Finite Group Databasebeta

← #14787673

Subgroups — #14787673

Order 2816.

1238 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×#10623094C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3C2×C4×#4323C211yesmaximal, characteristic, complemented
4#13069805C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069411C211yesmaximal, characteristic, complemented
8#13068939C212yesmaximal, complemented
9#13068813C212yesmaximal, complemented
10#13068613C211yesmaximal, characteristic, complemented
11C11×#2537C211yesmaximal, characteristic, complemented
12C2×C11×#121—21no—
13C2×C11×#121C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66991—21no—
17C22×#4323C2211yescharacteristic
18C2×#66983C2212yes—
19C2×#66979C2212yes—
20#10623094—24no—
21#10623094—24no—
22C2×#66945—21no—
23C2×#66938—22no—
24C2×C4×D44C2211yescharacteristic
25C2×#66922C2211yescharacteristic
26C11×#394—22no—
27C11×#384C2211yescharacteristic
28C11×#380—21no—
29C11×#380C2212yes—
30C2×#66896C2212yes—
31C2×#66896C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34C4×#4323—24no—
35#10622621—24no—
36C2×#66873C2211yescharacteristic
37C2×#66873C2212yes—
38C2×#66872C2212yes—
39C2×#66871C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×C4×C11⋊C8C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×D4×C11—22no—
46C22×D4×C11D411yescharacteristic
47C22×D4×C11C2311yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2312yes—
50C22×C22⋊D11—22no—
51C22×D44C2311yescharacteristic
52C22×C4×D11—21no—
53C22×Dic22—21no—
54C11×#121—24no—
55C11×#121—42no—
56C11×#121—44no—
57C4×D4×C11—22no—
58C4×D4×C11—22no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—21no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—22no—
72#66991—28no—
73C2×#4323—22no—
74C2×#4323—22no—
75C2×#4323—22no—
76#66983—24no—
77#66983—24no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—22no—
80#66979—24no—
81#66979—24no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11C2312yes—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4×Dic11—22no—
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C22×C11⋊C8C2311yescharacteristic
89#66945—28no—
90#66938—216no—
91C4×D44—22no—
92C4×D44D414yescomplemented
93#66922—22no—
94#66922D414yescomplemented
95C11×#95—22no—
96#66896—24no—
97#66896—22no—
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)—42no—
100#66873—22no—
101#66873—42no—
102#66872—24no—
103#66871—22no—
104C4⋊(C11⋊C8)—22no—
105C4×C11⋊C8—22no—
106#24117—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11C2×D412yes—
109C23×D11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—22no—
112C2×D4×C11—22no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—44no—
119C2×D4×C11—44no—
120C2×D4×C11—82no—
121C2×D4×C11#4112yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11—42no—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C2×C22⋊D11—28no—
138C2×C22⋊D11—82no—
139C2×C22⋊D11—82no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44C2×D412yes—
148C2×C4×D11—24no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×Dic22—24no—
152C2×Dic22—81no—
153C2×Dic22—81no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—42no—
160C11×C4⋊C4—81no—
161C11×C22⋊C4—24no—
162C11×C22⋊C4—44no—
163C11×C22⋊C4—44no—
164C11×C22⋊C4—42no—
165C42×C11C2×D412yes—
166C42×C11C2×D412yes—
167C22⋊Dic11—28no—
168#4323—28no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—24no—
171C4⋊Dic11—24no—
172C4⋊Dic11—22no—
173C4⋊Dic11—21no—
174C4⋊Dic11C2×D412yes—
175C4⋊Dic11C2×D414yes—
176C4×Dic11—28no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8#4112yes—
186C2×#555—111no—
187C2×#476—111no—
188C2×C4×D8—111no—
