Finite Group Databasebeta

← #14660731

Subgroups — #14660731

Order 2816.

1110 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66880C211yesmaximal, characteristic
2C22×#66874C211yesmaximal, characteristic
3C2×#10622587C211yesmaximal, characteristic
4C2×#10622589C211yesmaximal, characteristic
5C2×#10622167C211yesmaximal, characteristic
6C2×#10622188C211yesmaximal, characteristic
7C2×C11×#340C211yesmaximal, characteristic
8C23×Dic22C2211yescharacteristic
9C23×C8×C11C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C11×C4⋊C4C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4—22no—
14C22×C4×Dic11C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×C11⋊#95—22no—
17C2×#66880—22no—
18C2×#66880—22no—
19C2×#66880—22no—
20#10622589—22no—
21#10622589—22no—
22#10622587—22no—
23#10622587C414yescomplemented
24C2×#66874—22no—
25C2×#66874—22no—
26C2×#66874—22no—
27C11×#340—22no—
28#10622188—22no—
29#10622167—22no—
30C23×C4×C11—21no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—21no—
34C23×Dic11—21no—
35C23×Dic11D412yes—
36C22×Dic22—21no—
37C22×Dic22—21no—
38C22×Dic22—21no—
39C22×Dic22—21no—
40C22×Dic22—21no—
41C22×Dic22—21no—
42C22×Dic22—21no—
43C22×Dic22—21no—
44C22×Dic22—21no—
45C22×Dic22—21no—
46C22×Dic22—21no—
47C22×Dic22C2×C412yes—
48C22×Dic22D412yes—
49C22×Dic22Q812yes—
50C22×C8×C11—21no—
51C22×C8×C11—21no—
52C22×C8×C11—21no—
53C22×C8×C11—21no—
54C22×C8×C11—21no—
55C22×C8×C11—21no—
56C22×C8×C11D412yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2×C412yes—
68C2×C11×C4⋊C4D412yes—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11D412yes—
75C2×Dic11⋊C4—28no—
76C2×Dic11⋊C4—44no—
77C2×Dic11⋊C4—44no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11C2×C412yes—
83C2×C4×Dic11D412yes—
84C22×C11⋊C8—21no—
85C22×C11⋊C8—21no—
86C22×C11⋊C8—21no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8—21no—
89C22×C11⋊C8—21no—
90C22×C11⋊C8D412yes—
91C11⋊#95—28no—
92#66880—28no—
93#66874—28no—
94#11050—111nomaximal, Sylow
95C24×C11C2×D411yescharacteristic
96C22×C4×C11—22no—
97C22×C4×C11—22no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—42no—
103C22×C4×C11—42no—
104C22×C4×C11—42no—
105C22×C4×C11—42no—
106C22×C4×C11C22×C411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×Q811yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11#4111yescharacteristic
117C22×C4×C11#4111yescharacteristic
118C22×C4×C11#4111yescharacteristic
119C22×C4×C11#4111yescharacteristic
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—41no—
129C22×Dic11—41no—
130C22×Dic11—41no—
131C22×Dic11—41no—
132C22×Dic11—41no—
133C22×Dic11—41no—
134C22×Dic11—42no—
135C22×Dic11—42no—
136C22×Dic11C22⋊C414yes—
137C22×Dic11SD1614yes—
138C22×Dic11Q1614yes—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—22no—
142C2×Dic22—22no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—22no—
149C2×Dic22—22no—
150C2×Dic22—22no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—41no—
155C2×Dic22—41no—
156C2×Dic22—41no—
157C2×Dic22—41no—
158C2×Dic22—41no—
159C2×Dic22—41no—
160C2×Dic22—41no—
161C2×Dic22—41no—
162C2×Dic22—41no—
163C2×Dic22—41no—
164C2×Dic22—41no—
165C2×Dic22—41no—
166C2×Dic22C4⋊C414yescomplemented
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—41no—
179C11×C4⋊C4—41no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—41no—
182C4⋊Dic11—22no—
183C4⋊Dic11—22no—
184C4⋊Dic11—41no—
185C4⋊Dic11—41no—
