Finite Group Databasebeta

← #14926674

Subgroups — #14926674

Order 2816.

2322 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623133C212yesmaximal, complemented
2#13076942C212yesmaximal, complemented
3#13076915C212yesmaximal, complemented
4#13074730C211yesmaximal, characteristic, complemented
5#13074360C212yesmaximal, complemented
6#13073701C214yesmaximal, complemented
7#13073677C214yesmaximal, complemented
8#13073284C214yesmaximal, complemented
9#13072578C214yesmaximal, complemented
10#13071321C212yesmaximal, complemented
11#121×Dic11C212yesmaximal, complemented
12C2×#10622262C211yesmaximal, characteristic, complemented
13C11×#2656C211yesmaximal, characteristic
14C2×C11×#121C2212yes—
15C2×C11×#121C2212yes—
16C2×C11×#121C2212yes—
17C2×#66989C2212yes—
18C2×#66988C2214yes—
19C2×#66988C2214yes—
20C2×D4×Dic11C2214yes—
21C2×D4×Dic11C2212yes—
22C2×#66977C2212yes—
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28#10623133—216no—
29C2×#66942C2214yes—
30C2×#66932C2214yes—
31C2×#66931C2214yes—
32C11×#399C2214yes—
33C11×#392C2214yes—
34C2×C11×#95C2211yescharacteristic
35#10622835C2214yes—
36#10622834C2212yes—
37#10622834C2212yes—
38#10622834C2212yes—
39#10622834C2212yes—
40#10622833C2214yes—
41#10622833C2214yes—
42#10622833C2214yes—
43#10622825C2212yes—
44#10622825C2212yes—
45C2×C11⋊#95C2211yescharacteristic
46#10622598C2212yes—
47#10622594C2214yes—
48#10622593C2214yes—
49#10622590C2212yes—
50C4⋊C4×Dic11C2212yes—
51#10622587C2212yes—
52#10622586C2212yes—
53#10622586C2212yes—
54#10622564C2214yes—
55#10622564C2214yes—
56#10622563C2214yes—
57#10622561C2214yes—
58#10622561C2214yes—
59#10622558C2214yes—
60#10622558C2214yes—
61#10622557C2214yes—
62#10622557C2214yes—
63C22⋊C4×Dic11C2214yes—
64#10622274C2214yes—
65#10622269C2214yes—
66#10622262C2214yes—
67#10622262C2214yes—
68C22×D4×C11C2314yes—
69C22×D4×C11C2312yes—
70C22×D4×C11C2312yes—
71C22×D4×C11C2312yes—
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2314yes—
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C22×Dic22C2312yes—
81C11×#121—28no—
82C11×#121—28no—
83C11×#121—28no—
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2312yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2314yes—
90C2×C22⋊Dic11C2314yes—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2314yes—
95C2×C22⋊Dic11C2314yes—
96C2×C22⋊Dic11C2314yes—
97C2×C22⋊Dic11C2314yes—
98#66989—44no—
99#66988—216no—
100#66988—216no—
101D4×Dic11—216no—
102D4×Dic11—44no—
103C2×C4⋊Dic11C2314yes—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2312yes—
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2312yes—
108C2×C4⋊Dic11C2312yes—
109#66977—28no—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4D418yescomplemented
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×Dic11⋊C4C2314yes—
117C2×C4×Dic11—24no—
118C2×C4×Dic11—42no—
119C2×C4×Dic11—42no—
120C2×C4×Dic11C2314yes—
121C2×C4×Dic11C2312yes—
122C2×C4×Dic11C2312yes—
123C2×C4×Dic11C2312yes—
124C2×C4×Dic11C2312yes—
125C2×C4×Dic11C2312yes—
126C2×C4×Dic11C2312yes—
127#66942—216no—
128#66932—216no—
129#66931—216no—
130C11×#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134C11⋊#95C2314yes—
135C11⋊#95C2314yes—
136C11⋊#95C2314yes—
