Finite Group Databasebeta

← #13078840

Subgroups — #13078840

Order 1408.

370 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623134C211yesmaximal, characteristic
2#10623047C211yesmaximal, characteristic, complemented
3C11×#482C211yesmaximal, characteristic
4#10622653C211yesmaximal, characteristic
5#10622609C211yesmaximal, characteristic, complemented
6#10622488C211yesmaximal, characteristic, complemented
7#10622486C211yesmaximal, characteristic, complemented
8#10622467C211yesmaximal, characteristic, complemented
9#10622466C211yesmaximal, characteristic, complemented
10#10622380C211yesmaximal, characteristic, complemented
11#10622380C211yesmaximal, characteristic, complemented
12#10622371C211yesmaximal, characteristic, complemented
13#10622370C211yesmaximal, characteristic, complemented
14#10622352C211yesmaximal, characteristic, complemented
15#10622333C211yesmaximal, characteristic, complemented
16C22×Dic22C2211yescharacteristic
17C11×#121C2211yescharacteristic
18C11×#117C2211yescharacteristic
19#66989—21no—
20#66989C2211yescharacteristic
21#66988—21no—
22D4×Dic11C2211yescharacteristic
23C2×#4324C2211yescharacteristic
24C2×#4324C2211yescharacteristic
25#66979C2211yescharacteristic
26#66977C2211yescharacteristic
27C2×Dic44C2211yescharacteristic
28C2×Dic44C2211yescharacteristic
29#66941C2211yescharacteristic
30#66940C2211yescharacteristic
31#66940C2211yescharacteristic
32#66940C2211yescharacteristic
33#66940C2211yescharacteristic
34#66940C2211yescharacteristic
35#66932—21no—
36#66931—21no—
37#66930—21no—
38#66930—21no—
39C4×Dic22—21no—
40C4×Dic22—21no—
41C11×#107C2211yescharacteristic
42C11×#106C2211yescharacteristic
43C11×#102C2211yescharacteristic
44C11×#102C2211yescharacteristic
45C11×C22⋊C8C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic
47#66880C2211yescharacteristic
48#66880C2211yescharacteristic
49#66879C2211yescharacteristic
50Dic11⋊C8C2211yescharacteristic
51Dic11⋊C8C2211yescharacteristic
52C8×Dic11C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66874C2211yescharacteristic
56#66874C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×D4×C11—21no—
60C2×D4×C11C2311yescharacteristic
61C22×C4×C11C2311yescharacteristic
62C22×Dic11—21no—
63C22×Dic11—21no—
64C2×Dic22—22no—
65C2×Dic22—22no—
66C2×Dic22—21no—
67C2×Dic22—21no—
68C2×Dic22C2311yescharacteristic
69C2×Dic22C2311yescharacteristic
70C2×Dic22C2311yescharacteristic
71C2×C8×C11C2311yescharacteristic
72C2×C8×C11C2311yescharacteristic
73C11×C4⋊C4C2311yescharacteristic
74C11×C4⋊C4C2311yescharacteristic
75C11×C4⋊C4C2311yescharacteristic
76C11×C22⋊C4—21no—
77C11×C22⋊C4—21no—
78C42×C11—21no—
79C22⋊Dic11—21no—
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11D411yescharacteristic
84C22⋊Dic11D411yescharacteristic
85#4324—22no—
86#4324—22no—
87C4⋊Dic11D411yescharacteristic
88C4⋊Dic11D411yescharacteristic
89C4⋊Dic11C2311yescharacteristic
90Dic11⋊C4—21no—
91Dic11⋊C4—21no—
92Dic11⋊C4—21no—
93Dic11⋊C4—21no—
94Dic11⋊C4—21no—
95Dic11⋊C4—21no—
96Dic11⋊C4—21no—
97C4×Dic11—21no—
98C4×Dic11—21no—
99C4×Dic11—21no—
100C4×Dic11—21no—
101C4×Dic11—21no—
102C4×Dic11C2311yescharacteristic
103C4×Dic11C2311yescharacteristic
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106Dic44—22no—
107Dic44—22no—
108#3121—111nomaximal, Sylow
109C23×C11—21no—
110C23×C11C2×D411yescharacteristic
111D4×C11—21no—
112D4×C11—21no—
113D4×C11—81no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11C2×D411yescharacteristic
120C2×C4×C11C2411yescharacteristic
121C2×Dic11—24no—
122C2×Dic11—21no—
123C2×Dic11—21no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—81no—
127C2×Dic11C2×D411yescharacteristic
128C2×Dic11C2×D411yescharacteristic
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131Dic22—24no—
132Dic22—21no—
133Dic22—21no—
134Dic22—21no—
135Dic22—21no—
136Dic22—81no—
137Dic22#4112yes—
138Dic22#4112yes—
139C8×C11—21no—
140C8×C11—21no—
141C11⋊C8—21no—
142C11⋊C8—21no—
143#542—111no—
144#519—111no—
145#485—111no—
146#482D1111yescharacteristic
147#477—111no—
148#475—111no—
149#464—111no—
150#464—111no—
151#451—111no—
