Finite Group Databasebeta

← #14651102

Subgroups — #14651102

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077642C211yesmaximal, characteristic, complemented
2#13073576C211yesmaximal, characteristic
3#13068601C211yesmaximal, characteristic, complemented
4#13067185C211yesmaximal, characteristic, complemented
5#13067183C211yesmaximal, characteristic, complemented
6#13066495C211yesmaximal, characteristic, complemented
7C11×#1294C211yesmaximal, characteristic, complemented
8C2×#66983—21no—
9C2×#66983C2211yescharacteristic
10C2×C4×C22⋊D11C2211yescharacteristic
11C2×C11×C22⋊C8C2211yescharacteristic
12C11×#380C2211yescharacteristic
13C2×C11×#95C2211yescharacteristic
14#10622826—21no—
15#10622825C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622724—22no—
18C2×#66870—21no—
19#10622343—22no—
20#10622339—21no—
21#10622332—21no—
22#10622287C411yescharacteristic, complemented
23#10622285C411yescharacteristic, complemented
24#10622284C411yescharacteristic, complemented
25#10622283—21no—
26#10622278—21no—
27#10622274C411yescharacteristic, complemented
28#10622165—21no—
29#10622108—22no—
30#10622089—22no—
31C23×C4×C11—21no—
32C23×C4×C11C2311yescharacteristic
33C22×C22⋊D11—21no—
34C22×C22⋊D11D411yescharacteristic
35C22×D44—21no—
36C22×D44C2×C411yescharacteristic
37C22×C4×D11D411yescharacteristic
38C22×C8×C11—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C22⋊C4—21no—
41C2×C22⋊Dic11—21no—
42C2×C22⋊Dic11D411yescharacteristic
43#66983—21no—
44#66983—21no—
45#66983—21no—
46#66983—21no—
47#66983—42no—
48#66983—42no—
49C4×C22⋊D11—21no—
50C4×C22⋊D11—21no—
51C4×C22⋊D11—21no—
52C4×C22⋊D11—21no—
53C2×(C2×D11)⋊C4—21no—
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4C2×C411yescharacteristic
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11C2×C411yescharacteristic
62C2×Dic11⋊C4C2×C411yescharacteristic
63C2×C4×Dic11D411yescharacteristic
64C22×C11⋊C8—21no—
65C2×#4313—22no—
66C11×C22⋊C8—21no—
67C11×C22⋊C8D412yescomplemented
68C11×#95—21no—
69C11×#95—21no—
70C11×#95C2×C411yescharacteristic
71C11×#95C2×C411yescharacteristic
72C11⋊#95—21no—
73C11⋊#95—21no—
74C11⋊#95—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)D412yescomplemented
77(C2×D11)⋊C8—22no—
78#66879—22no—
79Dic11⋊C8—22no—
80#66870—42no—
81#9386—111nomaximal, Sylow
82C24×C11C2×D411yescharacteristic
83C23×D11—21no—
84C23×D11C22⋊C411yescharacteristic
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—42no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—81no—
92C22×C4×C11—81no—
93C22×C4×C11C22×C411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×C4×C11#4111yescharacteristic
99C2×C22⋊D11—21no—
100C2×C22⋊D11—21no—
101C2×C22⋊D11—21no—
102C2×C22⋊D11—21no—
103C2×C22⋊D11—21no—
104C2×C22⋊D11—21no—
105C2×C22⋊D11—41no—
106C2×C22⋊D11—41no—
107C2×C22⋊D11—41no—
108C2×C22⋊D11—41no—
109C2×C22⋊D11—41no—
110C2×C22⋊D11—41no—
111C22×Dic11—21no—
112C22×Dic11—41no—
113C22×Dic11C22⋊C411yescharacteristic
114C22×Dic11C22⋊C411yescharacteristic
115C22×Dic11C22⋊C411yescharacteristic
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—42no—
119C2×D44—42no—
120C2×D44—81no—
121C2×D44—81no—
122C2×C4×D11—21no—
123C2×C4×D11—21no—
124C2×C4×D11—81no—
125C2×C8×C11—22no—
126C2×C8×C11—81no—
127C11×C4⋊C4—81no—
128C11×C22⋊C4—41no—
129C11×C22⋊C4—41no—
130C22⋊Dic11—21no—
131C22⋊Dic11—21no—
132C22⋊Dic11—41no—
133C22⋊Dic11—41no—
134(C2×D11)⋊C4—21no—
135(C2×D11)⋊C4—21no—
136(C2×D11)⋊C4—42no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—41no—
140(C2×D11)⋊C4—41no—
141(C2×D11)⋊C4—81no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—42no—
145C4⋊Dic11—81no—
146Dic11⋊C4—21no—
147Dic11⋊C4—21no—
148C4×Dic11—21no—
149C4×Dic11—21no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—81no—
152#4313—82no—
153#2973—111no—
154#2543—111no—
