Finite Group Databasebeta

← #14682170

Subgroups — #14682170

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622552C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3C2×#10622281C212yesmaximal, complemented
4#13066868C212yesmaximal, complemented
5#13066862C212yesmaximal, complemented
6#13066860C212yesmaximal, complemented
7#13066846C211yesmaximal, characteristic, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9C11×#1434C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C42×C11C2211yescharacteristic
13C22×(C2×D11)⋊C4C2212yes—
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×C4⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31#10622552C418yescomplemented
32#10622281—28no—
33#10622278—28no—
34C24×D11C2312yes—
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C22×D44—42no—
44C22×D44—42no—
45C22×D44C2×C414yes—
46C22×D44D414yes—
47C22×D44Q814yes—
48C22×C4×D11—24no—
49C22×C4×D11—24no—
50C22×C4×D11—24no—
51C22×C4×D11—42no—
52C22×C4×D11—42no—
53C22×C4×D11—42no—
54C22×C4×D11—42no—
55C2×C42×C11—42no—
56C2×C42×C11C2×C414yescomplemented
57C2×(C2×D11)⋊C4—24no—
58C2×(C2×D11)⋊C4—24no—
59C2×(C2×D11)⋊C4—24no—
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—42no—
65C2×(C2×D11)⋊C4—42no—
66C2×(C2×D11)⋊C4—42no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4C2×C418yescomplemented
71C2×(C2×D11)⋊C4C2×C418yescomplemented
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11—42no—
75C2×C4⋊Dic11—42no—
76C2×C4⋊Dic11C2×C414yescomplemented
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—42no—
79C2×Dic11⋊C4—42no—
80C11×#95—24no—
81C11×#95—22no—
82C11×#95—42no—
83C11×#95D414yescomplemented
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95—41no—
89C11⋊#95—41no—
90#14438—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
92C23×D11—22no—
93C23×D11—22no—
94C23×D11—22no—
95C23×D11—22no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11—22no—
101C23×D11—22no—
102C23×D11—22no—
103C23×D11—22no—
104C23×D11C22×C414yes—
105C23×D11C2×D414yes—
106C23×D11C2×Q814yes—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C22×C412yes—
131C22×C4×C11C2×D414yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×Q812yes—
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—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11C22×C414yes—
156C22×Dic11#4114yes—
157C2×D44—44no—
158C2×D44—44no—
159C2×D44—48no—
160C2×D44—48no—
161C2×D44C4⋊C4116yescomplemented
162C2×C4×D11—48no—
163C2×C4×D11—48no—
164C2×C4×D11—48no—
165C2×C4×D11—48no—
166C2×C4×D11—48no—
167C2×C4×D11—48no—
168C2×C4×D11—48no—
169C42×C11—44no—
170(C2×D11)⋊C4—216no—
171(C2×D11)⋊C4—48no—
172(C2×D11)⋊C4—48no—
173(C2×D11)⋊C4—48no—
174(C2×D11)⋊C4—48no—
175C4⋊Dic11—44no—
176C4⋊Dic11—48no—
177Dic11⋊C4—48no—
178C2×#390—111no—
179C2×#386—112no—
180C2×#385—112no—
181#1441—112no—
182#1439—112no—
183#1439—112no—
184C4⋊#95—111no—
185#1434D1111yescharacteristic, complemented
186C22⋊#95—112no—
187C23×C11C23×C411yescharacteristic
188C23×C11C22×D411yescharacteristic
189C23×C11C22×D411yescharacteristic
190C23×C11C22×Q811yescharacteristic
191C23×C11C2×#4111yescharacteristic
192C23×C11C2×#4112yes—
193C23×C11H(5,𝔽2)12yes—
194C23×C11H(5,𝔽2)12yes—
195C23×C11H(5,𝔽2)12yes—
196C23×C11H(5,𝔽2)11yescharacteristic
197C23×C112−1+411yescharacteristic
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—24no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222C22×D11—42no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11C2×C4⋊C418yes—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11C2×C4⋊C414yes—
