Finite Group Databasebeta

← #14682536

Subgroups — #14682536

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622542C211yesmaximal, characteristic
2#13066886C212yesmaximal
3#13066875C212yesmaximal
4#13066872C212yesmaximal
5#13066850C212yesmaximal
6#13066850C212yesmaximal
7#13066848C212yesmaximal
8#13066846C211yesmaximal, characteristic
9C11×C4⋊#95C211yesmaximal, characteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C4⋊Dic11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4×Dic11C2212yes—
18C2×C11×#95C2212yes—
19C2×C11×#95C2212yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622542C418yescomplemented
32C23×C4×C11C2312yes—
33C23×C4×C11C2312yes—
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C22×Dic22—22no—
42C22×Dic22—22no—
43C22×Dic22—41no—
44C22×Dic22—41no—
45C22×Dic22—41no—
46C22×Dic22—41no—
47C22×Dic22C2×C414yes—
48C2×C11×C4⋊C4—22no—
49C2×C11×C4⋊C4—41no—
50C2×C11×C4⋊C4—41no—
51C2×C11×C4⋊C4—41no—
52C2×C11×C4⋊C4—41no—
53C2×C11×C4⋊C4Q814yescomplemented
54C2×C42×C11—41no—
55C2×C42×C11—41no—
56C2×C42×C11C2×C414yes—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—41no—
59C2×C4⋊Dic11—41no—
60C2×C4⋊Dic11—41no—
61C2×C4⋊Dic11—41no—
62C2×C4⋊Dic11—41no—
63C2×C4⋊Dic11—41no—
64C2×C4⋊Dic11C2×C414yes—
65C2×C4⋊Dic11Q814yescomplemented
66C2×C4×Dic11—42no—
67C2×C4×Dic11—42no—
68C2×C4×Dic11—42no—
69C11×#95—24no—
70C11×#95—24no—
71C11⋊#95—24no—
72C11⋊#95—24no—
73C11⋊#95—42no—
74C11⋊#95—42no—
75C11⋊#95—42no—
76C11⋊#95—42no—
77C11⋊#95—42no—
78C11⋊#95—42no—
79C11⋊#95—42no—
80C11⋊#95C2×C418yes—
81C11⋊#95C2×C418yes—
82#14471—111nomaximal, Sylow
83C24×C11C2411yescharacteristic
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
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—22no—
108C22×C4×C11—22no—
109C22×C4×C11C22×C412yes—
110C22×C4×C11C22×C412yes—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×Q814yes—
113C22×C4×C11C2×Q812yes—
114C22×C4×C11C2×Q812yes—
115C22×C4×C11#4112yes—
116C22×C4×C11#4112yes—
117C22×C4×C11#4112yes—
118C22×C4×C11#4112yes—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
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×Dic11C22×C414yes—
145C22×Dic11C22×C414yes—
146C22×Dic11C2×Q814yes—
147C2×Dic22—28no—
148C2×Dic22—44no—
149C2×Dic22—44no—
150C2×Dic22—44no—
151C2×Dic22—44no—
152C2×Dic22—44no—
153C2×Dic22—44no—
154C11×C4⋊C4—44no—
155C11×C4⋊C4—44no—
156C42×C11—44no—
157C4⋊Dic11—44no—
158C4⋊Dic11—44no—
159C4⋊Dic11—44no—
160C4×Dic11—48no—
161C2×#391—111no—
162#1446—112no—
163#1442—112no—
164#1442—112no—
165#1436—112no—
166#1436—112no—
167#1436—112no—
168C4⋊#95—111no—
169C4⋊#95D1111yescharacteristic
170C23×C11C23×C411yescharacteristic
171C23×C11C22×Q811yescharacteristic
172C23×C11C22×Q811yescharacteristic
173C23×C11C2×#4111yescharacteristic
174C23×C11C2×#4111yescharacteristic
175C23×C11C2×#4111yescharacteristic
176C23×C11C2×#4111yescharacteristic
177C23×C11H(5,𝔽2)11yescharacteristic
178C23×C11H(5,𝔽2)11yescharacteristic
179C23×C11H(5,𝔽2)11yescharacteristic
180C23×C11H(5,𝔽2)11yescharacteristic
181C23×C11H(5,𝔽2)11yescharacteristic
182C23×C11H(5,𝔽2)11yescharacteristic
183C23×C112−1+411yescharacteristic
184C23×C112−1+411yescharacteristic
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11—42no—
217C2×C4×C11#11714yes—
218C2×C4×C11C4×Q814yes—
219C2×C4×C11C4×Q814yes—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—42no—
234C2×Dic11—42no—
235C2×Dic11—42no—
236C2×Dic11—42no—
237C2×Dic11—42no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248Dic22—416no—
249C23×Q8—111no—
250C22×C4⋊C4—111no—
