Finite Group Databasebeta

← #14656130

Subgroups — #14656130

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#13079531C211yesmaximal, characteristic, complemented
2#13073562C211yesmaximal, characteristic, complemented
3#13067285C211yesmaximal, characteristic, complemented
4#13067111C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066517C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66993—21no—
12C2×#66983—22no—
13C2×#66927C2211yescharacteristic
14C11×#463—22no—
15C11×#461—21no—
16C11×#459—21no—
17C11×#423C2211yescharacteristic
18C11×#417—21no—
19#10622701—21no—
20#10622686—21no—
21#10622649—22no—
22#10622628—22no—
23#10622601—21no—
24#10622573—22no—
25C4×C4⋊Dic11C2211yescharacteristic
26#10622538C2211yescharacteristic
27#10622538C2211yescharacteristic
28#10622175—22no—
29D4⋊(C11⋊C8)—22no—
30#10622123—22no—
31C2×C11×#41—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×C22⋊D11—24no—
35C22×D44—21no—
36C22×D44—21no—
37C22×D44D412yes—
38C11×AGL(1,ℤ/8)—42no—
39C11×AGL(1,ℤ/8)—42no—
40C2×C11×SD16—22no—
41C2×C11×D8—22no—
42C2×C11×M16—21no—
43C11×C4⋊Q8D411yescharacteristic, complemented
44C11×#127D411yescharacteristic, complemented
45C11×#124—21no—
46C11×#121—21no—
47C11×#121—21no—
48C4×D4×C11—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C2×C11×C4⋊C4D411yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C42×C11C2311yescharacteristic
57#66993—42no—
58#66993—42no—
59C2×#4323—24no—
60#66983—48no—
61C2×(C2×D11)⋊C4—24no—
62C2×C4⋊Dic11—21no—
63C2×C4×Dic11—21no—
64#66927—21no—
65#66927—21no—
66#66927—21no—
67#66927—21no—
68C11×C4⋊C8—21no—
69C11×C4⋊C8D412yescomplemented
70C11×#103—22no—
71C11×#102—22no—
72C11⋊#95D412yes—
73C22⋊(C11⋊C8)—21no—
74C22⋊(C11⋊C8)—21no—
75#66873—24no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yescomplemented
78C4×C11⋊C8—21no—
79C4×C11⋊C8—21no—
80#10238—111nomaximal, Sylow
81C24×C11—21no—
82C23×D11—22no—
83C11×#41—41no—
84C11×#41—41no—
85C11×#41—41no—
86C11×#41—41no—
87C2×Q8×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11—21no—
93C2×D4×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—41no—
97C2×D4×C11D812yescomplemented
98C22×C4×C11—21no—
99C22×C4×C11—44no—
100C22×C4×C11—41no—
101C22×C4×C11—41no—
102C22×C4×C11—41no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C2×C22⋊D11—48no—
107C2×C22⋊D11—48no—
108C2×C22⋊D11—84no—
109C22×Dic11—22no—
110C2×D44—22no—
111C2×D44—22no—
112C2×D44—44no—
113C2×D44—41no—
114C2×D44—41no—
115C2×D44—41no—
116C2×D44—41no—
117C2×D44—41no—
118C2×D44—41no—
119C2×D44—41no—
120C2×D44—41no—
121C2×D44—82no—
122C11×SD16—44no—
123C11×D8—44no—
124C11×M16—41no—
125C11×M16—41no—
126C2×C8×C11—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—21no—
131C11×C22⋊C4—41no—
132C11×C22⋊C4—41no—
133C11×C22⋊C4—41no—
134C11×C22⋊C4—41no—
135C42×C11C2×D411yescharacteristic
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11#4111yescharacteristic
139#4323—84no—
140(C2×D11)⋊C4—48no—
141C4⋊Dic11—24no—
142C4×Dic11—41no—
143C4×Dic11—41no—
144C2×C11⋊C8—22no—
145C2×C11⋊C8—41no—
146#3205—111no—
147#3036D1111yescharacteristic, complemented
148#2541—111no—
149#1545—111no—
150#1502—111no—
151#1478—111no—
152#1303—111no—
153C23×C11—22no—
154C23×C11—42no—
155C23×C11—42no—
156C23×C11—41no—
157C23×C11—41no—
158C23×C11—41no—
159C23×C11#12011yescharacteristic
160C22×D11—44no—