137C11⋊#95C2314yes—
138#35004—111nomaximal, Sylow
139C24×C11C2414yes—
140C24×C11C2411yescharacteristic
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—24no—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C22×C4×C11—41no—
154C22×C4×C11—41no—
155C22×C4×C11—41no—
156C22×C4×C11—41no—
157C22×C4×C11—41no—
158C22×C4×C11—41no—
159C22×C4×C11C2×D414yes—
160C22×C4×C11#4114yes—
161C22×C4×C11#4114yes—
162C22×C4×C11C2414yes—
163C22×C4×C11C2412yes—
164C22×C4×C11C2412yes—
165C22×C4×C11C2412yes—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—28no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—41no—
174C22×Dic11—41no—
175C22×Dic11—41no—
176C22×Dic11—41no—
177C22×Dic11—44no—
178C22×Dic11—44no—
179C22×Dic11C2×D414yes—
180C22×Dic11C2×D414yes—
181C22×Dic11C2412yes—
182C22×Dic11C2414yes—
183C22×Dic11C2414yes—
184C22×Dic11C2412yes—
185C22×Dic11C2412yes—
186C22×Dic11C2411yescharacteristic
187C22×Dic11C2411yescharacteristic
188C2×Dic22—24no—
189C2×Dic22—42no—
190C2×Dic22—42no—
191C11×C4⋊C4—24no—
192C11×C4⋊C4—24no—
193C11×C4⋊C4—24no—
194C11×C22⋊C4—28no—
195C11×C22⋊C4—28no—
196C11×C22⋊C4—28no—
197C22⋊Dic11—28no—
198C22⋊Dic11—28no—
199C22⋊Dic11—28no—
200C22⋊Dic11—28no—
201C22⋊Dic11—28no—
202C22⋊Dic11—28no—
203C22⋊Dic11—44no—
204C22⋊Dic11—44no—
205C4⋊Dic11—28no—
206C4⋊Dic11—24no—
207C4⋊Dic11—42no—
208C4⋊Dic11—42no—
209C4⋊Dic11—42no—
210C4⋊Dic11—42no—
211Dic11⋊C4—28no—
212Dic11⋊C4—28no—
213Dic11⋊C4—28no—
214Dic11⋊C4—28no—
215Dic11⋊C4C2×D4116yes—
216C4×Dic11—28no—
217C4×Dic11—24no—
218C4×Dic11—24no—
219C4×Dic11—24no—
220C4×Dic11—24no—
221C4×Dic11—42no—
222C4×Dic11—42no—
223C2×#539—112no—
224#2854—112no—
225#2850—112no—
226#2659—111no—
227#2656D1111yescharacteristic
228#2618—112no—
229#2556—114no—
230#2554—114no—
231#2519—114no—
232#2461—114no—
233#2325—112no—
234C4×#121—112no—
235C2×C4×C4⋊C4—111no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—24no—
246C23×C11—24no—
247C23×C11C22×D412yes—
248C23×C11C2×#4112yes—
249C23×C11C2×#4112yes—
250C23×C11C2511yescharacteristic
251D4×C11—48no—
252D4×C11—416no—
253D4×C11—84no—
254D4×C11—84no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—24no—
264C2×C4×C11—44no—
265C2×C4×C11—44no—
266C2×C4×C11—44no—
267C2×C4×C11C22×D414yes—
268C2×C4×C11C2×#4114yes—
269C2×C4×C11C2×#4114yes—
270C2×Dic11—28no—
271C2×Dic11—28no—
272C2×Dic11—22no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—22no—
289C2×Dic11—44no—
290C2×Dic11—44no—
291C2×Dic11—88no—
292C2×Dic11C22×D414yes—
293C2×Dic11C22×D414yes—
294C2×Dic11H(5,𝔽2)12yes—
295C2×Dic112−1+412yes—
296Dic22—84no—
297#539—2216no—
298C2×#126—114no—
299C2×#125—114no—
300C2×#124—112no—
301C2×#123—114no—
302C2×#123—114no—
303C2×C22⋊Q8—112no—
304C2×C22⋊Q8—114no—
305C2×#121C2×D1112yes—
306C2×#121C2×D1112yes—
307C2×#121C2×D1112yes—
308C2×C4×D4—114no—
309C2×C4×D4—112no—
310C22×C4⋊C4—111no—
311C22×C4⋊C4—111no—
312C22×C42—111no—
313C22×C42—111no—
314C22×C42—111no—
315#399C2×D1114yes—
316#398—114no—
317#398—114no—
318#396—114no—
319#396—114no—
320#395—114no—
321#394—114no—
322#392C2×D1114yes—
323#391—112no—
324#390—112no—
325#390—112no—
326#390—112no—
327#390—112no—
328#389—112no—
329#389—112no—
330#389—112no—
331#388—114no—
332#388—114no—
333#388—114no—
