Finite Group Databasebeta

← #14657104

Subgroups — #14657104

Order 2816.

602 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068934C211yesmaximal, characteristic
2#13068924C211yesmaximal, characteristic, complemented
3C2×#10622176C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic
5#13066872C211yesmaximal, characteristic, complemented
6#13066459C211yesmaximal, characteristic, complemented
7C11×#2639C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C22×C4⋊Dic11C2211yescharacteristic
11C11×#400—21no—
12C11×#397—21no—
13C11×#394—21no—
14C11×#393—21no—
15C11×#386—21no—
16C11×#386—21no—
17C2×C11×#95C2211yescharacteristic
18C2×#66899—21no—
19C2×#66896—21no—
20C2×C11⋊#95—21no—
21C2×C11⋊#95—21no—
22C2×C11⋊#95C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25#10622176—22no—
26#10622175—22no—
27#10622167—21no—
28#10622167—21no—
29C22×Q8×C11D411yescharacteristic
30C22×D4×C11—21no—
31C22×D4×C11D411yescharacteristic
32C23×C4×C11D411yescharacteristic
33C23×C4×C11D411yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×Dic11—21no—
36C23×Dic11—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C11×#121—21no—
42C11×#121—21no—
43C11×#121—21no—
44C11×#121—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4D411yescharacteristic
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C11×C22⋊C4—21no—
50C2×C11×C22⋊C4—21no—
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C11×C22⋊C4—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—21no—
56C2×C4⋊Dic11—42no—
57C22×C11⋊C8—21no—
58C22×C11⋊C8—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64C11×#95—21no—
65#66899—42no—
66#66896—42no—
67C11⋊#95—21no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C11⋊#95D412yes—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75#10404—111nomaximal, Sylow
76C24×C11—21no—
77C24×C11C2×D411yescharacteristic
78C2×Q8×C11—21no—
79C2×Q8×C11—21no—
80C2×Q8×C11—41no—
81C2×Q8×C11—41no—
82C2×D4×C11—21no—
83C2×D4×C11—21no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C22×Dic11—41no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—41no—
132C11×C4⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—81no—
138C11×C22⋊C4—81no—
139C11×C22⋊C4—81no—
140C11×C22⋊C4—81no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—41no—
144C4⋊Dic11—41no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147C2×C11⋊C8—41no—
148C2×C11⋊C8—41no—
149C2×C11⋊C8—41no—
150C2×C11⋊C8—41no—
151#2639D1111yescharacteristic
152#1874—111no—
153#1872—111no—
154C2×#328—111no—
155C2×#327—111no—
156#1442—111no—
157#1280—111no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11—21no—
162C23×C11—41no—
163C23×C11—41no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11#12011yescharacteristic
170C23×C11#12111yescharacteristic
171C23×C11#12411yescharacteristic
172C23×C11#13511yescharacteristic
173C23×C11#13511yescharacteristic
174C23×C11AGL(1,ℤ/8)11yescharacteristic
175C23×C11#13711yescharacteristic
176Q8×C11—42no—
177Q8×C11—81no—
178D4×C11—42no—
179D4×C11—81no—
180D4×C11—81no—
181D4×C11—81no—
182D4×C11—81no—
183D4×C11—81no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
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—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—81no—
210C2×C4×C11—81no—
211C2×C4×C11#12111yescharacteristic
212C2×C4×C11#12111yescharacteristic
213C2×C4×C11#12311yescharacteristic
214C2×C4×C11#12311yescharacteristic
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—81no—
222C2×Dic11—81no—
223C2×Dic11—81no—
224C2×Dic11—81no—
225C2×Dic11—81no—
226C2×Dic11—81no—
227C2×Dic11—81no—
228C2×Dic11—81no—
229C11⋊C8—81no—
230C11⋊C8—81no—
231C2×C22⋊Q8C2×D1111yescharacteristic
232C2×#121C2×D1111yescharacteristic
233C22×C4⋊C4—111no—
234C2×#103—221no—
235C2×#102—221no—
236C2×C22⋊C8—111no—
237C2×C22⋊C8—111no—
238#400—21no—
239#397—21no—
240#394—21no—
241#393—21no—
242#386—21no—
243#386—21no—
244C2×#95—111no—
245C2×#95—221no—
246C2×#95—221no—
247C2×#95C2×D1111yescharacteristic
248#340—221no—
249#340—221no—
250#328—222no—
251#327—222no—
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—21no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—81no—
265C22×C11—81no—
266C22×C11—81no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11#39411yescharacteristic
272C22×C11#44911yescharacteristic
273C22×C11#45211yescharacteristic
274C22×C11#45411yescharacteristic
275C22×C11#45511yescharacteristic
276C22×C11B(4,𝔽2)11yescharacteristic
277C22×C11#45811yescharacteristic
278C22×C11#46311yescharacteristic
279C22×C11#46411yescharacteristic
280C22×C11#48811yescharacteristic