161C22×D11—44no—
162C22×D11—42no—
163C22×D11—42no—
164C22×D11—42no—
165Q8×C11—41no—
166Q8×C11—41no—
167D4×C11—22no—
168D4×C11—22no—
169D4×C11—41no—
170D4×C11—41no—
171D4×C11—41no—
172D4×C11—42no—
173D4×C11—41no—
174D4×C11—81no—
175D4×C11—81no—
176D4×C11—81no—
177C2×C4×C11—22no—
178C2×C4×C11—41no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—41no—
182C2×C4×C11—82no—
183C2×C4×C11—82no—
184C2×C4×C11—81no—
185C2×C4×C11—81no—
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11#12111yescharacteristic
189C2×C4×C11#12111yescharacteristic
190C2×C4×C11#12111yescharacteristic
191C2×C4×C11#12711yescharacteristic
192C2×C4×C11C2×D811yescharacteristic
193C2×C4×C11#13511yescharacteristic
194C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
196C22⋊D11—816no—
197C2×Dic11—24no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200D44—44no—
201D44—82no—
202D44—82no—
203D44—82no—
204D44—81no—
205D44—81no—
206D44—81no—
207D44—81no—
208C8×C11—42no—
209C11⋊C8—42no—
210C11⋊C8—81no—
211C2×AGL(1,ℤ/8)—21no—
212#532C2×D1111yescharacteristic
213C2×#127—111no—
214C2×#127—221no—
215C2×#121—222no—
216C2×C4×D4C2×D1111yescharacteristic
217#493—221no—
218#486—221no—
219#463—22no—
220#461—21no—
221#459—21no—
222#459—222no—
223#447—222no—
224#431—111no—
225#431—111no—
226#423C2×D1111yescharacteristic
227#417—21no—
228#392—222no—
229#390—221no—
230C4×C4⋊C4—111no—
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—81no—
240C22×C11—81no—
241C22×C11—81no—
242C22×C11—81no—
243C22×C11—81no—
244C22×C11#39211yescharacteristic
245C22×C11#44711yescharacteristic
246C22×C11#44911yescharacteristic
247C2×D11—84no—
248C2×D11—84no—
249C2×D11—82no—
250C2×D11—82no—
251C2×D11—82no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—21no—
255C4×C11—81no—
256C4×C11—81no—
257C4×C11#44711yescharacteristic
258C4×C11#44911yescharacteristic
259C4×C11#45312yes—
260C4×C11#46611yescharacteristic
261C4×C11#46911yescharacteristic
262Dic11—44no—
263C2×#41—21no—
264C22×D4—112no—
265C22×D4—224no—
266C22×D4—221no—
267C22×D4—221no—
268C22×D4C22⋊D1111yescharacteristic
269C23×C4—21no—
270AGL(1,ℤ/8)—42no—
271AGL(1,ℤ/8)—42no—
272C2×SD16—22no—
273C2×D8—22no—
274C2×D8—224no—
275C2×M16—21no—
276C4⋊Q8C22⋊D1111yescharacteristic, complemented
277#127—221no—
278#127—221no—
279#127—221no—
280#127—221no—
281#127—442no—
282#127—442no—
283#127C22⋊D1111yescharacteristic, complemented
284#124—21no—
285#121—21no—
286#121—21no—
287#121—448no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4—21no—
294C2×C4⋊C4—221no—
295C2×C4⋊C4C22⋊D1111yescharacteristic
296C2×C22⋊C4—21no—
297C2×C22⋊C4—224no—
298C2×C42—221no—
299C2×C42C22×D1111yescharacteristic
300C4⋊C8—21no—
301C4⋊C8—112no—
302C4⋊C8—221no—
303C4⋊C8C22⋊D1112yescomplemented
304#103—22no—
305#102—22no—
306#102—224no—
307C22⋊C8—221no—
308C22⋊C8—221no—
309C4×C8—221no—
310C4×C8—221no—
311#95—112no—
312C2×C11—21no—
313C2×C11—21no—
314C2×C11—82no—
315C2×C11—161no—
316C2×C11#199911yescharacteristic
317C2×C11#200211yescharacteristic
318C2×C11#200811yescharacteristic
319D11—162no—
320C24—21no—
321C24—222no—
322#41—41no—
323#41—41no—
324#41—41no—
325#41—41no—
326C2×Q8—21no—
327C2×D4—21no—
328C2×D4—21no—
329C2×D4—21no—
330C2×D4—21no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4—21no—
334C2×D4—21no—
335C2×D4—41no—
336C2×D4—222no—
337C2×D4—222no—