155#1799—111no—
156#1519—111no—
157#1519—111no—
158#1294—111no—
159#1294D1111yescharacteristic, complemented
160C23×C11—41no—
161C23×C11—41no—
162C23×C11C2×C22⋊C411yescharacteristic
163C23×C11#12111yescharacteristic
164C23×C11#12111yescharacteristic
165C23×C11AGL(1,ℤ/8)11yescharacteristic
166C23×C11AGL(1,ℤ/8)11yescharacteristic
167C23×C11AGL(1,ℤ/8)11yescharacteristic
168C23×C11#13711yescharacteristic
169C22×D11—21no—
170C22×D11—21no—
171C22×D11—21no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181C2×C4×C11—22no—
182C2×C4×C11—41no—
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—41no—
192C2×C4×C11—41no—
193C2×C4×C11—82no—
194C2×C4×C11—82no—
195C2×C4×C11—81no—
196C2×C4×C11—81no—
197C2×C4×C11—81no—
198C2×C4×C11C4×D411yescharacteristic
199C2×C4×C11C4×D411yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#12311yescharacteristic
202C22⋊D11—41no—
203C22⋊D11—41no—
204C22⋊D11—41no—
205C22⋊D11—41no—
206C22⋊D11—81no—
207C22⋊D11—81no—
208C22⋊D11—81no—
209C22⋊D11—81no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—21no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—41no—
220C2×Dic11—81no—
221C2×Dic11—81no—
222C2×Dic11—81no—
223D44—81no—
224D44—81no—
225D44—84no—
226C4×D11—42no—
227C4×D11—81no—
228C8×C11—42no—
229C11⋊C8—42no—
230C2×#121—111no—
231C2×#121—221no—
232C2×C4×D4—111no—
233#435—222no—
234#435—222no—
235#432—221no—
236C2×#99—221no—
237#407—221no—
238C2×C22⋊C8—111no—
239C2×C22⋊C8C2×D1111yescharacteristic
240#398—111no—
241#397—111no—
242#394—111no—
243#392—111no—
244#388—221no—
245#386—221no—
246#386—221no—
247#380—111no—
248#380C2×D1111yescharacteristic
249C2×#95C2×D1111yescharacteristic
250#342—221no—
251#327—222no—
252#327—222no—
253C22×C11—21no—
254C22×C11—21no—
255C22×C11—21no—
256C22×C11—21no—
257C22×C11—21no—
258C22×C11—21no—
259C22×C11—41no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11#38611yescharacteristic
264C22×C11#41711yescharacteristic
265C22×C11#41811yescharacteristic
266C22×C11#46811yescharacteristic
267C22×C11#46811yescharacteristic
268C22×C11#46911yescharacteristic
269C22×C11#46911yescharacteristic
270C2×D11—42no—
271C2×D11—41no—
272C2×D11—41no—
273C2×D11—41no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C2×D11—81no—
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C2×D11—81no—
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—42no—
287C4×C11—81no—
288C4×C11—161no—
289Dic11—41no—
290Dic11—41no—
291Dic11—41no—
292Dic11—81no—
293Dic11—161no—
294C22×D4—111no—
295C22×D4—111no—
296C22×D4—221no—
297C22×D4—221no—
298C23×C4—21no—
299C23×C4—111no—
300C23×C4C22×D1111yescharacteristic
301C2×M16—222no—
302C22×C8—21no—
303C22×C8—221no—
304#121—221no—
305#121—221no—
306#121—221no—
307#121—221no—
308#121—442no—
309#121—442no—
310C4×D4—221no—
311C4×D4—221no—
312C4×D4—221no—
313C4×D4—221no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—111no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4—221no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—111no—
321C2×C22⋊C4—111no—
322C2×C22⋊C4—221no—
323C2×C22⋊C4—221no—
324C2×C22⋊C4—221no—
325C2×C22⋊C4—221no—
326C2×C22⋊C4—221no—
327C2×C22⋊C4—221no—
328C2×C42—111no—
329C4⋊C8—222no—
330#99—442no—
331C22⋊C8—21no—
332C22⋊C8—112no—
333C22⋊C8—222no—
334C22⋊C8—221no—
335C22⋊C8D4412yescomplemented
336#97—222no—
337#95—21no—
338#95—21no—
339#95—221no—
340#95—221no—
341#95—221no—
342#95C4×D1111yescharacteristic
343#95C4×D1111yescharacteristic
344C2×C11—21no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—21no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11#188411yescharacteristic
351C2×C11#189511yescharacteristic
352C2×C11#191311yescharacteristic
353D11—81no—
354D11—161no—
355C24—111no—
356C24—221no—
357C24D4×D1111yescharacteristic
358C2×D4—221no—
359C2×D4—221no—
360C2×D4—221no—
