Finite Group Databasebeta

← #14764146

Subgroups — #14764146

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊C8C211yesmaximal, characteristic
2#13071012C211yesmaximal, characteristic
3#13071009C211yesmaximal, characteristic
4#13069387C211yesmaximal, characteristic, complemented
5#13069386C211yesmaximal, characteristic, complemented
6#13069385C211yesmaximal, characteristic, complemented
7#13069384C211yesmaximal, characteristic, complemented
8#13069383C211yesmaximal, characteristic, complemented
9#13069382C211yesmaximal, characteristic, complemented
10#13069381C211yesmaximal, characteristic, complemented
11#13068644C211yesmaximal, characteristic
12#13068642C211yesmaximal, characteristic
13#13068640C211yesmaximal, characteristic
14#13068638C211yesmaximal, characteristic
15C11×#1949C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×C42×D11C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C2×C11×#106C2211yescharacteristic
21C2×C11×C4⋊C8C2211yescharacteristic
22C11×#382C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×#66881C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28#10622600C2211yescharacteristic
29#10622600C2211yescharacteristic
30#10622600C2211yescharacteristic
31#10622600C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622590C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C4×(C2×D11)⋊C4—21no—
41#10622549C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622545—21no—
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45D11×C4⋊C8C418yescomplemented
46#10622279—21no—
47#10622277—21no—
48#10622277—21no—
49#10622264—21no—
50#10622264—21no—
51#10622261—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4×Dic11—21no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—21no—
82C2×C4×Dic11D411yescharacteristic
83C2×C4×Dic11D411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C2×C8×D11—41no—
88C2×C8×D11—41no—
89C2×C8×D11—41no—
90C2×C8×D11—41no—
91C2×C8×D11C2×C414yes—
92C2×C8×D11C2×C414yes—
93C42×D11C2×C414yes—
94C42×D11Q814yes—
95C11×#107—41no—
96C11×#106—41no—
97C11×C4⋊C8C2×C414yes—
98C11×#95—21no—
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—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114#66882—41no—
115#66881—41no—
116Dic11⋊C8C2×C414yes—
117Dic11⋊C8C2×C414yes—
118#66872—41no—
119#66872—41no—
120#66871—41no—
121#66871—41no—
122C4⋊(C11⋊C8)C2×C414yes—
123#21960—111nomaximal, Sylow
124C23×D11C2×D411yescharacteristic
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—21no—
145C2×C4×D11—41no—
146C2×C4×D11—41no—
147C2×C4×D11C4⋊C414yes—
148C2×C4×D11C4⋊C414yes—
149C2×C4×D11C22×C412yes—
150C2×C4×D11C2×Q812yes—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11C22×C412yes—
156C2×C8×C11C22×C412yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C42×C11—42no—
166C42×C11C22×C412yes—
167C42×C11C2×Q812yes—
168(C2×D11)⋊C4—42no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4×Dic11—42no—
181C4×Dic11—42no—
182C4×Dic11—42no—
183C4×Dic11C4⋊C414yes—
184C4×Dic11C4⋊C414yes—
185C4×Dic11C22×C412yes—
186C4×Dic11C2×Q812yes—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8C22×C412yes—
192C2×C11⋊C8C22×C412yes—
193C8×D11—44no—
194C8×D11—44no—
195C22×C4⋊C8—111no—
196#2283—111no—
197#2283—111no—
198#1949—111no—
199#1949—111no—
200#1949—111no—
201#1949—111no—
202#1949—111no—
203#1949—111no—
204#1949—111no—
205#1949D1111yescharacteristic, complemented
206#1808—111no—
207#1808—111no—
208#1807—111no—
209#1807—111no—
210C23×C11C22×D411yescharacteristic
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11C2×C4⋊C412yes—
216C22×D11#13512yes—
217C22×D11#13512yes—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—41no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11C2×C4⋊C412yes—
235C2×C4×C11C2×C4⋊C412yes—
236C2×C4×C11C23×C411yescharacteristic
237C2×C4×C11C22×Q811yescharacteristic
238C2×C4×C11H(5,𝔽2)11yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—41no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11C2×C4⋊C412yes—
261C2×Dic11C2×C4⋊C412yes—
262C2×Dic11C2×C4⋊C412yes—
263C4×D11—28no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—44no—
269C8×C11—22no—
270C8×C11—22no—
271C11⋊C8—22no—
272C11⋊C8—22no—
273C23×C8—111no—
274C23×C8—111no—
275C22×C42—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#107—111no—
279C2×#107C2×D1111yescharacteristic
280C2×#106—111no—
281C2×#106—111no—
282C2×#106—111no—
283C2×#106C2×D1111yescharacteristic
284C2×C4⋊C8—111no—
285C2×C4⋊C8—111no—
286C2×C4⋊C8—111no—
287C2×C4⋊C8—118no—
288C2×C4⋊C8C2×D1111yescharacteristic
289#383—221no—
290#383—221no—
291#382—111no—
292#382—111no—
293#382—111no—
294#382C2×D1111yescharacteristic
295#381—221no—
296#381—221no—
297#380—111no—
298#380—111no—
299#380—111no—
300#380—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4C2×D1111yescharacteristic
305C4×C22⋊C4—221no—
306C4×C22⋊C4—221no—
307#376—221no—
308#376—221no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340C2×D1111yescharacteristic
