Finite Group Databasebeta

← #14788091

Subgroups — #14788091

Order 2816.

1198 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623001C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3C2×#10622632C211yesmaximal, characteristic, complemented
4#13069812C212yesmaximal, complemented
5#13069619C212yesmaximal
6#13069564C211yesmaximal, characteristic, complemented
7#13069539C211yesmaximal, characteristic, complemented
8#13068974C212yesmaximal, complemented
9#13068883C212yesmaximal, complemented
10#13068596C211yesmaximal, characteristic, complemented
11C4×C11×#121C211yesmaximal, characteristic
12C2×C11×#121C2211yescharacteristic
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×#4324C2212yes—
17C2×#66979—21no—
18C2×#66977—21no—
19C2×#66977C2212yes—
20#10623001—24no—
21#10623001—24no—
22C2×#66923—21no—
23C2×#66922C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C4×Dic22—21no—
26C2×C4×Dic22C2212yes—
27C11×#390C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#388—21no—
30C11×#386—21no—
31C11×#380C2211yescharacteristic
32C4×C11×C4⋊C4C2211yescharacteristic
33C4×C11×C22⋊C4—21no—
34C2×#66896C2212yes—
35C2×C22⋊(C11⋊C8)C2212yes—
36#10622632—24no—
37#10622621—24no—
38C2×#66874C2212yes—
39C2×#66874C2212yes—
40C2×#66874C2212yes—
41C2×#66872C2212yes—
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44#10622167C2212yes—
45#10622167C2212yes—
46#10622162C2212yes—
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×Dic22—21no—
54C22×Dic22C2312yes—
55C11×#121—22no—
56C11×#121—22no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11—44no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4C2311yescharacteristic
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—21no—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11—21no—
72C2×C42×C11D411yescharacteristic
73C2×C42×C11D411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C22⋊Dic11—22no—
77C2×#4324—24no—
78C2×#4324—24no—
79C2×#4324—42no—
80#66979—28no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2312yes—
85#66977—28no—
86#66977—24no—
87#66977—24no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×C4×Dic11—22no—
91C22×C11⋊C8C2312yes—
92C22×C11⋊C8C2312yes—
93#66923—28no—
94#66922—22no—
95#66922—22no—
96#66922D414yescomplemented
97#66922D414yescomplemented
98C4×Dic22—28no—
99C4×Dic22—24no—
100C4×Dic22—24no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104#66896—24no—
105C22⋊(C11⋊C8)—42no—
106#66874—24no—
107#66874—24no—
108#66874—42no—
109#66872—24no—
110C4⋊(C11⋊C8)—22no—
111C4⋊(C11⋊C8)—22no—
112#24151—111nomaximal, Sylow
113C24×C11—21no—
114C24×C11C2×D411yescharacteristic
115C2×D4×C11—24no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—21no—
120C2×D4×C11—21no—
121C2×D4×C11—42no—
122C2×D4×C11—42no—
123C2×D4×C11#4112yes—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—41no—
137C22×C4×C11—41no—
138C22×C4×C11—42no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11SD1614yescomplemented
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—22no—
149C22×Dic11—22no—
150C2×Dic22—24no—
151C2×Dic22—22no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—42no—
157C2×Dic22—42no—
158C2×Dic22C2×D414yes—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4#4112yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—42no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C42×C11—22no—
172C42×C11—22no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—42no—
176C42×C11C2×D412yes—
177C42×C11C2×D412yes—
178C22⋊Dic11—28no—
179#4324—48no—
180C4⋊Dic11—24no—
181C4⋊Dic11—24no—
182C4⋊Dic11—24no—
183C4⋊Dic11—22no—
184C4⋊Dic11C2×D414yes—
185Dic11⋊C4—28no—
186Dic11⋊C4—28no—
