Finite Group Databasebeta

← #13079886

Subgroups — #13079886

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#10623050C211yesmaximal, characteristic
2#10623049C211yesmaximal, characteristic
3C11×#433C211yesmaximal, characteristic
4#10622464C211yesmaximal, characteristic, complemented
5#10622463C211yesmaximal, characteristic, complemented
6#10622442C211yesmaximal, characteristic, complemented
7#10622442C211yesmaximal, characteristic, complemented
8#10622336C211yesmaximal, characteristic
9#10622336C211yesmaximal, characteristic
10#10622335C211yesmaximal, characteristic
11#10622334C211yesmaximal, characteristic
12#10622316C211yesmaximal, characteristic, complemented
13#10622315C211yesmaximal, characteristic, complemented
14#10622296C211yesmaximal, characteristic, complemented
15#10622294C211yesmaximal, characteristic, complemented
16C11×#117C2211yescharacteristic
17#66979C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19#66977C2211yescharacteristic
20#66977C2211yescharacteristic
21#66943—21no—
22#66942—21no—
23#66942—21no—
24#66941—21no—
25#66932—21no—
26#66932—21no—
27#66931—21no—
28#66931—21no—
29#66923C2211yescharacteristic
30#66923C2211yescharacteristic
31#66923C2211yescharacteristic
32#66922C2211yescharacteristic
33#66922C2211yescharacteristic
34#66922C2211yescharacteristic
35C4×Dic22C2211yescharacteristic
36C4×Dic22C2211yescharacteristic
37C11×C4⋊C8C2211yescharacteristic
38C11×C4⋊C8C2211yescharacteristic
39C11×C22⋊C8C2211yescharacteristic
40C11×C22⋊C8C2211yescharacteristic
41C11×#97C2211yescharacteristic
42C4×C8×C11C2211yescharacteristic
43#66882C2211yescharacteristic
44#66882C2211yescharacteristic
45#66882C2211yescharacteristic
46#66882C2211yescharacteristic
47#66881C2211yescharacteristic
48#66881C2211yescharacteristic
49#66881C2211yescharacteristic
50#66881C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66880C2211yescharacteristic
55#66880C2211yescharacteristic
56#66880C2211yescharacteristic
57#66880C2211yescharacteristic
58#66880C2211yescharacteristic
59C22×C4×C11C2311yescharacteristic
60C22×Dic11—21no—
61C2×Dic22—21no—
62C2×Dic22—21no—
63C2×Dic22C2311yescharacteristic
64C2×Dic22C2311yescharacteristic
65C2×C8×C11C2311yescharacteristic
66C2×C8×C11C2311yescharacteristic
67C2×C8×C11C2311yescharacteristic
68C2×C8×C11C2311yescharacteristic
69C11×C4⋊C4D411yescharacteristic
70C11×C4⋊C4D411yescharacteristic
71C11×C22⋊C4D411yescharacteristic
72C11×C22⋊C4D411yescharacteristic
73C42×C11C2311yescharacteristic
74C42×C11C2311yescharacteristic
75C22⋊Dic11—21no—
76C22⋊Dic11—21no—
77C22⋊Dic11—21no—
78C4⋊Dic11—21no—
79C4⋊Dic11—21no—
80C4⋊Dic11—21no—
81C4⋊Dic11—21no—
82C4⋊Dic11—21no—
83C4⋊Dic11C2311yescharacteristic
84C4⋊Dic11C2311yescharacteristic
85C4⋊Dic11C2311yescharacteristic
86C4⋊Dic11C2311yescharacteristic
87C4⋊Dic11C2311yescharacteristic
88C4⋊Dic11C2311yescharacteristic
89Dic11⋊C4—21no—
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102#3242—111nomaximal, Sylow
103C23×C11C2×D411yescharacteristic
104C2×C4×C11—21no—
105C2×C4×C11—21no—
106C2×C4×C11C2×D411yescharacteristic
107C2×C4×C11C2×D411yescharacteristic
108C2×C4×C11C2×D411yescharacteristic
109C2×C4×C11C2×D411yescharacteristic
110C2×C4×C11C2×D411yescharacteristic
111C2×C4×C11C2411yescharacteristic
112C2×Dic11—21no—
113C2×Dic11—21no—
114C2×Dic11—21no—
115C2×Dic11—21no—
116C2×Dic11—21no—
117C2×Dic11—21no—
118C2×Dic11—21no—
119C2×Dic11—21no—
120C2×Dic11—81no—
121Dic22—21no—
122Dic22—21no—
123Dic22—21no—
124Dic22—21no—
125Dic22—81no—
126Dic22—81no—
127C8×C11—21no—
128C8×C11—21no—
129C8×C11—21no—
130C8×C11—21no—
131#544—111no—
132#541—111no—
133#501—111no—
