Finite Group Databasebeta

← #14656113

Subgroups — #14656113

Order 2816.

712 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622697C211yesmaximal, characteristic, complemented
2#13073529C211yesmaximal, characteristic
3#13069419C211yesmaximal, characteristic, complemented
4C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#476C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66991—21no—
11C2×#66983—21no—
12C2×C4×D44C2211yescharacteristic
13C11×#476—22no—
14C11×#476—22no—
15C2×C11×#106—21no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#102—21no—
18C2×#66899—22no—
19#10622825—21no—
20#10622697—22no—
21#10622697—22no—
22#10622600—21no—
23C2×#66873—21no—
24C2×#66872—21no—
25#10622574—22no—
26#10622548C2211yescharacteristic
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29D4⋊(C11⋊C8)—22no—
30#10622121—22no—
31C22×Q8×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×C22⋊D11—22no—
35C22×D44D411yescharacteristic
36C22×C4×D11—21no—
37C22×C8×C11—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8—21no—
40C11×C4⋊Q8—21no—
41C11×C4⋊Q8D412yescomplemented
42C4×D4×C11—21no—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C2×C11×C4⋊C4—21no—
47C2×C11×C4⋊C4—21no—
48C2×C11×C4⋊C4D411yescharacteristic
49C2×C11×C22⋊C4—21no—
50C2×C42×C11C2311yescharacteristic
51C2×C22⋊Dic11—22no—
52#66991—42no—
53#66991—42no—
54#66983—42no—
55#66983—42no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×C4⋊Dic11D412yes—
62C22×C11⋊C8—21no—
63C22×C11⋊C8—21no—
64C4×D44—21no—
65C4×D44—21no—
66C4×D44—21no—
67C4×D44—21no—
68C11×#106—24no—
69C11×C4⋊C8—21no—
70C11×C4⋊C8D412yescomplemented
71C11×#102—24no—
72#66899—44no—
73C11⋊#95—22no—
74#66873—24no—
75#66872—24no—
76C4⋊(C11⋊C8)—21no—
77C4⋊(C11⋊C8)D412yescomplemented
78C4×C11⋊C8—21no—
79C4×C11⋊C8—21no—
80#10235—111nomaximal, Sylow
81C24×C11—21no—
82C23×D11—21no—
83C2×Q8×C11—22no—
84C2×Q8×C11—42no—
85C2×Q8×C11—42no—
86C2×Q8×C11—41no—
87C2×D4×C11—21no—
88C2×D4×C11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—21no—
92C2×D4×C11SD1612yes—
93C22×C4×C11—21no—
94C22×C4×C11—41no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—41no—
98C22×C4×C11—41no—
99C22×C4×C11—41no—
100C22×C4×C11—41no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C2×C22⋊D11—44no—
105C2×C22⋊D11—44no—
106C2×C22⋊D11—82no—
107C22×Dic11—21no—
108C22×Dic11—22no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44—21no—
113C2×D44—21no—
114C2×D44SD1612yes—
115C2×C4×D11—41no—
116C2×C4×D11—41no—
117C2×C4×D11—41no—
118C2×C4×D11—41no—
119C2×C4×D11—41no—
120C2×C4×D11—41no—
121C2×C8×C11—22no—
122C2×C8×C11—41no—
123C2×C8×C11—41no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—41no—
129C11×C4⋊C4—41no—
130C11×C22⋊C4—41no—
131C11×C22⋊C4—41no—
132C42×C11C2×D411yescharacteristic
133C42×C11C2×D411yescharacteristic
134C42×C11C2×D411yescharacteristic
135C42×C11#4111yescharacteristic
136C22⋊Dic11—44no—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—41no—
139(C2×D11)⋊C4—41no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—42no—
143C4⋊Dic11—41no—
144C4⋊Dic11—41no—
145C4⋊Dic11—41no—
146C4⋊Dic11—41no—
147C2×C11⋊C8—22no—
148C2×C11⋊C8—22no—
149C2×C11⋊C8—41no—
150C2×C11⋊C8—41no—
151C2×C11⋊C8—41no—
152C2×C11⋊C8—41no—
153C2×#476—111no—
154C2×#476D1111yescharacteristic, complemented
155#2537—111no—
156#1956—111no—
157C2×D4⋊C8—111no—
158C2×D4⋊C8—111no—
159#1296—111no—
160C23×C11—22no—
161C23×C11—41no—
162C23×C11—41no—
163C23×C11—41no—
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—44no—
