Finite Group Databasebeta

← #14764384

Subgroups — #14764384

Order 2816.

762 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071239C211yesmaximal, characteristic
2#13071225C211yesmaximal, characteristic
3#13069386C211yesmaximal, characteristic, complemented
4#13069386C211yesmaximal, characteristic, complemented
5#13069380C211yesmaximal, characteristic, complemented
6#13069375C211yesmaximal, characteristic, complemented
7#13068817C211yesmaximal, characteristic
8#13068817C211yesmaximal, characteristic
9#13068811C211yesmaximal, characteristic
10#13068806C211yesmaximal, characteristic
11#13068784C211yesmaximal, characteristic, complemented
12#13068780C211yesmaximal, characteristic, complemented
13#13068750C211yesmaximal, characteristic, complemented
14#13068744C211yesmaximal, characteristic, complemented
15C2×C11×#433C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C11×#433C418yescomplemented
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622825C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×#66882C2211yescharacteristic
30C2×#66882C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×#66881C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36#10622598—21no—
37#10622598—21no—
38#10622594—21no—
39#10622594—21no—
40#10622564—21no—
41#10622564—21no—
42#10622563—21no—
43#10622563—21no—
44#10622549C2211yescharacteristic
45#10622549C2211yescharacteristic
46#10622549C2211yescharacteristic
47#10622548C2211yescharacteristic
48#10622548C2211yescharacteristic
49#10622548C2211yescharacteristic
50C4×C4⋊Dic11C2211yescharacteristic
51C4×C4⋊Dic11C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#117C2×C414yes—
67C11×#117Q814yes—
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C22⋊C4D411yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77#66979—41no—
78#66979—41no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—41no—
87C2×C4⋊Dic11—41no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C11×C4⋊C8C2×C414yescomplemented
100C11×C4⋊C8C2×C414yescomplemented
101C11×C22⋊C8C2×C414yes—
102C11×C22⋊C8C2×C414yes—
103C11×#97C2×C414yescomplemented
104C4×C8×C11C2×C414yescomplemented
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115#66882—41no—
116#66882—41no—
117#66882—41no—
118#66882—41no—
119#66881—41no—
120#66881—41no—
121#66881—41no—
122#66881—41no—
123#21992—111nomaximal, Sylow
124C24×C11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×Q812yes—
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—42no—
146C22×Dic11—81no—
147C22×Dic11—81no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C22×C412yes—
157C2×C8×C11C22×C412yes—
158C2×C8×C11C22×C412yes—
159C2×C8×C11C22×C412yes—
160C11×C4⋊C4C4⋊C414yes—
161C11×C4⋊C4C4⋊C414yes—
162C11×C22⋊C4C4⋊C414yes—
163C11×C22⋊C4C4⋊C414yes—
164C42×C11C22×C412yes—
165C42×C11C22×C412yes—
166C42×C11C2×Q812yes—
167C42×C11C2×Q812yes—
168C22⋊Dic11—42no—
169C22⋊Dic11—81no—
170C22⋊Dic11—81no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—42no—
188C4⋊Dic11—81no—
189C4⋊Dic11—81no—
190C4⋊Dic11—81no—
191C4⋊Dic11—81no—
192C4⋊Dic11—81no—
193C4⋊Dic11—81no—
194C4×Dic11—42no—
195C4×Dic11—81no—
196C4×Dic11—81no—
197C2×#433D1111yescharacteristic
198#2317—111no—
199#2314—111no—
200#1949—111no—
201#1949—111no—
202#1948—111no—
203#1947—111no—
204#1854—111no—
205#1854—111no—
206#1853—111no—