152#448—111no—
153#441—111no—
154#440—111no—
155C4×Q16—111no—
156C4×SD16—111no—
157#433—111no—
158C22×C11—21no—
159C22×C11—21no—
160C22×C11—21no—
161C22×C11—41no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11C22×D411yescharacteristic
165C4×C11—21no—
166C4×C11—41no—
167C4×C11—41no—
168C4×C11—41no—
169C4×C11C2×#4111yescharacteristic
170C4×C11C2×#4111yescharacteristic
171Dic11—22no—
172Dic11—22no—
173Dic11—21no—
174Dic11—21no—
175Dic11—21no—
176Dic11—21no—
177Dic11—41no—
178Dic11—41no—
179C22×Q8—111no—
180C2×Q16—111no—
181C2×Q16—111no—
182C2×SD16—111no—
183C2×SD16—111no—
184C4⋊Q8—111no—
185#126—221no—
186#124—111no—
187#124—221no—
188#123—221no—
189C22⋊Q8—111no—
190C22⋊Q8—221no—
191#121C2×D1111yescharacteristic
192C4×Q8—111no—
193C4×Q8—111no—
194C4×Q8—111no—
195C4×Q8—111no—
196C4×Q8—111no—
197C4×Q8—221no—
198C4×Q8—221no—
199C4×D4—111no—
200#117—111no—
201#117—221no—
202#117—221no—
203#117C2×D1111yescharacteristic
204#107—111no—
205#107C2×D1111yescharacteristic
206#106—111no—
207#106C2×D1111yescharacteristic
208C4⋊C8—111no—
209C4⋊C8—111no—
210#103—111no—
211#103—111no—
212#103—111no—
213#103—111no—
214#103—111no—
215#103—111no—
216#102C2×D1111yescharacteristic
217#102C2×D1111yescharacteristic
218C22⋊C8—111no—
219C22⋊C8C2×D1111yescharacteristic
220#97—111no—
221C4×C8—111no—
222C2×C11—41no—
223C2×C11—81no—
224C2×C11#52511yescharacteristic
225C2×C11#57711yescharacteristic
226C2×C11#57811yescharacteristic
227C2×Q8—111no—
228C2×Q8—111no—
229C2×Q8—111no—
230C2×Q8—221no—
231C2×Q8—222no—
232C2×Q8—222no—
233C2×Q8—221no—
234C2×D4—21no—
235C2×D4C22×D1111yescharacteristic
236C22×C4—221no—
237C22×C4—221no—
238C22×C4C22×D1111yescharacteristic
239Q16—222no—
240Q16—222no—
241SD16—222no—
242SD16—222no—
243C2×C8—111no—
244C2×C8—111no—
245C2×C8C22×D1111yescharacteristic
246C2×C8C22×D1111yescharacteristic
247C4⋊C4—111no—
248C4⋊C4—111no—
249C4⋊C4—111no—
250C4⋊C4—221no—
251C4⋊C4—221no—
252C4⋊C4—221no—
253C4⋊C4—221no—
254C4⋊C4—221no—
255C4⋊C4—221no—
256C4⋊C4—221no—
257C4⋊C4C22×D1111yescharacteristic
258C4⋊C4C22×D1111yescharacteristic
259C4⋊C4C22×D1111yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—111no—
263C22⋊C4—111no—
264C22⋊C4—221no—
265C22⋊C4—221no—
266C22⋊C4—221no—
267C22⋊C4—221no—
268C42—21no—
269C42—111no—
270C42—111no—
271C42—221no—
272C42—221no—
273C42—221no—
274C42—221no—
275C42—221no—
276C11#312111yescharacteristic, complemented, Sylow
277C23—21no—
278C23D4×D1111yescharacteristic
279Q8—112no—
280Q8—112no—
281Q8—224no—
282Q8—221no—
283Q8—221no—
284Q8—221no—
285Q8—221no—
286Q8—881no—
287D4—21no—
288D4—21no—
289D4—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—111no—
296C2×C4—111no—
297C2×C4—111no—
298C2×C4—111no—
299C2×C4—224no—
300C2×C4—221no—
301C2×C4—221no—
302C2×C4—221no—
303C2×C4—221no—
304C2×C4—881no—
305C2×C4D4×D1111yescharacteristic
306C2×C4C23×D1111yescharacteristic
307C8—21no—
308C8—21no—
309C8—221no—
310C8—221no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22C2×D4×D1111yescharacteristic
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—221no—
323C4—221no—
324C4—221no—
325C4—221no—
326C4—222no—
327C4—222no—
328C4—441no—
329C4—441no—
330C4#41×D1111yescharacteristic
331C4#41×D1111yescharacteristic
332C2—41no—
333C2—81no—
334C2#1062318711yescharacteristic
335C2#1062330211yescharacteristic
336C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#482C2
socleC22×C11C22×D4
prime radicalC11×#121C22
hypercenter#482D11
hypocenterC11#3121
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
2. #10623047C2semidirect
5. #10622609C2semidirect
6. #10622488C2semidirect
7. #10622486C2semidirect
8. #10622467C2semidirect
9. #10622466C2semidirect
10. #10622380C2semidirect
11. #10622380C2semidirect
12. #10622371C2semidirect
13. #10622370C2semidirect
14. #10622352C2semidirect
15. #10622333C2semidirect
276. C11#3121semidirect

Maximal subgroups

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

subgroupindex
#106231342
#106230472
C11×#4822
#106226532
#106226092
#106224882
#106224862
#106224672
#106224662
#106223802
#106223712
#106223702
#106223522
#106223332
#312111