Finite Group Databasebeta

← #14654501

Subgroups — #14654501

Order 2816.

686 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 101 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#13078612C211yesmaximal, characteristic, complemented
2#13073513C211yesmaximal, characteristic, complemented
3#13067176C211yesmaximal, characteristic, complemented
4#13067040C211yesmaximal, characteristic, complemented
5#13067007C211yesmaximal, characteristic, complemented
6#13066476C211yesmaximal, characteristic, complemented
7C11×#3036C211yesmaximal, characteristic, complemented
8C2×C11×AGL(1,ℤ/8)—21no—
9C11×#532C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66991—21no—
12C2×C4×D44C2211yescharacteristic
13C11×#463—22no—
14C11×#461—21no—
15C11×#459—21no—
16C11×#423C2211yescharacteristic
17C11×#417—21no—
18#10622826—22no—
19#10622700—21no—
20#10622685—21no—
21#10622649—21no—
22#10622646—21no—
23C4×#4323—22no—
24#10622600—21no—
25#10622573—21no—
26#10622566—21no—
27#10622549C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622538C2211yescharacteristic
30#10622175—22no—
31D4⋊(C11⋊C8)—22no—
32#10622121—22no—
33C2×C11×#41—21no—
34C22×D4×C11D411yescharacteristic
35C23×C4×C11—21no—
36C22×C22⋊D11—22no—
37C22×D44D411yescharacteristic
38C22×C4×D11—21no—
39C11×AGL(1,ℤ/8)—42no—
40C11×AGL(1,ℤ/8)—42no—
41C2×C11×SD16—22no—
42C2×C11×D8—22no—
43C2×C11×M16—21no—
44C11×C4⋊Q8D411yescharacteristic, complemented
45C11×#127D411yescharacteristic, complemented
46C11×#124—21no—
47C11×#121—21no—
48C11×#121—21no—
49C4×D4×C11—21no—
50C4×D4×C11—21no—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11—21no—
54C4×D4×C11—21no—
55C2×C11×C4⋊C4D411yescharacteristic
56C2×C11×C22⋊C4—21no—
57C2×C42×C11C2311yescharacteristic
58C2×C22⋊Dic11—22no—
59#66991—42no—
60#66991—42no—
61C2×#4323—22no—
62C2×(C2×D11)⋊C4—21no—
63C2×(C2×D11)⋊C4—22no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11D411yescharacteristic
66C4×D44—21no—
67C4×D44—21no—
68C4×D44—21no—
69C4×D44—21no—
70C11×C4⋊C8—21no—
71C11×C4⋊C8D412yescomplemented
72C11×#103—22no—
73C11×#102—22no—
74#66896—22no—
75C11⋊#95—22no—
76C11⋊#95—21no—
77C11⋊#95D412yes—
78C22⋊(C11⋊C8)—21no—
79C22⋊(C11⋊C8)—21no—
80#66873—22no—
81#66871—22no—
82C4⋊(C11⋊C8)—21no—
83C4⋊(C11⋊C8)—21no—
84C4×C11⋊C8—21no—
85C4×C11⋊C8D412yescomplemented
86#9996—111nomaximal, Sylow
87C24×C11—21no—
88C23×D11—21no—
89C11×#41—41no—
90C11×#41—41no—
91C11×#41—41no—
92C11×#41—41no—
93C2×Q8×C11—21no—
94C2×D4×C11—21no—
95C2×D4×C11—21no—
96C2×D4×C11—21no—
97C2×D4×C11—21no—
98C2×D4×C11—21no—
99C2×D4×C11—21no—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—41no—
103C2×D4×C11D812yescomplemented
104C22×C4×C11—21no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—82no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C2×C22⋊D11—44no—
113C2×C22⋊D11—44no—
114C2×C22⋊D11—82no—
115C22×Dic11—22no—
116C22×Dic11—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—42no—
120C2×C4×D11—41no—
121C2×C4×D11—41no—
122C2×C4×D11—41no—
123C2×C4×D11—41no—
124C2×C4×D11—41no—
125C2×C4×D11—41no—
126C11×SD16—44no—
127C11×D8—44no—
128C11×M16—41no—
129C11×M16—41no—
130C2×C8×C11—22no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—21no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—21no—
135C11×C22⋊C4—41no—
136C11×C22⋊C4—41no—
137C11×C22⋊C4—41no—
138C11×C22⋊C4—41no—
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11#4111yescharacteristic
143C22⋊Dic11—44no—
144#4323—44no—
145(C2×D11)⋊C4—41no—
146(C2×D11)⋊C4—41no—
147(C2×D11)⋊C4—82no—
148C4⋊Dic11—21no—
