Finite Group Databasebeta

← #14647868

Subgroups — #14647868

Order 2816.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071321C211yesmaximal, characteristic
2#13068809C211yesmaximal, characteristic, complemented
3C2×#10622175C211yesmaximal, characteristic
4#13066879C211yesmaximal, characteristic, complemented
5#13066496C211yesmaximal, characteristic, complemented
6#13066458C211yesmaximal, characteristic, complemented
7C11×#1874C211yesmaximal, characteristic
8C2×C11×#121C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×D4×Dic11—21no—
11C22×Dic11⋊C4—21no—
12C2×C11×#102—21no—
13C2×C11×C22⋊C8C2211yescharacteristic
14#10622833—21no—
15#10622833—21no—
16#10622825C2211yescharacteristic
17C2×C11⋊#95—21no—
18C2×C11⋊#95C2211yescharacteristic
19C2×C11⋊#95C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21#10622594—21no—
22C2×#66872—21no—
23#10622564—21no—
24#10622563—21no—
25C11×#340—21no—
26#10622175C414yescomplemented
27#10622167—21no—
28C22×D4×C11—21no—
29C22×D4×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—21no—
33C23×Dic11—21no—
34C23×Dic11D411yescharacteristic
35C23×Dic11D411yescharacteristic
36C22×C8×C11—21no—
37C11×#121—21no—
38C11×#121—21no—
39C11×#121C2×C412yes—
40C11×#121Q812yes—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—42no—
44C2×C11×C4⋊C4D411yescharacteristic
45C2×C11×C22⋊C4—21no—
46C2×C22⋊Dic11—21no—
47C2×C22⋊Dic11—21no—
48C2×C22⋊Dic11—21no—
49C2×C22⋊Dic11—21no—
50D4×Dic11—42no—
51D4×Dic11—42no—
52C2×C4⋊Dic11—21no—
53C2×C4⋊Dic11D411yescharacteristic
54C2×C4⋊Dic11D411yescharacteristic
55C2×Dic11⋊C4—42no—
56C2×Dic11⋊C4—42no—
57C2×Dic11⋊C4—42no—
58C2×C4×Dic11—21no—
59C22×C11⋊C8—21no—
60C11×#102—42no—
61C11×C22⋊C8—21no—
62C11×C22⋊C8—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—42no—
70C11⋊#95C2×C412yescomplemented
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)C2×C412yescomplemented
73#66872—42no—
74#8873—111nomaximal, Sylow
75C24×C11—21no—
76C24×C11C2×D411yescharacteristic
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—21no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11C4⋊C412yescomplemented
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11—41no—
93C22×C4×C11—41no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11C22×C411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×Q811yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—21no—
107C22×Dic11—21no—
108C22×Dic11—21no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—42no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—81no—
123C22×Dic11—81no—
124C22×Dic11SD1612yes—
125C2×C8×C11—41no—
126C2×C8×C11—41no—
127C2×C8×C11—41no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4C4⋊C412yescomplemented
134C11×C22⋊C4—22no—
135C11×C22⋊C4—22no—
136C22⋊Dic11—42no—
137C22⋊Dic11—41no—
138C22⋊Dic11—41no—
139C22⋊Dic11—81no—
140C22⋊Dic11—81no—
141C4⋊Dic11—41no—
142C4⋊Dic11—41no—
143C4⋊Dic11—42no—
144Dic11⋊C4—48no—
145C4×Dic11—42no—
146C2×C11⋊C8—22no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149#2325—111no—
150#1874D1111yescharacteristic
151#1853—111no—
152C2×#327—111no—
153#1444—111no—
154#1294—111no—
155#1280—111no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—22no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11C4×D411yescharacteristic
168C23×C11#12011yescharacteristic
169C23×C11C22⋊Q811yescharacteristic
170C23×C11C2×SD1611yescharacteristic
171C23×C11#13511yescharacteristic
