Finite Group Databasebeta

← #14656744

Subgroups — #14656744

Order 2816.

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

normal subgroups only

This group has 900 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
1#13074730C211yesmaximal, characteristic, complemented
2#13068548C212yesmaximal
3#13066856C211yesmaximal, characteristic
4#13066496C212yesmaximal, complemented
5C11×#1280C211yesmaximal, characteristic, complemented
6C23×D44C2211yescharacteristic
7C22×(C2×D11)⋊C4—21no—
8C22×(C2×D11)⋊C4—21no—
9C2×#66977—21no—
10C2×C11×C22⋊C8C2212yes—
11C2×C11×#95C2211yescharacteristic
12#10622825—21no—
13#10622825C2212yes—
14C2×C11⋊#95C2211yescharacteristic
15C2×#66885—22no—
16C2×#66885—22no—
17#10622274—22no—
18#10622269—22no—
19C24×D11—21no—
20C23×C4×C11D411yescharacteristic
21C23×C4×C11D411yescharacteristic
22C23×C4×C11C2311yescharacteristic
23C23×Dic11—21no—
24C22×D44—22no—
25C22×D44—22no—
26C22×D44—21no—
27C22×D44—42no—
28C22×D44—42no—
29C22×D44Q812yescomplemented
30C22×Dic22—21no—
31C22×C8×C11—22no—
32C2×C22⋊Dic11—22no—
33C2×(C2×D11)⋊C4—42no—
34C2×(C2×D11)⋊C4—42no—
35C2×(C2×D11)⋊C4—42no—
36C2×(C2×D11)⋊C4—42no—
37C2×(C2×D11)⋊C4—42no—
38C2×(C2×D11)⋊C4—42no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11—21no—
42C2×C4⋊Dic11D412yes—
43C2×C4⋊Dic11D412yes—
44#66977—42no—
45#66977—42no—
46C2×Dic11⋊C4—22no—
47C11×C22⋊C8—22no—
48C11×C22⋊C8—22no—
49C11×#95—22no—
50C11⋊#95—22no—
51C11⋊#95—22no—
52C11⋊#95—22no—
53#66885—44no—
54#66885—44no—
55#10340—111nomaximal, Sylow
56C24×C11C2×D411yescharacteristic
57C23×D11—22no—
58C23×D11—22no—
59C23×D11—22no—
60C23×D11—41no—
61C23×D11—41no—
62C23×D11—41no—
63C23×D11—41no—
64C23×D11—41no—
65C23×D11—41no—
66C23×D11—41no—
67C23×D11—41no—
68C23×D11—41no—
69C23×D11—41no—
70C23×D11—41no—
71C23×D11—41no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—21no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11—41no—
80C22×C4×C11—41no—
81C22×C4×C11—41no—
82C22×C4×C11D812yes—
83C22×C4×C11SD1612yes—
84C22×C4×C11C2×D412yes—
85C22×C4×C11C2×Q811yescharacteristic
86C22×C4×C11#4112yes—
87C22×C4×C11#4111yescharacteristic
88C22×Dic11—22no—
89C22×Dic11—22no—
90C22×Dic11—22no—
91C22×Dic11—41no—
92C22×Dic11—41no—
93C22×Dic11—41no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96C22×Dic11—41no—
97C2×D44—24no—
98C2×D44—24no—
99C2×D44—24no—
100C2×D44—42no—
101C2×D44—42no—
102C2×D44—44no—
103C2×D44—44no—
104C2×D44—48no—
105C2×D44—42no—
106C2×Dic22—42no—
107C2×Dic22—81no—
108C2×Dic22—81no—
109C2×C8×C11—42no—
110C2×C8×C11—42no—
111C2×C8×C11—42no—
112C22⋊Dic11—42no—
113C22⋊Dic11—42no—
114(C2×D11)⋊C4—48no—
115(C2×D11)⋊C4—48no—
116C4⋊Dic11—42no—
117C4⋊Dic11—42no—
118C4⋊Dic11—42no—
119C4⋊Dic11—81no—
120C4⋊Dic11—81no—
121Dic11⋊C4—44no—
122#2659—111no—
123#1786—112no—
124#1438—111no—
125#1294—112no—
126#1280D1111yescharacteristic, complemented
127C23×C11—21no—
128C23×C11—21no—
129C23×C11—21no—
130C23×C11—21no—
131C23×C11#12011yescharacteristic
132C23×C11C22⋊Q811yescharacteristic
133C23×C11#12411yescharacteristic
134C23×C11C2×D811yescharacteristic
135C23×C11C2×SD1611yescharacteristic
136C23×C11AGL(1,ℤ/8)11yescharacteristic
137C23×C11#13711yescharacteristic
138C22×D11—24no—
139C22×D11—42no—
140C22×D11—42no—
141C22×D11—42no—
142C22×D11—42no—
