Finite Group Databasebeta

← #14810377

Subgroups — #14810377

Order 2816.

1306 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2C2×#10622405C212yesmaximal, complemented
3#13076965C211yesmaximal, characteristic
4#13069758C211yesmaximal, characteristic, complemented
5#13069757C211yesmaximal, characteristic, complemented
6#13069754C211yesmaximal, characteristic, complemented
7#13069575C212yesmaximal, complemented
8#13068922C212yesmaximal
9#13068920C212yesmaximal
10#13068373C211yesmaximal, characteristic
11C11×#2024C211yesmaximal, characteristic, complemented
12C22×Q8×D11—21no—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999C2211yescharacteristic
15C2×#66997—21no—
16C2×#66997C2211yescharacteristic
17D11×C4⋊Q8—28no—
18C2×#66950C2211yescharacteristic
19C2×C4⋊C4×D11—21no—
20C2×C4⋊C4×D11C2212yes—
21C2×#66941—21no—
22C2×#66941C2212yes—
23C2×C42×D11C2211yescharacteristic
24C2×#66922C2211yescharacteristic
25C2×C11×#103C2212yes—
26C11×#391C2211yescharacteristic
27C2×#66899C2212yes—
28C2×(C2×D11)⋊C8C2212yes—
29C2×#66880C2212yes—
30C2×C8×Dic11C2212yes—
31#10622589C2211yescharacteristic
32C2×#66874C2212yes—
33#10622542C2211yescharacteristic
34#10622405—28no—
35#10622280—21no—
36#10622280—21no—
37#10622260—21no—
38#10622260—21no—
39C11×#340C2212yes—
40C11×#336C2211yescharacteristic
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622162C2211yescharacteristic
45C22×Q8×C11—21no—
46C22×Q8×C11C2311yescharacteristic
47C2×Q8×D11—28no—
48C2×Q8×D11—44no—
49C2×Q8×D11—44no—
50C22×C4×D11—22no—
51C22×C4×D11D411yescharacteristic
52C22×C4×D11D411yescharacteristic
53C22×C4×D11C2311yescharacteristic
54C22×Dic22—21no—
55C22×Dic22—22no—
56C22×Dic22C2311yescharacteristic
57C22×C8×C11C2312yes—
58C11×C4⋊Q8—24no—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C4⋊C4C2312yes—
62C2×C42×C11C2311yescharacteristic
63#66999—24no—
64#66997—28no—
65#66997—24no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11C2311yescharacteristic
71C2×C4⋊Dic11C2312yes—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—21no—
75C2×Dic11⋊C4—21no—
76C2×Dic11⋊C4—21no—
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×C4×Dic11D411yescharacteristic
80C2×C4×Dic11D411yescharacteristic
81C2×C4×Dic11C2311yescharacteristic
82C22×C11⋊C8C2312yes—
83#66950—24no—
84C4⋊C4×D11—28no—
85C4⋊C4×D11—24no—
86C4⋊C4×D11—24no—
87#66941—28no—
88#66941—24no—
89#66941D418yes—
90C42×D11—24no—
91#66922—24no—
92C11×#103—24no—
93C11×#95—21no—
94C11×#95—21no—
95#66899—24no—
96C11⋊#95—21no—
97C11⋊#95—21no—
98(C2×D11)⋊C8—24no—
99#66880—24no—
100C8×Dic11—24no—
101#66874—24no—
102#25902—111nomaximal, Sylow
103C23×D11C2×D411yescharacteristic
104C2×Q8×C11—24no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—21no—
108C2×Q8×C11—21no—
109C2×Q8×C11—42no—
