Finite Group Databasebeta

← #14760189

Subgroups — #14760189

Order 2816.

1044 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622461C211yesmaximal, characteristic
2C2×#10622323C211yesmaximal, characteristic, complemented
3C2×C4×#4314C211yesmaximal, characteristic, complemented
4#13071341C211yesmaximal, characteristic
5#13070979C211yesmaximal, characteristic, complemented
6#13069542C211yesmaximal, characteristic
7#13069386C211yesmaximal, characteristic, complemented
8#13069244C211yesmaximal, characteristic, complemented
9#13069237C211yesmaximal, characteristic, complemented
10#13068970C211yesmaximal, characteristic, complemented
11#13068970C211yesmaximal, characteristic, complemented
12#13068632C211yesmaximal, characteristic, complemented
13#13068442C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1768C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C22×#4314C2211yescharacteristic
18C2×#66927C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#97C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28C11×#376C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622552C2211yescharacteristic
41#10622549C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622461C418yescomplemented
46#10622323—24no—
47C4×#4314—24no—
48#10622278—21no—
49#10622278—21no—
50#10622278—21no—
51#10622278—21no—
52#10622262—21no—
53#10622262—21no—
54#10622262—21no—
55#10622261—21no—
56C11×#336C2211yescharacteristic
57C11×#336C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61#10622189C2211yescharacteristic
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2311yescharacteristic
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C22×C4×D11—21no—
68C22×Dic22C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×#4314—22no—
97C2×#4314—22no—
98C2×#4314—22no—
99C2×#4314—22no—
100C2×#4314C2×C414yescomplemented
101C2×#4314C2×C414yescomplemented
102#66927—22no—
103#66927C2×C414yes—
104C4×D44—22no—
105C4×D44—22no—
106C4×D44—22no—
107C4×D44—22no—
108C4×Dic22—22no—
109C4×Dic22—22no—
110C4×Dic22—22no—
111C4×Dic22—22no—
112C4×Dic22C2×C414yescomplemented
113C4×Dic22D414yescomplemented
114C11×C4⋊C8—22no—
115C11×C4⋊C8C2×C414yescomplemented
116C11×#97—22no—
117C4×C8×C11—22no—
118C11×#95D411yescharacteristic
119C11×#95D411yescharacteristic
120C11×#95D411yescharacteristic
121C11×#95D411yescharacteristic
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127#66885—22no—
128#66885—22no—
129#66885—22no—
130#66885—22no—
131#66885C2×C414yescomplemented
132#66885C2×C414yescomplemented
133#66882—22no—
134#66881—22no—
135#66880—22no—
136#66880—22no—
137#21515—111nomaximal, Sylow
138C23×D11—21no—
139C23×D11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C2×D44—24no—
154C2×D44—24no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—81no—
166C2×D44—81no—
167C2×D44—81no—
168C2×D44—81no—
169C2×D44C22×C412yes—
170C2×D44C22×C412yes—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—81no—
174C2×C4×D11—81no—
175C2×C4×D11—81no—
176C2×C4×D11—81no—
177C2×Dic22—21no—
178C2×Dic22—21no—
179C2×Dic22—21no—
180C2×Dic22C22×C412yes—
181C2×Dic22C2×D412yes—
182C2×Dic22#4112yes—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11C22×C412yes—
194C2×C8×C11C22×C412yes—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11C22×C412yes—
198C42×C11C2×D412yes—
199C42×C11#4112yes—
200C42×C11#4112yes—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—81no—
204(C2×D11)⋊C4—81no—
205(C2×D11)⋊C4—81no—
206(C2×D11)⋊C4—81no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11C22×C412yes—
215C4⋊Dic11C2×D412yes—
216C4⋊Dic11#4112yes—
217Dic11⋊C4—24no—
218Dic11⋊C4—24no—
219Dic11⋊C4—24no—
220C4×Dic11—24no—
221C4×Dic11—24no—
222C4×Dic11—24no—
223C4×Dic11—81no—
224C4×Dic11—81no—
225C4×Dic11—81no—
226#4314—28no—
227#4314—28no—
228C2×#460—111no—
229C2×#440—111no—
230C2×C4×SD16—111no—
231#2328—111no—
232#2276—111no—
233#1982—111no—
234#1949—111no—
235#1926—111no—
236#1925—111no—
237#1880—111no—
238#1880—111no—
239#1805—111no—
240#1768D1111yescharacteristic, complemented
241#1762—111no—
242C4×#102—111no—
243C23×C11C22×D411yescharacteristic
