Finite Group Databasebeta

← #14676670

Subgroups — #14676670

Order 2816.

2358 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic
3C2×#10622601C211yesmaximal, characteristic
4C2×#10622586C211yesmaximal, characteristic, complemented
5#13066860C214yesmaximal, complemented
6#13066845C211yesmaximal, characteristic, complemented
7(C2×D11)⋊#95C214yesmaximal, complemented
8C4×C11⋊#95C211yesmaximal, characteristic, complemented
9C2×C11×#382C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2214yes—
17C22×(C2×D11)⋊C4C2214yes—
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C2×#66946—24no—
23C2×#66946—24no—
24C2×#66946—24no—
25C11×#382—24no—
26C2×C11×#95C2214yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2214yes—
31#10622601—24no—
32#10622586—24no—
33#10622552C418yescomplemented
34C24×D11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2311yescharacteristic
41C23×Dic11C2312yes—
42C23×Dic11C2311yescharacteristic
43C22×D44—22no—
44C22×D44—22no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44C2×C414yes—
48C22×D44D414yes—
49C22×D44Q814yes—
50C22×C4×D11—24no—
51C22×C4×D11—24no—
52C22×C4×D11—24no—
53C22×C4×D11—28no—
54C22×C4×D11—44no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D414yes—
61C2×C42×C11—22no—
62C2×C42×C11—22no—
63C2×C42×C11C2×C414yescomplemented
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—28no—
68C2×(C2×D11)⋊C4—28no—
69C2×(C2×D11)⋊C4—44no—
70C2×(C2×D11)⋊C4—44no—
71C2×(C2×D11)⋊C4—44no—
72C2×(C2×D11)⋊C4C2×C4116yescomplemented
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11C2×C414yescomplemented
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—44no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11—22no—
80C2×C4×Dic11—22no—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11D414yes—
84#66946—232no—
85C11×#95—28no—
86C11⋊#95—24no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—44no—
90#13979—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
92C23×D11—22no—
93C23×D11—22no—
94C23×D11—24no—
95C23×D11—24no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—24no—
99C23×D11—24no—
100C23×D11C22×C414yes—
101C23×D11C2×D414yes—
102C23×D11C2×Q814yes—
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—24no—
110C22×C4×C11—24no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11C22×C414yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C2×D414yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×Q812yes—
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—21no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11C22×C414yes—
145C22×Dic11C2×D412yes—
146C22×Dic11C2×D412yes—
147C22×Dic11#4114yes—
148C22×Dic11#4114yes—
149C2×D44—28no—
150C2×D44—28no—
151C2×D44—28no—
152C2×D44—28no—
153C2×D44—28no—
154C2×D44—28no—
155C2×D44C4⋊C4116yescomplemented
156C2×C4×D11—216no—
157C2×C4×D11—416no—
158C2×C4×D11—416no—
159C2×C4×D11—48no—
160C2×C4×D11—48no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—44no—
163C42×C11—28no—
164(C2×D11)⋊C4—216no—
165(C2×D11)⋊C4—416no—
166(C2×D11)⋊C4—416no—
167C4⋊Dic11—28no—
168Dic11⋊C4—48no—
169C4×Dic11—28no—
170C4×Dic11—44no—
171C22×C4×D4—111no—
172C2×#390—111no—
173C2×#390—111no—
174C2×#389—111no—
175C2×#382D1111yescharacteristic, complemented
176#1439—114no—
177C4⋊#95—111no—
178C22⋊#95—114no—
179C4×#95—111no—
180C23×C11C23×C411yescharacteristic
181C23×C11C22×D411yescharacteristic
182C23×C11C22×D411yescharacteristic
183C23×C11C22×D411yescharacteristic
184C23×C11C22×Q811yescharacteristic
185C23×C11C2×#4111yescharacteristic
186C23×C11C2×#4111yescharacteristic
187C23×C11C2×#4112yes—
188C23×C11C2×#4112yes—
189C23×C11H(5,𝔽2)12yes—
190C23×C11H(5,𝔽2)12yes—
191C22×D11—24no—
192C22×D11—24no—
193C22×D11—28no—
194C22×D11—28no—
195C22×D11—24no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—24no—
199C22×D11—28no—
200C22×D11—28no—
201C22×D11—28no—
202C22×D11—28no—
203C22×D11—42no—
204C22×D11—44no—
205C22×D11—42no—
206C22×D11—42no—
207C22×D11—42no—
208C22×D11—44no—
209C22×D11—44no—
210C22×D11—44no—
211C22×D11—44no—
212C22×D11—44no—