110C2×Q8×C11—42no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—22no—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11C2×D411yescharacteristic
121C22×Dic11C2×D411yescharacteristic
122C22×Dic11C2×D411yescharacteristic
123Q8×D11—432no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—28no—
129C2×C4×D11—22no—
130C2×C4×D11—21no—
131C2×C4×D11—21no—
132C2×C4×D11—44no—
133C2×C4×D11—44no—
134C2×C4×D11SD1614yes—
135C2×C4×D11Q1614yes—
136C2×C4×D11#4114yes—
137C2×Dic22—24no—
138C2×Dic22—28no—
139C2×Dic22—22no—
140C2×Dic22—22no—
141C2×Dic22—21no—
142C2×Dic22—21no—
143C2×Dic22—42no—
144C2×Dic22—44no—
145C2×Dic22—44no—
146C2×Dic22—42no—
147C2×C8×C11—22no—
148C2×C8×C11—22no—
149C2×C8×C11—22no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4C2×D414yes—
154C42×C11—22no—
155(C2×D11)⋊C4—42no—
156(C2×D11)⋊C4—42no—
157C4⋊Dic11—24no—
158C4⋊Dic11—22no—
159C4⋊Dic11—22no—
160C4⋊Dic11—42no—
161C4⋊Dic11C2×D414yes—
162Dic11⋊C4—28no—
163Dic11⋊C4—28no—
164Dic11⋊C4—42no—
165Dic11⋊C4—42no—
166Dic11⋊C4—42no—
167Dic11⋊C4—42no—
168Dic11⋊C4—42no—
169C4×Dic11—22no—
170C4×Dic11—22no—
171C4×Dic11C2×D414yes—
172C2×C11⋊C8—22no—
173C2×C11⋊C8—22no—
174C2×C11⋊C8—22no—
175C22×C4⋊Q8—111no—
176C2×#487—112no—
177#2857—111no—
178#2024—111no—
179#2024—111no—
180#2024—111no—
181#2024D1111yescharacteristic, complemented
182#1990—112no—
183#1872—112no—
184#1872—112no—
185C4×C22⋊C8—111no—
186C23×C11C22×D411yescharacteristic
187C22×D11—21no—
188C22×D11—21no—
189C22×D11—21no—
190C22×D11—21no—
191C22×D11#12412yes—
192C22×D11C2×SD1612yes—
193C22×D11C2×Q1612yes—
194Q8×C11—48no—
195Q8×C11—42no—
196Q8×C11—42no—
197C2×C4×C11—21no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—21no—
201C2×C4×C11—24no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11C2×SD1612yes—
211C2×C4×C11C2×Q1612yes—
212C2×C4×C11C22×D412yes—
213C2×C4×C11C2×#4112yes—
214C2×C4×C112−1+411yescharacteristic
215C2×C4×C112−1+411yescharacteristic
216C2×Dic11—21no—
217C2×Dic11—21no—
218C2×Dic11—24no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11—41no—
226C2×Dic11—41no—
227C2×Dic11#12012yes—
228C2×Dic11#12012yes—
229C2×Dic11#12412yes—
230C2×Dic11C2×SD1612yes—
231C2×Dic11C2×Q1612yes—
232C2×Dic11AGL(1,ℤ/8)12yes—
233C2×Dic11#13712yes—
234C4×D11—24no—
235C4×D11—24no—
236C4×D11—28no—
237C4×D11—28no—
238C4×D11—416no—
239Dic22—48no—
240Dic22—416no—
241Dic22—42no—
242Dic22—42no—
243C8×C11—42no—
244C11⋊C8—42no—
245C23×Q8—221no—
246C2×C4⋊Q8—112no—
247C2×C4⋊Q8—111no—
248C2×C4⋊Q8—111no—
249C2×C4⋊Q8—221no—
250C2×C4⋊Q8—221no—
251C2×C4⋊Q8—228no—
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×C22⋊Q8—111no—
254C2×C22⋊Q8—111no—
255C22×C4⋊C4—112no—
256C22×C4⋊C4—221no—
257C22×C42—111no—
258#487—228no—
259C2×#103—112no—
260C2×#103—112no—
261C2×#103—112no—
262C2×#103C2×D1112yes—
263C2×C22⋊C8—112no—
264C2×C4×C8—112no—
265#391—111no—
266#391C2×D1111yescharacteristic