316#340C2×D1111yescharacteristic
317C22×C11C22×C4⋊C411yescharacteristic
318C22×C11#53711yescharacteristic
319C22×C11#53711yescharacteristic
320C22×C11C2×#13511yescharacteristic
321C22×C11C2×#13511yescharacteristic
322C22×C11#57511yescharacteristic
323C22×C11#57511yescharacteristic
324C2×D11—22no—
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11—22no—
330C2×D11#42714yes—
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11#51811yescharacteristic
338C4×C11#51911yescharacteristic
339C4×C11#54411yescharacteristic
340C4×C11#54411yescharacteristic
341Dic11—22no—
342Dic11—22no—
343Dic11—22no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347Dic11—81no—
348C23×C4—111no—
349C23×C4—111no—
350C23×C4—111no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—114no—
354C22×C8—114no—
355C22×C8—441no—
356C22×C8—441no—
357C22×C8—441no—
358C22×C8—441no—
359C22×C8C22×D1111yescharacteristic
360C22×C8C22×D1111yescharacteristic
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4C22×D1111yescharacteristic
366C2×C4⋊C4C22×D1111yescharacteristic
367C2×C4⋊C4C22×D1111yescharacteristic
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C22⋊C4—221no—
370C2×C22⋊C4—221no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—221no—
373C2×C42—21no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—114no—
378C2×C42—114no—
379C2×C42—221no—
380C2×C42—221no—
381C2×C42—221no—
382C2×C42C22×D1111yescharacteristic
383#107—41no—
384#107—441no—
385#107—441no—
386#107—441no—
387#106—41no—
388#106—441no—
389#106—441no—
390#106—441no—
391C4⋊C8—114no—
392C4⋊C8—114no—
393C4⋊C8—114no—
394C4⋊C8C4×D1114yes—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411C2×C11#231611yescharacteristic
412C2×C11C2×#42711yescharacteristic
413C2×C11#291111yescharacteristic
414C2×C11#325011yescharacteristic
415C2×C11#325011yescharacteristic
416C2×C11#325011yescharacteristic
417C2×C11#325011yescharacteristic
418D11—24no—
419C24—111no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—114no—
428C22×C4—112no—
429C22×C4—112no—
430C22×C4—114no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4D4×D1111yescharacteristic
444C22×C4D4×D1111yescharacteristic
445C22×C4C23×D1111yescharacteristic
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—112no—
451C2×C8—112no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—444no—
457C2×C8—444no—
458C2×C8C2×C4×D1112yes—
459C2×C8C2×C4×D1112yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C22⋊C4—442no—
477C22⋊C4—442no—
478C22⋊C4—442no—
479C22⋊C4—442no—
480C42—42no—
481C42—114no—
482C42—114no—
483C42—112no—
484C42—112no—
485C42—442no—
486C42—442no—
487C42—442no—
488C42C2×C4×D1112yes—
489C42Q8×D1112yes—
490C11#2196011yescharacteristic, complemented, Sylow
491C23—112no—
492C23—112no—
493C23—112no—
494C23—221no—
495C23—221no—
496C23—221no—
497C23—221no—
498C23C2×D4×D1111yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—112no—
516C2×C4—112no—
517C2×C4—112no—
518C2×C4—228no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—444no—
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—441no—
541C2×C4—441no—
542C2×C4C4⋊C4×D1112yes—
543C2×C4C4⋊C4×D1112yes—
544C2×C4C22×C4×D1111yescharacteristic
545C2×C4#6703711yescharacteristic
546C2×C4C2×Q8×D1111yescharacteristic
547C2×C4#6704011yescharacteristic
548C2×C4#6704211yescharacteristic
549C2×C4#6704311yescharacteristic
550C8—22no—
551C8—22no—
552C8—222no—
553C8—222no—
554C22—114no—
555C22—222no—
556C22—222no—
557C22—222no—
558C22—222no—
559C22—222no—
560C22—222no—
561C22C2×C4⋊C4×D1111yescharacteristic
562C22#1062313911yescharacteristic
563C22#1062316011yescharacteristic
564C22D11×#13511yescharacteristic
565C22D11×#13511yescharacteristic
566C22#1062330411yescharacteristic
567C22#1062330811yescharacteristic
568C4—22no—
569C4—22no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—222no—
575C4—222no—
576C4—222no—
577C4—881no—
578C4—881no—
579C4—881no—
580C4—881no—
581C4#1062307611yescharacteristic
582C4#1062310311yescharacteristic
583C4#1062322011yescharacteristic
584C4#1062326011yescharacteristic
585C2—224no—
586C2#1307123111yescharacteristic
587C2D11×#42711yescharacteristic
588C2#1307720311yescharacteristic
589C2#1307996511yescharacteristic
590C2#1307996611yescharacteristic
591C2#1307996711yescharacteristic
592C2#1307997011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1949C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1949D11
hypocenterC11#21960
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #13069387C2semidirect
5. #13069386C2semidirect
6. #13069385C2semidirect
7. #13069384C2semidirect
8. #13069383C2semidirect
9. #13069382C2semidirect
10. #13069381C2semidirect
15. C11×#1949C2semidirect
45. D11×C4⋊C8C4semidirect
205. #1949D11semidirect
490. C11#21960semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊C82
#130710122
#130710092
#130693872
#130693862
#130693852
#130693842
#130693832
#130693822
#130693812
#130686442
#130686422
#130686402
#130686382
C11×#19492
#2196011