Finite Group Databasebeta

← #14675751

Subgroups — #14675751

Order 2816.

2006 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic
2C2×#10622548C211yesmaximal, characteristic, complemented
3C2×#10622590C211yesmaximal, characteristic, complemented
4C2×#10622600C211yesmaximal, characteristic
5C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
6#13066862C214yesmaximal
7#13066850C214yesmaximal, complemented
8#13066845C211yesmaximal, characteristic, complemented
9C11×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×C4×D11C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2214yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2211yescharacteristic
22C2×#66945—24no—
23C2×#66945—24no—
24C2×#66945—24no—
25C2×C11×#95C2214yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2214yes—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30#10622600—24no—
31#10622590—24no—
32C4×(C2×D11)⋊C4C418yescomplemented
33#10622548—24no—
34C24×D11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2311yescharacteristic
43C22×C4×D11—22no—
44C22×C4×D11—22no—
45C22×C4×D11—22no—
46C22×C4×D11—22no—
47C22×C4×D11C2×C414yes—
48C22×C4×D11D414yes—
49C22×C4×D11Q814yes—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4D414yes—
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11C2×C414yes—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—44no—
66C2×(C2×D11)⋊C4C2×C418yes—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—28no—
73C2×C4⋊Dic11—28no—
74C2×C4⋊Dic11—44no—
75C2×C4⋊Dic11D414yes—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—24no—
80C2×C4×Dic11—24no—
81C2×C4×Dic11C2×C414yes—
82#66945—232no—
83C11×#95—28no—
84C11⋊#95—28no—
85C11⋊#95—24no—
86C11⋊#95—44no—
87C11⋊#95C2×C418yes—
88#13879—111nomaximal, Sylow
89C24×C11C2411yescharacteristic
90C23×D11—21no—
91C23×D11—21no—
92C23×D11—22no—
93C23×D11—22no—
94C23×D11—21no—
95C23×D11—21no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11C22×C412yes—
99C23×D11C2×D412yes—
100C23×D11C2×Q812yes—
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—24no—
108C22×C4×C11—24no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—24no—
114C22×C4×C11C22×C414yes—
115C22×C4×C11C22×C412yes—
116C22×C4×C11C2×D414yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D412yes—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×Q812yes—
121C22×C4×C11#4114yes—
122C22×C4×C11#4114yes—
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
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—21no—
134C22×Dic11—21no—
135C22×Dic11—22no—
136C22×Dic11—24no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11C22×C414yes—
145C22×Dic11C22×C412yes—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×D412yes—
148C22×Dic11C2×Q812yes—
149C2×C4×D11—28no—
150C2×C4×D11—28no—
151C2×C4×D11—28no—
152C2×C4×D11—28no—
153C2×C4×D11—28no—
154C2×C4×D11—28no—
155C2×C4×D11C4⋊C4116yescomplemented
156C11×C4⋊C4—28no—
157C11×C4⋊C4—44no—
158C42×C11—28no—
159(C2×D11)⋊C4—216no—
160(C2×D11)⋊C4—216no—
161(C2×D11)⋊C4—48no—
162C4⋊Dic11—28no—
163C4⋊Dic11—416no—
164C4⋊Dic11—44no—
165C4×Dic11—216no—
166C4×Dic11—28no—
167C22×#117—111no—
168C2×#384—111no—
169C2×#382—111no—
170C2×#380—111no—
171C2×C4×C22⋊C4—111no—
172#1439—114no—
173#1436—114no—
174C4⋊#95—111no—
175C4⋊#95D1111yescharacteristic, complemented
176C23×C11C23×C411yescharacteristic
177C23×C11C22×D411yescharacteristic
178C23×C11C22×D411yescharacteristic
179C23×C11C22×D411yescharacteristic
180C23×C11C22×Q811yescharacteristic
181C23×C11C2×#4111yescharacteristic
182C23×C11C2×#4112yes—
183C23×C11C2×#4111yescharacteristic
184C23×C11C2×#4112yes—
185C23×C11H(5,𝔽2)12yes—
186C23×C112−1+412yes—
187C22×D11—24no—
188C22×D11—22no—
189C22×D11—22no—
190C22×D11—24no—
191C22×D11—22no—
192C22×D11—22no—
193C22×D11—22no—
194C22×D11—22no—
195C22×D11—22no—
196C22×D11—22no—
