Finite Group Databasebeta

← #14783691

Subgroups — #14783691

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071097C211yesmaximal, characteristic
2#13071022C211yesmaximal, characteristic
3#13070185C211yesmaximal, characteristic, complemented
4#13070184C211yesmaximal, characteristic, complemented
5#13070183C211yesmaximal, characteristic, complemented
6#13070182C211yesmaximal, characteristic, complemented
7#13070181C211yesmaximal, characteristic, complemented
8#13070177C211yesmaximal, characteristic, complemented
9#13070176C211yesmaximal, characteristic, complemented
10#13068331C211yesmaximal, characteristic
11#13068331C211yesmaximal, characteristic
12#13068331C211yesmaximal, characteristic
13#13068331C211yesmaximal, characteristic
14D11×#336C211yesmaximal, characteristic
15C11×#2101C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66945C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×C42×D11C2211yescharacteristic
23C11×#389C2211yescharacteristic
24C11×#382C2211yescharacteristic
25#10622602—21no—
26#10622598C2211yescharacteristic
27#10622589C2211yescharacteristic
28#10622589C2211yescharacteristic
29C4⋊C4×Dic11—21no—
30#10622586C2211yescharacteristic
31#10622549C2211yescharacteristic
32#10622541C2211yescharacteristic
33#10622281—21no—
34#10622280—21no—
35#10622280—21no—
36#10622262—21no—
37#10622262—21no—
38#10622262—21no—
39C11×#340C2211yescharacteristic
40C11×#340C2211yescharacteristic
41C11×#340C2211yescharacteristic
42C11×#340C2211yescharacteristic
43C11×#336C2211yescharacteristic
44#10622189C2211yescharacteristic
45#10622189C2211yescharacteristic
46#10622189C2211yescharacteristic
47#10622189C2211yescharacteristic
48#10622188C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×C8×D11—22no—
95C2×C8×D11—22no—
96C2×C8×D11—22no—
97C2×C8×D11—22no—
98C2×C8×D11—22no—
99C2×C8×D11—22no—
100#66945—22no—
101#66945—22no—
102#66945—22no—
103#66945—22no—
104#66945—22no—
105#66945—22no—
106#66945—22no—
107#66945Q814yes—
108C42×D11—22no—
109C42×D11—22no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#23744—111nomaximal, Sylow
119C23×D11C2×D411yescharacteristic
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11C2×D411yescharacteristic
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—22no—
138C2×C4×D11—41no—
139C2×C4×D11—41no—
140C2×C4×D11C2×Q812yes—
141C2×C4×D11#4112yes—
142C2×C4×D11#4112yes—
143C2×C4×D11#4112yes—
144C2×C4×D11#4112yes—
145C2×C4×D11#4112yes—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4C2×Q812yes—
161C42×C11—21no—
162C42×C11—21no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—42no—
165(C2×D11)⋊C4—42no—
166(C2×D11)⋊C4—42no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—42no—
175C4⋊Dic11C2×Q812yes—
176Dic11⋊C4—42no—
177Dic11⋊C4—42no—
178Dic11⋊C4—42no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182C4×Dic11—24no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—42no—
188C4×Dic11—42no—
189C4×Dic11—42no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C8×D11—44no—
197C8×D11—44no—
198#2296—111no—
199#2285—111no—
200#2101—111no—
201#2101—111no—
202#2101—111no—
203#2101D1111yescharacteristic, complemented
204#2100—111no—
205#2100—111no—
206#2099—111no—
207#2099—111no—
208#1735—111no—
209#1735—111no—
210#1735—111no—
211#1735—111no—
212C2×#336—111no—
213C23×C11C22×D411yescharacteristic
214C22×D11—21no—
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—21no—
218C22×D11C22⋊Q812yes—
219C22×D11#12312yes—
220C22×D11#12412yes—
221C2×C4×C11—22no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
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×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11C22×Q811yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—22no—
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×Dic11—41no—
261C2×Dic11C22⋊Q812yes—
262C2×Dic11#12312yes—
263C2×Dic11#12412yes—
264C2×Dic11#13512yes—
265C2×Dic11#13512yes—
266C4×D11—44no—
267C4×D11—44no—
268C4×D11#12514yes—
269C4×D11#12514yes—
270C4×D11#12614yes—
271C4×D11#12614yes—
272C8×C11—41no—
273C8×C11—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C23×C8—111no—
277C23×C8—111no—
278C2×#117—111no—
279C2×#117—111no—
280C2×#117—111no—
281C2×#117—111no—
282C22×C42—111no—
283#389—111no—
284#389—111no—
285#389—111no—
286#389C2×D1111yescharacteristic
287#385—221no—
288#385—221no—
289#384—111no—
290#384—111no—
291#382—111no—
292#382C2×D1111yescharacteristic
293#380—221no—
294#380—221no—
295C4×C4⋊C4—221no—
296C4×C4⋊C4—221no—
297C4×C4⋊C4—221no—
298C4×C4⋊C4—221no—
299#340—111no—
300#340—111no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340C2×D1111yescharacteristic
312#340C2×D1111yescharacteristic
313#340C2×D1111yescharacteristic
314#340C2×D1111yescharacteristic
315#336—111no—
316#336—111no—
317#336—111no—
318#336C2×D1111yescharacteristic
319C22×C11C2×C22⋊Q811yescharacteristic
320C22×C11C2×#12311yescharacteristic
