Finite Group Databasebeta

← #14755151

Subgroups — #14755151

Order 2816.

1830 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67004C211yesmaximal, characteristic
2C2×#10622845C211yesmaximal, characteristic
3C2×#10622617C211yesmaximal, characteristic, complemented
4C2×#10622542C211yesmaximal, characteristic, complemented
5#13068957C214yesmaximal, complemented
6#13068950C214yesmaximal, complemented
7#13068337C211yesmaximal, characteristic, complemented
8#13068310C211yesmaximal, characteristic, complemented
9C2×C4×C11×#41C211yesmaximal, characteristic
10C22×C11×#41C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C4×C11×#41—24no—
13C4×C11×#41—24no—
14C2×C4×Q8×C11C2212yes—
15C2×C4×D4×C11—22no—
16C2×C4×D4×C11C2212yes—
17C2×C11×#117—21no—
18C2×C11×#117C2211yescharacteristic
19C22×C42×C11—21no—
20C22×C42×C11C2211yescharacteristic
21C2×#67004—24no—
22C2×#67004—24no—
23C2×#67004C418yescomplemented
24C22×#4326C2212yes—
25C22×#4324C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C22×#4318C2211yescharacteristic
29#10622845—24no—
30C2×#66899C2212yes—
31C2×#66896C2212yes—
32C2×C11⋊#95—22no—
33#10622617—24no—
34C2×#66874C2214yes—
35#10622542—21no—
36#10622542—21no—
37#10622542C2214yes—
38#10622167C2214yes—
39#10622162C2214yes—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41C2×C414yes—
44C2×C11×#41D414yes—
45C2×C11×#41D414yes—
46C22×Q8×C11C2311yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11C2311yescharacteristic
49C23×C4×C11—21no—
50C23×C4×C11—22no—
51C23×C4×C11D412yes—
52C23×C4×C11C2311yescharacteristic
53C23×Dic11—21no—
54C23×Dic11—21no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22—22no—
58C22×Dic22—22no—
59C22×Dic22—21no—
60C22×Dic22—22no—
61C22×Dic22C2×C414yescomplemented
62C22×Dic22C2312yes—
63C4×Q8×C11—24no—
64C4×Q8×C11—24no—
65C4×D4×C11—216no—
66C4×D4×C11—24no—
67C4×D4×C11—24no—
68C11×#117—28no—
69C11×#117—22no—
70C11×#117D414yes—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—22no—
75C2×C42×C11—28no—
76C2×C42×C11—21no—
77C2×C42×C11—22no—
78C2×C42×C11—22no—
79C2×C42×C11—22no—
80C2×C42×C11D411yescharacteristic
81C2×C42×C11D411yescharacteristic
82C2×C42×C11C2312yes—
83#67004—232no—
84C2×#4326—24no—
85C2×#4326—24no—
86C2×#4326C2×C418yescomplemented
87C2×#4324—24no—
88C2×#4324—24no—
89C2×#4324C2×C418yescomplemented
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2312yes—
94C2×#4318—22no—
95C2×#4318—22no—
96C2×#4318—22no—
97C2×#4318—22no—
98C2×#4318—22no—
99C2×#4318C2×C414yescomplemented
100C22×C11⋊C8C2312yes—
101C22×C11⋊C8C2312yes—
102#66899—24no—
103#66896—24no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106#66874—28no—
107#20927—111nomaximal, Sylow
108C24×C11—21no—
109C24×C11C2×D411yescharacteristic
110C11×#41—28no—
111C11×#41—28no—
112C11×#41—28no—
113C11×#41C22⋊C4116yes—
114C2×Q8×C11—21no—
115C2×Q8×C11—21no—
116C2×Q8×C11—21no—
117C2×Q8×C11C22×C412yes—
118C2×Q8×C11C2×D412yes—
119C2×Q8×C11C2×D412yes—
120C2×D4×C11—24no—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11C22×C412yes—
