Finite Group Databasebeta

← #14657111

Subgroups — #14657111

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 560 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#13066880C211yesmaximal, characteristic, complemented
6#13066459C211yesmaximal, characteristic, complemented
7C11×#2639C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C2×C11×#121C2211yescharacteristic
10C22×C4⋊Dic11C2211yescharacteristic
11C22×Dic11⋊C4—21no—
12C11×#400—21no—
13C11×#397—21no—
14C11×#394—21no—
15C11×#393—21no—
16C11×#386—21no—
17C11×#386—21no—
18C2×C11×#95C2211yescharacteristic
19C2×#66899—21no—
20C2×#66896—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—
57C2×Dic11⋊C4—42no—
58C2×Dic11⋊C4—42no—
59C2×Dic11⋊C4—42no—
60C22×C11⋊C8—21no—
61C22×C11⋊C8—21no—
62C11×#95—21no—
63C11×#95—21no—
64C11×#95—21no—
65C11×#95—21no—
66C11×#95—21no—
67C11×#95—21no—
68#66899—42no—
69#66896—42no—
70C11⋊#95—21no—
71C11⋊#95—42no—
72C11⋊#95D412yes—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75C22⋊(C11⋊C8)—21no—
76C22⋊(C11⋊C8)—21no—
77#10405—111nomaximal, Sylow
78C24×C11—21no—
79C24×C11C2×D411yescharacteristic
80C2×Q8×C11—21no—
81C2×Q8×C11—21no—
82C2×Q8×C11—41no—
83C2×Q8×C11—41no—
84C2×D4×C11—21no—
85C2×D4×C11—21no—
86C2×D4×C11—41no—
87C2×D4×C11—41no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—41no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
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—21no—
102C22×C4×C11—21no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—41no—
120C22×Dic11—41no—
121C22×Dic11—41no—
122C22×Dic11—41no—
123C22×Dic11—41no—
124C22×Dic11—41no—
125C22×Dic11—41no—
126C22×Dic11—41no—
127C22×Dic11—41no—
128C22×Dic11—41no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—41no—
134C11×C4⋊C4—41no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C11×C22⋊C4—81no—
140C11×C22⋊C4—81no—
141C11×C22⋊C4—81no—
142C11×C22⋊C4—81no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—41no—
146C4⋊Dic11—41no—
147Dic11⋊C4—48no—
148C2×C11⋊C8—41no—
149C2×C11⋊C8—41no—
150C2×C11⋊C8—41no—
151C2×C11⋊C8—41no—
152C2×C11⋊C8—41no—
153C2×C11⋊C8—41no—
154#2639D1111yescharacteristic
155#1874—111no—
156#1872—111no—
157C2×#328—111no—
158C2×#327—111no—
159#1444—111no—
160#1280—111no—
161C23×C11—21no—
162C23×C11—21no—
163C23×C11—21no—
164C23×C11—21no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11—41no—
168C23×C11—41no—
169C23×C11—41no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11#12011yescharacteristic
173C23×C11#12111yescharacteristic
174C23×C11#12411yescharacteristic
175C23×C11#13511yescharacteristic
176C23×C11#13511yescharacteristic
177C23×C11AGL(1,ℤ/8)11yescharacteristic
178C23×C11#13711yescharacteristic
179Q8×C11—42no—
180Q8×C11—81no—
181D4×C11—42no—
182D4×C11—81no—
183D4×C11—81no—
184D4×C11—81no—
185D4×C11—81no—
186D4×C11—81no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
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—41no—
210C2×C4×C11—41no—
211C2×C4×C11—41no—
212C2×C4×C11—81no—
213C2×C4×C11—81no—
214C2×C4×C11#12111yescharacteristic
215C2×C4×C11#12111yescharacteristic
216C2×C4×C11#12311yescharacteristic
217C2×C4×C11#12311yescharacteristic
218C2×Dic11—24no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—81no—
229C2×Dic11—81no—
230C2×Dic11—81no—
231C2×Dic11—81no—
232C11⋊C8—81no—
233C11⋊C8—81no—
234C2×C22⋊Q8C2×D1111yescharacteristic
235C2×#121C2×D1111yescharacteristic
236C22×C4⋊C4—111no—
237C22×C4⋊C4—221no—
238C2×#103—221no—
239C2×#102—221no—
240C2×C22⋊C8—111no—
241C2×C22⋊C8—111no—
242#400—21no—
243#397—21no—
244#394—21no—
245#393—21no—
246#386—21no—
247#386—21no—
248C2×#95—111no—
249C2×#95—221no—
250C2×#95C2×D1111yescharacteristic
251#340—221no—
252#340—221no—
253#328—222no—
254#327—222no—
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—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—81no—
268C22×C11—81no—
269C22×C11—81no—
270C22×C11—81no—
271C22×C11—81no—
272C22×C11—81no—
273C22×C11—81no—
274C22×C11#39411yescharacteristic
275C22×C11#44911yescharacteristic
276C22×C11#45211yescharacteristic
277C22×C11#45311yescharacteristic
278C22×C11#45611yescharacteristic
279C22×C11B(4,𝔽2)11yescharacteristic
280C22×C11#45811yescharacteristic
281C22×C11#46311yescharacteristic
282C22×C11#46411yescharacteristic
283C22×C11#48811yescharacteristic
284C22×C11#48911yescharacteristic
285C4×C11—21no—
286C4×C11—21no—
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—81no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11—81no—
294Dic11—44no—
