Finite Group Databasebeta

← #14722364

Subgroups — #14722364

Order 2816.

1178 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2#13077248C211yesmaximal, characteristic
3#13077244C211yesmaximal, characteristic
4#13067331C214yesmaximal, complemented
5#13067299C214yesmaximal, complemented
6#13067289C211yesmaximal, characteristic, complemented
7#13067288C211yesmaximal, characteristic, complemented
8#13067287C211yesmaximal, characteristic, complemented
9C11×#1546C211yesmaximal, 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×#431C2211yescharacteristic
28C11×#423C2211yescharacteristic
29#10622739—21no—
30M16×Dic11—21no—
31#10622538C2211yescharacteristic
32#10622537C2211yescharacteristic
33#10622450C2212yes—
34#10622448—21no—
35#10622448C2212yes—
36#10622448C2212yes—
37#10622446—21no—
38#10622446C2212yes—
39#10622339—21no—
40#10622332—21no—
41C4×#4313—21no—
42#10622298—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—44no—
53C2×Q8×D11—44no—
54C22×C4×D11—22no—
55C22×C4×D11C2×C411yescharacteristic
56C22×C4×D11D411yescharacteristic
57C22×C4×D11D411yescharacteristic
58C22×Dic22—21no—
59C22×Dic22—22no—
60C2×C11×M16—21no—
61C11×C4⋊Q8—21no—
62C11×C4⋊Q8—21no—
63C11×C4⋊Q8C2×C412yes—
64C11×C4⋊Q8C2312yes—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2×C412yes—
67C2×C42×C11C2311yescharacteristic
68#66997—22no—
69#66997—22no—
70#66997—22no—
71#66997—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11C2×C412yes—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×C4×Dic11C2×C411yescharacteristic
77C2×C4×Dic11D411yescharacteristic
78C2×C4×Dic11D411yescharacteristic
79C2×#4318—21no—
80C2×#4313—22no—
81C4⋊C4×D11—22no—
82C4⋊C4×D11—22no—
83C4⋊C4×D11—22no—
84C4⋊C4×D11—22no—
85C4⋊C4×D11—22no—
86C4⋊C4×D11—22no—
87C4⋊C4×D11C2×C414yes—
88C4⋊C4×D11C2×C414yes—
89#66941—22no—
90#66941—22no—
91#66941—22no—
92#66941—22no—
93#66941—22no—
94#66941—22no—
95#66941C2×C414yes—
96#66941C2×C414yes—
97C42×D11C2×C411yescharacteristic
98C42×D11C2×C411yescharacteristic
99C42×D11D411yescharacteristic
100C42×D11D411yescharacteristic
101C42×D11D411yescharacteristic
102C42×D11D411yescharacteristic
103C42×D11C2311yescharacteristic
104C42×D11C2311yescharacteristic
105#66922—21no—
106#66922—21no—
107#66922C2×C412yes—
108#66922C2312yes—
109C11×C4⋊C8—21no—
110C11×C4⋊C8C2312yes—
111C11×C4⋊C8C2312yes—
112C11×C22⋊C8—21no—
113C4×C8×C11—21no—
114C22⋊(C11⋊C8)—21no—
115(C2×D11)⋊C8—22no—
116(C2×D11)⋊C8—22no—
117(C2×D11)⋊C8—22no—
118#66879—22no—
119#66879—22no—
120Dic11⋊C8—22no—
121C8×Dic11—22no—
122C4⋊(C11⋊C8)—21no—
123C4⋊(C11⋊C8)C2312yes—
124C4⋊(C11⋊C8)C2312yes—
125C4×C11⋊C8—21no—
126#17742—111nomaximal, Sylow
127C23×D11C22⋊C411yescharacteristic
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—42no—
131C2×Q8×C11—42no—
132C22×C4×C11—22no—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×Dic11—22no—
137C22×Dic11C22⋊C411yescharacteristic
138C22×Dic11C22⋊C411yescharacteristic
139C22×Dic11C22⋊C411yescharacteristic
140Q8×D11—44no—
