Finite Group Databasebeta

← #14775240

Subgroups — #14775240

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622480C211yesmaximal, characteristic
2#13071642C211yesmaximal, characteristic
3#13071500C211yesmaximal, characteristic
4#13069307C211yesmaximal, characteristic, complemented
5#13069256C211yesmaximal, characteristic, complemented
6#13069205C211yesmaximal, characteristic, complemented
7#13069196C211yesmaximal, characteristic, complemented
8#13069038C211yesmaximal, characteristic
9#13068883C211yesmaximal, characteristic, complemented
10#13068812C211yesmaximal, characteristic
11#13068512C211yesmaximal, characteristic, complemented
12#13068447C211yesmaximal, characteristic, complemented
13#13068393C211yesmaximal, characteristic
14#13068331C211yesmaximal, characteristic
15C11×#1944C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×#66950C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×C4×Dic22C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#97C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30#10622603—21no—
31#10622603—21no—
32#10622600C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622590—21no—
35C4⋊C4×Dic11—21no—
36C4⋊C4×Dic11C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38#10622587C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45#10622480C418yescomplemented
46#10622283—21no—
47#10622282—21no—
48#10622267—21no—
49#10622261—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60C22×C4×D11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×(C2×D11)⋊C4D411yescharacteristic
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C2×C8×D11—22no—
93C2×C8×D11—22no—
94C2×C8×D11—41no—
95#66950—22no—
96#66950C2×C414yes—
97#66945—22no—
98#66945—22no—
99#66945—41no—
100#66945C2×C414yes—
101C4×Dic22—22no—
102C4×Dic22—41no—
103C11×#107—41no—
104C11×#106C2×C414yes—
105C11×#97—41no—
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—
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117(C2×D11)⋊C8C2×C414yes—
118#66880—22no—
119#66880C2×C414yes—
120#66879—22no—
121#66874—41no—
122#66874C2×C414yes—
123#66872—22no—
124#66871C2×C414yes—
125#22939—111nomaximal, Sylow
126C23×D11C2×D411yescharacteristic
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11C22×C412yes—
146C2×C4×D11#4112yes—
147C2×Dic22—21no—
148C2×Dic22—21no—
149C2×Dic22—21no—
150C2×Dic22—21no—
151C2×Dic22—21no—
152C2×Dic22C22×C412yes—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11C22×C412yes—
158C2×C8×C11#4112yes—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4C22×C412yes—
168C11×C4⋊C4C22×C412yes—
169C42×C11—21no—
170C42×C11—21no—
171(C2×D11)⋊C4—24no—
172(C2×D11)⋊C4—24no—
173(C2×D11)⋊C4—41no—
174(C2×D11)⋊C4—41no—
175(C2×D11)⋊C4—42no—
176(C2×D11)⋊C4—81no—
177C4⋊Dic11—24no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—81no—
183C4⋊Dic11C22×C412yes—
184C4⋊Dic11#4112yes—
185Dic11⋊C4—42no—
186C4×Dic11—24no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—42no—
190C4×Dic11—42no—
191C4×Dic11—42no—
192C4×Dic11—42no—
193C4×Dic11—42no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C412yes—
200C8×D11—44no—
201C2×#485—111no—
202#2362—111no—
203#2346—111no—
204#1944D1111yescharacteristic, complemented
205#1935—111no—
206#1928—111no—
207#1921—111no—
208#1919—111no—
209#1892—111no—
210#1865—111no—
211#1854—111no—
212#1776—111no—
213#1763—111no—
214#1752—111no—
215#1735—111no—
216C23×C11C22×D411yescharacteristic
217C22×D11—21no—
218C22×D11—21no—
219C22×D11—21no—
220C22×D11—21no—
221C22×D11—21no—
222C22×D11—21no—
223C22×D11C4×D412yes—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
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×C11C23×C411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×C4×C112−1+411yescharacteristic
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
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×Dic11C4×D412yes—
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—22no—
273Dic22—22no—
274Dic22—22no—
275Dic22—41no—
276Dic22—41no—
277C8×C11—22no—
278C8×C11—22no—
279C11⋊C8—22no—
280C11⋊C8—41no—
281C23×C8—111no—
282C2×C22⋊Q8—111no—
283C2×C4×Q8—111no—
284C2×#117—111no—
285C2×#117—111no—
286#485—118no—
287C2×#107—111no—
288C2×#107C2×D1111yescharacteristic
289C2×#106—111no—
290C2×#106C2×D1111yescharacteristic
291C2×#103—111no—
292C2×#103—111no—
293C2×#103—111no—
294C2×#103—111no—
295C2×C22⋊C8—111no—
296C2×#97—111no—
297C2×#97C2×D1111yescharacteristic
298#391—111no—
299#389—111no—
300#389C2×D1111yescharacteristic
301#389C2×D1111yescharacteristic
302#388—221no—
303#388—221no—
304#388—221no—
305#388—221no—
306#387—221no—
307#382—221no—
308#380—111no—
309C4×C4⋊C4—111no—
310C4×C4⋊C4—111no—
311C4×C4⋊C4—111no—
312C4×C4⋊C4—221no—
313C4×C22⋊C4—111no—
314#376—221no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340C2×D1111yescharacteristic
322#340C2×D1111yescharacteristic
323#336—111no—
324#336—111no—
325C22×C11C2×C4×D411yescharacteristic
326C22×C11#54611yescharacteristic
327C22×C11#54711yescharacteristic
328C22×C11#57511yescharacteristic
