Finite Group Databasebeta

← #14722363

Subgroups — #14722363

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2#13077246C211yesmaximal, characteristic
3#13077246C211yesmaximal, characteristic
4#13067334C211yesmaximal, characteristic, complemented
5#13067333C211yesmaximal, characteristic, complemented
6#13067332C211yesmaximal, characteristic, complemented
7#13067299C214yesmaximal, complemented
8#13067286C214yesmaximal, complemented
9C11×#1556C211yesmaximal, characteristic, complemented
10C22×Q8×D11—21no—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997—21no—
13D11×C4⋊Q8—21no—
14D11×C4⋊Q8—21no—
15D11×C4⋊Q8—21no—
16D11×C4⋊Q8—21no—
17D11×C4⋊Q8C412yes—
18D11×C4⋊Q8C412yes—
19D11×C4⋊Q8C2212yes—
20D11×C4⋊Q8C2212yes—
21C2×C4⋊C4×D11—21no—
22C2×C4⋊C4×D11C412yes—
23C2×#66941—21no—
24C2×#66941C412yes—
25C2×C42×D11C2211yescharacteristic
26C2×#66922C2211yescharacteristic
27C11×#432C2211yescharacteristic
28C11×#432C2211yescharacteristic
29#10622539C2211yescharacteristic
30#10622539C2211yescharacteristic
31#10622450C2212yes—
32#10622450C2212yes—
33#10622446C2212yes—
34#10622446C2212yes—
35#10622339—21no—
36#10622339—21no—
37#10622331—21no—
38#10622331—21no—
39#10622320—21no—
40#10622320—21no—
41#10622318—21no—
42#10622318—21no—
43C11×#332C2214yescomplemented
44#10622185C2214yescomplemented
45#10622124C2214yescomplemented
46#10622120C2214yescomplemented
47C22×Q8×C11—21no—
48C2×Q8×D11—22no—
49C2×Q8×D11—22no—
50C2×Q8×D11—22no—
51C2×Q8×D11—22no—
52C2×Q8×D11—48no—
53C22×C4×D11—22no—
54C22×C4×D11C2×C411yescharacteristic
55C22×C4×D11D411yescharacteristic
56C22×C4×D11D411yescharacteristic
57C22×Dic22—21no—
58C22×Dic22—22no—
59C11×C4⋊Q8—21no—
60C11×C4⋊Q8—21no—
61C11×C4⋊Q8C2×C412yes—
62C11×C4⋊Q8C2312yes—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2×C412yes—
65C2×C42×C11C2311yescharacteristic
66#66997—22no—
67#66997—22no—
68#66997—22no—
69#66997—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2×C412yes—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×C4×Dic11C2×C411yescharacteristic
75C2×C4×Dic11D411yescharacteristic
76C2×C4×Dic11D411yescharacteristic
77C2×#4313—22no—
78C2×#4313—22no—
79C4⋊C4×D11—22no—
80C4⋊C4×D11—22no—
81C4⋊C4×D11—22no—
82C4⋊C4×D11—22no—
83C4⋊C4×D11—22no—
84C4⋊C4×D11—22no—
85C4⋊C4×D11C2×C414yes—
86C4⋊C4×D11C2×C414yes—
87#66941—22no—
88#66941—22no—
89#66941—22no—
90#66941—22no—
91#66941—22no—
92#66941—22no—
93#66941C2×C414yes—
94#66941C2×C414yes—
95C42×D11C2×C411yescharacteristic
96C42×D11C2×C411yescharacteristic
97C42×D11D411yescharacteristic
98C42×D11D411yescharacteristic
99C42×D11D411yescharacteristic
100C42×D11D411yescharacteristic
101C42×D11C2311yescharacteristic
102C42×D11C2311yescharacteristic
103#66922—21no—
104#66922—21no—
105#66922C2×C412yes—
106#66922C2312yes—
107C11×C4⋊C8C2312yes—
108C11×C4⋊C8C2312yes—
109C11×C22⋊C8—21no—
110C11×C22⋊C8—21no—
111C11×#97—21no—
112C11×#97—21no—
113C22⋊(C11⋊C8)—21no—
114C22⋊(C11⋊C8)—21no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117Dic11⋊C8—22no—