197C22×D11—24no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—24no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—42no—
209C22×D11C2×C4⋊C414yes—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—28no—
218C2×C4×C11—42no—
219C2×C4×C11—42no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11—44no—
225C2×C4×C11—44no—
226C2×C4×C11C2×C4⋊C414yes—
227C2×C4×C11#11718yescomplemented
228C2×C4×C11C4×D414yes—
229C2×C4×C11C4×D414yes—
230C2×C4×C11#12014yes—
231C2×C4×C11C22⋊Q814yes—
232C2×C4×C11C22⋊Q814yes—
233C2×C4×C11#12314yes—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—28no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—44no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—44no—
256C2×Dic11—44no—
257C2×Dic11C2×C4⋊C414yes—
258C4×D11—232no—
259C24×C4—111no—
260C2×#117—224no—
261C2×#117—224no—
262C2×#117—224no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—111no—
265C22×C4⋊C4—114no—
266C22×C4⋊C4C2×D1111yescharacteristic
267C22×C4⋊C4C2×D1111yescharacteristic
268C22×C22⋊C4—112no—
269C22×C22⋊C4—112no—
270C22×C22⋊C4—112no—
271C22×C42—111no—
272C22×C42—112no—
273C22×C42C2×D1111yescharacteristic
274#384—224no—
275#382—224no—
276#380—224no—
277C4×C22⋊C4—118no—
278C2×#95—112no—
279C2×#95—112no—
280C2×#95—114no—
281C2×#95—114no—
282C2×#95C2×D1114yes—
283C22×C11C22×C4⋊C411yescharacteristic
284C22×C11C2×#11712yes—
285C22×C11C2×C4×D411yescharacteristic
286C22×C11C2×C4×D411yescharacteristic
287C22×C11#52012yes—
288C22×C11C2×#12011yescharacteristic
289C22×C11C2×C22⋊Q811yescharacteristic
290C22×C11C2×C22⋊Q811yescharacteristic
291C22×C11C2×#12311yescharacteristic
292C22×C11#53211yescharacteristic
293C22×C11#53211yescharacteristic
294C22×C11#53312yes—
295C22×C11#53511yescharacteristic
296C22×C11#53611yescharacteristic
297C22×C11#54412yes—
298C22×C11#54612yes—
299C22×C11#54712yes—
300C22×C11#54812yes—
301C22×C11#55012yes—
302C22×C11#55212yes—
303C22×C11#55312yes—
304C22×C11#55512yes—
305C22×C11#55612yes—
306C2×D11—24no—
307C2×D11—24no—
308C2×D11—24no—
309C2×D11—44no—
310C2×D11—44no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—44no—
314C2×D11—44no—
315C2×D11—42no—
316C2×D11—42no—
317C4×C11—28no—
318C4×C11—44no—
319C4×C11—82no—
320C4×C11#38518yes—
321Dic11—24no—
322Dic11—44no—
323Dic11—44no—
324Dic11—82no—
325C25—111no—
326C23×C4—111no—
327C23×C4—114no—
328C23×C4—114no—
329C23×C4—114no—
330C23×C4—112no—
331C23×C4—112no—
332C23×C4—112no—
333C23×C4—222no—
334C23×C4—222no—
335C23×C4—222no—
336C23×C4—222no—
337C23×C4C22×D1112yes—
338C23×C4C22×D1112yes—
339C23×C4C22×D1112yes—
340C23×C4C22×D1111yescharacteristic
341#117—2232no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—114no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—228no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—228no—
355C2×C4⋊C4—444no—
356C2×C4⋊C4D4414yes—
357C2×C22⋊C4—118no—
358C2×C22⋊C4—224no—
359C2×C22⋊C4—224no—
360C2×C22⋊C4—224no—
361C2×C22⋊C4—224no—
362C2×C22⋊C4—224no—
363C2×C22⋊C4—224no—
364C2×C22⋊C4—444no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—114no—
368C2×C42—224no—
369C2×C42—224no—
370C2×C42—224no—
371C2×C42—222no—
372C2×C42—222no—
373C2×C42C4×D1114yes—
374#95—28no—
375#95—118no—
376#95—224no—
377#95—228no—
378#95—444no—
379C2×C11#228511yescharacteristic
380C2×C11C2×#38511yescharacteristic
381C2×C11#231711yescharacteristic
382C2×C11#235212yes—
383C2×C11#235412yes—
384C2×C11#243111yescharacteristic
385C2×C11#243211yescharacteristic
386C2×C11#243912yes—
387C2×C11#244112yes—
388C2×C11#249911yescharacteristic
389C2×C11#250011yescharacteristic
390D11—44no—
391C24—112no—
392C24—112no—
393C24—112no—
394C24—221no—
395C24—221no—
396C24—221no—
397C24—222no—
398C24—221no—
399C24—222no—
400C24—222no—
401C24—222no—
402C24C23×D1111yescharacteristic
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—112no—
417C22×C4—112no—
418C22×C4—112no—
419C22×C4—1116no—
420C22×C4—114no—
421C22×C4—114no—
