Finite Group Databasebeta

← #14657087

Subgroups — #14657087

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068924C211yesmaximal, characteristic
2#13068808C211yesmaximal, characteristic
3C2×#10622176C211yesmaximal, characteristic
4C2×#10622166C211yesmaximal, characteristic
5#13066869C211yesmaximal, characteristic
6#13066494C211yesmaximal, characteristic
7C11×#2627C211yesmaximal, characteristic
8C2×C11×C22⋊Q8C2211yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×C4⋊Dic11C2211yescharacteristic
11C11×#400—21no—
12C11×#398—21no—
13C11×#398—21no—
14C11×#395—21no—
15C11×#385—21no—
16C11×#381—21no—
17C11×#380C2211yescharacteristic
18C2×#66899—21no—
19C2×C11⋊#95—21no—
20C2×C11⋊#95—21no—
21C2×C11⋊#95C2211yescharacteristic
22C2×C22⋊(C11⋊C8)C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×#66872—21no—
25#10622176—22no—
26#10622167—21no—
27#10622167—21no—
28#10622166—22no—
29C22×Q8×C11D411yescharacteristic
30C23×C4×C11D411yescharacteristic
31C23×C4×C11D411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×Dic11—21no—
34C23×Dic11—21no—
35C11×C22⋊Q8—21no—
36C11×C22⋊Q8—21no—
37C11×C22⋊Q8—21no—
38C11×C22⋊Q8—21no—
39C2×C11×C4⋊C4—21no—
40C2×C11×C4⋊C4—21no—
41C2×C11×C4⋊C4—21no—
42C2×C11×C4⋊C4—21no—
43C2×C11×C4⋊C4—21no—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C4⋊C4D411yescharacteristic
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—21no—
52C2×C11×C22⋊C4—21no—
53C2×C4⋊Dic11—21no—
54C2×C4⋊Dic11—21no—
55C2×C4⋊Dic11—42no—
56C22×C11⋊C8—21no—
57C22×C11⋊C8—21no—
58C11×#95—21no—
59C11×#95—21no—
60C11×#95—21no—
61C11×#95—21no—
62C11×#95—21no—
63C11×#95—21no—
64C11×#95—21no—
65#66899—42no—
66C11⋊#95—21no—
67C11⋊#95—21no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72C22⋊(C11⋊C8)—21no—
73C22⋊(C11⋊C8)D412yes—
74#66872—42no—
75#10401—111nomaximal, Sylow
76C24×C11C2×D411yescharacteristic
77C2×Q8×C11—21no—
78C2×Q8×C11—21no—
79C2×Q8×C11—41no—
80C2×Q8×C11—41no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—21no—
89C22×C4×C11—21no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11SD1612yes—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4111yescharacteristic
103C22×C4×C11#4111yescharacteristic
104C22×C4×C11#4111yescharacteristic
105C22×Dic11—22no—
106C22×Dic11—22no—
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×Dic11—41no—
116C22×Dic11—41no—
117C22×Dic11—41no—
118C22×Dic11—41no—
119C11×C4⋊C4—21no—
120C11×C4⋊C4—21no—
121C11×C4⋊C4—41no—
122C11×C4⋊C4—41no—
123C11×C4⋊C4—41no—
124C11×C4⋊C4—41no—
125C11×C4⋊C4—41no—
126C11×C4⋊C4—41no—
127C11×C4⋊C4—41no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—81no—
130C11×C4⋊C4—81no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C4⋊Dic11—22no—
136C4⋊Dic11—22no—
137C4⋊Dic11—41no—
138C4⋊Dic11—41no—
139C2×C11⋊C8—22no—
140C2×C11⋊C8—41no—
141C2×C11⋊C8—41no—
142C2×C11⋊C8—41no—
143C2×C11⋊C8—41no—
144C2×C11⋊C8—41no—
145#2627D1111yescharacteristic
146#1872—111no—
147#1853—111no—
148C2×#328—111no—
149C2×#324—111no—
150#1441—111no—
151#1294—111no—
152C23×C11—21no—
153C23×C11—21no—
154C23×C11—21no—
155C23×C11—21no—
156C23×C11#12011yescharacteristic
157C23×C11#12111yescharacteristic
158C23×C11#12311yescharacteristic
159C23×C11C2×SD1611yescharacteristic
160C23×C11#13511yescharacteristic
161C23×C11#13711yescharacteristic
162C23×C11#13711yescharacteristic
163Q8×C11—42no—
164Q8×C11—81no—
165C2×C4×C11—21no—
166C2×C4×C11—21no—
167C2×C4×C11—21no—
168C2×C4×C11—21no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—41no—
177C2×C4×C11—41no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
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—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11—81no—
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12311yescharacteristic
200C2×C4×C11#12411yescharacteristic
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—81no—
208C2×Dic11—81no—
209C2×Dic11—81no—
210C2×Dic11—81no—
211C2×Dic11—81no—
212C2×Dic11—81no—
213C2×Dic11—81no—
214C2×Dic11—81no—
215C11⋊C8—42no—
216C11⋊C8—81no—
217C2×C22⋊Q8C2×D1111yescharacteristic
218C22×C4⋊C4—111no—
219C22×C4⋊C4C2×D1111yescharacteristic
220C2×#106—221no—
221C2×#103—221no—
222C2×C22⋊C8—111no—
223C2×C22⋊C8—111no—
224#400—21no—
225#398—21no—
226#398—21no—
227#395—21no—
228#385—21no—
229#381—21no—
230#380C2×D1111yescharacteristic
231C2×#95—111no—
232C2×#95—221no—
233C2×#95—221no—
234#340—221no—
235#340—221no—
236#328—222no—
237#324—222no—
238C22×C11—21no—
239C22×C11—21no—
