Finite Group Databasebeta

← #14769942

Subgroups — #14769942

Order 2816.

1068 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623060C211yesmaximal, characteristic
2M16×C22⋊D11C212yesmaximal
3#13069607C212yesmaximal, complemented
4#13069084C212yesmaximal, complemented
5#13069083C212yesmaximal, complemented
6#13068699C211yesmaximal, characteristic, complemented
7#13068695C211yesmaximal, characteristic, complemented
8#13068611C211yesmaximal, characteristic, complemented
9#13068411C211yesmaximal, characteristic, complemented
10D11×#343C211yesmaximal, characteristic, complemented
11C11×#1742C211yesmaximal, characteristic, complemented
12C22×C11×M16C2212yes—
13C2×C11×#117C2211yescharacteristic
14C2×C4×C22⋊D11C2211yescharacteristic
15C2×#66977C2211yescharacteristic
16C2×M16×D11C2212yes—
17#10623060—22no—
18#10623060—22no—
19#10623060—22no—
20#10623060—22no—
21C2×#66950C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×#66943C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×#66936C412yes—
26C2×#66932C412yes—
27C2×#66925C412yes—
28C2×#66923C412yes—
29#10622820C2212yes—
30C2×#66888C2212yes—
31C2×#66888C2212yes—
32#10622741—22no—
33#10622740—22no—
34#10622739C2212yes—
35#10622731C2212yes—
36M16×Dic11C2212yes—
37#10622724—22no—
38C8×C22⋊D11—22no—
39C11×#343C2212yes—
40C11×#343C2211yescharacteristic
41C11×#343C2211yescharacteristic
42#10622192C2212yes—
43#10622192C2212yes—
44#10622168C2212yes—
45#10622168C2211yescharacteristic
46#10622168C2211yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C22×C22⋊D11C2×C411yescharacteristic
49C22×C4×D11C2×C412yes—
50C22×C4×D11C2311yescharacteristic
51C22×Dic22C2311yescharacteristic
52C2×C11×M16—22no—
53C2×C11×M16—24no—
54C2×C11×M16—42no—
55C2×C11×M16C2312yes—
56C2×C11×M16C2312yes—
57C22×C8×C11—22no—
58C11×#117—22no—
59C11×#117—22no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C22⋊C4C2×C412yes—
63C2×C42×C11C2×C412yes—
64C2×C22⋊Dic11C2×C412yes—
65C2×C22⋊Dic11C2×C411yescharacteristic
66C4×C22⋊D11D412yes—
67C4×C22⋊D11D412yes—
68C4×C22⋊D11D412yes—
69C4×C22⋊D11D412yes—
70C2×(C2×D11)⋊C4C2×C412yes—
71C2×(C2×D11)⋊C4C2×C411yescharacteristic
72C2×C4⋊Dic11C2×C412yes—
73C2×C4⋊Dic11C2×C412yes—
74C2×C4⋊Dic11C2311yescharacteristic
75#66977—22no—
76#66977—22no—
77C2×Dic11⋊C4C2×C412yes—
78C2×Dic11⋊C4C2×C412yes—
79C2×Dic11⋊C4C2×C412yes—
80C2×Dic11⋊C4C2×C412yes—
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×C4×Dic11C2×C412yes—
83C2×C4×Dic11C2311yescharacteristic
84C2×#4318C2312yes—
85C2×#4318C2312yes—
86M16×D11—24no—
87M16×D11—42no—
88C2×#4313—22no—
89C2×C8×D11—22no—
90#66950—22no—
91#66950—22no—
92C4⋊C4×D11—22no—
93C4⋊C4×D11—22no—
94#66943—22no—
95#66943—22no—
96#66940—22no—
97#66940—22no—
98#66936—24no—
99#66936—24no—
100#66932—24no—
101#66932—24no—
102#66925—22no—
103#66925—22no—
104#66925—22no—
105#66925—22no—
106#66923—24no—
107#66923—24no—
108C22⋊(C11⋊C8)—22no—
109C22⋊(C11⋊C8)—22no—
110#66888—24no—
111#66888—42no—
112(C2×D11)⋊C8—22no—
