Finite Group Databasebeta

← #14676499

Subgroups — #14676499

Order 2816.

1622 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic22C211yesmaximal, characteristic
2C2×#10622264C211yesmaximal, characteristic
3C2×#10622261C211yesmaximal, characteristic
4#13066886C212yesmaximal
5#13066882C212yesmaximal
6#13066850C212yesmaximal
7#13066847C212yesmaximal
8#13066843C211yesmaximal, characteristic
9#13066840C211yesmaximal, characteristic
10#13066840C211yesmaximal, characteristic
11C11×#1434C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4C2211yescharacteristic
16C22×Dic11⋊C4C2211yescharacteristic
17C22×C4×Dic11C2212yes—
18C22×C4×Dic11C2211yescharacteristic
19C22×C4×Dic11C2211yescharacteristic
20C2×C4×Dic22—24no—
21C2×C4×Dic22—24no—
22C2×C4×Dic22C418yescomplemented
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622264—24no—
39#10622261—24no—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22C2×C414yes—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11C2×C414yes—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11C2×C414yes—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—22no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—22no—
68C2×Dic11⋊C4C2×C414yes—
69C2×Dic11⋊C4C2×C414yes—
70C2×C4×Dic11—22no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—24no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11C2×C414yes—
76C2×C4×Dic11C2×C414yes—
77C2×C4×Dic11D414yes—
78C2×C4×Dic11D414yes—
79C4×Dic22—232no—
80C11×#95—22no—
81C11×#95—22no—
82C11×#95—24no—
83C11×#95—24no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—24no—
90C11⋊#95—24no—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—24no—
95#13961—111nomaximal, Sylow
96C24×C11C2411yescharacteristic
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C22×C412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11#4114yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—22no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11C22×C412yes—
156C22×Dic11C22×C412yes—
157C22×Dic11C22×C412yes—
158C22×Dic11C22×C412yes—
159C22×Dic11C2×D412yes—
160C22×Dic11C2×D412yes—
161C22×Dic11C2×D412yes—
162C22×Dic11C2×D412yes—
163C22×Dic11#4114yes—
164C22×Dic11#4112yes—
165C22×Dic11#4112yes—
166C2×Dic22—28no—
167C2×Dic22—28no—
168C2×Dic22—28no—
169C2×Dic22—28no—
170C2×Dic22—28no—
171C2×Dic22—28no—
172C2×Dic22—28no—
173C42×C11—28no—
174C4⋊Dic11—28no—
175Dic11⋊C4—28no—
176Dic11⋊C4—28no—
177C4×Dic11—216no—
178C4×Dic11—28no—
179C4×Dic11C22⋊C4116yes—
180C22×C4×Q8—111no—
181C2×#383—111no—
182C2×#376—111no—
183#1446—112no—
184#1445—112no—
185#1436—112no—
186#1436—112no—
187#1434—111no—
188#1434—111no—
189#1434—111no—
190#1434D1111yescharacteristic
191C23×C11C23×C411yescharacteristic
192C23×C11C22×D411yescharacteristic
193C23×C11C22×D411yescharacteristic
194C23×C11C2×#4112yes—
195C23×C11C2×#4111yescharacteristic
196C23×C11C2×#4111yescharacteristic
197C23×C11C2×#4111yescharacteristic
198C23×C11C2×#4111yescharacteristic
199C23×C11C2×#4112yes—
200C23×C112−1+412yes—
201C23×C112−1+412yes—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11C2×C22⋊C414yes—
232C2×C4×C11#11714yes—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—42no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11C2×C22⋊C414yes—
269C2×Dic11C2×C22⋊C414yes—
270C2×Dic11#11714yes—
271Dic22—232no—
272C23×Q8—111no—
273C2×C4×Q8—118no—
274C2×C4×Q8—224no—
275C2×C4×Q8—224no—
276C22×C4⋊C4—111no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—111no—
279C22×C42—111no—
280C22×C42—111no—
281C22×C42—112no—
282C22×C42C2×D1111yescharacteristic
283#383—224no—
284#376—224no—
285C2×#95—111no—
286C2×#95—111no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—112no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95C2×D1111yescharacteristic
297C2×#95C2×D1111yescharacteristic
298C2×#95C2×D1112yes—
299C2×#95C2×D1112yes—
300C22×C11C22×C22⋊C411yescharacteristic
301C22×C11C2×#11711yescharacteristic
302C22×C11C2×#11711yescharacteristic
303C22×C11C4×#4111yescharacteristic
304C22×C11C4×#4111yescharacteristic
305C22×C11#51911yescharacteristic
306C22×C11#51911yescharacteristic
307C22×C11#52512yes—
308C22×C11#52511yescharacteristic
309C22×C11#52511yescharacteristic
310C22×C11#52511yescharacteristic
311C22×C11#52511yescharacteristic
312C22×C11#53212yes—
313C22×C11#53612yes—
314C22×C11#53612yes—
315C22×C11#55212yes—
316C22×C11#55212yes—
317C22×C11#55212yes—
318C22×C11#55212yes—
319C22×C11#55612yes—
