Finite Group Databasebeta

← #14724534

Subgroups — #14724534

Order 2816.

606 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077592C212yesmaximal, complemented
2#13067495C212yesmaximal, complemented
3#13067488C212yesmaximal, complemented
4#13067481C212yesmaximal, complemented
5#13067474C212yesmaximal, complemented
6#13067379C211yesmaximal, characteristic, complemented
7#13067076C212yesmaximal, complemented
8C2×#10622092C211yesmaximal, characteristic, complemented
9C11×#3168C211yesmaximal, characteristic
10C11×#529C2212yes—
11C11×#499C411yescharacteristic
12C11×#495C411yescharacteristic
13C11×#488C412yes—
14C11×#467C411yescharacteristic
15C11×#466C411yescharacteristic
16C11×#465C412yes—
17C4×C11×Q16C2211yescharacteristic
18C4×C11×SD16C2212yes—
19C4×C11×D8C2211yescharacteristic
20C2×C4×C8×C11C2211yescharacteristic
21#10622637C2212yes—
22Q8×C11⋊C8C2212yes—
23#10622625C2212yes—
24#10622624—22no—
25D4×C11⋊C8—22no—
26D4×C11⋊C8C2212yes—
27#10622613—22no—
28#10622610—22no—
29#10622539C2212yes—
30C2×C4×C11⋊C8C2211yescharacteristic
31C2×C4×C11⋊C8C2211yescharacteristic
32Q8⋊(C11⋊C8)C2212yes—
33Q8⋊(C11⋊C8)C2212yes—
34D4⋊(C11⋊C8)C2212yes—
35D4⋊(C11⋊C8)C2212yes—
36#10622096C2211yescharacteristic
37#10622096C2211yescharacteristic
38#10622095C2212yes—
39#10622092C2212yes—
40#10622092C2212yes—
41C2×C11×Q16C2×C411yescharacteristic
42C2×C11×SD16C2×C412yes—
43C2×C11×D8C2×C411yescharacteristic
44C22×C8×C11C2×C411yescharacteristic
45C22×C8×C11C2×C411yescharacteristic
46C11×#126—22no—
47C11×#125C2×C412yes—
48C11×#124C2×C412yes—
49C11×#123—22no—
50C11×C22⋊Q8C2×C412yes—
51C11×#121C2×C412yes—
52C4×Q8×C11C2312yes—
53C4×D4×C11—22no—
54C4×D4×C11C2312yes—
55C11×#117—22no—
56C2×C42×C11C2311yescharacteristic
57C2×#4318—22no—
58C22×C11⋊C8—21no—
59C22×C11⋊C8—22no—
60C22×C11⋊C8D411yescharacteristic
61C22×C11⋊C8D411yescharacteristic
62C11×#107C2×C411yescharacteristic
63C11×#107C2×C411yescharacteristic
64C11×#106C2×C412yes—
65C11×#103C2×C412yes—
66C11×#103C2×C412yes—
67C11×#102C2×C412yes—
68C11×#102C2×C412yes—
69C4×C8×C11C2×C411yescharacteristic
70C4×C8×C11C2×C411yescharacteristic
71C4×C8×C11C2311yescharacteristic
72C4×C8×C11C2311yescharacteristic
73C22⋊(C11⋊C8)—22no—
74C22⋊(C11⋊C8)—22no—
75C22⋊(C11⋊C8)—22no—
76C4⋊(C11⋊C8)—22no—
77C4⋊(C11⋊C8)—22no—
78C4⋊(C11⋊C8)C2312yes—
79C4⋊(C11⋊C8)C2312yes—
80#66867—22no—
81#66867—22no—
82C4×C11⋊C8—21no—
83C4×C11⋊C8—22no—
84C4×C11⋊C8D412yes—
85C4×C11⋊C8C2312yes—
86C4×C11⋊C8C2312yes—
87#17982—111nomaximal, Sylow
88C2×Q8×C11C22×C412yes—
89C2×D4×C11—22no—
90C2×D4×C11C22×C412yes—
91C22×C4×C11—22no—
92C22×C4×C11C22×C411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C11×Q16—41no—
96C11×SD16—42no—
97C11×D8—41no—
98C2×C8×C11—41no—
99C2×C8×C11—41no—
100C2×C8×C11C22×C411yescharacteristic
101C2×C8×C11C22×C411yescharacteristic
102C2×C8×C11C22×C411yescharacteristic
103C2×C8×C11C22×C411yescharacteristic
104C11×C4⋊C4—22no—
105C11×C4⋊C4—22no—
106C11×C4⋊C4—22no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4C22×C412yes—
109C11×C4⋊C4C22×C412yes—
