Finite Group Databasebeta

← #14656771

Subgroups — #14656771

Order 2816.

500 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074589C211yesmaximal, characteristic
2#13068702C211yesmaximal, characteristic
3#13066884C211yesmaximal, characteristic
4#13066496C211yesmaximal, characteristic
5#13066494C211yesmaximal, characteristic
6#13066458C211yesmaximal, characteristic
7C11×#1823C211yesmaximal, characteristic
8C22×C11×C4⋊C4C2211yescharacteristic
9C2×C11×C22⋊C8C2211yescharacteristic
10C11×#380C2211yescharacteristic
11#10622825C2211yescharacteristic
12C2×C11⋊#95—21no—
13C2×C11⋊#95—21no—
14C2×C11⋊#95C2211yescharacteristic
15C2×C11⋊#95C2211yescharacteristic
16C2×C22⋊(C11⋊C8)C2211yescharacteristic
17#10622599—21no—
18#10622597—21no—
19#10622563—21no—
20#10622559—21no—
21#10622274—21no—
22#10622273—21no—
23C11×#340—21no—
24C11×#340—21no—
25#10622167—21no—
26#10622167—21no—
27C23×C4×C11—21no—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11—21no—
30C23×Dic11D411yescharacteristic
31C23×Dic11D411yescharacteristic
32C22×C8×C11—21no—
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×C11×C4⋊C4—21no—
36C2×C11×C4⋊C4—21no—
37C2×C11×C4⋊C4—21no—
38C2×C11×C4⋊C4D411yescharacteristic
39C2×C11×C4⋊C4D411yescharacteristic
40C2×C11×C4⋊C4Q812yes—
41C2×C11×C22⋊C4—21no—
42C2×C22⋊Dic11—21no—
43C2×C4⋊Dic11—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C2×C4⋊Dic11D411yescharacteristic
47C2×Dic11⋊C4—21no—
48C2×Dic11⋊C4—21no—
49C22×C11⋊C8—21no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95—42no—
63C11⋊#95—42no—
64C22⋊(C11⋊C8)—21no—
65C22⋊(C11⋊C8)—21no—
66#10346—111nomaximal, Sylow
67C24×C11C2×D411yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—22no—
71C22×C4×C11—41no—
72C22×C4×C11—41no—
73C22×C4×C11—41no—
74C22×C4×C11—41no—
75C22×C4×C11—41no—
76C22×C4×C11—41no—
77C22×C4×C11—41no—
78C22×C4×C11—41no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×Q811yescharacteristic
82C22×C4×C11#4111yescharacteristic
83C22×C4×C11#4111yescharacteristic
84C22×C4×C11#4111yescharacteristic
85C22×Dic11—22no—
86C22×Dic11—21no—
87C22×Dic11—21no—
88C22×Dic11—21no—
89C22×Dic11—21no—
90C22×Dic11—21no—
91C22×Dic11—21no—
92C22×Dic11—21no—
93C22×Dic11—21no—
94C22×Dic11—41no—
95C22×Dic11—41no—
96C22×Dic11—41no—
97C22×Dic11—41no—
98C22×Dic11—41no—
99C22×Dic11—41no—
100C22×Dic11—41no—
101C22×Dic11—41no—
102C22×Dic11—41no—
103C22×Dic11—41no—
104C2×C8×C11—41no—
105C2×C8×C11—41no—
106C2×C8×C11—41no—
107C11×C4⋊C4—22no—
108C11×C4⋊C4—22no—
109C11×C4⋊C4—41no—
110C11×C4⋊C4—41no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C11×C22⋊C4—41no—
114C11×C22⋊C4—41no—
115C22⋊Dic11—41no—
116C22⋊Dic11—41no—
117C4⋊Dic11—41no—
118C4⋊Dic11—41no—
119C4⋊Dic11—81no—
120C4⋊Dic11—81no—
121Dic11⋊C4—81no—
122Dic11⋊C4—81no—
123C2×C11⋊C8—41no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126#2646—111no—
127#1823—111no—
128#1823D1111yescharacteristic
129#1445—111no—
130#1294—111no—
131#1294—111no—
132#1280—111no—
133C23×C11—21no—
134C23×C11—21no—
135C23×C11—21no—
136C23×C11—21no—
137C23×C11#12011yescharacteristic
138C23×C11C22⋊Q811yescharacteristic
139C23×C11#12411yescharacteristic
140C23×C11#13511yescharacteristic
141C23×C11#13511yescharacteristic
