Finite Group Databasebeta

← #14772180

Subgroups — #14772180

Order 2816.

1062 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4323C211yesmaximal, characteristic
2C2×#10622369C212yesmaximal
3#13071526C211yesmaximal, characteristic, complemented
4#13071524C211yesmaximal, characteristic, complemented
5#13069348C212yesmaximal, complemented
6#13068878C212yesmaximal, complemented
7#13068875C212yesmaximal, complemented
8#13068778C211yesmaximal, characteristic, complemented
9#13068627C211yesmaximal, characteristic, complemented
10#13068481C211yesmaximal, characteristic, complemented
11C11×#1804C211yesmaximal, characteristic, complemented
12C2×C4×D4×C11C2211yescharacteristic
13C2×D4×Dic11C2212yes—
14C22×#4323C2211yescharacteristic
15C2×#66946C2212yes—
16C2×C4×D44C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#102C2212yes—
19C11×#382C2211yescharacteristic
20C2×#66896C2211yescharacteristic
21#10622825—21no—
22C2×C11⋊#95—21no—
23C2×#66885C2212yes—
24C2×C8×Dic11C2212yes—
25C4×#4323C418yescomplemented
26#10622598C2212yes—
27#10622586C2212yes—
28C2×#66873C2211yescharacteristic
29C2×#66872C2212yes—
30C2×#66871C2212yes—
31C2×#66871C2211yescharacteristic
32#10622563—22no—
33#10622549C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36#10622369—28no—
37#10622281—22no—
38#10622280—21no—
39D11×#95—21no—
40C11×#340C2212yes—
41#10622189C2212yes—
42#10622188C2212yes—
43C22×D4×C11C2311yescharacteristic
44C23×C4×C11—21no—
45C23×Dic11—22no—
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C22×C4×D11—22no—
49C22×C8×C11C2312yes—
50C4×D4×C11—22no—
51C4×D4×C11C2×C414yescomplemented
52C2×C11×C4⋊C4C2312yes—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C22⋊C4—21no—
55C2×C42×C11C2311yescharacteristic
56C2×C22⋊Dic11—22no—
57D4×Dic11—24no—
58D4×Dic11—42no—
59C2×#4323C2×C414yes—
60C2×#4323D414yes—
61C2×#4323Q814yes—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11D412yes—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11C2312yes—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2311yescharacteristic
72#66946—24no—
73#66946—42no—
74C4×D44—22no—
75C4×D44C2×C414yescomplemented
76C11×C4⋊C8—22no—
77C11×#102—24no—
78C11×#95—21no—
79C11×#95—21no—
80#66896C2×C414yescomplemented
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95D411yescharacteristic
86C11⋊#95D411yescharacteristic
87#66885—24no—
88C8×Dic11—24no—
89#66873C2×C414yescomplemented
90#66872—42no—
91#66871—24no—
92#66871C2×C414yescomplemented
93C4×C11⋊C8C2×C414yescomplemented
94#22682—111nomaximal, Sylow
95C24×C11—21no—
96C23×D11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11C22×C412yes—
101C2×D4×C11C2×D412yes—
102C2×D4×C11C2×Q812yes—
103C22×C4×C11—21no—
104C22×C4×C11—24no—
105C22×C4×C11—22no—
106C22×C4×C11—82no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11—44no—
113C22×Dic11—44no—
114C22×Dic11—82no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44C22×C412yes—
121C2×D44C2×D412yes—
122C2×D44C2×Q812yes—
123C2×C4×D11—24no—
124C2×C4×D11—44no—
125C2×C4×D11—44no—
126C2×C4×D11—82no—
127C2×C4×D11—82no—
128C2×C8×C11—22no—
129C2×C8×C11—22no—
130C2×C8×C11—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4C22×C412yes—
135C11×C22⋊C4—24no—
136C42×C11C22×C412yes—
137C42×C11#4112yes—
138C22⋊Dic11—44no—
139#4323C4⋊C4116yescomplemented
140(C2×D11)⋊C4—24no—
141(C2×D11)⋊C4—44no—
142C4⋊Dic11—24no—
143C4⋊Dic11—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11—22no—
146C4⋊Dic11—82no—
147C4⋊Dic11C22×C412yes—