338C2×D4—444no—
339C2×D4—448no—
340C2×D4—448no—
341C2×D4—441no—
342C2×D4—441no—
343C2×D4—441no—
344C2×D4—441no—
345C2×D4—441no—
346C2×D4—441no—
347C2×D4—441no—
348C2×D4—441no—
349C2×D4—882no—
350C2×D4—884no—
351C2×D4#432312yescomplemented
352C22×C4—21no—
353C22×C4—44no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—222no—
358C22×C4D4×D1111yescharacteristic
359C22×C4D4×D1111yescharacteristic
360C22×C4C2×C22⋊D1111yescharacteristic
361SD16—44no—
362D8—44no—
363D8—884no—
364M16—41no—
365M16—41no—
366C2×C8—22no—
367C2×C8—222no—
368C2×C8—441no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—21no—
373C4⋊C4—224no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—448no—
379C42—441no—
380C42—441no—
381C42D4×D1111yescharacteristic
382C42#434111yescharacteristic
383C42C2×C22⋊D1111yescharacteristic
384C42C2×C22⋊D1111yescharacteristic
385C11#1023811yescharacteristic, complemented, Sylow
386C23—22no—
387C23—42no—
388C23—42no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—444no—
393C23—444no—
394C23—442no—
395C23—442no—
396C23—442no—
397C23#6699011yescharacteristic
398Q8—41no—
399Q8—41no—
400D4—22no—
401D4—22no—
402D4—42no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—41no—
407D4—81no—
408D4—81no—
409D4—81no—
410D4—444no—
411D4—882no—
412D4—882no—
413D4—882no—
414D4—8816no—
415D4—881no—
416D4—881no—
417D4—881no—
418D4—881no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—82no—
425C2×C4—82no—
426C2×C4—81no—
427C2×C4—81no—
428C2×C4—224no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4C2×#432311yescharacteristic
432C2×C4#6698511yescharacteristic
433C2×C4#6699011yescharacteristic
434C2×C4#6699111yescharacteristic
435C2×C4#6699211yescharacteristic
436C2×C4#6699211yescharacteristic
437C2×C4#6699311yescharacteristic
438C2×C4#6700211yescharacteristic
439C2×C4#6700311yescharacteristic
440C2×C4#6700611yescharacteristic
441C8—42no—
442C8—442no—
443C8—881no—
444C22—21no—
445C22—21no—
446C22—44no—
447C22—42no—
448C22—82no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—884no—
455C22—884no—
456C22—882no—
457C22—882no—
458C22—882no—
459C22#1062264911yescharacteristic
460C22#1062265011yescharacteristic
461C22#1062283611yescharacteristic
462C4—21no—
463C4—21no—
464C4—21no—
465C4—81no—
466C4—81no—
467C4—444no—
468C4#1062265111yescharacteristic
469C4#1062265211yescharacteristic
470C4#1062281112yes—
471C4#1062283011yescharacteristic
472C4#1062285111yescharacteristic
473C2—21no—
474C2—21no—
475C2—82no—
476C2—161no—
477C2—1762no—
478C2#1306961211yescharacteristic
479C2#1306962811yescharacteristic
480C2#1306966611yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3036C2
socleC22×C11#392
hypercenter#3036D11
hypocenterC11#10238
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #13079531C2semidirect
2. #13073562C2semidirect
3. #13067285C2semidirect
4. #13067111C2semidirect
5. #13067007C2semidirect
6. #13066517C2semidirect
7. C11×#3036C2semidirect
43. C11×C4⋊Q8D4semidirect
44. C11×#127D4semidirect
69. C11×C4⋊C8D4semidirect
77. C4⋊(C11⋊C8)D4semidirect
97. C2×D4×C11D8semidirect
147. #3036D11semidirect
276. C4⋊Q8C22⋊D11semidirect
283. #127C22⋊D11semidirect
303. C4⋊C8C22⋊D11semidirect
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
#130795312
#130735622
#130672852
#130671112
#130670072
#130665172
C11×#30362
#1023811