Finite Group Databasebeta

← #14755143

Subgroups — #14755143

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66962C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic
4C2×#10622617C211yesmaximal, characteristic, complemented
5#13071104C211yesmaximal, characteristic
6#13068972C214yesmaximal, complemented
7#13068958C214yesmaximal, complemented
8#13068309C211yesmaximal, characteristic, complemented
9C11×#1736C211yesmaximal, characteristic, complemented
10C22×#4339C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×Dic11⋊C4—21no—
16C22×C4×Dic11—21no—
17C22×C4×Dic11C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19C2×#66962—24no—
20C2×#66962—24no—
21C2×#66962C418yescomplemented
22C22×Dic44C2212yes—
23C22×#4314C2212yes—
24C2×#66940—24no—
25C2×#66940—24no—
26C2×#66940—22no—
27C2×#66940C2214yes—
28#10622617—24no—
29#10622601C2212yes—
30#10622587C2212yes—
31C2×#66874C2214yes—
32C2×#66874C2212yes—
33#10622579—24no—
34C2×#66873C2212yes—
35#10622571—21no—
36#10622571—21no—
37C4×(C2×D11)⋊C4—22no—
38C11×#340C2214yes—
39#10622188C2214yes—
40C23×C4×C11—21no—
41C23×C4×C11C2311yescharacteristic
42C22×C22⋊D11—21no—
43C23×Dic11—21no—
44C23×Dic11D411yescharacteristic
45C23×Dic11D411yescharacteristic
46C2×#4339—22no—
47C2×#4339—22no—
48C2×#4339—22no—
49C2×#4339—22no—
50C2×#4339—22no—
51C2×#4339C2×C414yes—
52C22×D44C2311yescharacteristic
53C22×C4×D11—21no—
54C22×Dic22—22no—
55C22×Dic22—21no—
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22C2×C414yes—
59C22×Dic22D414yes—
60C22×Dic22D414yes—
61C22×Dic22C2311yescharacteristic
62C22×Dic22C2312yes—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16C2×C414yes—
66C22×C8×C11C2312yes—
67C11×#117—22no—
68C11×#117—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4D414yes—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C22⋊C4—21no—
75C2×C42×C11—21no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×Dic11⋊C4—28no—
79C2×Dic11⋊C4—24no—
80C2×C4×Dic11—28no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11D412yes—
85C2×C4×Dic11C2312yes—
86C2×#4318—22no—
87C2×#4318—22no—
88C2×#4318—22no—
89C22×C11⋊C8C2312yes—
90#66962—232no—
91C2×Dic44—24no—
92C2×Dic44—24no—
93C2×Dic44C2×C418yescomplemented
94C2×#4314—24no—
95C2×#4314—24no—
96C2×#4314C2×C418yescomplemented
97#66940—216no—
98#66940—28no—
99#66940—28no—
100C11⋊#95—22no—
101C11⋊#95—22no—
102#66874—28no—
103#66874—24no—
104#66873—24no—
105#20926—111nomaximal, Sylow
106C24×C11C2×D411yescharacteristic
107C23×D11—21no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—44no—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D412yes—
117C22×C4×C11#4112yes—
118C22×C4×C11#4112yes—
119C22×C4×C11C2411yescharacteristic
120C2×C22⋊D11—24no—
121C2×C22⋊D11—42no—
122C2×C22⋊D11—42no—
123C22×Dic11—24no—
124C22×Dic11—24no—
125C22×Dic11—22no—
126C22×Dic11—24no—
127C22×Dic11—22no—
128C22×Dic11—24no—
129C22×Dic11—22no—
130C22×Dic11—21no—
131C22×Dic11—42no—
132C22×Dic11C2×D412yes—
133C22×Dic11C2×D412yes—
134#4339—28no—
135#4339—28no—
136#4339—44no—
137#4339—44no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44C22×C412yes—
144C2×C4×D11—24no—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×Dic22—28no—
148C2×Dic22—24no—
149C2×Dic22—24no—
150C2×Dic22—24no—
151C2×Dic22—28no—
152C2×Dic22—28no—
153C2×Dic22—22no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×Dic22—21no—
160C2×Dic22—21no—
161C2×Dic22C22⋊C4116yescomplemented
162C2×Dic22C22×C412yes—
163C2×Dic22C22×C414yes—
164C2×Dic22C2×D414yes—
165C2×Dic22C2×D414yes—
166C11×M16—28no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11C22×C414yes—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—22no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4C2×D414yes—
175C11×C22⋊C4—42no—
176C42×C11—42no—
177(C2×D11)⋊C4—44no—
178(C2×D11)⋊C4—44no—
179Dic11⋊C4—216no—
180C4×Dic11—216no—
181C4×Dic11—24no—
182C4×Dic11—22no—
183C4×Dic11—22no—
184#4318—44no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188Dic44—216no—
