Finite Group Databasebeta

← #14675749

Subgroups — #14675749

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×#66979C211yesmaximal, characteristic
2C2×#10622548C211yesmaximal, characteristic, complemented
3C2×#10622549C211yesmaximal, characteristic, complemented
4C2×#10622825C211yesmaximal, characteristic
5#13066861C214yesmaximal
6#13066850C214yesmaximal, complemented
7#13066846C211yesmaximal, characteristic, complemented
8#13066846C211yesmaximal, characteristic, complemented
9C2×C4×C11×C22⋊C4C211yesmaximal, characteristic
10C24×C4×C11C2211yescharacteristic
11C22×C11×C22⋊C4C2212yes—
12C22×C42×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2212yes—
16C2×#66979—24no—
17C2×#66979—24no—
18C2×#66979—24no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2214yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4×Dic11C2212yes—
25C4×C11×C22⋊C4C418yescomplemented
26C2×C11×#95C2212yes—
27#10622825—24no—
28C2×C11⋊#95C2214yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31C2×C11⋊#95C2214yes—
32#10622549—24no—
33#10622548—24no—
34C25×C11C2311yescharacteristic
35C23×C4×C11—22no—
36C23×C4×C11—22no—
37C23×C4×C11—22no—
38C23×C4×C11—22no—
39C23×C4×C11C2×C414yes—
40C23×C4×C11D414yes—
41C23×C4×C11Q814yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2312yes—
50C2×C11×C22⋊C4—24no—
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4C2×C418yes—
53C2×C42×C11—22no—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11—22no—
57C2×C42×C11C2×C414yes—
58C2×C42×C11C2×C414yes—
59C2×C22⋊Dic11—24no—
60C2×C22⋊Dic11—24no—
61C2×C22⋊Dic11—24no—
62C2×C22⋊Dic11—24no—
63C2×C22⋊Dic11—44no—
64#66979—232no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—22no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—28no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—28no—
77C2×C4⋊Dic11—44no—
78C2×C4⋊Dic11D414yes—
79C2×C4⋊Dic11D414yes—
80C2×C4×Dic11—24no—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—24no—
83C11×#95C2×C418yes—
84C11⋊#95—24no—
85C11⋊#95—28no—
86C11⋊#95—28no—
87C11⋊#95—44no—
88#13879—111nomaximal, Sylow
89C24×C11—21no—
90C24×C11—21no—
91C24×C11—22no—
92C24×C11—22no—
93C24×C11—21no—
94C24×C11—21no—
95C24×C11—22no—
96C24×C11—22no—
97C24×C11C22×C412yes—
98C24×C11C2×D412yes—
99C24×C11C2×Q812yes—
100C24×C11C2411yescharacteristic
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—28no—
110C22×C4×C11—28no—
111C22×C4×C11—28no—
112C22×C4×C11—28no—
113C22×C4×C11—28no—
114C22×C4×C11—28no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11C4⋊C4116yescomplemented
122C22×C4×C11C22×C414yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C414yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×Q812yes—
131C22×C4×C11C2×Q812yes—
132C22×C4×C11#4114yes—
133C22×C4×C11#4114yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11C2×D414yes—
155C22×Dic11C2×D414yes—
156C11×C22⋊C4—216no—
157C42×C11—28no—
158C42×C11—28no—
159C22⋊Dic11—216no—
160C22⋊Dic11—48no—
161C4⋊Dic11—28no—
162C4⋊Dic11—28no—
163C4⋊Dic11—416no—
164C4⋊Dic11—44no—
165C4⋊Dic11—44no—
166C4×Dic11—216no—
167C22×#117—111no—
168C2×#384—111no—
169C2×#382—111no—
170C2×#380—111no—
171C2×C4×C22⋊C4D1111yescharacteristic
172#1439—114no—
173#1436—114no—
174C4⋊#95—111no—
175C4⋊#95—111no—
176C23×C11—24no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—24no—
180C23×C11—22no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—24no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11C2×C4⋊C414yes—
199C23×C11C23×C411yescharacteristic
200C23×C11C22×D411yescharacteristic
201C23×C11C22×D411yescharacteristic
202C23×C11C22×D411yescharacteristic
203C23×C11C22×Q811yescharacteristic
204C23×C11C2×#4112yes—
205C23×C11C2×#4112yes—
206C23×C11C2×#4111yescharacteristic
207C23×C11C2×#4111yescharacteristic
208C23×C11H(5,𝔽2)12yes—
