Finite Group Databasebeta

← #14775331

Subgroups — #14775331

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622584C211yesmaximal, characteristic
2#13071643C211yesmaximal, characteristic
3#13071493C211yesmaximal, characteristic
4#13069358C211yesmaximal, characteristic, complemented
5#13069293C211yesmaximal, characteristic, complemented
6#13069255C211yesmaximal, characteristic, complemented
7#13069204C211yesmaximal, characteristic, complemented
8#13069199C211yesmaximal, characteristic, complemented
9#13069049C211yesmaximal, characteristic
10#13068885C211yesmaximal, characteristic, complemented
11#13068815C211yesmaximal, characteristic
12#13068504C211yesmaximal, characteristic, complemented
13#13068445C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic
15C11×#1736C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×#66940C2211yescharacteristic
21#10622825—21no—
22#10622825C2211yescharacteristic
23C4×C22⋊Dic11—21no—
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66880C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×C8×Dic11C2211yescharacteristic
30#10622598C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622594—21no—
33#10622594—21no—
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37#10622587C2211yescharacteristic
38#10622586C2211yescharacteristic
39#10622584C418yescomplemented
40C2×#66874C2211yescharacteristic
41C2×#66874C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622558—21no—
47#10622557—21no—
48#10622546—21no—
49C4×Dic11⋊C4—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×Dic22C2311yescharacteristic
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16—41no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#117—22no—
69C11×#117—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4C2×C414yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11D411yescharacteristic
82C2×C22⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88#66977—22no—
89#66977C2×C414yes—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66940—22no—
102#66940—41no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114C22⋊(C11⋊C8)C2×C414yes—
115#66880—22no—
116#66880—41no—
117#66879—41no—
118C8×Dic11—22no—
119#66874C2×C414yes—
120#66874C2×C414yes—
121#66872—22no—
122#66872C2×C414yes—
123#66872C2×C414yes—
124#66871—41no—
125#22945—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
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×C11—21no—
134C22×C4×C11—24no—
135C22×C4×C11—21no—
136C22×C4×C11—81no—
137C22×C4×C11—81no—
138C22×C4×C11C22×C412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11#4112yes—
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22C22×C412yes—
156C11×M16—44no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11#4112yes—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4C22×C412yes—
170C11×C4⋊C4C22×C412yes—
171C11×C4⋊C4#4112yes—
172C11×C22⋊C4—42no—
173C42×C11—42no—
174C22⋊Dic11—22no—
175C22⋊Dic11—24no—
176C22⋊Dic11—41no—
177C22⋊Dic11—42no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—81no—
184C4⋊Dic11—81no—
185C4⋊Dic11C22×C412yes—
186Dic11⋊C4—24no—
187Dic11⋊C4—42no—
188Dic11⋊C4—42no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—42no—
194C4×Dic11—42no—
195C4×Dic11—81no—
196C4×Dic11—81no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8C22×C412yes—
202C2×C11⋊C8C22×C412yes—
203C2×#483—111no—
204#2362—111no—
205#2345—111no—
206#1944—111no—
207#1933—111no—
208#1928—111no—
209#1920—111no—
210#1920—111no—
211#1894—111no—
212#1865—111no—
213#1854—111no—
214C4×#106—111no—
215#1763—111no—
216#1753—111no—
217#1736D1111yescharacteristic
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11C4×D412yes—
225C23×C11C22×D411yescharacteristic
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
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—84no—
245C2×C4×C11C4×D412yes—
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11H(5,𝔽2)11yescharacteristic
251C2×C4×C112−1+411yescharacteristic
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11#13712yes—
276Dic22—22no—
277Dic22—22no—
278Dic22—41no—
279Dic22—41no—
280C8×C11—22no—
281C8×C11—41no—
282C11⋊C8—22no—
283C11⋊C8—22no—
284C22×M16C2×D1111yescharacteristic
285C2×C22⋊Q8—111no—
286C2×C4×Q8—111no—
287C2×#117C2×D1111yescharacteristic
288C22×C4⋊C4C2×D1111yescharacteristic
289#483—118no—
290C2×#107—111no—
291C2×#106—111no—
292C2×#106—111no—
293C2×#106—111no—
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×C22⋊C8—111no—
299C2×#97—111no—
300C2×C4×C8—111no—
301#391—111no—
302#389—111no—
303#389—111no—
304#389—111no—
305#388—221no—
306#388—221no—
307#387—221no—
308#387—221no—
309#387—221no—
310#380—111no—
311#380—221no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—111no—
314C4×C4⋊C4—111no—
315C4×C4⋊C4—221no—
316C4×C22⋊C4—111no—
317C4×C22⋊C4—221no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340C2×D1111yescharacteristic
323#340C2×D1111yescharacteristic
324#340C2×D1111yescharacteristic
325#340C2×D1111yescharacteristic
326#336—111no—
327#336—111no—
328C22×C11—22no—