261C2×C4×C11C4×D414yes—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283D44—416no—
284C4×D11—432no—
285C23×D4—111no—
286C24×C4—112no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—112no—
289C22×C4⋊C4—112no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C42C2×D1111yescharacteristic
296#390—118no—
297#386—228no—
298#385—228no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—111no—
302C2×#95—112no—
303C2×#95—111no—
304C2×#95—112no—
305C2×#95C2×D1111yescharacteristic
306C2×#95C2×D1112yes—
307C2×#95C2×D1112yes—
308C2×#95C2×D1111yescharacteristic
309C22×C11C22×C4⋊C411yescharacteristic
310C22×C11C2×C4×D411yescharacteristic
311C22×C11C4×#4111yescharacteristic
312C22×C11#51811yescharacteristic
313C22×C11#51811yescharacteristic
314C22×C11#51811yescharacteristic
315C22×C11#52011yescharacteristic
316C22×C11#53412yes—
317C22×C11#53512yes—
318C22×C11#53812yes—
319C22×C11#54012yes—
320C22×C11#54212yes—
321C22×C11#54312yes—
322C22×C11D4211yescharacteristic
323C22×C11#54612yes—
324C22×C11#54612yes—
325C22×C11#54711yescharacteristic
326C22×C11D4×Q811yescharacteristic
327C22×C11#55312yes—
328C22×C11#55411yescharacteristic
329C22×C11#55412yes—
330C22×C11#56012yes—
331C22×C11#56212yes—
332C2×D11—28no—
333C2×D11—28no—
334C2×D11—28no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C4×C11—24no—
348C4×C11—24no—
349C4×C11—42no—
350C4×C11—44no—
351C4×C11—82no—
352Dic11—44no—
353Dic11—44no—
354Dic11—82no—
355C25—112no—
356C22×D4—114no—
357C22×D4—114no—
358C22×D4—114no—
359C22×D4—442no—
360C22×D4—442no—
361C23×C4—112no—
362C23×C4—112no—
363C23×C4—112no—
364C23×C4—224no—
365C23×C4—224no—
366C23×C4—224no—
367C23×C4—442no—
368C23×C4—442no—
369C23×C4—442no—
370C23×C4—442no—
371C23×C4C22×D1112yes—
372C23×C4C22×D1111yescharacteristic
373C23×C4C22×D1112yes—
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1111yescharacteristic
376C2×C4⋊C4—114no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—442no—
381C2×C4⋊C4—442no—
382C2×C4⋊C4—442no—
383C2×C4⋊C4—442no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—118no—
386C2×C22⋊C4—224no—
387C2×C22⋊C4—224no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—224no—
390C2×C22⋊C4—224no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—442no—
394C2×C22⋊C4—442no—
395C2×C22⋊C4—442no—
396C2×C22⋊C4—442no—
397C2×C22⋊C4—442no—
398C2×C22⋊C4—442no—
399C2×C42—42no—
400C2×C42C4×D1114yescomplemented
401#95—22no—
402#95—24no—
403#95—42no—
404#95—224no—
405#95—224no—
406#95—441no—
407#95—441no—
408#95—442no—
409#95—442no—
410#95D4414yescomplemented
411C2×C11#231511yescharacteristic
412C2×C11#232811yescharacteristic
413C2×C11#233711yescharacteristic
414C2×C11D4×C4⋊C411yescharacteristic
415C2×C11#234911yescharacteristic
416C2×C11#236411yescharacteristic
417C2×C11#237711yescharacteristic
418C2×C11#267812yes—
419C2×C11#269212yes—
420C2×C11#270112yes—
421C2×C11#278012yes—
422D11—48no—
423C24—114no—
424C24—114no—
425C24—114no—
426C24—222no—
427C24—222no—
428C24—222no—
429C24—222no—
430C24—222no—
431C24—222no—
432C24—222no—
433C24—222no—
434C24—222no—
435C24—222no—
436C24—222no—
437C24—222no—
438C24C23×D1111yescharacteristic
439C2×D4—1116no—
440C2×D4—444no—
441C2×D4—444no—
442C2×D4—448no—
443C2×D4—448no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—114no—
466C22×C4—114no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—448no—
487C22×C4—448no—
488C22×C4—448no—
489C22×C4—448no—
490C22×C4—448no—
491C22×C4—448no—
492C22×C4—448no—
493C22×C4C2×C4×D1112yes—
