Finite Group Databasebeta

← #14676198

Subgroups — #14676198

Order 2816.

1650 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×C4×Dic22C211yesmaximal, characteristic
2C2×#10622265C212yesmaximal
3#13066886C212yesmaximal
4#13066868C212yesmaximal
5#13066851C212yesmaximal
6Dic11⋊#95C211yesmaximal, characteristic
7#13066842C211yesmaximal, characteristic
8#13066841C211yesmaximal, characteristic
9#13066841C211yesmaximal, characteristic
10C4×C11⋊#95C211yesmaximal, characteristic
11C11×#1434C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×Dic11⋊C4C2212yes—
16C22×Dic11⋊C4C2211yescharacteristic
17C22×Dic11⋊C4C2211yescharacteristic
18C22×C4×Dic11C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C2×C4×Dic22—28no—
22C2×C4×Dic22C418yescomplemented
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622265—28no—
38C23×C4×C11C2312yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C22×Dic22—24no—
50C22×Dic22—24no—
51C22×Dic22—22no—
52C22×Dic22—22no—
53C22×Dic22C2×C414yes—
54C2×C42×C11—24no—
55C2×C42×C11C2×C414yes—
56C2×C4⋊Dic11—24no—
57C2×C4⋊Dic11C2×C414yes—
58C2×Dic11⋊C4—24no—
59C2×Dic11⋊C4—24no—
60C2×Dic11⋊C4—24no—
61C2×Dic11⋊C4—42no—
62C2×Dic11⋊C4C2×C414yes—
63C2×Dic11⋊C4C2×C414yes—
64C2×Dic11⋊C4D418yes—
65C2×C4×Dic11—24no—
66C2×C4×Dic11—24no—
67C2×C4×Dic11—24no—
68C2×C4×Dic11—24no—
69C2×C4×Dic11—42no—
70C2×C4×Dic11C2×C414yes—
71C2×C4×Dic11C2×C414yes—
72C4×Dic22—232no—
73C11×#95—24no—
74C11×#95—24no—
75C11×#95—22no—
76C11×#95—22no—
77C11⋊#95—24no—
78C11⋊#95—22no—
79C11⋊#95—24no—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—42no—
86C11⋊#95Q814yescomplemented
87#13927—111nomaximal, Sylow
88C24×C11C2411yescharacteristic
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C412yes—
114C22×C4×C11C2×D414yes—
115C22×C4×C11C2×Q812yes—
116C22×C4×C11#4114yes—
117C22×C4×C11#4112yes—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—21no—
126C22×Dic11—21no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11C22×C412yes—
143C22×Dic11C22×C412yes—
144C22×Dic11C22×C412yes—
145C22×Dic11C22×C412yes—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×D414yes—
148C22×Dic11C2×Q814yes—
149C22×Dic11#4114yes—
150C22×Dic11#4112yes—
151C22×Dic11#4112yes—
152C2×Dic22—216no—
153C2×Dic22—216no—
154C2×Dic22—28no—
155C2×Dic22—28no—
156C2×Dic22—28no—
157C42×C11—28no—
158C4⋊Dic11—28no—
159Dic11⋊C4—28no—
160Dic11⋊C4—48no—
161Dic11⋊C4C22⋊C4116yes—
162C4×Dic11—28no—
163C4×Dic11—28no—
164C4×Dic11—48no—
165C22×C4×Q8—111no—
166C2×#387—112no—
167#1446—112no—
168#1441—112no—
169#1436—112no—
170C4⋊#95—111no—
171#1434—111no—
172#1434—111no—
173#1434—111no—
174#1434D1111yescharacteristic
175C4×#95—111no—
176C23×C11C23×C411yescharacteristic
177C23×C11C22×D412yes—
178C23×C11C22×Q811yescharacteristic
179C23×C11C2×#4112yes—
180C23×C11C2×#4111yescharacteristic
181C23×C11C2×#4111yescharacteristic
182C23×C11C2×#4111yescharacteristic
183C23×C11C2×#4112yes—
184C23×C11H(5,𝔽2)11yescharacteristic
185C23×C112−1+412yes—
186C23×C112−1+411yescharacteristic