149C4⋊Dic11—21no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—41no—
154#3100—111no—
155#3036D1111yescharacteristic, complemented
156#2535—111no—
157#1517—111no—
158#1486—111no—
159#1478—111no—
160#1286—111no—
161C23×C11—22no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—41no—
165C23×C11—41no—
166C23×C11—41no—
167C23×C11#12011yescharacteristic
168C22×D11—22no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175Q8×C11—41no—
176Q8×C11—41no—
177D4×C11—22no—
178D4×C11—22no—
179D4×C11—42no—
180D4×C11—41no—
181D4×C11—41no—
182D4×C11—41no—
183D4×C11—41no—
184D4×C11—81no—
185D4×C11—81no—
186D4×C11—81no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—82no—
193C2×C4×C11—82no—
194C2×C4×C11—81no—
195C2×C4×C11—81no—
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#12111yescharacteristic
199C2×C4×C11#12111yescharacteristic
200C2×C4×C11#12111yescharacteristic
201C2×C4×C11#12711yescharacteristic
202C2×C4×C11C2×D811yescharacteristic
203C2×C4×C11#13511yescharacteristic
204C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
206C22⋊D11—88no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213D44—22no—
214D44—22no—
215D44—41no—
216D44—41no—
217C4×D11—81no—
218C4×D11—81no—
219C4×D11—81no—
220C4×D11—81no—
221C8×C11—42no—
222C11⋊C8—42no—
223C11⋊C8—81no—
224C2×AGL(1,ℤ/8)—21no—
225#532C2×D1111yescharacteristic
226C2×#121—221no—
227C2×C4×D4—111no—
228C2×C4×D4C2×D1111yescharacteristic
229#480—221no—
230#474—221no—
231#463—22no—
232#461—21no—
233#459—21no—
234#459—221no—
235#447—221no—
236C4×D8—222no—
237#431—111no—
238#431—111no—
239#423C2×D1111yescharacteristic
240#417—21no—
241#397—221no—
242#392—221no—
243#386—222no—
244#382—111no—
245#380—221no—
246#327—222no—
247D4⋊C8—222no—
248D4⋊C8—222no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—44no—
252C22×C11—42no—
253C22×C11—82no—
254C22×C11—81no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11#39211yescharacteristic
260C22×C11#44711yescharacteristic
261C22×C11#44911yescharacteristic
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C2×D11—81no—
269C4×C11—21no—
270C4×C11—21no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—81no—
274C4×C11—81no—
275C4×C11#44711yescharacteristic
276C4×C11#44911yescharacteristic
277C4×C11#46611yescharacteristic
278C4×C11#46911yescharacteristic
279Dic11—82no—
280Dic11—81no—
281C2×#41—21no—
282C22×D4—111no—
283C22×D4—222no—
284C22×D4C22⋊D1111yescharacteristic
285C23×C4—21no—
286C23×C4—221no—
287AGL(1,ℤ/8)—42no—
288AGL(1,ℤ/8)—42no—
289C2×SD16—22no—
290C2×D8—22no—
291C2×D8—222no—
292C2×M16—21no—
293C4⋊Q8C22⋊D1111yescharacteristic, complemented
294#127C22⋊D1111yescharacteristic, complemented
295#124—21no—
296#121—21no—
297#121—21no—
298#121—442no—
299#121—442no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4—221no—
307C4×D4—221no—
308C4×D4—221no—
309C4×D4—221no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—221no—
312C2×C4⋊C4C22⋊D1111yescharacteristic
313C2×C22⋊C4—21no—
314C2×C22⋊C4—222no—
315C2×C22⋊C4—221no—
316C2×C22⋊C4—222no—
317C2×C42C22×D1111yescharacteristic
318#107—222no—
319C4⋊C8—21no—
320C4⋊C8—221no—
321C4⋊C8—221no—
322C4⋊C8C22⋊D1112yescomplemented
323#103—22no—
324#102—22no—
325#102—222no—
326#102—222no—
327C22⋊C8—221no—
328C22⋊C8—221no—
329C4×C8—112no—
330C4×C8—221no—
331#95—112no—
332#95—222no—
333#95—221no—
334C2×C11—21no—
335C2×C11—21no—
336C2×C11—82no—
337C2×C11—161no—
338C2×C11#199911yescharacteristic
339C2×C11#200811yescharacteristic
340C2×C11#201011yescharacteristic
341D11—82no—
342C24—21no—
343C24—221no—
344#41—41no—
345#41—41no—
346#41—41no—
347#41—41no—