118Dic11⋊C8—22no—
119C8×Dic11—22no—
120C8×Dic11—22no—
121C4⋊(C11⋊C8)C2312yes—
122C4⋊(C11⋊C8)C2312yes—
123#66867—21no—
124#66867—21no—
125#17742—111nomaximal, Sylow
126C23×D11C22⋊C411yescharacteristic
127C2×Q8×C11—22no—
128C2×Q8×C11—22no—
129C2×Q8×C11—44no—
130C22×C4×C11—22no—
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×Dic11—22no—
135C22×Dic11C22⋊C411yescharacteristic
136C22×Dic11C22⋊C411yescharacteristic
137C22×Dic11C22⋊C411yescharacteristic
138Q8×D11—48no—
139Q8×D11—48no—
140Q8×D11—48no—
141Q8×D11—48no—
142C2×C4×D11—24no—
143C2×C4×D11—24no—
144C2×C4×D11—24no—
145C2×C4×D11—24no—
146C2×C4×D11—24no—
147C2×C4×D11—48no—
148C2×C4×D11C22⋊C411yescharacteristic
149C2×C4×D11C22⋊C411yescharacteristic
150C2×C4×D11C22⋊C411yescharacteristic
151C2×C4×D11C22⋊C411yescharacteristic
152C2×C4×D11C22⋊C411yescharacteristic
153C2×C4×D11C22⋊C411yescharacteristic
154C2×C4×D11C22×C411yescharacteristic
155C2×C4×D11C22×C411yescharacteristic
156C2×C4×D11C2×D411yescharacteristic
157C2×C4×D11C2×D411yescharacteristic
158C2×C4×D11C2×D411yescharacteristic
159C2×C4×D11C2×D411yescharacteristic
160C2×Dic22—24no—
161C2×Dic22—24no—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C2×Dic22—44no—
165C2×Dic22—48no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C11×C4⋊C4—22no—
169C11×C4⋊C4—22no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4C22×C414yes—
172C42×C11C22×C411yescharacteristic
173C42×C11C2×D411yescharacteristic
174C42×C11C2×D411yescharacteristic
175C42×C11C2411yescharacteristic
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11C22×C414yes—
180Dic11⋊C4—24no—
181Dic11⋊C4—24no—
182Dic11⋊C4—24no—
183Dic11⋊C4—24no—
184C4×Dic11C22⋊C411yescharacteristic
185C4×Dic11C22⋊C411yescharacteristic
186C4×Dic11C22⋊C411yescharacteristic
187C4×Dic11C22⋊C411yescharacteristic
188C4×Dic11C22⋊C411yescharacteristic
189C4×Dic11C22⋊C411yescharacteristic
190C4×Dic11C22×C411yescharacteristic
191C4×Dic11C22×C411yescharacteristic
192C4×Dic11C2×D411yescharacteristic
193C4×Dic11C2×D411yescharacteristic
194C4×Dic11C2×D411yescharacteristic
195C4×Dic11C2×D411yescharacteristic
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198#4313—44no—
199#4313—44no—
200C22×C4⋊Q8—111no—
201#2920—111no—
202#2920—111no—
203#1556—111no—
204#1556—111no—
205#1556—111no—
206#1556D1111yescharacteristic, complemented
207#1549—114no—
208#1546—114no—
209C23×C11C2×C22⋊C411yescharacteristic
210C22×D11—22no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11C2×C22⋊C411yescharacteristic
214C22×D11C2×C22⋊C411yescharacteristic
215Q8×C11—44no—
216Q8×C11—44no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—44no—
222C2×C4×C11C2×C22⋊C411yescharacteristic
223C2×C4×C11C2×C22⋊C411yescharacteristic
224C2×C4×C11C2×C22⋊C411yescharacteristic
225C2×C4×C11C23×C411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—44no—
232C2×Dic11#10114yes—
233C2×Dic11C2×C22⋊C411yescharacteristic
234C2×Dic11C2×C22⋊C411yescharacteristic
235C2×Dic11C2×C22⋊C411yescharacteristic
236C2×Dic11C2×C22⋊C411yescharacteristic
