Finite Group Databasebeta

← #14856901

Subgroups — #14856901

Order 2816.

724 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076984C211yesmaximal, characteristic
2#13071094C211yesmaximal, characteristic, complemented
3#13070120C211yesmaximal, characteristic, complemented
4#13070009C211yesmaximal, characteristic, complemented
5#13069999C211yesmaximal, characteristic
6#13069930C211yesmaximal, characteristic
7#13069467C211yesmaximal, characteristic
8#13069350C211yesmaximal, characteristic, complemented
9#13069300C211yesmaximal, characteristic
10#13069294C211yesmaximal, characteristic, complemented
11#13069237C211yesmaximal, characteristic
12#13069198C211yesmaximal, characteristic, complemented
13#13068971C211yesmaximal, characteristic
14#13068464C211yesmaximal, characteristic, complemented
15C11×#1863C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C22×#4325C2211yescharacteristic
18C2×#66951—21no—
19C2×C11×#107C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C11×#389C2211yescharacteristic
23#10622843C2211yescharacteristic
24#10622843C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66882C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622603—21no—
34#10622601C2211yescharacteristic
35#10622601C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622594—21no—
40#10622594—21no—
41#10622586C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44#10622552C2211yescharacteristic
45C4×C4⋊Dic11—21no—
46C4×C4⋊Dic11C2211yescharacteristic
47#10622545—21no—
48C42×Dic11C2211yescharacteristic
49#10622283—21no—
50#10622282—21no—
51C11×#340C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D44C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×#4325—22no—
73C2×#4325—22no—
74C2×#4325—41no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11D411yescharacteristic
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66951—44no—
98C11×#107—22no—
99C11×#103—22no—
100C11×#103—22no—
101C11×#95—21no—
102#66899—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—
112#66885—22no—
113#66885—41no—
114#66882—41no—
115Dic11⋊C8—22no—
116Dic11⋊C8—22no—
117C8×Dic11—41no—
118C8×Dic11—41no—
119#66873—22no—
120#66872—22no—
121#29435—111nomaximal, Sylow
122C23×D11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11#4112yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11#4112yes—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4#4112yes—
163C42×C11—24no—
164C42×C11—21no—
165C42×C11—21no—
166#4325—44no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4—42no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4—42no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—42no—
180C4⋊Dic11—42no—
181C4⋊Dic11—42no—
182Dic11⋊C4—42no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—42no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8#4112yes—
198#2860—111no—
199#2295—111no—
200#2088—111no—
201#2068—111no—
202#2067—111no—
203#2055—111no—
204#1968—111no—
205#1942—111no—
206#1934—111no—
207#1933—111no—
208#1925—111no—
209#1920—111no—
210#1880—111no—
211#1863D1111yescharacteristic, complemented
212C4×C4⋊C8—111no—
213C23×C11C22×D411yescharacteristic
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C22×D11—41no—
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—41no—
224Q8×C11—41no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
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×C11#13512yes—
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—41no—
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#13512yes—
268C2×Dic11AGL(1,ℤ/8)12yes—
269C2×Dic11#13712yes—
270D44—41no—
271D44—41no—
272D44—41no—
273D44—41no—
274C8×C11—22no—
275C8×C11—41no—
276C11⋊C8—22no—
277C11⋊C8—41no—
278C22×SD16—111no—
279C2×#126—221no—
280C2×C4×Q8C2×D1111yescharacteristic
281C2×#107—111no—
282C2×#107C2×D1111yescharacteristic
283C2×#106—111no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8—111no—
286C2×#103—111no—
287C2×#103C2×D1111yescharacteristic
288C2×#103C2×D1111yescharacteristic
289C2×#102—111no—
290C2×#102—111no—
291C2×#102—111no—
292C2×C4×C8—111no—
293C2×C4×C8—111no—
294#391—111no—
295#391—111no—
296#390—111no—
297#390—111no—
298#390—111no—
299#389—111no—
300#389—111no—
301#389—111no—
302#389—111no—
303#389C2×D1111yescharacteristic
304#388—221no—
305#388—221no—
306#388—221no—
307#387—221no—
308#387—221no—
309C4×C4⋊C4—111no—
310C4×C4⋊C4—221no—
311#376—221no—
312C43—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340C2×D1111yescharacteristic
319#336—111no—
320#336C2×D1111yescharacteristic
321C22×C11#52511yescharacteristic
322C22×C11#53211yescharacteristic
323C22×C11#53711yescharacteristic