189#2537D1111yescharacteristic, complemented
190#2034—112no—
191#1999—112no—
192#1990—111no—
193#1954—111no—
194#1875—112no—
195#1854—112no—
196#1802—111no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—41no—
206C23×C11—41no—
207C23×C11—41no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11C22×D411yescharacteristic
212C22×D11—22no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—44no—
224D4×C11—88no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—41no—
235C2×C4×C11—42no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—84no—
241C2×C4×C11#12012yes—
242C2×C4×C11#12012yes—
243C2×C4×C11#13512yes—
244C2×C4×C11AGL(1,ℤ/8)12yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11H(5,𝔽2)11yescharacteristic
250C2×C4×C112−1+411yescharacteristic
251C22⋊D11—88no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258D44—22no—
259D44—22no—
260D44—41no—
261D44—41no—
262C4×D11—48no—
263Dic22—84no—
264C11⋊C8—22no—
265C11⋊C8—41no—
266C11⋊C8—42no—
267C22×D8—111no—
268#555—224no—
269#555—224no—
270C2×C4⋊Q8—111no—
271C2×#124—222no—
272C2×#121—21no—
273C2×#121—112no—
274C2×#121—221no—
275C2×#121C2×D1112yes—
276C2×C4×D4—111no—
277C2×C4×D4C2×D1111yescharacteristic
278C2×C4×D4C2×D1111yescharacteristic
279C2×#117—112no—
280C2×#117—221no—
281#476—224no—
282C4×D8—224no—
283C2×#107—111no—
284C2×#106—112no—
285C2×C4⋊C8—111no—
286C2×#102—111no—
287C2×#102—112no—
288C2×#102—111no—
289C2×#102—112no—
290C2×C22⋊C8—112no—
291C2×C22⋊C8—112no—
292C2×C4×C8—111no—
293#394—22no—
294#384C2×D1111yescharacteristic
295#380—21no—
296#380C2×D1112yes—
297#340—112no—
298#340—112no—
299#340—112no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—42no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11C2×#12011yescharacteristic
315C22×C11#54611yescharacteristic
316C22×C11#54711yescharacteristic
317C22×C11C2×#13511yescharacteristic
318C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
319C22×C11#57611yescharacteristic
320C22×C11#57711yescharacteristic
321C2×D11—42no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—81no—
325C2×D11—81no—
326C2×D11—81no—
327C2×D11—81no—
328C4×C11—22no—
329C4×C11—42no—
330C4×C11—81no—
331C4×C11—82no—
332C4×C11#44914yes—
333C4×C11#52511yescharacteristic
334C4×C11#53711yescharacteristic
335C4×C11#54811yescharacteristic
336C4×C11#55011yescharacteristic
337Dic11—42no—
338Dic11—44no—
339C22×Q8—221no—
340C22×D4—22no—
341C22×D4—111no—
342C22×D4—222no—
343C22×D4C22⋊D1111yescharacteristic
344C22×D4C22×D1111yescharacteristic
345C23×C4—21no—
346C23×C4—221no—
347C23×C4C22×D1112yes—
348C2×D8—222no—
349C2×D8—222no—
350C2×D8—222no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—112no—
354C4⋊Q8—114no—
355C4⋊Q8—222no—
356#124—2216no—
357#121—24no—
358#121—42no—
359#121—44no—
360#121—224no—
361#121—224no—
362#121—228no—
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—114no—
368C4×D4—222no—
369#117—228no—
370#117—224no—
371#117—224no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4C22⋊D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1112yes—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4C22⋊D1112yes—
387C2×C42—222no—
388C2×C42C22×D1111yescharacteristic
389#107—222no—
390#106—224no—
391C4⋊C8—222no—
392#102—222no—
393#102—222no—
394#102—224no—
395#102—442no—
396C22⋊C8—224no—
397C22⋊C8—442no—
398C4×C8—222no—
399#95—22no—
400C2×C11—82no—
401C2×C11—82no—
402C2×C11#240711yescharacteristic
403C2×C11C2×#44911yescharacteristic
404C2×C11#301211yescharacteristic
405C2×C11#330311yescharacteristic
406C2×C11#332511yescharacteristic
407C2×C11#334111yescharacteristic
408C2×C11#335411yescharacteristic
409D11—82no—