334#388—114no—
335#388—114no—
336#388—114no—
337#387—114no—
338#386—114no—
339#386—114no—
340#386—114no—
341#385—114no—
342#382—112no—
343#380—112no—
344#380—112no—
345C4×C4⋊C4—112no—
346C4×C4⋊C4—114no—
347C4×C4⋊C4—114no—
348C4×C22⋊C4—114no—
349C2×#95—111no—
350C2×#95C2×D1111yescharacteristic
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—44no—
358C22×C11—44no—
359C22×C11—44no—
360C22×C11—44no—
361C22×C11—44no—
362C22×C11—44no—
363C22×C11—44no—
364C22×C11#53214yes—
365C22×C11C23×D411yescharacteristic
366C22×C11C22×#4111yescharacteristic
367C22×C11C22×#4111yescharacteristic
368C22×C11C2×H(5,𝔽2)11yescharacteristic
369C22×C11C2×2−1+411yescharacteristic
370C22×C11#58511yescharacteristic
371C22×C11#58511yescharacteristic
372C4×C11—24no—
373C4×C11—24no—
374C4×C11—24no—
375C4×C11—44no—
376Dic11—24no—
377Dic11—22no—
378Dic11—22no—
379Dic11—24no—
380Dic11—42no—
381Dic11—44no—
382Dic11—44no—
383C22×Q8—112no—
384C22×D4C22×D1114yes—
385C22×D4C22×D1112yes—
386C22×D4C22×D1112yes—
387C22×D4C22×D1112yes—
388C23×C4—111no—
389C23×C4—111no—
390C23×C4—111no—
391C23×C4—111no—
392C23×C4—114no—
393C23×C4C22×D1111yescharacteristic
394C23×C4C22×D1111yescharacteristic
395C23×C4C22×D1111yescharacteristic
396#126—2216no—
397#125—2216no—
398#124—444no—
399#123—2216no—
400#123—2216no—
401C22⋊Q8—2216no—
402C22⋊Q8—228no—
403#121—28no—
404#121—28no—
405#121—28no—
406C4×D4—2216no—
407C4×D4—444no—
408C2×C4⋊C4—118no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—114no—
411C2×C4⋊C4—114no—
412C2×C4⋊C4—114no—
413C2×C4⋊C4—114no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—114no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—112no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—112no—
420C2×C4⋊C4—224no—
421C2×C4⋊C4C22×D1112yes—
422C2×C4⋊C4C22×D1112yes—
423C2×C4⋊C4C22×D1112yes—
424C2×C22⋊C4—114no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—114no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—114no—
431C2×C22⋊C4—114no—
432C2×C22⋊C4C22×D1114yes—
433C2×C22⋊C4C22×D1114yes—
434C2×C22⋊C4C22×D1114yes—
435C2×C42—114no—
436C2×C42—112no—
437C2×C42—112no—
438C2×C42—112no—
439C2×C42—112no—
440C2×C42—112no—
441C2×C42—112no—
442C2×C42—224no—
443C2×C42—442no—
444C2×C42—442no—
445#95—114no—
446#95—114no—
447#95—114no—
448#95—114no—
449#95—114no—
450#95—114no—
451#95—114no—
452#95C22×D1114yes—
453C2×C11—24no—
454C2×C11—84no—
455C2×C11C2×#53211yescharacteristic
456C2×C11#345911yescharacteristic
457C2×C11#346111yescharacteristic
458C2×C11#349111yescharacteristic
459C2×C11#349211yescharacteristic
460C2×C11#349611yescharacteristic
461C2×C11#349711yescharacteristic
462C24C23×D1114yes—
463C24C23×D1111yescharacteristic
464C2×Q8—224no—
465C2×Q8—442no—
466C2×Q8—442no—
467C2×D4—28no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—24no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4—42no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484C22×C4—41no—
485C22×C4—114no—
486C22×C4—111no—
487C22×C4—111no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—114no—
491C22×C4—112no—
492C22×C4—114no—
493C22×C4—114no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—228no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—441no—
