Finite Group Databasebeta

← #14926520

Subgroups — #14926520

Order 2816.

2214 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076929C214yesmaximal, complemented
2#13074571C214yesmaximal, complemented
3#13073174C214yesmaximal, complemented
4#13072997C214yesmaximal, complemented
5#13072876C214yesmaximal, complemented
6#13072861C214yesmaximal, complemented
7#13071228C211yesmaximal, characteristic, complemented
8#13071228C211yesmaximal, characteristic, complemented
9#13071194C211yesmaximal, characteristic
10C2×#10622833C211yesmaximal, characteristic
11C2×#10622563C211yesmaximal, characteristic, complemented
12C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
13C11×#2308C211yesmaximal, characteristic
14C23×D4×C11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C4⋊Dic11C2212yescomplemented
23C22×C4×Dic11C2212yescomplemented
24C2×#66932C2214yescomplemented
25C11×#386C2214yes—
26C11×#386C2214yes—
27C11×#381C2212yes—
28C11×#379C2212yes—
29#10622860C2212yes—
30#10622833C2212yes—
31#10622833C2214yes—
32#10622833C2214yes—
33#10622833C2212yes—
34#10622833C2212yes—
35#10622833C2212yes—
36#10622824C2212yes—
37#10622823C2214yescomplemented
38#10622823C2214yescomplemented
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yescomplemented
41C2×C11⋊#95C2212yescomplemented
42#10622566C2214yescomplemented
43#10622565C2214yescomplemented
44#10622565C2214yescomplemented
45#10622564C2214yescomplemented
46#10622563C2214yes—
47#10622563C2212yescomplemented
48#10622563C2212yescomplemented
49#10622561C2214yescomplemented
50#10622559C2214yes—
51#10622559C2214yescomplemented
52#10622558C2214yescomplemented
53#10622557C2214yescomplemented
54#10622555C2214yes—
55#10622555C2212yescomplemented
56#10622555C2212yescomplemented
57C22⋊C4×Dic11C2214yes—
58C22⋊C4×Dic11C2214yescomplemented
59C11⋊#401C2214yescomplemented
60#10622273C2214yescomplemented
61#10622272C2214yescomplemented
62#10622271C2214yescomplemented
63#10622268C2214yescomplemented
64#10622266C2214yescomplemented
65#10622265C2214yescomplemented
66#10622264C2214yescomplemented
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C22×D4×C11—24no—
70C22×D4×C11—24no—
71C22×D4×C11—24no—
72C22×D4×C11C2312yes—
73C22×D4×C11C2312yes—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2312yes—
76C23×C4×C11C2312yes—
77C23×Dic11—24no—
78C23×Dic11—44no—
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2312yes—
81C23×Dic11C2312yes—
82C23×Dic11C2312yes—
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2312yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C2×C11×C22⋊C4—24no—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4C2312yes—
90C2×C11×C22⋊C4C2312yes—
91C2×C11×C22⋊C4C2312yes—
92C2×C11×C22⋊C4C2312yes—
93C2×C11×C22⋊C4C2314yes—
94C2×C11×C22⋊C4C2314yes—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11—24no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—44no—
99C2×C22⋊Dic11C2314yes—
100C2×C22⋊Dic11C2312yes—
101C2×C22⋊Dic11C2312yes—
102C2×C22⋊Dic11C2312yes—
103C2×C22⋊Dic11C2312yes—
104C2×C22⋊Dic11C2312yes—
105C2×C22⋊Dic11C2312yes—
106C2×C22⋊Dic11C2314yes—
107C2×C22⋊Dic11C2314yes—
108C2×C22⋊Dic11C2314yes—
109C2×C4⋊Dic11—44no—
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2314yes—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2314yes—
115C2×Dic11⋊C4C2314yes—
116C2×C4×Dic11—44no—
117C2×C4×Dic11C2314yes—
118C2×C4×Dic11C2314yes—
119#66932—48no—
120C11×#95C2314yes—
121C11×#95C2314yes—
122C11⋊#95C2314yes—
123C11⋊#95C2314yes—
124C11⋊#95C2314yes—
125C11⋊#95C2314yes—
126C11⋊#95C2314yes—
127C11⋊#95C2314yes—
128C11⋊#95C2314yes—
129C11⋊#95C2314yes—
130C11⋊#95C2314yes—
131C11⋊#95C2314yes—
132C11⋊#95C2314yes—
133C11⋊#95C2314yes—
134#34995—111nomaximal, Sylow
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—22no—
138C24×C11—42no—
139C24×C11—42no—
140C24×C11—42no—
141C24×C11—42no—
142C24×C11#4114yes—
143C24×C11#4114yes—
144C24×C11#4114yes—
145C24×C11C2412yes—
146C24×C11C2411yescharacteristic
147C24×C11C2411yescharacteristic
148C24×C11C2411yescharacteristic
149C2×D4×C11—24no—
150C2×D4×C11—24no—
151C2×D4×C11—24no—
152C2×D4×C11—24no—
153C2×D4×C11—24no—
154C2×D4×C11—24no—
155C2×D4×C11—416no—
156C22×C4×C11—24no—
157C22×C4×C11—24no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11—42no—