324C22×C11C2×#13511yescharacteristic
325C22×C11C2×#13511yescharacteristic
326C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C11C2×#13711yescharacteristic
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C2×D11—81no—
334C2×D11—81no—
335C4×C11—22no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#55111yescharacteristic
342C4×C11#55211yescharacteristic
343C4×C11#55311yescharacteristic
344C4×C11#55611yescharacteristic
345Dic11—22no—
346Dic11—22no—
347Dic11—22no—
348Dic11—41no—
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352C22×Q8C22×D1111yescharacteristic
353C22×D4—111no—
354C2×SD16—222no—
355C2×SD16—222no—
356C2×SD16—441no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8C22×D1111yescharacteristic
360C22×C8C22×D1111yescharacteristic
361#126—444no—
362C4×Q8—22no—
363C4×Q8—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C42—21no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—221no—
390C2×C42C22×D1111yescharacteristic
391#107—22no—
392#107—441no—
393#106—222no—
394C4⋊C8—222no—
395C4⋊C8—222no—
396#103—22no—
397#103—22no—
398#103—441no—
399#102—222no—
400#102—222no—
401#102—441no—
402C4×C8—441no—
403C4×C8—441no—
404#95—21no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414C2×C11#260111yescharacteristic
415C2×C11#310611yescharacteristic
416C2×C11#310811yescharacteristic
417C2×C11#316811yescharacteristic
418C2×C11#318211yescharacteristic
419C2×C11#324711yescharacteristic
420C2×C11#324811yescharacteristic
421D11—161no—
422C24—221no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8#434112yes—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—221no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4D4×D1111yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449SD16—444no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—112no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8#433912yes—
462C4⋊C4—24no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—42no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—442no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4—442no—
479C4⋊C4#434112yes—
480C22⋊C4—442no—
481C22⋊C4—442no—
482C22⋊C4—442no—
483C22⋊C4—442no—
484C22⋊C4—442no—
485C22⋊C4—442no—
486C42—24no—
487C42—21no—
488C42—21no—
489C42—222no—
490C42—222no—
491C42—222no—
492C42—222no—
493C42—221no—
494C42—221no—
495C42—221no—
496C42—221no—
497C42—442no—
498C11#2943511yescharacteristic, complemented, Sylow
499C23—441no—
500C23—441no—
501C23—441no—
502C23—441no—
503C23—441no—
504C23—441no—
505C23—441no—
506C23C2×D4×D1111yescharacteristic
507Q8—22no—
508Q8—22no—
509Q8—41no—
510Q8—41no—
511D4—441no—
512D4—441no—
513D4—441no—
514D4—441no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4#6697212yes—
554C2×C4C2×#433911yescharacteristic
555C2×C4C2×#434111yescharacteristic
556C2×C4C2×#434111yescharacteristic
557C2×C4#6704011yescharacteristic
558C2×C4#41×D1111yescharacteristic
559C2×C4#6704211yescharacteristic
560C8—22no—
561C8—41no—
562C8—222no—
563C8—441no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22—881no—
568C22—881no—
569C22—881no—
570C22—881no—
571C22#1062307911yescharacteristic
572C22#1062311711yescharacteristic
573C22#1062316011yescharacteristic
574C22C2×#6697211yescharacteristic
575C22D11×#13511yescharacteristic
576C22D11×AGL(1,ℤ/8)11yescharacteristic
577C22D11×#13711yescharacteristic
578C4—22no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—222no—
585C4—222no—
586C4—222no—
587C4—441no—
588C4—881no—
589C4—881no—
590C4—881no—
591C4#1062304411yescharacteristic
592C4#1062309611yescharacteristic
593C4#1062317211yescharacteristic
594C4#1062318911yescharacteristic
595C2—1761no—
596C2#1307421711yescharacteristic
597C2#1307866911yescharacteristic
598C2#1307869711yescharacteristic
599C2#1307918911yescharacteristic
600C2#1307933111yescharacteristic
601C2#1307994511yescharacteristic
602C2#1307995211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1863C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1863D11
hypocenterC11#29435
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1863

Complements

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

NH ≅ G/Ntype
2. #13071094C2semidirect
3. #13070120C2semidirect
4. #13070009C2semidirect
8. #13069350C2semidirect
10. #13069294C2semidirect
12. #13069198C2semidirect
14. #13068464C2semidirect
15. C11×#1863C2semidirect
211. #1863D11semidirect
498. C11#29435semidirect

Maximal subgroups

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

subgroupindex
#130769842
#130710942
#130701202
#130700092
#130699992
#130699302
#130694672
#130693502
#130693002
#130692942
#130692372
#130691982
#130689712
#130684642
C11×#18632
#2943511