Finite Group Databasebeta

← #14656133

Subgroups — #14656133

Order 2816.

794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079534C211yesmaximal, characteristic, complemented
2#13078080C211yesmaximal, characteristic, complemented
3#13067284C211yesmaximal, characteristic, complemented
4#13067110C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066519C211yesmaximal, characteristic, complemented
7C11×#2541C211yesmaximal, characteristic, complemented
8C2×C11×#127—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C11×#121—22no—
11C2×C4×D4×C11C2211yescharacteristic
12C2×#66985—21no—
13#10623008C2211yescharacteristic
14C11×#392—22no—
15C11×#390—21no—
16C4×C11×C4⋊C4C2211yescharacteristic
17#10622830—22no—
18#10622686—21no—
19#10622685—22no—
20#10622683—21no—
21#10622632—21no—
22#10622629—22no—
23#10622628—21no—
24#10622579—21no—
25#10622538C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622537C2211yescharacteristic
28#10622182—22no—
29D4⋊(C11⋊C8)—22no—
30#10622089—22no—
31C22×D4×C11—24no—
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11D411yescharacteristic
35C22×D4×C11D412yes—
36C23×C4×C11—21no—
37C2×#4339—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—42no—
43C11×#127—42no—
44C11×#121—48no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C22⋊C4—24no—
52C2×C11×C22⋊C4—21no—
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×#4324—22no—
56#66985—42no—
57#66985—42no—
58C2×#4323—22no—
59C2×#4323—24no—
60#66983—21no—
61#66983—21no—
62C2×#4318—21no—
63#66928—21no—
64#66927D411yescharacteristic, complemented
65C4×D44—21no—
66C4×D44—21no—
67#66922D411yescharacteristic, complemented
68C11×#95D412yes—
69#66896—24no—
70C22⋊(C11⋊C8)—21no—
71C22⋊(C11⋊C8)—21no—
72#66874—22no—
73#66873—22no—
74C4⋊(C11⋊C8)—21no—
75C4⋊(C11⋊C8)—21no—
76C4⋊(C11⋊C8)D412yescomplemented
77C4⋊(C11⋊C8)D412yescomplemented
78C4×C11⋊C8—21no—
79C4×C11⋊C8—21no—
80#10238—111nomaximal, Sylow
81C24×C11—21no—
82C24×C11—22no—
83C2×D4×C11—21no—
84C2×D4×C11—22no—
85C2×D4×C11—21no—
86C2×D4×C11—22no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—44no—
91C2×D4×C11—48no—
92C2×D4×C11—48no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—82no—
102C2×D4×C11—84no—
103C2×D4×C11D812yescomplemented
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—44no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C2×C22⋊D11—41no—
113#4339—41no—
114#4339—41no—
115#4339—41no—
116#4339—41no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×C4×D11—41no—
121C2×Dic22—21no—
122C11×C4⋊C4—24no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C22⋊C4—48no—
126C11×C22⋊C4—41no—
127C11×C22⋊C4—41no—
128C42×C11—41no—
129C42×C11—41no—
130C42×C11C2×D411yescharacteristic
131C42×C11C2×D411yescharacteristic
132C42×C11C2×D411yescharacteristic
133C42×C11#4111yescharacteristic
134#4324—44no—
135#4323—44no—
136#4323—84no—
137(C2×D11)⋊C4—41no—
138(C2×D11)⋊C4—41no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141#4318—41no—
142#4318—41no—
143C2×C11⋊C8—22no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—41no—
146#3205—111no—
147#3036—111no—
148#2541D1111yescharacteristic, complemented
149#1545—111no—
150#1502—111no—
151#1478—111no—
152#1303—111no—
153C23×C11—22no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—44no—
157C23×C11—44no—