213C22×D11C2×C4⋊C418yes—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—28no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—44no—
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—44no—
230C2×C4×C11—44no—
231C2×C4×C11C2×C4⋊C414yes—
232C2×C4×C11C4×D414yes—
233C2×C4×C11C4×D414yes—
234C2×C4×C11#12014yes—
235C2×C4×C11C22⋊Q814yes—
236C2×C4×C11C22⋊Q814yes—
237C2×C4×C11#12314yes—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—28no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—44no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11#12414yes—
260D44—232no—
261C4×D11—432no—
262C23×D4—111no—
263C24×C4—112no—
264C2×C4×D4—224no—
265C2×C4×D4—224no—
266C2×C4×D4—224no—
267C22×C4⋊C4—111no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4C2×D1111yescharacteristic
270C22×C4⋊C4C2×D1111yescharacteristic
271C22×C22⋊C4—114no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—114no—
274C22×C42—111no—
275C22×C42—111no—
276C22×C42C2×D1111yescharacteristic
277#390—118no—
278#390—224no—
279#389—224no—
280#382—24no—
281C2×#95—112no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—114no—
285C2×#95C2×D1114yes—
286C22×C11C22×C4⋊C411yescharacteristic
287C22×C11C2×C4×D411yescharacteristic
288C22×C11C2×C4×D411yescharacteristic
289C22×C11C4×#4112yes—
290C22×C11#51812yes—
291C22×C11C2×#12011yescharacteristic
292C22×C11C2×C22⋊Q811yescharacteristic
293C22×C11C2×C22⋊Q811yescharacteristic
294C22×C11C2×#12311yescharacteristic
295C22×C11C2×#12411yescharacteristic
296C22×C11#52912yes—
297C22×C11#53211yescharacteristic
298C22×C11#53511yescharacteristic
299C22×C11#53511yescharacteristic
300C22×C11#54012yes—
301C22×C11#54612yes—
302C22×C11#54612yes—
303C22×C11#54612yes—
304C22×C11#55012yes—
305C22×C11#55312yes—
306C22×C11#55412yes—
307C22×C11#55412yes—
308C22×C11#55512yes—
309C2×D11—216no—
310C2×D11—28no—
311C2×D11—44no—
312C2×D11—44no—
313C2×D11—44no—
314C2×D11—48no—
315C2×D11—48no—
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—48no—
319C2×D11—44no—
320C4×C11—44no—
321C4×C11—44no—
322C4×C11—82no—
323C4×C11#38518yes—
324Dic11—24no—
325Dic11—44no—
326Dic11—44no—
327Dic11—42no—
328C25—112no—
329C22×D4—114no—
330C22×D4—114no—
331C22×D4—114no—
332C22×D4—222no—
333C22×D4—222no—
334C22×D4—222no—
335C22×D4—222no—
336C23×C4—111no—
337C23×C4—112no—
338C23×C4—111no—
339C23×C4—112no—
340C23×C4—224no—
341C23×C4—228no—
342C23×C4—224no—
343C23×C4—224no—
344C23×C4—444no—
345C23×C4C22×D1112yes—
346C23×C4C22×D1112yes—
347C23×C4C22×D1112yes—
348C23×C4C22×D1111yescharacteristic
349C4×D4—2232no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—114no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—444no—
360C2×C4⋊C4C22⋊D1114yes—
361C2×C22⋊C4—1116no—
362C2×C22⋊C4—224no—
363C2×C22⋊C4—224no—
364C2×C22⋊C4—224no—
365C2×C22⋊C4—228no—
366C2×C22⋊C4—228no—
367C2×C22⋊C4—444no—
368C2×C22⋊C4—444no—
369C2×C22⋊C4—444no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—114no—
373C2×C42—222no—
374C2×C42—222no—
375C2×C42—222no—
376C2×C42—222no—
377C2×C42—222no—
378C2×C42C4×D1114yescomplemented
379#95—28no—
380#95—224no—
381#95—224no—
382#95—224no—
383#95—444no—
384C2×C11C2×#38511yescharacteristic
385C2×C11C4×#12411yescharacteristic
386C2×C11#232811yescharacteristic
387C2×C11#234912yes—
388C2×C11#236312yes—
389C2×C11#242012yes—
390C2×C11#243111yescharacteristic
391C2×C11#243511yescharacteristic
392C2×C11#245412yes—
393C2×C11#256311yescharacteristic
394C2×C11#256611yescharacteristic
395D11—48no—
396C24—114no—
397C24—114no—
398C24—114no—
399C24—222no—
400C24—222no—
401C24—222no—
402C24—224no—
403C24—224no—
404C24—224no—
405C24—224no—
406C24—222no—
407C24C23×D1111yescharacteristic
408C2×D4—1116no—
409C2×D4—228no—
410C2×D4—228no—
411C2×D4—228no—
412C2×D4—228no—
413C2×D4—228no—
414C2×D4—228no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—24no—
429C22×C4—22no—
430C22×C4—112no—
431C22×C4—114no—
432C22×C4—114no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—2216no—
436C22×C4—221no—
437C22×C4—222no—