361C2×D4—221no—
362C2×D4—221no—
363C2×D4—221no—
364C2×D4—221no—
365C2×D4—221no—
366C2×D4—442no—
367C2×D4—442no—
368C2×D4—441no—
369C2×D4—441no—
370C2×D4—441no—
371C2×D4—441no—
372C2×D4—441no—
373C2×D4—441no—
374C2×D4—881no—
375C2×D4—881no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—42no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—81no—
383C22×C4—81no—
384C22×C4—111no—
385C22×C4—111no—
386C22×C4—111no—
387C22×C4—221no—
388C22×C4—221no—
389C22×C4—221no—
390C22×C4—441no—
391C22×C4—881no—
392C22×C4C2×C4×D1111yescharacteristic
393C22×C4C2×D4411yescharacteristic
394C22×C4#433911yescharacteristic
395C22×C4D4×D1111yescharacteristic
396C22×C4D4×D1111yescharacteristic
397C22×C4#434311yescharacteristic
398M16—882no—
399C2×C8—22no—
400C2×C8—81no—
401C2×C8—222no—
402C2×C8—881no—
403C4⋊C4—81no—
404C4⋊C4—221no—
405C4⋊C4—221no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—442no—
409C4⋊C4—881no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—221no—
413C22⋊C4—221no—
414C22⋊C4—221no—
415C22⋊C4—221no—
416C22⋊C4—442no—
417C22⋊C4—442no—
418C22⋊C4—442no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C22⋊C4—441no—
422C22⋊C4—441no—
423C22⋊C4—881no—
424C42—221no—
425C42—221no—
426C11#938611yescharacteristic, complemented, Sylow
427C23—41no—
428C23—41no—
429C23—221no—
430C23—221no—
431C23—221no—
432C23—441no—
433C23—441no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23C22⋊C4×D1111yescharacteristic
442C23#6693711yescharacteristic
443C23#6694811yescharacteristic
444C23#6696411yescharacteristic
445C23#6696711yescharacteristic
446C23#6696711yescharacteristic
447C23#6697111yescharacteristic
448D4—441no—
449D4—441no—
450D4—441no—
451D4—441no—
452D4—881no—
453D4—881no—
454D4—884no—
455D4—881no—
456D4—881no—
457D4—881no—
458D4—881no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—221no—
477C2×C4—221no—
478C2×C4—221no—
479C2×C4—221no—
480C2×C4—221no—
481C2×C4—442no—
482C2×C4—441no—
483C2×C4—441no—
484C2×C4—441no—
485C2×C4—441no—
486C2×C4—441no—
487C2×C4—881no—
488C2×C4—881no—
489C2×C4—881no—
490C2×C4—881no—
491C2×C4C4×D4411yescharacteristic
492C2×C4#6693511yescharacteristic
493C2×C4#6694611yescharacteristic
494C2×C4#6694711yescharacteristic
495C8—42no—
496C8—442no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—442no—
508C22—441no—
509C22—441no—
510C22—441no—
511C22—881no—
512C22—881no—
513C22—881no—
514C22—881no—
515C22—881no—
516C22—881no—
517C22—881no—
518C22—881no—
519C22#1062227811yescharacteristic
520C22#1062238311yescharacteristic
521C22#1062239511yescharacteristic
522C22#1062241611yescharacteristic
523C22#1062242511yescharacteristic
524C22#1062247811yescharacteristic
525C22#1062249911yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—42no—
531C4—81no—
532C4—161no—
533C4—441no—
534C4—441no—
535C4—441no—
536C4—881no—
537C4—1761no—
538C2—21no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—881no—
545C2—1761no—
546C2#1306899811yescharacteristic
547C2#1306905311yescharacteristic
548C2#1306915711yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1294C2
socleC22×C11#386
prime radical#13073576C2
cosocleC23×C4×C11C23
hypercenter#1294D11
hypocenterC11#9386
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
1. #13077642C2semidirect
3. #13068601C2semidirect
4. #13067185C2semidirect
5. #13067183C2semidirect
6. #13066495C2semidirect
7. C11×#1294C2semidirect
22. #10622287C4semidirect
23. #10622285C4semidirect
24. #10622284C4semidirect
27. #10622274C4semidirect
67. C11×C22⋊C8D4semidirect
76. C22⋊(C11⋊C8)D4semidirect
159. #1294D11semidirect
335. C22⋊C8D44semidirect
426. C11#9386semidirect

Maximal subgroups

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

subgroupindex
#130776422
#130735762
#130686012
#130671852
#130671832
#130664952
C11×#12942
#938611