Finite Group Databasebeta

← #14790075

Subgroups — #14790075

Order 2816.

1036 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078409C211yesmaximal, characteristic, complemented
2C4×#67002C211yesmaximal, characteristic
3#13073790C211yesmaximal, characteristic, complemented
4#13069963C212yesmaximal, complemented
5#13069769C212yesmaximal, complemented
6#13069606C211yesmaximal, characteristic, complemented
7#13069561C211yesmaximal, characteristic, complemented
8#13068992C212yesmaximal
9#13068849C212yesmaximal, complemented
10#13068636C211yesmaximal, characteristic, complemented
11C11×#3503C211yesmaximal, characteristic, complemented
12Q82×C11—21no—
13C11×#557—21no—
14C11×#554—21no—
15C11×#554—22no—
16D4×Q8×C11—22no—
17D4×Q8×C11—21no—
18C11×#544—22no—
19C11×#544C2212yes—
20C11×#533—21no—
21C11×#533C2211yescharacteristic
22C2×C11×C4⋊Q8—21no—
23C2×C11×C4⋊Q8C2211yescharacteristic
24C11×#520C2212yes—
25C4×C11×#41C2211yescharacteristic
26C2×#67002C2211yescharacteristic
27C2×C4×D44C2211yescharacteristic
28C2×#66901C2212yes—
29#10622845C2211yescharacteristic
30#10622844—22no—
31#10622700—21no—
32#10622697—21no—
33#10622679—22no—
34#10622639—21no—
35C4×#4325—21no—
36#10622627—21no—
37C4×#4323—21no—
38#10622614C2212yes—
39#10622614C2211yescharacteristic
40#10622608C2212yes—
41#10622608C2211yescharacteristic
42#10622601C2212yes—
43#10622600—22no—
44#10622590C2212yes—
45C4×C4⋊Dic11C2211yescharacteristic
46#10622537C2211yescharacteristic
47C4×#4318C2211yescharacteristic
48#10622170C2212yes—
49#10622170C2212yes—
50#10622170C2212yes—
51#10622168C2212yes—
52#10622168C2212yes—
53C2×C11×#41C2311yescharacteristic
54C22×Q8×C11—22no—
55C22×Q8×C11D412yes—
56C22×D44C2311yescharacteristic
57C22×C4×D11—21no—
58C11×C4⋊Q8—22no—
59C11×C4⋊Q8—22no—
60C11×C4⋊Q8—24no—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8—21no—
64C11×C4⋊Q8—21no—
65C11×C4⋊Q8—21no—
66C11×C4⋊Q8—21no—
67C11×C4⋊Q8D411yescharacteristic
68C11×C4⋊Q8D411yescharacteristic
69C11×#125—24no—
70C11×#125—22no—
71C11×#125—22no—
72C11×#125D412yes—
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×C22⋊Q8—24no—
76C11×C22⋊Q8—24no—
77C11×C22⋊Q8—21no—
78C11×C22⋊Q8—21no—
79C11×C22⋊Q8—24no—
80C4×Q8×C11—22no—
81C4×Q8×C11—22no—
82C4×Q8×C11—22no—
83C4×Q8×C11—21no—
84C4×Q8×C11—21no—
85C4×Q8×C11D411yescharacteristic
86C4×Q8×C11D411yescharacteristic
87C4×D4×C11—22no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11—24no—
91C4×D4×C11D411yescharacteristic
92C4×D4×C11D411yescharacteristic
93C11×#117—22no—
94C11×#117—21no—
95C11×#117C2311yescharacteristic
96C11×#117C2312yes—
97C2×C11×C4⋊C4—22no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4D412yes—
100C2×C11×C4⋊C4C2312yes—
101C2×C42×C11—21no—
102C2×C42×C11C2311yescharacteristic
103#67002—22no—
104#67002Q814yescomplemented
105C2×#4325—21no—
106C2×#4323—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—24no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4×Dic11C2312yes—
112C2×#4318C2311yescharacteristic
113C2×#4318C2312yes—
114C2×#4318C2311yescharacteristic
115C4×D44—21no—
116C4×D44—21no—
117C4×D44—21no—
118C4×D44—21no—
119#66901—24no—
120#66899—21no—
121#66896—21no—
122C11⋊#95—21no—
123C11⋊#95—24no—
124#66873—21no—
125#66873—21no—
126#66873—22no—
127#66873—22no—
128#66872—21no—
