Finite Group Databasebeta

← #14767601

Subgroups — #14767601

Order 2816.

922 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622309C211yesmaximal, characteristic
2#13071327C212yesmaximal, complemented
3#13069432C212yesmaximal, complemented
4#13068970C212yesmaximal, complemented
5#13068963C212yesmaximal
6#13068956C212yesmaximal, complemented
7#13068949C212yesmaximal, complemented
8#13068744C211yesmaximal, characteristic, complemented
9C11×#1746C211yesmaximal, characteristic, complemented
10C22×Dic44C2211yescharacteristic
11C22×D88C2211yescharacteristic
12C22×#4314C2212yes—
13C2×#66928C2212yes—
14C2×C4×D44C2212yes—
15C2×C4×Dic22C2212yes—
16C2×C11×#97C2211yescharacteristic
17C2×C4×C8×C11C2211yescharacteristic
18C11×#376C2211yescharacteristic
19C2×#66885C2212yes—
20C2×#66885C2212yes—
21C2×#66880C2212yes—
22C2×#66880C2212yes—
23#10622552C2212yes—
24#10622548C2212yes—
25#10622542C2212yes—
26#10622309C418yescomplemented
27#10622283—22no—
28#10622283—22no—
29#10622281—22no—
30#10622281—22no—
31C11×#336C2212yes—
32C11×#336C2212yes—
33#10622189C2211yescharacteristic
34#10622189C2212yes—
35#10622189C2211yescharacteristic
36C22×D44C2312yes—
37C22×C4×D11—22no—
38C22×Dic22C2312yes—
39C22×C8×C11C2312yes—
40C22×C8×C11C2311yescharacteristic
41C22×C8×C11C2311yescharacteristic
42C2×C42×C11C2312yes—
43C2×C42×C11C2311yescharacteristic
44C2×(C2×D11)⋊C4—22no—
45C2×(C2×D11)⋊C4—22no—
46C2×(C2×D11)⋊C4—22no—
47C2×(C2×D11)⋊C4—22no—
48C2×(C2×D11)⋊C4—22no—
49C2×C4⋊Dic11—22no—
50C2×C4⋊Dic11—22no—
51C2×C4⋊Dic11C2312yes—
52C2×C4⋊Dic11C2312yes—
53C2×Dic11⋊C4—22no—
54C2×C4×Dic11—22no—
55C2×Dic44—42no—
56C2×Dic44C2×C414yescomplemented
57C2×D88—42no—
58C2×D88C2×C414yes—
59C2×#4314—42no—
60C2×#4314—42no—
61C2×#4314C2×C418yescomplemented
62#66928—24no—
63#66928C2×C418yescomplemented
64C4×D44—42no—
65C4×D44—42no—
66C4×Dic22—42no—
67C4×Dic22—42no—
68C11×#97—22no—
69C4×C8×C11C2×C414yescomplemented
70C11×#95D411yescharacteristic
71C11×#95D412yes—
72C11×#95D411yescharacteristic
73C11⋊#95—22no—
74C11⋊#95—22no—
75#66885—42no—
76#66885—42no—
77#66880—42no—
78#66880—42no—
79#22274—111nomaximal, Sylow
80C23×D11—22no—
81C22×C4×C11C2×D412yes—
82C22×C4×C11C2×D412yes—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D411yescharacteristic
85C22×C4×C11C2411yescharacteristic
86C22×Dic11—22no—
87C22×Dic11—22no—
88C22×Dic11—22no—
89C2×D44—22no—
90C2×D44—22no—
91C2×D44—22no—
92C2×D44—22no—
93C2×D44—22no—
94C2×D44C22×C414yes—
95C2×C4×D11—44no—
96C2×C4×D11—82no—
97C2×C4×D11—82no—
98C2×Dic22—22no—
99C2×Dic22—22no—
100C2×Dic22—22no—
101C2×Dic22—22no—
102C2×Dic22—22no—
103C2×Dic22C22×C414yes—
104C2×C8×C11—22no—
105C2×C8×C11—22no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C2×C8×C11C22×C412yes—
110C2×C8×C11C22×C412yes—
111C42×C11—22no—
112C42×C11—22no—
113C42×C11C22×C412yes—
114C42×C11#4112yes—
115(C2×D11)⋊C4—28no—
116(C2×D11)⋊C4—28no—
117(C2×D11)⋊C4—44no—
118(C2×D11)⋊C4—82no—
119(C2×D11)⋊C4—82no—
120C4⋊Dic11—22no—
121C4⋊Dic11—22no—
122C4⋊Dic11—22no—
123C4⋊Dic11—22no—
124C4⋊Dic11—82no—
125C4⋊Dic11—82no—
