Finite Group Databasebeta

← #14759450

Subgroups — #14759450

Order 2816.

1436 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×Dic11C211yesmaximal, characteristic
2C2×#10622797C212yesmaximal, complemented
3C22⋊Q8×Dic11C211yesmaximal, characteristic
4#13068959C212yesmaximal, complemented
5#13068924C211yesmaximal, characteristic
6#13068886C212yesmaximal, complemented
7#13068811C211yesmaximal, characteristic
8#13068551C211yesmaximal, characteristic
9#13068448C212yesmaximal, complemented
10#13068380C211yesmaximal, characteristic
11C2×C11×#451C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C22×C11×Q16C2212yes—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×Q8×Dic11—28no—
16C2×Q8×Dic11—21no—
17C2×Q8×Dic11—21no—
18C2×Q8×Dic11C2211yescharacteristic
19C2×Q8×Dic11C2212yes—
20C2×Q8×Dic11C2212yes—
21C22×C4⋊Dic11—21no—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4×Dic11—21no—
24C22×C4×Dic11C2211yescharacteristic
25C11×#451C418yescomplemented
26C2×C11×#103C2212yes—
27C2×C11×C22⋊C8C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2212yes—
30C2×#66899C2212yes—
31C2×#66899C2212yes—
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34#10622797—28no—
35C2×#66881C2212yes—
36C2×#66879C2212yes—
37#10622598C2211yescharacteristic
38#10622594—21no—
39C4⋊C4×Dic11—21no—
40C4⋊C4×Dic11C2211yescharacteristic
41#10622563—21no—
42C22⋊C4×Dic11—21no—
43#10622189C2212yes—
44#10622188C2212yes—
45#10622167C2212yes—
46C22×Q8×C11—24no—
47C22×Q8×C11—24no—
48C22×Q8×C11—21no—
49C22×Q8×C11—22no—
50C22×Q8×C11C2×C414yes—
51C22×Q8×C11C2311yescharacteristic
52C22×Q8×C11C2312yes—
53C23×C4×C11—21no—
54C23×C4×C11C2311yescharacteristic
55C23×Dic11—21no—
56C23×Dic11D411yescharacteristic
57C23×Dic11D411yescharacteristic
58C2×C11×Q16—24no—
59C2×C11×Q16—24no—
60C2×C11×Q16C2×C418yescomplemented
61C22×C8×C11C2312yes—
62C11×C22⋊Q8—22no—
63C11×C22⋊Q8C2×C414yes—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C22⋊Dic11—21no—
68Q8×Dic11—28no—
69Q8×Dic11—28no—
70Q8×Dic11—24no—
71Q8×Dic11—24no—
72Q8×Dic11—24no—
73Q8×Dic11—24no—
74Q8×Dic11D418yes—
75C2×C4⋊Dic11—28no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—24no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2312yes—
85C2×C4×Dic11—28no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11—24no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2312yes—
96C11×#103C2×C418yescomplemented
97C11×C22⋊C8C2×C414yes—
98#66899—24no—
99#66899—24no—
100#66899—24no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C22⋊(C11⋊C8)—22no—
107#66881—24no—
108#66879—24no—
109#21455—111nomaximal, Sylow
110C24×C11C2×D411yescharacteristic
111C2×Q8×C11—24no—
112C2×Q8×C11—216no—
113C2×Q8×C11—24no—
114C2×Q8×C11—216no—
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—21no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11C22×C412yes—
123C2×Q8×C11C22×C414yes—
124C2×Q8×C11C2×D414yes—
125C2×Q8×C11#4114yes—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11#4112yes—
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—41no—
148C22×Dic11—42no—
149C22×Dic11—42no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C11×Q16—216no—
155C2×C8×C11—22no—
156C2×C8×C11—22no—
157C2×C8×C11C22×C414yes—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4C22×C412yes—
161C11×C22⋊C4—24no—
162C22⋊Dic11—42no—
163C4⋊Dic11—28no—
164C4⋊Dic11—24no—
165C4⋊Dic11—28no—
166C4⋊Dic11—22no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—42no—
170C4⋊Dic11—42no—
171C4⋊Dic11C2×D414yes—
172C4×Dic11—28no—
173C4×Dic11—28no—
174C4×Dic11—22no—
175C4×Dic11—22no—
176C4×Dic11—22no—
177C4×Dic11—42no—
178C4×Dic11—42no—
179C4×Dic11C2×D414yes—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8—22no—
183C22×C4×Q8—111no—
184C2×#451D1111yescharacteristic
185C2×#441—112no—
