Finite Group Databasebeta

← #14654012

Subgroups — #14654012

Order 2816.

856 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 856 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622581C211yesmaximal, characteristic, complemented
2#13074353C211yesmaximal, characteristic
3C2×#10622605C211yesmaximal, characteristic, complemented
4C2×#10622108C211yesmaximal, characteristic, complemented
5C2×#10622106C211yesmaximal, characteristic, complemented
6#13066494C211yesmaximal, characteristic, complemented
7C11×#1824C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×#66983C2211yescharacteristic
10C22×(C2×D11)⋊C4—21no—
11C22×(C2×D11)⋊C4C2211yescharacteristic
12C22×Dic11⋊C4—21no—
13C2×#66935—21no—
14C2×C11×C22⋊C8C2211yescharacteristic
15C11×#380C2211yescharacteristic
16C2×C11⋊#95C2211yescharacteristic
17C2×C22⋊(C11⋊C8)C2211yescharacteristic
18#10622605—22no—
19#10622605—22no—
20#10622604—22no—
21#10622581—22no—
22#10622581—22no—
23C2×#66873—21no—
24C2×#66872—21no—
25#10622571—21no—
26#10622287—21no—
27#10622284—21no—
28C11×#340—22no—
29#10622108—22no—
30#10622106—22no—
31C24×D11D411yescharacteristic
32C23×C4×C11—21no—
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C23×Dic11—21no—
36C23×Dic11D411yescharacteristic
37C22×D44—22no—
38C22×D44D411yescharacteristic
39C22×C8×C11—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4D412yes—
46C2×C11×C4⋊C4D412yescomplemented
47C2×C11×C22⋊C4—21no—
48#66983—21no—
49#66983—21no—
50#66983—21no—
51#66983—21no—
52C2×(C2×D11)⋊C4—22no—
53C2×(C2×D11)⋊C4—24no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—44no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×Dic11⋊C4—24no—
65C2×Dic11⋊C4—44no—
66C22×C11⋊C8—21no—
67#66935—42no—
68#66935—42no—
69C11×C22⋊C8—21no—
70C11×C22⋊C8—21no—
71C11×#95—21no—
72C11⋊#95—22no—
73C11⋊#95—21no—
74C11⋊#95D412yescomplemented
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yescomplemented
77#66873—24no—
78#66872—24no—
79#9920—111nomaximal, Sylow
80C24×C11C2×D411yescharacteristic
81C23×D11—21no—
82C23×D11—21no—
83C23×D11—21no—
84C23×D11—21no—
85C23×D11—21no—
86C23×D11—21no—
87C23×D11—21no—
88C23×D11—42no—
89C23×D11—42no—
90C23×D11SD1612yes—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—42no—
94C22×C4×C11—42no—
95C22×C4×C11—42no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C2×C22⋊D11—41no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—41no—
107C2×C22⋊D11—41no—
108C2×C22⋊D11—41no—
109C2×C22⋊D11—41no—
110C22×Dic11—24no—
111C22×Dic11—22no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—42no—
117C22×Dic11—42no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—42no—
123C2×D44—44no—
124C2×D44—82no—
125C2×D44—82no—
126C2×C8×C11—42no—
127C2×C8×C11—41no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—42no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—48no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—41no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—82no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146Dic11⋊C4—48no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—42no—
149C2×#481—111no—
150#2617—111no—
151C2×#399—111no—
152#1824D1111yescharacteristic, complemented
153C2×#327—111no—
154C2×#323—111no—
155#1294—111no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11#12011yescharacteristic
159C23×C11#12011yescharacteristic
160C23×C11#12111yescharacteristic
161C23×C11C2×SD1611yescharacteristic
162C23×C11#13511yescharacteristic
163C23×C11AGL(1,ℤ/8)11yescharacteristic