113(C2×D11)⋊C8—22no—
114#66879—22no—
115Dic11⋊C8—22no—
116Dic11⋊C8—22no—
117C8×Dic11—22no—
118#22480—111nomaximal, Sylow
119C24×C11C22×C411yescharacteristic
120C23×D11C22×C411yescharacteristic
121C22×C4×C11—22no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C22×C411yescharacteristic
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—42no—
131C2×C22⋊D11C22⋊C412yes—
132C2×C22⋊D11C22⋊C412yes—
133C22×Dic11C22×C412yes—
134C22×Dic11C22×C411yescharacteristic
135C22×Dic11C22×C412yes—
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—44no—
144C2×C4×D11C2×D412yes—
145C2×C4×D11C2×D412yes—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C11×M16—22no—
151C11×M16—22no—
152C11×M16—22no—
153C11×M16—44no—
154C11×M16#4114yes—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11—44no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C22⋊C4—24no—
161C42×C11—22no—
162C42×C11—22no—
163C22⋊Dic11—24no—
164C22⋊Dic11C22⋊C412yes—
165C22⋊Dic11C22⋊C412yes—
166(C2×D11)⋊C4—22no—
167(C2×D11)⋊C4—22no—
168(C2×D11)⋊C4C22⋊C411yescharacteristic
169(C2×D11)⋊C4C22⋊C411yescharacteristic
170(C2×D11)⋊C4C22⋊C411yescharacteristic
171(C2×D11)⋊C4C22⋊C411yescharacteristic
172C4⋊Dic11—24no—
173C4⋊Dic11—24no—
174C4⋊Dic11—22no—
175Dic11⋊C4—24no—
176Dic11⋊C4—24no—
177Dic11⋊C4—22no—
178Dic11⋊C4—22no—
179Dic11⋊C4—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4C22⋊C412yes—
182Dic11⋊C4C22⋊C412yes—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11C2×D412yes—
186C4×Dic11C2×D412yes—
187#4318—22no—
188#4318—22no—
189#4318—22no—
190#4318—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193#4313—44no—
194C8×D11—44no—
195C2×#552—111no—
196D4×M16—112no—
197#1998—112no—
198#1901—112no—
199#1901—112no—
200#1822—111no—
201#1821—111no—
202#1801—111no—
203C4×#101—111no—
204#1742D1111yescharacteristic, complemented
205C2×#343—111no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11C2×C22⋊C412yes—
211C23×C11C23×C411yescharacteristic
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—22no—
215C22×D11—41no—
216C22×D11C2×C22⋊C411yescharacteristic
217C22×D11C2×C22⋊C411yescharacteristic
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11C2×C22⋊C411yescharacteristic
229C2×C4×C11C2×C22⋊C411yescharacteristic
230C2×C4×C11C22×D412yes—
231C2×C4×C11C2×#4112yes—
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C112−1+411yescharacteristic
234C22⋊D11—24no—
235C22⋊D11—42no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—42no—
245C2×Dic11C2×C22⋊C411yescharacteristic
246C2×Dic11C2×C22⋊C411yescharacteristic
247C2×Dic11C2×C22⋊C412yes—
248C2×Dic11C2×C22⋊C412yes—
249C4×D11—22no—
250C4×D11—22no—
251C4×D11—22no—
252C4×D11—22no—
253C4×D11—44no—
254C4×D11—44no—
255Dic22—42no—
256Dic22—42no—
257C8×C11—24no—
258C8×C11—42no—
259C11⋊C8—42no—
260C11⋊C8—42no—
261C22×M16—112no—
262C22×M16C2×D1112yes—
263#552—222no—
264#552—222no—
265#552—222no—
266#552—222no—
267C2×#126—112no—
268C2×#125—111no—
269C2×#125—112no—
270C2×#123—112no—