237C2×Dic11C2×C22⋊C411yescharacteristic
238C2×Dic11C2×C22⋊C411yescharacteristic
239C4×D11—22no—
240C4×D11—22no—
241C4×D11—22no—
242C4×D11—22no—
243C4×D11—22no—
244C4×D11—22no—
245C4×D11—22no—
246C4×D11—22no—
247C4×D11—22no—
248C4×D11—22no—
249C4×D11—48no—
250C4×D11—48no—
251C4×D11AGL(1,ℤ/8)14yes—
252C4×D11#13714yes—
253Dic22—48no—
254Dic22—44no—
255Dic22—44no—
256Dic22—48no—
257C8×C11—42no—
258C8×C11—42no—
259C11⋊C8—42no—
260C11⋊C8—42no—
261C23×Q8—221no—
262C2×C4⋊Q8—112no—
263C2×C4⋊Q8—112no—
264C2×C4⋊Q8—112no—
265C2×C4⋊Q8—112no—
266C2×C4⋊Q8—112no—
267C2×C4⋊Q8—111no—
268C2×C4⋊Q8—221no—
269C2×C4⋊Q8—221no—
270C2×C4⋊Q8—221no—
271C2×C4⋊Q8—221no—
272C2×C4⋊Q8—221no—
273C2×C4⋊Q8—221no—
274C2×C4⋊Q8C2×D1111yescharacteristic
275C22×C4⋊C4—112no—
276C22×C4⋊C4—221no—
277C22×C42—111no—
278#432—111no—
279#432—111no—
280#432—221no—
281#432—221no—
282#432C2×D1111yescharacteristic
283#432C2×D1111yescharacteristic
284#431—112no—
285#431—112no—
286#431—221no—
287#431—221no—
288#423—112no—
289#423—112no—
290#407—221no—
291#407—221no—
292C4×M16—221no—
293C4×M16—221no—
294#332—114no—
295#332—114no—
296#332—114no—
297#332C2×D1114yescomplemented
298C22×C11—21no—
299C22×C11—21no—
300C22×C11C2×#10112yes—
301C22×C11C22×C22⋊C411yescharacteristic
302C2×D11—28no—
303C2×D11—21no—
304C2×D11—21no—
305C2×D11—21no—
306C2×D11—21no—
307C2×D11#41812yes—
308C2×D11#41912yes—
309C4×C11—21no—
310C4×C11—21no—
311C4×C11—21no—
312C4×C11—21no—
313C4×C11—44no—
314C4×C11C2×AGL(1,ℤ/8)12yes—
315C4×C11C2×#13712yes—
316Dic11—21no—
317Dic11—21no—
318Dic11—44no—
319Dic11C2×#10112yes—
320Dic11C2×#10112yes—
321Dic11#41812yes—
322Dic11#41912yes—
323C22×Q8—21no—
324C22×Q8—222no—
325C22×Q8—222no—
326C22×Q8—222no—
327C22×Q8—222no—
328C22×Q8—222no—
329C22×Q8—221no—
330C22×Q8—448no—
331C23×C4—111no—
332C23×C4—111no—
333C23×C4—111no—
334C23×C4—222no—
335C2×M16—222no—
336C2×M16—222no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—114no—
340C4⋊Q8—114no—
341C4⋊Q8—112no—
342C4⋊Q8—112no—
343C4⋊Q8—222no—
344C4⋊Q8—222no—
345C4⋊Q8—222no—
346C4⋊Q8—222no—
347C4⋊Q8—222no—
348C4⋊Q8—222no—
349C4⋊Q8—222no—
350C4⋊Q8—222no—
351C4⋊Q8—222no—
352C4⋊Q8—222no—
353C4⋊Q8—221no—
354C4⋊Q8—221no—
355C4⋊Q8C4×D1112yes—
356C4⋊Q8C22×D1112yes—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—114no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—222no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4C4×D1112yes—
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42C22×D1111yescharacteristic
383C4⋊C8—112no—
384C4⋊C8—112no—
385C4⋊C8—222no—
386C4⋊C8—222no—
387C4⋊C8C22×D1112yes—
388C4⋊C8C22×D1112yes—
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8—222no—
392C22⋊C8—222no—
393C22⋊C8—221no—
394C22⋊C8—221no—
395#97—21no—
396#97—21no—
397#97—221no—
398#97—221no—
399C4×C8—222no—
400C4×C8—222no—
401C2×C11—22no—
402C2×C11C22×#10111yescharacteristic
403C2×C11C2×#41811yescharacteristic
404C2×C11C2×#41911yescharacteristic
405D11—22no—
406D11—22no—