187C4×Dic11—28no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×#533—111no—
195C2×#476—111no—
196C2×#461—111no—
197C4×#121D1111yescharacteristic
198#2035—112no—
199#2000—112no—
200#1987—111no—
201#1981—111no—
202#1880—112no—
203#1865—112no—
204#1797—111no—
205C23×C11—21no—
206C23×C11—21no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—22no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11C2×SD1612yes—
219C23×C11C22×D411yescharacteristic
220D4×C11—22no—
221D4×C11—22no—
222D4×C11—48no—
223D4×C11—41no—
224D4×C11—41no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—28no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—44no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—84no—
251C2×C4×C11#12012yes—
252C2×C4×C11#12012yes—
253C2×C4×C11C2×SD1612yes—
254C2×C4×C11C2×SD1612yes—
255C2×C4×C11#13712yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C112−1+411yescharacteristic
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268Dic22—24no—
269Dic22—24no—
270Dic22—48no—
271Dic22—42no—
272Dic22—42no—
273C11⋊C8—42no—
274C11⋊C8—42no—
275C22×SD16—112no—
276#533—224no—
277#533—224no—
278C2×C4⋊Q8—111no—
279C2×C4⋊Q8—111no—
280C2×#125—221no—
281C2×C22⋊Q8—112no—
282C2×C22⋊Q8—221no—
283C2×#121C2×D1111yescharacteristic
284C2×C4×Q8—112no—
285C2×C4×Q8—221no—
286C2×C4×D4—21no—
287C2×C4×D4C2×D1111yescharacteristic
288C2×#117—221no—
289C22×C42C2×D1111yescharacteristic
290#476—224no—
291#461—224no—
292C2×#106—112no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×#103—112no—
296C2×#103—112no—
297C2×#103—112no—
298C2×#102—112no—
299C2×C22⋊C8—112no—
300#390C2×D1111yescharacteristic
301#389C2×D1111yescharacteristic
302#388—21no—
303#386—21no—
304#380C2×D1111yescharacteristic
305C4×C4⋊C4C2×D1111yescharacteristic
306C4×C22⋊C4—21no—
307#340—112no—
308#340—112no—
309#336—112no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—41no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—42no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11C2×#12011yescharacteristic
325C22×C11#52511yescharacteristic
326C22×C11#53711yescharacteristic
327C22×C11C22×SD1611yescharacteristic
328C22×C11C2×#13711yescharacteristic
329C22×C11#57511yescharacteristic
330C22×C11#57511yescharacteristic
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11#44814yes—
339C4×C11#54611yescharacteristic
340C4×C11#54711yescharacteristic
341C4×C11#54811yescharacteristic
342C4×C11#55011yescharacteristic
343Dic11—44no—
344Dic11—44no—
345C22×Q8—112no—
346C22×Q8—221no—
347C22×D4—21no—
348C22×D4C22×D1111yescharacteristic
349C23×C4—21no—
350C23×C4C22⋊D1111yescharacteristic
351C23×C4C22⋊D1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353C2×SD16—224no—
354C2×SD16—224no—
355C2×SD16—442no—
356C22×C8—112no—
357C22×C8—112no—
358C4⋊Q8—114no—
359C4⋊Q8—114no—
360C4⋊Q8—222no—
361C4⋊Q8—222no—
362#125—228no—
363C22⋊Q8—224no—
364C22⋊Q8—224no—
365C22⋊Q8—228no—
366#121—22no—
367#121—22no—
368C4×Q8—224no—
369C4×Q8—224no—
370C4×Q8—228no—
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—44no—
374#117—228no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C22⋊C4—21no—
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—222no—
391C2×C42—22no—
392C2×C42—22no—
393C2×C42—21no—
394C2×C42—222no—
395C2×C42C22⋊D1111yescharacteristic
396C2×C42C22⋊D1111yescharacteristic
397C2×C42C22×D1111yescharacteristic
398C2×C42C22×D1111yescharacteristic
399#106—224no—
400C4⋊C8—222no—
401C4⋊C8—222no—
402#103—224no—
403#103—224no—
404#103—442no—
405#102—224no—
406C22⋊C8—442no—
407#95—21no—
408#95—21no—
409#95—21no—
410C2×C11—42no—
411C2×C11—82no—
412C2×C11#240711yescharacteristic
413C2×C11C2×#44811yescharacteristic
414C2×C11#300511yescharacteristic