165C22×C4×C11C2412yes—
166C22×C4×C11C2414yes—
167C22×C4×C11C2414yes—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—22no—
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11—22no—
175C22×Dic11—24no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—24no—
179C22×Dic11—42no—
180C22×Dic11—42no—
181C22×Dic11—42no—
182C22×Dic11—42no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C22×Dic11—42no—
186C22×Dic11—42no—
187C22×Dic11—42no—
188C22×Dic11—416no—
189C22×Dic11C2412yes—
190C22×Dic11C2412yes—
191C22×Dic11C2414yes—
192C22×Dic11C2414yes—
193C22×Dic11C2412yes—
194C22×Dic11C2412yes—
195C11×C22⋊C4—24no—
196C11×C22⋊C4—24no—
197C11×C22⋊C4—24no—
198C11×C22⋊C4—24no—
199C11×C22⋊C4—44no—
200C11×C22⋊C4—44no—
201C22⋊Dic11—28no—
202C22⋊Dic11—24no—
203C22⋊Dic11—24no—
204C22⋊Dic11—24no—
205C22⋊Dic11—24no—
206C22⋊Dic11—24no—
207C22⋊Dic11—24no—
208C22⋊Dic11—44no—
209C22⋊Dic11—44no—
210C22⋊Dic11—44no—
211C4⋊Dic11—28no—
212C4⋊Dic11—44no—
213Dic11⋊C4—44no—
214Dic11⋊C4—44no—
215Dic11⋊C4—44no—
216Dic11⋊C4—44no—
217C4×Dic11—28no—
218C4×Dic11—44no—
219#2852—114no—
220#2643—114no—
221#2510—114no—
222#2493—114no—
223#2481—114no—
224#2480—114no—
225#2315—111no—
226#2315—111no—
227#2308—111no—
228#2308D1111yescharacteristic
229C2×#386—111no—
230C2×#385—111no—
231C2×C4×C22⋊C4—111no—
232C23×C11—22no—
233C23×C11—22no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—44no—
244C23×C11—44no—
245C23×C11—48no—
246C23×C11—48no—
247C23×C11—48no—
248C23×C11—44no—
249C23×C11—82no—
250C23×C11—82no—
251C23×C11—84no—
252C23×C11#126116yescomplemented
253C23×C11C2×#4112yes—
254C23×C11C2×#4112yes—
255C23×C11C2×#4112yes—
256C23×C11C2×#4112yes—
257C23×C11C2×#4112yes—
258C23×C11C2×#4112yes—
259C23×C11C2×#4112yes—
260C23×C11C2×#4112yes—
261C23×C11C2×#4112yes—
262C23×C11C2511yescharacteristic
263D4×C11—48no—
264D4×C11—48no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
269C2×C4×C11—22no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—48no—
275C2×C4×C11—48no—
276C2×C4×C11—44no—
277C2×Dic11—28no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—24no—
291C2×Dic11—24no—
292C2×Dic11—24no—
293C2×Dic11—48no—
294C2×Dic11—48no—
295C2×Dic11—48no—
296C2×Dic11—44no—
297C2×Dic11—82no—
298C2×Dic11—82no—
299C2×Dic11—84no—
300C2×Dic11H(5,𝔽2)14yes—
301C23×D4C2×D1111yescharacteristic
302C24×C4—111no—
303C2×#126—114no—
304C22×C4⋊C4—112no—
305C22×C22⋊C4—111no—
306C22×C22⋊C4—111no—
307C22×C22⋊C4—111no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4C2×D1111yescharacteristic
310C22×C22⋊C4C2×D1111yescharacteristic
311C22×C42—112no—
312#401—114no—
313#400—114no—
314#400—114no—
315#400—114no—
316#397—114no—
317#397—114no—
318#397—114no—
319#396—114no—
320#388—114no—
321#388—114no—
322#388—114no—
323#387—114no—
324#387—114no—
325#387—114no—
326#386—114no—
327#386—112no—
328#386—112no—
329#386—112no—
330#386—112no—
331#386—114no—
332#386C2×D1114yes—
333#386C2×D1114yes—
334#385—114no—
335#385—114no—
336#385—114no—
337#385—114no—
338#385—112no—
339#385—112no—
340#385—114no—
341#383—114no—
342#381—112no—
343#381C2×D1112yes—
344#380—114no—
345#380—112no—
346#380—112no—
347#379—112no—
348#379C2×D1112yes—
349C4×C22⋊C4—114no—
350C4×C22⋊C4—114no—
351C2×#95—112no—
352C2×#95—112no—
353C2×#95—112no—
354C22×C11—24no—
355C22×C11—24no—
356C22×C11—24no—
357C22×C11—22no—
358C22×C11—22no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—24no—
364C22×C11—24no—
365C22×C11—24no—
366C22×C11—416no—
367C22×C11—42no—
368C22×C11—44no—
369C22×C11—42no—
370C22×C11—42no—
371C22×C11—44no—
372C22×C11—88no—
373C22×C11C2×#12614yes—
374C22×C11C2×#12614yes—
375C22×C11C2×#12614yes—
376C22×C11C22×#4111yescharacteristic
377C22×C11C22×#4111yescharacteristic
378C22×C11C22×#4111yescharacteristic
379C22×C11C2×H(5,𝔽2)12yes—
380C22×C11#58512yes—
381C4×C11—42no—
382C4×C11—44no—
383C4×C11—44no—
384Dic11—24no—
385Dic11—44no—
386Dic11—42no—
387Dic11—42no—
388Dic11—42no—
389Dic11—44no—
390C25C22×D1111yescharacteristic
391C25C22×D1111yescharacteristic
392C22×D4—24no—
393C22×D4—24no—
394C22×D4—24no—
395C22×D4C22×D1112yes—
396C22×D4C22×D1112yes—
397C23×C4—111no—
398C23×C4—112no—
399C23×C4—112no—
400C23×C4—112no—
401C23×C4—111no—
402C23×C4—111no—
403C23×C4—112no—
404C23×C4—111no—
405C23×C4—224no—
406C23×C4—444no—
407C23×C4C22×D1111yescharacteristic