129#66872—22no—
130#66871—21no—
131#66871—22no—
132C4⋊(C11⋊C8)—21no—
133C4⋊(C11⋊C8)—21no—
134#66867—21no—
135C4×C11⋊C8—21no—
136#24321—111nomaximal, Sylow
137C23×D11—21no—
138C11×#41—21no—
139C11×#41—21no—
140C11×#41C2×Q812yes—
141C11×#41#4112yes—
142C2×Q8×C11—24no—
143C2×Q8×C11—21no—
144C2×Q8×C11—22no—
145C2×Q8×C11—21no—
146C2×Q8×C11—22no—
147C2×Q8×C11—82no—
148C2×Q8×C11—84no—
149C2×Q8×C11C2×D411yescharacteristic
150C2×D4×C11—21no—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—21no—
153C22×C4×C11—24no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—22no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44C2×Q812yescomplemented
168C2×C4×D11—44no—
169C2×C4×D11—41no—
170C2×C4×D11—41no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4—22no—
185C11×C4⋊C4C2×D412yes—
186C11×C4⋊C4C2×D411yescharacteristic
187C11×C4⋊C4C2×D412yes—
188C11×C4⋊C4C2×D411yescharacteristic
189C11×C22⋊C4—24no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—21no—
192C11×C22⋊C4—21no—
193C11×C22⋊C4—21no—
194C42×C11—24no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198C42×C11—22no—
199C42×C11C2×D411yescharacteristic
200C42×C11C2×D411yescharacteristic
201C42×C11C2×D411yescharacteristic
202C42×C11C2×D411yescharacteristic
203#4325—24no—
204#4323—24no—
205(C2×D11)⋊C4—41no—
206(C2×D11)⋊C4—41no—
207(C2×D11)⋊C4—84no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—42no—
211C4×Dic11—22no—
212C4×Dic11—22no—
213#4318—21no—
214#4318—22no—
215#4318—21no—
216#4318—22no—
217#4318—21no—
218#4318C2×Q812yescomplemented
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—22no—
222#3503D1111yescharacteristic, complemented
223#3077—111no—
224C4×AGL(1,ℤ/8)—111no—
225#2563—111no—
226#2061—112no—
227#2027—112no—
228#1997—111no—
229#1986—111no—
230#1883—112no—
231#1860—112no—
232#1806—111no—
233C23×C11—21no—
234C23×C11C22×D411yescharacteristic
235C22×D11—22no—
236C22×D11—42no—
237C22×D11—42no—
238C22×D11—41no—
239C22×D11—41no—
240Q8×C11—21no—
241Q8×C11—44no—
242Q8×C11—42no—
243Q8×C11—42no—
244Q8×C11—82no—
245Q8×C11—84no—
246Q8×C11C22⋊Q812yes—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—21no—
250D4×C11C22⋊Q812yes—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—41no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11—44no—
264C2×C4×C11—84no—
265C2×C4×C11#12011yescharacteristic
266C2×C4×C11#12011yescharacteristic
267C2×C4×C11#12011yescharacteristic
268C2×C4×C11#12011yescharacteristic
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C22×Q811yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C112−1+411yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—41no—
279C2×Dic11—42no—
280D44—22no—
281D44—22no—
282D44—41no—
283D44—41no—
284C4×D11—82no—
285C4×D11—82no—
286C11⋊C8—22no—
287C11⋊C8—41no—
288C11⋊C8—42no—
289C2×AGL(1,ℤ/8)—111no—
290Q82—21no—
291#557—21no—
292#554—21no—
293#554—22no—
294D4×Q8—22no—
295D4×Q8—21no—
296#544—22no—
297#544C2×D1112yes—
298#533—21no—
299#533C2×D1111yescharacteristic
300C2×C4⋊Q8—21no—
301C2×C4⋊Q8C2×D1111yescharacteristic
302#520C2×D1112yes—
303C4×#41C2×D1111yescharacteristic
304C2×C4×D4—111no—
305#478—222no—
306#476—221no—
307#474—221no—
308#442—221no—
309#440—221no—
310C4×SD16—221no—
311C4×D8—221no—
312#428—112no—
313#428—111no—
314#423—111no—
315C2×#104—112no—