415C2×C11#310111yescharacteristic
416C2×C11#311611yescharacteristic
417C2×C11#324611yescharacteristic
418C2×C11#325211yescharacteristic
419C24—21no—
420C24C2×C22⋊D1111yescharacteristic
421C2×Q8—114no—
422C2×Q8—224no—
423C2×Q8—222no—
424C2×Q8—222no—
425C2×Q8—222no—
426C2×Q8—222no—
427C2×Q8—222no—
428C2×Q8—442no—
429C2×Q8—442no—
430C2×D4—24no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4#433912yes—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4#432414yescomplemented
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C2×C22⋊D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465SD16—448no—
466C2×C8—222no—
467C2×C8—222no—
468C2×C8—222no—
469C2×C8—222no—
470C2×C8—222no—
471C2×C8—222no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4—114no—
479C4⋊C4—228no—
480C4⋊C4—228no—
481C4⋊C4—224no—
482C4⋊C4—224no—
483C4⋊C4—224no—
484C4⋊C4—222no—
485C4⋊C4#433912yes—
486C22⋊C4—24no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C22⋊C4—42no—
490C22⋊C4—42no—
491C22⋊C4—228no—
492C42—22no—
493C42—22no—
494C42—21no—
495C42—21no—
496C42—42no—
497C42—228no—
498C42D4×D1112yes—
499C42D4×D1112yes—
500C11#2415111yescharacteristic, complemented, Sylow
501C23—21no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23—22no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23C2×#432412yes—
515C23C22×C22⋊D1111yescharacteristic
516Q8—224no—
517Q8—224no—
518Q8—448no—
519Q8—442no—
520Q8—442no—
521D4—22no—
522D4—22no—
523D4—48no—
524D4—41no—
525D4—41no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—28no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—44no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—84no—
552C2×C4—224no—
553C2×C4—224no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4C2×#432412yes—
559C2×C4C2×#432412yes—
560C2×C4#6699012yes—
561C2×C4#6699012yes—
562C2×C4#6700412yes—
563C2×C4C2×#433911yescharacteristic
564C2×C4C2×#433911yescharacteristic
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4C2×D4×D1111yescharacteristic
567C2×C4#6704211yescharacteristic
568C2×C4#6704311yescharacteristic
569C8—442no—
570C8—442no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—42no—
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22#1062332211yescharacteristic
586C22C22×#432411yescharacteristic
587C22C2×#6699011yescharacteristic
588C22#1062335311yescharacteristic
589C22#1062335311yescharacteristic
590C22C2×#6700411yescharacteristic
591C22#1062336411yescharacteristic
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—444no—
600C4—444no—
601C4#1062265314yes—
602C4#1062308111yescharacteristic
603C4#1062308211yescharacteristic
604C4#1062308311yescharacteristic
605C4#1062308411yescharacteristic
606C2—42no—
607C2—82no—
608C2#1307196111yescharacteristic
609C2C2×#1062265311yescharacteristic
610C2#1307785611yescharacteristic
611C2#1307862411yescharacteristic
612C2#1307877811yescharacteristic
613C2#1307993211yescharacteristic
614C2#1307998911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC4×#121D11
hypocenterC11#24151
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623001C2semidirect
2. C2×#10622621C2semidirect
3. C2×#10622632C2semidirect
4. #13069812C2semidirect
6. #13069564C2semidirect
7. #13069539C2semidirect
8. #13068974C2semidirect
9. #13068883C2semidirect
10. #13068596C2semidirect
96. #66922D4semidirect
97. #66922D4semidirect
141. C22×C4×C11SD16semidirect
458. C22×C4#4324semidirect
500. C11#24151semidirect

Maximal subgroups

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

subgroupindex
C2×#106230012
C2×#106226212
C2×#106226322
#130698122
#130696192
#130695642
#130695392
#130689742
#130688832
#130685962
C4×C11×#1212
#2415111