Finite Group Databasebeta

← #14656073

Subgroups — #14656073

Order 2816.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622685C211yesmaximal, characteristic
2#13073534C211yesmaximal, characteristic, complemented
3#13069423C211yesmaximal, characteristic, complemented
4C2×Q8⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
5C2×#10622121C211yesmaximal, characteristic, complemented
6#13066500C211yesmaximal, characteristic, complemented
7C2×C11×#460C211yesmaximal, characteristic, complemented
8C22×C11×SD16—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C4×Q8×C11C2211yescharacteristic
11C2×#66999—21no—
12C22×#4323—21no—
13C2×C4×D44C2211yescharacteristic
14C11×#460—22no—
15C11×#460—22no—
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#102—21no—
18C2×#66896—21no—
19C2×#66896—22no—
20#10622685—22no—
21#10622685—22no—
22#10622607—22no—
23#10622600—21no—
24#10622552—21no—
25#10622548C2211yescharacteristic
26#10622541—21no—
27C2×C4⋊(C11⋊C8)C2211yescharacteristic
28C2×C4×C11⋊C8C2211yescharacteristic
29Q8⋊(C11⋊C8)—22no—
30#10622121—22no—
31C22×Q8×C11D411yescharacteristic
32C22×D4×C11—21no—
33C22×D4×C11—21no—
34C22×D4×C11—21no—
35C22×D44D411yescharacteristic
36C22×C4×D11—21no—
37C2×C11×SD16—24no—
38C2×C11×SD16—42no—
39C2×C11×SD16—42no—
40C22×C8×C11—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127—21no—
44C11×#127D412yes—
45C4×Q8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C42×C11—21no—
52C2×C42×C11C2311yescharacteristic
53#66999—42no—
54#66999—42no—
55C2×#4323—24no—
56C2×#4323—42no—
57C2×#4323—42no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×C4⋊Dic11D412yes—
65C2×Dic11⋊C4—22no—
66C22×C11⋊C8—21no—
67C22×C11⋊C8—21no—
68C4×D44—21no—
69C4×D44—21no—
70C4×D44—21no—
71C4×D44—21no—
72C11×C4⋊C8—21no—
73C11×C4⋊C8D412yes—
74C11×#102—24no—
75#66896—24no—
76#66896—44no—
77C11⋊#95—22no—
78C4⋊(C11⋊C8)—21no—
79C4⋊(C11⋊C8)D412yes—
80C4×C11⋊C8—21no—
81C4×C11⋊C8—21no—
82#10229—111nomaximal, Sylow
83C24×C11—41no—
84C23×D11—21no—
85C2×Q8×C11—21no—
86C2×Q8×C11—21no—
87C2×Q8×C11—21no—
88C2×Q8×C11—21no—
89C2×Q8×C11—21no—
90C2×Q8×C11D812yescomplemented
91C2×D4×C11—22no—
92C2×D4×C11—22no—
93C2×D4×C11—22no—
94C2×D4×C11—42no—
95C2×D4×C11—42no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C2×D4×C11—41no—
100C2×D4×C11—41no—
101C2×D4×C11—41no—
102C2×D4×C11—41no—
103C2×D4×C11—41no—
104C2×D4×C11—41no—
105C2×D4×C11—41no—
106C2×D4×C11—41no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×Dic11—21no—
113C22×Dic11—22no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44SD1612yescomplemented
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—48no—
127C2×C8×C11—22no—
128C2×C8×C11—41no—
129C2×C8×C11—41no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—41no—
133C11×C4⋊C4—41no—
134C42×C11—41no—
135C42×C11—41no—
136C42×C11C2×D411yescharacteristic
137C42×C11C2×D411yescharacteristic
138C42×C11C2×D411yescharacteristic
139C42×C11#4111yescharacteristic
140#4323—48no—
141(C2×D11)⋊C4—44no—
142(C2×D11)⋊C4—41no—
143(C2×D11)⋊C4—41no—
144(C2×D11)⋊C4—82no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—42no—
148C4⋊Dic11—41no—
149C4⋊Dic11—41no—
150C4⋊Dic11—41no—
151C4⋊Dic11—41no—
152Dic11⋊C4—44no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—41no—
156C2×C11⋊C8—41no—
157C2×C11⋊C8—41no—
158C2×C11⋊C8—41no—
159C2×#460D1111yescharacteristic, complemented
160C2×#459—111no—
161#2538—111no—
162#1957—111no—
163C2×Q8⋊C8—111no—
164C2×D4⋊C8—111no—
165#1296—111no—
166C23×C11—42no—
167C23×C11—81no—
168C23×C11—81no—
169C23×C11—81no—
170C23×C11—81no—
171C23×C11—81no—
172C23×C11—81no—
173C23×C11#12011yescharacteristic
174C22×D11—22no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—41no—
184Q8×C11—41no—
185D4×C11—44no—
186D4×C11—42no—
187D4×C11—42no—
188D4×C11—42no—
189D4×C11—42no—
190D4×C11—82no—
