Finite Group Databasebeta

← #14724533

Subgroups — #14724533

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#13079186C211yesmaximal, characteristic
2#13077585C212yesmaximal, complemented
3#13067493C212yesmaximal, complemented
4#13067486C212yesmaximal, complemented
5#13067479C212yesmaximal, complemented
6#13067472C212yesmaximal, complemented
7#13067074C212yesmaximal, complemented
8C2×#10622092C211yesmaximal, characteristic, complemented
9C11×#1568C211yesmaximal, characteristic, complemented
10#10623010C2212yes—
11C11×#432C2212yes—
12C2×C4×C8×C11C2211yescharacteristic
13#10622729C411yescharacteristic
14#10622728C411yescharacteristic
15#10622727C412yes—
16C2×C4×C11⋊C8C2211yescharacteristic
17C2×C4×C11⋊C8C2211yescharacteristic
18#10622451C2212yes—
19#10622447C2212yes—
20#10622444C2212yes—
21#10622443C2212yes—
22#10622343—22no—
23(C22⋊D11)⋊C8—22no—
24#10622322—22no—
25#10622321—22no—
26C4×Dic44C2211yescharacteristic
27#10622310C412yes—
28#10622309C411yescharacteristic
29C4×D88C2211yescharacteristic
30C4×#4314C2212yes—
31#10622296C411yescharacteristic
32C11×#335C2211yescharacteristic
33C11×#335C2211yescharacteristic
34C11×#334C2212yes—
35#10622122C2212yes—
36#10622122C2212yes—
37#10622121C2212yes—
38#10622121C2212yes—
39#10622092C2212yes—
40#10622092C2212yes—
41C22×C8×C11C2×C411yescharacteristic
42C22×C8×C11C2×C411yescharacteristic
43C2×C42×C11C2311yescharacteristic
44#66983C2×C412yes—
45#66982—22no—
46C4×C22⋊D11—22no—
47#66977C2×C412yes—
48C22×C11⋊C8—21no—
49C22×C11⋊C8D411yescharacteristic
50C22×C11⋊C8D411yescharacteristic
51C2×Dic44C2×C411yescharacteristic
52C2×D88C2×C411yescharacteristic
53C2×#4314C2×C412yes—
54C2×#4313—22no—
55C2×C8×D11—22no—
56#66929—22no—
57#66928C2×C412yes—
58C4×D44C2312yes—
59#66925—22no—
60#66923C2×C412yes—
61C4×Dic22C2312yes—
62C11×C4⋊C8C2312yes—
63C11×C4⋊C8C2312yes—
64C11×C22⋊C8—22no—
65C11×#97—22no—
66C4×C8×C11C2×C411yescharacteristic
67C4×C8×C11C2×C411yescharacteristic
68C4×C8×C11C2311yescharacteristic
69C4×C8×C11C2311yescharacteristic
70#66885C2×C412yes—
71#66885C2×C412yes—
72(C2×D11)⋊C8—22no—
73(C2×D11)⋊C8—22no—
74#66882C2×C411yescharacteristic
75#66882C2×C411yescharacteristic
76#66881C2×C412yes—
77#66880C2×C412yes—
78#66880C2×C412yes—
79#66879—22no—
80Dic11⋊C8—22no—
81Dic11⋊C8—22no—
82C8×Dic11—22no—
83C4×C11⋊C8—21no—
84C4×C11⋊C8D412yes—
85C4×C11⋊C8C2312yes—
86C4×C11⋊C8C2312yes—
87#17982—111nomaximal, Sylow
88C22×C4×C11C22×C411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C2×C22⋊D11—22no—
92C2×D44C22×C412yes—
93C2×C4×D11—22no—
94C2×Dic22C22×C412yes—
95C2×C8×C11—22no—
96C2×C8×C11—22no—
97C2×C8×C11—41no—
98C2×C8×C11—41no—
99C2×C8×C11C22×C411yescharacteristic
100C2×C8×C11C22×C411yescharacteristic
101C2×C8×C11C22×C411yescharacteristic
102C2×C8×C11C22×C411yescharacteristic
103C42×C11C22×C411yescharacteristic
104C42×C11C2×D411yescharacteristic
105C42×C11#4111yescharacteristic
106C42×C11C2411yescharacteristic
107C22⋊Dic11—22no—