329C22×C11#57511yescharacteristic
330C22×C11#57711yescharacteristic
331C22×C11#57811yescharacteristic
332C2×D11—22no—
333C2×D11—22no—
334C2×D11—22no—
335C2×D11—41no—
336C2×D11—41no—
337C2×D11—41no—
338C2×D11—41no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—81no—
344C4×C11—81no—
345C4×C11C4×#4111yescharacteristic
346C4×C11#52011yescharacteristic
347C4×C11#55111yescharacteristic
348C4×C11#55211yescharacteristic
349Dic11—22no—
350Dic11—41no—
351Dic11—41no—
352Dic11—42no—
353Dic11—42no—
354Dic11—42no—
355Dic11—81no—
356C22×Q8—111no—
357C23×C4—111no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8—222no—
361C22×C8—222no—
362C22×C8—441no—
363C22×C8C22×D1111yescharacteristic
364C22×C8C22×D1111yescharacteristic
365C22⋊Q8—114no—
366C22⋊Q8—222no—
367C4×Q8—222no—
368C4×Q8—441no—
369#117—114no—
370#117—222no—
371#117—222no—
372#117—441no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C22⋊C4—111no—
386C2×C22⋊C4—111no—
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C42—111no—
392C2×C42—221no—
393C2×C42—221no—
394C2×C42—221no—
395C2×C42—221no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42C22×D1111yescharacteristic
399#107—41no—
400#107—114no—
401#106—222no—
402#106C4×D1114yes—
403#103—114no—
404#103—114no—
405#103—222no—
406#103—441no—
407C22⋊C8—114no—
408#97—41no—
409#97—222no—
410#95—21no—
411#95—21no—
412#95—111no—
413#95—111no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419#95—221no—
420#95—221no—
421C2×C11#235911yescharacteristic
422C2×C11#294311yescharacteristic
423C2×C11#294711yescharacteristic
424C2×C11#331511yescharacteristic
425C2×C11#332111yescharacteristic
426C2×C11#334811yescharacteristic
427C2×C11#334911yescharacteristic
428D11—42no—
429C24—111no—
430C2×Q8—112no—
431C2×Q8—221no—
432C2×Q8—221no—
433C2×Q8—221no—
434C2×Q8—221no—
435C2×Q8—221no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—111no—
441C22×C4—112no—
442C22×C4—112no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—112no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—444no—
467C2×C8C2×C4×D1112yes—
468C2×C8#434312yes—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—42no—
476C4⋊C4—81no—
477C4⋊C4—112no—
478C4⋊C4—112no—
479C4⋊C4—224no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—442no—
485C4⋊C4—881no—
486C4⋊C4C2×C4×D1112yes—
487C4⋊C4C2×C4×D1112yes—
488C22⋊C4—224no—
489C22⋊C4—224no—
490C22⋊C4—441no—
491C22⋊C4—441no—
492C22⋊C4—442no—
493C22⋊C4—881no—
494C42—21no—
495C42—21no—
496C42—224no—
497C42—221no—
498C42—221no—
499C42—442no—
500C42—442no—
501C42—442no—
502C42—442no—
503C42—442no—
504C11#2293911yescharacteristic, complemented, Sylow
505C23—112no—
506C23—221no—
507C23—221no—
508C23—221no—
509C23—221no—
510C23—221no—
511C23—221no—
512C23C2×D4×D1111yescharacteristic
513Q8—222no—
514Q8—222no—
515Q8—441no—
516Q8—441no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—112no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4—221no—
547C2×C4—221no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—222no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4C22×C4×D1111yescharacteristic
561C2×C4#6703711yescharacteristic
562C2×C4C2×#434311yescharacteristic
563C2×C4#6704011yescharacteristic
564C2×C4#41×D1111yescharacteristic
565C2×C4#41×D1111yescharacteristic
566C8—22no—
567C8—22no—
568C8—222no—
569C8—441no—
570C22—222no—
571C22—222no—
572C22—222no—
573C22—441no—
574C22—441no—
575C22—441no—
576C22—441no—
577C22C4×D4×D1111yescharacteristic
578C22#1062314111yescharacteristic
579C22#1062325711yescharacteristic
580C22#1062330411yescharacteristic
581C22#1062330611yescharacteristic
582C22#1062330811yescharacteristic
583C22#1062331011yescharacteristic
584C4—41no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—222no—
591C4—441no—
592C4—441no—
593C4—442no—
594C4—442no—
595C4—442no—
596C4—881no—
597C4#1062303511yescharacteristic
598C4C4×#434311yescharacteristic
599C4#1062316811yescharacteristic
600C4#1062322411yescharacteristic
601C2—442no—
602C2#1307160311yescharacteristic
603C2#1307741111yescharacteristic
604C2#1307745611yescharacteristic
605C2#1308070711yescharacteristic
606C2#1308079711yescharacteristic
607C2#1308113011yescharacteristic
608C2#1308114511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1944C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1944D11
hypocenterC11#22939
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1944

Complements

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

NH ≅ G/Ntype
4. #13069307C2semidirect
5. #13069256C2semidirect
6. #13069205C2semidirect
7. #13069196C2semidirect
9. #13068883C2semidirect
11. #13068512C2semidirect
12. #13068447C2semidirect
15. C11×#1944C2semidirect
45. #10622480C4semidirect
204. #1944D11semidirect
504. C11#22939semidirect

Maximal subgroups

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

subgroupindex
C2×#106224802
#130716422
#130715002
#130693072
#130692562
#130692052
#130691962
#130690382
#130688832
#130688122
#130685122
#130684472
#130683932
#130683312
C11×#19442
#2293911