207#1852—111no—
208#1847—111no—
209#1846—111no—
210#1836—111no—
211#1834—111no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11C2×C4⋊C412yes—
219C23×C11C22×D411yescharacteristic
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11C2×C4⋊C412yes—
235C2×C4×C11C2×C4⋊C412yes—
236C2×C4×C11C2×C4⋊C412yes—
237C2×C4×C11C2×C4⋊C412yes—
238C2×C4×C11C2×C4⋊C412yes—
239C2×C4×C11C23×C411yescharacteristic
240C2×C4×C11C22×Q811yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—84no—
270C8×C11—22no—
271C8×C11—22no—
272C8×C11—22no—
273C8×C11—22no—
274C2×#117—111no—
275C2×#117C2×D1111yescharacteristic
276C22×C4⋊C4—111no—
277#433Dic1118yescomplemented
278C2×#107—111no—
279C2×#107—111no—
280C2×#107—111no—
281C2×#107—111no—
282C2×#106—111no—
283C2×#106—111no—
284C2×#106—111no—
285C2×#106—111no—
286C2×C4⋊C8C2×D1111yescharacteristic
287C2×C4⋊C8C2×D1111yescharacteristic
288C2×C22⋊C8C2×D1111yescharacteristic
289C2×C22⋊C8C2×D1111yescharacteristic
290C2×#97C2×D1111yescharacteristic
291C2×C4×C8C2×D1111yescharacteristic
292#389—221no—
293#389—221no—
294#388—221no—
295#388—221no—
296#387—221no—
297#387—221no—
298#385—221no—
299#385—221no—
300#384—111no—
301#384—111no—
302#384—111no—
303#382—111no—
304#382—111no—
305#382—111no—
306#380—111no—
307#380—111no—
308C4×C4⋊C4—111no—
309C4×C4⋊C4—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318C22×C11—22no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11C22×C4⋊C411yescharacteristic
326C22×C11#53511yescharacteristic
327C22×C11#53611yescharacteristic
328C22×C11#57611yescharacteristic
329C22×C11#57711yescharacteristic
330C22×C11#57711yescharacteristic
331C22×C11#57811yescharacteristic
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—22no—
337C4×C11#52011yescharacteristic
338C4×C11#52011yescharacteristic
339C4×C11#54411yescharacteristic
340C4×C11#54411yescharacteristic
341Dic11—81no—
342Dic11—81no—
343Dic11—81no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347Dic11—81no—
348Dic11—81no—
349C23×C4—221no—
350C23×C4C22×D1111yescharacteristic
351C22×C8C22×D1111yescharacteristic
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355#117—441no—
356#117—441no—
357#117Dic2214yes—
358#117C2×Dic1114yes—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—441no—
375C2×C4⋊C4—441no—
376C2×C4⋊C4D4411yescharacteristic
377C2×C4⋊C4D4411yescharacteristic
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4D4411yescharacteristic
382C2×C22⋊C4D4411yescharacteristic
383C2×C42—221no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1111yescharacteristic
388#107—441no—
389#107—441no—
390#107—441no—
391#107—441no—
392#106—441no—
393#106—441no—
394#106—441no—
395#106—441no—
396C4⋊C8C2×Dic1114yescomplemented
397C4⋊C8C2×Dic1114yescomplemented
398C22⋊C8C2×Dic1114yes—
399C22⋊C8C2×Dic1114yes—
400#97C2×Dic1114yescomplemented
401C4×C8C2×Dic1114yescomplemented
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412C2×C11—42no—
413C2×C11#231711yescharacteristic
414C2×C11#291211yescharacteristic
415C2×C11#291311yescharacteristic
416C2×C11#322411yescharacteristic
417C2×C11#322511yescharacteristic
418C2×C11#324111yescharacteristic
419C2×C11#324211yescharacteristic
420C24C2×D4411yescharacteristic
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—221no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—442no—
434C22×C4—881no—