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#39411yescharacteristic
251C22×C11#44811yescharacteristic
252C22×C11#45211yescharacteristic
253C22×C11#45411yescharacteristic
254C22×C11#45611yescharacteristic
255C22×C11B(4,𝔽2)11yescharacteristic
256C22×C11#45811yescharacteristic
257C22×C11#46511yescharacteristic
258C22×C11#47011yescharacteristic
259C22×C11#48311yescharacteristic
260C22×C11#48511yescharacteristic
261C4×C11—21no—
262C4×C11—21no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—42no—
266C4×C11—81no—
267C4×C11—81no—
268C4×C11—81no—
269C4×C11—81no—
270C4×C11—81no—
271Dic11—82no—
272Dic11—82no—
273C22×Q8C22⋊D1111yescharacteristic
274C23×C4—221no—
275C23×C4—221no—
276C23×C4C22⋊D1111yescharacteristic
277C23×C4C22⋊D1111yescharacteristic
278C23×C4C22×D1111yescharacteristic
279C22×C8—221no—
280C22×C8—221no—
281C22⋊Q8—21no—
282C22⋊Q8—21no—
283C22⋊Q8—21no—
284C22⋊Q8—21no—
285C2×C4⋊C4—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4—221no—
296C2×C4⋊C4—442no—
297C2×C4⋊C4C22⋊D1111yescharacteristic
298C2×C4⋊C4C22⋊D1111yescharacteristic
299C2×C4⋊C4C22⋊D1111yescharacteristic
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302#106—442no—
303#103—442no—
304C22⋊C8—112no—
305C22⋊C8—221no—
306C22⋊C8—221no—
307C22⋊C8—221no—
308#95—21no—
309#95—21no—
310#95—21no—
311#95—21no—
312#95—21no—
313#95—21no—
314#95—21no—
315#95—221no—
316#95—221no—
317#95—442no—
318#95—442no—
319C2×C11—21no—
320C2×C11—21no—
321C2×C11—21no—
322C2×C11—21no—
323C2×C11#159911yescharacteristic
324C2×C11#160311yescharacteristic
325C2×C11#161111yescharacteristic
326C2×C11#161511yescharacteristic
327C2×C11#203511yescharacteristic
328C2×C11#203811yescharacteristic
329C2×C11#204411yescharacteristic
330C24C2×C22⋊D1111yescharacteristic
331C2×Q8—21no—
332C2×Q8—21no—
333C2×Q8—41no—
334C2×Q8—41no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—441no—
355C22×C4—441no—
356C22×C4—441no—
357C22×C4—441no—
358C22×C4—441no—
359C22×C4—441no—
360C22×C4—441no—
361C22×C4—441no—
362C22×C4—441no—
363C22×C4—441no—
364C22×C4—441no—
365C22×C4—441no—
366C22×C4#432512yes—
367C22×C4D4×D1111yescharacteristic
368C22×C4#434111yescharacteristic
369C22×C4#434111yescharacteristic
370C22×C4#434111yescharacteristic
371C22×C4C2×C22⋊D1111yescharacteristic
372C22×C4C2×C22⋊D1111yescharacteristic
373C2×C8—222no—
374C2×C8—441no—
375C2×C8—441no—
376C2×C8—441no—
377C2×C8—441no—
378C2×C8—441no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—81no—
390C4⋊C4—81no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C11#1040111yescharacteristic, complemented, Sylow
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23#6698811yescharacteristic
405C23#6699211yescharacteristic
406C23C2×#432511yescharacteristic
407C23#6699511yescharacteristic
408C23#6700311yescharacteristic
409C23#6700411yescharacteristic
410C23#6700611yescharacteristic
411Q8—42no—
412Q8—81no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—81no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—881no—
452C2×C4—881no—
453C2×C4—881no—
454C2×C4—881no—
455C2×C4—881no—
456C2×C4—881no—
457C2×C4—881no—
458C2×C4—881no—
459C2×C4#6698811yescharacteristic
460C2×C4#6698911yescharacteristic
461C2×C4#6699111yescharacteristic
462C2×C4#6699211yescharacteristic
463C8—442no—
464C8—881no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22#1062265611yescharacteristic
478C22#1062265811yescharacteristic
479C22#1062266111yescharacteristic
480C22#1062266511yescharacteristic
481C22#1062283511yescharacteristic
482C22#1062284011yescharacteristic
483C22#1062285211yescharacteristic
484C22#1062285611yescharacteristic
485C22#1062285711yescharacteristic
486C22#1062285811yescharacteristic
487C22#1062285911yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—81no—
494C4—81no—
495C4—81no—
496C4—81no—
497C4—81no—
498C4—882no—
499C4—882no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2#1306755611yescharacteristic
505C2#1306757911yescharacteristic
506C2#1306762411yescharacteristic
507C2#1306764711yescharacteristic
508C2#1306980911yescharacteristic
509C2#1306983011yescharacteristic
510C2#1306986411yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#2627C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#2627D11
hypocenterC11#10401
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
399. C11#10401semidirect

Maximal subgroups

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

subgroupindex
#130689242
#130688082
C2×#106221762
C2×#106221662
#130668692
#130664942
C11×#26272
#1040111