251C22×C4⋊C4—111no—
252C22×C4⋊C4—111no—
253C22×C4⋊C4C2×D1111yescharacteristic
254C22×C4⋊C4C2×D1111yescharacteristic
255C22×C42—112no—
256C22×C42C2×D1111yescharacteristic
257#391—118no—
258C2×#95—112no—
259C2×#95—112no—
260C2×#95—112no—
261C2×#95—112no—
262C2×#95—112no—
263C2×#95—112no—
264C2×#95—112no—
265C2×#95—112no—
266C2×#95—112no—
267C2×#95—112no—
268C2×#95—112no—
269C2×#95C2×D1112yes—
270C2×#95C2×D1112yes—
271C22×C11C2×#11711yescharacteristic
272C22×C11C2×C4×Q811yescharacteristic
273C22×C11C2×C4×Q811yescharacteristic
274C22×C11#51811yescharacteristic
275C22×C11#51811yescharacteristic
276C22×C11#52011yescharacteristic
277C22×C11#52011yescharacteristic
278C22×C11#53811yescharacteristic
279C22×C11#53811yescharacteristic
280C22×C11#53811yescharacteristic
281C22×C11#53811yescharacteristic
282C22×C11#53811yescharacteristic
283C22×C11#53811yescharacteristic
284C22×C11#53911yescharacteristic
285C22×C11#53911yescharacteristic
286C22×C11#54311yescharacteristic
287C22×C11#54311yescharacteristic
288C22×C11#54411yescharacteristic
289C22×C11#54411yescharacteristic
290C22×C11#55411yescharacteristic
291C22×C11#55411yescharacteristic
292C22×C11#55411yescharacteristic
293C22×C11#55411yescharacteristic
294C22×C11#55511yescharacteristic
295C22×C11#55611yescharacteristic
296C22×C11#55611yescharacteristic
297C22×C11#55711yescharacteristic
298C22×C11#55711yescharacteristic
299C22×C11Q8211yescharacteristic
300C22×C11#55911yescharacteristic
301C22×C11#55911yescharacteristic
302C22×C11H(3,𝔽4)11yescharacteristic
303C22×C11#56211yescharacteristic
304C22×C11#56211yescharacteristic
305C22×C11#56311yescharacteristic
306C4×C11—24no—
307C4×C11—24no—
308C4×C11—24no—
309C4×C11—44no—
310C4×C11—82no—
311Dic11—44no—
312Dic11—44no—
313Dic11—44no—
314Dic11—82no—
315C22×Q8—114no—
316C22×Q8—222no—
317C22×Q8—222no—
318C22×Q8—441no—
319C22×Q8—441no—
320C22×Q8—441no—
321C22×Q8—441no—
322C23×C4—112no—
323C23×C4—112no—
324C23×C4—112no—
325C23×C4—112no—
326C23×C4C22×D1112yes—
327C23×C4C22×D1112yes—
328C23×C4C22×D1111yescharacteristic
329C23×C4C22×D1111yescharacteristic
330C23×C4C22×D1111yescharacteristic
331C2×C4⋊C4—22no—
332C2×C4⋊C4—41no—
333C2×C4⋊C4—41no—
334C2×C4⋊C4—41no—
335C2×C4⋊C4—41no—
336C2×C4⋊C4—114no—
337C2×C4⋊C4—114no—
338C2×C4⋊C4—222no—
339C2×C4⋊C4—441no—
340C2×C4⋊C4—441no—
341C2×C4⋊C4—441no—
342C2×C4⋊C4—441no—
343C2×C4⋊C4—441no—
344C2×C4⋊C4—441no—
345C2×C4⋊C4Dic2214yescomplemented
346C2×C42—41no—
347C2×C42—41no—
348C2×C42—442no—
349C2×C42—442no—
350C2×C42—442no—
351C2×C42C4×D1114yes—
352#95—24no—
353#95—24no—
354#95—118no—
355#95—118no—
356#95—224no—
357#95—224no—
358#95—442no—
359#95—442no—
360#95—442no—
361#95—442no—
362#95—442no—
363#95—442no—
364#95—442no—
365C2×C11#231211yescharacteristic
366C2×C11#232911yescharacteristic
367C2×C11#232911yescharacteristic
368C2×C11#235511yescharacteristic
369C2×C11#235511yescharacteristic
370C2×C11#236911yescharacteristic
371C2×C11#237911yescharacteristic
372C2×C11#280411yescharacteristic
373C2×C11#280411yescharacteristic
374C2×C11#280511yescharacteristic
375C2×C11#280511yescharacteristic
376C2×C11#280611yescharacteristic
377C2×C11#280611yescharacteristic
378C2×C11#280811yescharacteristic
379C2×C11#280811yescharacteristic
380C24C23×D1111yescharacteristic
381C2×Q8—228no—
382C2×Q8—444no—
383C2×Q8—444no—
384C2×Q8—444no—
385C2×Q8—444no—
386C2×Q8—444no—
387C2×Q8—444no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—114no—
414C22×C4—114no—
415C22×C4—114no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—222no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—222no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4C2×Dic2214yes—