141Q8×D11—44no—
142Q8×D11—44no—
143Q8×D11—44no—
144Q8×D11—48no—
145Q8×D11—48no—
146C2×C4×D11—24no—
147C2×C4×D11—24no—
148C2×C4×D11—24no—
149C2×C4×D11—24no—
150C2×C4×D11—22no—
151C2×C4×D11—22no—
152C2×C4×D11—48no—
153C2×C4×D11C22⋊C411yescharacteristic
154C2×C4×D11C22⋊C411yescharacteristic
155C2×C4×D11C22⋊C411yescharacteristic
156C2×C4×D11C22⋊C411yescharacteristic
157C2×C4×D11C22⋊C411yescharacteristic
158C2×C4×D11C22⋊C411yescharacteristic
159C2×C4×D11C22×C411yescharacteristic
160C2×C4×D11C22×C411yescharacteristic
161C2×C4×D11C2×D411yescharacteristic
162C2×C4×D11C2×D411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×C4×D11C2×D411yescharacteristic
165C2×Dic22—24no—
166C2×Dic22—24no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—48no—
170C2×Dic22—42no—
171C2×Dic22—42no—
172C11×M16—42no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4C22×C414yes—
179C42×C11C22×C411yescharacteristic
180C42×C11C2×D411yescharacteristic
181C42×C11C2×D411yescharacteristic
182C42×C11C2411yescharacteristic
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11C22×C414yes—
187Dic11⋊C4—24no—
188Dic11⋊C4—24no—
189Dic11⋊C4—24no—
190Dic11⋊C4—24no—
191C4×Dic11C22⋊C411yescharacteristic
192C4×Dic11C22⋊C411yescharacteristic
193C4×Dic11C22⋊C411yescharacteristic
194C4×Dic11C22⋊C411yescharacteristic
195C4×Dic11C22⋊C411yescharacteristic
196C4×Dic11C22⋊C411yescharacteristic
197C4×Dic11C22×C411yescharacteristic
198C4×Dic11C22×C411yescharacteristic
199C4×Dic11C2×D411yescharacteristic
200C4×Dic11C2×D411yescharacteristic
201C4×Dic11C2×D411yescharacteristic
202C4×Dic11C2×D411yescharacteristic
203#4318—42no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206#4313—44no—
207C22×C4⋊Q8—111no—
208#2920—111no—
209#2920—111no—
210#1556—114no—
211#1549—114no—
212#1546—111no—
213#1546—111no—
214#1546—111no—
215#1546D1111yescharacteristic, complemented
216C23×C11C2×C22⋊C411yescharacteristic
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11C2×C22⋊C411yescharacteristic
221C22×D11C2×C22⋊C411yescharacteristic
222Q8×C11—42no—
223Q8×C11—42no—
224Q8×C11—44no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—44no—
229C2×C4×C11C2×C22⋊C411yescharacteristic
230C2×C4×C11C2×C22⋊C411yescharacteristic
231C2×C4×C11C2×C22⋊C411yescharacteristic
232C2×C4×C11AGL(1,ℤ/8)12yes—
233C2×C4×C11AGL(1,ℤ/8)12yes—
234C2×C4×C11C23×C411yescharacteristic
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—44no—
242C2×Dic11C2×C22⋊C411yescharacteristic
243C2×Dic11C2×C22⋊C411yescharacteristic
244C2×Dic11C2×C22⋊C411yescharacteristic
245C2×Dic11C2×C22⋊C411yescharacteristic
246C2×Dic11C2×C22⋊C411yescharacteristic
247C2×Dic11C2×C22⋊C411yescharacteristic
248C4×D11—22no—
249C4×D11—22no—
250C4×D11—21no—
251C4×D11—21no—
252C4×D11—21no—
253C4×D11—21no—
254C4×D11—22no—
255C4×D11—22no—
256C4×D11—22no—
257C4×D11—22no—
258C4×D11—22no—
259C4×D11—22no—
260C4×D11—48no—
261C4×D11—48no—
262C4×D11#10114yes—
263C4×D11#13714yes—
264Dic22—48no—
265Dic22—48no—
266Dic22—42no—
267Dic22—42no—