127C2×D4×C11C2×D412yes—
128C2×D4×C11C2×D412yes—
129C22×C4×C11—21no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—28no—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—42no—
138C22×C4×C11—44no—
139C22×C4×C11—44no—
140C22×C4×C11C22×C412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D412yes—
147C22×C4×C11#4112yes—
148C22×C4×C11#4112yes—
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—44no—
154C22×Dic11—42no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C2×Dic22—28no—
158C2×Dic22—28no—
159C2×Dic22—24no—
160C2×Dic22—22no—
161C2×Dic22—22no—
162C2×Dic22—22no—
163C2×Dic22—22no—
164C2×Dic22—22no—
165C2×Dic22—42no—
166C2×Dic22—44no—
167C2×Dic22—42no—
168C2×Dic22—44no—
169C2×Dic22C22×C414yes—
170C11×C4⋊C4—28no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4C2×D414yes—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—24no—
175C42×C11—28no—
176C42×C11—22no—
177C42×C11—24no—
178C42×C11—22no—
179C42×C11—22no—
180C42×C11—22no—
181#4326—216no—
182#4324—216no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—42no—
186#4318—28no—
187#4318—44no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8C22×C414yes—
194C22×#137—111no—
195C2×C4×#41D1111yescharacteristic
196C2×#417—111no—
197C2×#419—111no—
198C2×#391—111no—
199#1878—114no—
200#1877—114no—
201#1736—111no—
202#1728—111no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—22no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11C4×D412yes—
211C23×C11#12012yes—
212C23×C11#12112yes—
213C23×C11C22×D411yescharacteristic
214Q8×C11—22no—
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11C2×C22⋊C414yes—
218D4×C11—216no—
219D4×C11—22no—
220D4×C11—22no—
221D4×C11—22no—
222D4×C11C2×C22⋊C414yes—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—216no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—48no—
234C2×C4×C11—416no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11C2×C22⋊C414yes—
238C2×C4×C11C4×D414yes—
239C2×C4×C11C4×D412yes—
240C2×C4×C11#12012yes—
241C2×C4×C11#12114yes—
242C2×C4×C11#12112yes—
243C2×C4×C11#12314yes—
244C2×C4×C11#13714yescomplemented
245C2×C4×C11C23×C411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×Dic11—24no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—48no—
255C2×Dic11—42no—
256C2×Dic11—44no—
257C2×Dic11—84no—
258Dic22—24no—
259Dic22—24no—
260Dic22—42no—
261Dic22—42no—
262Dic22—48no—
263C11⋊C8—24no—
264C11⋊C8—42no—
265C22×#41C2×D1111yescharacteristic
266C23×Q8—111no—
267C2×#137—118no—
268C2×#137—224no—
269C2×#137—224no—
270C22×Q16—112no—
271C22×SD16—112no—
272C22×M16—111no—
273C22×M16—111no—
274C4×#41—24no—
275C4×#41—24no—
276C2×C4×Q8C2×D1112yes—
277C2×C4×D4—22no—
278C2×C4×D4C2×D1112yes—
279C2×#117—21no—
280C2×#117C2×D1111yescharacteristic
281C22×C4⋊C4—111no—
282C22×C42—21no—
283C22×C42C2×D1111yescharacteristic
284#419—224no—
285#417—224no—
286C2×#103—112no—
287C2×#103—114no—
288C2×#102—112no—
289#391—114no—
290#391—221no—
291#391—221no—
292C2×#95—222no—
293#340—114no—
294#336—114no—
295C22×C11—24no—