143C22×D11—42no—
144C22×D11—42no—
145C22×D11—42no—
146C22×D11—42no—
147C22×D11—42no—
148C22×D11—42no—
149C22×D11—42no—
150C22×D11—42no—
151C22×D11—42no—
152C22×D11—42no—
153C22×D11—42no—
154C22×D11—42no—
155C22×D11—42no—
156C22×D11—42no—
157C22×D11—81no—
158C22×D11—81no—
159C22×D11—81no—
160C22×D11—81no—
161C22×D11—81no—
162C22×D11—81no—
163C22×D11—81no—
164C22×D11—81no—
165C22×D11—81no—
166C22×D11—81no—
167C22×D11—81no—
168C22×D11—81no—
169C22×D11—81no—
170C22×D11—81no—
171C22×D11—81no—
172C22×D11—81no—
173C2×C4×C11—22no—
174C2×C4×C11—22no—
175C2×C4×C11—22no—
176C2×C4×C11—22no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11C22⋊Q812yes—
189C2×C4×C11#12412yes—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—81no—
200C2×Dic11—81no—
201C2×Dic11—81no—
202C2×Dic11—81no—
203D44—28no—
204D44—44no—
205D44—44no—
206D44—44no—
207Dic22—84no—
208C8×C11—82no—
209C23×D4—111no—
210C2×C22⋊Q8—221no—
211C22×C22⋊C4—221no—
212C22×C22⋊C4—221no—
213C2×#102—222no—
214C2×#102—222no—
215C2×C22⋊C8C2×D1112yes—
216#398—222no—
217#395—222no—
218#380—112no—
219#380—221no—
220C2×#95—111no—
221C2×#95C2×D1111yescharacteristic
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11—21no—
226C22×C11—21no—
227C22×C11—21no—
228C22×C11—21no—
229C22×C11—21no—
230C22×C11—21no—
231C22×C11—21no—
232C22×C11—21no—
233C22×C11—21no—
234C22×C11#39311yescharacteristic
235C22×C11#44711yescharacteristic
236C22×C11#44811yescharacteristic
237C22×C11#45311yescharacteristic
238C22×C11#45411yescharacteristic
239C22×C11B(4,𝔽2)11yescharacteristic
240C22×C11B(4,𝔽2)11yescharacteristic
241C22×C11#47411yescharacteristic
242C22×C11#47611yescharacteristic
243C22×C11#48611yescharacteristic
244C22×C11#48911yescharacteristic
245C2×D11—44no—
246C2×D11—44no—
247C2×D11—44no—
248C2×D11—82no—
249C2×D11—82no—
250C2×D11—82no—
251C2×D11—82no—
252C2×D11—82no—
253C2×D11—82no—
254C2×D11—82no—
255C2×D11—82no—
256C2×D11—82no—
257C2×D11—82no—
258C2×D11—82no—
259C2×D11—82no—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—42no—
263C4×C11—42no—
264Dic11—82no—
265Dic11—82no—
266Dic11—82no—
267C25—221no—
268C22×Q8—221no—
269C22×D4—112no—
270C22×D4—222no—
271C22×D4—222no—
272C22×D4—221no—
273C22×D4—442no—
274C22×D4—442no—
275C23×C4—221no—
276C23×C4D4411yescharacteristic
277C23×C4D4411yescharacteristic
278C23×C4C22×D1111yescharacteristic
279C22×C8—22no—
280C22⋊Q8—442no—
281C22⋊Q8—442no—
282C2×C4⋊C4—112no—
283C2×C4⋊C4—112no—
284C2×C4⋊C4—222no—
285C2×C4⋊C4—221no—
286C2×C4⋊C4—221no—
287C2×C4⋊C4—221no—
288C2×C22⋊C4—222no—
289C2×C22⋊C4—442no—
290C2×C22⋊C4—442no—
291C2×C22⋊C4—442no—
292C2×C22⋊C4—442no—
293C2×C22⋊C4—442no—
294C2×C22⋊C4—442no—
295#102—444no—
296#102—444no—
297C22⋊C8—22no—
298C22⋊C8—22no—
299#95—22no—
300#95—222no—
301#95—222no—
302#95—222no—
303C2×C11—21no—
304C2×C11—21no—
305C2×C11—21no—
306C2×C11—21no—
307C2×C11#159511yescharacteristic
308C2×C11#159611yescharacteristic
309C2×C11#159811yescharacteristic
310C2×C11#159911yescharacteristic
311C2×C11#202311yescharacteristic
312C2×C11#202711yescharacteristic
313C2×C11#202911yescharacteristic
314D11—84no—
315C24—222no—
316C24—222no—
317C24—222no—
318C24—441no—
319C24—441no—
320C24—441no—
321C24—441no—
322C24—441no—
323C24—441no—
324C24—441no—
325C24—441no—
326C24—441no—