189#4314—216no—
190C22×#137—111no—
191C22×C4×Q8—111no—
192C2×#417—111no—
193C2×#419—111no—
194#2297—111no—
195#1880—114no—
196#1878—114no—
197#1736D1111yescharacteristic, complemented
198#1728—111no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11C4×D412yes—
202C23×C11#12012yes—
203C23×C11#12112yes—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—42no—
209C22×D11—42no—
210C2×C4×C11—24no—
211C2×C4×C11—48no—
212C2×C4×C11—44no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11C2×C22⋊C414yes—
217C2×C4×C11C4×D414yes—
218C2×C4×C11C4×D412yes—
219C2×C4×C11#12012yes—
220C2×C4×C11#12112yes—
221C2×C4×C11#12114yes—
222C2×C4×C11#12314yes—
223C2×C4×C11C23×C411yescharacteristic
224C2×C4×C11C22×D411yescharacteristic
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D411yescharacteristic
227C2×C4×C11C2×#4111yescharacteristic
228C2×C4×C11C2×#4111yescharacteristic
229C22⋊D11—48no—
230C2×Dic11—28no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—216no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—44no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11#13714yescomplemented
245D44—22no—
246D44—22no—
247D44—41no—
248D44—41no—
249C4×D11—48no—
250Dic22—24no—
251Dic22—24no—
252Dic22—24no—
253Dic22—216no—
254Dic22—22no—
255Dic22—22no—
256Dic22—41no—
257Dic22—41no—
258Dic22C2×C22⋊C418yes—
259C8×C11—24no—
260C11⋊C8—42no—
261C22×#41—111no—
262C23×Q8—111no—
263C2×#137—118no—
264C2×#137—224no—
265C2×#137—224no—
266C22×Q16—112no—
267C22×SD16—112no—
268C22×M16—111no—
269C22×M16C2×D1111yescharacteristic
270C2×C4×Q8—114no—
271C2×C4×Q8—222no—
272C2×C4×Q8—224no—
273C2×C4×Q8—224no—
274C2×#117C2×D1111yescharacteristic
275C22×C4⋊C4—221no—
276C22×C4⋊C4C2×D1111yescharacteristic
277C22×C42—111no—
278C22×C42—221no—
279#419—224no—
280#417—224no—
281C2×#103—114no—
282C2×#103—112no—
283C2×#102—112no—
284#391—112no—
285#390—112no—
286#386—221no—
287#386—221no—
288C4×C22⋊C4—222no—
289#340C2×D1114yes—
290#336—114no—
291C22×C11—24no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11—24no—
295C22×C11#38614yes—
296C22×C11C2×C4×D411yescharacteristic
297C22×C11C2×#12011yescharacteristic
298C22×C11C2×#12111yescharacteristic
299C22×C11C2×#13712yes—
300C22×C11#57512yes—
301C2×D11—44no—
302C2×D11—42no—
303C2×D11—81no—
304C2×D11—81no—
305C2×D11—82no—
306C4×C11—44no—
307C4×C11—82no—
308C4×C11#38614yes—
309C4×C11C22×C22⋊C411yescharacteristic
310C4×C11C2×C4×D411yescharacteristic
311C4×C11C2×#12111yescharacteristic
312C4×C11C2×#12311yescharacteristic
313Dic11—24no—
314Dic11—28no—
315Dic11—42no—
316Dic11—42no—
317C2×#41—114no—
318C2×#41—222no—
319C2×#41—222no—
320C2×#41—222no—
321C2×#41—222no—
322C2×#41—222no—
323C22×Q8—114no—
324C22×Q8—114no—
325C22×Q8—114no—
326C22×Q8—112no—
327C22×Q8—111no—
328C22×Q8—222no—
329C22×Q8—222no—
330C22×Q8—221no—
331C22×Q8—222no—
332C22×D4—111no—
333C22×D4—221no—
334C23×C4—21no—
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—221no—
338C23×C4—221no—
339C23×C4C22×D1111yescharacteristic
340#137—2232no—
341C2×Q16—118no—
342C2×Q16—224no—
343C2×Q16—224no—
344C2×SD16—118no—
345C2×SD16—224no—
346C2×SD16—224no—
347C2×M16—22no—
348C2×M16—22no—
349C2×M16—222no—
350C2×M16—222no—
351C2×M16—222no—
352C2×M16C4×D1114yes—
353C22×C8—112no—
354C22×C8C22×D1112yes—
355C4×Q8—228no—
356C4×Q8—2216no—
357C4×Q8—228no—
358#117—22no—
359#117—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—224no—
363C2×C4⋊C4—228no—
364C2×C4⋊C4D4414yes—
365C2×C4⋊C4C22×D1112yes—
366C2×C4⋊C4C22×D1112yes—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4—222no—
370C2×C42—21no—
371C2×C42—112no—
372C2×C42—112no—
373C2×C42—224no—
374C2×C42—228no—
375C2×C42—222no—
376C2×C42—222no—
377#103—228no—
378#103—224no—
379#102—224no—
380#95—222no—
381#95—222no—
382C2×C11—24no—
383C2×C11C2×#38611yescharacteristic
384C2×C11C4×#13712yes—
385C2×C11#300411yescharacteristic
386C2×C11#300511yescharacteristic
387C2×C11#303712yes—
388D11—82no—