108(C2×D11)⋊C4—22no—
109(C2×D11)⋊C4—22no—
110(C2×D11)⋊C4—22no—
111(C2×D11)⋊C4—22no—
112C4⋊Dic11C22×C412yes—
113C4⋊Dic11C22×C412yes—
114Dic11⋊C4—22no—
115Dic11⋊C4—22no—
116Dic11⋊C4—22no—
117Dic11⋊C4—22no—
118C4×Dic11—22no—
119C2×C11⋊C8—24no—
120C2×C11⋊C8—22no—
121C2×C11⋊C8—41no—
122C2×C11⋊C8—41no—
123C2×C11⋊C8C2×D412yes—
124C2×C11⋊C8C2×D412yes—
125Dic44—41no—
126D88—41no—
127#4314—42no—
128#4313—44no—
129C8×D11—44no—
130#3168—111no—
131#2966—112no—
132#1588—112no—
133#1587—112no—
134#1586—112no—
135#1585—112no—
136#1568D1111yescharacteristic, complemented
137#1494—112no—
138C2×#322—111no—
139C23×C11C4×D411yescharacteristic
140C22×D11—22no—
141C2×C4×C11—22no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11C4×D411yescharacteristic
147C2×C4×C11C4×D411yescharacteristic
148C2×C4×C11C4×D411yescharacteristic
149C2×C4×C11C23×C411yescharacteristic
150C2×C4×C11C22×D411yescharacteristic
151C2×C4×C11C2×#4111yescharacteristic
152C22⋊D11—44no—
153C2×Dic11—22no—
154C2×Dic11—22no—
155C2×Dic11—22no—
156D44—22no—
157D44—22no—
158C4×D11—42no—
159C4×D11—42no—
160Dic22—22no—
161Dic22—22no—
162C8×C11—21no—
163C8×C11—21no—
164C8×C11—21no—
165C8×C11—21no—
166C8×C11—42no—
167C8×C11—42no—
168C11⋊C8—24no—
169C11⋊C8—22no—
170C11⋊C8—22no—
171#529—112no—
172#499—111no—
173#495—111no—
174#488—112no—
175#467—111no—
176#466—111no—
177#465—112no—
178#446—112no—
179C8×Q8—112no—
180C4×Q16—111no—
181C4×SD16—112no—
182C4×D8—111no—
183#436—112no—
184#435—222no—
185C8×D4—112no—
186C8×D4—222no—
187#433—222no—
188#432C2×D1112yes—
189#405—222no—
190C2×C4×C8—111no—
191C2×C4×C8—111no—
192C2×C4×C8C2×D1111yescharacteristic
193#335C2×D1111yescharacteristic
194#335C2×D1111yescharacteristic
195#334C2×D1112yes—
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#44312yes—
205C22×C11C2×C4×D411yescharacteristic
206C2×D11—42no—
207C2×D11—42no—
208C2×D11—42no—
209C4×C11—21no—
210C4×C11—21no—
211C4×C11—21no—
212C4×C11—21no—
213C4×C11#56811yescharacteristic
214C4×C11#56811yescharacteristic
215C4×C11#57511yescharacteristic
216C4×C11#57511yescharacteristic
217Dic11—42no—
218Dic11—42no—
219Dic11—42no—
220C2×Q16—111no—
221C2×SD16—112no—
222C2×D8—111no—
223C2×M16—222no—
224C22×C8—111no—
225C22×C8—111no—
226C22×C8—222no—
227C22×C8—221no—
228C22×C8C4×D1111yescharacteristic
229C22×C8C4×D1111yescharacteristic
230#126—222no—
231#125—112no—
232#124—112no—
233#123—222no—
234C22⋊Q8—112no—
235#121—112no—
236C4×Q8—112no—
237C4×D4—112no—
238C4×D4—222no—
239#117—222no—
240C2×C42C22×D1111yescharacteristic
241#107—111no—
242#107—111no—
243#106—112no—
244C4⋊C8—222no—
245C4⋊C8—222no—
246C4⋊C8C22×D1112yes—
247C4⋊C8C22×D1112yes—
248#103—112no—
249#103—112no—
250#102—112no—
251#102—112no—
252C22⋊C8—22no—
253C22⋊C8—222no—
254C22⋊C8—222no—
255#97—22no—
256#97—222no—
257C4×C8—112no—
258C4×C8—112no—
259C4×C8—112no—
260C4×C8—222no—
261C4×C8—221no—
262C4×C8C4×D1111yescharacteristic
263C4×C8C4×D1111yescharacteristic