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—24no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11—42no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11C2×C22⋊C414yes—
214C2×C4×C11#11714yes—
215C2×C4×C11C4×Q814yes—
216C2×Dic11—22no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—22no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—22no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11C2×C22⋊C414yes—
248C2×Dic11C2×C22⋊C414yes—
249C2×Dic11#11714yes—
250Dic22—232no—
251C23×Q8—111no—
252C2×C4×Q8—118no—
253C2×C4×Q8—228no—
254C22×C4⋊C4—111no—
255C22×C4⋊C4—111no—
256C22×C4⋊C4—111no—
257C22×C4⋊C4—112no—
258C22×C42—111no—
259C22×C42—111no—
260C22×C42—112no—
261C22×C42C2×D1111yescharacteristic
262#387—228no—
263C2×#95—111no—
264C2×#95—111no—
265C2×#95—112no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95—112no—
270C2×#95—112no—
271C2×#95—112no—
272C2×#95—112no—
273C2×#95C2×D1111yescharacteristic
274C2×#95C2×D1111yescharacteristic
275C2×#95C2×D1112yes—
276C2×#95C2×D1112yes—
277C22×C11C22×C22⋊C411yescharacteristic
278C22×C11C2×#11711yescharacteristic
279C22×C11C2×#11711yescharacteristic
280C22×C11C2×C4×Q811yescharacteristic
281C22×C11C4×#4111yescharacteristic
282C22×C11#51911yescharacteristic
283C22×C11#52011yescharacteristic
284C22×C11#52512yes—
285C22×C11#52512yes—
286C22×C11#52912yes—
287C22×C11#53312yes—
288C22×C11#54112yes—
289C22×C11#54212yes—
290C22×C11#54612yes—
291C22×C11#54712yes—
292C22×C11#54812yes—
293C22×C11D4×Q812yes—
294C22×C11#55212yes—
295C22×C11#55411yescharacteristic
296C22×C11#55612yes—
297C22×C11#55611yescharacteristic
298C22×C11#55711yescharacteristic
299C22×C11#55911yescharacteristic
300C4×C11—24no—
301C4×C11—24no—
302C4×C11—24no—
303C4×C11—82no—
304C4×C11—82no—
305Dic11—24no—
306Dic11—24no—
307Dic11—24no—
308Dic11—42no—
309Dic11—44no—
310Dic11—44no—
311C22×Q8—114no—
312C22×Q8—224no—
313C22×Q8—222no—
314C22×Q8—222no—
315C22×Q8—224no—
316C23×C4—111no—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—111no—
320C23×C4—112no—
321C23×C4—112no—
322C23×C4C22×D1112yes—
323C23×C4C22×D1112yes—
324C23×C4C22×D1111yescharacteristic
325C23×C4C22×D1111yescharacteristic
326C23×C4C22×D1111yescharacteristic
327C4×Q8—2232no—
328C2×C4⋊C4—114no—
329C2×C4⋊C4—118no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—114no—
332C2×C4⋊C4—224no—
333C2×C4⋊C4—224no—
334C2×C4⋊C4—224no—
335C2×C4⋊C4—224no—
336C2×C4⋊C4—442no—
337C2×C42—24no—
338C2×C42—114no—
339C2×C42—114no—
340C2×C42—224no—
341C2×C42—224no—
342C2×C42—224no—
343C2×C42—224no—
344C2×C42—442no—
345C2×C42C4×D1114yes—
346#95—24no—
347#95—24no—
348#95—22no—
349#95—22no—
350#95—114no—
351#95—224no—
352#95—224no—
353#95—224no—
354#95—224no—
355#95—224no—
356#95—224no—
357#95—224no—
358#95—222no—
359#95—442no—
360C2×C11#228011yescharacteristic
361C2×C11#229511yescharacteristic
362C2×C11#232011yescharacteristic
363C2×C11#233911yescharacteristic
364C2×C11Q8×C22⋊C411yescharacteristic
365C2×C11#235511yescharacteristic
366C2×C11#235611yescharacteristic
367C2×C11#245812yes—
368C2×C11#246212yes—
369C2×C11#246512yes—
370C2×C11#246912yes—
371C24C23×D1111yescharacteristic
372C2×Q8—228no—
373C2×Q8—228no—