267#389—221no—
268#389—221no—
269#384—111no—
270#380—221no—
271#380—221no—
272#340—112no—
273#340—112no—
274#340—112no—
275#340C2×D1112yes—
276#336—111no—
277#336C2×D1111yescharacteristic
278C22×C11C2×#12011yescharacteristic
279C22×C11C2×#12411yescharacteristic
280C22×C11#53611yescharacteristic
281C22×C11C22×SD1611yescharacteristic
282C22×C11C22×Q1611yescharacteristic
283C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C11C2×#13711yescharacteristic
285C2×D11—22no—
286C2×D11—22no—
287C2×D11—22no—
288C2×D11—22no—
289C2×D11—22no—
290C2×D11—22no—
291C2×D11#48714yescomplemented
292C4×C11—22no—
293C4×C11—22no—
294C4×C11—44no—
295C4×C11—81no—
296C4×C11—81no—
297C4×C11#54812yes—
298C4×C11#54812yes—
299Dic11—22no—
300Dic11—44no—
301Dic11—81no—
302Dic11—81no—
303Dic11#45014yes—
304Dic11#45114yes—
305C22×Q8—21no—
306C22×Q8—111no—
307C22×Q8—222no—
308C22×Q8—228no—
309C22×Q8—221no—
310C22×Q8—444no—
311C22×Q8—444no—
312C22×Q8C22×D1111yescharacteristic
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—222no—
317C22×C8—112no—
318C22×C8C22×D1112yes—
319C4⋊Q8—24no—
320C4⋊Q8—118no—
321C4⋊Q8—224no—
322C4⋊Q8—224no—
323C4⋊Q8—224no—
324C4⋊Q8—228no—
325C4⋊Q8—228no—
326C22⋊Q8—224no—
327C22⋊Q8—224no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—112no—
330C2×C4⋊C4—111no—
331C2×C4⋊C4—224no—
332C2×C4⋊C4—228no—
333C2×C4⋊C4—222no—
334C2×C4⋊C4—222no—
335C2×C4⋊C4—221no—
336C2×C4⋊C4—224no—
337C2×C4⋊C4—221no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4C22×D1111yescharacteristic
344C2×C4⋊C4C22×D1112yes—
345C2×C22⋊C4—221no—
346C2×C22⋊C4—221no—
347C2×C42—111no—
348C2×C42—111no—
349C2×C42—111no—
350C2×C42—224no—
351C2×C42C22×D1111yescharacteristic
352#103—24no—
353#103—224no—
354#103—224no—
355#103—224no—
356C22⋊C8—224no—
357C4×C8—224no—
358#95—21no—
359#95—21no—
360#95—221no—
361#95—221no—
362C2×C11#243611yescharacteristic
363C2×C11C2×#45011yescharacteristic
364C2×C11C2×#45111yescharacteristic
365C2×C11C2×#48711yescharacteristic
366C2×C11#314111yescharacteristic
367C2×C11#322911yescharacteristic
368C2×C11#323011yescharacteristic
369D11—24no—
370C24—111no—
371C2×Q8—24no—
372C2×Q8—22no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—21no—
376C2×Q8—42no—
377C2×Q8—42no—
378C2×Q8—228no—
379C2×Q8—224no—
380C2×Q8—222no—
381C2×Q8—221no—
382C2×Q8—222no—
383C2×Q8—221no—
384C2×Q8—442no—
385C2×Q8—444no—
386C2×Q8—444no—
387C2×Q8—4432no—
388C2×Q8—442no—
389C22×C4—22no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—111no—
393C22×C4—111no—
394C22×C4—111no—
395C22×C4—114no—
396C22×C4—114no—
397C22×C4—114no—
398C22×C4—222no—
399C22×C4—222no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—228no—
403C22×C4—222no—
404C22×C4—221no—
405C22×C4—221no—
406C22×C4—222no—
407C22×C4—221no—
408C22×C4—221no—
409C22×C4—444no—
410C22×C4—444no—