191D4×C11—81no—
192D4×C11—81no—
193D4×C11—81no—
194D4×C11—81no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—22no—
198C2×C4×C11—41no—
199C2×C4×C11—41no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11#12011yescharacteristic
204C2×C4×C11#12011yescharacteristic
205C2×C4×C11#12111yescharacteristic
206C2×C4×C11#12111yescharacteristic
207C2×C4×C11#12111yescharacteristic
208C2×C4×C11#12711yescharacteristic
209C2×C4×C11C2×D811yescharacteristic
210C2×C4×C11C2×SD1611yescharacteristic
211C2×C4×C11#13511yescharacteristic
212C2×C4×C11#13511yescharacteristic
213C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
214C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
215C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
216C2×C4×C11#13711yescharacteristic
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—41no—
222C2×Dic11—42no—
223D44—22no—
224D44—22no—
225D44—41no—
226D44—41no—
227C4×D11—81no—
228C4×D11—81no—
229C4×D11—81no—
230C4×D11—81no—
231C8×C11—42no—
232C11⋊C8—42no—
233C11⋊C8—42no—
234C22×SD16—21no—
235C22×D8—221no—
236C2×#127C2×D1111yescharacteristic
237C2×C22⋊Q8—221no—
238C2×C4×Q8C2×D1111yescharacteristic
239C2×C4×D4—111no—
240#460—22no—
241#460—22no—
242#459—222no—
243#459—222no—
244C2×C4⋊C8—111no—
245C2×C4⋊C8C2×D1111yescharacteristic
246C2×#102—21no—
247C2×#102—221no—
248C2×#102—222no—
249C2×C4×C8—111no—
250#396—222no—
251#390—221no—
252#389—221no—
253#384—111no—
254#380—221no—
255Q8⋊C8—222no—
256D4⋊C8—222no—
257C22×C11—82no—
258C22×C11—82no—
259C22×C11—82no—
260C22×C11—161no—
261C22×C11—161no—
262C22×C11—161no—
263C22×C11—161no—
264C22×C11#39211yescharacteristic
265C22×C11#44711yescharacteristic
266C22×C11#44811yescharacteristic
267C22×C11#44911yescharacteristic
268C22×C11#44911yescharacteristic
269C22×C11#45311yescharacteristic
270C22×C11#45411yescharacteristic
271C2×D11—42no—
272C2×D11—42no—
273C2×D11—42no—
274C2×D11—81no—
275C2×D11—81no—
276C2×D11—81no—
277C2×D11—81no—
278C4×C11—21no—
279C4×C11—21no—
280C4×C11—42no—
281C4×C11—81no—
282C4×C11#44711yescharacteristic
283C4×C11#44911yescharacteristic
284C4×C11#45011yescharacteristic
285C4×C11#45211yescharacteristic
286C4×C11#46511yescharacteristic
287C4×C11#46611yescharacteristic
288C4×C11#46811yescharacteristic
289C4×C11#46911yescharacteristic
290Dic11—82no—
291Dic11—81no—
292C22×Q8C22⋊D1111yescharacteristic
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—111no—
297C23×C4—221no—
298C2×SD16—24no—
299C2×SD16—42no—
300C2×SD16—42no—
301C2×D8—224no—
302C2×D8—442no—
303C2×D8—442no—
304C22×C8—21no—
305C22×C8—221no—
306C22×C8—221no—
307#127—21no—
308#127—21no—
309#127—21no—
310#127C22⋊D1112yes—
311C22⋊Q8—442no—
312C22⋊Q8—442no—
313C4×Q8—21no—
314C4×Q8—21no—
315C4×Q8—21no—
316C4×Q8—21no—
317C4×D4—221no—
318C4×D4—221no—
319C4×D4—221no—
320C4×D4—221no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—111no—
323C2×C4⋊C4—112no—
324C2×C4⋊C4—222no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4C22⋊D1111yescharacteristic
328C2×C22⋊C4—222no—
329C2×C22⋊C4—221no—
330C2×C22⋊C4—222no—
331C2×C42—21no—
332C2×C42C22×D1111yescharacteristic
333C4⋊C8—21no—
334C4⋊C8—112no—
335C4⋊C8—221no—
336C4⋊C8C22⋊D1112yes—
337#102—24no—
338#102—224no—
339#102—444no—
340C4×C8—221no—
341C4×C8—221no—
342#95—222no—
343C2×C11—162no—
344C2×C11#162111yescharacteristic
345C2×C11#162211yescharacteristic
346C2×C11#162711yescharacteristic
347C2×C11#162811yescharacteristic
348C2×C11#199911yescharacteristic
349C2×C11#200011yescharacteristic
350C2×C11#200611yescharacteristic
351D11—82no—
352C24—41no—
353C24—221no—
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8#432312yescomplemented
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—112no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—221no—
380C2×D4—221no—
