Finite Group Databasebeta

← #14753854

Subgroups — #14753854

Order 2816.

1382 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4343C211yesmaximal, characteristic
2C2×#10622318C211yesmaximal, characteristic, complemented
3#13071020C211yesmaximal, characteristic, complemented
4#13068710C212yesmaximal, complemented
5#13068619C212yesmaximal, complemented
6#13068615C212yesmaximal, complemented
7#13068555C212yesmaximal
8#13068446C211yesmaximal, characteristic, complemented
9#13068444C211yesmaximal, characteristic, complemented
10#13068442C211yesmaximal, characteristic, complemented
11C11×#1763C211yesmaximal, characteristic, complemented
12C22×#4343C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×Q8×Dic11C2211yescharacteristic
15C4×#4343—24no—
16C4×#4343C418yescomplemented
17C2×#66946—21no—
18C2×#66946C2211yescharacteristic
19C2×#66945—21no—
20C2×#66945C2211yescharacteristic
21C2×C4×D44—21no—
22C2×C4×D44C2211yescharacteristic
23C2×#66925—21no—
24C2×C42×D11—21no—
25C2×C42×D11C2211yescharacteristic
26C2×C11×#103C2212yes—
27C2×C11×#97C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66885C2212yes—
31C2×(C2×D11)⋊C8C2212yes—
32C2×Dic11⋊C8C2212yes—
33#10622600C2212yes—
34#10622589C2212yes—
35C2×#66873C2212yes—
36C4×C4⋊Dic11C2211yescharacteristic
37C4×Dic11⋊C4—21no—
38C2×#66867C2211yescharacteristic
39#10622318—24no—
40#10622280—21no—
41#10622263—21no—
42C11×#340C2212yes—
43#10622189C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C22×Q8×C11C2311yescharacteristic
47C2×#4343—24no—
48C2×#4343—24no—
49C2×#4343—22no—
50C2×#4343C2×C414yes—
51C22×D44—21no—
52C22×D44C2311yescharacteristic
53C22×C4×D11—21no—
54C22×C4×D11—21no—
55C22×C4×D11—21no—
56C22×C4×D11D411yescharacteristic
57C22×C4×D11D411yescharacteristic
58C22×C4×D11C2311yescharacteristic
59C22×C8×C11C2312yes—
60C4×Q8×C11—22no—
61C4×Q8×C11C2×C414yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4C2312yes—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C42×C11—21no—
66C2×C42×C11—21no—
67C2×C42×C11C2311yescharacteristic
68Q8×Dic11—22no—
69Q8×Dic11C2×C414yes—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—22no—
78C2×Dic11⋊C4—22no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86#66946—28no—
87#66946—22no—
88#66946C2×C414yes—
89#66945—22no—
90#66945—28no—
91#66945C2×C414yes—
92C4×D44—28no—
93C4×D44—22no—
94C4×D44C2×C414yes—
95#66925—44no—
96C42×D11—28no—
97C42×D11C2×C414yes—
98C42×D11D414yes—
99C11×#103—24no—
100C11×#97—22no—
101C11×#95—21no—
102#66899—24no—
103C11⋊#95—21no—
104C11⋊#95—22no—
105#66885—24no—
106(C2×D11)⋊C8—24no—
107Dic11⋊C8—24no—
108#66873—24no—
109#66867—22no—
110#20743—111nomaximal, Sylow
111C23×D11—21no—
112C23×D11C2×D411yescharacteristic
113C2×Q8×C11—21no—
114C2×Q8×C11—22no—
115C2×Q8×C11C22×C412yes—
116C2×Q8×C11#4114yes—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—22no—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2411yescharacteristic
123C22×Dic11—21no—
124C22×Dic11—22no—
125C22×Dic11C2×D411yescharacteristic
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128#4343—216no—
129#4343—28no—
130#4343—28no—
131C2×D44—28no—
132C2×D44—24no—
133C2×D44—21no—
134C2×D44—22no—
135C2×D44C22×C412yes—
136C2×D44#4114yes—
137C2×C4×D11—28no—
138C2×C4×D11—24no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—24no—
142C2×C4×D11—24no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—42no—
146C2×C4×D11—44no—
147C2×C4×D11—42no—
148C2×C4×D11—42no—
149C2×C4×D11C22⋊C414yes—
150C2×C4×D11C22⋊C414yes—
151C2×C4×D11C22×C412yes—
152C2×C4×D11C2×D412yes—
153C2×C8×C11—22no—
154C2×C8×C11—22no—
155C2×C8×C11—22no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4C22×C412yes—
161C42×C11—24no—
162C42×C11—42no—
163C42×C11C22×C412yes—
164C42×C11C2×D412yes—
165(C2×D11)⋊C4—24no—
166(C2×D11)⋊C4—24no—
167(C2×D11)⋊C4—24no—
168(C2×D11)⋊C4—44no—