348C2×Q8—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—41no—
358C2×D4—221no—
359C2×D4—221no—
360C2×D4—442no—
361C2×D4—444no—
362C2×D4—444no—
363C2×D4—882no—
364C2×D4#432312yescomplemented
365C22×C4—21no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—82no—
370C22×C4—222no—
371C22×C4—221no—
372C22×C4—441no—
373C22×C4—441no—
374C22×C4—441no—
375C22×C4—441no—
376C22×C4—441no—
377C22×C4—441no—
378C22×C4D4×D1111yescharacteristic
379C22×C4D4×D1111yescharacteristic
380C22×C4C2×C22⋊D1111yescharacteristic
381SD16—44no—
382D8—44no—
383D8—444no—
384M16—41no—
385M16—41no—
386C2×C8—22no—
387C2×C8—222no—
388C2×C8—441no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—444no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—882no—
405C42D4×D1111yescharacteristic
406C42#434111yescharacteristic
407C42C2×C22⋊D1111yescharacteristic
408C42C2×C22⋊D1111yescharacteristic
409C11#999611yescharacteristic, complemented, Sylow
410C23—22no—
411C23—42no—
412C23—42no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—222no—
417C23—441no—
418C23—441no—
419C23—441no—
420C23—441no—
421C23—441no—
422C23—441no—
423C23#6699011yescharacteristic
424Q8—41no—
425Q8—41no—
426D4—22no—
427D4—22no—
428D4—42no—
429D4—41no—
430D4—41no—
431D4—41no—
432D4—41no—
433D4—81no—
434D4—81no—
435D4—81no—
436D4—222no—
437D4—222no—
438D4—441no—
439D4—441no—
440D4—888no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—82no—
447C2×C4—82no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—442no—
455C2×C4—441no—
456C2×C4—881no—
457C2×C4—881no—
458C2×C4—881no—
459C2×C4—881no—
460C2×C4C2×#432311yescharacteristic
461C2×C4#6698511yescharacteristic
462C2×C4#6699011yescharacteristic
463C2×C4#6699111yescharacteristic
464C2×C4#6699211yescharacteristic
465C2×C4#6699211yescharacteristic
466C2×C4#6699311yescharacteristic
467C2×C4#6700211yescharacteristic
468C2×C4#6700311yescharacteristic
469C2×C4#6700611yescharacteristic
470C8—42no—
471C8—442no—
472C8—881no—
473C22—21no—
474C22—21no—
475C22—44no—
476C22—42no—
477C22—82no—
478C22—81no—
479C22—81no—
480C22—81no—
481C22—81no—
482C22—81no—
483C22—442no—
484C22—442no—
485C22—442no—
486C22—881no—
487C22—881no—
488C22—881no—
489C22—881no—
490C22#1062264911yescharacteristic
491C22#1062265011yescharacteristic
492C22#1062283611yescharacteristic
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—81no—
498C4—81no—
499C4—882no—
500C4—881no—
501C4#1062265111yescharacteristic
502C4#1062265211yescharacteristic
503C4#1062283011yescharacteristic
504C4#1062285111yescharacteristic
505C2—21no—
506C2—21no—
507C2—82no—
508C2—161no—
509C2—882no—
510C2#1306961211yescharacteristic
511C2#1306966711yescharacteristic
512C2#1306968011yescharacteristic
subgroupG/H
centerC22#10622836
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#3036C2
socleC22×C11#392
hypercenter#3036D11
hypocenterC11#9996
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. #13078612C2semidirect
2. #13073513C2semidirect
3. #13067176C2semidirect
4. #13067040C2semidirect
5. #13067007C2semidirect
6. #13066476C2semidirect
7. C11×#3036C2semidirect
44. C11×C4⋊Q8D4semidirect
45. C11×#127D4semidirect
71. C11×C4⋊C8D4semidirect
85. C4×C11⋊C8D4semidirect
103. C2×D4×C11D8semidirect
155. #3036D11semidirect
293. C4⋊Q8C22⋊D11semidirect
294. #127C22⋊D11semidirect
322. C4⋊C8C22⋊D11semidirect
364. C2×D4#4323semidirect
409. C11#9996semidirect

Maximal subgroups

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

subgroupindex
#130786122
#130735132
#130671762
#130670402
#130670072
#130664762
C11×#30362
#999611