271C2×C22⋊Q8—111no—
272C2×C22⋊Q8—111no—
273C2×C4×Q8—111no—
274C2×C4×D4—111no—
275C2×#117—112no—
276C2×#117C2×D1111yescharacteristic
277C22×C4⋊C4—111no—
278#436—222no—
279#435—222no—
280#435—222no—
281C8×D4—222no—
282#423—112no—
283C2×#101—112no—
284C2×#101—112no—
285#407—112no—
286#407—112no—
287C4×M16—112no—
288#343—112no—
289#343—112no—
290#343—111no—
291#343—111no—
292#343—112no—
293#343C2×D1111yescharacteristic
294#343C2×D1112yes—
295#343C2×D1111yescharacteristic
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—22no—
301C22×C11—81no—
302C22×C11—81no—
303C22×C11C22×C22⋊C411yescharacteristic
304C22×C11C4×#4111yescharacteristic
305C22×C11#52011yescharacteristic
306C2×D11—21no—
307C2×D11—21no—
308C2×D11—21no—
309C2×D11—21no—
310C2×D11—21no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11#41312yes—
314C4×C11—21no—
315C4×C11—21no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11#54612yes—
319C4×C11#54712yes—
320Dic11—22no—
321Dic11—22no—
322Dic11—21no—
323Dic11—21no—
324Dic11—42no—
325Dic11—42no—
326C22×Q8—111no—
327C22×D4—111no—
328C23×C4—111no—
329C23×C4—112no—
330C23×C4C22×D1111yescharacteristic
331C2×M16—22no—
332C2×M16—24no—
333C2×M16—42no—
334C2×M16—112no—
335C2×M16—112no—
336C2×M16—222no—
337C2×M16—224no—
338C2×M16—442no—
339C2×M16C22×D1112yes—
340C2×M16C22×D1112yes—
341C22×C8—22no—
342C22×C8—222no—
343#126—224no—
344#126—224no—
345#125—224no—
346#125—224no—
347#125—222no—
348#125—222no—
349#123—224no—
350#123—224no—
351C22⋊Q8—222no—
352C22⋊Q8—222no—
353C22⋊Q8—222no—
354C22⋊Q8—222no—
355C4×Q8—222no—
356C4×Q8—222no—
357C4×D4—112no—
358C4×D4—112no—
359C4×D4—112no—
360C4×D4—112no—
361#117—22no—
362#117—22no—
363#117—222no—
364#117—222no—
365#117—222no—
366#117—222no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—112no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4—111no—
380C2×C22⋊C4—111no—
381C2×C22⋊C4—112no—
382C2×C22⋊C4—112no—
383C2×C22⋊C4C4×D1112yes—
384C2×C42—111no—
385C2×C42—112no—
386C2×C42C4×D1112yes—
387C4⋊C8—222no—
388C4⋊C8—222no—
389#101—224no—
390#101—442no—
391C22⋊C8—222no—
392C22⋊C8—222no—
393C22⋊C8—222no—
394C22⋊C8—222no—
395#97—222no—
396C4×C8—222no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—42no—
400C2×C11#233911yescharacteristic
401C2×C11C2×#41311yescharacteristic
402C2×C11#288911yescharacteristic
403D11—22no—
404D11—41no—
405C24—111no—
406C24C2×C4×D1111yescharacteristic
407C2×Q8—222no—
408C2×Q8—222no—
409C2×Q8—221no—
410C2×Q8—221no—
411C2×D4—112no—
412C2×D4—112no—
413C2×D4—442no—
414C22×C4—22no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—111no—
418C22×C4—111no—
419C22×C4—111no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—112no—
423C22×C4—112no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—444no—
430C22×C4C2×C4×D1111yescharacteristic
431C22×C4C2×C4×D1112yes—
432C22×C4C2×C4×D1112yes—
433C22×C4D4×D1112yes—
434C22×C4D4×D1112yes—
435C22×C4C23×D1111yescharacteristic
436M16—22no—
437M16—22no—
438M16—22no—
