Finite Group Databasebeta

← #14657124

Subgroups — #14657124

Order 2816.

576 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074732C211yesmaximal, characteristic
2#13068923C211yesmaximal, characteristic
3C2×#10622105C211yesmaximal, characteristic
4C2×#10622176C211yesmaximal, characteristic
5#13066875C211yesmaximal, characteristic
6#13066458C211yesmaximal, characteristic
7C11×#1872C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66977C2211yescharacteristic
11C2×C11×#103—21no—
12C2×C11×C22⋊C8C2211yescharacteristic
13#10622842—21no—
14C2×C11⋊#95—21no—
15C2×C11⋊#95—21no—
16C2×C11⋊#95C2211yescharacteristic
17C2×C11⋊#95C2211yescharacteristic
18C2×C22⋊(C11⋊C8)C2211yescharacteristic
19#10622596—21no—
20#10622593—21no—
21#10622592—21no—
22C2×#66874—21no—
23#10622555—21no—
24#10622555—21no—
25C11×#340—21no—
26#10622176—22no—
27#10622167—21no—
28#10622105—22no—
29C22×Q8×C11D411yescharacteristic
30C23×C4×C11—21no—
31C23×C4×C11C2311yescharacteristic
32C23×Dic11—21no—
33C23×Dic11D411yescharacteristic
34C23×Dic11D411yescharacteristic
35C22×Dic22D411yescharacteristic
36C22×C8×C11—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C11×C22⋊Q8—21no—
40C11×C22⋊Q8—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—42no—
45C2×C11×C4⋊C4D411yescharacteristic
46C2×C11×C22⋊C4—21no—
47C2×C22⋊Dic11—21no—
48C2×C4⋊Dic11D411yescharacteristic
49#66977—21no—
50#66977—21no—
51#66977—21no—
52#66977—21no—
53C2×Dic11⋊C4—21no—
54C2×Dic11⋊C4—21no—
55C2×Dic11⋊C4—21no—
56C2×Dic11⋊C4—21no—
57C2×Dic11⋊C4—21no—
58C22×C11⋊C8—21no—
59C11×#103—42no—
60C11×C22⋊C8—21no—
61C11×C22⋊C8—21no—
62C11⋊#95—21no—
63C11⋊#95—21no—
64C11⋊#95—21no—
65C11⋊#95—21no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—21no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C11⋊#95D412yes—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)—21no—
74#66874—42no—
75#10407—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—41no—
85C22×C4×C11—41no—
86C22×C4×C11—41no—
87C22×C4×C11—41no—
88C22×C4×C11—41no—
89C22×C4×C11—41no—
90C22×C4×C11—41no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11#4111yescharacteristic
96C22×C4×C11#4111yescharacteristic
97C22×C4×C11#4111yescharacteristic
98C22×Dic11—21no—
99C22×Dic11—21no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—22no—
103C22×Dic11—21no—
104C22×Dic11—21no—
105C22×Dic11—41no—
106C22×Dic11—41no—
107C22×Dic11—41no—
108C22×Dic11—41no—
109C22×Dic11—41no—
110C22×Dic11—41no—
111C22×Dic11—41no—
112C22×Dic11—41no—
113C22×Dic11—41no—
114C22×Dic11—41no—
115C22×Dic11SD1612yes—
116C22×Dic11Q1612yes—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—41no—
120C2×Dic22—41no—
121C2×C8×C11—41no—
122C2×C8×C11—41no—
123C2×C8×C11—41no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C4⋊C4—41no—
131C11×C4⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C22⋊Dic11—41no—
135C22⋊Dic11—41no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138Dic11⋊C4—41no—
139Dic11⋊C4—41no—
140Dic11⋊C4—81no—
141Dic11⋊C4—81no—
142Dic11⋊C4—81no—
143Dic11⋊C4—81no—
144C2×C11⋊C8—41no—
145C2×C11⋊C8—41no—
146C2×C11⋊C8—41no—
147#2659—111no—
148#1872—111no—
149#1872D1111yescharacteristic
150C2×#328—111no—
151C2×#328—111no—
152#1442—111no—
153#1280—111no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11—21no—
157C23×C11—21no—
158C23×C11#12011yescharacteristic
159C23×C11#12111yescharacteristic
160C23×C11#12411yescharacteristic
161C23×C11C2×SD1611yescharacteristic
162C23×C11C2×Q1611yescharacteristic
163C23×C11#13711yescharacteristic
164C23×C11#13711yescharacteristic
165Q8×C11—42no—
166Q8×C11—81no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—21no—
170C2×C4×C11—21no—
171C2×C4×C11—41no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—42no—
183C2×C4×C11—41no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11—81no—
187C2×C4×C11—81no—
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12311yescharacteristic
191C2×C4×C11#12311yescharacteristic
192C2×Dic11—22no—
193C2×Dic11—22no—
194C2×Dic11—41no—
195C2×Dic11—41no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—42no—
209C2×Dic11—81no—
210C2×Dic11—81no—
211C2×Dic11—81no—
212C2×Dic11—81no—
213C2×Dic11—81no—
214C2×Dic11—81no—
215Dic22—42no—
216Dic22—81no—
217C8×C11—81no—
218C11⋊C8—81no—
219C2×C22⋊Q8—111no—
220C2×C22⋊Q8C2×D1111yescharacteristic
221C22×C4⋊C4C2×D1111yescharacteristic
222C2×#103—21no—
223C2×#103—221no—
224C2×C22⋊C8—111no—
225C2×C22⋊C8C2×D1111yescharacteristic
226#398—221no—
227#398—221no—
228#395—221no—
229#395—221no—
230#380—221no—
231#380—221no—
232C2×#95—111no—
233C2×#95—111no—
234C2×#95—221no—
235C2×#95—221no—
236#340—21no—
237#340—221no—
238#328—222no—
239#328—222no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—21no—
252C22×C11#39411yescharacteristic
253C22×C11#44811yescharacteristic
254C22×C11#45111yescharacteristic
255C22×C11#45411yescharacteristic