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11C2×C4×D411yescharacteristic
336C22×C11#54611yescharacteristic
337C22×C11#54711yescharacteristic
338C22×C11C2×#13711yescharacteristic
339C22×C11#57511yescharacteristic
340C22×C11#57711yescharacteristic
341C22×C11#57711yescharacteristic
342C4×C11—22no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—81no—
347C4×C11C4×#4111yescharacteristic
348C4×C11#52011yescharacteristic
349C4×C11#55111yescharacteristic
350C4×C11#55211yescharacteristic
351Dic11—22no—
352Dic11—41no—
353Dic11—41no—
354Dic11—42no—
355Dic11—42no—
356Dic11—41no—
357Dic11—81no—
358Dic11—81no—
359C22×Q8—111no—
360C23×C4—21no—
361C23×C4C22×D1111yescharacteristic
362C2×M16—22no—
363C2×M16—22no—
364C2×M16—41no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8C22×D1111yescharacteristic
368C22×C8C22×D1111yescharacteristic
369C22⋊Q8—114no—
370C22⋊Q8—222no—
371C4×Q8—222no—
372C4×Q8—441no—
373#117—22no—
374#117—41no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C4×D1114yes—
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—111no—
392C2×C22⋊C4—111no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C42—21no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42—221no—
401C2×C42—221no—
402#107—441no—
403#106—114no—
404#106—114no—
405#106—222no—
406#103—114no—
407#103—114no—
408#103—222no—
409#103—441no—
410C22⋊C8—114no—
411#97—441no—
412C4×C8—222no—
413#95—111no—
414#95—111no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424C2×C11—42no—
425C2×C11#235911yescharacteristic
426C2×C11C4×#13711yescharacteristic
427C2×C11#294911yescharacteristic
428C2×C11#332611yescharacteristic
429C2×C11#333111yescharacteristic
430C2×C11#334411yescharacteristic
431C2×C11#335011yescharacteristic
432C24D4×D1111yescharacteristic
433C2×Q8—112no—
434C2×Q8—221no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8—221no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—81no—
449C22×C4—81no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—111no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4—221no—
458C22×C4C2×C4×D1112yes—
459C22×C4D4×D1111yescharacteristic
460C22×C4#434112yes—
461C22×C4C23×D1111yescharacteristic
462M16—44no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—112no—
469C2×C8—112no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8#433912yes—
475C4⋊C4—24no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—112no—
482C4⋊C4—224no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—442no—
489C4⋊C4—442no—
490C4⋊C4—881no—
491C4⋊C4—881no—
492C4⋊C4C2×C4×D1112yes—
493C4⋊C4C2×C4×D1112yes—
494C4⋊C4#433912yes—
495C22⋊C4—42no—
496C22⋊C4—222no—
497C22⋊C4—224no—
498C22⋊C4—441no—
499C22⋊C4—442no—
500C42—42no—
501C42—221no—
502C42—221no—
503C42—221no—
504C42—221no—
505C42—442no—
506C42—442no—
507C42—881no—
508C42—881no—
509C11#2294511yescharacteristic, complemented, Sylow
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23(C22⋊D11)⋊C412yes—
517C23C2×D4×D1111yescharacteristic
518Q8—222no—
519Q8—222no—
520Q8—441no—
521Q8—441no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—84no—
541C2×C4—112no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—441no—
556C2×C4—441no—
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(C22⋊D11)⋊C412yes—
566C2×C4C22×C4×D1111yescharacteristic
567C2×C4C2×#433911yescharacteristic
568C2×C4C2×#433911yescharacteristic
569C2×C4C2×#434111yescharacteristic
570C2×C4#6703711yescharacteristic
571C2×C4#6704011yescharacteristic
572C8—22no—
573C8—41no—
574C8—222no—
575C8—222no—
576C22—22no—
577C22—22no—
578C22—22no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22C2×(C22⋊D11)⋊C411yescharacteristic
584C22#1062302111yescharacteristic
585C22#1062303811yescharacteristic
586C22#1062330611yescharacteristic
587C22#1062330611yescharacteristic
588C22D11×#13711yescharacteristic
589C22#1062330811yescharacteristic
590C4—22no—
591C4—42no—
592C4—42no—
593C4—42no—
594C4—81no—
595C4—222no—
596C4—441no—
597C4—441no—
598C4—441no—
599C4—442no—
600C4—442no—
601C4—881no—
602C4—881no—
603C4C4×#433911yescharacteristic
604C4#1062302611yescharacteristic
605C4#1062303511yescharacteristic
606C4#1062304411yescharacteristic
607C2—42no—
608C2#1307160411yescharacteristic
609C2#1307743111yescharacteristic
610C2#1307747811yescharacteristic
611C2#1308087011yescharacteristic
612C2#1308092811yescharacteristic
613C2#1308107211yescharacteristic
614C2#1308116211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#22945
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #13069358C2semidirect
5. #13069293C2semidirect
6. #13069255C2semidirect
7. #13069204C2semidirect
8. #13069199C2semidirect
10. #13068885C2semidirect
12. #13068504C2semidirect
13. #13068445C2semidirect
39. #10622584C4semidirect
509. C11#22945semidirect

Maximal subgroups

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

subgroupindex
C2×#106225842
#130716432
#130714932
#130693582
#130692932
#130692552
#130692042
#130691992
#130690492
#130688852
#130688152
#130685042
#130684452
#130683972
C11×#17362
#2294511