Finite Group Databasebeta

← #14773552

Subgroups — #14773552

Order 2816.

846 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622371C211yesmaximal, characteristic
2#13071569C211yesmaximal, characteristic, complemented
3#13071564C211yesmaximal, characteristic
4#13069498C211yesmaximal, characteristic
5#13069496C211yesmaximal, characteristic
6#13069258C211yesmaximal, characteristic, complemented
7#13069256C211yesmaximal, characteristic, complemented
8#13069238C211yesmaximal, characteristic
9#13068774C211yesmaximal, characteristic, complemented
10#13068620C211yesmaximal, characteristic, complemented
11#13068614C211yesmaximal, characteristic
12#13068514C211yesmaximal, characteristic, complemented
13#13068512C211yesmaximal, characteristic, complemented
14#13068482C211yesmaximal, characteristic, complemented
15C11×#1925C211yesmaximal, characteristic
16C2×D4×Dic11C2211yescharacteristic
17C22×#4324C2211yescharacteristic
18C2×#66940C2211yescharacteristic
19C2×#66930—21no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C11×#390C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25#10622834C2211yescharacteristic
26C2×#66896C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622589C2211yescharacteristic
34#10622589C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622558—21no—
43#10622557—21no—
44#10622555—21no—
45C4×C4⋊Dic11C2211yescharacteristic
46#10622546—21no—
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4C2211yescharacteristic
49#10622542C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51#10622371C418yescomplemented
52#10622265—21no—
53#10622263—21no—
54C11×#340C2211yescharacteristic
55C11×#336C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×Dic11—21no—
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75D4×Dic11—22no—
76D4×Dic11C2×C414yes—
77C2×#4324—22no—
78C2×#4324—22no—
79C2×#4324C2×C414yes—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4D411yescharacteristic
89C2×Dic11⋊C4D411yescharacteristic
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66940—22no—
99#66940C2×C414yes—
100#66930—44no—
101C11×#107—41no—
102C11×#102—41no—
103C11×#102C2×C414yes—
104C11×#95—21no—
105#66896—41no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115#66882—41no—
116#66880—41no—
117#66880C2×C414yes—
118#66879—22no—
119Dic11⋊C8—22no—
120C8×Dic11C2×C414yes—
121#66874—41no—
122#66872C2×C414yes—
123#66871—22no—
124#66871—22no—
125#66867—22no—
126#22811—111nomaximal, Sylow
127C24×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11C22×C412yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—24no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22C22×C412yes—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11C22×C412yes—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4C22×C412yes—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—81no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—81no—
174C22⋊Dic11—24no—
175C22⋊Dic11—42no—
176C22⋊Dic11—81no—
177#4324—28no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11C22×C412yes—
184Dic11⋊C4—24no—
185Dic11⋊C4—22no—
186Dic11⋊C4—22no—
187Dic11⋊C4—42no—
188Dic11⋊C4—42no—
189Dic11⋊C4—81no—
190Dic11⋊C4—81no—
191C4×Dic11—24no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—42no—
195C4×Dic11—42no—
196C4×Dic11—81no—
197C4×Dic11C22×C412yes—
198C4×Dic11#4112yes—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8C22×C412yes—
203C2×C11⋊C8#4112yes—
204C2×C11⋊C8#4112yes—
205C2×C4×SD16—111no—
206#2355—111no—
207#2354—111no—
208#1973—111no—
209#1973—111no—
210#1928—111no—
211#1928—111no—
212#1925—111no—
213#1925D1111yescharacteristic
214#1845—111no—
215#1803—111no—
216#1802—111no—
217#1776—111no—
218#1776—111no—
219#1770—111no—
220C23×C11—22no—
221C23×C11—41no—
222C23×C11—41no—
223C23×C11—41no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11C22×D411yescharacteristic
228D4×C11—22no—
229D4×C11—22no—
230D4×C11—41no—
231D4×C11—41no—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
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×C11C23×C411yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11H(5,𝔽2)11yescharacteristic
252C2×C4×C112−1+411yescharacteristic
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—48no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11C4×D412yes—
275C2×Dic11C4×D412yes—
276C2×Dic11AGL(1,ℤ/8)12yes—
277C2×Dic11#13712yes—
278Dic22—22no—
279Dic22—22no—
280Dic22—41no—
281Dic22—41no—
282C8×C11—22no—
283C8×C11—41no—
284C11⋊C8—41no—
285C11⋊C8#11714yescomplemented
286C22×SD16—111no—
287C2×C4×Q8—111no—
288C2×C4×D4—111no—
289C2×#117—221no—
290C4×SD16—118no—
291C2×#107—111no—
292C2×#107—111no—
293C2×#107—111no—
294C2×#107C2×D1111yescharacteristic
295C2×#106—111no—
296C2×C4⋊C8—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#102—111no—
301C2×#102C2×D1111yescharacteristic
302C2×#102C2×D1111yescharacteristic
303C2×#97—111no—
304C2×#97—111no—
305C2×C4×C8—111no—
306#391—111no—
307#391—111no—
308#390—111no—
309#390C2×D1111yescharacteristic
310#388—221no—
311#388—221no—
312#387—221no—
313#387—221no—
314#384—111no—
315#384—111no—
316#382—221no—
317#380—221no—
318C4×C4⋊C4—111no—
319C4×C4⋊C4—111no—
320C4×C4⋊C4—111no—
321C4×C4⋊C4—111no—