256C22×C11#45511yescharacteristic
257C22×C11B(4,𝔽2)11yescharacteristic
258C22×C11#45811yescharacteristic
259C22×C11#46111yescharacteristic
260C22×C11#46211yescharacteristic
261C22×C11#48711yescharacteristic
262C22×C11#49111yescharacteristic
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—21no—
266C4×C11—21no—
267C4×C11—82no—
268C4×C11—81no—
269C4×C11—81no—
270Dic11—42no—
271Dic11—42no—
272Dic11—82no—
273Dic11—81no—
274Dic11—81no—
275C22×Q8—111no—
276C22×Q8C22⋊D1111yescharacteristic
277C23×C4—21no—
278C23×C4—111no—
279C23×C4—111no—
280C23×C4—221no—
281C23×C4C22×D1111yescharacteristic
282C22×C8—21no—
283C22×C8—221no—
284C22⋊Q8—21no—
285C22⋊Q8—21no—
286C22⋊Q8—21no—
287C22⋊Q8—21no—
288C22⋊Q8—221no—
289C22⋊Q8—221no—
290C22⋊Q8—221no—
291C22⋊Q8—221no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—42no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—221no—
298C2×C4⋊C4—221no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4C22⋊D1111yescharacteristic
303C2×C22⋊C4—21no—
304C2×C22⋊C4—221no—
305#103—42no—
306#103—442no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—221no—
310C22⋊C8—221no—
311#95—112no—
312#95—221no—
313#95—221no—
314#95—221no—
315#95—221no—
316#95—221no—
317#95—221no—
318#95—221no—
319#95—442no—
320#95—442no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11#159911yescharacteristic
326C2×C11#160211yescharacteristic
327C2×C11#160811yescharacteristic
328C2×C11#161711yescharacteristic
329C2×C11#204011yescharacteristic
330C2×C11#204311yescharacteristic
331C2×C11#204411yescharacteristic
332C24D4×D1111yescharacteristic
333C2×Q8—21no—
334C2×Q8—21no—
335C2×Q8—41no—
336C2×Q8—41no—
337C2×Q8—221no—
338C2×Q8—221no—
339C2×Q8—441no—
340C2×Q8—441no—
341C22×C4—22no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—112no—
353C22×C4—112no—
354C22×C4—221no—
355C22×C4—221no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—222no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4—441no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4—441no—
368C22×C4—441no—
369C22×C4—441no—
370C22×C4—441no—
371C22×C4#433911yescharacteristic
372C22×C4#433911yescharacteristic
373C22×C4D4×D1111yescharacteristic
374C22×C4D4×D1111yescharacteristic
375C22×C4#434111yescharacteristic
376C22×C4C2×C22⋊D1111yescharacteristic
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—41no—
380C2×C8—441no—
381C2×C8—441no—
382C2×C8—441no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—221no—
392C4⋊C4—221no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—881no—
396C4⋊C4—881no—
397C4⋊C4—881no—
398C4⋊C4—881no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C11#1040711yescharacteristic, complemented, Sylow
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23#6693711yescharacteristic
409C23#6693811yescharacteristic
410C23SD16×D1111yescharacteristic
411C23#6696811yescharacteristic
412C23Q16×D1111yescharacteristic
413C23#6697111yescharacteristic
414C23#6699011yescharacteristic
415Q8—42no—
416Q8—81no—
417Q8—442no—
418Q8—881no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—81no—
437C2×C4—81no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—222no—
441C2×C4—222no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—441no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—441no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—442no—
457C2×C4—881no—
458C2×C4—881no—
459C2×C4—881no—
460C2×C4—881no—
461C2×C4—881no—
462C2×C4—881no—
463C2×C4#6693611yescharacteristic
464C2×C4#6693711yescharacteristic
465C2×C4#6698211yescharacteristic
466C2×C4#6699211yescharacteristic
467C8—81no—
468C8—881no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22#1062240511yescharacteristic
482C22#1062240611yescharacteristic
483C22#1062241011yescharacteristic
484C22#1062243111yescharacteristic
485C22#1062257211yescharacteristic
486C22#1062264511yescharacteristic
487C22#1062266611yescharacteristic
488C22#1062278311yescharacteristic
489C22#1062279911yescharacteristic
490C22#1062281411yescharacteristic
491C22#1062281511yescharacteristic
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—81no—
497C4—82no—
498C4—81no—
499C4—442no—
500C4—442no—
501C4—882no—
502C4—881no—
503C4—881no—
504C2—21no—
505C2—21no—
506C2—21no—
507C2—21no—
508C2#1306755411yescharacteristic
509C2#1306757111yescharacteristic
510C2#1306760511yescharacteristic
511C2#1306765611yescharacteristic
512C2#1306984311yescharacteristic
513C2#1306986011yescharacteristic
514C2#1306986511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1872C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1872D11
hypocenterC11#10407
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
403. C11#10407semidirect

Maximal subgroups

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

subgroupindex
#130747322
#130689232
C2×#106221052
C2×#106221762
#130668752
#130664582
C11×#18722
#1040711