407C24—111no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—44no—
411C2×Q8—224no—
412C2×Q8—224no—
413C2×Q8—222no—
414C2×Q8—222no—
415C2×Q8—444no—
416C2×Q8—448no—
417C2×Q8—448no—
418C2×Q8—448no—
419C2×Q8—448no—
420C2×Q8—448no—
421C22×C4—22no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—111no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—448no—
444C22×C4C2×C4×D1111yescharacteristic
445C22×C4D4×D1111yescharacteristic
446C22×C4D4×D1111yescharacteristic
447M16—444no—
448M16—444no—
449C2×C8—22no—
450C2×C8—22no—
451C2×C8—222no—
452C2×C8—222no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—114no—
457C4⋊C4—224no—
458C4⋊C4—224no—
459C4⋊C4—224no—
460C4⋊C4—224no—
461C4⋊C4—222no—
462C4⋊C4—222no—
463C4⋊C4—222no—
464C4⋊C4C2×C4×D1114yes—
465C42—111no—
466C42—111no—
467C42—111no—
468C42—111no—
469C42—111no—
470C42—111no—
471C42—111no—
472C42—111no—
473C42—111no—
474C42—111no—
475C42—111no—
476C42—111no—
477C42C2×C4×D1111yescharacteristic
478C42D4×D1111yescharacteristic
479C42D4×D1111yescharacteristic
480C42C23×D1111yescharacteristic
481C11#1774211yescharacteristic, complemented, Sylow
482C23—111no—
483C23—111no—
484C23—222no—
485C23—222no—
486C23—222no—
487C23C22⋊C4×D1111yescharacteristic
488Q8—44no—
489Q8—44no—
490Q8—444no—
491Q8—448no—
492Q8—448no—
493Q8—444no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—44no—
499C2×C4—111no—
500C2×C4—111no—
501C2×C4—111no—
502C2×C4—111no—
503C2×C4—114no—
504C2×C4—114no—
505C2×C4—114no—
506C2×C4—111no—
507C2×C4—111no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—224no—
521C2×C4—448no—
522C2×C4—448no—
523C2×C4—444no—
524C2×C4C22⋊C4×D1111yescharacteristic
525C2×C4C22⋊C4×D1111yescharacteristic
526C2×C4C22⋊C4×D1111yescharacteristic
527C2×C4C22×C4×D1111yescharacteristic
528C2×C4C2×D4×D1111yescharacteristic
529C2×C4C2×D4×D1111yescharacteristic
530C8—42no—
531C8—42no—
532C8—442no—
533C8—442no—
534C22—21no—
535C22—21no—
536C22—112no—
537C22—112no—
538C22—228no—
539C22—221no—
540C22—221no—
541C22—221no—
542C22—221no—
543C22D11×#10112yes—
544C22C2×C22⋊C4×D1111yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—44no—
550C4—112no—
551C4—112no—
552C4—112no—
553C4—112no—
554C4—221no—
555C4—221no—
556C4—444no—
557C4D11×AGL(1,ℤ/8)12yes—
558C4D11×#13712yes—
559C2—22no—
560C2—222no—
561C2—222no—
562C2C2×D11×#10111yescharacteristic
563C2D11×#41811yescharacteristic
564C2D11×#41911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1556C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1556D11
hypocenterC11#17742
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
4. #13067334C2semidirect
5. #13067333C2semidirect
6. #13067332C2semidirect
7. #13067299C2semidirect
8. #13067286C2semidirect
9. C11×#1556C2semidirect
43. C11×#332C22semidirect
44. #10622185C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
206. #1556D11semidirect
297. #332C2×D11semidirect
481. C11#17742semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
#130772462
#130673342
#130673332
#130673322
#130672992
#130672862
C11×#15562
#1774211