439M16—44no—
440M16—222no—
441M16—222no—
442M16—222no—
443M16—222no—
444M16—444no—
445M16#433914yes—
446C2×C8—22no—
447C2×C8—22no—
448C2×C8—44no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—444no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—112no—
455C4⋊C4—112no—
456C4⋊C4—224no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4—224no—
460C4⋊C4—224no—
461C4⋊C4—224no—
462C4⋊C4—222no—
463C4⋊C4—222no—
464C4⋊C4—222no—
465C22⋊C4—24no—
466C22⋊C4—112no—
467C22⋊C4—112no—
468C22⋊C4—111no—
469C22⋊C4—111no—
470C22⋊C4—111no—
471C22⋊C4—111no—
472C22⋊C4—222no—
473C22⋊C4—222no—
474C22⋊C4—224no—
475C42—22no—
476C42—22no—
477C42—112no—
478C42—112no—
479C42—222no—
480C42—222no—
481C11#2248011yescharacteristic, complemented, Sylow
482C23—21no—
483C23—21no—
484C23—41no—
485C23—41no—
486C23—111no—
487C23—111no—
488C23—222no—
489C23—221no—
490C23—221no—
491C23—441no—
492C23C22⋊C4×D1112yes—
493C23C22×C4×D1111yescharacteristic
494Q8—442no—
495Q8—442no—
496D4—224no—
497D4—442no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—111no—
509C2×C4—111no—
510C2×C4—112no—
511C2×C4—112no—
512C2×C4—221no—
513C2×C4—221no—
514C2×C4—222no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—444no—
523C2×C4—444no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—442no—
527C2×C4C22⋊C4×D1111yescharacteristic
528C2×C4C22⋊C4×D1111yescharacteristic
529C2×C4C2×#433912yes—
530C2×C4C2×D4×D1112yes—
531C2×C4#6703711yescharacteristic
532C2×C4#6704011yescharacteristic
533C8—24no—
534C8—42no—
535C8—442no—
536C8—442no—
537C22—21no—
538C22—21no—
539C22—22no—
540C22—22no—
541C22—22no—
542C22—81no—
543C22—81no—
544C22—112no—
545C22—221no—
546C22—221no—
547C22—221no—
548C22—221no—
549C22—221no—
550C22—442no—
551C22—442no—
552C22C4×#433911yescharacteristic
553C22C2×C22⋊C4×D1111yescharacteristic
554C22#1062303511yescharacteristic
555C4—21no—
556C4—21no—
557C4—42no—
558C4—42no—
559C4—222no—
560C4—222no—
561C4—221no—
562C4—221no—
563C4—442no—
564C4—442no—
565C4#1062302112yes—
566C4#1062303812yes—
567C2—21no—
568C2—21no—
569C2—42no—
570C2—222no—
571C2—441no—
572C2#1307144311yescharacteristic
573C2D11×#41311yescharacteristic
574C2#1307709711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1742C2
socleC22×C11C22×C22⋊C4
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1742D11
hypocenterC11#22480
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1742

Complements

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

NH ≅ G/Ntype
3. #13069607C2semidirect
4. #13069084C2semidirect
5. #13069083C2semidirect
6. #13068699C2semidirect
7. #13068695C2semidirect
8. #13068611C2semidirect
9. #13068411C2semidirect
10. D11×#343C2semidirect
11. C11×#1742C2semidirect
204. #1742D11semidirect
481. C11#22480semidirect

Maximal subgroups

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

subgroupindex
C2×#106230602
M16×C22⋊D112
#130696072
#130690842
#130690832
#130686992
#130686952
#130686112
#130684112
D11×#3432
C11×#17422
#2248011