422C22×C4—221no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—221no—
426C22×C4—228no—
427C22×C4—228no—
428C22×C4—228no—
429C22×C4—228no—
430C22×C4—228no—
431C22×C4—228no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—224no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—224no—
446C22×C4—224no—
447C22×C4C2×C4×D1114yes—
448C22×C4C2×C4×D1112yes—
449C22×C4C2×D4414yes—
450C22×C4C2×D4412yes—
451C22×C4#433912yes—
452C22×C4D4×D1112yes—
453C22×C4D4×D1112yes—
454C22×C4#434114yes—
455C22×C4#434112yes—
456C22×C4Q8×D1112yes—
457C22×C4#434314yes—
458C4⋊C4—28no—
459C4⋊C4—44no—
460C4⋊C4—228no—
461C4⋊C4—4416no—
462C4⋊C4—444no—
463C22⋊C4—2216no—
464C22⋊C4—2216no—
465C22⋊C4—448no—
466C42—28no—
467C42—2216no—
468C42—228no—
469C11#1387911yescharacteristic, complemented, Sylow
470C23—114no—
471C23—222no—
472C23—222no—
473C23—224no—
474C23—222no—
475C23—222no—
476C23—222no—
477C23—222no—
478C23—224no—
479C23—222no—
480C23—222no—
481C23—224no—
482C23—222no—
483C23—222no—
484C23—224no—
485C23—442no—
486C23—442no—
487C23—442no—
488C23—442no—
489C23—442no—
490C23—442no—
491C23—442no—
492C23—442no—
493C23C22×C4×D1111yescharacteristic
494C23C22×D4411yescharacteristic
495C23C2×#433911yescharacteristic
496C23C2×D4×D1111yescharacteristic
497C23C2×D4×D1111yescharacteristic
498C23C2×#434112yes—
499C23C2×#434111yescharacteristic
500C23C2×Q8×D1111yescharacteristic
501C23C2×#434312yes—
502C23#6704212yes—
503C23#6704312yes—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—28no—
512C2×C4—42no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—114no—
521C2×C4—222no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—2232no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—228no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—444no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—444no—
543C2×C4—444no—
544C2×C4—442no—
545C2×C4C4×D4414yes—
546C2×C4(C22⋊D11)⋊C414yes—
547C2×C4#6693514yes—
548C2×C4#6693614yes—
549C2×C4C4⋊C4×D1114yes—
550C2×C4#6694518yescomplemented
551C2×C4#6694914yes—
552C2×C4#6695014yes—
553C22—224no—
554C22—224no—
555C22—224no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22—444no—
560C22—442no—
561C22—444no—
562C22—444no—
563C22—444no—
564C22C2×C4×D4411yescharacteristic
565C22C2×(C22⋊D11)⋊C411yescharacteristic
566C22C2×#6693511yescharacteristic
567C22C2×#6693611yescharacteristic
568C22C2×C4⋊C4×D1111yescharacteristic
569C22C2×#6694512yes—
570C22C2×#6694911yescharacteristic
571C22C2×#6695011yescharacteristic
572C22#1062305412yes—
573C22#1062308612yes—
574C22#1062309412yes—
575C22#1062310812yes—
576C22#1062311512yes—
577C22#1062312912yes—
578C22#1062314912yes—
579C22#1062316112yes—
580C22#1062317312yes—
581C22#1062320511yescharacteristic
582C22#1062320611yescharacteristic
583C22#1062322012yes—
584C22#1062324711yescharacteristic
585C22#1062325611yescharacteristic
586C22#1062325912yes—
587C4—28no—
588C4—44no—
589C4—82no—
590C4—224no—
591C4—444no—
592C4—444no—
593C4—882no—
594C4#1062228118yes—
595C2—444no—
596C2#1307102111yescharacteristic
597C2C2×#1062228111yescharacteristic
598C2#1307124111yescharacteristic
599C2#1307154712yes—
600C2#1307156312yes—
601C2#1307223711yescharacteristic
602C2#1307224611yescharacteristic
603C2#1307230912yes—
604C2#1307232712yes—
605C2#1307307111yescharacteristic
606C2#1307308011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#13879
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#10622548C2semidirect
3. C2×#10622590C2semidirect
7. #13066850C2semidirect
8. #13066845C2semidirect
9. C11×C4⋊#95C2semidirect
32. C4×(C2×D11)⋊C4C4semidirect
155. C2×C4×D11C4⋊C4semidirect
175. C4⋊#95D11semidirect
227. C2×C4×C11#117semidirect
469. C11#13879semidirect
550. C2×C4#66945semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
C2×#106225482
C2×#106225902
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668622
#130668502
#130668452
C11×C4⋊#952
#1387911