Finite Group Databasebeta

← #14787810

Subgroups — #14787810

Order 2816.

1400 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic, complemented
2C2×#10622621C211yesmaximal, characteristic, complemented
3C2×#10622627C211yesmaximal, characteristic, complemented
4#13069805C212yesmaximal, complemented
5#13069612C212yesmaximal, complemented
6#13069588C211yesmaximal, characteristic, complemented
7#13069415C211yesmaximal, characteristic, complemented
8#13068934C212yesmaximal, complemented
9#13068808C212yesmaximal, complemented
10#13068623C211yesmaximal, characteristic, complemented
11C11×#2535C211yesmaximal, characteristic, complemented
12C22×#4341—21no—
13C2×C11×#121C2212yes—
14C2×C4×D4×C11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C22×#4323C2211yescharacteristic
17C2×#66983C2212yes—
18C22×C4⋊Dic11C2212yes—
19#10623086—24no—
20#10623086—24no—
21C2×#66950—21no—
22C2×#66939—22no—
23C2×C4×D44C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C11×#397—21no—
26C11×#392—21no—
27C11×#386—22no—
28C11×#382C2211yescharacteristic
29C11×#380C2212yes—
30C2×#66896C2212yes—
31C2×#66896C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2212yes—
33C2×C22⋊(C11⋊C8)C2212yes—
34#10622627—24no—
35#10622621—24no—
36C2×#66873C2211yescharacteristic
37C2×#66873C2212yes—
38C2×#66872C2211yescharacteristic
39C2×#66872C2212yes—
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
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—
51C23×Dic11—22no—
52C2×#4341—28no—
53C2×#4341—48no—
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C22×Dic22—21no—
57C11×#121—24no—
58C11×#121—42no—
59C4×D4×C11—22no—
60C4×D4×C11—22no—
61C4×D4×C11—22no—
62C4×D4×C11—22no—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C22⋊C4—21no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C42×C11C2311yescharacteristic
71C2×#4323—22no—
72C2×#4323—22no—
73C2×#4323—22no—
74#66983—24no—
75#66983—24no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—22no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11C2312yes—
83C2×C4⋊Dic11C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2312yes—
86C22×C11⋊C8C2311yescharacteristic
87#66950—28no—
88#66939—216no—
89C4×D44—22no—
90C4×D44D414yescomplemented
91#66922—22no—
92#66922D414yescomplemented
93C11×#95—22no—
94C11×#95—21no—
95C11×#95—21no—
96#66896—24no—
97#66896—22no—
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)—42no—
100#66873—22no—
101#66873—42no—
102#66872—24no—
103#66872—22no—
104C4⋊(C11⋊C8)—22no—
105#66867—22no—
106#24128—111nomaximal, Sylow
107C24×C11—21no—
108C24×C11C2×D412yes—
109C23×D11—21no—
110C2×D4×C11—24no—
111C2×D4×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11—21no—
116C2×D4×C11—21no—
117C2×D4×C11—44no—
118C2×D4×C11—44no—
119C2×D4×C11—82no—
120C2×D4×C11#4112yescomplemented
121C22×C4×C11—22no—
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—42no—
130C22×C4×C11—82no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—28no—
136C2×C22⋊D11—44no—
137C2×C22⋊D11—44no—
138C22×Dic11—28no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—44no—
142C22×Dic11—44no—
143#4341—432no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44C2×D412yes—
150C2×C4×D11—24no—
151C2×C4×D11—44no—
152C2×Dic22—24no—
153C2×Dic22—44no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—44no—
161C11×C22⋊C4—42no—
162C11×C22⋊C4—82no—
163C42×C11C2×D412yes—
164C42×C11C2×D412yes—
165#4323—28no—
166(C2×D11)⋊C4—28no—
167(C2×D11)⋊C4—24no—
168C4⋊Dic11—28no—
169C4⋊Dic11—24no—
170C4⋊Dic11—22no—
171C4⋊Dic11—21no—
172C4⋊Dic11C2×D414yes—
173C4⋊Dic11C2×D412yes—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8#4112yescomplemented
183C2×#547—111no—
184C2×#476—111no—
185C2×#442—111no—
186#2535D1111yescharacteristic, complemented
