Finite Group Databasebeta

← #14810768

Subgroups — #14810768

Order 2816.

1100 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622680C211yesmaximal, characteristic
2C2×#10622640C211yesmaximal, characteristic
3#13073615C211yesmaximal, characteristic
4#13069759C212yesmaximal, complemented
5#13069749C212yesmaximal, complemented
6#13069574C211yesmaximal, characteristic, complemented
7#13069557C211yesmaximal, characteristic, complemented
8#13068971C212yesmaximal, complemented
9#13068971C212yesmaximal, complemented
10#13068446C211yesmaximal, characteristic, complemented
11C2×C11×#557C211yesmaximal, characteristic, complemented
12C11×#557—24no—
13C11×#557—24no—
14C2×C11×C4⋊Q8—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×#125—21no—
18C2×C11×#125C2211yescharacteristic
19C2×C11×#125C2211yescharacteristic
20C2×C4×Q8×C11—21no—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2211yescharacteristic
25C2×#67000—21no—
26C22×#4325C2212yes—
27C2×#66927C2211yescharacteristic
28C2×#66899C2212yes—
29#10622680—24no—
30#10622640—24no—
31#10622604—21no—
32#10622604—21no—
33#10622601—21no—
34C2×#66873C2212yes—
35C2×#66873C2212yes—
36C2×#66873C2212yes—
37#10622552C2212yes—
38#10622552C2212yes—
39C4×C4⋊Dic11C2211yescharacteristic
40C2×C4⋊(C11⋊C8)C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622162C2212yes—
46#10622162C2212yes—
47C22×Q8×C11—21no—
48C22×Q8×C11D411yescharacteristic
49C22×Q8×C11C2311yescharacteristic
50C22×D44—21no—
51C22×D44—21no—
52C22×D44C2312yes—
53C11×C4⋊Q8—28no—
54C11×C4⋊Q8—22no—
55C11×C4⋊Q8—22no—
56C11×#125—28no—
57C11×#125—28no—
58C11×#125—22no—
59C11×#125—22no—
60C11×#125—22no—
61C11×#125D414yes—
62C4×Q8×C11—28no—
63C4×Q8×C11—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11D414yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91#67000—44no—
92C2×#4325—24no—
93C2×#4325—24no—
94C2×#4325—24no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×C4⋊Dic11C2312yes—
100C2×C4×Dic11—21no—
101C22×C11⋊C8C2312yes—
102C22×C11⋊C8C2312yes—
103#66927—22no—
104#66927—22no—
105#66899—24no—
106C11⋊#95—21no—
107#66873—24no—
108#66873—24no—
109#66873—24no—
110C4⋊(C11⋊C8)—22no—
111#66867—22no—
112#25944—111nomaximal, Sylow
113C23×D11—22no—
114C2×Q8×C11—24no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—21no—
118C2×Q8×C11—22no—
119C2×Q8×C11—41no—
120C2×Q8×C11—42no—
121C2×Q8×C11—42no—
122C2×Q8×C11C2×D412yes—
123C2×Q8×C11#4114yes—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—22no—
136C2×D44—22no—
137C2×D44—22no—
138C2×D44—22no—
139C2×D44—22no—
140C2×D44—22no—
141C2×D44—22no—
142C2×D44—42no—
143C2×D44—42no—
144C2×D44—42no—
145C2×D44—42no—
146C2×D44—82no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—24no—
151C11×C4⋊C4—24no—
152C11×C4⋊C4—24no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4C2×D412yes—
162C11×C4⋊C4C2×D412yes—
163C11×C4⋊C4C2×D412yes—
164C42×C11—24no—
165C42×C11—24no—
166C42×C11—24no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11C2×D412yes—
172C42×C11C2×D412yes—
173#4325—48no—
174(C2×D11)⋊C4—44no—
175(C2×D11)⋊C4—44no—
176(C2×D11)⋊C4—82no—
177(C2×D11)⋊C4—82no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4×Dic11—42no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8—22no—
187C2×#557D1111yescharacteristic, complemented
