Finite Group Databasebeta

← #14764378

Subgroups — #14764378

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
1C2×#10622613C211yesmaximal, characteristic
2#13071239C211yesmaximal, characteristic
3#13069384C211yesmaximal, characteristic, complemented
4#13069384C211yesmaximal, characteristic, complemented
5#13069379C211yesmaximal, characteristic, complemented
6#13069374C211yesmaximal, characteristic, complemented
7#13068813C211yesmaximal, characteristic
8#13068813C211yesmaximal, characteristic
9#13068808C211yesmaximal, characteristic
10#13068803C211yesmaximal, characteristic
11#13068785C211yesmaximal, characteristic, complemented
12#13068778C211yesmaximal, characteristic, complemented
13#13068751C211yesmaximal, characteristic, complemented
14#13068743C211yesmaximal, characteristic, complemented
15C11×#2314C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C11×#388—21no—
20C11×#388—21no—
21C11×#387—21no—
22C11×#387—21no—
23C11×#384C2211yescharacteristic
24C11×#382C2211yescharacteristic
25C11×#380C2211yescharacteristic
26C11×#380C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31#10622613C418yescomplemented
32#10622598—21no—
33#10622598—21no—
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622563—21no—
43#10622563—21no—
44#10622549C2211yescharacteristic
45#10622549C2211yescharacteristic
46#10622548C2211yescharacteristic
47#10622548C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×C4×C11⋊C8C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C11×#117C2×C414yes—
63C11×#117Q814yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81#66979—41no—
82#66979—41no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—41no—
89C2×C4⋊Dic11—41no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C22⋊(C11⋊C8)C2×C414yes—
110C22⋊(C11⋊C8)C2×C414yes—
111#66872—41no—
112#66872—41no—
113#66872—41no—
114#66872—41no—
115#66871—41no—
116#66871—41no—
117#66871—41no—
118#66871—41no—
119C4⋊(C11⋊C8)C2×C414yescomplemented
120C4⋊(C11⋊C8)C2×C414yescomplemented
121#66867C2×C414yescomplemented
122C4×C11⋊C8C2×C414yescomplemented
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×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×Q812yes—
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—42no—
146C22×Dic11—81no—
147C22×Dic11—81no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—81no—
157C11×C4⋊C4—81no—
158C11×C4⋊C4C4⋊C414yes—
159C11×C4⋊C4C4⋊C414yes—
160C11×C22⋊C4—81no—
161C11×C22⋊C4—81no—
162C11×C22⋊C4C4⋊C414yes—
163C11×C22⋊C4C4⋊C414yes—
164C42×C11—81no—
165C42×C11—81no—
166C42×C11C22×C412yes—
167C42×C11C22×C412yes—
168C42×C11C2×Q812yes—
169C42×C11C2×Q812yes—
170C22⋊Dic11—42no—
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—42no—
180C4⋊Dic11—81no—
181C4⋊Dic11—81no—
182C4⋊Dic11—81no—
183C4⋊Dic11—81no—
184C4×Dic11—42no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8C22×C412yes—
194C2×C11⋊C8C22×C412yes—
195C2×C11⋊C8C22×C412yes—
196C2×C11⋊C8C22×C412yes—
197C2×#433—111no—
198#2317—111no—
199#2314D1111yescharacteristic
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×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
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×C11C2×C4⋊C412yes—
247C2×C4×C11C2×C4⋊C412yes—
248C2×C4×C11C2×C4⋊C412yes—
249C2×C4×C11C2×C4⋊C412yes—
250C2×C4×C11C2×C4⋊C412yes—
251C2×C4×C11C23×C411yescharacteristic
252C2×C4×C11C22×Q811yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C11H(5,𝔽2)11yescharacteristic
255C2×C4×C112−1+411yescharacteristic
256C2×C4×C112−1+411yescharacteristic
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—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C2×#117—111no—
275C2×#117C2×D1111yescharacteristic
276C22×C4⋊C4—111no—
277#433—118no—
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⋊C8—111no—
287C2×C4⋊C8—111no—
288C2×C22⋊C8—111no—
289C2×C22⋊C8—111no—
290C2×#97—111no—
291C2×C4×C8—111no—
292#389—221no—
293#389—221no—
294#388—21no—
295#388—21no—
296#387—21no—
297#387—21no—
298#385—221no—
299#385—221no—
300#384—111no—
301#384—111no—
302#384C2×D1111yescharacteristic
303#382—111no—
304#382—111no—
305#382C2×D1111yescharacteristic
306#380C2×D1111yescharacteristic
307#380C2×D1111yescharacteristic
308C4×C4⋊C4C2×D1111yescharacteristic