110C11×C22⋊C4—22no—
111C11×C22⋊C4—22no—
112C11×C22⋊C4—22no—
113C11×C22⋊C4—22no—
114C11×C22⋊C4—22no—
115C42×C11—22no—
116C42×C11C22×C411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C42×C11#4111yescharacteristic
119C42×C11C2411yescharacteristic
120#4318—44no—
121C2×C11⋊C8—24no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—44no—
128C2×C11⋊C8C2×D412yes—
129C2×C11⋊C8C2×D412yes—
130#3168D1111yescharacteristic
131#2966—112no—
132#1588—112no—
133#1587—112no—
134#1586—112no—
135#1585—112no—
136#1568—111no—
137#1494—112no—
138C2×#322—111no—
139C23×C11—22no—
140C23×C11C4×D411yescharacteristic
141Q8×C11—22no—
142Q8×C11—22no—
143D4×C11—22no—
144D4×C11—22no—
145D4×C11—44no—
146C2×C4×C11—22no—
147C2×C4×C11—21no—
148C2×C4×C11—21no—
149C2×C4×C11—21no—
150C2×C4×C11—21no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—42no—
155C2×C4×C11—42no—
156C2×C4×C11C4×D411yescharacteristic
157C2×C4×C11C4×D411yescharacteristic
158C2×C4×C11C4×D411yescharacteristic
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C22×D411yescharacteristic
161C2×C4×C11C2×#4111yescharacteristic
162C8×C11—21no—
163C8×C11—21no—
164C8×C11—21no—
165C8×C11—21no—
166C11⋊C8—24no—
167C11⋊C8—22no—
168C11⋊C8—22no—
169C11⋊C8—42no—
170C11⋊C8—42no—
171#529C2×D1112yes—
172#499Dic1111yescharacteristic
173#495Dic1111yescharacteristic
174#488Dic1112yes—
175#467Dic1111yescharacteristic
176#466Dic1111yescharacteristic
177#465Dic1112yes—
178#446—112no—
179C8×Q8—112no—
180C4×Q16C2×D1111yescharacteristic
181C4×SD16C2×D1112yes—
182C4×D8C2×D1111yescharacteristic
183#436—112no—
184#435—222no—
185C8×D4—112no—
186C8×D4—222no—
187#433—222no—
188#432—112no—
189#405—222no—
190C2×C4×C8—111no—
191C2×C4×C8—111no—
192C2×C4×C8C2×D1111yescharacteristic
193#335—111no—
194#335—111no—
195#334—112no—
196Q8⋊C8—112no—
197Q8⋊C8—112no—
198D4⋊C8—112no—
199D4⋊C8—112no—
200#322—112no—
201#322—112no—
202C22×C11—21no—
203C22×C11—21no—
204C22×C11—42no—
205C22×C11—42no—
206C22×C11—42no—
207C22×C11#44312yes—
208C22×C11C2×C4×D411yescharacteristic
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11—42no—
214C4×C11—42no—
215C4×C11—42no—
216C4×C11#56811yescharacteristic
217C4×C11#56811yescharacteristic
218C4×C11#57511yescharacteristic
219C4×C11#57511yescharacteristic
220C2×Q16C2×Dic1111yescharacteristic
221C2×SD16C2×Dic1112yes—
222C2×D8C2×Dic1111yescharacteristic
223C2×M16—222no—
224C22×C8—111no—
225C22×C8—111no—
226C22×C8—222no—
227C22×C8—221no—
228C22×C8C2×Dic1111yescharacteristic
229C22×C8C2×Dic1111yescharacteristic
230#126—22no—
231#125C2×Dic1112yes—
232#124C2×Dic1112yes—
233#123—22no—
234C22⋊Q8C2×Dic1112yes—
235#121C2×Dic1112yes—
236C4×Q8C22×D1112yes—
237C4×D4—22no—
238C4×D4C22×D1112yes—
239#117—22no—
240C2×C42C22×D1111yescharacteristic
241#107C2×Dic1111yescharacteristic
242#107C2×Dic1111yescharacteristic
243#106C2×Dic1112yes—
244C4⋊C8—112no—
245C4⋊C8—112no—
246C4⋊C8—222no—
247C4⋊C8—222no—
248#103C2×Dic1112yes—
249#103C2×Dic1112yes—
250#102C2×Dic1112yes—
251#102C2×Dic1112yes—
252C22⋊C8—222no—
253C22⋊C8—222no—
254C22⋊C8—222no—