126Dic11⋊C4—44no—
127C4×Dic11—44no—
128Dic44—44no—
129D88—44no—
130#4314—48no—
131C2×#495—111no—
132#2326—112no—
133#1959—112no—
134#1880—112no—
135#1879—112no—
136#1878—112no—
137#1877—112no—
138#1834—111no—
139#1746D1111yescharacteristic, complemented
140C23×C11C22×D411yescharacteristic
141C22×D11—24no—
142C22×D11—42no—
143C22×D11—42no—
144C22×D11—42no—
145C22×D11—42no—
146C22×D11—42no—
147C22×D11—42no—
148C2×C4×C11—21no—
149C2×C4×C11—22no—
150C2×C4×C11—21no—
151C2×C4×C11—22no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11C4×D412yes—
158C2×C4×C11C4×D412yes—
159C2×C4×C11C23×C411yescharacteristic
160C2×C4×C11C2×#4111yescharacteristic
161C2×C4×C11H(5,𝔽2)12yes—
162C2×C4×C11H(5,𝔽2)12yes—
163C2×Dic11—24no—
164C2×Dic11—42no—
165C2×Dic11—42no—
166C2×Dic11—42no—
167C2×Dic11—42no—
168C2×Dic11—42no—
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172D44—24no—
173D44—24no—
174D44—42no—
175D44—42no—
176C4×D11—88no—
177Dic22—24no—
178Dic22—24no—
179Dic22—42no—
180Dic22—42no—
181C8×C11—22no—
182C8×C11—22no—
183C8×C11—42no—
184C22×Q16—111no—
185C22×SD16—112no—
186C22×D8—111no—
187C2×#124—112no—
188C2×C4×Q8—112no—
189C2×C4×D4—112no—
190#495—118no—
191C2×#103—112no—
192C2×#103—112no—
193C2×#102—112no—
194C2×#102—112no—
195C2×#97C2×D1111yescharacteristic
196C2×C4×C8C2×D1111yescharacteristic
197#391—112no—
198#390—112no—
199#388—222no—
200#388—222no—
201#385—222no—
202#385—222no—
203#384—112no—
204#376C2×D1111yescharacteristic
205#340—111no—
206#340—112no—
207#340—111no—
208#336C2×D1112yes—
209#336C2×D1112yes—
210C22×C11C2×C4×D411yescharacteristic
211C22×C11#53512yes—
212C22×C11#57611yescharacteristic
213C22×C11#57712yes—
214C22×C11#57811yescharacteristic
215C2×D11—44no—
216C2×D11—44no—
217C2×D11—44no—
218C2×D11—82no—
219C2×D11—82no—
220C2×D11—82no—
221C2×D11—82no—
222C4×C11—22no—
223C4×C11—22no—
224C4×C11—42no—
225C4×C11—42no—
226C4×C11#51811yescharacteristic
227C4×C11#51811yescharacteristic
228C4×C11#54012yes—
229Dic11—44no—
230Dic11—82no—
231Dic11—82no—
232C22×Q8—112no—
233C22×D4—112no—
234C23×C4—222no—
235C2×Q16—114no—
236C2×Q16—442no—
237C2×SD16—118no—
238C2×SD16—442no—
239C2×SD16—442no—
240C2×D8—114no—
241C2×D8—442no—
242C22×C8C22×D1112yes—
243C22×C8C22×D1111yescharacteristic
244C22×C8C22×D1111yescharacteristic
245#124—118no—
246#124—224no—
247C4×Q8—442no—
248C4×Q8—442no—
249C4×D4—442no—
250C4×D4—442no—
251C2×C4⋊C4—112no—
252C2×C4⋊C4—112no—
253C2×C4⋊C4—222no—
254C2×C4⋊C4—222no—
255C2×C4⋊C4—222no—
256C2×C22⋊C4—222no—
257C2×C22⋊C4—222no—
258C2×C22⋊C4—222no—
259C2×C22⋊C4—222no—
260C2×C22⋊C4—222no—
261C2×C42—222no—
262C2×C42C22×D1112yes—
263C2×C42C22×D1111yescharacteristic
264#103—442no—
265#103—442no—
266#102—442no—
267#102—442no—
268#97—22no—
269C4×C8C4×D1114yescomplemented
270#95—222no—
271#95—222no—
272#95D4411yescharacteristic
273#95D4412yes—
274#95D4411yescharacteristic
275C2×C11#232811yescharacteristic
276C2×C11#295111yescharacteristic
277C2×C11#295211yescharacteristic
278C2×C11#322412yes—
279C2×C11#322512yes—
280D11—84no—
281C24—222no—
282C2×Q8—114no—
283C2×Q8—222no—