281C22×C11#48911yescharacteristic
282C4×C11—21no—
283C4×C11—21no—
284C4×C11—21no—
285C4×C11—21no—
286C4×C11—81no—
287C4×C11—81no—
288C4×C11—81no—
289C4×C11—81no—
290C4×C11—81no—
291Dic11—82no—
292Dic11—82no—
293C22×Q8C22⋊D1111yescharacteristic
294C22×D4—21no—
295C22×D4C22⋊D1111yescharacteristic
296C23×C4—221no—
297C23×C4—221no—
298C23×C4C22⋊D1111yescharacteristic
299C23×C4C22⋊D1111yescharacteristic
300C23×C4C22×D1111yescharacteristic
301C22×C8—221no—
302C22×C8—221no—
303C22⋊Q8—21no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306C22⋊Q8—21no—
307#121—21no—
308#121—21no—
309#121—21no—
310#121—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4—442no—
315C2×C4⋊C4C22⋊D1111yescharacteristic
316C2×C4⋊C4C22⋊D1111yescharacteristic
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323#103—442no—
324#102—442no—
325C22⋊C8—221no—
326C22⋊C8—221no—
327C22⋊C8—221no—
328C22⋊C8—221no—
329#95—21no—
330#95—21no—
331#95—21no—
332#95—21no—
333#95—21no—
334#95—21no—
335#95—112no—
336#95—221no—
337#95—442no—
338#95—442no—
339C2×C11—21no—
340C2×C11—21no—
341C2×C11—21no—
342C2×C11—21no—
343C2×C11—161no—
344C2×C11#159711yescharacteristic
345C2×C11#160611yescharacteristic
346C2×C11#161211yescharacteristic
347C2×C11#161511yescharacteristic
348C2×C11#204011yescharacteristic
349C2×C11#204211yescharacteristic
350C2×C11#204411yescharacteristic
351C24—21no—
352C24C2×C22⋊D1111yescharacteristic
353C2×Q8—21no—
354C2×Q8—21no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—441no—
385C22×C4—441no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4—441no—
392C22×C4—441no—
393C22×C4—441no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4D4×D1111yescharacteristic
397C22×C4#434111yescharacteristic
398C22×C4#434111yescharacteristic
399C22×C4#434111yescharacteristic
400C22×C4C2×C22⋊D1111yescharacteristic
401C22×C4C2×C22⋊D1111yescharacteristic
402C2×C8—441no—
403C2×C8—441no—
404C2×C8—441no—
405C2×C8—441no—
406C2×C8—441no—
407C2×C8—441no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—21no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—222no—
415C4⋊C4—222no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—41no—
422C22⋊C4—81no—
423C22⋊C4—81no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C11#1040411yescharacteristic, complemented, Sylow
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—41no—
438C23#6698911yescharacteristic
439C23#6699111yescharacteristic
440C23#6700211yescharacteristic
441C23#6700311yescharacteristic
442C23#6700311yescharacteristic
443C23#6700411yescharacteristic
444C23#6700611yescharacteristic
445Q8—42no—
446Q8—81no—
447D4—42no—
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452D4—81no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
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—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—442no—
481C2×C4—442no—
482C2×C4—442no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—881no—
487C2×C4—881no—
488C2×C4—881no—
489C2×C4—881no—
490C2×C4—881no—
491C2×C4—881no—
492C2×C4—881no—
493C2×C4—881no—
494C2×C4#6698811yescharacteristic
495C2×C4#6698811yescharacteristic
496C2×C4#6699211yescharacteristic
497C2×C4#6699211yescharacteristic
498C8—881no—
499C8—881no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22#1062266711yescharacteristic
520C22#1062266811yescharacteristic
521C22#1062266911yescharacteristic
522C22#1062267011yescharacteristic
523C22#1062283511yescharacteristic
524C22#1062285111yescharacteristic
525C22#1062285211yescharacteristic
526C22#1062285511yescharacteristic
527C22#1062285611yescharacteristic
528C22#1062285711yescharacteristic
529C22#1062285811yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—81no—
539C4—882no—
540C4—882no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—161no—
546C2#1306754511yescharacteristic
547C2#1306759611yescharacteristic
548C2#1306763011yescharacteristic
549C2#1306764711yescharacteristic
550C2#1306984211yescharacteristic
551C2#1306985211yescharacteristic
552C2#1306986411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2639C2
socleC23×C11#120
prime radicalC2×C11×#121C22
hypercenter#2639D11
hypocenterC11#10404
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2639

Complements

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

NH ≅ G/Ntype
2. #13068924C2semidirect
3. C2×#10622176C2semidirect
5. #13066872C2semidirect
6. #13066459C2semidirect
426. C11#10404semidirect

Maximal subgroups

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

subgroupindex
#130689342
#130689242
C2×#106221762
C2×#106221752
#130668722
#130664592
C11×#26392
#1040411