411C22×C4D4×D1111yescharacteristic
412C22×C4D4×D1111yescharacteristic
413C22×C4C23×D1111yescharacteristic
414C2×C8—22no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—222no—
418C2×C8—222no—
419C2×C8—222no—
420C4⋊C4—24no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—114no—
424C4⋊C4—228no—
425C4⋊C4—228no—
426C4⋊C4—224no—
427C4⋊C4—222no—
428C4⋊C4—222no—
429C4⋊C4—442no—
430C4⋊C4—442no—
431C4⋊C4—442no—
432C4⋊C4—442no—
433C4⋊C4—442no—
434C4⋊C4—442no—
435C4⋊C4D4×D1114yes—
436C22⋊C4—442no—
437C22⋊C4—442no—
438C42—22no—
439C42—114no—
440C42—222no—
441C42—222no—
442C11#2590211yescharacteristic, complemented, Sylow
443C23—112no—
444C23—112no—
445C23—112no—
446C23—221no—
447C23—221no—
448C23—221no—
449C23—221no—
450C23C2×D4×D1111yescharacteristic
451Q8—48no—
452Q8—42no—
453Q8—42no—
454Q8—448no—
455Q8—4416no—
456Q8—442no—
457Q8—442no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—112no—
472C2×C4—112no—
473C2×C4—112no—
474C2×C4—112no—
475C2×C4—112no—
476C2×C4—112no—
477C2×C4—112no—
478C2×C4—228no—
479C2×C4—228no—
480C2×C4—221no—
481C2×C4—221no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—4416no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—441no—
489C2×C4—441no—
490C2×C4—441no—
491C2×C4—441no—
492C2×C4—441no—
493C2×C4—441no—
494C2×C4SD16×D1112yes—
495C2×C4Q16×D1112yes—
496C2×C4C2×D4×D1112yes—
497C2×C4#6704011yescharacteristic
498C2×C4#41×D1112yes—
499C2×C4#6704311yescharacteristic
500C8—42no—
501C8—442no—
502C22—114no—
503C22—222no—
504C22—222no—
505C22—222no—
506C22—222no—
507C22—222no—
508C22—222no—
509C22D11×#12011yescharacteristic
510C22#1062315911yescharacteristic
511C22D11×#12411yescharacteristic
512C22C2×SD16×D1111yescharacteristic
513C22C2×Q16×D1111yescharacteristic
514C22D11×AGL(1,ℤ/8)11yescharacteristic
515C22D11×#13711yescharacteristic
516C4—22no—
517C4—22no—
518C4—44no—
519C4—81no—
520C4—81no—
521C4—114no—
522C4—114no—
523C4—222no—
524C4—444no—
525C4—881no—
526C4—881no—
527C4#1062316412yes—
528C4#1062320812yes—
529C2—224no—
530C2#1307226911yescharacteristic
531C2D11×#45011yescharacteristic
532C2D11×#45111yescharacteristic
533C2D11×#48711yescharacteristic
534C2#1307900811yescharacteristic
535C2#1307975911yescharacteristic
536C2#1307976611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2024C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2024D11
hypocenterC11#25902
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
2. C2×#10622405C2semidirect
4. #13069758C2semidirect
5. #13069757C2semidirect
6. #13069754C2semidirect
7. #13069575C2semidirect
11. C11×#2024C2semidirect
181. #2024D11semidirect
291. C2×D11#487semidirect
442. C11#25902semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106224052
#130769652
#130697582
#130697572
#130697542
#130695752
#130689222
#130689202
#130683732
C11×#20242
#2590211