295Dic11—82no—
296C22×Q8C22⋊D1111yescharacteristic
297C22×D4—21no—
298C22×D4C22⋊D1111yescharacteristic
299C23×C4—221no—
300C23×C4—221no—
301C23×C4C22⋊D1111yescharacteristic
302C23×C4C22⋊D1111yescharacteristic
303C23×C4C22×D1111yescharacteristic
304C22×C8—221no—
305C22×C8—221no—
306C22⋊Q8—21no—
307C22⋊Q8—21no—
308C22⋊Q8—21no—
309C22⋊Q8—21no—
310#121—21no—
311#121—21no—
312#121—21no—
313#121—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—442no—
318C2×C4⋊C4—442no—
319C2×C4⋊C4—442no—
320C2×C4⋊C4—442no—
321C2×C4⋊C4C22⋊D1111yescharacteristic
322C2×C4⋊C4C22⋊D1111yescharacteristic
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329#103—442no—
330#102—442no—
331C22⋊C8—221no—
332C22⋊C8—221no—
333C22⋊C8—221no—
334C22⋊C8—221no—
335#95—21no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—21no—
340#95—21no—
341#95—112no—
342#95—221no—
343#95—442no—
344C2×C11—21no—
345C2×C11—21no—
346C2×C11—21no—
347C2×C11—21no—
348C2×C11—161no—
349C2×C11#160011yescharacteristic
350C2×C11#160311yescharacteristic
351C2×C11#160911yescharacteristic
352C2×C11#161811yescharacteristic
353C2×C11#203911yescharacteristic
354C2×C11#204211yescharacteristic
355C2×C11#204411yescharacteristic
356C24—21no—
357C24C2×C22⋊D1111yescharacteristic
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—41no—
361C2×Q8—41no—
362C2×D4—21no—
363C2×D4—21no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—222no—
390C22×C4—222no—
391C22×C4—441no—
392C22×C4—441no—
393C22×C4—441no—
394C22×C4—441no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4—441no—
398C22×C4—441no—
399C22×C4—441no—
400C22×C4—441no—
401C22×C4D4×D1111yescharacteristic
402C22×C4#434111yescharacteristic
403C22×C4#434111yescharacteristic
404C22×C4#434111yescharacteristic
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1111yescharacteristic
407C2×C8—441no—
408C2×C8—441no—
409C2×C8—441no—
410C2×C8—441no—
411C2×C8—441no—
412C2×C8—441no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—21no—
416C4⋊C4—21no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—222no—
420C4⋊C4—222no—
421C4⋊C4—441no—
422C4⋊C4—441no—
423C4⋊C4—448no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—41no—
428C22⋊C4—81no—
429C22⋊C4—81no—
430C22⋊C4—81no—
431C22⋊C4—81no—
432C11#1040511yescharacteristic, complemented, Sylow
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—41no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23#6698911yescharacteristic
445C23#6699111yescharacteristic
446C23#6700211yescharacteristic
447C23#6700311yescharacteristic
448C23#6700311yescharacteristic
449C23#6700411yescharacteristic
450C23#6700611yescharacteristic
451Q8—42no—
452Q8—81no—
453D4—42no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—81no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
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—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—224no—
487C2×C4—442no—
488C2×C4—442no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—442no—
492C2×C4—442no—
493C2×C4—442no—
494C2×C4—442no—
495C2×C4—442no—
496C2×C4—881no—
497C2×C4—881no—
498C2×C4—881no—
499C2×C4—881no—
500C2×C4#6698811yescharacteristic
501C2×C4#6698811yescharacteristic
502C2×C4#6699211yescharacteristic
503C2×C4#6699211yescharacteristic
504C8—881no—
505C8—881no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22#1062266711yescharacteristic
526C22#1062266811yescharacteristic
527C22#1062266911yescharacteristic
528C22#1062267011yescharacteristic
529C22#1062283511yescharacteristic
530C22#1062285111yescharacteristic
531C22#1062285211yescharacteristic
532C22#1062285411yescharacteristic
533C22#1062285611yescharacteristic
534C22#1062285711yescharacteristic
535C22#1062285911yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—81no—
541C4—81no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—444no—
546C4—882no—
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—161no—
552C2#1306756211yescharacteristic
553C2#1306757911yescharacteristic
554C2#1306761311yescharacteristic
555C2#1306766411yescharacteristic
556C2#1306983711yescharacteristic
557C2#1306985211yescharacteristic
558C2#1306986411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2639C2
socleC23×C11#120
prime radicalC2×C11×#121C22
hypercenter#2639D11
hypocenterC11#10405
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. #13066880C2semidirect
6. #13066459C2semidirect
432. C11#10405semidirect

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
#130668802
#130664592
C11×#26392
#1040511