381C2×D4—221no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—221no—
385C22×C4—222no—
386C22×C4—441no—
387C22×C4—441no—
388C22×C4—441no—
389C22×C4—441no—
390C22×C4—441no—
391C22×C4—441no—
392C22×C4D4×D1111yescharacteristic
393C22×C4D4×D1111yescharacteristic
394C22×C4C2×C22⋊D1111yescharacteristic
395SD16—48no—
396D8—448no—
397C2×C8—22no—
398C2×C8—41no—
399C2×C8—41no—
400C2×C8—222no—
401C2×C8—222no—
402C2×C8—441no—
403C2×C8—441no—
404C2×C8—441no—
405C2×C8—441no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—221no—
411C4⋊C4—221no—
412C4⋊C4—442no—
413C4⋊C4—444no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C22⋊C4—444no—
419C22⋊C4—441no—
420C22⋊C4—441no—
421C22⋊C4—882no—
422C42—41no—
423C42—41no—
424C42D4×D1111yescharacteristic
425C42#434111yescharacteristic
426C42C2×C22⋊D1111yescharacteristic
427C42C2×C22⋊D1111yescharacteristic
428C11#1022911yescharacteristic, complemented, Sylow
429C23—42no—
430C23—81no—
431C23—81no—
432C23—81no—
433C23—81no—
434C23—81no—
435C23—81no—
436C23—222no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23—441no—
441C23—441no—
442C23—441no—
443C23#6699011yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—41no—
447Q8—41no—
448D4—44no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—82no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—222no—
459D4—222no—
460D4—441no—
461D4—441no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—442no—
471C2×C4—442no—
472C2×C4—441no—
473C2×C4—442no—
474C2×C4—441no—
475C2×C4—441no—
476C2×C4—881no—
477C2×C4—881no—
478C2×C4—881no—
479C2×C4—881no—
480C2×C4SD16×D1111yescharacteristic
481C2×C4#6696711yescharacteristic
482C2×C4#6696811yescharacteristic
483C2×C4#6696911yescharacteristic
484C2×C4C2×#432311yescharacteristic
485C2×C4#6698511yescharacteristic
486C2×C4#6699011yescharacteristic
487C2×C4#6699111yescharacteristic
488C2×C4#6699211yescharacteristic
489C2×C4#6699211yescharacteristic
490C2×C4#6699311yescharacteristic
491C2×C4#6700211yescharacteristic
492C2×C4#6700311yescharacteristic
493C2×C4#6700611yescharacteristic
494C8—42no—
495C8—442no—
496C8—442no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—161no—
501C22—161no—
502C22—161no—
503C22—161no—
504C22—442no—
505C22—442no—
506C22—442no—
507C22—881no—
508C22—881no—
509C22—881no—
510C22—881no—
511C22#1062264911yescharacteristic
512C22#1062265011yescharacteristic
513C22#1062278311yescharacteristic
514C22#1062278511yescharacteristic
515C22#1062281111yescharacteristic
516C22#1062281411yescharacteristic
517C22#1062283611yescharacteristic
518C4—21no—
519C4—21no—
520C4—42no—
521C4—81no—
522C4—881no—
523C4—882no—
524C4#1062265111yescharacteristic
525C4#1062265211yescharacteristic
526C4#1062278211yescharacteristic
527C4#1062278411yescharacteristic
528C4#1062278611yescharacteristic
529C4#1062278711yescharacteristic
530C4#1062283011yescharacteristic
531C4#1062285111yescharacteristic
532C2—162no—
533C2—882no—
534C2#1306767911yescharacteristic
535C2#1306768711yescharacteristic
536C2#1306771711yescharacteristic
537C2#1306772511yescharacteristic
538C2#1306961211yescharacteristic
539C2#1306961611yescharacteristic
540C2#1306965611yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#460C2
socleC23×C11#120
prime radicalC2×#10622685C2
hypercenterC2×#460D11
hypocenterC11#10229
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. #13073534C2semidirect
3. #13069423C2semidirect
4. C2×Q8⋊(C11⋊C8)C2semidirect
5. C2×#10622121C2semidirect
6. #13066500C2semidirect
7. C2×C11×#460C2semidirect
90. C2×Q8×C11D8semidirect
119. C2×D44SD16semidirect
159. C2×#460D11semidirect
359. C2×Q8#4323semidirect
428. C11#10229semidirect

Maximal subgroups

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

subgroupindex
C2×#106226852
#130735342
#130694232
C2×Q8⋊(C11⋊C8)2
C2×#106221212
#130665002
C2×C11×#4602
#1022911