284C2×Q8—222no—
285C2×Q8—222no—
286C2×Q8—222no—
287C2×Q8—222no—
288C2×D4—114no—
289C2×D4—222no—
290C2×D4—222no—
291C2×D4—222no—
292C2×D4—222no—
293C2×D4—222no—
294C22×C4—222no—
295C22×C4—222no—
296C22×C4—222no—
297C22×C4—444no—
298C22×C4—882no—
299C22×C4—882no—
300C22×C4C2×D4412yes—
301C22×C4C2×D4412yes—
302C22×C4C2×D4411yescharacteristic
303C22×C4C2×D4411yescharacteristic
304C22×C4C23×D1111yescharacteristic
305Q16—444no—
306SD16—448no—
307D8—444no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8—22no—
311C2×C8—22no—
312C2×C8—22no—
313C2×C8C2×C4×D1112yes—
314C2×C8C2×C4×D1112yes—
315C4⋊C4—222no—
316C4⋊C4—222no—
317C4⋊C4—222no—
318C4⋊C4—222no—
319C4⋊C4—444no—
320C4⋊C4—882no—
321C4⋊C4—882no—
322C22⋊C4—228no—
323C22⋊C4—228no—
324C22⋊C4—444no—
325C22⋊C4—882no—
326C22⋊C4—882no—
327C42—22no—
328C42—22no—
329C42—444no—
330C42C2×C4×D1112yes—
331C42#433912yes—
332C11#2227411yescharacteristic, complemented, Sylow
333C23—224no—
334C23—442no—
335C23—442no—
336C23—442no—
337C23—442no—
338C23—442no—
339C23—442no—
340C23C22×D4411yescharacteristic
341Q8—224no—
342Q8—224no—
343Q8—442no—
344Q8—442no—
345D4—224no—
346D4—224no—
347D4—442no—
348D4—442no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—224no—
359C2×C4—442no—
360C2×C4—442no—
361C2×C4—442no—
362C2×C4—442no—
363C2×C4—442no—
364C2×C4—442no—
365C2×C4—442no—
366C2×C4—442no—
367C2×C4—888no—
368C2×C4C4×D4412yes—
369C2×C4C4×D4412yes—
370C2×C4C22×C4×D1111yescharacteristic
371C2×C4C2×#433911yescharacteristic
372C2×C4#6704212yes—
373C2×C4#6704212yes—
374C8—22no—
375C8—22no—
376C8—42no—
377C22—444no—
378C22—444no—
379C22—444no—
380C22—882no—
381C22—882no—
382C22—882no—
383C22—882no—
384C22C2×C4×D4411yescharacteristic
385C22#1062305612yes—
386C22#1062328212yes—
387C22#1062328311yescharacteristic
388C22#1062328411yescharacteristic
389C4—22no—
390C4—22no—
391C4—42no—
392C4—42no—
393C4—444no—
394C4—882no—
395C4—882no—
396C4#1062305211yescharacteristic
397C4#1062305211yescharacteristic
398C4#1062306612yes—
399C2—884no—
400C2#1307134111yescharacteristic
401C2#1307749311yescharacteristic
402C2#1307750111yescharacteristic
403C2#1307971212yes—
404C2#1307972712yes—
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1746C2
socleC23×C11C22×D4
prime radicalC22×D88C22
cosocleC22×C4×C11C24
hypercenter#1746D11
hypocenterC11#22274
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1746

Complements

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

NH ≅ G/Ntype
2. #13071327C2semidirect
3. #13069432C2semidirect
4. #13068970C2semidirect
6. #13068956C2semidirect
7. #13068949C2semidirect
8. #13068744C2semidirect
9. C11×#1746C2semidirect
26. #10622309C4semidirect
56. C2×Dic44C2×C4semidirect
61. C2×#4314C2×C4semidirect
63. #66928C2×C4semidirect
69. C4×C8×C11C2×C4semidirect
139. #1746D11semidirect
269. C4×C8C4×D11semidirect
332. C11#22274semidirect

Maximal subgroups

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

subgroupindex
C2×#106223092
#130713272
#130694322
#130689702
#130689632
#130689562
#130689492
#130687442
C11×#17462
#2227411