187#2034—112no—
188#1999—112no—
189#1993—111no—
190#1955—111no—
191#1874—112no—
192#1853—112no—
193#1804—111no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—41no—
202C23×C11—41no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11AGL(1,ℤ/8)14yes—
206C23×C11C22×D411yescharacteristic
207C22×D11—22no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—42no—
211C22×D11—42no—
212D4×C11—28no—
213D4×C11—22no—
214D4×C11—22no—
215D4×C11—41no—
216D4×C11—41no—
217D4×C11—88no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—41no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—84no—
233C2×C4×C11#12012yes—
234C2×C4×C11#12012yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11H(5,𝔽2)11yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C22⋊D11—416no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—416no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248D44—22no—
249D44—22no—
250D44—41no—
251D44—41no—
252C4×D11—48no—
253Dic22—48no—
254C11⋊C8—22no—
255C11⋊C8—41no—
256C11⋊C8—42no—
257C22×#41—221no—
258C22×D8—111no—
259#547—224no—
260#547—224no—
261C2×C4⋊Q8—111no—
262C2×#123—222no—
263C2×C22⋊Q8—221no—
264C2×#121—112no—
265C2×#121C2×D1112yes—
266C2×C4×D4—111no—
267C2×C4×D4C2×D1111yescharacteristic
268C2×C4×D4C2×D1111yescharacteristic
269C22×C4⋊C4—112no—
270#476—224no—
271#442—224no—
272C2×#106—111no—
273C2×#106—112no—
274C2×C4⋊C8—111no—
275C2×#102—111no—
276C2×#102—112no—
277C2×#102—111no—
278C2×#102—112no—
279C2×C22⋊C8—112no—
280C2×C22⋊C8—112no—
281C2×#97—111no—
282#397—21no—
283#392—21no—
284#386—22no—
285#382C2×D1111yescharacteristic
286#380C2×D1112yes—
287#340—112no—
288#340—112no—
289#340—112no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—42no—
298C22×C11—44no—
299C22×C11—82no—
300C22×C11—81no—
301C22×C11—81no—
302C22×C11C2×#12011yescharacteristic
303C22×C11#54611yescharacteristic
304C22×C11#54711yescharacteristic
305C22×C11C2×AGL(1,ℤ/8)12yes—
306C22×C11#57712yes—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—82no—
311C2×D11—82no—
312C4×C11—22no—
313C4×C11—22no—
314C4×C11—42no—
315C4×C11—81no—
316C4×C11—82no—
317C4×C11#52511yescharacteristic
318C4×C11#53711yescharacteristic
319C4×C11#54811yescharacteristic
320C4×C11#55011yescharacteristic
321Dic11—44no—
322Dic11—42no—
323C2×#41—228no—
324C2×#41—448no—
325C22×Q8—221no—
326C22×D4—22no—
327C22×D4—111no—
328C22×D4—222no—
329C22×D4C22⋊D1111yescharacteristic
330C22×D4C22×D1111yescharacteristic
331C23×C4—21no—
332C23×C4—222no—
333C23×C4—221no—
334C23×C4C22×D1112yes—
335C2×D8—222no—
336C2×D8—222no—
337C2×D8—222no—
338C22×C8—111no—
339C22×C8—111no—
340C22×C8—112no—
341C4⋊Q8—114no—
342C4⋊Q8—222no—
343#123—2216no—
344C22⋊Q8—228no—
345#121—24no—
346#121—42no—
347#121—224no—
348#121—224no—
349C4×D4—22no—
350C4×D4—22no—
351C4×D4—22no—
352C4×D4—22no—
353C4×D4—114no—
354C4×D4—222no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—112no—
357C2×C4⋊C4—224no—
358C2×C4⋊C4—224no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4C22⋊D1111yescharacteristic
362C2×C4⋊C4C22×D1111yescharacteristic
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—22no—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—221no—
368C2×C22⋊C4—222no—
369C2×C22⋊C4C22⋊D1112yes—
370C2×C42C22×D1111yescharacteristic
371#106—222no—
372#106—224no—
373C4⋊C8—222no—
374#102—222no—
375#102—222no—
376#102—224no—
377#102—442no—
378C22⋊C8—224no—
379C22⋊C8—442no—
380#97—222no—
381#95—22no—
382#95—21no—
383#95—21no—
384C2×C11—44no—
385C2×C11—82no—
386C2×C11#240711yescharacteristic
387C2×C11#300311yescharacteristic
388C2×C11#301011yescharacteristic
389C2×C11#330612yes—
390C2×C11#334512yes—
391D11—82no—
392C24—21no—
393C24—221no—
394C24C2×C22⋊D1112yes—
395#41—4432no—
396C2×Q8—224no—
397C2×Q8—444no—