142C23×C11AGL(1,ℤ/8)11yescharacteristic
143C23×C11AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C11—21no—
145C2×C4×C11—21no—
146C2×C4×C11—21no—
147C2×C4×C11—21no—
148C2×C4×C11—41no—
149C2×C4×C11—41no—
150C2×C4×C11—41no—
151C2×C4×C11—41no—
152C2×C4×C11—42no—
153C2×C4×C11—41no—
154C2×C4×C11—41no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—81no—
162C2×C4×C11—81no—
163C2×C4×C11—81no—
164C2×C4×C11—81no—
165C2×C4×C11C22⋊Q811yescharacteristic
166C2×C4×C11C22⋊Q811yescharacteristic
167C2×C4×C11#12411yescharacteristic
168C2×C4×C11#12411yescharacteristic
169C2×Dic11—42no—
170C2×Dic11—42no—
171C2×Dic11—42no—
172C2×Dic11—42no—
173C2×Dic11—42no—
174C2×Dic11—41no—
175C2×Dic11—41no—
176C2×Dic11—41no—
177C2×Dic11—41no—
178C2×Dic11—41no—
179C2×Dic11—41no—
180C2×Dic11—41no—
181C2×Dic11—41no—
182C2×Dic11—41no—
183C2×Dic11—41no—
184C2×Dic11—41no—
185C2×Dic11—41no—
186C2×Dic11—81no—
187C2×Dic11—81no—
188C2×Dic11—81no—
189C2×Dic11—81no—
190C2×Dic11—81no—
191C2×Dic11—81no—
192C8×C11—81no—
193C11⋊C8—81no—
194C22×C4⋊C4C2×D1111yescharacteristic
195C2×C22⋊C8—111no—
196C2×C22⋊C8C2×D1111yescharacteristic
197#400—221no—
198#400—221no—
199#398—221no—
200#398—221no—
201#385—221no—
202#385—221no—
203#380—111no—
204#380C2×D1111yescharacteristic
205C2×#95—111no—
206C2×#95—111no—
207C2×#95—221no—
208C2×#95—221no—
209#340—21no—
210#340—21no—
211#340—221no—
212#340—221no—
213C22×C11—21no—
214C22×C11—21no—
215C22×C11—21no—
216C22×C11—21no—
217C22×C11—21no—
218C22×C11—21no—
219C22×C11—21no—
220C22×C11—21no—
221C22×C11—21no—
222C22×C11—21no—
223C22×C11—21no—
224C22×C11—21no—
225C22×C11#39311yescharacteristic
226C22×C11#44911yescharacteristic
227C22×C11#44911yescharacteristic
228C22×C11#45511yescharacteristic
229C22×C11#45611yescharacteristic
230C22×C11#45811yescharacteristic
231C22×C11#45811yescharacteristic
232C22×C11#47811yescharacteristic
233C22×C11#47811yescharacteristic
234C22×C11#48811yescharacteristic
235C22×C11#49011yescharacteristic
236C4×C11—21no—
237C4×C11—21no—
238C4×C11—21no—
239C4×C11—21no—
240C4×C11—81no—
241C4×C11—81no—
242C4×C11—82no—
243Dic11—82no—
244Dic11—81no—
245Dic11—81no—
246Dic11—81no—
247Dic11—81no—
248C23×C4—21no—
249C23×C4—111no—
250C23×C4—111no—
251C23×C4—221no—
252C23×C4C22×D1111yescharacteristic
253C22×C8—21no—
254C22×C8—221no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—111no—
261C2×C4⋊C4—111no—
262C2×C4⋊C4—221no—
263C2×C4⋊C4—221no—
264C2×C4⋊C4—221no—
265C2×C4⋊C4—221no—
266C2×C4⋊C4Dic2212yes—
267C2×C4⋊C4C22⋊D1111yescharacteristic
268C2×C4⋊C4C22⋊D1111yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—221no—
271C22⋊C8—21no—
272C22⋊C8—21no—
273C22⋊C8—221no—
274C22⋊C8—221no—
275#95—21no—
276#95—221no—
277#95—221no—
278#95—221no—
279#95—221no—
280#95—221no—
281#95—221no—
282#95—221no—
283#95—221no—
284#95—221no—
285#95—442no—
286#95—442no—
287C2×C11—21no—
288C2×C11—21no—
289C2×C11—21no—
290C2×C11—21no—
291C2×C11#160911yescharacteristic
292C2×C11#160911yescharacteristic
293C2×C11#161211yescharacteristic
294C2×C11#161211yescharacteristic
295C2×C11#202511yescharacteristic
296C2×C11#202811yescharacteristic
297C2×C11#203011yescharacteristic
298C24D4×D1111yescharacteristic