408C23×C4C22×D1112yes—
409C23×C4C22×D1112yes—
410#126—448no—
411C2×C4⋊C4—114no—
412C2×C4⋊C4—114no—
413C2×C4⋊C4—114no—
414C2×C4⋊C4—114no—
415C2×C4⋊C4—114no—
416C2×C4⋊C4—114no—
417C2×C4⋊C4—444no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4—114no—
421C2×C22⋊C4—112no—
422C2×C22⋊C4—112no—
423C2×C22⋊C4—112no—
424C2×C22⋊C4—112no—
425C2×C22⋊C4—112no—
426C2×C22⋊C4—112no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—114no—
430C2×C22⋊C4—224no—
431C2×C22⋊C4—224no—
432C2×C22⋊C4—224no—
433C2×C22⋊C4—444no—
434C2×C22⋊C4C22×D1112yes—
435C2×C22⋊C4C22×D1112yes—
436C2×C22⋊C4C22×D1112yes—
437C2×C22⋊C4C22×D1112yes—
438C2×C22⋊C4C22×D1114yes—
439C2×C22⋊C4C22×D1114yes—
440C2×C42—114no—
441C2×C42—114no—
442C2×C42—444no—
443#95—114no—
444#95—114no—
445#95—114no—
446#95—114no—
447#95—114no—
448#95—114no—
449#95—114no—
450#95—114no—
451#95—114no—
452#95—114no—
453#95—114no—
454#95—114no—
455#95C22×D1114yes—
456#95C22×D1114yes—
457C2×C11—24no—
458C2×C11—24no—
459C2×C11—24no—
460C2×C11—82no—
461C2×C11C22×#12611yescharacteristic
462C2×C11#345912yes—
463C2×C11#349011yescharacteristic
464C2×C11#349111yescharacteristic
465C2×C11#350512yes—
466C24—22no—
467C24—22no—
468C24—22no—
469C24—42no—
470C24—42no—
471C24—42no—
472C24—42no—
473C24#433914yes—
474C24#434114yes—
475C24#434114yes—
476C24C23×D1112yes—
477C24C23×D1111yescharacteristic
478C24C23×D1111yescharacteristic
479C24C23×D1111yescharacteristic
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—416no—
487C22×C4—22no—
488C22×C4—24no—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—112no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—114no—
500C22×C4—114no—
501C22×C4—112no—
502C22×C4—224no—
503C22×C4—224no—
504C22×C4—224no—
505C22×C4—222no—
506C22×C4—224no—
507C22×C4—224no—
508C22×C4—222no—
509C22×C4—224no—
510C22×C4—222no—
511C22×C4—222no—
512C22×C4—224no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4—442no—
522C22×C4—4416no—
523C22×C4C23×D1112yes—
524C22×C4C23×D1114yes—
525C22×C4C23×D1114yes—
526C4⋊C4—228no—
527C4⋊C4—444no—
528C4⋊C4—444no—
529C4⋊C4—444no—
530C4⋊C4—444no—
531C4⋊C4—444no—
532C22⋊C4—24no—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—44no—
537C22⋊C4—44no—
538C22⋊C4—228no—
539C22⋊C4—224no—
540C22⋊C4—224no—
541C22⋊C4—224no—
542C22⋊C4—224no—
543C22⋊C4—224no—
544C22⋊C4—224no—
545C22⋊C4—444no—
546C22⋊C4—444no—
547C22⋊C4—444no—
548C42—228no—
549C42—444no—
550C11#3499511yescharacteristic, complemented, Sylow
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—22no—
558C23—22no—
559C23—22no—
560C23—24no—
561C23—24no—
562C23—44no—
563C23—44no—
564C23—48no—
565C23—48no—
566C23—48no—
567C23—44no—
568C23—84no—
569C23—82no—
570C23—82no—
571C23#66932116yescomplemented
572C23C2×#433912yes—
573C23C2×#433912yes—
574C23C2×#433912yes—
575C23C2×#434112yes—
576C23C2×#434112yes—
577C23C2×#434112yes—
578C23C2×#434112yes—
579C23C2×#434112yes—
580C23C2×#434112yes—
581C23C24×D1111yescharacteristic
582D4—48no—
583D4—48no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—48no—
594C2×C4—48no—
595C2×C4—44no—
596C2×C4—114no—
597C2×C4—228no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—222no—
608C2×C4—224no—
609C2×C4—222no—
610C2×C4—224no—
611C2×C4—224no—
612C2×C4—224no—
613C2×C4—448no—
614C2×C4—448no—
615C2×C4—444no—
616C2×C4—448no—
617C2×C4—884no—
618C2×C4—882no—
619C2×C4—882no—
620C22—24no—
621C22—24no—
622C22—24no—
623C22—24no—
624C22—24no—
625C22—24no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—416no—
633C22—42no—
634C22—44no—
635C22—44no—
636C22—42no—
637C22—42no—
638C22—88no—
639C22C2×#6693214yes—
640C22C2×#6693214yes—
641C22C2×#6693214yes—
642C22C22×#433911yescharacteristic
643C22C22×#434111yescharacteristic
644C22C22×#434111yescharacteristic
645C22D11×H(5,𝔽2)12yes—
646C22#1062345512yes—
647C4—42no—
648C4—44no—
649C4—44no—
650C4—224no—
651C4—444no—
652C4—444no—
653C4—442no—
654C4—442no—
655C4—442no—
656C2—24no—
657C2—24no—
658C2—24no—
659C2—82no—
660C2C22×#6693211yescharacteristic
661C2#1308202212yes—
662C2#1308230111yescharacteristic
663C2#1308230911yescharacteristic
664C2#1308245312yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2308C2
prime radicalC23×D4×C11C22
hypercenter#2308D11
hypocenterC11#34995
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2308