374C2×Q8—2216no—
375C2×Q8—2216no—
376C2×Q8—228no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—22no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—114no—
403C22×C4—114no—
404C22×C4—112no—
405C22×C4—112no—
406C22×C4—112no—
407C22×C4—114no—
408C22×C4—114no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—222no—
413C22×C4—221no—
414C22×C4—221no—
415C22×C4—221no—
416C22×C4—221no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—221no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—221no—
432C22×C4—222no—
433C22×C4C2×C4×D1112yes—
434C22×C4C2×C4×D1112yes—
435C22×C4C2×C4×D1112yes—
436C22×C4#433914yes—
437C22×C4D4×D1114yes—
438C22×C4#434112yes—
439C22×C4Q8×D1112yes—
440C4⋊C4—1116no—
441C4⋊C4—228no—
442C4⋊C4—228no—
443C4⋊C4—448no—
444C42—28no—
445C42—228no—
446C42—228no—
447C42—448no—
448C11#1392711yescharacteristic, complemented, Sylow
449C23C22×C4×D1111yescharacteristic
450C23C2×#433912yes—
451C23C2×D4×D1112yes—
452C23C2×#434111yescharacteristic
453C23C2×Q8×D1111yescharacteristic
454C23#41×D1111yescharacteristic
455C23#41×D1112yes—
456C23#41×D1111yescharacteristic
457C23#6704211yescharacteristic
458C23#6704312yes—
459C23#6704311yescharacteristic
460Q8—2232no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—114no—
488C2×C4—114no—
489C2×C4—114no—
490C2×C4—222no—
491C2×C4—222no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—222no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—442no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—442no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4#6692514yes—
522C2×C4C22⋊C4×D1114yes—
523C2×C4#6694014yes—
524C22C2×#6692511yescharacteristic
525C22C2×C22⋊C4×D1111yescharacteristic
526C22C2×#6694011yescharacteristic
527C22#1062304711yescharacteristic
528C22#1062304912yes—
529C22D11×#11711yescharacteristic
530C22#1062305311yescharacteristic
531C22#1062305411yescharacteristic
532C22#1062306512yes—
533C22#1062307812yes—
534C22#1062307812yes—
535C22#1062308812yes—
536C22#1062310912yes—
537C22#1062312912yes—
538C22#1062316312yes—
539C22#1062318512yes—
540C22#1062318612yes—
541C22#1062320211yescharacteristic
542C22#1062321211yescharacteristic
543C22#1062321611yescharacteristic
544C22#1062322111yescharacteristic
545C22#1062323312yes—
546C22#1062323912yes—
547C4—24no—
548C4—24no—
549C4—24no—
550C4—82no—
551C4—82no—
552C4—224no—
553C4—224no—
554C4—224no—
555C4—442no—
556C4—444no—
557C4—444no—
558C2#1307099711yescharacteristic
559C2#1307109011yescharacteristic
560C2#1307126811yescharacteristic
561C2#1307144011yescharacteristic
562C2#1307144811yescharacteristic
563C2#1307156811yescharacteristic
564C2#1307157611yescharacteristic
565C2#1307254012yes—
566C2#1307260012yes—
567C2#1307263912yes—
568C2#1307269912yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1434D11
hypocenterC11#13927
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
86. C11⋊#95Q8semidirect
448. C11#13927semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic222
C2×#106222652
#130668862
#130668682
#130668512
Dic11⋊#952
#130668422
#130668412
C4×C11⋊#952
C11×#14342
#1392711