Finite Group Databasebeta

← #14719863

Subgroups — #14719863

Order 2816.

1386 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C211yesmaximal, characteristic
2D11×#407C212yesmaximal
3#13066978C218yesmaximal, complemented
4#13066946C211yesmaximal, characteristic, complemented
5#13066945C212yesmaximal, complemented
6C11×#1463C211yesmaximal, characteristic, complemented
7C23×C4×D11C2211yescharacteristic
8C23×Dic22C411yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×(C2×D11)⋊C4C411yescharacteristic
11C22×(C2×D11)⋊C4C411yescharacteristic
12C22×Dic11⋊C4C411yescharacteristic
13C22×Dic11⋊C4C2211yescharacteristic
14C2×M16×D11—22no—
15C2×#66949—22no—
16C2×#66949—22no—
17C2×#66949—22no—
18C2×#66949—22no—
19C2×#66949C414yes—
20C2×#66949C2214yes—
21C11×#407C2212yes—
22#10622820C2212yes—
23#10622739—22no—
24#10622339—22no—
25#10622339C2214yes—
26D11×C22⋊C8—22no—
27D11×C22⋊C8C2214yes—
28C11×#324C2214yescomplemented
29#10622166C2214yescomplemented
30#10622107C2218yescomplemented
31C24×D11C2×C411yescharacteristic
32C23×C4×C11C2×C411yescharacteristic
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11C2×C411yescharacteristic
36C23×Dic11C2×C411yescharacteristic
37C23×Dic11C2×C411yescharacteristic
38C22×C4×D11—44no—
39C22×C4×D11C2×C412yes—
40C22×C4×D11D412yes—
41C22×C4×D11D412yes—
42C22×C4×D11D412yes—
43C22×C4×D11D412yes—
44C22×C4×D11C2312yes—
45C22×Dic22—21no—
46C22×Dic22—22no—
47C22×Dic22—21no—
48C22×Dic22—44no—
49C22×Dic22C2×C414yes—
50C2×C11×M16—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4C2×C412yes—
54C2×C11×C4⋊C4C2312yes—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4C2×C414yes—
62C2×(C2×D11)⋊C4C2×C414yes—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—21no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—21no—
68C2×Dic11⋊C4C2×C412yes—
69C2×Dic11⋊C4C2×C414yes—
70C2×Dic11⋊C4C2312yes—
71C2×#4318—22no—
72M16×D11—48no—
73C2×#4313—24no—
74C2×C8×D11—24no—
75#66949—24no—
76#66949—24no—
77#66949—24no—
78#66949—24no—
79#66949—24no—
80#66949—24no—
81#66949—24no—
82#66949—24no—
83C11×C22⋊C8—22no—
84C11×C22⋊C8C2314yes—
85C22⋊(C11⋊C8)—22no—
86C22⋊(C11⋊C8)C2314yes—
87(C2×D11)⋊C8—24no—
88(C2×D11)⋊C8—24no—
89#17397—111nomaximal, Sylow
90C24×C11C22×C411yescharacteristic
91C23×D11—24no—
92C23×D11—42no—
93C23×D11—42no—
94C23×D11C22⋊C412yes—
95C23×D11C22⋊C411yescharacteristic
96C23×D11C22⋊C411yescharacteristic
97C23×D11C22×C412yes—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11C22×C412yes—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—24no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—42no—
117C22×Dic11—42no—
118C22×Dic11C22⋊C411yescharacteristic
119C22×Dic11C22⋊C412yes—
120C22×Dic11C22⋊C411yescharacteristic
121C22×Dic11C22×C412yes—
122C22×Dic11C22×C412yes—
123C22×Dic11C22×C412yes—
124C2×C4×D11—28no—
125C2×C4×D11—44no—
126C2×C4×D11—44no—
127C2×C4×D11—44no—
128C2×C4×D11—44no—
129C2×C4×D11—44no—
130C2×C4×D11C22⋊C412yes—
131C2×C4×D11C22⋊C412yes—
132C2×C4×D11C22⋊C412yes—
133C2×C4×D11C22⋊C412yes—
134C2×C4×D11C2×D412yes—
135C2×C4×D11C2×D412yes—
136C2×C4×D11C2×D412yes—
137C2×C4×D11C2×D412yes—
138C2×Dic22—24no—
139C2×Dic22—24no—
140C2×Dic22—48no—
141C2×Dic22—44no—
142C2×Dic22—44no—
143C2×Dic22—48no—
144C11×M16—44no—
145C2×C8×C11—24no—
146C11×C4⋊C4—24no—
147C11×C4⋊C4—24no—
148(C2×D11)⋊C4—24no—
149(C2×D11)⋊C4—24no—
150(C2×D11)⋊C4—24no—
151(C2×D11)⋊C4—24no—
