Finite Group Databasebeta

← #14647849

Subgroups — #14647849

Order 2816.

658 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068934C211yesmaximal, characteristic
2#13068808C211yesmaximal, characteristic, complemented
3C2×#10622175C211yesmaximal, characteristic
4#13066872C211yesmaximal, characteristic, complemented
5#13066494C211yesmaximal, characteristic, complemented
6#13066459C211yesmaximal, characteristic, complemented
7C11×#2325C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C2×C4×D4×C11—21no—
10C22×C4⋊Dic11C2211yescharacteristic
11C11×#388—21no—
12C11×#387—21no—
13C11×#386—21no—
14C11×#386—21no—
15C11×#385—21no—
16C11×#380C2211yescharacteristic
17C2×C11×#95C2211yescharacteristic
18C2×#66896—21no—
19C2×C11⋊#95—21no—
20C2×C11⋊#95—21no—
21C2×C11⋊#95C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×#66872—21no—
25#10622175C414yescomplemented
26#10622167—21no—
27#10622167—21no—
28C22×D4×C11—21no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C23×Dic11—21no—
35C23×Dic11—21no—
36C11×#121—21no—
37C11×#121—21no—
38C11×#121C2×C412yes—
39C11×#121Q812yes—
40C4×D4×C11—42no—
41C4×D4×C11—42no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4D411yescharacteristic
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C11×C22⋊C4—21no—
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C42×C11—21no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—42no—
55C22×C11⋊C8—21no—
56C22×C11⋊C8—21no—
57C11×#95—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62#66896—42no—
63C11⋊#95—21no—
64C11⋊#95—42no—
65C11⋊#95—42no—
66C11⋊#95C2×C412yescomplemented
67C22⋊(C11⋊C8)—21no—
68C22⋊(C11⋊C8)—21no—
69C22⋊(C11⋊C8)—21no—
70C22⋊(C11⋊C8)C2×C412yescomplemented
71#66872—42no—
72#8870—111nomaximal, Sylow
73C24×C11—21no—
74C24×C11C2×D411yescharacteristic
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—21no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11C4⋊C412yes—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—42no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—81no—
101C22×C4×C11—81no—
102C22×C4×C11SD1612yes—
103C22×C4×C11C22×C411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2×Q811yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—42no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4C4⋊C412yes—
128C11×C22⋊C4—22no—
129C11×C22⋊C4—22no—
130C11×C22⋊C4—42no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—81no—
134C11×C22⋊C4—81no—
135C42×C11—42no—
136C4⋊Dic11—22no—
137C4⋊Dic11—22no—
138C4⋊Dic11—41no—
139C4⋊Dic11—41no—
140C2×C11⋊C8—22no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146#2325D1111yescharacteristic
147#1874—111no—
148#1853—111no—
149C2×#327—111no—
150#1442—111no—
151#1294—111no—
152#1280—111no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—22no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—41no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11C4×D411yescharacteristic
165C23×C11#12011yescharacteristic
166C23×C11C22⋊Q811yescharacteristic
167C23×C11C2×SD1611yescharacteristic
168C23×C11#13511yescharacteristic
169C23×C11AGL(1,ℤ/8)11yescharacteristic
170C23×C11AGL(1,ℤ/8)11yescharacteristic
171D4×C11—42no—
172D4×C11—42no—
173D4×C11—42no—
174D4×C11—42no—
175D4×C11—42no—
176D4×C11—81no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—41no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—81no—
203C2×C4×C11—84no—
204C2×C4×C11—81no—
205C2×C4×C11C2×C4⋊C411yescharacteristic
206C2×C4×C11C4×D411yescharacteristic
207C2×C4×C11C22⋊Q811yescharacteristic
208C2×C4×C11#12311yescharacteristic
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—81no—
216C2×Dic11—81no—
217C2×Dic11—81no—
218C2×Dic11—81no—
219C2×Dic11—81no—
220C2×Dic11—81no—
221C2×Dic11—81no—
222C2×Dic11—81no—
223C11⋊C8—42no—
224C11⋊C8—81no—
225C2×#121C2×D1111yescharacteristic
226C2×C4×D4—21no—
227C22×C4⋊C4—111no—
228C2×#106—221no—
229C2×#102—221no—
230C2×C22⋊C8—111no—
231C2×C22⋊C8—111no—
232#388—21no—
233#387—21no—
234#386—21no—
235#386—21no—
236#385—21no—
237#380C2×D1111yescharacteristic
238C2×#95—111no—
239C2×#95—221no—
240C2×#95—221no—
241C2×#95C2×D1111yescharacteristic
242#340—221no—
243#340—221no—
244#327—114no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11—21no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—81no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11#38511yescharacteristic
265C22×C11C4×SD1611yescharacteristic
266C22×C11#44211yescharacteristic
267C22×C11#44911yescharacteristic
268C22×C11#45011yescharacteristic
269C22×C11#45411yescharacteristic
270C22×C11#45511yescharacteristic
271C22×C11B(4,𝔽2)11yescharacteristic
272C22×C11#45811yescharacteristic
273C22×C11#47611yescharacteristic
274C22×C11#47811yescharacteristic
275C4×C11—21no—
276C4×C11—21no—
277C4×C11—21no—
278C4×C11—21no—
279C4×C11—42no—
280C4×C11—42no—
281C4×C11—81no—