148Dic11⋊C4—82no—
149C4×Dic11—22no—
150C4×Dic11—22no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8C22×C412yes—
154C2×C11⋊C8C22×C412yes—
155C2×C11⋊C8C2×D412yes—
156C2×C11⋊C8C2×Q812yes—
157C2×C4×D8—112no—
158C2×C4×D8—111no—
159#2349—111no—
160#2349—111no—
161#1942—112no—
162#1864—112no—
163#1864—112no—
164#1846—111no—
165#1804—111no—
166#1804D1111yescharacteristic, complemented
167C8×C4⋊C4—111no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11C22×D411yescharacteristic
174C22×D11—22no—
175C22×D11—22no—
176C22×D11—22no—
177C22×D11—42no—
178C22×D11—42no—
179D4×C11—22no—
180D4×C11—22no—
181D4×C11—22no—
182D4×C11C2×C4⋊C414yes—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—84no—
191C2×C4×C11C4×D412yes—
192C2×C4×C11C4×D412yes—
193C2×C4×C11C23×C411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×Q811yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11H(5,𝔽2)11yescharacteristic
198C2×C4×C112−1+411yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—88no—
210C2×Dic11#13514yes—
211D44—22no—
212D44—22no—
213D44—22no—
214D44C2×C4⋊C414yes—
215C4×D11—88no—
216C4×D11—84no—
217C8×C11—42no—
218C11⋊C8—22no—
219C11⋊C8C2×C4⋊C414yes—
220C22×D8—111no—
221C2×C4×D4—112no—
222C2×C4×D4—112no—
223C2×C4×D4—111no—
224C2×C4×D4C2×D1111yescharacteristic
225C4×D8—118no—
226C4×D8—228no—
227C2×#107—111no—
228C2×#107—112no—
229C2×#106—112no—
230C2×C4⋊C8C2×D1111yescharacteristic
231C2×#102—111no—
232C2×#102—111no—
233C2×#102—112no—
234C2×#102C2×D1112yes—
235C2×C4×C8—111no—
236C2×C4×C8—112no—
237#389—112no—
238#389—112no—
239#385—222no—
240#385—222no—
241#382—111no—
242#382C2×D1111yescharacteristic
243#380—221no—
244#380—221no—
245C4×C4⋊C4—111no—
246C2×#95—221no—
247C2×#95—221no—
248#340—112no—
249#340C2×D1112yes—
250#336—112no—
251C22×C11—24no—
252C22×C11—44no—
253C22×C11—42no—
254C22×C11—42no—
255C22×C11—44no—
256C22×C11C2×C4×D411yescharacteristic
257C22×C11D4211yescharacteristic
258C22×C11D4×Q811yescharacteristic
259C22×C11C2×#13512yes—
260C22×C11#57612yes—
261C2×D11—24no—
262C2×D11—44no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—44no—
266C4×C11—22no—
267C4×C11—22no—
268C4×C11—42no—
269C4×C11—82no—
270C4×C11C22×C4⋊C411yescharacteristic
271C4×C11#52011yescharacteristic
272C4×C11#54711yescharacteristic
273C4×C11#55411yescharacteristic
274Dic11—24no—
275Dic11—42no—
276Dic11—42no—
277Dic11—82no—
278C22×D4—111no—
279C22×D4C22×D1111yescharacteristic
280C23×C4—21no—
281C23×C4—222no—
282C23×C4—222no—
283C23×C4—221no—
284C2×D8—114no—
285C2×D8—114no—
286C2×D8—114no—
287C22×C8—111no—
288C22×C8—111no—
289C22×C8C22×D1112yes—
290C4×D4—22no—
291C4×D4—114no—
292C4×D4—224no—
293C4×D4—224no—
294C4×D4—222no—
295C4×D4—442no—
296C4×D4—442no—
297C4×D4C4×D1114yescomplemented
298C2×C4⋊C4—111no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4C22×D1112yes—
304C2×C4⋊C4C22×D1111yescharacteristic
305C2×C22⋊C4—21no—
306C2×C22⋊C4—221no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C42—112no—
310C2×C42C22×D1111yescharacteristic
311#107—114no—
312#107—224no—
313#106—442no—
314C4⋊C8—22no—
315#102—24no—
316#102—114no—
317#102—114no—
318#102—224no—
319C4×C8—114no—
320C4×C8—224no—
321#95—21no—
322#95—21no—
323#95—111no—
324#95—111no—
325#95—222no—
326#95—222no—
327#95—221no—
328#95—221no—
329C2×C11—44no—
330C2×C11D4×C4⋊C411yescharacteristic
331C2×C11C4×#13511yescharacteristic
332C2×C11#294811yescharacteristic
333C2×C11#328012yes—
334C2×C11#338012yes—
335D11—44no—
336C24—21no—