Complements

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

NH ≅ G/Ntype
1. #13076929C2semidirect
2. #13074571C2semidirect
3. #13073174C2semidirect
4. #13072997C2semidirect
5. #13072876C2semidirect
6. #13072861C2semidirect
7. #13071228C2semidirect
8. #13071228C2semidirect
11. C2×#10622563C2semidirect
12. C2×C22⋊C4×Dic11C2semidirect
22. C22×C4⋊Dic11C22semidirect
23. C22×C4×Dic11C22semidirect
24. C2×#66932C22semidirect
37. #10622823C22semidirect
38. #10622823C22semidirect
40. C2×C11⋊#95C22semidirect
41. C2×C11⋊#95C22semidirect
42. #10622566C22semidirect
43. #10622565C22semidirect
44. #10622565C22semidirect
45. #10622564C22semidirect
47. #10622563C22semidirect
48. #10622563C22semidirect
49. #10622561C22semidirect
51. #10622559C22semidirect
52. #10622558C22semidirect
53. #10622557C22semidirect
55. #10622555C22semidirect
56. #10622555C22semidirect
58. C22⋊C4×Dic11C22semidirect
59. C11⋊#401C22semidirect
60. #10622273C22semidirect
61. #10622272C22semidirect
62. #10622271C22semidirect
63. #10622268C22semidirect
64. #10622266C22semidirect
65. #10622265C22semidirect
66. #10622264C22semidirect
252. C23×C11#126semidirect
550. C11#34995semidirect
571. C23#66932semidirect

Maximal subgroups

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

subgroupindex
#130769292
#130745712
#130731742
#130729972
#130728762
#130728612
#130712282
#130711942
C2×#106228332
C2×#106225632
C2×C22⋊C4×Dic112
C11×#23082
#3499511