164C23×C11#13711yescharacteristic
165C22×D11—22no—
166C22×D11—22no—
167C22×D11—22no—
168C22×D11—44no—
169C22×D11—42no—
170C22×D11—44no—
171C22×D11—42no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—82no—
184C22×D11—82no—
185C22×D11—81no—
186C22×D11—81no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11—82no—
200C2×C4×C11—82no—
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11#12111yescharacteristic
203C2×C4×C11#12111yescharacteristic
204C2×C4×C11#12711yescharacteristic
205C22⋊D11—81no—
206C22⋊D11—81no—
207C22⋊D11—81no—
208C22⋊D11—81no—
209C2×Dic11—24no—
210C2×Dic11—44no—
211C2×Dic11—44no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—81no—
221D44—42no—
222D44—81no—
223D44—88no—
224C8×C11—81no—
225C11⋊C8—42no—
226C2×#121—111no—
227C2×#120—221no—
228C22×C4⋊C4—221no—
229C22×C4⋊C4C2×D1111yescharacteristic
230C22×C22⋊C4—111no—
231C22×C22⋊C4—221no—
232#481—222no—
233#481—222no—
234C2×#106—221no—
235C2×#102—221no—
236C2×C22⋊C8—111no—
237C2×C22⋊C8C2×D1111yescharacteristic
238#399—222no—
239#399—222no—
240#397—221no—
241#394—222no—
242#392—221no—
243#386—221no—
244#380C2×D1111yescharacteristic
245C2×#95—111no—
246#340—22no—
247#327—222no—
248#323—222no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11#39211yescharacteristic
258C22×C11#44811yescharacteristic
259C22×C11#44911yescharacteristic
260C22×C11#45011yescharacteristic
261C22×C11#45211yescharacteristic
262C22×C11#45312yes—
263C22×C11#45812yes—
264C22×C11#46511yescharacteristic
265C22×C11#46811yescharacteristic
266C2×D11—44no—
267C2×D11—44no—
268C2×D11—42no—
269C2×D11—82no—
270C2×D11—82no—
271C2×D11—82no—
272C2×D11—81no—
273C2×D11—81no—
274C2×D11—82no—
275C2×D11—82no—
276C2×D11—82no—
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—81no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—82no—
285C4×C11—82no—
286Dic11—44no—
287Dic11—81no—
288Dic11—81no—
289C25—111no—
290C22×D4—111no—
291C22×D4—222no—
292C22×D4—221no—
293C23×C4—21no—
294C23×C4—111no—
295C23×C4—221no—
296C23×C4C22×D1111yescharacteristic
297C22×C8—21no—
298C22×C8—221no—
299#121—221no—
300#121—221no—
301#121—221no—
302#121—221no—
303#120—442no—
304#120—442no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—224no—
312C2×C4⋊C4—444no—
313C2×C4⋊C4D4412yescomplemented
314C2×C4⋊C4C22⋊D1112yes—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—224no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—221no—
320C2×C22⋊C4—221no—
321C2×C22⋊C4—221no—
322C2×C22⋊C4—221no—
323C2×C22⋊C4—221no—
324C2×C22⋊C4—221no—
325C2×C22⋊C4—222no—
326C2×C22⋊C4—444no—
327#106—224no—
328#102—224no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331C22⋊C8—112no—
332C22⋊C8—221no—
333#95—21no—
334#95—112no—
335#95—222no—
336#95—221no—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11#161312yes—
342C2×C11#161812yes—
343C2×C11#200011yescharacteristic
344C2×C11#200211yescharacteristic
345C2×C11#202211yescharacteristic
346D11—82no—
347D11—161no—
348C24—112no—
349C24—221no—
350C24—221no—
351C24—221no—
352C24—221no—
353C24—221no—
354C24—221no—
355C24—221no—
356C24—442no—
357C24—442no—
358C24D4×D1111yescharacteristic
359C2×D4—221no—
360C2×D4—221no—
361C2×D4—442no—
362C2×D4—444no—
363C2×D4—441no—
364C2×D4—441no—
365C2×D4—441no—
366C2×D4—441no—
367C2×D4—441no—
368C2×D4—441no—
369C2×D4—882no—
370C2×D4—882no—
371C22×C4—22no—
372C22×C4—22no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—42no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—224no—
379C22×C4—222no—