172C23×C11AGL(1,ℤ/8)11yescharacteristic
173C23×C11AGL(1,ℤ/8)11yescharacteristic
174D4×C11—42no—
175D4×C11—42no—
176D4×C11—42no—
177D4×C11—42no—
178D4×C11—42no—
179D4×C11—81no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
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—42no—
194C2×C4×C11—81no—
195C2×C4×C11—81no—
196C2×C4×C11—81no—
197C2×C4×C11—81no—
198C2×C4×C11C2×C4⋊C411yescharacteristic
199C2×C4×C11C4×D411yescharacteristic
200C2×C4×C11C22⋊Q811yescharacteristic
201C2×C4×C11#12311yescharacteristic
202C2×Dic11—24no—
203C2×Dic11—22no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—41no—
221C2×Dic11—41no—
222C2×Dic11—41no—
223C2×Dic11—81no—
224C2×Dic11—84no—
225C2×Dic11—81no—
226C8×C11—81no—
227C11⋊C8—42no—
228C2×#121C2×D1111yescharacteristic
229C2×C4×D4—221no—
230C22×C4⋊C4—221no—
231C22×C4⋊C4C2×D1111yescharacteristic
232C2×#106—221no—
233C2×#102—21no—
234C2×C22⋊C8—111no—
235C2×C22⋊C8C2×D1111yescharacteristic
236#388—221no—
237#387—221no—
238#386—221no—
239#386—221no—
240#385—221no—
241#380—111no—
242C2×#95—111no—
243C2×#95—111no—
244C2×#95—221no—
245#340—21no—
246#340—221no—
247#327—114no—
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—21no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11#38511yescharacteristic
268C22×C11C4×SD1611yescharacteristic
269C22×C11#44211yescharacteristic
270C22×C11#44911yescharacteristic
271C22×C11#45011yescharacteristic
272C22×C11#45311yescharacteristic
273C22×C11#45611yescharacteristic
274C22×C11B(4,𝔽2)11yescharacteristic
275C22×C11#45811yescharacteristic
276C22×C11#47611yescharacteristic
277C22×C11#47811yescharacteristic
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—21no—
281C4×C11—21no—
282C4×C11—42no—
283C4×C11—82no—
284Dic11—44no—
285Dic11—42no—
286Dic11—81no—
287Dic11—81no—
288Dic11—81no—
289C22×D4—21no—
290C22×D4C22⋊D1111yescharacteristic
291C23×C4—21no—
292C23×C4—111no—
293C23×C4—111no—
294C23×C4—221no—
295C23×C4—221no—
296C23×C4C22×D1111yescharacteristic
297C22×C8—21no—
298C22×C8—221no—
299#121—21no—
300#121—21no—
301#121Dic2212yes—
302#121C4×D1112yes—
303C4×D4—442no—
304C4×D4—442no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—42no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4—442no—
312C2×C4⋊C4—442no—
313C2×C4⋊C4—442no—
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C22⋊C4—21no—
316C2×C22⋊C4—221no—
317C2×C22⋊C4—221no—
318C2×C22⋊C4—221no—
319C2×C22⋊C4—221no—
320C2×C42—221no—
321#106—442no—
322#102—42no—
323C22⋊C8—21no—
324C22⋊C8—21no—
325C22⋊C8—112no—
326C22⋊C8—221no—
327#95—112no—
328#95—221no—
329#95—221no—
330#95—221no—
331#95—221no—
332#95—221no—
333#95—221no—
334#95—442no—
335C2×C11—21no—
336C2×C11—21no—
337C2×C11—21no—
338C2×C11—21no—
339C2×C11—82no—
340C2×C11#160011yescharacteristic
341C2×C11#160411yescharacteristic
342C2×C11#160911yescharacteristic
343C2×C11#161311yescharacteristic
344C2×C11#185911yescharacteristic
345C2×C11#186411yescharacteristic
346C2×C11#186711yescharacteristic
347C24—21no—
348C24D4×D1111yescharacteristic
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—21no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4Dic11⋊C412yescomplemented
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—112no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—221no—
374C22×C4—221no—
375C22×C4—221no—
376C22×C4—221no—
377C22×C4—221no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—442no—