152Dic11⋊C4—24no—
153Dic11⋊C4—24no—
154Dic11⋊C4—24no—
155Dic11⋊C4—24no—
156#4318—44no—
157C2×C11⋊C8—24no—
158#4313—48no—
159C8×D11—48no—
160C22×C22⋊Q8—111no—
161C2×#407—112no—
162#1472—118no—
163#1463—112no—
164#1463—111no—
165#1463D1111yescharacteristic, complemented
166C23×C11—22no—
167C23×C11—22no—
168C23×C11—22no—
169C23×C11C2×C22⋊C411yescharacteristic
170C23×C11C2×C22⋊C411yescharacteristic
171C23×C11C23×C411yescharacteristic
172C22×D11—24no—
173C22×D11—24no—
174C22×D11—22no—
175C22×D11—24no—
176C22×D11—24no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—42no—
180C22×D11—41no—
181C22×D11—42no—
182C22×D11—41no—
183C22×D11—416no—
184C22×D11#10114yes—
185C22×D11C2×C22⋊C412yes—
186C22×D11C2×C22⋊C412yes—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11C2×C22⋊C412yes—
200C2×C4×C11C22×D412yes—
201C2×Dic11—22no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—24no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11#9914yes—
213C2×Dic11C2×C22⋊C412yes—
214C2×Dic11C2×C22⋊C412yes—
215C4×D11—24no—
216C4×D11—24no—
217C4×D11—24no—
218C4×D11—24no—
219C4×D11—42no—
220C4×D11—42no—
221C4×D11—42no—
222C4×D11—42no—
223Dic22—48no—
224Dic22—48no—
225C8×C11—44no—
226C11⋊C8—44no—
227C23×Q8—111no—
228C24×C4—111no—
229C22×M16—222no—
230C2×C22⋊Q8—114no—
231C2×C22⋊Q8—114no—
232C2×C22⋊Q8—222no—
233C2×C22⋊Q8—222no—
234C2×C22⋊Q8—222no—
235C2×C22⋊Q8—222no—
236C22×C4⋊C4—111no—
237C22×C4⋊C4—111no—
238C22×C4⋊C4C2×D1111yescharacteristic
239C22×C22⋊C4—111no—
240C22×C22⋊C4—111no—
241#407—112no—
242#407—114no—
243#407—222no—
244#407—222no—
245#407C2×D1112yes—
246C2×C22⋊C8—114no—
247C2×C22⋊C8—222no—
248#324—114no—
249#324—118no—
250#324C2×D1114yescomplemented
251C22×C11—28no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11C2×#9912yes—
259C22×C11C2×#10112yes—
260C22×C11C22×C22⋊C411yescharacteristic
261C22×C11#56812yes—
262C2×D11—22no—
263C2×D11—22no—
264C2×D11—22no—
265C2×D11—22no—
266C2×D11—22no—
267C2×D11—44no—
268C2×D11—48no—
269C2×D11—48no—
270C2×D11—44no—
271C2×D11C2×#10114yes—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—42no—
276Dic11—22no—
277Dic11—42no—
278Dic11—42no—
279Dic11C2×#9914yes—
280C25—111no—
281C22×Q8—114no—
282C22×Q8—221no—
283C22×Q8—222no—
284C22×Q8—221no—
285C22×Q8—444no—
286C23×C4—111no—
287C23×C4—112no—
288C23×C4—112no—
289C23×C4—112no—
290C23×C4—112no—
291C23×C4—112no—
292C23×C4—112no—
293C23×C4—111no—
294C23×C4—111no—
295C23×C4—444no—
296C23×C4C4×D1111yescharacteristic
297C23×C4C4×D1111yescharacteristic
298C23×C4C22×D1111yescharacteristic
299C2×M16—22no—
300C2×M16—224no—
301C2×M16—222no—
302C2×M16—448no—
303C22×C8—224no—
304C22⋊Q8—224no—
305C22⋊Q8—224no—
306C22⋊Q8—224no—
307C22⋊Q8—224no—
308C22⋊Q8—224no—
309C22⋊Q8—224no—
310C22⋊Q8—224no—
311C22⋊Q8—224no—
312C2×C4⋊C4—22no—
313C2×C4⋊C4—22no—
314C2×C4⋊C4—114no—
315C2×C4⋊C4—112no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—221no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4—222no—
322C2×C4⋊C4C4×D1112yes—
323C2×C4⋊C4C22×D1112yes—
324C2×C22⋊C4—114no—
325C2×C22⋊C4—114no—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—221no—
329C2×C22⋊C4—221no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—221no—
332C22⋊C8—22no—
333C22⋊C8—114no—
334C22⋊C8—224no—
335C22⋊C8—224no—
336C22⋊C8—222no—
337C22⋊C8C22×D1114yes—
338C2×C11—22no—
339C2×C11—22no—
340C2×C11—22no—
341C2×C11#287911yescharacteristic