380C22×C4—221no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—442no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4—442no—
388C22×C4C2×D4411yescharacteristic
389C22×C4#433911yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4D4×D1111yescharacteristic
392C22×C4D4×D1111yescharacteristic
393C22×C4C2×C22⋊D1111yescharacteristic
394C2×C8—42no—
395C2×C8—41no—
396C2×C8—222no—
397C2×C8—442no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—42no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—221no—
404C4⋊C4—221no—
405C4⋊C4—448no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—448no—
409C22⋊C4—444no—
410C22⋊C4—441no—
411C22⋊C4—441no—
412C22⋊C4—441no—
413C22⋊C4—441no—
414C22⋊C4—441no—
415C22⋊C4—441no—
416C22⋊C4—882no—
417C11#992011yescharacteristic, complemented, Sylow
418C23—22no—
419C23—22no—
420C23—222no—
421C23—222no—
422C23—222no—
423C23—444no—
424C23—442no—
425C23—444no—
426C23—442no—
427C23—441no—
428C23—442no—
429C23—441no—
430C23—442no—
431C23—441no—
432C23—441no—
433C23—441no—
434C23—441no—
435C23—442no—
436C23—441no—
437C23—442no—
438C23—882no—
439C23—881no—
440C23—882no—
441C23—881no—
442C23#6693511yescharacteristic
443C23#6693711yescharacteristic
444C23SD16×D1111yescharacteristic
445C23#6696711yescharacteristic
446C23#6697111yescharacteristic
447C23#6697211yescharacteristic
448C23#6699011yescharacteristic
449D4—442no—
450D4—881no—
451D4—888no—
452D4—881no—
453D4—881no—
454D4—881no—
455D4—881no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4—224no—
471C2×C4—444no—
472C2×C4—444no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—442no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—881no—
482C2×C4#6693511yescharacteristic
483C2×C4#6693711yescharacteristic
484C2×C4#6698311yescharacteristic
485C2×C4#6699311yescharacteristic
486C8—81no—
487C8—442no—
488C22—21no—
489C22—21no—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—21no—
495C22—21no—
496C22—444no—
497C22—442no—
498C22—444no—
499C22—882no—
500C22—882no—
501C22—882no—
502C22—881no—
503C22—882no—
504C22—881no—
505C22—881no—
506C22—881no—
507C22—882no—
508C22—882no—
509C22—881no—
510C22#1062241911yescharacteristic
511C22#1062242011yescharacteristic
512C22#1062242411yescharacteristic
513C22#1062242511yescharacteristic
514C22#1062257311yescharacteristic
515C22#1062266612yes—
516C22#1062278211yescharacteristic
517C22#1062280011yescharacteristic
518C22#1062281112yes—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—21no—
523C4—82no—
524C4—82no—
525C4—444no—
526C4—881no—
527C4—881no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—882no—
533C2—1761no—
534C2#1306763412yes—
535C2#1306766312yes—
536C2#1306961811yescharacteristic
537C2#1306963211yescharacteristic
538C2#1306974711yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1824C2
socleC23×C11#120
prime radical#13074353C2
hypercenter#1824D11
hypocenterC11#9920
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1824

Complements

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

NH ≅ G/Ntype
1. C2×#10622581C2semidirect
3. C2×#10622605C2semidirect
4. C2×#10622108C2semidirect
5. C2×#10622106C2semidirect
6. #13066494C2semidirect
7. C11×#1824C2semidirect
46. C2×C11×C4⋊C4D4semidirect
74. C11⋊#95D4semidirect
76. C22⋊(C11⋊C8)D4semidirect
152. #1824D11semidirect
313. C2×C4⋊C4D44semidirect
417. C11#9920semidirect

Maximal subgroups

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

subgroupindex
C2×#106225812
#130743532
C2×#106226052
C2×#106221082
C2×#106221062
#130664942
C11×#18242
#992011