296C22×C11—24no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—24no—
300C22×C11—44no—
301C22×C11—44no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11#38614yes—
305C22×C11C2×C4×D411yescharacteristic
306C22×C11C2×#12011yescharacteristic
307C22×C11C2×#12111yescharacteristic
308C22×C11C2×#13712yes—
309C22×C11#57512yes—
310C4×C11—24no—
311C4×C11—24no—
312C4×C11—42no—
313C4×C11—44no—
314C4×C11#38614yes—
315C4×C11C22×C22⋊C411yescharacteristic
316C4×C11C2×C4×D411yescharacteristic
317C4×C11C2×#12111yescharacteristic
318C4×C11C2×#12311yescharacteristic
319Dic11—44no—
320Dic11—82no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41C4×D1114yes—
325C2×#41D4414yes—
326C2×#41C22⋊D1114yes—
327C22×Q8—114no—
328C22×Q8—112no—
329C22×Q8—222no—
330C22×Q8—221no—
331C22×Q8—222no—
332C22×Q8—222no—
333C22×Q8—222no—
334C22×Q8—222no—
335C22×Q8C22×D1111yescharacteristic
336C22×D4—21no—
337C22×D4C22×D1111yescharacteristic
338C23×C4—21no—
339C23×C4—22no—
340C23×C4—221no—
341C23×C4—221no—
342C23×C4C22⋊D1112yes—
343C23×C4C22×D1111yescharacteristic
344#137—2232no—
345C2×Q16—118no—
346C2×Q16—224no—
347C2×Q16—224no—
348C2×SD16—118no—
349C2×SD16—224no—
350C2×SD16—224no—
351C2×M16—114no—
352C2×M16—222no—
353C2×M16—222no—
354C2×M16—222no—
355C2×M16—222no—
356C2×M16—222no—
357C22×C8—112no—
358C22×C8—112no—
359C4×Q8—24no—
360C4×Q8—24no—
361C4×D4—216no—
362C4×D4—24no—
363C4×D4—24no—
364#117—28no—
365#117—22no—
366#117C22⋊D1114yes—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4C22×D1112yes—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—22no—
375C2×C42—28no—
376C2×C42—21no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42C22⋊D1111yescharacteristic
381C2×C42C22⋊D1111yescharacteristic
382C2×C42C22×D1112yes—
383#103—224no—
384#103—228no—
385#102—224no—
386#95—224no—
387#95—224no—
388C2×C11—24no—
389C2×C11—44no—
390C2×C11C2×#38611yescharacteristic
391C2×C11C4×#13712yes—
392C2×C11#300712yes—
393C2×C11#303911yescharacteristic
394C2×C11#304011yescharacteristic
395C24—21no—
396C24C2×C22⋊D1111yescharacteristic
397#41—28no—
398#41—28no—
399#41—28no—
400#41(C2×D11)⋊C4116yes—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—114no—
405C2×Q8—224no—
406C2×Q8—222no—
407C2×Q8—228no—
408C2×Q8—228no—
409C2×Q8—222no—
410C2×Q8—222no—
411C2×Q8—222no—
412C2×Q8—222no—
413C2×Q8—444no—
414C2×Q8—442no—
415C2×Q8—444no—
416C2×Q8—442no—
417C2×Q8C2×C4×D1112yes—
418C2×Q8C2×D4412yes—
419C2×Q8C2×C22⋊D1112yes—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4C2×C4×D1112yes—
427C2×D4C2×D4412yes—
428C2×D4C2×C22⋊D1112yes—
429C22×C4—21no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—28no—
434C22×C4—24no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—42no—
438C22×C4—44no—
439C22×C4—44no—
440C22×C4—224no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4—444no—
446C22×C4—442no—
447C22×C4C2×C4×D1112yes—
448C22×C4C2×D4412yes—
449C22×C4#433912yes—
450C22×C4#433912yes—
451C22×C4C2×C22⋊D1112yes—
452C22×C4C2×C22⋊D1112yes—
453C22×C4C2×C22⋊D1112yes—
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1112yes—
