Finite Group Databasebeta

← #14757445

Subgroups — #14757445

Order 2816.

1638 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic
2C2×#10622416C214yesmaximal, complemented
3C2×#10622320C211yesmaximal, characteristic, complemented
4D11×#382C211yesmaximal, characteristic, complemented
5#13069440C211yesmaximal, characteristic, complemented
6#13069439C211yesmaximal, characteristic, complemented
7#13069437C211yesmaximal, characteristic, complemented
8#13069424C214yesmaximal, complemented
9C11×#1960C211yesmaximal, characteristic, complemented
10C22×#4343C2212yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#67000C2212yes—
13C22×#4313C2212yes—
14#10623256—24no—
15#10623256C418yescomplemented
16C2×#66948—22no—
17C2×#66946—22no—
18C2×C4⋊C4×D11C2212yes—
19C2×#66927C2211yescharacteristic
20C2×C42×D11C2211yescharacteristic
21C2×C11×#103C2214yes—
22C2×C11×#97C2211yescharacteristic
23C11×#382C2211yescharacteristic
24C2×#66899C2214yes—
25C2×#66885C2214yes—
26C2×C8×Dic11C2212yes—
27#10622590C2212yes—
28C2×#66873C2214yes—
29#10622549C2211yescharacteristic
30C2×#66867C2211yescharacteristic
31#10622416—216no—
32#10622320—24no—
33D11×#95—22no—
34#10622263—22no—
35C22×Q8×C11C2312yes—
36C2×#4343—24no—
37C2×#4343—28no—
38C2×#4343—28no—
39C2×#4343C2×C418yes—
40C22×D44—22no—
41C22×D44—22no—
42C22×D44C2312yes—
43C22×C4×D11—22no—
44C22×C4×D11—22no—
45C22×C4×D11D412yes—
46C22×C4×D11C2311yescharacteristic
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8C2×C414yescomplemented
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2312yes—
52C2×C42×C11C2311yescharacteristic
53#67000—24no—
54#67000C2×C418yescomplemented
55C2×(C2×D11)⋊C4—24no—
56C2×C4⋊Dic11C2312yes—
57C2×Dic11⋊C4—22no—
58C2×C4×Dic11D412yes—
59C2×C4×Dic11C2311yescharacteristic
60C22×C11⋊C8C2312yes—
61C2×#4313—24no—
62C2×#4313—24no—
63C2×#4313D418yescomplemented
64#66948—216no—
65#66946—216no—
66C4⋊C4×D11—28no—
67#66927—22no—
68#66927C2×C414yescomplemented
69C42×D11C2×C414yes—
70C42×D11D414yes—
71C11×#103—28no—
72C11×#97—22no—
73C11×#95—22no—
74#66899—28no—
75C11⋊#95—22no—
76C11⋊#95—24no—
77#66885—28no—
78C8×Dic11—24no—
79#66873—28no—
80#66867—22no—
81#21201—111nomaximal, Sylow
82C23×D11—22no—
83C23×D11C2×D411yescharacteristic
84C2×Q8×C11—22no—
85C2×Q8×C11—24no—
86C2×Q8×C11—24no—
87C2×Q8×C11C22×C414yes—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11C2×D412yes—
91C22×C4×C11C2411yescharacteristic
92C22×Dic11—22no—
93C22×Dic11C2×D412yes—
94C22×Dic11C2×D411yescharacteristic
95#4343—232no—
96#4343—416no—
97C2×D44—28no—
98C2×D44—28no—
99C2×D44—22no—
100C2×D44—24no—
101C2×D44—24no—
102C2×D44—48no—
103C2×D44—44no—
104C2×D44—44no—
105C2×D44C22×C414yes—
106C2×C4×D11—28no—
107C2×C4×D11—44no—
108C2×C4×D11—48no—
109C2×C4×D11—44no—
110C2×C4×D11—44no—
111C2×C4×D11—44no—
112C2×C4×D11C22⋊C418yes—
113C2×C4×D11C22×C412yes—
114C2×C4×D11C2×D412yes—
115C2×C4×D11C2×D414yes—
116C2×C4×D11#4114yes—
117C2×C8×C11—22no—
118C2×C8×C11—22no—
119C2×C8×C11C2×D414yes—
120C11×C4⋊C4—28no—
121C11×C4⋊C4—24no—