494C22×C4C2×C4×D1112yes—
495C22×C4C2×C4×D1112yes—
496C22×C4C2×D4414yes—
497C22×C4C2×D4412yes—
498C22×C4#433912yes—
499C22×C4D4×D1112yes—
500C22×C4Q8×D1112yes—
501C4⋊C4—444no—
502C4⋊C4—448no—
503C4⋊C4—448no—
504C22⋊C4—2216no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C22⋊C4—448no—
509C42—44no—
510C11#1443811yescharacteristic, complemented, Sylow
511C23—118no—
512C23—224no—
513C23—224no—
514C23—224no—
515C23—224no—
516C23—224no—
517C23—224no—
518C23—224no—
519C23—224no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—224no—
530C23—442no—
531C23—442no—
532C23—442no—
533C23—442no—
534C23—442no—
535C23—442no—
536C23—442no—
537C23—442no—
538C23—442no—
539C23—442no—
540C23—442no—
541C23—442no—
542C23—442no—
543C23—442no—
544C23—442no—
545C23—442no—
546C23C22×C4×D1111yescharacteristic
547C23C22×D4411yescharacteristic
548C23C2×#433911yescharacteristic
549C23C2×D4×D1111yescharacteristic
550C23#6703712yes—
551C23C2×Q8×D1111yescharacteristic
552C23#41×D1112yes—
553C23#6704211yescharacteristic
554C23#6704212yes—
555C23#6704212yes—
556C23#6704311yescharacteristic
557D4—4416no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—42no—
580C2×C4—42no—
581C2×C4—42no—
582C2×C4—42no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—4432no—
592C2×C4—442no—
593C2×C4—442no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—442no—
604C2×C4—442no—
605C2×C4—442no—
606C2×C4—442no—
607C2×C4C4×D4414yes—
608C2×C4C4⋊C4×D1114yes—
609C22—228no—
610C22—228no—
611C22—228no—
612C22—444no—
613C22—444no—
614C22—444no—
615C22—444no—
616C22—444no—
617C22—444no—
618C22—444no—
619C22—444no—
620C22—444no—
621C22—444no—
622C22—444no—
623C22—444no—
624C22C2×C4×D4411yescharacteristic
625C22#1062301711yescharacteristic
626C22C2×C4⋊C4×D1111yescharacteristic
627C22#1062305211yescharacteristic
628C22#1062305211yescharacteristic
629C22#1062305311yescharacteristic
630C22#1062305411yescharacteristic
631C22#1062305612yes—
632C22#1062306612yes—
633C22#1062307112yes—
634C22D4×D4411yescharacteristic
635C22#1062308211yescharacteristic
636C22#1062308512yes—
637C22Q8×D4411yescharacteristic
638C22#1062311011yescharacteristic
639C22#1062313612yes—
640C22#1062316512yes—
641C22#1062319712yes—
642C22#1062319812yes—
643C22#1062320712yes—
644C22#1062322112yes—
645C22#1062323512yes—
646C22#1062324112yes—
647C4—24no—
648C4—24no—
649C4—42no—
650C4—44no—
651C4—82no—
652C4—444no—
653C4—444no—
654C4—882no—
655C2—448no—
656C2#1307122911yescharacteristic
657C2#1307134111yescharacteristic
658C2#1307142611yescharacteristic
659C2C4⋊C4×D4411yescharacteristic
660C2#1307152411yescharacteristic
661C2#1307166611yescharacteristic
662C2#1307177511yescharacteristic
663C2#1307493912yes—
664C2#1307511012yes—
665C2#1307522612yes—
666C2#1307626712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#14438
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#10622281C2semidirect
4. #13066868C2semidirect
5. #13066862C2semidirect
6. #13066860C2semidirect
7. #13066846C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C11×#1434C2semidirect
31. #10622552C4semidirect
56. C2×C42×C11C2×C4semidirect
70. C2×(C2×D11)⋊C4C2×C4semidirect
71. C2×(C2×D11)⋊C4C2×C4semidirect
76. C2×C4⋊Dic11C2×C4semidirect
83. C11×#95D4semidirect
161. C2×D44C4⋊C4semidirect
185. #1434D11semidirect
400. C2×C42C4×D11semidirect
410. #95D44semidirect
510. C11#14438semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106222782
C2×#106222812
#130668682
#130668622
#130668602
#130668462
(C2×D11)⋊#952
C11×#14342
#1443811