209C23×C112−1+412yes—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—232no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11C2×C4⋊C414yes—
231C2×C4×C11C2×C4⋊C414yes—
232C2×C4×C11#11718yescomplemented
233C2×C4×C11C4×D414yes—
234C2×C4×C11C4×D414yes—
235C2×C4×C11#12014yes—
236C2×C4×C11C22⋊Q814yes—
237C2×C4×C11C22⋊Q814yes—
238C2×C4×C11#12314yes—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—28no—
242C2×Dic11—28no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—44no—
248C2×Dic11—44no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—44no—
256C2×Dic11—44no—
257C2×Dic11—44no—
258C2×Dic11—44no—
259C24×C4C2×D1111yescharacteristic
260C2×#117—224no—
261C2×#117—224no—
262C2×#117—224no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—111no—
265C22×C4⋊C4—111no—
266C22×C4⋊C4—111no—
267C22×C4⋊C4—114no—
268C22×C22⋊C4—112no—
269C22×C22⋊C4—112no—
270C22×C22⋊C4C2×D1112yes—
271C22×C42—112no—
272C22×C42C2×D1111yescharacteristic
273C22×C42C2×D1111yescharacteristic
274#384—224no—
275#382—224no—
276#380—224no—
277C4×C22⋊C4Dic1118yescomplemented
278C2×#95—114no—
279C2×#95—112no—
280C2×#95—114no—
281C2×#95—114no—
282C2×#95C2×D1112yes—
283C22×C11—24no—
284C22×C11—24no—
285C22×C11—24no—
286C22×C11—44no—
287C22×C11—44no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—44no—
291C22×C11—44no—
292C22×C11—42no—
293C22×C11—42no—
294C22×C11C22×C4⋊C411yescharacteristic
295C22×C11C2×#11712yes—
296C22×C11C2×C4×D411yescharacteristic
297C22×C11C2×C4×D411yescharacteristic
298C22×C11#52012yes—
299C22×C11C2×#12011yescharacteristic
300C22×C11C2×C22⋊Q811yescharacteristic
301C22×C11C2×C22⋊Q811yescharacteristic
302C22×C11C2×#12311yescharacteristic
303C22×C11#53211yescharacteristic
304C22×C11#53211yescharacteristic
305C22×C11#53312yes—
306C22×C11#53511yescharacteristic
307C22×C11#53611yescharacteristic
308C22×C11#54412yes—
309C22×C11#54612yes—
310C22×C11#54712yes—
311C22×C11#54812yes—
312C22×C11#55012yes—
313C22×C11#55212yes—
314C22×C11#55312yes—
315C22×C11#55512yes—
316C22×C11#55612yes—
317C4×C11—28no—
318C4×C11—24no—
319C4×C11—44no—
320C4×C11#38518yes—
321Dic11—44no—
322Dic11—44no—
323Dic11—82no—
324Dic11—82no—
325C25C22×D1111yescharacteristic
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—22no—
329C23×C4—22no—
330C23×C4—112no—
331C23×C4—112no—
332C23×C4—112no—
333C23×C4—112no—
334C23×C4Dic2214yes—
335C23×C4D4414yes—
336C23×C4C2×Dic1114yes—
337C23×C4C22×D1112yes—
338C23×C4C22×D1111yescharacteristic
339C23×C4C22×D1112yes—
340C23×C4C22×D1111yescharacteristic
341#117—2232no—
342C2×C4⋊C4—114no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—228no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—228no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—444no—
357C2×C22⋊C4—24no—
358C2×C22⋊C4—24no—
359C2×C22⋊C4—224no—
360C2×C22⋊C4—224no—
361C2×C22⋊C4—224no—
362C2×C22⋊C4—224no—
363C2×C22⋊C4—444no—
364C2×C22⋊C4C2×Dic1118yes—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—224no—
370C2×C42—224no—
371C2×C42—224no—
372C2×C42C2×Dic1114yes—
373C2×C42C2×Dic1114yes—
374#95—228no—
375#95—224no—
376#95—228no—
377#95—444no—
378#95C2×Dic1118yes—
379C2×C11—44no—
380C2×C11#228511yescharacteristic
381C2×C11C2×#38511yescharacteristic
382C2×C11#231711yescharacteristic
383C2×C11#235212yes—
384C2×C11#235412yes—
385C2×C11#243111yescharacteristic
386C2×C11#243211yescharacteristic
387C2×C11#243912yes—
388C2×C11#244112yes—
389C2×C11#249911yescharacteristic
390C2×C11#250011yescharacteristic
391C24—22no—
392C24—22no—
393C24—21no—
394C24—21no—
395C24—21no—
396C24—21no—
397C24—22no—
398C24—22no—
399C24C2×Dic2212yes—
400C24C2×D4412yes—
401C24C22×Dic1112yes—
402C24C23×D1111yescharacteristic
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—28no—
412C22×C4—28no—
413C22×C4—28no—
414C22×C4—28no—
415C22×C4—28no—