186Dic11⋊C4—416no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—22no—
190C4×Dic11—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—41no—
195C2×C11⋊C8—41no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C22×#103—111no—
199C22×#103—111no—
200C2×#391—111no—
201C2×#384—111no—
202C2×#340—111no—
203C2×#340D1111yescharacteristic
204C2×#336—111no—
205C23×C11C2×C22⋊C411yescharacteristic
206C23×C11#12011yescharacteristic
207C23×C11#12111yescharacteristic
208C23×C11C22⋊Q811yescharacteristic
209C23×C11#12311yescharacteristic
210C23×C11#12411yescharacteristic
211C23×C11#12711yescharacteristic
212C23×C11C2×SD1612yes—
213C23×C11C2×Q1612yes—
214C23×C11AGL(1,ℤ/8)12yes—
215C23×C11#13712yes—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—44no—
219C2×C4×C11—44no—
220C2×C4×C11—82no—
221C2×C4×C11—82no—
222C2×C4×C11—81no—
223C2×C4×C11—81no—
224C2×C4×C11—81no—
225C2×C4×C11—81no—
226C2×C4×C11C2×C4⋊C411yescharacteristic
227C2×C4×C11#11711yescharacteristic
228C2×C4×C11C4×D411yescharacteristic
229C2×C4×C11C4×D411yescharacteristic
230C2×C4×C11C4×D411yescharacteristic
231C2×C4×C11C4×D411yescharacteristic
232C2×C4×C11#12011yescharacteristic
233C2×C4×C11#12011yescharacteristic
234C2×C4×C11#12111yescharacteristic
235C2×C4×C11#12111yescharacteristic
236C2×C4×C11#12111yescharacteristic
237C2×C4×C11#12111yescharacteristic
238C2×C4×C11#12111yescharacteristic
239C2×C4×C11#12111yescharacteristic
240C2×C4×C11#12111yescharacteristic
241C2×C4×C11C22⋊Q811yescharacteristic
242C2×C4×C11C22⋊Q811yescharacteristic
243C2×C4×C11C22⋊Q811yescharacteristic
244C2×C4×C11C22⋊Q811yescharacteristic
245C2×C4×C11C22⋊Q811yescharacteristic
246C2×C4×C11#12311yescharacteristic
247C2×C4×C11#12311yescharacteristic
248C2×C4×C11#12311yescharacteristic
249C2×C4×C11#12311yescharacteristic
250C2×C4×C11#12411yescharacteristic
251C2×C4×C11#12411yescharacteristic
252C2×C4×C11#12611yescharacteristic
253C2×C4×C11#12611yescharacteristic
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—42no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—44no—
269C2×Dic11—82no—
270C2×Dic11—81no—
271C2×Dic11—81no—
272C2×Dic11#10318yescomplemented
273Dic22—24no—
274Dic22—24no—
275Dic22—42no—
276Dic22—42no—
277Dic22—42no—
278Dic22—42no—
279Dic22—42no—
280Dic22—42no—
281C8×C11—42no—
282C11⋊C8—42no—
283C23×Q8—111no—
284C23×C8—111no—
285C23×C8C2×D1111yescharacteristic
286C22×C4⋊C4—111no—
287C22×C4⋊C4—222no—
288C22×C4⋊C4C2×D1111yescharacteristic
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C42—111no—
291C2×#103—222no—
292C2×#103—222no—
293C2×#103—222no—
294C2×#103—222no—
295C2×#103—222no—
296C2×#103—222no—
297#391—114no—
298#391—222no—
299#384—222no—
300#384—222no—
301C2×#95—222no—
302#340—22no—
303#340—222no—
304#336—222no—
305C22×C11#38011yescharacteristic
306C22×C11#38611yescharacteristic
307C22×C11#39011yescharacteristic
308C22×C11#39211yescharacteristic
309C22×C11#39311yescharacteristic
310C22×C11#39711yescharacteristic
311C22×C11#39911yescharacteristic
312C22×C11C2×#10312yes—
313C22×C11#41712yes—
314C22×C11#45012yes—
315C22×C11#45112yes—
316C22×C11#46012yes—
317C22×C11#46212yes—
318C22×C11#47512yes—
319C22×C11#47712yes—
320C22×C11#48312yes—
321C22×C11#48412yes—
322C22×C11#48712yes—
323C22×C11#48912yes—
324C22×C11#49211yescharacteristic
325C22×C11#49411yescharacteristic
326C22×C11#49611yescharacteristic
327C22×C11#49711yescharacteristic
328C4×C11—82no—