320C22×C11#55612yes—
321C22×C11#55612yes—
322C22×C11#55612yes—
323C4×C11—24no—
324C4×C11—24no—
325C4×C11—44no—
326C4×C11—42no—
327C4×C11—82no—
328Dic11—24no—
329Dic11—24no—
330Dic11—24no—
331Dic11—44no—
332Dic11—42no—
333Dic11—82no—
334C22×Q8—114no—
335C22×Q8—222no—
336C22×Q8—222no—
337C22×Q8—222no—
338C22×Q8—222no—
339C22×Q8—222no—
340C22×Q8—222no—
341C23×C4—111no—
342C23×C4—111no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—112no—
346C23×C4—112no—
347C23×C4C22×D1112yes—
348C23×C4C22×D1111yescharacteristic
349C23×C4C22×D1112yes—
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352C4×Q8—2232no—
353C2×C4⋊C4—114no—
354C2×C4⋊C4—114no—
355C2×C4⋊C4—114no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—114no—
365C2×C42—114no—
366C2×C42—114no—
367C2×C42—114no—
368C2×C42—224no—
369C2×C42—224no—
370C2×C42—224no—
371C2×C42—222no—
372C2×C42—222no—
373C2×C42C4×D1114yes—
374#95—24no—
375#95—22no—
376#95—22no—
377#95—24no—
378#95—224no—
379#95—224no—
380#95—224no—
381#95—224no—
382#95—224no—
383#95—224no—
384#95—224no—
385#95—224no—
386#95—222no—
387#95—222no—
388#95—224no—
389C2×C11#228011yescharacteristic
390C2×C11#229711yescharacteristic
391C2×C11#231011yescharacteristic
392C2×C11#235611yescharacteristic
393C2×C11#235611yescharacteristic
394C2×C11#235611yescharacteristic
395C2×C11#235611yescharacteristic
396C2×C11#259912yes—
397C2×C11#259912yes—
398C2×C11#260412yes—
399C2×C11#260412yes—
400C24C23×D1111yescharacteristic
401C2×Q8—228no—
402C2×Q8—228no—
403C2×Q8—228no—
404C2×Q8—228no—
405C2×Q8—228no—
406C2×Q8—228no—
407C2×Q8—228no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—112no—
432C22×C4—112no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—112no—
438C22×C4—112no—
439C22×C4—112no—
440C22×C4—112no—
441C22×C4—114no—
442C22×C4—222no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—222no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4C2×C4×D1112yes—
470C22×C4C2×C4×D1112yes—
471C22×C4C2×C4×D1112yes—
472C22×C4#433914yes—
473C22×C4D4×D1112yes—
474C22×C4D4×D1112yes—
475C22×C4#434112yes—
476C22×C4#434312yes—
477C4⋊C4—228no—
478C4⋊C4—228no—
479C4⋊C4—228no—
480C42—28no—
481C42—1116no—
482C42—2216no—
483C42—228no—
484C11#1396111yescharacteristic, complemented, Sylow
485C23C22×C4×D1111yescharacteristic
486C23C2×#433912yes—
487C23C2×D4×D1111yescharacteristic
488C23C2×D4×D1111yescharacteristic
489C23C2×#434111yescharacteristic
490C23C2×#434311yescharacteristic
491C23#41×D1111yescharacteristic
492C23#41×D1112yes—
493C23#41×D1111yescharacteristic
494C23#6704312yes—
495C23#6704312yes—
496Q8—2232no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—114no—
527C2×C4—114no—
528C2×C4—114no—
529C2×C4—222no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—224no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—222no—
549C2×C4—224no—
550C2×C4—224no—
551C2×C4—442no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4C22⋊C4×D1114yes—
565C2×C4#6694514yes—
566C22C4×#433911yescharacteristic
567C22C2×C22⋊C4×D1111yescharacteristic
568C22C2×#6694511yescharacteristic
569C22#1062304711yescharacteristic
570C22#1062304711yescharacteristic
571C22D11×#11711yescharacteristic
572C22#1062305311yescharacteristic
573C22#1062306212yes—
574C22#1062306412yes—
575C22#1062307212yes—
576C22#1062307812yes—
577C22#1062307912yes—
578C22#1062311512yes—
579C22#1062313711yescharacteristic
580C22#1062313711yescharacteristic
581C22#1062315811yescharacteristic
582C22#1062315811yescharacteristic
583C22#1062317912yes—
584C22#1062317912yes—
585C22#1062320212yes—
586C22#1062322512yes—
587C22#1062323312yes—
588C22#1062323912yes—
589C4—24no—
590C4—24no—
591C4—44no—
592C4—42no—
593C4—82no—
594C4—224no—
595C4—224no—
596C4—224no—
597C4—444no—
598C4—442no—
599C4—882no—
600C2#1307099811yescharacteristic
601C2#1307110211yescharacteristic
602C2#1307120111yescharacteristic
603C2#1307157611yescharacteristic
604C2#1307157911yescharacteristic
605C2#1307158211yescharacteristic
606C2#1307158311yescharacteristic
607C2#1307419012yes—
608C2#1307419212yes—
609C2#1307425112yes—
610C2#1307425312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1434D11
hypocenterC11#13961
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
22. C2×C4×Dic22C4semidirect
484. C11#13961semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
C2×#106222642
C2×#106222612
#130668862
#130668822
#130668502
#130668472
#130668432
#130668402
C11×#14342
#1396111