381C22×C4—441no—
382C22×C4—441no—
383C22×C4—441no—
384C22×C4—441no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—881no—
390C22×C4—881no—
391C22×C4C2×Dic2211yescharacteristic
392C22×C4C2×C4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4#434111yescharacteristic
395C22×C4#434111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397C2×C8—41no—
398C2×C8—41no—
399C2×C8—41no—
400C2×C8—222no—
401C2×C8—441no—
402C2×C8—441no—
403C4⋊C4—21no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—441no—
409C4⋊C4—441no—
410C4⋊C4—442no—
411C4⋊C4—448no—
412C4⋊C4Dic11⋊C412yescomplemented
413C22⋊C4—22no—
414C22⋊C4—22no—
415C22⋊C4—442no—
416C22⋊C4—441no—
417C22⋊C4—441no—
418C22⋊C4—881no—
419C22⋊C4—881no—
420C42—442no—
421C11#887311yescharacteristic, complemented, Sylow
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—22no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23#6693111yescharacteristic
434C23(C22⋊D11)⋊C411yescharacteristic
435C23#6696411yescharacteristic
436C23#6696511yescharacteristic
437C23SD16×D1111yescharacteristic
438C23#6696711yescharacteristic
439C23#6699011yescharacteristic
440D4—42no—
441D4—42no—
442D4—42no—
443D4—42no—
444D4—42no—
445D4—81no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—224no—
465C2×C4—222no—
466C2×C4—442no—
467C2×C4—442no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—441no—
472C2×C4—442no—
473C2×C4—441no—
474C2×C4—442no—
475C2×C4—442no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—441no—
479C2×C4—441no—
480C2×C4—441no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—881no—
486C2×C4—884no—
487C2×C4—881no—
488C2×C4#6693111yescharacteristic
489C2×C4(C22⋊D11)⋊C411yescharacteristic
490C2×C4C2×Dic11⋊C411yescharacteristic
491C2×C4#6698811yescharacteristic
492C8—81no—
493C8—442no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22#1062237111yescharacteristic
514C22#1062237411yescharacteristic
515C22#1062237911yescharacteristic
516C22#1062239811yescharacteristic
517C22#1062255911yescharacteristic
518C22#1062264511yescharacteristic
519C22#1062266611yescharacteristic
520C22#1062277111yescharacteristic
521C22#1062278211yescharacteristic
522C22#1062281111yescharacteristic
523C22#1062281811yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—42no—
529C4—82no—
530C4—444no—
531C4—442no—
532C4—881no—
533C4—881no—
534C4—881no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—82no—
540C2#1306755911yescharacteristic
541C2#1306758311yescharacteristic
542C2#1306761011yescharacteristic
543C2#1306763411yescharacteristic
544C2#1306884011yescharacteristic
545C2#1306887511yescharacteristic
546C2#1306889611yescharacteristic
subgroupG/H
centerC23#66990
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1874C2
socleC23×C11#120
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenter#1874D11
hypocenterC11#8873
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. #13068809C2semidirect
4. #13066879C2semidirect
5. #13066496C2semidirect
6. #13066458C2semidirect
26. #10622175C4semidirect
70. C11⋊#95C2×C4semidirect
72. C22⋊(C11⋊C8)C2×C4semidirect
86. C2×D4×C11C4⋊C4semidirect
133. C11×C4⋊C4C4⋊C4semidirect
358. C2×D4Dic11⋊C4semidirect
412. C4⋊C4Dic11⋊C4semidirect
421. C11#8873semidirect

Maximal subgroups

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

subgroupindex
#130713212
#130688092
C2×#106221752
#130668792
#130664962
#130664582
C11×#18742
#887311