329C4×C11—82no—
330C4×C11#38511yescharacteristic
331C4×C11#38511yescharacteristic
332C4×C11#38811yescharacteristic
333C4×C11#38811yescharacteristic
334C4×C11#39411yescharacteristic
335C4×C11#39411yescharacteristic
336C4×C11#39611yescharacteristic
337C4×C11#39611yescharacteristic
338Dic11—28no—
339Dic11—44no—
340Dic11—82no—
341C22×Q8—112no—
342C22×Q8—112no—
343C22×Q8—112no—
344C22×Q8—221no—
345C22×Q8—221no—
346C22×Q8—221no—
347C22×Q8—221no—
348C22×Q8—221no—
349C22×Q8—221no—
350C22×Q8—221no—
351C22×Q8—221no—
352C22×Q8—221no—
353C22×Q8—221no—
354C22×Q8—221no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4—112no—
358C23×C4—221no—
359C23×C4—221no—
360C23×C4C22×D1111yescharacteristic
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—112no—
368C22×C8—221no—
369C22×C8—221no—
370C22×C8—221no—
371C22×C8—221no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8C22⋊D1112yes—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—112no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—228no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—444no—
393C2×C4⋊C4—444no—
394C2×C4⋊C4C4×D1112yes—
395C2×C4⋊C4D4412yes—
396C2×C42—112no—
397C2×C42—112no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42—221no—
402#103—228no—
403#103—228no—
404#95—228no—
405C2×C11#143911yescharacteristic
406C2×C11#180312yes—
407C2×C11#187212yes—
408C2×C11#195611yescharacteristic
409C2×C11#195911yescharacteristic
410C2×C11#201411yescharacteristic
411C2×C11#201611yescharacteristic
412C2×C11#202412yes—
413C2×C11#207212yes—
414C2×C11#209511yescharacteristic
415C2×C11#209611yescharacteristic
416C24D4×D1111yescharacteristic
417C2×Q8—114no—
418C2×Q8—222no—
419C2×Q8—222no—
420C2×Q8—222no—
421C2×Q8—222no—
422C2×Q8—222no—
423C2×Q8—222no—
424C2×Q8—222no—
425C2×Q8—222no—
426C2×Q8—222no—
427C2×Q8—222no—
428C2×Q8—222no—
429C2×Q8—222no—
430C2×Q8—222no—
431C2×Q8—222no—
432C2×Q8—222no—
433C2×Q8—441no—
434C2×Q8—441no—
435C2×Q8—441no—
436C2×Q8—441no—
437C2×Q8—441no—
438C2×Q8—441no—
439C2×Q8—441no—
440C2×Q8—441no—
441C2×Q8—441no—
442C2×Q8—441no—
443C2×Q8—441no—
444C2×Q8—441no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—114no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—441no—
467C22×C4—441no—
468C22×C4—441no—
469C22×C4—441no—
470C22×C4—441no—
471C22×C4—442no—
472C22×C4—442no—
473C22×C4—441no—
474C22×C4C2×C4×D1111yescharacteristic
475C22×C4C2×D4411yescharacteristic
476C22×C4#433911yescharacteristic
477C22×C4#433911yescharacteristic
478C22×C4#433911yescharacteristic
479C22×C4#433911yescharacteristic
480C22×C4D4×D1111yescharacteristic
481C22×C4D4×D1111yescharacteristic
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4#434111yescharacteristic
485C22×C4Q8×D1111yescharacteristic
486C22×C4#434311yescharacteristic
487C22×C4C2×C22⋊D1111yescharacteristic
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—222no—
496C2×C8—222no—
497C2×C8—222no—
498C2×C8—441no—
499C2×C8—441no—
500C2×C8—441no—
501C2×C8—441no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—41no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—4416no—
513C4⋊C4—441no—
514C4⋊C4—441no—
515C42—222no—
516C42—222no—
517C42—222no—
518C42—222no—
519C11#1105011yescharacteristic, complemented, Sylow
520C23C22⋊C4×D1111yescharacteristic
521C23#6693511yescharacteristic
522C23#6693711yescharacteristic
523C23#6693811yescharacteristic
524C23#6694711yescharacteristic