158C23×C11—41no—
159C23×C11—41no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11#12011yescharacteristic
164C22×D11—41no—
165D4×C11—22no—
166D4×C11—22no—
167D4×C11—41no—
168D4×C11—44no—
169D4×C11—41no—
170D4×C11—82no—
171D4×C11—82no—
172D4×C11—82no—
173D4×C11—816no—
174D4×C11—81no—
175D4×C11—81no—
176D4×C11—81no—
177D4×C11—81no—
178C2×C4×C11—22no—
179C2×C4×C11—24no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—82no—
186C2×C4×C11—82no—
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12111yescharacteristic
192C2×C4×C11#12711yescharacteristic
193C2×C4×C11C2×D811yescharacteristic
194C2×C4×C11#13511yescharacteristic
195C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
197C22⋊D11—81no—
198C22⋊D11—81no—
199C2×Dic11—41no—
200D44—41no—
201D44—41no—
202D44—42no—
203D44—81no—
204C4×D11—81no—
205C4×D11—81no—
206Dic22—41no—
207Dic22—41no—
208C11⋊C8—42no—
209C11⋊C8—42no—
210C11⋊C8—81no—
211C2×AGL(1,ℤ/8)—221no—
212#532—111no—
213C2×#127—21no—
214C2×#127C2×D1111yescharacteristic
215C2×#121—22no—
216C2×C4×D4C2×D1111yescharacteristic
217#493—221no—
218#486—221no—
219#463—222no—
220#461—221no—
221#459—222no—
222#459—221no—
223#447—222no—
224#431—111no—
225#431—111no—
226#423—111no—
227#417—221no—
228#392—22no—
229#390—21no—
230C4×C4⋊C4C2×D1111yescharacteristic
231#331—222no—
232#327—222no—
233D4⋊C8—222no—
234C22×C11—21no—
235C22×C11—21no—
236C22×C11—44no—
237C22×C11—42no—
238C22×C11—82no—
239C22×C11—84no—
240C22×C11—84no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—82no—
244C22×C11—82no—
245C22×C11—82no—
246C22×C11#39211yescharacteristic
247C22×C11#44711yescharacteristic
248C22×C11#44911yescharacteristic
249C2×D11—81no—
250C2×D11—81no—
251C2×D11—81no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—44no—
256C4×C11—81no—
257C4×C11#44711yescharacteristic
258C4×C11#44911yescharacteristic
259C4×C11#45312yes—
260C4×C11#46611yescharacteristic
261C4×C11#46911yescharacteristic
262Dic11—81no—
263C2×#41—221no—
264C22×D4—24no—
265C22×D4—21no—
266C22×D4—21no—
267C22×D4C22⋊D1111yescharacteristic
268C22×D4C22⋊D1112yes—
269C23×C4—21no—
270AGL(1,ℤ/8)—442no—
271AGL(1,ℤ/8)—442no—
272C2×SD16—222no—
273C2×D8—222no—
274C2×D8—224no—
275C2×M16—221no—
276C4⋊Q8—111no—
277#127—21no—
278#127—21no—
279#127—21no—
280#127—21no—
281#127—42no—
282#127—42no—
283#127—111no—
284#124—221no—
285#121—48no—
286#121—221no—
287#121—221no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—221no—
293C4×D4—221no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4C22⋊D1111yescharacteristic
296C2×C22⋊C4—24no—
297C2×C22⋊C4—21no—
298C2×C42—21no—
299C2×C42C22×D1111yescharacteristic
300C4⋊C8—112no—
301C4⋊C8—112no—
302C4⋊C8—221no—
303C4⋊C8—221no—
304#103—222no—
305#102—222no—
306#102—224no—
307C22⋊C8—221no—
308C22⋊C8—221no—
309C4×C8—221no—
310C4×C8—221no—
311#95C22⋊D1112yes—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11—82no—
315C2×C11—162no—
316C2×C11#199911yescharacteristic
317C2×C11#200211yescharacteristic
318C2×C11#200811yescharacteristic
319D11—161no—
320C24—21no—
321C24—22no—
322#41—441no—
323#41—441no—
324#41—441no—
325#41—441no—
326C2×Q8—221no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—22no—
330C2×D4—21no—
331C2×D4—22no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—44no—
335C2×D4—48no—