122C42×C11C22×C412yes—
123C42×C11C2×D412yes—
124(C2×D11)⋊C4—216no—
125C4⋊Dic11—24no—
126Dic11⋊C4—44no—
127C4×Dic11C22⋊C418yes—
128C4×Dic11C22×C412yes—
129C4×Dic11C2×D412yes—
130C2×C11⋊C8—22no—
131C2×C11⋊C8—22no—
132C2×C11⋊C8C2×D414yes—
133#4313—216no—
134C2×#532—111no—
135C2×#417—114no—
136C2×C4×M16—111no—
137C2×#382—111no—
138#1961—111no—
139#1961—111no—
140#1960—111no—
141#1960D1111yescharacteristic, complemented
142#1958—114no—
143C23×C11C22×D411yescharacteristic
144C22×D11—24no—
145C22×D11—24no—
146C22×D11—42no—
147C22×D11—42no—
148C22×D11—48no—
149C22×D11C2×C22⋊C412yes—
150C22×D11#12412yes—
151C22×D11#12712yes—
152Q8×C11—28no—
153Q8×C11—44no—
154C2×C4×C11—24no—
155C2×C4×C11—24no—
156C2×C4×C11—42no—
157C2×C4×C11—42no—
158C2×C4×C11—42no—
159C2×C4×C11—44no—
160C2×C4×C11C2×C22⋊C414yes—
161C2×C4×C11C23×C411yescharacteristic
162C2×C4×C11C22×D412yes—
163C2×C4×C11C22×D411yescharacteristic
164C2×C4×C11C2×#4112yes—
165C2×Dic11—24no—
166C2×Dic11—42no—
167C2×Dic11—44no—
168C2×Dic11C2×C22⋊C414yes—
169C2×Dic11C2×C22⋊C412yes—
170C2×Dic11#12412yes—
171C2×Dic11#12712yes—
172D44—28no—
173D44—416no—
174D44—416no—
175D44—44no—
176C4×D11—48no—
177C4×D11—416no—
178C4×D11—88no—
179C4×D11C4×D418yes—
180C4×D11#12118yes—
181C8×C11—24no—
182C11⋊C8—24no—
183C22×#41—112no—
184C22×M16—112no—
185#532—118no—
186#532—224no—
187C2×C4⋊Q8C2×D1111yescharacteristic
188C2×#127—111no—
189C2×#124—112no—
190C2×#121—222no—
191C2×C4×D4—222no—
192C22×C4⋊C4—112no—
193C22×C42—111no—
194#417—2216no—
195C2×#103—114no—
196C2×#103C2×D1114yes—
197C2×#102—114no—
198C2×#102—114no—
199C4×M16—224no—
200C2×#97—111no—
201C2×#97C2×D1111yescharacteristic
202C2×C4×C8—112no—
203#382—112no—
204#382—111no—
205#382—222no—
206#382C2×D1111yescharacteristic
207C2×#95—222no—
208C22×C11C22×C22⋊C411yescharacteristic
209C22×C11C2×#12411yescharacteristic
210C22×C11C2×#12711yescharacteristic
211C22×C11#57514yes—
212C2×D11—24no—
213C2×D11—24no—
214C2×D11—24no—
215C2×D11—48no—
216C2×D11—44no—
217C2×D11—84no—
218C2×D11—84no—
219C2×D11#39014yes—
220C4×C11—24no—
221C4×C11—44no—
222C4×C11—82no—
223C4×C11C2×C4×D412yes—
224C4×C11C2×#12112yes—
225Dic11—24no—
226Dic11—82no—
227Dic11#39014yes—
228C2×#41—118no—
229C2×#41—224no—
230C2×#41—228no—
231C2×#41—228no—
232C22×Q8C22×D1112yes—
233C22×D4—112no—
234C22×D4—222no—
235C22×D4—222no—
236C23×C4—111no—
237C23×C4—112no—
238C23×C4—222no—
239C23×C4—222no—
240C2×M16—118no—
241C2×M16—224no—
242C2×M16—224no—
243C22×C8—112no—
244C22×C8C22×D1112yes—
245C4⋊Q8—22no—
246C4⋊Q8C4×D1114yescomplemented
247#127—114no—
248#127—222no—
249#124—118no—
250#124—224no—
251#121—2216no—
252C4×D4—2216no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—112no—
255C2×C4⋊C4—228no—
256C2×C4⋊C4—222no—
257C2×C4⋊C4C22×D1112yes—
258C2×C22⋊C4—224no—
259C2×C42—112no—
260C2×C42—111no—
261C2×C42—114no—
262C2×C42—114no—
263C2×C42C22×D1111yescharacteristic
264#103—28no—
265#103—228no—
266#102—228no—
267#102—228no—
268#97—22no—
269#97—222no—
270C4×C8—224no—
271#95—22no—
272#95—224no—