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11C4×D412yes—
273C2×C4×C11C4×D412yes—
274C2×C4×C11#12112yes—
275C2×C4×C11#12112yes—
276C2×C4×C11C23×C411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C2×#4111yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300D44—22no—
301D44—22no—
302D44—22no—
303D44—22no—
304D44—41no—
305D44—41no—
306D44—41no—
307D44—41no—
308D44—84no—
309D44—84no—
310C4×D11—84no—
311C4×D11—84no—
312Dic22—22no—
313Dic22—22no—
314Dic22—22no—
315Dic22C4×D414yes—
316C8×C11—22no—
317C8×C11—22no—
318C8×C11—41no—
319C8×C11—41no—
320C22×SD16—111no—
321C22×SD16—111no—
322C2×#127—111no—
323C2×C4×Q8—111no—
324C2×C4×Q8—111no—
325C2×C4×Q8—111no—
326C2×C4×D4—111no—
327C2×C4×D4—111no—
328#460—118no—
329#440—224no—
330C4×SD16—224no—
331C2×#107—111no—
332C2×#106—111no—
333C2×C4⋊C8C2×D1111yescharacteristic
334C2×C4⋊C8C2×D1111yescharacteristic
335C2×#103—111no—
336C2×#103—111no—
337C2×#102—111no—
338C2×#102—111no—
339C2×#102—111no—
340C2×#102—111no—
341C2×#102—111no—
342C2×#102—111no—
343C2×#97C2×D1111yescharacteristic
344C2×C4×C8C2×D1111yescharacteristic
345#390—111no—
346#390—111no—
347#386—221no—
348#386—221no—
349#386—221no—
350#386—221no—
351#382—111no—
352C4×C4⋊C4—111no—
353C4×C4⋊C4—111no—
354C4×C4⋊C4—111no—
355C4×C4⋊C4—221no—
356C4×C4⋊C4—221no—
357C4×C4⋊C4—221no—
358#376—221no—
359#376C2×D1111yescharacteristic
360#340—111no—
361#340—111no—
362#340—111no—
363#340—111no—
364#336C2×D1111yescharacteristic
365#336C2×D1111yescharacteristic
366C22×C11C2×C4×D411yescharacteristic
367C22×C11C2×#12111yescharacteristic
368C22×C11#52511yescharacteristic
369C22×C11#57611yescharacteristic
370C22×C11#57711yescharacteristic
371C22×C11#57711yescharacteristic
372C22×C11#57711yescharacteristic
373C2×D11—42no—
374C2×D11—42no—
375C2×D11—42no—
376C2×D11—42no—
377C2×D11—42no—
378C2×D11—42no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C4×C11—22no—
388C4×C11—22no—
389C4×C11—22no—
390C4×C11—22no—
391C4×C11—41no—
392C4×C11—41no—
393C4×C11C2×C4×D411yescharacteristic
394C4×C11C4×#4111yescharacteristic
395C4×C11#52911yescharacteristic
396C4×C11#53211yescharacteristic
397Dic11—24no—
398Dic11—42no—
399Dic11—42no—
400Dic11—42no—
401Dic11—81no—
402Dic11—81no—
403C22×Q8—111no—
404C22×D4—111no—
405C22×D4—111no—
406C22×D4—221no—
407C22×D4—221no—
408C23×C4—221no—
409C23×C4—221no—
410C2×SD16—114no—
411C2×SD16—114no—
412C2×SD16—222no—
413C2×SD16—222no—
414C2×SD16—222no—
415C2×SD16—222no—
416C22×C8C22×D1111yescharacteristic
417C22×C8C22×D1111yescharacteristic
418C22×C8C22×D1111yescharacteristic
419C22×C8C22×D1111yescharacteristic
420#127—114no—
421#127—222no—
422C4×Q8—114no—
423C4×Q8—114no—
424C4×Q8—222no—
425C4×Q8—222no—
426C4×Q8—222no—
427C4×Q8—222no—
428C4×D4—222no—
429C4×D4—222no—
430C4×D4—222no—
431C4×D4—222no—
432C2×C4⋊C4—111no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C42—221no—
447C2×C42—221no—
448C2×C42—221no—
449C2×C42—221no—
450C2×C42—221no—
451C2×C42—221no—
452C2×C42C22×D1111yescharacteristic
453C2×C42C22×D1111yescharacteristic
454C2×C42C22×D1111yescharacteristic
455#107—222no—
456#106—222no—
457C4⋊C8—22no—
458C4⋊C8C4×D1114yescomplemented
459#103—222no—
460#103—222no—
461#102—114no—
462#102—114no—
463#102—222no—
464#102—222no—
465#102—222no—
466#102—222no—
467#97—22no—
468C4×C8—22no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474#95D4411yescharacteristic
475#95D4411yescharacteristic
476#95D4411yescharacteristic
477#95D4411yescharacteristic
478C2×C11C4×#12111yescharacteristic
479C2×C11#294611yescharacteristic
480C2×C11#294911yescharacteristic
481C2×C11#304311yescharacteristic
482C2×C11#304511yescharacteristic
483C2×C11#311911yescharacteristic
484C2×C11#312611yescharacteristic
485D11—82no—
486D11—82no—
487C24—221no—
488C24—221no—
489C2×Q8—112no—
490C2×Q8—112no—
491C2×Q8—112no—
492C2×Q8—221no—
493C2×Q8—221no—
494C2×Q8—221no—
495C2×D4—112no—
496C2×D4—112no—
497C2×D4—224no—
498C2×D4—224no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—221no—
505C2×D4—221no—
506C2×D4—221no—
507C2×D4—221no—
508C2×D4—221no—
509C2×D4—881no—
510C2×D4—881no—
511C2×D4—881no—
