Finite Group Databasebeta

← #14756894

Subgroups — #14756894

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622639C211yesmaximal, characteristic
2#13071260C211yesmaximal, characteristic
3#13069243C211yesmaximal, characteristic
4#13069236C211yesmaximal, characteristic
5#13069208C211yesmaximal, characteristic, complemented
6#13069187C211yesmaximal, characteristic, complemented
7#13068971C211yesmaximal, characteristic
8#13068971C211yesmaximal, characteristic
9#13068884C211yesmaximal, characteristic, complemented
10#13068870C211yesmaximal, characteristic, complemented
11#13068514C211yesmaximal, characteristic, complemented
12C4×#66899C211yesmaximal, characteristic, complemented
13C4×#66873C211yesmaximal, characteristic
14#13068368C211yesmaximal, characteristic, complemented
15C11×#2276C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C4×C11×C4⋊C4—21no—
22C4×C11×C4⋊C4—21no—
23C4×C11×C4⋊C4—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C11×#376—21no—
28C11×#376C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622639C418yescomplemented
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622552C2211yescharacteristic
40#10622552C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46#10622282—21no—
47#10622282—21no—
48#10622280—21no—
49#10622277—21no—
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11C2×C414yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×#4325—22no—
85C2×#4325—22no—
86C2×#4325C2×C414yes—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C4×D44—22no—
103C4×D44C2×C414yes—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107C11×#95D411yescharacteristic
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111#66899—22no—
112#66899—22no—
113#66899C2×C414yes—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66873—22no—
118#66873—22no—
119#66873C2×C414yes—
120#66872—22no—
121#66871—22no—
122#66871C2×C414yes—
123#66867C2×C414yes—
124C4×C11⋊C8—22no—
125#21128—111nomaximal, Sylow
126C23×D11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11C22×C412yes—
131C2×Q8×C11#4112yes—
132C2×Q8×C11#4112yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44C22×C412yes—
153C2×C4×D11—24no—
154C2×C4×D11—81no—
155C2×C4×D11—81no—
156C11×C4⋊C4—24no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4C22×C412yes—
163C11×C4⋊C4#4112yes—
164C11×C4⋊C4#4112yes—
165C42×C11—24no—
166C42×C11—24no—
167C42×C11—24no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—81no—
173C42×C11—81no—
174C42×C11—81no—
175C42×C11C22×C412yes—
176C42×C11#4112yes—
177#4325—28no—
178(C2×D11)⋊C4—24no—
179(C2×D11)⋊C4—81no—
180(C2×D11)⋊C4—81no—
181(C2×D11)⋊C4—81no—
182(C2×D11)⋊C4—81no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11C22×C412yes—
189Dic11⋊C4—81no—
190Dic11⋊C4—81no—
191C4×Dic11—81no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8C22×C412yes—
204C2×#440—111no—
205#2319—111no—
206#2276D1111yescharacteristic, complemented
207#1926—111no—
208#1925—111no—
209#1921—111no—
210#1918—111no—
211#1880—111no—
212#1880—111no—
213#1865—111no—
214#1863—111no—
215#1776—111no—
216C4×#103—111no—
217C4×#102—111no—
218#1746—111no—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—41no—
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11#11714yes—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11C4×D412yes—
260C2×C4×C11C4×D412yes—
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×Dic11—22no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276D44—22no—
277D44—22no—
278D44—41no—
279D44—41no—
280C4×D11—84no—
281C11⋊C8—22no—
282C11⋊C8—22no—
283C11⋊C8—41no—
284C11⋊C8—41no—
285C22×SD16—111no—
286C2×C4×Q8C2×D1111yescharacteristic
287C2×C4×Q8C2×D1111yescharacteristic
288C2×C4×Q8C2×D1111yescharacteristic
289C2×C4×D4—111no—
290#440—118no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#106—111no—
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#102—111no—
298C2×#102—111no—
299C2×#102—111no—
300C2×#97—111no—
301C2×C4×C8—111no—
302#390—111no—
303#390—111no—
304#389—111no—
305#389—111no—
306#388—221no—
307#388—221no—
308#381—221no—
309#380—221no—
310C4×C4⋊C4—21no—
311C4×C4⋊C4—21no—
312C4×C4⋊C4—21no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4C2×D1111yescharacteristic
315C4×C4⋊C4C2×D1111yescharacteristic
316C4×C4⋊C4C2×D1111yescharacteristic
317#376—21no—
318#376C2×D1111yescharacteristic
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#336—111no—
326#336—111no—
327#336—111no—
328#336—111no—
329C22×C11C2×C4×D411yescharacteristic
330C22×C11#52511yescharacteristic
331C22×C11#52511yescharacteristic
332C22×C11#57611yescharacteristic
333C22×C11#57711yescharacteristic
334C22×C11#57711yescharacteristic
335C22×C11#57811yescharacteristic