176Q8×C11—82no—
177D4×C11—22no—
178D4×C11—22no—
179D4×C11—41no—
180D4×C11—41no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—41no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—81no—
188C2×C4×C11—81no—
189C2×C4×C11—81no—
190C2×C4×C11—81no—
191C2×C4×C11—81no—
192C2×C4×C11—81no—
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11#12111yescharacteristic
196C2×C4×C11#12111yescharacteristic
197C2×C4×C11#12111yescharacteristic
198C2×C4×C11#12711yescharacteristic
199C2×C4×C11C2×SD1611yescharacteristic
200C2×C4×C11C2×SD1611yescharacteristic
201C2×C4×C11#13511yescharacteristic
202C2×C4×C11#13511yescharacteristic
203C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
205C2×C4×C11#13711yescharacteristic
206C2×C4×C11#13711yescharacteristic
207C22⋊D11—88no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214D44—22no—
215D44—22no—
216D44—41no—
217D44—41no—
218C4×D11—81no—
219C4×D11—81no—
220C4×D11—81no—
221C4×D11—81no—
222C8×C11—42no—
223C11⋊C8—42no—
224C11⋊C8—42no—
225C2×C4⋊Q8C2×D1111yescharacteristic
226C2×#121—221no—
227C2×#121—221no—
228C2×C4×D4—111no—
229C2×C4×D4C2×D1111yescharacteristic
230#476—22no—
231#476—22no—
232#476—222no—
233#476—222no—
234C2×#106—21no—
235C2×#106—221no—
236C2×C4⋊C8—111no—
237C2×C4⋊C8C2×D1111yescharacteristic
238C2×#103—222no—
239C2×#102—21no—
240C2×#102—221no—
241C2×C4×C8—111no—
242#394—222no—
243#384—111no—
244#380—221no—
245#380—221no—
246D4⋊C8—222no—
247D4⋊C8—222no—
248C22×C11—42no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—81no—
252C22×C11—81no—
253C22×C11—81no—
254C22×C11—81no—
255C22×C11#39211yescharacteristic
256C22×C11#45011yescharacteristic
257C22×C11#45011yescharacteristic
258C22×C11#45211yescharacteristic
259C22×C11#45211yescharacteristic
260C22×C11#45311yescharacteristic
261C22×C11#45411yescharacteristic
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—81no—
272C4×C11—82no—
273C4×C11#44811yescharacteristic
274C4×C11#44811yescharacteristic
275C4×C11#44911yescharacteristic
276C4×C11#44911yescharacteristic
277C4×C11#46511yescharacteristic
278C4×C11#46511yescharacteristic
279C4×C11#46811yescharacteristic
280C4×C11#46811yescharacteristic
281Dic11—82no—
282Dic11—81no—
283C22×Q8—21no—
284C22×D4—111no—
285C22×D4—222no—
286C22×D4C22⋊D1111yescharacteristic
287C23×C4—21no—
288C23×C4—221no—
289C22×C8—21no—
290C22×C8—221no—
291C22×C8—221no—
292C4⋊Q8—21no—
293C4⋊Q8—21no—
294C4⋊Q8—21no—
295C4⋊Q8C22⋊D1112yescomplemented
296#121—442no—
297#121—442no—
298#121—442no—
299#121—442no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4—221no—
305C4×D4—221no—
306C4×D4—221no—
307C4×D4—221no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—221no—
313C2×C4⋊C4—221no—
314C2×C4⋊C4C22⋊D1111yescharacteristic
315C2×C22⋊C4—21no—
316C2×C22⋊C4—222no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—221no—
319C2×C42C22×D1111yescharacteristic
320#106—24no—
321#106—224no—
322C4⋊C8—21no—
323C4⋊C8—112no—
324C4⋊C8—221no—
325C4⋊C8C22⋊D1112yescomplemented
326#103—444no—
327#102—24no—
328#102—224no—
329C4×C8—221no—
330C4×C8—221no—
331#95—222no—
332C2×C11—82no—
333C2×C11#162911yescharacteristic
334C2×C11#163411yescharacteristic
335C2×C11#163511yescharacteristic
336C2×C11#163511yescharacteristic
337C2×C11#200011yescharacteristic
338C2×C11#200011yescharacteristic
339C2×C11#200611yescharacteristic
340D11—82no—
341C24—21no—
342C24—221no—
343C2×Q8—22no—
344C2×Q8—42no—
345C2×Q8—42no—
346C2×Q8—41no—
347C2×D4—21no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—112no—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—444no—