316#418—112no—
317#418—111no—
318#417—111no—
319C4×M16—111no—
320#393—222no—
321#390—112no—
322#382—112no—
323#380—222no—
324C4×C4⋊C4—111no—
325#343—112no—
326#343—112no—
327#339—112no—
328#339—112no—
329#339—112no—
330C22×C11—21no—
331C22×C11—21no—
332C22×C11—22no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11C2×#12011yescharacteristic
336C22×C11#54811yescharacteristic
337C22×C11D4×Q811yescharacteristic
338C2×D11—44no—
339C2×D11—42no—
340C2×D11—82no—
341C2×D11—81no—
342C2×D11—81no—
343C4×C11—22no—
344C4×C11—21no—
345C4×C11—21no—
346C4×C11—21no—
347C4×C11—41no—
348C4×C11—42no—
349C4×C11—41no—
350C4×C11—44no—
351C4×C11—42no—
352C4×C11#45412yes—
353C4×C11C2×C22⋊Q811yescharacteristic
354C4×C11#53611yescharacteristic
355C4×C11#54811yescharacteristic
356C4×C11D4×Q811yescharacteristic
357Dic11—82no—
358Dic11—81no—
359C2×#41C22×D1111yescharacteristic
360C22×Q8—22no—
361C22×Q8C22⋊D1112yes—
362C22×D4—111no—
363C23×C4—221no—
364AGL(1,ℤ/8)—114no—
365AGL(1,ℤ/8)—222no—
366C2×SD16—221no—
367C2×D8—221no—
368C2×M16—111no—
369C2×M16—111no—
370C2×M16—112no—
371C4⋊Q8—22no—
372C4⋊Q8—22no—
373C4⋊Q8—24no—
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4⋊Q8—21no—
377C4⋊Q8—21no—
378C4⋊Q8—21no—
379C4⋊Q8—21no—
380C4⋊Q8C22⋊D1111yescharacteristic
381C4⋊Q8C22⋊D1111yescharacteristic
382#125—24no—
383#125—22no—
384#125—22no—
385#125C22⋊D1112yes—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—24no—
389C22⋊Q8—24no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—24no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—22no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8C22⋊D1111yescharacteristic
399C4×Q8C22⋊D1111yescharacteristic
400C4×D4—22no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—24no—
404C4×D4—221no—
405C4×D4—221no—
406C4×D4—221no—
407C4×D4—221no—
408C4×D4C22⋊D1111yescharacteristic
409C4×D4C22⋊D1111yescharacteristic
410#117—22no—
411#117—21no—
412#117C22×D1111yescharacteristic
413#117C22×D1112yes—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22⋊D1112yes—
419C2×C4⋊C4C22×D1112yes—
420C2×C22⋊C4—221no—
421C2×C22⋊C4—224no—
422C2×C42—21no—
423C2×C42—112no—
424C2×C42C22×D1111yescharacteristic
425#107—221no—
426#107—222no—
427#106—221no—
428#106—222no—
429C4⋊C8—221no—
430C4⋊C8—221no—
431#104—224no—
432#103—221no—
433#102—221no—
434#102—221no—
435#102—221no—
436#102—222no—
437#102—222no—
438#97—221no—
439C4×C8—221no—
440#95—221no—
441#95—224no—
442C2×C11—21no—
443C2×C11—21no—
444C2×C11—42no—
445C2×C11#240911yescharacteristic
446C2×C11C2×#45411yescharacteristic
447C2×C11#301911yescharacteristic
448D11—82no—
449C24—221no—
450#41—21no—
451#41—21no—
452#41Q8×D1112yes—
453#41#434312yes—
454C2×Q8—24no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—21no—
458C2×Q8—22no—
459C2×Q8—82no—
460C2×Q8—84no—
461C2×Q8C2×C22⋊D1111yescharacteristic
462C2×D4—21no—
463C2×D4—112no—
464C2×D4—221no—
465C2×D4—221no—
466C2×D4—221no—
467C2×D4—221no—
468C2×D4—221no—
469C2×D4C2×C22⋊D1111yescharacteristic
470C22×C4—21no—
471C22×C4—24no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—221no—
475C22×C4—222no—
476C22×C4—444no—
477C22×C4—441no—
478C22×C4—441no—
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1114yes—
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C23×D1111yescharacteristic