389C24—221no—
390C24D4×D1111yescharacteristic
391#41—228no—
392#41—228no—
393#41—444no—
394#41—444no—
395C2×Q8—1116no—
396C2×Q8—114no—
397C2×Q8—112no—
398C2×Q8—114no—
399C2×Q8—114no—
400C2×Q8—228no—
401C2×Q8—224no—
402C2×Q8—224no—
403C2×Q8—224no—
404C2×Q8—228no—
405C2×Q8—228no—
406C2×Q8—222no—
407C2×Q8—222no—
408C2×Q8—222no—
409C2×Q8—221no—
410C2×Q8—221no—
411C2×Q8—221no—
412C2×Q8—221no—
413C2×Q8—221no—
414C2×D4—112no—
415C2×D4—224no—
416C2×D4—221no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—442no—
422C2×D4—442no—
423C22×C4—24no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—44no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—224no—
430C22×C4—222no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—224no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—221no—
437C22×C4—224no—
438C22×C4—442no—
439C22×C4—442no—
440C22×C4—442no—
441C22×C4C2×C4×D1112yes—
442C22×C4C2×D4412yes—
443C22×C4#433912yes—
444C22×C4D4×D1112yes—
445C22×C4D4×D1112yes—
446C22×C4D4×D1111yescharacteristic
447C22×C4#434312yes—
448C22×C4C23×D1111yescharacteristic
449Q16—2216no—
450SD16—2216no—
451M16—28no—
452M16—444no—
453C2×C8—22no—
454C2×C8—22no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—222no—
458C2×C8C2×C4×D1114yes—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—2216no—
464C4⋊C4C2×D4414yes—
465C22⋊C4—42no—
466C22⋊C4—444no—
467C22⋊C4—444no—
468C42—42no—
469C42—2216no—
470C42—224no—
471C42—222no—
472C42—222no—
473C11#2092611yescharacteristic, complemented, Sylow
474C23—22no—
475C23—22no—
476C23—222no—
477C23—441no—
478C23—441no—
479C23—442no—
480C23—442no—
481C23#6693512yes—
482C23#6693712yes—
483C23#6694612yes—
484C23C2×D4×D1111yescharacteristic
485Q8—118no—
486Q8—224no—
487Q8—224no—
488Q8—224no—
489Q8—2216no—
490Q8—222no—
491Q8—222no—
492Q8—441no—
493Q8—441no—
494D4—222no—
495D4—222no—
496D4—448no—
497D4—441no—
498D4—441no—
499C2×C4—24no—
500C2×C4—48no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—114no—
506C2×C4—228no—
507C2×C4—222no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—2216no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—444no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—448no—
521C2×C4C4×D4414yes—
522C2×C4C22⋊C4×D1114yes—
523C2×C4#6693512yes—
524C2×C4#6693712yes—
525C2×C4#6694612yes—
526C2×C4#6694714yes—
527C2×C4#6694814yes—
528C2×C4C22×C4×D1111yescharacteristic
529C2×C4C22×D4411yescharacteristic
530C2×C4C2×#433911yescharacteristic
531C2×C4C2×D4×D1111yescharacteristic
532C2×C4C2×D4×D1111yescharacteristic
533C2×C4C2×#434311yescharacteristic
534C8—24no—
535C8—442no—
536C22—24no—
537C22—22no—
538C22—22no—
539C22—24no—
540C22—442no—
541C22—444no—
542C22—882no—
543C22—881no—
544C22—881no—
545C22#1062227814yes—
546C22C2×#6693511yescharacteristic
547C22C2×#6693711yescharacteristic
548C22C2×#6694611yescharacteristic
549C22#1062330412yes—
550C22D11×#13712yes—
551C4—44no—
552C4—82no—
553C4—224no—
554C4—228no—
555C4—442no—
556C4—442no—
557C4#1062227814yes—
558C4C2×C4×D4411yescharacteristic
559C4C2×C22⋊C4×D1111yescharacteristic
560C4C2×#6694711yescharacteristic
561C4C2×#6694811yescharacteristic
562C2—24no—
563C2—882no—
564C2C2×#1062227811yescharacteristic
565C2#1307743412yes—
566C2#1307785211yescharacteristic
567C2#1307786011yescharacteristic
568C2#1307808712yes—
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#20926
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
4. C2×#10622617C2semidirect
6. #13068972C2semidirect
7. #13068958C2semidirect
8. #13068309C2semidirect
9. C11×#1736C2semidirect
21. C2×#66962C4semidirect
93. C2×Dic44C2×C4semidirect
96. C2×#4314C2×C4semidirect
161. C2×Dic22C22⋊C4semidirect
197. #1736D11semidirect
244. C2×Dic11#137semidirect
473. C11#20926semidirect

Maximal subgroups

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

subgroupindex
C22×#669622
C22×#669402
C2×#106225792
C2×#106226172
#130711042
#130689722
#130689582
#130683092
C11×#17362
#2092611