327C24—441no—
328C24—441no—
329C24—441no—
330C24C2×D4411yescharacteristic
331C2×Q8—442no—
332C2×Q8—881no—
333C2×Q8—881no—
334C2×D4—224no—
335C2×D4—224no—
336C2×D4—224no—
337C2×D4—442no—
338C2×D4—442no—
339C2×D4—444no—
340C2×D4—448no—
341C2×D4—444no—
342C2×D4—442no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4#431412yes—
363C22×C4D8812yes—
364C22×C4#433912yes—
365C22×C4D4×D1112yes—
366C22×C4#434111yescharacteristic
367C22×C4Q8×D1111yescharacteristic
368C2×C8—42no—
369C2×C8—42no—
370C2×C8—42no—
371C4⋊C4—442no—
372C4⋊C4—442no—
373C4⋊C4—444no—
374C4⋊C4—442no—
375C4⋊C4—881no—
376C4⋊C4—881no—
377C22⋊C4—448no—
378C22⋊C4—448no—
379C22⋊C4—442no—
380C22⋊C4—442no—
381C11#1034011yescharacteristic, complemented, Sylow
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—224no—
387C23—442no—
388C23—442no—
389C23—442no—
390C23—442no—
391C23—442no—
392C23—442no—
393C23—442no—
394C23—442no—
395C23—442no—
396C23—442no—
397C23—442no—
398C23—442no—
399C23—442no—
400C23—442no—
401C23—442no—
402C23—442no—
403C23—442no—
404C23—442no—
405C23—881no—
406C23—881no—
407C23—881no—
408C23—881no—
409C23—881no—
410C23—881no—
411C23—881no—
412C23—881no—
413C23—881no—
414C23—881no—
415C23—881no—
416C23—881no—
417C23—881no—
418C23—881no—
419C23—881no—
420C23—881no—
421C23#6692811yescharacteristic
422C23#6693511yescharacteristic
423C23#6695011yescharacteristic
424C23C2×#431411yescharacteristic
425C23C2×D8811yescharacteristic
426C23#6696111yescharacteristic
427C23#6696211yescharacteristic
428Q8—884no—
429D4—228no—
430D4—444no—
431D4—444no—
432D4—444no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—881no—
458C2×C4—881no—
459C2×C4—881no—
460C2×C4—881no—
461C2×C4#6693812yes—
462C2×C4#6694912yes—
463C8—82no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—444no—
477C22—444no—
478C22—444no—
479C22—882no—
480C22—882no—
481C22—882no—
482C22—882no—
483C22—882no—
484C22—882no—
485C22—882no—
486C22—882no—
487C22—882no—
488C22—882no—
489C22—882no—
490C22—882no—
491C22#1062228611yescharacteristic
492C22#1062230711yescharacteristic
493C22#1062232711yescharacteristic
494C22#1062234511yescharacteristic
495C22#1062235111yescharacteristic
496C22#1062235411yescharacteristic
497C22#1062235411yescharacteristic
498C22#1062236011yescharacteristic
499C22#1062236611yescharacteristic
500C22#1062245511yescharacteristic
501C22#1062245911yescharacteristic
502C4—22no—
503C4—22no—
504C4—42no—
505C4—42no—
506C4—882no—
507C4—882no—
508C4—882no—
509C2—21no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—884no—
514C2#1306753611yescharacteristic
515C2#1306754111yescharacteristic
516C2#1306755311yescharacteristic
517C2#1306755811yescharacteristic
518C2#1306975311yescharacteristic
519C2#1306977311yescharacteristic
520C2#1306978111yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1280C2
socleC23×C11#120
prime radicalC23×D44C22
hypercenter#1280D11
hypocenterC11#10340
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
1. #13074730C2semidirect
4. #13066496C2semidirect
5. C11×#1280C2semidirect
29. C22×D44Q8semidirect
126. #1280D11semidirect
381. C11#10340semidirect

Maximal subgroups

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

subgroupindex
#130747302
#130685482
#130668562
#130664962
C11×#12802
#1034011