273#95—222no—
274C2×C11C2×#39011yescharacteristic
275C2×C11#289612yes—
276C2×C11#314212yes—
277C2×C11#315312yes—
278D11—24no—
279D11—84no—
280C24—111no—
281C24—222no—
282#41—2232no—
283#41—4416no—
284C2×Q8—22no—
285C2×Q8—24no—
286C2×Q8—24no—
287C2×Q8C2×C4×D1114yes—
288C2×D4—114no—
289C2×D4—228no—
290C2×D4—228no—
291C2×D4—224no—
292C2×D4—222no—
293C2×D4—224no—
294C2×D4—448no—
295C2×D4—444no—
296C2×D4—444no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—111no—
300C22×C4—112no—
301C22×C4—112no—
302C22×C4—114no—
303C22×C4—114no—
304C22×C4—112no—
305C22×C4—118no—
306C22×C4—228no—
307C22×C4—222no—
308C22×C4—444no—
309C22×C4—444no—
310C22×C4—444no—
311C22×C4—444no—
312C22×C4—448no—
313C22×C4D4×D1112yes—
314C22×C4C23×D1111yescharacteristic
315M16—2216no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—114no—
319C2×C8—222no—
320C2×C8—222no—
321C2×C8D4×D1114yes—
322C4⋊C4—28no—
323C4⋊C4—24no—
324C4⋊C4—224no—
325C4⋊C4—444no—
326C22⋊C4—2216no—
327C42—118no—
328C42—112no—
329C42—112no—
330C42C2×C4×D1112yes—
331C42D4×D1112yes—
332C11#2120111yescharacteristic, complemented, Sylow
333C23—112no—
334C23—112no—
335C23—112no—
336C23—224no—
337C23—224no—
338C23—442no—
339C23—448no—
340C23—442no—
341C23C2×D4×D1111yescharacteristic
342Q8—28no—
343Q8—44no—
344D4—228no—
345D4—4416no—
346D4—4416no—
347D4—444no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—112no—
355C2×C4—112no—
356C2×C4—112no—
357C2×C4—118no—
358C2×C4—118no—
359C2×C4—114no—
360C2×C4—224no—
361C2×C4—448no—
362C2×C4—4416no—
363C2×C4—442no—
364C2×C4—444no—
365C2×C4—888no—
366C2×C4C22⋊C4×D1114yes—
367C2×C4C22×C4×D1111yescharacteristic
368C2×C4C2×D4×D1112yes—
369C2×C4C2×D4×D1111yescharacteristic
370C2×C4#41×D1112yes—
371C8—24no—
372C8—224no—
373C22—114no—
374C22—224no—
375C22—224no—
376C22—224no—
377C22—448no—
378C22—444no—
379C22—884no—
380C22—884no—
381C22C2×C22⋊C4×D1111yescharacteristic
382C22D11×#12411yescharacteristic
383C22D11×#12711yescharacteristic
384C22#1062330814yes—
385C4—24no—
386C4—44no—
387C4—82no—
388C4—114no—
389C4—224no—
390C4—882no—
391C4C4×D4×D1112yes—
392C4D11×#12112yes—
393C2—224no—
394C2—884no—
395C2D11×#39011yescharacteristic
396C2#1307713412yes—
397C2#1307901812yes—
398C2#1307907912yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1960C2
socleC23×C11C22×D4
prime radicalC2×#10623256C2
cosocleC22×C4×C11C24
hypercenter#1960D11
hypocenterC11#21201
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
2. C2×#10622416C2semidirect
3. C2×#10622320C2semidirect
4. D11×#382C2semidirect
5. #13069440C2semidirect
6. #13069439C2semidirect
7. #13069437C2semidirect
8. #13069424C2semidirect
9. C11×#1960C2semidirect
15. #10623256C4semidirect
49. C11×C4⋊Q8C2×C4semidirect
54. #67000C2×C4semidirect
63. C2×#4313D4semidirect
68. #66927C2×C4semidirect
141. #1960D11semidirect
246. C4⋊Q8C4×D11semidirect
332. C11#21201semidirect

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106224162
C2×#106223202
D11×#3822
#130694402
#130694392
#130694372
#130694242
C11×#19602
#2120111