186C4×C22⋊Q8—111no—
187#1878—112no—
188#1872—111no—
189#1865—112no—
190#1853—111no—
191#1787—111no—
192#1763—112no—
193#1749—111no—
194C23×C11—21no—
195C23×C11—21no—
196C23×C11—21no—
197C23×C11—21no—
198C23×C11C4×D412yes—
199C23×C11#13712yes—
200C23×C11#13712yes—
201C23×C11C22×D411yescharacteristic
202Q8×C11—216no—
203Q8×C11—24no—
204Q8×C11—24no—
205Q8×C11—24no—
206Q8×C11—24no—
207Q8×C11—42no—
208Q8×C11C4×D418yes—
209C2×C4×C11—216no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—21no—
213C2×C4×C11—24no—
214C2×C4×C11—21no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11C4×D412yes—
224C2×C4×C11C23×C411yescharacteristic
225C2×C4×C11C22×D412yes—
226C2×C4×C11C2×#4112yes—
227C2×C4×C11C2×#4111yescharacteristic
228C2×Dic11—28no—
229C2×Dic11—21no—
230C2×Dic11—21no—
231C2×Dic11—21no—
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—24no—
237C2×Dic11—21no—
238C2×Dic11—21no—
239C2×Dic11—44no—
240C2×Dic11—48no—
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11#12012yes—
250C2×Dic11#12012yes—
251C2×Dic11#13712yes—
252C8×C11—24no—
253C11⋊C8—42no—
254C23×Q8C2×D1111yescharacteristic
255C22×Q16C2×D1112yes—
256C2×C22⋊Q8C2×D1111yescharacteristic
257C2×C4×Q8—112no—
258C2×C4×Q8—112no—
259C2×C4×Q8—111no—
260C2×C4×Q8—221no—
261C2×C4×Q8—221no—
262C2×C4×Q8—228no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—221no—
265C22×C42—111no—
266C22×C42—221no—
267#451Dic1118yescomplemented
268#441—228no—
269C2×#106—112no—
270C2×#103—112no—
271C2×#103—112no—
272C2×#103—112no—
273C2×#103C2×D1112yes—
274C2×C22⋊C8—111no—
275C2×C22⋊C8C2×D1111yescharacteristic
276C2×#97—112no—
277#391—111no—
278#389—111no—
279#387—221no—
280#385—221no—
281#380—111no—
282C4×C4⋊C4—111no—
283C4×C4⋊C4—221no—
284C4×C22⋊C4—221no—
285#340—112no—
286#340—112no—
287#336—112no—
288C22×C11—22no—
289C22×C11—22no—
290C22×C11—22no—
291C22×C11—22no—
292C22×C11—22no—
293C22×C11—22no—
294C22×C11#44114yescomplemented
295C22×C11C2×C4×D411yescharacteristic
296C22×C11C2×#12011yescharacteristic
297C22×C11#52511yescharacteristic
298C22×C11C2×#13711yescharacteristic
299C22×C11C2×#13711yescharacteristic
300C22×C11C2×#13711yescharacteristic
301C22×C11#57511yescharacteristic
302C4×C11—28no—
303C4×C11—22no—
304C4×C11—42no—
305C4×C11—42no—
306C4×C11C2×C4×D412yes—
307C4×C11#52512yes—
308Dic11—22no—
309Dic11—22no—
310Dic11—22no—
311Dic11—41no—
312Dic11—44no—
313Dic11—81no—
314Dic11—81no—
315C22×Q8—24no—
316C22×Q8—24no—
317C22×Q8—21no—
318C22×Q8—22no—
319C22×Q8C2×Dic1114yes—
320C22×Q8C22×D1111yescharacteristic
321C22×Q8C22×D1112yes—
322C23×C4—21no—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—221no—
326C23×C4C22×D1111yescharacteristic
327C2×Q16—24no—
328C2×Q16—24no—
329C2×Q16C2×Dic1118yescomplemented
330C22×C8—112no—
331C22×C8C22×D1112yes—
332C22⋊Q8—22no—
333C22⋊Q8C2×Dic1114yes—
334C4×Q8—118no—
335C4×Q8—224no—
336C4×Q8—224no—
337C4×Q8—224no—
338C4×Q8—228no—
339C4×Q8—228no—
340C4×Q8—224no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—112no—
343C2×C4⋊C4—111no—
344C2×C4⋊C4—111no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—228no—
349C2×C4⋊C4—221no—
350C2×C4⋊C4—221no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4C22×D1111yescharacteristic
353C2×C22⋊C4—21no—
354C2×C22⋊C4—221no—
355C2×C42—111no—
356C2×C42—111no—
357C2×C42—111no—
358C2×C42—111no—
359C2×C42—224no—
360C2×C42—222no—
361C2×C42—222no—
362C2×C42—228no—
363C2×C42—221no—
364C2×C42—221no—
365#106—224no—
366#103—224no—
367#103—224no—
368#103—224no—
369#103C2×Dic1118yescomplemented
370C22⋊C8—222no—
371C22⋊C8C2×Dic1114yes—
372#97—224no—
373#95—221no—
374#95—221no—
375#95—221no—
376#95—221no—
377#95—221no—
378C2×C11—24no—
379C2×C11C4×#12011yescharacteristic
380C2×C11C2×#44111yescharacteristic
381C2×C11C4×#13711yescharacteristic
382C2×C11#300411yescharacteristic