438C22×C4—221no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—221no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4—222no—
447C22×C4—222no—
448C22×C4—224no—
449C22×C4—222no—
450C22×C4—224no—
451C22×C4—222no—
452C22×C4—221no—
453C22×C4—4416no—
454C22×C4—448no—
455C22×C4—4416no—
456C22×C4—448no—
457C22×C4C2×C4×D1114yes—
458C22×C4C2×C4×D1112yes—
459C22×C4#433912yes—
460C22×C4D4×D1112yes—
461C22×C4D4×D1112yes—
462C22×C4Q8×D1112yes—
463C22×C4#434312yes—
464C22×C4C2×C22⋊D1114yes—
465C22×C4C2×C22⋊D1112yes—
466C4⋊C4—28no—
467C4⋊C4—44no—
468C4⋊C4—228no—
469C4⋊C4—448no—
470C22⋊C4—2216no—
471C22⋊C4—4416no—
472C22⋊C4—4416no—
473C42—28no—
474C42—228no—
475C42—444no—
476C11#1397911yescharacteristic, complemented, Sylow
477C23—118no—
478C23—224no—
479C23—224no—
480C23—224no—
481C23—228no—
482C23—228no—
483C23—224no—
484C23—224no—
485C23—224no—
486C23—228no—
487C23—228no—
488C23—228no—
489C23—228no—
490C23—444no—
491C23—444no—
492C23—444no—
493C23—444no—
494C23—442no—
495C23—442no—
496C23—442no—
497C23—442no—
498C23—444no—
499C23—444no—
500C23C22×C4×D1111yescharacteristic
501C23C2×#433911yescharacteristic
502C23C2×D4×D1111yescharacteristic
503C23C2×D4×D1111yescharacteristic
504C23C2×Q8×D1111yescharacteristic
505C23C2×#434311yescharacteristic
506C23#41×D1112yes—
507C23#41×D1112yes—
508C23#6704212yes—
509C23#6704212yes—
510C23C22×C22⋊D1111yescharacteristic
511D4—2232no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—28no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—44no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—44no—
529C2×C4—114no—
530C2×C4—222no—
531C2×C4—224no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—228no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—4432no—
543C2×C4—442no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—442no—
547C2×C4—442no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4—444no—
551C2×C4—442no—
552C2×C4C4⋊C4×D1114yes—
553C2×C4#6694614yes—
554C2×C4#6694714yes—
555C2×C4#6694914yes—
556C2×C4C4×C22⋊D1114yes—
557C2×C4#6699014yes—
558C2×C4#6699914yes—
559C22—2216no—
560C22—228no—
561C22—448no—
562C22—444no—
563C22—448no—
564C22—444no—
565C22—444no—
566C22—444no—
567C22—444no—
568C22—444no—
569C22—448no—
570C22C2×C4⋊C4×D1111yescharacteristic
571C22C2×#6694611yescharacteristic
572C22C2×#6694711yescharacteristic
573C22C2×#6694911yescharacteristic
574C22#1062305212yes—
575C22#1062305312yes—
576C22#1062306112yes—
577C22#1062306312yes—
578C22#1062319911yescharacteristic
579C22D11×#12411yescharacteristic
580C22#1062320511yescharacteristic
581C22#1062320511yescharacteristic
582C22#1062320712yes—
583C22#1062320712yes—
584C22#1062322112yes—
585C22#1062322112yes—
586C22#1062322212yes—
587C22#1062322912yes—
588C22C2×C4×C22⋊D1111yescharacteristic
589C22C2×#6699011yescharacteristic
590C22C2×#6699911yescharacteristic
591C22#1062336012yes—
592C22#1062336512yes—
593C4—44no—
594C4—44no—
595C4—82no—
596C4—224no—
597C4—442no—
598C4—444no—
599C4—444no—
600C4#1062260218yes—
601C2—448no—
602C2C2×#1062260211yescharacteristic
603C2#1307115511yescharacteristic
604C2#1307133911yescharacteristic
605C2#1307152412yes—
606C2#1307165412yes—
607C2#1307211112yes—
608C2#1307223811yescharacteristic
609C2#1307226411yescharacteristic
610C2#1307248412yes—
611C2#1307378811yescharacteristic
612C2#1307381511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#382C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#382D11
hypocenterC11#13979
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
4. C2×#10622586C2semidirect
5. #13066860C2semidirect
6. #13066845C2semidirect
7. (C2×D11)⋊#95C2semidirect
8. C4×C11⋊#95C2semidirect
9. C2×C11×#382C2semidirect
33. #10622552C4semidirect
63. C2×C42×C11C2×C4semidirect
72. C2×(C2×D11)⋊C4C2×C4semidirect
75. C2×C4⋊Dic11C2×C4semidirect
155. C2×D44C4⋊C4semidirect
175. C2×#382D11semidirect
378. C2×C42C4×D11semidirect
476. C11#13979semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
C2×#106225522
C2×#106226012
C2×#106225862
#130668602
#130668452
(C2×D11)⋊#952
C4×C11⋊#952
C2×C11×#3822
#1397911