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#433D1111yescharacteristic
146C22×C11—21no—
147C22×C11—21no—
148C22×C11—21no—
149C22×C11C22×D411yescharacteristic
150C4×C11—21no—
151C4×C11—21no—
152C4×C11—21no—
153C4×C11—21no—
154C4×C11—21no—
155C4×C112−1+411yescharacteristic
156C4×C112−1+411yescharacteristic
157Dic11—41no—
158Dic11—41no—
159Dic11—41no—
160Dic11—41no—
161Dic11—41no—
162Dic11—41no—
163Dic11—41no—
164Dic11—41no—
165C4⋊Q8—111no—
166C4⋊Q8—111no—
167C4⋊Q8—111no—
168C4⋊Q8—221no—
169#126—221no—
170#126—221no—
171#125—111no—
172#125—111no—
173#125—111no—
174#125—221no—
175#125—221no—
176#125—221no—
177C22⋊Q8—111no—
178C22⋊Q8—111no—
179C22⋊Q8—221no—
180C22⋊Q8—221no—
181C4×Q8—111no—
182C4×Q8—111no—
183#117—111no—
184#117C2×D1111yescharacteristic
185C2×C4⋊C4—111no—
186#107—111no—
187#107—111no—
188#107—111no—
189#107—111no—
190#106—111no—
191#106—111no—
192#106—111no—
193#106—111no—
194C4⋊C8C2×D1111yescharacteristic
195C4⋊C8C2×D1111yescharacteristic
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⋊C8C2×D1111yescharacteristic
205C22⋊C8C2×D1111yescharacteristic
206#97C2×D1111yescharacteristic
207C4×C8C2×D1111yescharacteristic
208C2×C11—41no—
209C2×C11#53611yescharacteristic
210C2×C11#57711yescharacteristic
211C2×C11#57811yescharacteristic
212C2×Q8—111no—
213C2×Q8—111no—
214C2×Q8—221no—
215C2×Q8—221no—
216C22×C4—221no—
217C22×C4C22×D1111yescharacteristic
218C2×C8C22×D1111yescharacteristic
219C2×C8C22×D1111yescharacteristic
220C2×C8C22×D1111yescharacteristic
221C2×C8C22×D1111yescharacteristic
222C4⋊C4—111no—
223C4⋊C4—111no—
224C4⋊C4—111no—
225C4⋊C4—111no—
226C4⋊C4—111no—
227C4⋊C4—111no—
228C4⋊C4—221no—
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⋊C4—221no—
242C4⋊C4—221no—
243C4⋊C4D4411yescharacteristic
244C4⋊C4D4411yescharacteristic
245C22⋊C4—221no—
246C22⋊C4—221no—
247C22⋊C4—221no—
248C22⋊C4D4411yescharacteristic
249C22⋊C4D4411yescharacteristic
250C42—221no—
251C42—221no—
252C42—221no—
253C42C22×D1111yescharacteristic
254C42C22×D1111yescharacteristic
255C11#324211yescharacteristic, complemented, Sylow
256C23C2×D4411yescharacteristic
257Q8—221no—
258Q8—221no—
259Q8—221no—
260Q8—221no—
261Q8—881no—
262Q8—881no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—221no—
266C2×C4—221no—
267C2×C4—221no—
268C2×C4—221no—
269C2×C4—221no—
270C2×C4—221no—
271C2×C4—221no—
272C2×C4—221no—
273C2×C4—881no—
274C2×C4C2×D4411yescharacteristic
275C2×C4C2×D4411yescharacteristic
276C2×C4C2×D4411yescharacteristic
277C2×C4C2×D4411yescharacteristic
278C2×C4C2×D4411yescharacteristic
279C2×C4C23×D1111yescharacteristic
280C8—21no—
281C8—21no—
282C8—21no—
283C8—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C22×D4411yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—441no—
294C4—441no—
295C4—441no—
296C4—441no—
297C4—441no—
298C4—441no—
299C4—441no—
300C4—441no—
301C4#6704311yescharacteristic
302C4#6704311yescharacteristic
303C2—41no—
304C2#1062305711yescharacteristic
305C2#1062328211yescharacteristic
306C2#1062328411yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#433C2
socleC22×C11C22×D4
prime radicalC23×C11C2×D4
hypercenter#433D11
hypocenterC11#3242
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
4. #10622464C2semidirect
5. #10622463C2semidirect
6. #10622442C2semidirect
7. #10622442C2semidirect
12. #10622316C2semidirect
13. #10622315C2semidirect
14. #10622296C2semidirect
15. #10622294C2semidirect
255. C11#3242semidirect

Maximal subgroups

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

subgroupindex
#106230502
#106230492
C11×#4332
#106224642
#106224632
#106224422
#106223362
#106223352
#106223342
#106223162
#106223152
#106222962
#106222942
#324211