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—81no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—81no—
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—24no—
346C4×C11—41no—
347C4×C11—42no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—42no—
351C4×C11—41no—
352C4×C11—42no—
353C4×C11C2×#11711yescharacteristic
354C4×C11C4×#4111yescharacteristic
355C4×C11#52911yescharacteristic
356C4×C11#52911yescharacteristic
357Dic11—42no—
358Dic11—81no—
359Dic11—81no—
360C22×Q8C22×D1111yescharacteristic
361C22×D4—111no—
362C23×C4—221no—
363C2×SD16—114no—
364C2×SD16—222no—
365C2×SD16—222no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C4×Q8—22no—
371C4×Q8—22no—
372C4×Q8—22no—
373C4×Q8—22no—
374C4×Q8—22no—
375C4×Q8C4×D1114yes—
376C4×D4—114no—
377C4×D4—222no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402C2×C42C22×D1111yescharacteristic
403C2×C42C22×D1111yescharacteristic
404#107—114no—
405#107—222no—
406#106—222no—
407#103—114no—
408#103—222no—
409#103—222no—
410#102—114no—
411#102—222no—
412#102—222no—
413#97—114no—
414C4×C8—222no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95C22⋊D1111yescharacteristic
422#95C22⋊D1111yescharacteristic
423#95C22⋊D1111yescharacteristic
424#95C22⋊D1111yescharacteristic
425C2×C11#229011yescharacteristic
426C2×C11#294611yescharacteristic
427C2×C11#294711yescharacteristic
428C2×C11#311911yescharacteristic
429C2×C11#312111yescharacteristic
430C2×C11#312411yescharacteristic
431C2×C11#312611yescharacteristic
432D11—82no—
433C24—221no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×C4×D1112yes—
438C2×Q8#433912yes—
439C2×Q8#433912yes—
440C2×D4—112no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—221no—
451C22×C4—224no—
452C22×C4—221no—
453C22×C4—221no—
454C22×C4—881no—
455C22×C4—881no—
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463SD16—228no—
464C2×C8—112no—
465C2×C8—112no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—112no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—881no—
489C4⋊C4—881no—
490C4⋊C4C2×C4×D1112yes—
491C4⋊C4#433912yes—
492C4⋊C4#433912yes—
493C22⋊C4—224no—
494C22⋊C4—881no—
495C22⋊C4—881no—
496C22⋊C4—881no—
497C22⋊C4—881no—
498C42—24no—
499C42—24no—
500C42—24no—
501C42—21no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—81no—
506C42—81no—
507C42—81no—
508C42—881no—
509C42C2×C4×D1112yes—
510C42#433912yes—
511C11#2112811yescharacteristic, complemented, Sylow
512C23—222no—
513C23—441no—
514C23—441no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23C22×C22⋊D1111yescharacteristic
520Q8—22no—
521Q8—22no—
522Q8—22no—
523Q8#6692514yes—
524D4—222no—
525D4—222no—
526D4—441no—
527D4—441no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—222no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—884no—
566C2×C4C4×C22⋊D1112yes—
567C2×C4C4×C22⋊D1112yes—
568C2×C4C22×C4×D1111yescharacteristic
569C2×C4C2×#433911yescharacteristic
570C2×C4C2×#433911yescharacteristic
571C2×C4C2×#433911yescharacteristic
572C2×C4C2×#433911yescharacteristic
573C2×C4C2×#433911yescharacteristic
574C8—222no—
575C8—222no—
576C8—441no—
577C8—441no—
578C22—442no—
579C22—442no—
580C22—442no—
581C22—881no—
582C22—881no—
583C22—881no—
584C22—881no—
585C22C2×C4×C22⋊D1111yescharacteristic
586C22#1062332211yescharacteristic
587C22#1062332211yescharacteristic
588C22#1062336611yescharacteristic
589C22#1062336811yescharacteristic
590C22#1062336811yescharacteristic
591C22#1062336911yescharacteristic
592C4—22no—
593C4—24no—
594C4—22no—
595C4—41no—
596C4—42no—
597C4—41no—
598C4—41no—
599C4—42no—
600C4—41no—
601C4—42no—
602C4—442no—
603C4—881no—
604C4—881no—
605C4C2×#6692511yescharacteristic
606C4C4×#433911yescharacteristic
607C4#1062301011yescharacteristic
608C4#1062301011yescharacteristic
609C2—882no—
610C2#1307105911yescharacteristic
611C2#1307744411yescharacteristic
612C2#1307745911yescharacteristic
613C2#1307881511yescharacteristic
614C2#1307884511yescharacteristic
615C2#1307887811yescharacteristic
616C2#1307890711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2276C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2276D11
hypocenterC11#21128
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2276

Complements

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

NH ≅ G/Ntype
5. #13069208C2semidirect
6. #13069187C2semidirect
9. #13068884C2semidirect
10. #13068870C2semidirect
11. #13068514C2semidirect
12. C4×#66899C2semidirect
14. #13068368C2semidirect
15. C11×#2276C2semidirect
32. #10622639C4semidirect
206. #2276D11semidirect
511. C11#21128semidirect

Maximal subgroups

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

subgroupindex
C2×#106226392
#130712602
#130692432
#130692362
#130692082
#130691872
#130689712
#130688842
#130688702
#130685142
C4×#668992
C4×#668732
#130683682
C11×#22762
#2112811