502C22×C4—441no—
503C22×C4—441no—
504C22×C4—441no—
505C22×C4—444no—
506C22×C4—444no—
507C22×C4D4×D1114yes—
508C22×C4#434114yes—
509C22×C4#434114yes—
510C22×C4C23×D1114yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1112yes—
513C22×C4C23×D1112yes—
514C4⋊C4—24no—
515C4⋊C4—24no—
516C4⋊C4—24no—
517C4⋊C4—1116no—
518C4⋊C4—228no—
519C4⋊C4—228no—
520C4⋊C4—228no—
521C4⋊C4—228no—
522C4⋊C4—224no—
523C4⋊C4—228no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—442no—
527C4⋊C4—442no—
528C22⋊C4—28no—
529C22⋊C4—28no—
530C22⋊C4—28no—
531C22⋊C4—228no—
532C22⋊C4—228no—
533C22⋊C4—228no—
534C22⋊C4—228no—
535C22⋊C4—228no—
536C22⋊C4—228no—
537C22⋊C4—444no—
538C22⋊C4—444no—
539C42—224no—
540C42—224no—
541C42—228no—
542C42—224no—
543C42—224no—
544C42—442no—
545C42—442no—
546C11#3500411yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23C2×D4×D1112yes—
559C23C2×#434112yes—
560C23C2×#434112yes—
561C23C24×D1111yescharacteristic
562Q8—884no—
563D4—48no—
564D4—416no—
565D4—84no—
566D4—84no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—44no—
577C2×C4—44no—
578C2×C4—44no—
579C2×C4—114no—
580C2×C4—114no—
581C2×C4—112no—
582C2×C4—112no—
583C2×C4—228no—
584C2×C4—228no—
585C2×C4—222no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—221no—
591C2×C4—222no—
592C2×C4—221no—
593C2×C4—224no—
594C2×C4—224no—
595C2×C4—222no—
596C2×C4—222no—
597C2×C4—224no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—444no—
603C2×C4—444no—
604C2×C4—888no—
605C2×C4C2×D4×D1114yes—
606C2×C4C2×#434114yes—
607C2×C4C2×#434114yes—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—44no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22#1062324714yes—
622C22C22×D4×D1111yescharacteristic
623C22C22×#434111yescharacteristic
624C22C22×#434111yescharacteristic
625C22D11×H(5,𝔽2)11yescharacteristic
626C22#1062345511yescharacteristic
627C22#1062345511yescharacteristic
628C22D11×2−1+411yescharacteristic
629C4—24no—
630C4—24no—
631C4—24no—
632C4—44no—
633C4—224no—
634C4—224no—
635C4—222no—
636C4—222no—
637C4—444no—
638C4—444no—
639C4—442no—
640C2—24no—
641C2—84no—
642C2C2×#1062324711yescharacteristic
643C2#1308202211yescharacteristic
644C2#1308204411yescharacteristic
645C2#1308231311yescharacteristic
646C2#1308232311yescharacteristic
647C2#1308237711yescharacteristic
648C2#1308238511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
Fitting, prime radicalC11×#2656C2
hypercenter#2656D11
hypocenterC11#35004
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2656

Complements

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

NH ≅ G/Ntype
1. C2×#10623133C2semidirect
2. #13076942C2semidirect
3. #13076915C2semidirect
4. #13074730C2semidirect
5. #13074360C2semidirect
6. #13073701C2semidirect
7. #13073677C2semidirect
8. #13073284C2semidirect
9. #13072578C2semidirect
10. #13071321C2semidirect
11. #121×Dic11C2semidirect
12. C2×#10622262C2semidirect
111. C2×Dic11⋊C4D4semidirect
546. C11#35004semidirect

Maximal subgroups

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

subgroupindex
C2×#106231332
#130769422
#130769152
#130747302
#130743602
#130737012
#130736772
#130732842
#130725782
#130713212
#121×Dic112
C2×#106222622
C11×#26562
#3500411