Finite Group Databasebeta

← #14682175

Subgroups — #14682175

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×#10622602C212yesmaximal, complemented
4#13066868C212yesmaximal, complemented
5#13066860C212yesmaximal, complemented
6#13066858C212yesmaximal, complemented
7#13066843C211yesmaximal, characteristic, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9C11×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C22×(C2×D11)⋊C4C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4C2212yes—
21C2×C11×#95C2212yes—
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31#10622602—28no—
32#10622552C418yescomplemented
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×C11×C4⋊C4—24no—
56C2×C11×C4⋊C4—24no—
57C2×C11×C4⋊C4—42no—
58C2×C42×C11—42no—
59C2×C42×C11C2×C414yescomplemented
60C2×(C2×D11)⋊C4—24no—
61C2×(C2×D11)⋊C4—24no—
62C2×(C2×D11)⋊C4—24no—
63C2×(C2×D11)⋊C4—24no—
64C2×(C2×D11)⋊C4—24no—
65C2×(C2×D11)⋊C4—24no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—42no—
68C2×(C2×D11)⋊C4—42no—
69C2×(C2×D11)⋊C4—42no—
70C2×(C2×D11)⋊C4—42no—
71C2×(C2×D11)⋊C4—42no—
72C2×(C2×D11)⋊C4—42no—
73C2×(C2×D11)⋊C4C2×C418yescomplemented
74C2×(C2×D11)⋊C4C2×C418yescomplemented
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—41no—
82C11×#95—41no—
83C11⋊#95—24no—
84C11⋊#95—22no—
85C11⋊#95—24no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95—42no—
89C11⋊#95D414yescomplemented
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—22no—
114C22×C4×C11—22no—
115C22×C4×C11—21no—
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×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×Q812yes—
134C22×C4×C11#4114yes—
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×Dic11C2×D414yes—
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—
169C11×C4⋊C4—48no—
170C42×C11—44no—
171(C2×D11)⋊C4—216no—
172(C2×D11)⋊C4—48no—
173(C2×D11)⋊C4—48no—
174(C2×D11)⋊C4—48no—
175(C2×D11)⋊C4—48no—
176C4⋊Dic11—44no—
177Dic11⋊C4—48no—
178C2×#390—111no—
179C2×#386—112no—
180C2×#385—112no—
181#1441—112no—
182#1439—112no—
183#1439—112no—
184C4⋊#95D1111yescharacteristic, complemented
185#1434—111no—
186C22⋊#95—112no—
187C23×C11C23×C411yescharacteristic
188C23×C11C22×D411yescharacteristic
189C23×C11C22×D411yescharacteristic
190C23×C11C22×Q811yescharacteristic
191C23×C11C2×#4112yes—
192C23×C11C2×#4111yescharacteristic
193C23×C11H(5,𝔽2)12yes—
194C23×C11H(5,𝔽2)11yescharacteristic
195C23×C11H(5,𝔽2)12yes—
196C23×C11H(5,𝔽2)12yes—
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⋊C4C2×D1112yes—
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—111no—
300C2×#95—112no—
301C2×#95—111no—
302C2×#95—112no—
303C2×#95—112no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95C2×D1112yes—
307C2×#95C2×D1111yescharacteristic
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—24no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—224no—
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—24no—
402#95—41no—
403#95—41no—
404#95—114no—
405#95—224no—
406#95—224no—
407#95—222no—
408#95—442no—
409#95—442no—
410#95—442no—
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—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
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×C4#433914yes—
497C22×C4D4×D1112yes—
498C22×C4D4×D1112yes—
499C22×C4Q8×D1112yes—
500C22×C4#434312yes—
501C4⋊C4—48no—
502C4⋊C4—444no—
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
547C23C2×#433912yes—
548C23C2×D4×D1111yescharacteristic
549C23C2×D4×D1111yescharacteristic
550C23#6703711yescharacteristic
551C23#6703712yes—
552C23C2×Q8×D1111yescharacteristic
553C23C2×#434311yescharacteristic
554C23#6704011yescharacteristic
555C23#6704212yes—
556C23#6704212yes—
557D4—4416no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
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⋊C4×D1114yes—
608C2×C4#6694614yes—
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—
624C22C4×#433911yescharacteristic
625C22#1062301711yescharacteristic
626C22#1062302112yes—
627C22C2×C4⋊C4×D1111yescharacteristic
628C22C2×#6694611yescharacteristic
629C22#1062303511yescharacteristic
630C22#1062304512yes—
631C22#1062305211yescharacteristic
632C22#1062305211yescharacteristic
633C22#1062308112yes—
634C22#1062309112yes—
635C22#1062311012yes—
636C22#1062311312yes—
637C22#1062313612yes—
638C22#1062315112yes—
639C22#1062316512yes—
640C22#1062317812yes—
641C22#1062320512yes—
642C22#1062322912yes—
643C22#1062324811yescharacteristic
644C22#1062325711yescharacteristic
645C22#1062325811yescharacteristic
646C22#1062326111yescharacteristic
647C4—24no—
648C4—24no—
649C4—42no—
650C4—44no—
651C4—82no—
652C4—444no—
653C4—444no—
654C4—882no—
655C2—448no—
656C2#1307122911yescharacteristic
657C2#1307133911yescharacteristic
658C2#1307142911yescharacteristic
659C2#1307151611yescharacteristic
660C2#1307152711yescharacteristic
661C2#1307166311yescharacteristic
662C2#1307177011yescharacteristic
663C2#1307493812yes—
664C2#1307510712yes—
665C2#1307522412yes—
666C2#1307625812yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#14438
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622602C2semidirect
4. #13066868C2semidirect
5. #13066860C2semidirect
6. #13066858C2semidirect
7. #13066843C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. C11×C4⋊#95C2semidirect
32. #10622552C4semidirect
59. C2×C42×C11C2×C4semidirect
73. C2×(C2×D11)⋊C4C2×C4semidirect
74. C2×(C2×D11)⋊C4C2×C4semidirect
76. C2×C4⋊Dic11C2×C4semidirect
89. C11⋊#95D4semidirect
161. C2×D44C4⋊C4semidirect
184. C4⋊#95D11semidirect
400. C2×C42C4×D11semidirect
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×#106226022
#130668682
#130668602
#130668582
#130668432
(C2×D11)⋊#952
C11×C4⋊#952
#1443811