188C2×#490—111no—
189C2×#460—111no—
190#2548—111no—
191#2025—112no—
192#2023—112no—
193#1989—111no—
194#1985—111no—
195#1880—112no—
196#1880—112no—
197#1763—111no—
198C23×C11C22×D411yescharacteristic
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—42no—
206Q8×C11—22no—
207Q8×C11—24no—
208Q8×C11—44no—
209Q8×C11—48no—
210Q8×C11#12414yescomplemented
211C2×C4×C11—22no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—22no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—42no—
233C2×C4×C11#12012yes—
234C2×C4×C11#12012yes—
235C2×C4×C11AGL(1,ℤ/8)12yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C2×#4112yes—
239C2×C4×C112−1+412yes—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243D44—42no—
244D44—42no—
245D44—42no—
246D44—42no—
247D44—84no—
248D44—84no—
249C11⋊C8—42no—
250C11⋊C8—42no—
251C22×SD16—112no—
252#557—24no—
253#557—24no—
254C2×C4⋊Q8—21no—
255C2×C4⋊Q8C2×D1111yescharacteristic
256C2×#127—111no—
257C2×#125—21no—
258C2×#125—21no—
259C2×#125C2×D1111yescharacteristic
260C2×#125C2×D1111yescharacteristic
261C2×#124—221no—
262C2×C4×Q8—21no—
263C2×C4×Q8C2×D1111yescharacteristic
264C2×C4×Q8C2×D1111yescharacteristic
265C2×C4×Q8C2×D1111yescharacteristic
266C2×C4×Q8C2×D1111yescharacteristic
267#490—224no—
268#460—224no—
269C2×C4⋊C8—111no—
270C2×#103—112no—
271C2×#102—112no—
272C2×#102—112no—
273C2×#102—112no—
274C2×#97—111no—
275#394—221no—
276#394—221no—
277#390—112no—
278#390—112no—
279#390—221no—
280C4×C4⋊C4—111no—
281#340—112no—
282#340—112no—
283#340—112no—
284#336—112no—
285#336—112no—
286C22×C11C2×#12011yescharacteristic
287C22×C11#54812yes—
288C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
289C22×C11#57511yescharacteristic
290C22×C11#57712yes—
291C2×D11—82no—
292C2×D11—82no—
293C2×D11—82no—
294C2×D11—82no—
295C2×D11—82no—
296C2×D11—82no—
297C2×D11—82no—
298C4×C11—24no—
299C4×C11—22no—
300C4×C11—22no—
301C4×C11—22no—
302C4×C11—41no—
303C4×C11—42no—
304C4×C11—42no—
305C4×C11—41no—
306C4×C11—41no—
307C4×C11—42no—
308C4×C11C2×#12411yescharacteristic
309C4×C11#53611yescharacteristic
310C4×C11#54812yes—
311Dic11—82no—
312C22×Q8—21no—
313C22×Q8C22⋊D1111yescharacteristic
314C22×Q8C22×D1111yescharacteristic
315C22×D4—112no—
316C22×D4—221no—
317C22×D4—221no—
318C2×SD16—224no—
319C2×SD16—224no—
320C2×SD16—224no—
321C22×C8—112no—
322C22×C8—112no—
323C4⋊Q8—28no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326#127—222no—
327#127—222no—
328#125—28no—
329#125—28no—
330#125—22no—
331#125—22no—
332#125—22no—
333#125C22⋊D1114yes—
334#124—444no—
335C4×Q8—28no—
336C4×Q8—22no—
337C4×Q8—22no—
338C4×Q8—22no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—22no—
342C4×Q8—22no—
343C4×Q8C22⋊D1114yes—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—112no—
353C2×C4⋊C4C22⋊D1111yescharacteristic
354C2×C4⋊C4C22⋊D1111yescharacteristic
355C2×C4⋊C4C22⋊D1111yescharacteristic
356C2×C4⋊C4C22×D1111yescharacteristic
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C22⋊C4—222no—
360C2×C22⋊C4—222no—
361C2×C22⋊C4—222no—
362C2×C22⋊C4—222no—
363C2×C42—21no—
364C2×C42—21no—
365C2×C42—21no—
366C2×C42—221no—
367C2×C42C22×D1111yescharacteristic
368C2×C42C22×D1111yescharacteristic
369C2×C42C22×D1111yescharacteristic
370C4⋊C8—222no—
371#103—224no—