169C4⋊Dic11—24no—
170C4⋊Dic11—21no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11C22×C412yes—
174Dic11⋊C4—44no—
175Dic11⋊C4—44no—
176C4×Dic11—24no—
177C4×Dic11—24no—
178C4×Dic11—42no—
179C4×Dic11C22⋊C414yes—
180C4×Dic11C22⋊C414yes—
181C4×Dic11C22×C412yes—
182C4×Dic11C2×D412yes—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C4×#41—111no—
187C2×#432—111no—
188#2285—111no—
189#1825—112no—
190#1803—112no—
191#1802—112no—
192#1788—112no—
193#1763—111no—
194#1763D1111yescharacteristic, complemented
195#1762—111no—
196#1762—111no—
197C23×C11C22×D411yescharacteristic
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—24no—
201C22×D11—21no—
202C22×D11—21no—
203C22×D11—22no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—42no—
207C22×D11C2×C22⋊C412yes—
208Q8×C11—22no—
209Q8×C11—24no—
210Q8×C11#11714yescomplemented
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11C2×C22⋊C412yes—
223C2×C4×C11C2×C22⋊C412yes—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C2×#4112yes—
227C2×C4×C11C2×#4112yes—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11C2×C22⋊C412yes—
236C2×Dic11C2×C22⋊C412yes—
237C2×Dic11C2×C22⋊C412yes—
238C2×Dic11AGL(1,ℤ/8)12yes—
239C2×Dic11#13712yes—
240D44—216no—
241D44—22no—
242D44—24no—
243D44#11714yescomplemented
244C4×D11—216no—
245C4×D11—22no—
246C4×D11—22no—
247C4×D11—24no—
248C4×D11—28no—
249C4×D11—44no—
250C4×D11—48no—
251C4×D11—48no—
252C8×C11—42no—
253C11⋊C8—42no—
254C22×#41—111no—
255C4×#41—118no—
256C4×#41—224no—
257C2×C4×Q8—111no—
258C2×C4×Q8C2×D1111yescharacteristic
259C2×C4×D4—111no—
260C2×C4×D4—111no—
261C2×C4×D4—221no—
262C2×C4×D4—221no—
263C2×#117—111no—
264C2×#117—221no—
265C2×#117—221no—
266C22×C42—111no—
267C22×C42—221no—
268#432—224no—
269C2×C4⋊C8—112no—
270C2×#103—112no—
271C2×#103C2×D1112yes—
272C2×#102—112no—
273C2×#102—112no—
274C2×C22⋊C8—112no—
275C2×#97—111no—
276C2×#97C2×D1111yescharacteristic
277#384—112no—
278#382—221no—
279#380—112no—
280#380—221no—
281C4×C4⋊C4—111no—
282C4×C4⋊C4—221no—
283C4×C4⋊C4C2×D1111yescharacteristic
284#340—112no—
285#340—112no—
286#340—112no—
287#340C2×D1112yes—
288C22×C11C22×C22⋊C411yescharacteristic
289C22×C11#52512yes—
290C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
291C22×C11C2×#13711yescharacteristic
292C22×C11#57512yes—
293C2×D11—22no—
294C2×D11—22no—
295C2×D11—24no—
296C2×D11—22no—
297C2×D11—42no—
298C2×D11—44no—
299C2×D11—42no—
300C2×D11—44no—
301C2×D11—42no—
302C2×D11—42no—
303C4×C11—22no—
304C4×C11—22no—
305C4×C11—24no—
306C4×C11—42no—
307C4×C11—82no—
308C4×C11C2×#11711yescharacteristic
309C4×C11C2×#11711yescharacteristic
310C4×C11#52512yes—
311Dic11—22no—
312Dic11—22no—
313Dic11—42no—
314Dic11—82no—
315Dic11#41714yes—
316C2×#41—114no—
317C2×#41—222no—
318C2×#41—224no—
319C2×#41—224no—
320C22×Q8C22×D1111yescharacteristic
321C22×D4—111no—
322C22×D4—221no—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—111no—
326C23×C4—221no—
327C23×C4—221no—
328C23×C4—221no—
329C22×C8—112no—
330C22×C8C22×D1112yes—
331C4×Q8—22no—
332C4×Q8—114no—
333C4×Q8—222no—
334C4×Q8C4×D1114yes—
335C4×D4—114no—
336C4×D4—114no—
337C4×D4—228no—
338C4×D4—222no—
339C4×D4—228no—
340C4×D4—222no—
341#117—114no—
342#117—228no—
343#117—222no—
344#117—444no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—221no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4C22×D1112yes—
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C22⋊C4—221no—
354C2×C22⋊C4—221no—
355C2×C22⋊C4—221no—
356C2×C22⋊C4—222no—
357C2×C42—21no—
358C2×C42—21no—
359C2×C42—111no—
360C2×C42—111no—
361C2×C42—111no—
362C2×C42—114no—
363C2×C42—114no—
364C2×C42—228no—
365C2×C42—221no—
366C2×C42—221no—
367C2×C42—221no—
368C2×C42C22×D1111yescharacteristic
369C4⋊C8—224no—
370#103—24no—
371#103—224no—
372#102—224no—
373#102—224no—
374C22⋊C8—224no—
375#97—22no—
376#97—222no—
377#95—21no—