309C4×C4⋊C4C2×D1111yescharacteristic
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—81no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#52011yescharacteristic
342C4×C11#52011yescharacteristic
343C4×C11#54411yescharacteristic
344C4×C11#54411yescharacteristic
345Dic11—81no—
346Dic11—81no—
347Dic11—81no—
348Dic11—81no—
349C23×C4—221no—
350C23×C4C22×D1111yescharacteristic
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—111no—
355#117—441no—
356#117—441no—
357#117Dic2214yes—
358#117C4×D1114yes—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—441no—
371C2×C4⋊C4—441no—
372C2×C4⋊C4C22⋊D1111yescharacteristic
373C2×C4⋊C4C22⋊D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4C22⋊D1111yescharacteristic
382C2×C22⋊C4C22⋊D1111yescharacteristic
383C2×C42—21no—
384C2×C42—21no—
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⋊C8—114no—
397C4⋊C8—114no—
398C22⋊C8—114no—
399C22⋊C8—114no—
400#97—114no—
401C4×C8—114no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
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×C22⋊D1111yescharacteristic
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
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×C4×D1112yes—
438C22×C4C2×C22⋊D1111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C23×D1111yescharacteristic
444C2×C8—112no—
445C2×C8—112no—
446C2×C8—112no—
447C2×C8—112no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—81no—
465C4⋊C4—81no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—442no—
475C4⋊C4—881no—
476C4⋊C4—881no—
477C4⋊C4—881no—
478C4⋊C4—881no—
479C4⋊C4Dic11⋊C414yes—
480C4⋊C4Dic11⋊C414yes—
481C22⋊C4—81no—
482C22⋊C4—81no—
483C22⋊C4—442no—
484C22⋊C4Dic11⋊C414yes—
485C22⋊C4Dic11⋊C414yes—
486C42—81no—
487C42—81no—
488C42—442no—
489C42C2×Dic2212yes—
490C42C2×Dic2212yes—
491C42C2×C4×D1112yes—
492C42C2×C4×D1112yes—
493C11#2199211yescharacteristic, complemented, Sylow
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23C2×Dic11⋊C412yes—
501C23C22×C22⋊D1111yescharacteristic
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—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
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×Dic11⋊C412yes—
542C2×C4C2×Dic11⋊C412yes—
543C2×C4C2×Dic11⋊C412yes—
544C2×C4C2×Dic11⋊C412yes—
545C2×C4C2×Dic11⋊C412yes—
546C2×C4C22×Dic2211yescharacteristic
547C2×C4C22×C4×D1111yescharacteristic
548C2×C4#6704211yescharacteristic
549C2×C4#6704211yescharacteristic
550C2×C4#6704311yescharacteristic
551C2×C4#6704311yescharacteristic
552C8—222no—
553C8—222no—
554C8—222no—
555C8—222no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C22×Dic11⋊C411yescharacteristic
564C22#1062335611yescharacteristic
565C22#1062336111yescharacteristic
566C22#1062336611yescharacteristic
567C22#1062336711yescharacteristic
568C22#1062336811yescharacteristic
569C22#1062336911yescharacteristic
570C4—22no—
571C4—22no—
572C4—22no—
573C4—22no—
574C4—22no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—881no—
580C4—881no—
581C4—881no—
582C4—881no—
583C4#1062305011yescharacteristic
584C4#1062305011yescharacteristic
585C4#1062305411yescharacteristic
586C4#1062305411yescharacteristic
587C2—42no—
588C2#1307123611yescharacteristic
589C2#1307720911yescharacteristic
590C2#1307721411yescharacteristic
591C2#1307970411yescharacteristic
592C2#1307971911yescharacteristic
593C2#1307986311yescharacteristic
594C2#1307987811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2314C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#2314D11
hypocenterC11#21992
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
3. #13069384C2semidirect
4. #13069384C2semidirect
5. #13069379C2semidirect
6. #13069374C2semidirect
11. #13068785C2semidirect
12. #13068778C2semidirect
13. #13068751C2semidirect
14. #13068743C2semidirect
31. #10622613C4semidirect
119. C4⋊(C11⋊C8)C2×C4semidirect
120. C4⋊(C11⋊C8)C2×C4semidirect
121. #66867C2×C4semidirect
122. C4×C11⋊C8C2×C4semidirect
493. C11#21992semidirect

Maximal subgroups

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

subgroupindex
C2×#106226132
#130712392
#130693842
#130693792
#130693742
#130688132
#130688082
#130688032
#130687852
#130687782
#130687512
#130687432
C11×#23142
#2199211