435C22×C4—881no—
436C22×C4C2×Dic2212yes—
437C22×C4C2×D4411yescharacteristic
438C22×C4C2×D4411yescharacteristic
439C22×C4C2×D4411yescharacteristic
440C22×C4C2×D4411yescharacteristic
441C22×C4C2×D4411yescharacteristic
442C22×C4C22×Dic1112yes—
443C22×C4C23×D1111yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8C22×Dic1112yes—
453C2×C8C22×Dic1112yes—
454C2×C8C22×Dic1112yes—
455C2×C8C22×Dic1112yes—
456C4⋊C4—221no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—442no—
473C4⋊C4—881no—
474C4⋊C4—881no—
475C4⋊C4—881no—
476C4⋊C4—881no—
477C4⋊C4—881no—
478C4⋊C4—881no—
479C4⋊C4C4⋊Dic1114yes—
480C4⋊C4C4⋊Dic1114yes—
481C22⋊C4—442no—
482C22⋊C4—881no—
483C22⋊C4—881no—
484C22⋊C4C4⋊Dic1114yes—
485C22⋊C4C4⋊Dic1114yes—
486C42—442no—
487C42—881no—
488C42—881no—
489C42C2×Dic2212yes—
490C42C2×Dic2212yes—
491C42C22×Dic1112yes—
492C42C22×Dic1112yes—
493C11#2199211yescharacteristic, complemented, Sylow
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23C2×C4⋊Dic1112yes—
501C23C22×D4411yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—441no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—441no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—884no—
541C2×C4C2×C4⋊Dic1112yes—
542C2×C4C2×C4⋊Dic1112yes—
543C2×C4C2×C4⋊Dic1112yes—
544C2×C4C2×C4⋊Dic1112yes—
545C2×C4C2×C4⋊Dic1112yes—
546C2×C4C22×Dic2211yescharacteristic
547C2×C4#6704211yescharacteristic
548C2×C4#6704211yescharacteristic
549C2×C4#6704311yescharacteristic
550C2×C4#6704311yescharacteristic
551C2×C4C23×Dic1111yescharacteristic
552C8—22no—
553C8—22no—
554C8—22no—
555C8—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22#1062305611yescharacteristic
564C22#1062305711yescharacteristic
565C22#1062328211yescharacteristic
566C22#1062328211yescharacteristic
567C22#1062328311yescharacteristic
568C22#1062328411yescharacteristic
569C22C22×C4⋊Dic1111yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—22no—
575C4—881no—
576C4—881no—
577C4—881no—
578C4—881no—
579C4—881no—
580C4—881no—
581C4—881no—
582C4—881no—
583C4#1062305011yescharacteristic
584C4#1062305011yescharacteristic
585C4#1062335811yescharacteristic
586C4#1062335811yescharacteristic
587C2—42no—
588C2#1307123911yescharacteristic
589C2#1307721111yescharacteristic
590C2#1307721611yescharacteristic
591C2#1307971211yescharacteristic
592C2#1307972711yescharacteristic
593C2#1307987111yescharacteristic
594C2#1307988611yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#433C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#433D11
hypocenterC11#21992
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
3. #13069386C2semidirect
4. #13069386C2semidirect
5. #13069380C2semidirect
6. #13069375C2semidirect
11. #13068784C2semidirect
12. #13068780C2semidirect
13. #13068750C2semidirect
14. #13068744C2semidirect
19. C11×#433C4semidirect
99. C11×C4⋊C8C2×C4semidirect
100. C11×C4⋊C8C2×C4semidirect
103. C11×#97C2×C4semidirect
104. C4×C8×C11C2×C4semidirect
277. #433Dic11semidirect
396. C4⋊C8C2×Dic11semidirect
397. C4⋊C8C2×Dic11semidirect
400. #97C2×Dic11semidirect
401. C4×C8C2×Dic11semidirect
493. C11#21992semidirect

Maximal subgroups

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

subgroupindex
#130712392
#130712252
#130693862
#130693802
#130693752
#130688172
#130688112
#130688062
#130687842
#130687802
#130687502
#130687442
C2×C11×#4332
#2199211