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4—222no—
311C22×C4—221no—
312C22×C4—221no—
313C22×C4—221no—
314C22×C4—221no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318C22×C4—221no—
319C22×C4—441no—
320C22×C4—441no—
321C22×C4—441no—
322C22×C4—441no—
323C22×C4—441no—
324C22×C4—441no—
325C22×C4—441no—
326C22×C4—441no—
327C22×C4—441no—
328C22×C4—441no—
329C22×C4C2×Dic2211yescharacteristic
330C22×C4#433911yescharacteristic
331C22×C4D4×D1111yescharacteristic
332C22×C4#434111yescharacteristic
333C22×C4#434111yescharacteristic
334C22×C4C2×C22⋊D1111yescharacteristic
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—441no—
339C2×C8—441no—
340C2×C8—441no—
341C4⋊C4—22no—
342C4⋊C4—22no—
343C4⋊C4—41no—
344C4⋊C4—41no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—441no—
348C4⋊C4—441no—
349C4⋊C4—881no—
350C4⋊C4—881no—
351C4⋊C4—881no—
352C4⋊C4—881no—
353C22⋊C4—41no—
354C22⋊C4—41no—
355C22⋊C4—441no—
356C22⋊C4—441no—
357C11#1034611yescharacteristic, complemented, Sylow
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23#6693111yescharacteristic
363C23#6693811yescharacteristic
364C23#6696411yescharacteristic
365C23#6696511yescharacteristic
366C23#6696711yescharacteristic
367C23#6696911yescharacteristic
368C23#6699011yescharacteristic
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—442no—
391C2×C4—442no—
392C2×C4—442no—
393C2×C4—442no—
394C2×C4—442no—
395C2×C4—441no—
396C2×C4—441no—
397C2×C4—441no—
398C2×C4—441no—
399C2×C4—441no—
400C2×C4—441no—
401C2×C4—441no—
402C2×C4—441no—
403C2×C4—441no—
404C2×C4—441no—
405C2×C4—441no—
406C2×C4—441no—
407C2×C4—881no—
408C2×C4—881no—
409C2×C4—881no—
410C2×C4—881no—
411C2×C4—881no—
412C2×C4—881no—
413C2×C4#6693111yescharacteristic
414C2×C4#6693811yescharacteristic
415C2×C4#6697711yescharacteristic
416C2×C4#6698911yescharacteristic
417C8—81no—
418C8—881no—
419C22—21no—
420C22—21no—
421C22—21no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22#1062237611yescharacteristic
432C22#1062237711yescharacteristic
433C22#1062237911yescharacteristic
434C22#1062238111yescharacteristic
435C22#1062256011yescharacteristic
436C22#1062266611yescharacteristic
437C22#1062266611yescharacteristic
438C22#1062277111yescharacteristic
439C22#1062278511yescharacteristic
440C22#1062281511yescharacteristic
441C22#1062281811yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—82no—
449C4—882no—
450C4—881no—
451C4—881no—
452C4—881no—
453C4—881no—
454C2—21no—
455C2—21no—
456C2—21no—
457C2—21no—
458C2#1306761011yescharacteristic
459C2#1306761211yescharacteristic
460C2#1306762711yescharacteristic
461C2#1306762911yescharacteristic
462C2#1306976011yescharacteristic
463C2#1306977511yescharacteristic
464C2#1306978311yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC23×C4×C11C23
FrattiniC23×C4C22×D11
FittingC11×#1823C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenter#1823D11
hypocenterC11#10346
LCSG ▷ C23×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
357. C11#10346semidirect

Maximal subgroups

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

subgroupindex
#130745892
#130687022
#130668842
#130664962
#130664942
#130664582
C11×#18232
#1034611