268Dic22—44no—
269C8×C11—42no—
270C8×C11—42no—
271C11⋊C8—42no—
272C11⋊C8—42no—
273C23×Q8—221no—
274C2×C4⋊Q8—112no—
275C2×C4⋊Q8—112no—
276C2×C4⋊Q8—112no—
277C2×C4⋊Q8—112no—
278C2×C4⋊Q8—112no—
279C2×C4⋊Q8—111no—
280C2×C4⋊Q8—221no—
281C2×C4⋊Q8—221no—
282C2×C4⋊Q8—221no—
283C2×C4⋊Q8—221no—
284C2×C4⋊Q8—221no—
285C2×C4⋊Q8—221no—
286C2×C4⋊Q8C2×D1111yescharacteristic
287C22×C4⋊C4—112no—
288C22×C4⋊C4—221no—
289C22×C42—111no—
290#432—112no—
291#432—112no—
292#432—221no—
293#432—221no—
294#431—111no—
295#431—112no—
296#431—221no—
297#431—221no—
298#431C2×D1111yescharacteristic
299#423—111no—
300#423—112no—
301#423C2×D1111yescharacteristic
302#407—221no—
303#407—221no—
304C4×M16—221no—
305C4×M16—221no—
306#332—114no—
307#332—114no—
308#332—114no—
309#332C2×D1114yescomplemented
310C22×C11—21no—
311C22×C11—21no—
312C22×C11#41812yes—
313C22×C11C22×C22⋊C411yescharacteristic
314C2×D11—28no—
315C2×D11—21no—
316C2×D11—21no—
317C2×D11—21no—
318C2×D11—21no—
319C2×D11C2×#10112yes—
320C2×D11#41912yes—
321C4×C11—21no—
322C4×C11—21no—
323C4×C11—44no—
324C4×C11C2×#10112yes—
325C4×C11#41812yes—
326C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
327C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
328C4×C11C2×#13712yes—
329Dic11—21no—
330Dic11—21no—
331Dic11—21no—
332Dic11—21no—
333Dic11—44no—
334Dic11C2×#10112yes—
335Dic11#41912yes—
336C22×Q8—21no—
337C22×Q8—222no—
338C22×Q8—222no—
339C22×Q8—222no—
340C22×Q8—222no—
341C22×Q8—222no—
342C22×Q8—221no—
343C22×Q8—444no—
344C22×Q8—444no—
345C23×C4—111no—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4—222no—
349C2×M16—21no—
350C2×M16—222no—
351C2×M16—221no—
352C4⋊Q8—21no—
353C4⋊Q8—21no—
354C4⋊Q8—114no—
355C4⋊Q8—114no—
356C4⋊Q8—112no—
357C4⋊Q8—112no—
358C4⋊Q8—222no—
359C4⋊Q8—222no—
360C4⋊Q8—222no—
361C4⋊Q8—222no—
362C4⋊Q8—222no—
363C4⋊Q8—222no—
364C4⋊Q8—222no—
365C4⋊Q8—222no—
366C4⋊Q8—222no—
367C4⋊Q8—222no—
368C4⋊Q8—221no—
369C4⋊Q8—221no—
370C4⋊Q8C4×D1112yes—
371C4⋊Q8C22×D1112yes—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—114no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C4×D1112yes—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42C22×D1111yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—112no—
400C4⋊C8—112no—
401C4⋊C8—222no—
402C4⋊C8—221no—
403C4⋊C8C22×D1112yes—
404C4⋊C8C22×D1112yes—
405C22⋊C8—21no—
406C22⋊C8—222no—
407C22⋊C8—222no—
408C22⋊C8—222no—
409C22⋊C8—221no—
410#97—222no—
411#97—222no—
412C4×C8—21no—
413C4×C8—222no—
414C4×C8—221no—
415C2×C11—22no—
416C2×C11C22×#10111yescharacteristic
417C2×C11C2×#41811yescharacteristic
418C2×C11C2×#41911yescharacteristic
419D11—22no—
420D11—22no—
421C24—111no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—42no—
425C2×Q8—42no—
426C2×Q8—224no—
427C2×Q8—224no—
428C2×Q8—222no—
429C2×Q8—222no—
430C2×Q8—448no—
431C2×Q8—444no—
432C2×Q8—444no—
433C2×Q8—444no—
434C2×Q8—444no—
435C2×Q8—448no—
436C2×Q8—448no—
437C2×Q8—442no—
438C2×Q8—442no—