255#97—222no—
256#97—222no—
257C4×C8—112no—
258C4×C8—112no—
259C4×C8—112no—
260C4×C8—222no—
261C4×C8—221no—
262C4×C8C2×Dic1111yescharacteristic
263C4×C8C2×Dic1111yescharacteristic
264C4×C8C22×D1111yescharacteristic
265C4×C8C22×D1111yescharacteristic
266C2×C11—22no—
267C2×C11—82no—
268C2×C11#293211yescharacteristic
269C2×C11#294311yescharacteristic
270C2×C11C2×#44311yescharacteristic
271C2×Q8C22×Dic1112yes—
272C2×D4—22no—
273C2×D4C22×Dic1112yes—
274C22×C4—22no—
275C22×C4D4×D1111yescharacteristic
276C22×C4#434111yescharacteristic
277C22×C4C22×Dic1111yescharacteristic
278Q16—41no—
279SD16—42no—
280D8—41no—
281M16—444no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—112no—
285C2×C8—112no—
286C2×C8—224no—
287C2×C8—222no—
288C2×C8—222no—
289C2×C8—222no—
290C2×C8—441no—
291C2×C8—441no—
292C2×C8—444no—
293C2×C8C22×Dic1111yescharacteristic
294C2×C8C22×Dic1111yescharacteristic
295C2×C8C22×Dic1111yescharacteristic
296C2×C8C22×Dic1111yescharacteristic
297C4⋊C4—22no—
298C4⋊C4—22no—
299C4⋊C4—22no—
300C4⋊C4—22no—
301C4⋊C4C22×Dic1112yes—
302C4⋊C4C22×Dic1112yes—
303C22⋊C4—22no—
304C22⋊C4—22no—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C42—22no—
309C42D4×D1111yescharacteristic
310C42#434111yescharacteristic
311C42C22×Dic1111yescharacteristic
312C42C23×D1111yescharacteristic
313C11#1798211yescharacteristic, complemented, Sylow
314C23—22no—
315C23D4×Dic1111yescharacteristic
316Q8—22no—
317Q8—22no—
318D4—22no—
319D4—22no—
320D4—44no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4D4×Dic1111yescharacteristic
332C2×C4D4×Dic1111yescharacteristic
333C2×C4D4×Dic1111yescharacteristic
334C2×C4C2×D4×D1111yescharacteristic
335C2×C4C2×#434111yescharacteristic
336C2×C4C23×Dic1111yescharacteristic
337C8—21no—
338C8—21no—
339C8—21no—
340C8—21no—
341C8—224no—
342C8—222no—
343C8—222no—
344C8—442no—
345C8—442no—
346C22—21no—
347C22—21no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22#1062280912yes—
352C22C2×D4×Dic1111yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—42no—
358C4—42no—
359C4—42no—
360C4#1062329911yescharacteristic
361C4#1062329911yescharacteristic
362C4#1062335011yescharacteristic
363C4#1062335011yescharacteristic
364C2—22no—
365C2—82no—
366C2#1307733411yescharacteristic
367C2#1307741711yescharacteristic
368C2C2×#1062280911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#3168C2
socleC22×C11C2×C4×D4
prime radicalC11×#466C4
cosocleC42×C11C24
hypercenter#3168D11
hypocenterC11#17982
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3168

Complements

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

NH ≅ G/Ntype
1. #13077592C2semidirect
2. #13067495C2semidirect
3. #13067488C2semidirect
4. #13067481C2semidirect
5. #13067474C2semidirect
6. #13067379C2semidirect
7. #13067076C2semidirect
8. C2×#10622092C2semidirect
313. C11#17982semidirect

Maximal subgroups

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

subgroupindex
#130775922
#130674952
#130674882
#130674812
#130674742
#130673792
#130670762
C2×#106220922
C11×#31682
#1798211