282C4×C11—81no—
283C4×C11—81no—
284Dic11—82no—
285Dic11—82no—
286C22×D4—21no—
287C22×D4C22⋊D1111yescharacteristic
288C23×C4—21no—
289C23×C4—221no—
290C23×C4—221no—
291C23×C4C22⋊D1111yescharacteristic
292C23×C4C22⋊D1111yescharacteristic
293C23×C4C22×D1111yescharacteristic
294C22×C8—221no—
295C22×C8—221no—
296#121—21no—
297#121—21no—
298#121Dic2212yes—
299#121C4×D1112yes—
300C4×D4—42no—
301C4×D4—42no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—442no—
306C2×C4⋊C4C22⋊D1111yescharacteristic
307C2×C4⋊C4C22⋊D1111yescharacteristic
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C42—21no—
315#106—442no—
316#102—442no—
317C22⋊C8—112no—
318C22⋊C8—221no—
319C22⋊C8—221no—
320C22⋊C8—221no—
321#95—21no—
322#95—21no—
323#95—21no—
324#95—21no—
325#95—21no—
326#95—112no—
327#95—221no—
328#95—442no—
329#95—442no—
330C2×C11—21no—
331C2×C11—21no—
332C2×C11—21no—
333C2×C11—21no—
334C2×C11—82no—
335C2×C11#159711yescharacteristic
336C2×C11#160111yescharacteristic
337C2×C11#161211yescharacteristic
338C2×C11#161611yescharacteristic
339C2×C11#186011yescharacteristic
340C2×C11#186411yescharacteristic
341C2×C11#186711yescharacteristic
342C24—21no—
343C24C2×C22⋊D1111yescharacteristic
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—21no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4Dic11⋊C412yes—
354C22×C4—21no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—42no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—81no—
370C22×C4—81no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4—441no—
376C22×C4—441no—
377C22×C4—441no—
378C22×C4—441no—
379C22×C4—441no—
380C22×C4—441no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—441no—
385C22×C4#432412yes—
386C22×C4C2×Dic2211yescharacteristic
387C22×C4C2×C4×D1111yescharacteristic
388C22×C4#433911yescharacteristic
389C22×C4#433911yescharacteristic
390C22×C4C2×C22⋊D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392C2×C8—222no—
393C2×C8—441no—
394C2×C8—441no—
395C2×C8—441no—
396C2×C8—441no—
397C2×C8—441no—
398C4⋊C4—21no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—42no—
402C4⋊C4—222no—
403C4⋊C4—222no—
404C4⋊C4—441no—
405C4⋊C4—441no—
406C4⋊C4Dic11⋊C412yes—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—42no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—81no—
413C22⋊C4—81no—
414C42—42no—
415C11#887011yescharacteristic, complemented, Sylow
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—22no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23#6697711yescharacteristic
428C23C4×C22⋊D1111yescharacteristic
429C23#6698511yescharacteristic
430C23C2×#432411yescharacteristic
431C23#6700211yescharacteristic
432C23#6700311yescharacteristic
433C23#6700611yescharacteristic
434D4—42no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—42no—
439D4—81no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—81no—
466C2×C4—84no—
467C2×C4—81no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—442no—
473C2×C4—442no—
474C2×C4—881no—
475C2×C4—881no—
476C2×C4—881no—
477C2×C4—881no—
478C2×C4—881no—
479C2×C4—881no—
480C2×C4—881no—
481C2×C4—881no—
482C2×C4C2×Dic11⋊C411yescharacteristic
483C2×C4#6697711yescharacteristic
484C2×C4C4×C22⋊D1111yescharacteristic
485C2×C4#6698211yescharacteristic
486C8—442no—
487C8—881no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22#1062262111yescharacteristic
508C22#1062262211yescharacteristic
509C22#1062262711yescharacteristic
510C22C4×#432411yescharacteristic
511C22#1062282311yescharacteristic
512C22#1062283111yescharacteristic
513C22#1062285111yescharacteristic
514C22#1062285511yescharacteristic
515C22#1062285611yescharacteristic
516C22#1062285711yescharacteristic
517C22#1062285811yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—81no—
525C4—81no—
526C4—81no—
527C4—882no—
528C4—882no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—82no—
534C2#1306754511yescharacteristic
535C2#1306756811yescharacteristic
536C2#1306763011yescharacteristic
537C2#1306765311yescharacteristic
538C2#1306884911yescharacteristic
539C2#1306887711yescharacteristic
540C2#1306889711yescharacteristic
subgroupG/H
centerC23#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#2325C2
socleC23×C11#120
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#2325D11
hypocenterC11#8870
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2325

Complements

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

NH ≅ G/Ntype
2. #13068808C2semidirect
4. #13066872C2semidirect
5. #13066494C2semidirect
6. #13066459C2semidirect
25. #10622175C4semidirect
66. C11⋊#95C2×C4semidirect
70. C22⋊(C11⋊C8)C2×C4semidirect
415. C11#8870semidirect

Maximal subgroups

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

subgroupindex
#130689342
#130688082
C2×#106221752
#130668722
#130664942
#130664592
C11×#23252
#887011