264C4×C8C22×D1111yescharacteristic
265C4×C8C22×D1111yescharacteristic
266C2×C11—22no—
267C2×C11#293211yescharacteristic
268C2×C11#294311yescharacteristic
269C2×C11C2×#44311yescharacteristic
270D11—82no—
271C2×Q8—112no—
272C2×D4—112no—
273C2×D4—222no—
274C22×C4—222no—
275C22×C4C2×C4×D1111yescharacteristic
276C22×C4D4×D1111yescharacteristic
277C22×C4#434311yescharacteristic
278Q16—441no—
279SD16—442no—
280D8—441no—
281M16—444no—
282C2×C8—22no—
283C2×C8—22no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—112no—
287C2×C8—112no—
288C2×C8—224no—
289C2×C8—222no—
290C2×C8—444no—
291C2×C8—441no—
292C2×C8—441no—
293C2×C8C2×C4×D1111yescharacteristic
294C2×C8C2×C4×D1111yescharacteristic
295C2×C8C2×C4×D1111yescharacteristic
296C2×C8C2×C4×D1111yescharacteristic
297C4⋊C4—112no—
298C4⋊C4—112no—
299C4⋊C4—222no—
300C4⋊C4—222no—
301C4⋊C4—222no—
302C4⋊C4—222no—
303C22⋊C4—222no—
304C22⋊C4—222no—
305C22⋊C4—222no—
306C22⋊C4—222no—
307C22⋊C4—222no—
308C42—222no—
309C42C2×C4×D1111yescharacteristic
310C42D4×D1111yescharacteristic
311C42#434311yescharacteristic
312C42C23×D1111yescharacteristic
313C11#1798211yescharacteristic, complemented, Sylow
314C23—222no—
315C23#6694611yescharacteristic
316Q8—222no—
317Q8—222no—
318D4—222no—
319D4—222no—
320D4—444no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—222no—
327C2×C4—222no—
328C2×C4—222no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4#6694611yescharacteristic
332C2×C4#6694611yescharacteristic
333C2×C4#6694611yescharacteristic
334C2×C4C22×C4×D1111yescharacteristic
335C2×C4C2×D4×D1111yescharacteristic
336C2×C4C2×#434311yescharacteristic
337C8—21no—
338C8—21no—
339C8—21no—
340C8—21no—
341C8—42no—
342C8—42no—
343C8—224no—
344C8—222no—
345C8—222no—
346C22—21no—
347C22—21no—
348C22—442no—
349C22—442no—
350C22—442no—
351C22#1062250812yes—
352C22C2×#6694611yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—442no—
358C4—442no—
359C4—442no—
360C4#1062327611yescharacteristic
361C4#1062327611yescharacteristic
362C4#1062329911yescharacteristic
363C4#1062329911yescharacteristic
364C2—22no—
365C2—882no—
366C2#1307733311yescharacteristic
367C2#1307741611yescharacteristic
368C2C2×#1062250811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1568C2
socleC22×C11C2×C4×D4
prime radical#10622728C4
cosocleC42×C11C24
hypercenter#1568D11
hypocenterC11#17982
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1568

Complements

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

NH ≅ G/Ntype
2. #13077585C2semidirect
3. #13067493C2semidirect
4. #13067486C2semidirect
5. #13067479C2semidirect
6. #13067472C2semidirect
7. #13067074C2semidirect
8. C2×#10622092C2semidirect
9. C11×#1568C2semidirect
136. #1568D11semidirect
313. C11#17982semidirect

Maximal subgroups

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

subgroupindex
#130791862
#130775852
#130674932
#130674862
#130674792
#130674722
#130670742
C2×#106220922
C11×#15682
#1798211