416C22×C4—28no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—114no—
424C22×C4—114no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4C4⋊Dic11116yescomplemented
444C22×C4C2×Dic2212yes—
445C22×C4C2×Dic2212yes—
446C22×C4C2×D4412yes—
447C22×C4C2×D4412yes—
448C22×C4#433914yes—
449C22×C4#433914yes—
450C22×C4D4×D1112yes—
451C22×C4D4×D1112yes—
452C22×C4#434112yes—
453C22×C4#434112yes—
454C22×C4C22×Dic1114yes—
455C22×C4C22×Dic1112yes—
456C22×C4C22×Dic1114yes—
457C22×C4C22×Dic1112yes—
458C4⋊C4—228no—
459C4⋊C4—228no—
460C4⋊C4—4416no—
461C4⋊C4—444no—
462C4⋊C4—444no—
463C22⋊C4—216no—
464C22⋊C4—2216no—
465C22⋊C4—448no—
466C42—28no—
467C42—28no—
468C42—2216no—
469C11#1387911yescharacteristic, complemented, Sylow
470C23—24no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—22no—
477C23—24no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—22no—
482C23—22no—
483C23—24no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23C2×C4⋊Dic1114yes—
493C23C22×Dic2211yescharacteristic
494C23C22×D4411yescharacteristic
495C23C2×#433912yes—
496C23C2×#433912yes—
497C23C2×D4×D1111yescharacteristic
498C23C2×D4×D1111yescharacteristic
499C23C2×#434111yescharacteristic
500C23C2×#434111yescharacteristic
501C23#6704212yes—
502C23#6704312yes—
503C23C23×Dic1111yescharacteristic
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—232no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—228no—
527C2×C4—228no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—444no—
533C2×C4—444no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—444no—
541C2×C4—444no—
542C2×C4—444no—
543C2×C4—444no—
544C2×C4#6693114yes—
545C2×C4#6693114yes—
546C2×C4#6693514yes—
547C2×C4#6693914yes—
548C2×C4C2×C4⋊Dic1114yes—
549C2×C4C2×C4⋊Dic1114yes—
550C2×C4#6697918yescomplemented
551C2×C4D4×Dic1114yes—
552C2×C4D4×Dic1114yes—
553C22—24no—
554C22—24no—
555C22—24no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—44no—
560C22—42no—
561C22—44no—
562C22—44no—
563C22—44no—
564C22#1062300112yes—
565C22#1062300811yescharacteristic
566C22#1062300811yescharacteristic
567C22C2×#6693111yescharacteristic
568C22C2×#6693111yescharacteristic
569C22C2×#6693511yescharacteristic
570C22C2×#6693911yescharacteristic
571C22#1062305012yes—
572C22#1062305611yescharacteristic
573C22#1062305711yescharacteristic
574C22#1062307212yes—
575C22#1062307312yes—
576C22#1062308112yes—
577C22#1062308212yes—
578C22#1062308312yes—
579C22#1062308412yes—
580C22#1062309412yes—
581C22#1062309612yes—
582C22C22×C4⋊Dic1111yescharacteristic
583C22C2×#6697912yes—
584C22C2×D4×Dic1111yescharacteristic
585C22C2×D4×Dic1111yescharacteristic
586C22#1062335812yes—
587C4—24no—
588C4—28no—
589C4—44no—
590C4—444no—
591C4—444no—
592C4—882no—
593C4—882no—
594C4#1062256318yes—
595C2—44no—
596C2#1307102311yescharacteristic
597C2C2×#1062256311yescharacteristic
598C2#1307123911yescharacteristic
599C2#1307154512yes—
600C2#1307156512yes—
601C2#1307223511yescharacteristic
602C2#1307224411yescharacteristic
603C2#1307230712yes—
604C2#1307232912yes—
605C2#1307306911yescharacteristic
606C2#1307307811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C22⋊C4C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×C4×C22⋊C4D11
hypocenterC11#13879
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#10622548C2semidirect
3. C2×#10622549C2semidirect
6. #13066850C2semidirect
7. #13066846C2semidirect
8. #13066846C2semidirect
25. C4×C11×C22⋊C4C4semidirect
121. C22×C4×C11C4⋊C4semidirect
232. C2×C4×C11#117semidirect
277. C4×C22⋊C4Dic11semidirect
443. C22×C4C4⋊Dic11semidirect
469. C11#13879semidirect
550. C2×C4#66979semidirect

Maximal subgroups

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

subgroupindex
C22×#669792
C2×#106225482
C2×#106225492
C2×#106228252
#130668612
#130668502
#130668462
C2×C4×C11×C22⋊C42
#1387911