398C2×D4—24no—
399C2×D4—22no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—21no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—44no—
406C2×D4—44no—
407C2×D4—82no—
408C2×D4—112no—
409C2×D4—228no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4—221no—
414C2×D4—221no—
415C2×D4—444no—
416C2×D4—444no—
417C2×D4#434112yescomplemented
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—42no—
427C22×C4—82no—
428C22×C4—228no—
429C22×C4—221no—
430C22×C4—222no—
431C22×C4—224no—
432C22×C4—444no—
433C22×C4—444no—
434C22×C4—444no—
435C22×C4C2×C22⋊D1112yes—
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439D8—228no—
440C2×C8—112no—
441C2×C8—221no—
442C2×C8—221no—
443C2×C8—221no—
444C2×C8—222no—
445C2×C8—221no—
446C2×C8—222no—
447C2×C8—222no—
448C2×C8—221no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—112no—
455C4⋊C4—114no—
456C4⋊C4—228no—
457C4⋊C4—224no—
458C4⋊C4—221no—
459C4⋊C4—222no—
460C22⋊C4—24no—
461C22⋊C4—44no—
462C22⋊C4—42no—
463C22⋊C4—82no—
464C22⋊C4—228no—
465C22⋊C4—224no—
466C42D4×D1112yes—
467C42D4×D1112yes—
468C11#2412811yescharacteristic, complemented, Sylow
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—22no—
474C23—22no—
475C23—22no—
476C23—41no—
477C23—42no—
478C23—41no—
479C23—42no—
480C23—222no—
481C23—441no—
482C23—442no—
483C23—441no—
484C23—442no—
485C23#6700214yes—
486C23C22×C22⋊D1111yescharacteristic
487Q8—448no—
488D4—28no—
489D4—22no—
490D4—22no—
491D4—41no—
492D4—41no—
493D4—88no—
494D4—222no—
495D4—222no—
496D4—4416no—
497D4—441no—
498D4—441no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—41no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—84no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—448no—
517C2×C4—4416no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4#6699012yes—
522C2×C4#6699012yes—
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4C2×#434111yescharacteristic
526C2×C4#6703711yescharacteristic
527C2×C4#41×D1111yescharacteristic
528C2×C4#6704311yescharacteristic
529C8—222no—
530C8—442no—
531C8—441no—
532C22—24no—
533C22—24no—
534C22—24no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—42no—
539C22—44no—
540C22—42no—
541C22—81no—
542C22—81no—
543C22—82no—
544C22—442no—
545C22—442no—
546C22—442no—
547C22—882no—
548C22—882no—
549C22C2×#6699011yescharacteristic
550C22#1062333711yescharacteristic
551C22C2×#6700212yes—
552C22#1062335511yescharacteristic
553C22#1062336712yes—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—82no—
558C4—81no—
559C4—442no—
560C4—444no—
561C4#1062312911yescharacteristic
562C4#1062313011yescharacteristic
563C4#1062313711yescharacteristic
564C4#1062313911yescharacteristic
565C2—44no—
566C2—82no—
567C2—882no—
568C2#1307195711yescharacteristic
569C2#1307784211yescharacteristic
570C2#1307790011yescharacteristic
571C2#1308057712yes—
572C2#1308108012yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2535C2
socleC23×C11C22×D4
hypercenter#2535D11
hypocenterC11#24128
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#10623086C2semidirect
2. C2×#10622621C2semidirect
3. C2×#10622627C2semidirect
4. #13069805C2semidirect
5. #13069612C2semidirect
6. #13069588C2semidirect
7. #13069415C2semidirect
8. #13068934C2semidirect
9. #13068808C2semidirect
10. #13068623C2semidirect
11. C11×#2535C2semidirect
90. C4×D44D4semidirect
92. #66922D4semidirect
120. C2×D4×C11#41semidirect
182. C2×C11⋊C8#41semidirect
186. #2535D11semidirect
417. C2×D4#4341semidirect
468. C11#24128semidirect

Maximal subgroups

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

subgroupindex
C2×#106230862
C2×#106226212
C2×#106226272
#130698052
#130696122
#130695882
#130694152
#130689342
#130688082
#130686232
C11×#25352
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