342C2×C11C22×#9911yescharacteristic
343C2×C11C22×#10111yescharacteristic
344D11—24no—
345D11—42no—
346C24—111no—
347C24—112no—
348C24—112no—
349C24—111no—
350C24—224no—
351C24—442no—
352C24—442no—
353C24C2×C4×D1111yescharacteristic
354C2×Q8—224no—
355C2×Q8—224no—
356C2×Q8—444no—
357C2×Q8—448no—
358C2×Q8—448no—
359C2×Q8—444no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—42no—
367C22×C4—111no—
368C22×C4—112no—
369C22×C4—111no—
370C22×C4—112no—
371C22×C4—112no—
372C22×C4—112no—
373C22×C4—112no—
374C22×C4—112no—
375C22×C4—112no—
376C22×C4—112no—
377C22×C4—112no—
378C22×C4—112no—
379C22×C4—112no—
380C22×C4—112no—
381C22×C4—228no—
382C22×C4—224no—
383C22×C4—221no—
384C22×C4—221no—
385C22×C4—221no—
386C22×C4—221no—
387C22×C4—444no—
388C22×C4—444no—
389C22×C4—444no—
390C22×C4—444no—
391C22×C4—444no—
392C22×C4—442no—
393C22×C4—442no—
394C22×C4C2×C4×D1112yes—
395C22×C4C2×C4×D1112yes—
396C22×C4C2×C4×D1111yescharacteristic
397C22×C4D4×D1112yes—
398C22×C4D4×D1112yes—
399C22×C4C23×D1111yescharacteristic
400M16—44no—
401M16—448no—
402M16—444no—
403C2×C8—24no—
404C2×C8—224no—
405C2×C8—448no—
406C4⋊C4—24no—
407C4⋊C4—24no—
408C4⋊C4—224no—
409C4⋊C4—224no—
410C4⋊C4—224no—
411C4⋊C4—224no—
412C22⋊C4—224no—
413C22⋊C4—224no—
414C22⋊C4—224no—
415C22⋊C4—224no—
416C11#1739711yescharacteristic, complemented, Sylow
417C23—22no—
418C23—22no—
419C23—22no—
420C23—112no—
421C23—114no—
422C23—112no—
423C23—224no—
424C23—224no—
425C23—224no—
426C23—224no—
427C23—222no—
428C23—441no—
429C23—441no—
430C23—442no—
431C23—441no—
432C23—442no—
433C23—441no—
434C23—4416no—
435C23C22⋊C4×D1111yescharacteristic
436C23C22⋊C4×D1111yescharacteristic
437C23C22×C4×D1111yescharacteristic
438Q8—448no—
439Q8—448no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—24no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—112no—
453C2×C4—114no—
454C2×C4—112no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—224no—
458C2×C4—224no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—222no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—224no—
465C2×C4—442no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4C22⋊C4×D1112yes—
475C2×C4C2×D4×D1112yes—
476C8—44no—
477C8—444no—
478C22—28no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—114no—
486C22—222no—
487C22—222no—
488C22—222no—
489C22—222no—
490C22—222no—
491C22—444no—
492C22—448no—
493C22—448no—
494C22—444no—
495C22D11×#9912yes—
496C22D11×#10112yes—
497C22C2×C22⋊C4×D1111yescharacteristic
498C22#1062327612yes—
499C4—22no—
500C4—22no—
501C4—42no—
502C4—42no—
503C4—114no—
504C4—222no—
505C4—442no—
506C4—442no—
507C2—22no—
508C2—22no—
509C2—22no—
510C2—224no—
511C2—442no—
512C2#1307705911yescharacteristic
513C2C2×D11×#9911yescharacteristic
514C2C2×D11×#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1463C2
socleC22×C11C22×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1463D11
hypocenterC11#17397
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
3. #13066978C2semidirect
4. #13066946C2semidirect
5. #13066945C2semidirect
6. C11×#1463C2semidirect
28. C11×#324C22semidirect
29. #10622166C22semidirect
30. #10622107C22semidirect
165. #1463D11semidirect
250. #324C2×D11semidirect
416. C11#17397semidirect

Maximal subgroups

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

subgroupindex
C22×#669492
D11×#4072
#130669782
#130669462
#130669452
C11×#14632
#1739711