442C22×C4C2×Dic2212yes—
443C22×C4C2×C4×D1112yes—
444C22×C4C2×C4×D1112yes—
445C22×C4C2×C4×D1112yes—
446C22×C4#433912yes—
447C22×C4#434112yes—
448C22×C4#434112yes—
449C22×C4Q8×D1112yes—
450C22×C4#434312yes—
451C4⋊C4—44no—
452C4⋊C4—44no—
453C4⋊C4—444no—
454C4⋊C4—444no—
455C4⋊C4—444no—
456C42—44no—
457C42—448no—
458C11#1447111yescharacteristic, complemented, Sylow
459C23C22×Dic2211yescharacteristic
460C23C22×C4×D1111yescharacteristic
461C23C2×#433911yescharacteristic
462C23C2×#434111yescharacteristic
463C23C2×#434111yescharacteristic
464C23#6703711yescharacteristic
465C23#6703711yescharacteristic
466C23#6703711yescharacteristic
467C23C2×Q8×D1111yescharacteristic
468C23C2×#434311yescharacteristic
469C23#6704011yescharacteristic
470C23#6704211yescharacteristic
471C23#6704211yescharacteristic
472C23#6704211yescharacteristic
473C23#6704311yescharacteristic
474Q8—4416no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—442no—
523C2×C4—442no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—442no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4C4×Dic2214yes—
536C2×C4#6694014yes—
537C2×C4#6694514yes—
538C22C2×C4×Dic2211yescharacteristic
539C22#1062301411yescharacteristic
540C22#1062301711yescharacteristic
541C22#1062302511yescharacteristic
542C22C2×#6694011yescharacteristic
543C22#1062303111yescharacteristic
544C22C2×#6694511yescharacteristic
545C22#1062303511yescharacteristic
546C22#1062304611yescharacteristic
547C22#1062305211yescharacteristic
548C22#1062305411yescharacteristic
549C22#1062307311yescharacteristic
550C22#1062307411yescharacteristic
551C22#1062307411yescharacteristic
552C22#1062309411yescharacteristic
553C22Q8×Dic2211yescharacteristic
554C22#1062310111yescharacteristic
555C22#1062311011yescharacteristic
556C22#1062311611yescharacteristic
557C22#1062313311yescharacteristic
558C22#1062314811yescharacteristic
559C22#1062314811yescharacteristic
560C22#1062314811yescharacteristic
561C22#1062315411yescharacteristic
562C22#1062316511yescharacteristic
563C22#1062317511yescharacteristic
564C22#1062317511yescharacteristic
565C22#1062321411yescharacteristic
566C22#1062321511yescharacteristic
567C22#1062323011yescharacteristic
568C22#1062323111yescharacteristic
569C22#1062324411yescharacteristic
570C22#1062325211yescharacteristic
571C22#1062326111yescharacteristic
572C22#1062326311yescharacteristic
573C4—24no—
574C4—24no—
575C4—24no—
576C4—44no—
577C4—82no—
578C4—444no—
579C4—444no—
580C4—444no—
581C4—882no—
582C2#1307121311yescharacteristic
583C2#1307134611yescharacteristic
584C2#1307134911yescharacteristic
585C2#1307157111yescharacteristic
586C2#1307157511yescharacteristic
587C2#1307170511yescharacteristic
588C2#1307178711yescharacteristic
589C2#1307656011yescharacteristic
590C2#1307656211yescharacteristic
591C2#1307656611yescharacteristic
592C2#1307656911yescharacteristic
593C2#1307657811yescharacteristic
594C2#1307658011yescharacteristic
595C2#1307659311yescharacteristic
596C2#1307659611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4⋊#95D11
hypocenterC11#14471
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
31. #10622542C4semidirect
53. C2×C11×C4⋊C4Q8semidirect
65. C2×C4⋊Dic11Q8semidirect
345. C2×C4⋊C4Dic22semidirect
458. C11#14471semidirect

Maximal subgroups

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

subgroupindex
C2×#106225422
#130668862
#130668752
#130668722
#130668502
#130668482
#130668462
C11×C4⋊#952
#1447111