322C4×C4⋊C4—221no—
323C4×C4⋊C4C2×D1111yescharacteristic
324#340—111no—
325#340—111no—
326#340—111no—
327#340C2×D1111yescharacteristic
328#336—111no—
329#336C2×D1111yescharacteristic
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—81no—
334C22×C11—81no—
335C22×C11—81no—
336C22×C11—81no—
337C22×C11C2×C4×D411yescharacteristic
338C22×C11#54711yescharacteristic
339C22×C11#55011yescharacteristic
340C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C11C2×#13711yescharacteristic
342C22×C11#57611yescharacteristic
343C22×C11#57811yescharacteristic
344C4×C11—41no—
345C4×C11—41no—
346C4×C11—42no—
347C4×C11—81no—
348C4×C11—81no—
349C4×C11C2×#11711yescharacteristic
350C4×C11#52011yescharacteristic
351C4×C11#55511yescharacteristic
352C4×C11#55611yescharacteristic
353Dic11—22no—
354Dic11—41no—
355Dic11—41no—
356Dic11—42no—
357Dic11—42no—
358Dic11—81no—
359Dic11—81no—
360Dic11#44014yes—
361C22×Q8—111no—
362C22×D4C22×D1111yescharacteristic
363C23×C4—221no—
364C2×SD16—114no—
365C2×SD16—222no—
366C2×SD16—222no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C4×Q8—114no—
372C4×Q8—222no—
373C4×D4—114no—
374C4×D4—222no—
375#117—444no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—21no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402#107—41no—
403#107—222no—
404#107—222no—
405#107—441no—
406#106—114no—
407C4⋊C8—222no—
408#103—114no—
409#103—441no—
410#103—441no—
411#102—41no—
412#102—441no—
413#102C4×D1114yes—
414#97—222no—
415#97—222no—
416C4×C8—114no—
417#95—21no—
418#95—111no—
419#95—111no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426#95—221no—
427C2×C11—82no—
428C2×C11#235411yescharacteristic
429C2×C11C2×#44011yescharacteristic
430C2×C11#295111yescharacteristic
431C2×C11#335311yescharacteristic
432C2×C11#335711yescharacteristic
433C2×C11#339811yescharacteristic
434C2×C11#339911yescharacteristic
435C24—21no—
436C2×Q8—112no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8—221no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4C2×C4×D1112yes—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—224no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—442no—
461C22×C4—442no—
462C22×C4D4×D1111yescharacteristic
463C22×C4D4×D1111yescharacteristic
464C22×C4C23×D1111yescharacteristic
465SD16—228no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—112no—
472C2×C8—112no—
473C2×C8—112no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8C2×C4×D1112yes—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—112no—
484C4⋊C4—222no—
485C4⋊C4—222no—
486C4⋊C4—224no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—442no—
493C4⋊C4—442no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C4⋊C4C2×C4×D1112yes—
497C22⋊C4—42no—
498C22⋊C4—81no—
499C22⋊C4—224no—
500C22⋊C4—442no—
501C22⋊C4—881no—
502C42—21no—
503C42—21no—
504C42—81no—
505C42—112no—
506C42—112no—
507C42—224no—
508C42—221no—
509C42—221no—
510C42—442no—
511C42—442no—
512C42—881no—
513C11#2281111yescharacteristic, complemented, Sylow
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C2×D4×D1111yescharacteristic
522Q8—222no—
523Q8—222no—
524Q8—441no—
525Q8—441no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—112no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—222no—
556C2×C4—222no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—448no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4C22×C4×D1111yescharacteristic
571C2×C4#6703711yescharacteristic
572C2×C4#41×D1111yescharacteristic
573C2×C4#41×D1111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#6704311yescharacteristic
576C8—22no—
577C8—41no—
578C8—114no—
579C8—441no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C4×D4×D1111yescharacteristic
588C22#1062313011yescharacteristic
589C22#1062318611yescharacteristic
590C22#1062328811yescharacteristic
591C22#1062330211yescharacteristic
592C22D11×AGL(1,ℤ/8)11yescharacteristic
593C22D11×#13711yescharacteristic
594C4—41no—
595C4—41no—
596C4—42no—
597C4—81no—
598C4—81no—
599C4—114no—
600C4—222no—
601C4—441no—
602C4—442no—
603C4—441no—
604C4—442no—
605C4—881no—
606C4—881no—
607C4D11×#11711yescharacteristic
608C4#1062307711yescharacteristic
609C4#1062320111yescharacteristic
610C4#1062323311yescharacteristic
611C2—82no—
612C2#1307156211yescharacteristic
613C2D11×#44011yescharacteristic
614C2#1307748611yescharacteristic
615C2#1308119811yescharacteristic
616C2#1308123511yescharacteristic
617C2#1308165011yescharacteristic
618C2#1308166111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1925C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenter#1925D11
hypocenterC11#22811
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. #13071569C2semidirect
6. #13069258C2semidirect
7. #13069256C2semidirect
9. #13068774C2semidirect
10. #13068620C2semidirect
12. #13068514C2semidirect
13. #13068512C2semidirect
14. #13068482C2semidirect
51. #10622371C4semidirect
285. C11⋊C8#117semidirect
513. C11#22811semidirect

Maximal subgroups

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

subgroupindex
C2×#106223712
#130715692
#130715642
#130694982
#130694962
#130692582
#130692562
#130692382
#130687742
#130686202
#130686142
#130685142
#130685122
#130684822
C11×#19252
#2281111