321C22×C11C2×#12411yescharacteristic
322C22×C11C2×#13511yescharacteristic
323C22×C11C2×#13511yescharacteristic
324C22×C11#57511yescharacteristic
325C22×C11#57511yescharacteristic
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—22no—
332C2×D11#40014yes—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11—81no—
339C4×C11C2×#12511yescharacteristic
340C4×C11C2×#12511yescharacteristic
341C4×C11C2×#12611yescharacteristic
342C4×C11C2×#12611yescharacteristic
343Dic11—22no—
344Dic11—22no—
345Dic11—42no—
346Dic11—81no—
347Dic11—81no—
348Dic11—81no—
349Dic11#40014yes—
350C23×C4—111no—
351C23×C4—111no—
352C23×C4—111no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—222no—
356C22×C8—222no—
357C22×C8—222no—
358C22×C8—222no—
359C22×C8—222no—
360C22×C8—222no—
361C22×C8C22×D1111yescharacteristic
362C22×C8C22×D1111yescharacteristic
363#117—114no—
364#117—222no—
365#117—222no—
366#117—222no—
367#117—222no—
368#117—222no—
369#117—222no—
370#117—222no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C22⋊C4—221no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C42—111no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—222no—
395C2×C42—222no—
396C2×C42—221no—
397C2×C42—221no—
398C2×C42—221no—
399C2×C42—221no—
400C2×C42C22×D1111yescharacteristic
401#95—21no—
402#95—21no—
403#95—21no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409C2×C11C2×#40011yescharacteristic
410C2×C11#307611yescharacteristic
411C2×C11#307611yescharacteristic
412C2×C11#309111yescharacteristic
413C2×C11#309111yescharacteristic
414C2×C11#313111yescharacteristic
415C2×C11#313511yescharacteristic
416D11—24no—
417C24—111no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—111no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—112no—
426C22×C4—112no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—441no—
440C22×C4—441no—
441C22×C4D4×D1111yescharacteristic
442C22×C4D4×D1111yescharacteristic
443C22×C4C23×D1111yescharacteristic
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—444no—
457C2×C8—444no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—42no—
466C4⋊C4—112no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—442no—
475C4⋊C4—442no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4—442no—
479C4⋊C4—442no—
480C4⋊C4—442no—
481C4⋊C4Q8×D1112yes—
482C22⋊C4—224no—
483C22⋊C4—442no—
484C22⋊C4—442no—
485C22⋊C4—442no—
486C42—21no—
487C42—21no—
488C42—222no—
489C42—222no—
490C42—224no—
491C42—221no—
492C42—221no—
493C42—442no—
494C42—442no—
495C42—442no—
496C11#2374411yescharacteristic, complemented, Sylow
497C23—112no—
498C23—112no—
499C23—112no—
500C23—221no—
501C23—221no—
502C23—221no—
503C23—221no—
504C23C2×D4×D1111yescharacteristic
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—112no—
524C2×C4—112no—
525C2×C4—112no—
526C2×C4—114no—
527C2×C4—114no—
528C2×C4—114no—
529C2×C4—114no—
530C2×C4—112no—
531C2×C4—112no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—222no—
537C2×C4—444no—
538C2×C4—444no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4C2×Q8×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C2×C4#41×D1111yescharacteristic
553C2×C4#41×D1111yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C8—41no—
557C8—41no—
558C8—441no—
559C8—441no—
560C22—114no—
561C22—222no—
562C22—222no—
563C22—222no—
564C22—222no—
565C22—222no—
566C22—222no—
567C22D11×C22⋊Q811yescharacteristic
568C22D11×#12311yescharacteristic
569C22D11×#12411yescharacteristic
570C22D11×#13511yescharacteristic
571C22D11×#13511yescharacteristic
572C22#1062330411yescharacteristic
573C22#1062330811yescharacteristic
574C4—41no—
575C4—41no—
576C4—42no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—114no—
581C4—222no—
582C4—222no—
583C4—442no—
584C4—881no—
585C4—881no—
586C4—881no—
587C4D11×#12511yescharacteristic
588C4D11×#12511yescharacteristic
589C4D11×#12611yescharacteristic
590C4D11×#12611yescharacteristic
591C2—224no—
592C2D11×#40011yescharacteristic
593C2#1307840111yescharacteristic
594C2#1307840311yescharacteristic
595C2#1307852811yescharacteristic
596C2#1307853411yescharacteristic
597C2#1307893711yescharacteristic
598C2#1307895811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2101C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2101D11
hypocenterC11#23744
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2101

Complements

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

NH ≅ G/Ntype
3. #13070185C2semidirect
4. #13070184C2semidirect
5. #13070183C2semidirect
6. #13070182C2semidirect
7. #13070181C2semidirect
8. #13070177C2semidirect
9. #13070176C2semidirect
15. C11×#2101C2semidirect
203. #2101D11semidirect
496. C11#23744semidirect

Maximal subgroups

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

subgroupindex
#130710972
#130710222
#130701852
#130701842
#130701832
#130701822
#130701812
#130701772
#130701762
#130683312
D11×#3362
C11×#21012
#2374411