439C22×C4—22no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—111no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—224no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—448no—
463C22×C4C2×C4×D1111yescharacteristic
464C22×C4D4×D1111yescharacteristic
465C22×C4D4×D1111yescharacteristic
466M16—42no—
467M16—444no—
468M16—442no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—222no—
472C2×C8—222no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—114no—
477C4⋊C4—224no—
478C4⋊C4—224no—
479C4⋊C4—224no—
480C4⋊C4—224no—
481C4⋊C4—222no—
482C4⋊C4—222no—
483C4⋊C4—222no—
484C4⋊C4C2×C4×D1114yes—
485C42—111no—
486C42—111no—
487C42—111no—
488C42—111no—
489C42—111no—
490C42—111no—
491C42—111no—
492C42—111no—
493C42—111no—
494C42—111no—
495C42—111no—
496C42—111no—
497C42C2×C4×D1111yescharacteristic
498C42D4×D1111yescharacteristic
499C42D4×D1111yescharacteristic
500C42C23×D1111yescharacteristic
501C11#1774211yescharacteristic, complemented, Sylow
502C23—111no—
503C23—111no—
504C23—222no—
505C23—222no—
506C23—222no—
507C23C22⋊C4×D1111yescharacteristic
508Q8—42no—
509Q8—42no—
510Q8—44no—
511Q8—448no—
512Q8—448no—
513Q8—442no—
514Q8—442no—
515Q8—444no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—44no—
520C2×C4—111no—
521C2×C4—111no—
522C2×C4—114no—
523C2×C4—114no—
524C2×C4—111no—
525C2×C4—111no—
526C2×C4—111no—
527C2×C4—111no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—224no—
544C2×C4—448no—
545C2×C4—448no—
546C2×C4—444no—
547C2×C4C22⋊C4×D1111yescharacteristic
548C2×C4C22⋊C4×D1111yescharacteristic
549C2×C4C22⋊C4×D1111yescharacteristic
550C2×C4#6696412yes—
551C2×C4#6696712yes—
552C2×C4C22×C4×D1111yescharacteristic
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C8—42no—
556C8—42no—
557C8—442no—
558C8—442no—
559C22—21no—
560C22—21no—
561C22—112no—
562C22—112no—
563C22—228no—
564C22—221no—
565C22—221no—
566C22—221no—
567C22—221no—
568C22#1062238312yes—
569C22C2×C22⋊C4×D1111yescharacteristic
570C4—21no—
571C4—21no—
572C4—44no—
573C4—112no—
574C4—112no—
575C4—221no—
576C4—221no—
577C4—221no—
578C4—221no—
579C4—444no—
580C4D11×#10112yes—
581C4#1062238312yes—
582C4C2×#6696411yescharacteristic
583C4C2×#6696711yescharacteristic
584C4D11×#13712yes—
585C2—22no—
586C2—222no—
587C2—222no—
588C2C2×D11×#10111yescharacteristic
589C2C2×#1062238311yescharacteristic
590C2D11×#41911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1546C2
socleC22×C11C22×C22⋊C4
prime radicalC23×D11C22⋊C4
cosocleC42×C11C24
hypercenter#1546D11
hypocenterC11#17742
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
4. #13067331C2semidirect
5. #13067299C2semidirect
6. #13067289C2semidirect
7. #13067288C2semidirect
8. #13067287C2semidirect
9. C11×#1546C2semidirect
43. C11×#332C22semidirect
44. #10622185C22semidirect
45. #10622124C22semidirect
46. #10622120C22semidirect
215. #1546D11semidirect
309. #332C2×D11semidirect
501. 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
#130772482
#130772442
#130673312
#130672992
#130672892
#130672882
#130672872
C11×#15462
#1774211