410C24—21no—
411C24—221no—
412C24C2×C22⋊D1112yes—
413C2×Q8—224no—
414C2×Q8—881no—
415C2×Q8—881no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—44no—
425C2×D4—44no—
426C2×D4—82no—
427C2×D4—112no—
428C2×D4—228no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—221no—
433C2×D4—221no—
434C2×D4—882no—
435C2×D4—882no—
436C2×D4#434112yes—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—221no—
449C22×C4—222no—
450C22×C4—224no—
451C22×C4—442no—
452C22×C4—442no—
453C22×C4C2×C22⋊D1112yes—
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C23×D1111yescharacteristic
457D8—228no—
458C2×C8—112no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—222no—
463C2×C8—221no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8—221no—
467C4⋊C4—22no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—42no—
473C4⋊C4—81no—
474C4⋊C4—114no—
475C4⋊C4—112no—
476C4⋊C4—224no—
477C4⋊C4—221no—
478C4⋊C4—222no—
479C22⋊C4—24no—
480C22⋊C4—44no—
481C22⋊C4—44no—
482C22⋊C4—42no—
483C22⋊C4—228no—
484C22⋊C4—228no—
485C22⋊C4—224no—
486C42—228no—
487C42D4×D1112yes—
488C42D4×D1112yes—
489C11#2411711yescharacteristic, complemented, Sylow
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—222no—
505C23—441no—
506C23—441no—
507C23—441no—
508C23—441no—
509C23—441no—
510C23—441no—
511C23C22×C22⋊D1111yescharacteristic
512Q8—884no—
513D4—22no—
514D4—22no—
515D4—41no—
516D4—41no—
517D4—44no—
518D4—88no—
519D4—222no—
520D4—222no—
521D4—441no—
522D4—441no—
523D4—888no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—42no—
539C2×C4—84no—
540C2×C4—222no—
541C2×C4—224no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—442no—
545C2×C4—442no—
546C2×C4—448no—
547C2×C4#6698512yes—
548C2×C4#6699012yes—
549C2×C4#6699012yes—
550C2×C4#6700312yes—
551C2×C4C2×D4×D1111yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4C2×#434111yescharacteristic
554C2×C4#6703711yescharacteristic
555C2×C4#41×D1111yescharacteristic
556C2×C4#6704311yescharacteristic
557C8—222no—
558C8—442no—
559C8—441no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—442no—
575C22—442no—
576C22—442no—
577C22—881no—
578C22—881no—
579C22—881no—
580C22—881no—
581C22C2×#6698511yescharacteristic
582C22C2×#6699011yescharacteristic
583C22#1062333711yescharacteristic
584C22C2×#6700311yescharacteristic
585C22#1062335511yescharacteristic
586C22#1062336611yescharacteristic
587C22#1062336811yescharacteristic
588C4—22no—
589C4—42no—
590C4—82no—
591C4—81no—
592C4—442no—
593C4—444no—
594C4#1062265014yes—
595C4#1062312911yescharacteristic
596C4#1062313011yescharacteristic
597C4#1062313711yescharacteristic
598C4#1062313911yescharacteristic
599C2—82no—
600C2—82no—
601C2—882no—
602C2#1307195711yescharacteristic
603C2C2×#1062265011yescharacteristic
604C2#1307791711yescharacteristic
605C2#1308054411yescharacteristic
606C2#1308085811yescharacteristic
607C2#1308103411yescharacteristic
608C2#1308121111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2537C2
socleC23×C11C22×D4
hypercenter#2537D11
hypocenterC11#24117
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. C2×#10623094C2semidirect
2. C2×#10622621C2semidirect
3. C2×C4×#4323C2semidirect
4. #13069805C2semidirect
5. #13069612C2semidirect
6. #13069576C2semidirect
7. #13069411C2semidirect
8. #13068939C2semidirect
9. #13068813C2semidirect
10. #13068613C2semidirect
11. C11×#2537C2semidirect
92. C4×D44D4semidirect
94. #66922D4semidirect
189. #2537D11semidirect
489. C11#24117semidirect

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106226212
C2×C4×#43232
#130698052
#130696122
#130695762
#130694112
#130689392
#130688132
#130686132
C11×#25372
#2411711