456C22×C4C23×D1111yescharacteristic
457Q16—2216no—
458SD16—2216no—
459M16—228no—
460M16—444no—
461C2×C8—114no—
462C2×C8—222no—
463C2×C8—222no—
464C2×C8—222no—
465C2×C8—222no—
466C2×C8—222no—
467C4⋊C4—28no—
468C4⋊C4—22no—
469C4⋊C4—222no—
470C4⋊C4—222no—
471C4⋊C4—442no—
472C4⋊C4C2×C22⋊D1114yes—
473C22⋊C4—28no—
474C22⋊C4—24no—
475C42—28no—
476C42—22no—
477C42—24no—
478C42—22no—
479C42—22no—
480C42—22no—
481C11#2092711yescharacteristic, complemented, Sylow
482C23—22no—
483C23—22no—
484C23—22no—
485C23—22no—
486C23—22no—
487C23—42no—
488C23—42no—
489C23C4×C22⋊D1112yes—
490C23#6698312yes—
491C23#6700612yes—
492C23C22×C22⋊D1111yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—22no—
496Q8—224no—
497Q8—224no—
498Q8—442no—
499Q8—442no—
500Q8—448no—
501Q8C2×(C2×D11)⋊C414yes—
502D4—216no—
503D4—22no—
504D4—22no—
505D4—22no—
506D4C2×(C2×D11)⋊C414yes—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—216no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—24no—
517C2×C4—48no—
518C2×C4—416no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—224no—
522C2×C4—442no—
523C2×C4—448no—
524C2×C4—442no—
525C2×C4—442no—
526C2×C4—444no—
527C2×C4—884no—
528C2×C4C2×(C2×D11)⋊C414yes—
529C2×C4C4×C22⋊D1114yes—
530C2×C4C4×C22⋊D1112yes—
531C2×C4#6698214yes—
532C2×C4#6698314yes—
533C2×C4#6698312yes—
534C2×C4#6700414yescomplemented
535C2×C4#6700612yes—
536C2×C4C22×C4×D1111yescharacteristic
537C2×C4C22×D4411yescharacteristic
538C2×C4C2×#433911yescharacteristic
539C2×C4C2×#433911yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C8—224no—
543C8—442no—
544C22—22no—
545C22—22no—
546C22—24no—
547C22—24no—
548C22—24no—
549C22—42no—
550C22—42no—
551C22—44no—
552C22—44no—
553C22#1062282614yes—
554C22C2×C4×C22⋊D1111yescharacteristic
555C22C2×#6698311yescharacteristic
556C22#1062335312yes—
557C22C2×#6700412yes—
558C22C2×#6700611yescharacteristic
559C4—24no—
560C4—24no—
561C4—42no—
562C4—44no—
563C4—444no—
564C4—882no—
565C4#1062282614yes—
566C4C22×(C2×D11)⋊C411yescharacteristic
567C4C2×C4×C22⋊D1111yescharacteristic
568C4C2×#6698211yescharacteristic
569C4C2×#6698311yescharacteristic
570C2—24no—
571C2—44no—
572C2C2×#1062282611yescharacteristic
573C2C4×#6700412yes—
574C2#1307787612yes—
575C2#1307810311yescharacteristic
576C2#1307811011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C4×C11×#41C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×C4×#41D11
hypocenterC11#20927
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
3. C2×#10622617C2semidirect
4. C2×#10622542C2semidirect
5. #13068957C2semidirect
6. #13068950C2semidirect
7. #13068337C2semidirect
8. #13068310C2semidirect
23. C2×#67004C4semidirect
61. C22×Dic22C2×C4semidirect
86. C2×#4326C2×C4semidirect
89. C2×#4324C2×C4semidirect
99. C2×#4318C2×C4semidirect
244. C2×C4×C11#137semidirect
481. C11#20927semidirect
534. C2×C4#67004semidirect

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106228452
C2×#106226172
C2×#106225422
#130689572
#130689502
#130683372
#130683102
C2×C4×C11×#412
#2092711