336C2×D4—48no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—82no—
346C2×D4—84no—
347C2×D4—221no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—441no—
351C2×D4#432312yescomplemented
352C22×C4—22no—
353C22×C4—21no—
354C22×C4—44no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—441no—
358C22×C4C2×C22⋊D1111yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361SD16—444no—
362D8—444no—
363D8—884no—
364M16—441no—
365M16—441no—
366C2×C8—222no—
367C2×C8—222no—
368C2×C8—441no—
369C4⋊C4—24no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—221no—
373C4⋊C4—221no—
374C22⋊C4—48no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—441no—
378C22⋊C4—441no—
379C42—41no—
380C42—41no—
381C42D4×D1111yescharacteristic
382C42D4×D1111yescharacteristic
383C42D4×D1111yescharacteristic
384C42#434111yescharacteristic
385C11#1023811yescharacteristic, complemented, Sylow
386C23—22no—
387C23—42no—
388C23—42no—
389C23—44no—
390C23—44no—
391C23—41no—
392C23—41no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—441no—
397C23#6700611yescharacteristic
398Q8—441no—
399Q8—441no—
400D4—22no—
401D4—22no—
402D4—41no—
403D4—41no—
404D4—44no—
405D4—82no—
406D4—82no—
407D4—82no—
408D4—816no—
409D4—81no—
410D4—81no—
411D4—81no—
412D4—81no—
413D4—441no—
414D4—441no—
415D4—442no—
416D4—881no—
417D4—881no—
418D4—881no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—441no—
429C2×C4—881no—
430C2×C4—881no—
431C2×C4C2×#432311yescharacteristic
432C2×C4#6698511yescharacteristic
433C2×C4#6699011yescharacteristic
434C2×C4#6699011yescharacteristic
435C2×C4#6699111yescharacteristic
436C2×C4#6699211yescharacteristic
437C2×C4#6699211yescharacteristic
438C2×C4#6699311yescharacteristic
439C2×C4#6700211yescharacteristic
440C2×C4#6700311yescharacteristic
441C8—442no—
442C8—442no—
443C8—881no—
444C22—21no—
445C22—21no—
446C22—44no—
447C22—42no—
448C22—82no—
449C22—84no—
450C22—84no—
451C22—81no—
452C22—81no—
453C22—82no—
454C22—82no—
455C22—82no—
456C22—881no—
457C22—881no—
458C22—881no—
459C22#1062283011yescharacteristic
460C22#1062283611yescharacteristic
461C22#1062285111yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—44no—
466C4—81no—
467C4—881no—
468C4#1062264911yescharacteristic
469C4#1062265011yescharacteristic
470C4#1062265111yescharacteristic
471C4#1062265211yescharacteristic
472C4#1062269012yes—
473C2—21no—
474C2—21no—
475C2—82no—
476C2—162no—
477C2—1761no—
478C2#1306961211yescharacteristic
479C2#1306963111yescharacteristic
480C2#1306966911yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#2541C2
socleC22×C11#392
hypercenter#2541D11
hypocenterC11#10238
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2541

Complements

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

NH ≅ G/Ntype
1. #13079534C2semidirect
2. #13078080C2semidirect
3. #13067284C2semidirect
4. #13067110C2semidirect
5. #13067007C2semidirect
6. #13066519C2semidirect
7. C11×#2541C2semidirect
64. #66927D4semidirect
67. #66922D4semidirect
76. C4⋊(C11⋊C8)D4semidirect
77. C4⋊(C11⋊C8)D4semidirect
103. C2×D4×C11D8semidirect
148. #2541D11semidirect
351. C2×D4#4323semidirect
385. C11#10238semidirect

Maximal subgroups

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

subgroupindex
#130795342
#130780802
#130672842
#130671102
#130670072
#130665192
C11×#25412
#1023811