378#95—222no—
379#95—221no—
380C2×C11#228011yescharacteristic
381C2×C11C2×#41711yescharacteristic
382C2×C11#289611yescharacteristic
383C2×C11#311512yes—
384C2×C11#311612yes—
385D11—42no—
386D11—44no—
387C24—111no—
388C24—221no—
389#41—228no—
390#41—2216no—
391#41—228no—
392C2×Q8—21no—
393C2×Q8—22no—
394C2×Q8C2×C4×D1112yes—
395C2×Q8#433914yes—
396C2×D4—112no—
397C2×D4—114no—
398C2×D4—224no—
399C2×D4—228no—
400C2×D4—222no—
401C2×D4—221no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—111no—
406C22×C4—111no—
407C22×C4—111no—
408C22×C4—114no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—114no—
412C22×C4—224no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—224no—
416C22×C4—228no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—221no—
420C22×C4—224no—
421C22×C4—222no—
422C22×C4—442no—
423C22×C4—444no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4D4×D1111yescharacteristic
427C22×C4D4×D1111yescharacteristic
428C22×C4C23×D1111yescharacteristic
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—222no—
433C2×C8—222no—
434C2×C8—222no—
435C4⋊C4—24no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—112no—
440C4⋊C4—224no—
441C4⋊C4—221no—
442C4⋊C4—222no—
443C4⋊C4—222no—
444C4⋊C4—444no—
445C4⋊C4—444no—
446C4⋊C4C2×C4×D1112yes—
447C22⋊C4—224no—
448C22⋊C4—224no—
449C22⋊C4—224no—
450C22⋊C4—444no—
451C42—24no—
452C42—42no—
453C42—114no—
454C42—114no—
455C42—112no—
456C42—112no—
457C42—224no—
458C42—224no—
459C42—442no—
460C42C2×C4×D1112yes—
461C42D4×D1112yes—
462C11#2074311yescharacteristic, complemented, Sylow
463C23—112no—
464C23—222no—
465C23—221no—
466C23—221no—
467C23—222no—
468C23—224no—
469C23—222no—
470C23—441no—
471C23—441no—
472C23—442no—
473C23C2×D4×D1111yescharacteristic
474Q8—22no—
475Q8—24no—
476Q8#6692514yescomplemented
477D4—114no—
478D4—2216no—
479D4—222no—
480D4—224no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—112no—
493C2×C4—112no—
494C2×C4—112no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—228no—
498C2×C4—2216no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—224no—
504C2×C4—222no—
505C2×C4—444no—
506C2×C4—448no—
507C2×C4—448no—
508C2×C4—442no—
509C2×C4—442no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4C22⋊C4×D1112yes—
513C2×C4C22⋊C4×D1112yes—
514C2×C4C22×C4×D1111yescharacteristic
515C2×C4C2×#433912yes—
516C2×C4C2×D4×D1111yescharacteristic
517C2×C4#41×D1112yes—
518C8—42no—
519C8—442no—
520C22—222no—
521C22—222no—
522C22—224no—
523C22—222no—
524C22—442no—
525C22—442no—
526C22—442no—
527C22—444no—
528C22—442no—
529C22—444no—
530C22C2×C22⋊C4×D1111yescharacteristic
531C22#1062307812yes—
532C22D11×AGL(1,ℤ/8)11yescharacteristic
533C22D11×#13711yescharacteristic
534C22#1062330812yes—
535C4—22no—
536C4—22no—
537C4—24no—
538C4—42no—
539C4—82no—
540C4—114no—
541C4—222no—
542C4—222no—
543C4—442no—
544C4—882no—
545C4C2×#6692511yescharacteristic
546C4D11×#11711yescharacteristic
547C4#1062307812yes—
548C2—442no—
549C2—444no—
550C2#1307099711yescharacteristic
551C2D11×#41711yescharacteristic
552C2#1307713411yescharacteristic
553C2#1307876512yes—
554C2#1307877612yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC22×#4343C22
cosocleC22×C4×C11C24
hypercenter#1763D11
hypocenterC11#20743
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
2. C2×#10622318C2semidirect
3. #13071020C2semidirect
4. #13068710C2semidirect
5. #13068619C2semidirect
6. #13068615C2semidirect
8. #13068446C2semidirect
9. #13068444C2semidirect
10. #13068442C2semidirect
11. C11×#1763C2semidirect
16. C4×#4343C4semidirect
194. #1763D11semidirect
210. Q8×C11#117semidirect
243. D44#117semidirect
462. C11#20743semidirect
476. Q8#66925semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43432
C2×#106223182
#130710202
#130687102
#130686192
#130686152
#130685552
#130684462
#130684442
#130684422
C11×#17632
#2074311