512C2×D4—881no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—442no—
520C22×C4—442no—
521C22×C4—881no—
522C22×C4—881no—
523C22×C4—881no—
524C22×C4—881no—
525C22×C4C2×D4411yescharacteristic
526C22×C4C2×D4411yescharacteristic
527C22×C4C2×D4411yescharacteristic
528C22×C4C2×D4411yescharacteristic
529C22×C4C2×D4411yescharacteristic
530C22×C4C2×D4411yescharacteristic
531C22×C4C23×D1111yescharacteristic
532SD16—228no—
533SD16—228no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8C2×C4×D1112yes—
545C2×C8C2×C4×D1112yes—
546C4⋊C4—112no—
547C4⋊C4—112no—
548C4⋊C4—112no—
549C4⋊C4—224no—
550C4⋊C4—224no—
551C4⋊C4—224no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C4⋊C4—221no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C22⋊C4—881no—
562C22⋊C4—881no—
563C22⋊C4—881no—
564C22⋊C4—881no—
565C42—21no—
566C42—21no—
567C42—224no—
568C42—224no—
569C42—224no—
570C42—881no—
571C42—881no—
572C42—881no—
573C42C2×C4×D1112yes—
574C42#433912yes—
575C42D4×D1112yes—
576C42#434312yes—
577C11#2151511yescharacteristic, complemented, Sylow
578C23—222no—
579C23—222no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23—441no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23—441no—
592C23C22×D4411yescharacteristic
593Q8—114no—
594Q8—222no—
595Q8—222no—
596Q8—222no—
597D4—222no—
598D4—222no—
599D4—222no—
600D4—222no—
601D4—441no—
602D4—441no—
603D4—441no—
604D4—441no—
605D4—884no—
606D4—884no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—222no—
626C2×C4—222no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—884no—
640C2×C4—884no—
641C2×C4C4×D4412yes—
642C2×C4C4×D4412yes—
643C2×C4#6694812yes—
644C2×C4#6694812yes—
645C2×C4C22×C4×D1111yescharacteristic
646C2×C4C2×#433911yescharacteristic
647C2×C4C2×D4×D1111yescharacteristic
648C2×C4C2×#434311yescharacteristic
649C2×C4#41×D1111yescharacteristic
650C2×C4#41×D1111yescharacteristic
651C8—22no—
652C8—22no—
653C8—41no—
654C8—41no—
655C22—442no—
656C22—442no—
657C22—442no—
658C22—442no—
659C22—442no—
660C22—442no—
661C22—881no—
662C22—881no—
663C22—881no—
664C22—881no—
665C22—881no—
666C22—881no—
667C22—881no—
668C22—881no—
669C22C2×C4×D4411yescharacteristic
670C22C2×#6694811yescharacteristic
671C22#1062305511yescharacteristic
672C22#1062328211yescharacteristic
673C22#1062328211yescharacteristic
674C22#1062328211yescharacteristic
675C22#1062328311yescharacteristic
676C4—22no—
677C4—22no—
678C4—22no—
679C4—22no—
680C4—41no—
681C4—41no—
682C4—224no—
683C4—442no—
684C4—442no—
685C4—442no—
686C4—881no—
687C4—881no—
688C4C4×D4×D1111yescharacteristic
689C4#1062307911yescharacteristic
690C4C4×#434311yescharacteristic
691C4#1062311111yescharacteristic
692C2—882no—
693C2—882no—
694C2C4×#6694811yescharacteristic
695C2#1307745011yescharacteristic
696C2#1307747711yescharacteristic
697C2#1307813811yescharacteristic
698C2#1307815711yescharacteristic
699C2#1307881711yescharacteristic
700C2#1307890811yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1768C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
cosocleC22×C4×C11C24
hypercenter#1768D11
hypocenterC11#21515
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #1768

Complements

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

NH ≅ G/Ntype
2. C2×#10622323C2semidirect
3. C2×C4×#4314C2semidirect
5. #13070979C2semidirect
7. #13069386C2semidirect
8. #13069244C2semidirect
9. #13069237C2semidirect
10. #13068970C2semidirect
11. #13068970C2semidirect
12. #13068632C2semidirect
13. #13068442C2semidirect
14. C4×#66885C2semidirect
15. C11×#1768C2semidirect
45. #10622461C4semidirect
100. C2×#4314C2×C4semidirect
101. C2×#4314C2×C4semidirect
112. C4×Dic22C2×C4semidirect
113. C4×Dic22D4semidirect
115. C11×C4⋊C8C2×C4semidirect
131. #66885C2×C4semidirect
132. #66885C2×C4semidirect
240. #1768D11semidirect
458. C4⋊C8C4×D11semidirect
577. C11#21515semidirect

Maximal subgroups

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

subgroupindex
C2×#106224612
C2×#106223232
C2×C4×#43142
#130713412
#130709792
#130695422
#130693862
#130692442
#130692372
#130689702
#130686322
#130684422
C4×#668852
C11×#17682
#2151511