×D4
hypercenter#501D11
hypocenterC11#3242
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
3. C11×#501C2semidirect
4. #10622706C2semidirect
5. #10622677C2semidirect
8. #10622490C2semidirect
9. #10622488C2semidirect
12. #10622470C2semidirect
13. #10622467C2semidirect
15. #10622316C2semidirect
133. #501D11semidirect
255. C11#3242semidirect

Maximal subgroups

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

subgroupindex
#106232602
#106232282
C11×#5012
#106227062
#106226772
#106225012
#106224972
#106224902
#106224882
#106224802
#106224752
#106224702
#106224672
#106223222
#106223162
#324211