483SD16—224no—
484D8—224no—
485M16—112no—
486M16—221no—
487M16—222no—
488M16—221no—
489M16—221no—
490M16—222no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—222no—
494C4⋊C4—24no—
495C4⋊C4—24no—
496C4⋊C4—24no—
497C4⋊C4—24no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—442no—
511C4⋊C4C2×C22⋊D1112yes—
512C4⋊C4C2×C22⋊D1111yescharacteristic
513C4⋊C4C2×C22⋊D1112yes—
514C4⋊C4C2×C22⋊D1111yescharacteristic
515C22⋊C4—24no—
516C22⋊C4—22no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—441no—
521C22⋊C4—441no—
522C22⋊C4—884no—
523C42—24no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—22no—
528C42—222no—
529C42—222no—
530C42C2×C22⋊D1111yescharacteristic
531C42C2×C22⋊D1111yescharacteristic
532C42C2×C22⋊D1111yescharacteristic
533C42C2×C22⋊D1111yescharacteristic
534C11#2432111yescharacteristic, complemented, Sylow
535C23—21no—
536C23—222no—
537C23—442no—
538C23—442no—
539C23—441no—
540C23—441no—
541C23C22×C22⋊D1111yescharacteristic
542Q8—21no—
543Q8—44no—
544Q8—42no—
545Q8—42no—
546Q8—82no—
547Q8—84no—
548Q8#6699912yes—
549D4—22no—
550D4—22no—
551D4—21no—
552D4—222no—
553D4—222no—
554D4—441no—
555D4—441no—
556D4#6699912yes—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—44no—
570C2×C4—84no—
571C2×C4—442no—
572C2×C4—442no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—441no—
576C2×C4—882no—
577C2×C4—882no—
578C2×C4#6700611yescharacteristic
579C2×C4#6700611yescharacteristic
580C2×C4#6700611yescharacteristic
581C2×C4#6700611yescharacteristic
582C2×C4C2×Q8×D1111yescharacteristic
583C2×C4C2×#434311yescharacteristic
584C2×C4#6704011yescharacteristic
585C2×C4#6704011yescharacteristic
586C2×C4C22×C22⋊D1111yescharacteristic
587C2×C4C22×C22⋊D1111yescharacteristic
588C8—222no—
589C8—441no—
590C8—442no—
591C22—21no—
592C22—21no—
593C22—22no—
594C22—41no—
595C22—41no—
596C22—444no—
597C22—442no—
598C22—882no—
599C22—881no—
600C22—881no—
601C22Q8×C22⋊D1111yescharacteristic
602C22#1062334811yescharacteristic
603C22C2×#6700611yescharacteristic
604C4—22no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—41no—
609C4—42no—
610C4—41no—
611C4—44no—
612C4—42no—
613C4—882no—
614C4—881no—
615C4#1062285812yes—
616C4C2×#6699911yescharacteristic
617C4Q8×C22⋊D1111yescharacteristic
618C4#1062334711yescharacteristic
619C4#1062334811yescharacteristic
620C2—21no—
621C2—21no—
622C2—42no—
623C2—882no—
624C2#1307197511yescharacteristic
625C2C2×#1062285811yescharacteristic
626C2#1307797311yescharacteristic
subgroupG/H
centerC22C2×#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#3503C2
socleC22×C11C2×#120
prime radicalC2×#67002C22
hypercenter#3503D11
hypocenterC11#24321
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #13078409C2semidirect
3. #13073790C2semidirect
4. #13069963C2semidirect
5. #13069769C2semidirect
6. #13069606C2semidirect
7. #13069561C2semidirect
9. #13068849C2semidirect
10. #13068636C2semidirect
11. C11×#3503C2semidirect
104. #67002Q8semidirect
167. C2×D44C2×Q8semidirect
218. #4318C2×Q8semidirect
222. #3503D11semidirect
534. C11#24321semidirect

Maximal subgroups

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

subgroupindex
#130784092
C4×#670022
#130737902
#130699632
#130697692
#130696062
#130695612
#130689922
#130688492
#130686362
C11×#35032
#2432111