372#102—224no—
373#102—224no—
374#102—224no—
375#97—222no—
376#95—221no—
377C2×C11#243611yescharacteristic
378C2×C11#300611yescharacteristic
379C2×C11#301011yescharacteristic
380C2×C11#336812yes—
381C2×C11#337112yes—
382D11—162no—
383C24—222no—
384C2×Q8—24no—
385C2×Q8—22no—
386C2×Q8—22no—
387C2×Q8—22no—
388C2×Q8—21no—
389C2×Q8—41no—
390C2×Q8—42no—
391C2×Q8—42no—
392C2×Q8#434314yes—
393C2×Q8C2×C22⋊D1112yes—
394C2×D4—222no—
395C2×D4—222no—
396C2×D4—222no—
397C2×D4—222no—
398C2×D4—222no—
399C2×D4—222no—
400C2×D4—442no—
401C2×D4—442no—
402C2×D4—442no—
403C2×D4—442no—
404C2×D4—882no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—222no—
410C22×C4C2×C22⋊D1111yescharacteristic
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C2×C22⋊D1111yescharacteristic
413C22×C4C2×C22⋊D1111yescharacteristic
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417SD16—448no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8—222no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—222no—
439C4⋊C4—222no—
440C4⋊C4C2×C22⋊D1112yes—
441C4⋊C4C2×C22⋊D1112yes—
442C4⋊C4C2×C22⋊D1112yes—
443C22⋊C4—444no—
444C22⋊C4—444no—
445C22⋊C4—882no—
446C22⋊C4—882no—
447C42—24no—
448C42—24no—
449C42—24no—
450C42—21no—
451C42—21no—
452C42—21no—
453C42—21no—
454C42—442no—
455C42C2×C22⋊D1112yes—
456C42C2×C22⋊D1112yes—
457C11#2594411yescharacteristic, complemented, Sylow
458C23—442no—
459C23—442no—
460C23—442no—
461C23—442no—
462C23—442no—
463C23—442no—
464C23—442no—
465C23C22×C22⋊D1111yescharacteristic
466Q8—22no—
467Q8—24no—
468Q8—44no—
469Q8—48no—
470Q8#6700014yescomplemented
471D4—442no—
472D4—442no—
473D4—442no—
474D4—442no—
475D4—884no—
476D4—884no—
477C2×C4—24no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—442no—
502C2×C4#6700212yes—
503C2×C4#6700612yes—
504C2×C4#6700612yes—
505C2×C4C2×#434312yes—
506C2×C4#6704012yes—
507C2×C4C22×C22⋊D1111yescharacteristic
508C2×C4C22×C22⋊D1111yescharacteristic
509C8—442no—
510C8—442no—
511C22—882no—
512C22—882no—
513C22—882no—
514C22—882no—
515C22—882no—
516C22—882no—
517C22—882no—
518C22#1062334812yes—
519C22C2×#6700211yescharacteristic
520C22#1062335311yescharacteristic
521C22#1062336812yes—
522C22C2×#6700611yescharacteristic
523C4—22no—
524C4—22no—
525C4—24no—
526C4—22no—
527C4—41no—
528C4—42no—
529C4—42no—
530C4—41no—
531C4—41no—
532C4—42no—
533C4—882no—
534C4C2×#6700011yescharacteristic
535C4#1062334711yescharacteristic
536C4#1062334812yes—
537C2—1762no—
538C2#1307227011yescharacteristic
539C2#1307786811yescharacteristic
540C2#1307790211yescharacteristic
541C2#1308134512yes—
542C2#1308138412yes—
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenterC2×#557D11
hypocenterC11#25944
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
4. #13069759C2semidirect
5. #13069749C2semidirect
6. #13069574C2semidirect
7. #13069557C2semidirect
8. #13068971C2semidirect
9. #13068971C2semidirect
10. #13068446C2semidirect
11. C2×C11×#557C2semidirect
187. C2×#557D11semidirect
210. Q8×C11#124semidirect
457. C11#25944semidirect
470. Q8#67000semidirect

Maximal subgroups

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

subgroupindex
C2×#106226802
C2×#106226402
#130736152
#130697592
#130697492
#130695742
#130695572
#130689712
#130684462
C2×C11×#5572
#2594411