359C2×D4—444no—
360C2×D4—882no—
361C2×D4#432512yes—
362C22×C4—21no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—221no—
371C22×C4—222no—
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
381C2×C8—22no—
382C2×C8—41no—
383C2×C8—41no—
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—441no—
387C2×C8—441no—
388C2×C8—441no—
389C2×C8—441no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—221no—
397C4⋊C4—221no—
398C4⋊C4—442no—
399C4⋊C4—441no—
400C4⋊C4—441no—
401C4⋊C4—441no—
402C4⋊C4—441no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—444no—
406C22⋊C4—444no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C42D4×D1111yescharacteristic
410C42#434111yescharacteristic
411C42C2×C22⋊D1111yescharacteristic
412C42C2×C22⋊D1111yescharacteristic
413C11#1023511yescharacteristic, complemented, Sylow
414C23—22no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—222no—
422C23—441no—
423C23—441no—
424C23—441no—
425C23—441no—
426C23—441no—
427C23—441no—
428C23#6699011yescharacteristic
429Q8—44no—
430Q8—82no—
431D4—22no—
432D4—22no—
433D4—41no—
434D4—41no—
435D4—222no—
436D4—222no—
437D4—441no—
438D4—441no—
439D4—888no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—442no—
457C2×C4—441no—
458C2×C4—881no—
459C2×C4—881no—
460C2×C4—881no—
461C2×C4—881no—
462C2×C4SD16×D1111yescharacteristic
463C2×C4#6696711yescharacteristic
464C2×C4#6696811yescharacteristic
465C2×C4#6696911yescharacteristic
466C2×C4#6699011yescharacteristic
467C2×C4#6699111yescharacteristic
468C2×C4#6699211yescharacteristic
469C2×C4#6699211yescharacteristic
470C2×C4#6699311yescharacteristic
471C2×C4C2×#432511yescharacteristic
472C2×C4#6699511yescharacteristic
473C2×C4#6700211yescharacteristic
474C2×C4#6700311yescharacteristic
475C2×C4#6700611yescharacteristic
476C8—42no—
477C8—442no—
478C8—442no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—442no—
487C22—442no—
488C22—442no—
489C22—881no—
490C22—881no—
491C22—881no—
492C22—881no—
493C22#1062265911yescharacteristic
494C22#1062266011yescharacteristic
495C22#1062278211yescharacteristic
496C22#1062278611yescharacteristic
497C22#1062281111yescharacteristic
498C22#1062281411yescharacteristic
499C22#1062283611yescharacteristic
500C4—21no—
501C4—21no—
502C4—81no—
503C4—82no—
504C4—881no—
505C4—882no—
506C4#1062266111yescharacteristic
507C4#1062266211yescharacteristic
508C4#1062278311yescharacteristic
509C4#1062278411yescharacteristic
510C4#1062278511yescharacteristic
511C4#1062278711yescharacteristic
512C4#1062284011yescharacteristic
513C4#1062285111yescharacteristic
514C2—82no—
515C2—882no—
516C2#1306773111yescharacteristic
517C2#1306776011yescharacteristic
518C2#1306776511yescharacteristic
519C2#1306776611yescharacteristic
520C2#1306961611yescharacteristic
521C2#1306961711yescharacteristic
522C2#1306965611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#476C2
socleC23×C11#120
prime radical#13073529C2
hypercenterC2×#476D11
hypocenterC11#10235
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
3. #13069419C2semidirect
4. C2×D4⋊(C11⋊C8)C2semidirect
5. C2×#10622121C2semidirect
6. #13066500C2semidirect
7. C2×C11×#476C2semidirect
41. C11×C4⋊Q8D4semidirect
70. C11×C4⋊C8D4semidirect
77. C4⋊(C11⋊C8)D4semidirect
154. C2×#476D11semidirect
295. C4⋊Q8C22⋊D11semidirect
325. C4⋊C8C22⋊D11semidirect
413. C11#10235semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
#130735292
#130694192
C2×D4⋊(C11⋊C8)2
C2×#106221212
#130665002
C2×C11×#4762
#1023511