337C24—221no—
338C2×D4—21no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—112no—
342C2×D4—112no—
343C2×D4—112no—
344C2×D4—221no—
345C2×D4—221no—
346C2×D4—221no—
347C2×D4C2×C4×D1112yes—
348C2×D4D4×D1112yes—
349C2×D4Q8×D1112yes—
350C22×C4—21no—
351C22×C4—24no—
352C22×C4—22no—
353C22×C4—82no—
354C22×C4—112no—
355C22×C4—112no—
356C22×C4—221no—
357C22×C4—224no—
358C22×C4—222no—
359C22×C4—444no—
360C22×C4—444no—
361C22×C4—444no—
362C22×C4—444no—
363C22×C4—882no—
364C22×C4—882no—
365C22×C4—882no—
366C22×C4D4×D1111yescharacteristic
367C22×C4D4×D1111yescharacteristic
368C22×C4C23×D1111yescharacteristic
369D8—1116no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—112no—
374C2×C8—112no—
375C2×C8—112no—
376C2×C8—112no—
377C2×C8—221no—
378C2×C8—221no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—112no—
383C4⋊C4—224no—
384C4⋊C4—221no—
385C4⋊C4—222no—
386C4⋊C4—222no—
387C4⋊C4—882no—
388C4⋊C4—882no—
389C4⋊C4C2×C4×D1112yes—
390C22⋊C4—24no—
391C22⋊C4—224no—
392C22⋊C4—444no—
393C22⋊C4—444no—
394C42—222no—
395C42—222no—
396C42C2×C4×D1112yes—
397C42#434112yes—
398C11#2268211yescharacteristic, complemented, Sylow
399C23—22no—
400C23—22no—
401C23—22no—
402C23—42no—
403C23—42no—
404C23—222no—
405C23—222no—
406C23—222no—
407C23—442no—
408C23—442no—
409C23C2×D4×D1111yescharacteristic
410D4—22no—
411D4—22no—
412D4—22no—
413D4—114no—
414D4—222no—
415D4—222no—
416D4—222no—
417D4C4⋊C4×D1114yes—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—84no—
426C2×C4—114no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—884no—
438C2×C4—888no—
439C2×C4—888no—
440C2×C4(C22⋊D11)⋊C412yes—
441C2×C4(C22⋊D11)⋊C412yes—
442C2×C4C22×C4×D1111yescharacteristic
443C2×C4C2×D4×D1111yescharacteristic
444C2×C4C2×#434111yescharacteristic
445C2×C4C2×Q8×D1111yescharacteristic
446C2×C4#6704211yescharacteristic
447C2×C4#6704311yescharacteristic
448C8—42no—
449C8—114no—
450C8—222no—
451C22—24no—
452C22—44no—
453C22—42no—
454C22—42no—
455C22—44no—
456C22—224no—
457C22—444no—
458C22—442no—
459C22—442no—
460C22—444no—
461C22C2×(C22⋊D11)⋊C411yescharacteristic
462C22#1062314011yescharacteristic
463C22#1062316311yescharacteristic
464C22D11×#13512yes—
465C22#1062330512yes—
466C4—22no—
467C4—22no—
468C4—42no—
469C4—82no—
470C4—224no—
471C4—442no—
472C4—442no—
473C4—882no—
474C4C2×C4⋊C4×D1111yescharacteristic
475C4#1062305411yescharacteristic
476C4#1062314211yescharacteristic
477C4#1062316611yescharacteristic
478C2—44no—
479C2—444no—
480C2#1307151211yescharacteristic
481C2#1307738411yescharacteristic
482C2#1307746411yescharacteristic
483C2#1308029612yes—
484C2#1308147812yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
cosocleC22×C4×C11C24
hypercenter#1804D11
hypocenterC11#22682
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
3. #13071526C2semidirect
4. #13071524C2semidirect
5. #13069348C2semidirect
6. #13068878C2semidirect
7. #13068875C2semidirect
8. #13068778C2semidirect
9. #13068627C2semidirect
10. #13068481C2semidirect
11. C11×#1804C2semidirect
25. C4×#4323C4semidirect
51. C4×D4×C11C2×C4semidirect
75. C4×D44C2×C4semidirect
80. #66896C2×C4semidirect
89. #66873C2×C4semidirect
92. #66871C2×C4semidirect
93. C4×C11⋊C8C2×C4semidirect
139. #4323C4⋊C4semidirect
166. #1804D11semidirect
297. C4×D4C4×D11semidirect
398. C11#22682semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43232
C2×#106223692
#130715262
#130715242
#130693482
#130688782
#130688752
#130687782
#130686272
#130684812
C11×#18042
#2268211