383C2×C11#300711yescharacteristic
384C2×C11#311311yescharacteristic
385C2×C11#311711yescharacteristic
386C24D4×D1111yescharacteristic
387C2×Q8—24no—
388C2×Q8—216no—
389C2×Q8—24no—
390C2×Q8—216no—
391C2×Q8—24no—
392C2×Q8—22no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—21no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8D4×D1114yes—
399C2×Q8#434114yes—
400C2×Q8C22×Dic1112yes—
401C2×Q8C22×Dic1114yes—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—111no—
411C22×C4—111no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—221no—
422C22×C4—221no—
423C22×C4—441no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4D4×D1111yescharacteristic
427C22×C4#434112yes—
428C22×C4C22×Dic1112yes—
429C22×C4C23×D1111yescharacteristic
430Q16—216no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—222no—
434C2×C8—222no—
435C2×C8—222no—
436C2×C8C22×Dic1114yes—
437C4⋊C4—24no—
438C4⋊C4—21no—
439C4⋊C4—114no—
440C4⋊C4—228no—
441C4⋊C4—228no—
442C4⋊C4—224no—
443C4⋊C4—222no—
444C4⋊C4—222no—
445C4⋊C4—222no—
446C4⋊C4—442no—
447C4⋊C4—442no—
448C4⋊C4C22×Dic1112yes—
449C22⋊C4—24no—
450C22⋊C4—442no—
451C42—114no—
452C42—222no—
453C42—222no—
454C42—228no—
455C42—228no—
456C42—222no—
457C42—442no—
458C42—442no—
459C11#2145511yescharacteristic, complemented, Sylow
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23#6697112yes—
465C23#6697112yes—
466C23D4×Dic1112yes—
467C23C2×D4×D1111yescharacteristic
468Q8—216no—
469Q8—24no—
470Q8—24no—
471Q8—24no—
472Q8—24no—
473Q8—42no—
474Q8D4×Dic1118yes—
475C2×C4—216no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—21no—
479C2×C4—24no—
480C2×C4—21no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—112no—
490C2×C4—112no—
491C2×C4—112no—
492C2×C4—228no—
493C2×C4—221no—
494C2×C4—221no—
495C2×C4—221no—
496C2×C4—221no—
497C2×C4—221no—
498C2×C4—221no—
499C2×C4—221no—
500C2×C4—221no—
501C2×C4—224no—
502C2×C4—221no—
503C2×C4—444no—
504C2×C4—448no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—441no—
508C2×C4—441no—
509C2×C4—441no—
510C2×C4—441no—
511C2×C4—441no—
512C2×C4—441no—
513C2×C4D4×Dic1112yes—
514C2×C4C2×D4×D1112yes—
515C2×C4C2×#434112yes—
516C2×C4C2×#434111yescharacteristic
517C2×C4C23×Dic1111yescharacteristic
518C8—24no—
519C8—442no—
520C22—22no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—22no—
525C22—22no—
526C22#1062279714yescomplemented
527C22#1062311711yescharacteristic
528C22D11×#12011yescharacteristic
529C22C2×#6697111yescharacteristic
530C22C2×#6697111yescharacteristic
531C22D11×#13711yescharacteristic
532C22#1062330811yescharacteristic
533C22C2×D4×Dic1111yescharacteristic
534C4—28no—
535C4—22no—
536C4—42no—
537C4—42no—
538C4—222no—
539C4—222no—
540C4—222no—
541C4—441no—
542C4—444no—
543C4—881no—
544C4—881no—
545C4#1062311712yes—
546C4C2×D4×Dic1112yes—
547C2—24no—
548C2#120×Dic1111yescharacteristic
549C2C2×#1062279711yescharacteristic
550C2#137×Dic1111yescharacteristic
551C2#1307785111yescharacteristic
552C2#1307787511yescharacteristic
553C2#1307874111yescharacteristic
554C2#1307878811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#451C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenterC2×#451D11
hypocenterC11#21455
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#10622797C2semidirect
4. #13068959C2semidirect
6. #13068886C2semidirect
9. #13068448C2semidirect
25. C11×#451C4semidirect
60. C2×C11×Q16C2×C4semidirect
96. C11×#103C2×C4semidirect
267. #451Dic11semidirect
294. C22×C11#441semidirect
329. C2×Q16C2×Dic11semidirect
369. #103C2×Dic11semidirect
459. C11#21455semidirect
526. C22#10622797semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×Dic112
C2×#106227972
C22⋊Q8×Dic112
#130689592
#130689242
#130688862
#130688112
#130685512
#130684482
#130683802
C2×C11×#4512
#2145511