525C23#6694911yescharacteristic
526C23#6696412yes—
527C23SD16×D1112yes—
528C23#6696812yes—
529C23Q16×D1112yes—
530C23#6699311yescharacteristic
531Q8—224no—
532Q8—224no—
533Q8—442no—
534Q8—442no—
535Q8—442no—
536Q8—442no—
537Q8—442no—
538Q8—442no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—82no—
548C2×C4—82no—
549C2×C4—118no—
550C2×C4—224no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4—442no—
560C2×C4—442no—
561C2×C4—442no—
562C2×C4—442no—
563C2×C4—442no—
564C2×C4—444no—
565C2×C4—881no—
566C2×C4—881no—
567C2×C4—882no—
568C2×C4#6692511yescharacteristic
569C2×C4C4×D4411yescharacteristic
570C2×C4#6692811yescharacteristic
571C2×C4#6692911yescharacteristic
572C2×C4(C22⋊D11)⋊C411yescharacteristic
573C2×C4#6693511yescharacteristic
574C2×C4#6693611yescharacteristic
575C2×C4#6693711yescharacteristic
576C2×C4#6693711yescharacteristic
577C2×C4#6693711yescharacteristic
578C2×C4#6693711yescharacteristic
579C2×C4#6693811yescharacteristic
580C2×C4C4⋊C4×D1111yescharacteristic
581C2×C4#6694611yescharacteristic
582C2×C4#6694711yescharacteristic
583C2×C4#6694711yescharacteristic
584C2×C4#6694811yescharacteristic
585C2×C4#6694911yescharacteristic
586C2×C4#6694911yescharacteristic
587C2×C4#6694911yescharacteristic
588C2×C4#6695011yescharacteristic
589C2×C4#6695111yescharacteristic
590C2×C4C4×C22⋊D1111yescharacteristic
591C2×C4#6698211yescharacteristic
592C2×C4#6698311yescharacteristic
593C2×C4#6699011yescharacteristic
594C2×C4#6699211yescharacteristic
595C2×C4#6699911yescharacteristic
596C8—42no—
597C8—442no—
598C22#1062227811yescharacteristic
599C22#1062228011yescharacteristic
600C22#1062228611yescharacteristic
601C22#1062228811yescharacteristic
602C22#1062237512yes—
603C22#1062237812yes—
604C22#1062238412yes—
605C22#1062238912yes—
606C22#1062240512yes—
607C22#1062240612yes—
608C22D11×#10312yes—
609C22#1062242112yes—
610C22#1062246712yes—
611C22#1062247512yes—
612C22#1062248812yes—
613C22#1062249712yes—
614C22#1062257011yescharacteristic
615C22#1062257311yescharacteristic
616C22#1062260511yescharacteristic
617C22#1062276711yescharacteristic
618C22#1062278011yescharacteristic
619C22#1062278811yescharacteristic
620C22#1062279411yescharacteristic
621C4—82no—
622C4—82no—
623C4—228no—
624C4—444no—
625C4—882no—
626C4#1062228111yescharacteristic
627C4#1062228211yescharacteristic
628C4#1062228511yescharacteristic
629C4#1062228911yescharacteristic
630C4#1062255311yescharacteristic
631C4#1062257211yescharacteristic
632C4#1062260211yescharacteristic
633C4#1062260711yescharacteristic
634C2#1306686011yescharacteristic
635C2#1306862012yes—
636C2#1306892212yes—
637C2#1306941611yescharacteristic
638C2#1306943111yescharacteristic
639C2#1306970511yescharacteristic
640C2#1306971711yescharacteristic
641C2#1306975612yes—
642C2#1307002812yes—
643C2#1307015111yescharacteristic
644C2#1307015611yescharacteristic
subgroupG/H
centerC24D4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#340C2
socle, prime radicalC24×C11C2×D4
cosocleC23×C4×C11C23
hypercenterC2×#340D11
hypocenterC11#11050
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
23. #10622587C4semidirect
166. C2×Dic22C4⋊C4semidirect
272. C2×Dic11#103semidirect
519. C11#11050semidirect

Maximal subgroups

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

subgroupindex
C22×#668802
C22×#668742
C2×#106225872
C2×#106225892
C2×#106221672
C2×#106221882
C2×C11×#3402
#1105011