Finite Group Databasebeta

← #14758292

Subgroups — #14758292

Order 2816.

1250 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic
2C2×#10622731C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic
4#13069572C212yesmaximal, complemented
5#13069570C212yesmaximal, complemented
6#13069566C212yesmaximal, complemented
7#13069562C212yesmaximal, complemented
8#13068337C211yesmaximal, characteristic
9#13068336C211yesmaximal, characteristic
10#13068335C211yesmaximal, characteristic
11C11×#1736C211yesmaximal, characteristic
12C22×C11×M16C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4×Dic11—21no—
18C22×C4×Dic11C2211yescharacteristic
19C22×#4318C2211yescharacteristic
20#10623048—24no—
21#10623048C418yescomplemented
22C2×#66943C2211yescharacteristic
23C2×#66943C2211yescharacteristic
24C2×#66941C2211yescharacteristic
25C2×#66941C2211yescharacteristic
26C2×#66931—21no—
27C2×#66931—21no—
28C2×C4×Dic22—21no—
29C2×C4×Dic22—21no—
30C2×C11⋊#95—21no—
31#10622731—24no—
32C2×Dic11⋊C8C2212yes—
33C2×Dic11⋊C8C2212yes—
34C4⋊C4×Dic11—21no—
35C4⋊C4×Dic11—21no—
36C4⋊C4×Dic11C2212yes—
37C4⋊C4×Dic11C2212yes—
38C11×#340C2212yes—
39C11×#340C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45#10622167C2212yes—
46C23×C4×C11—21no—
47C23×C4×C11C2311yescharacteristic
48C23×Dic11—21no—
49C23×Dic11D411yescharacteristic
50C23×Dic11D411yescharacteristic
51C22×Dic22—21no—
52C22×Dic22—21no—
53C2×C11×M16—22no—
54C2×C11×M16—22no—
55C2×C11×M16—22no—
56C22×C8×C11C2312yes—
57C11×#117—22no—
58C11×#117C2×C414yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4Q814yescomplemented
62C2×C11×C4⋊C4C2311yescharacteristic
63C2×C11×C4⋊C4C2311yescharacteristic
64C2×C11×C4⋊C4C2312yes—
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C2×C22⋊Dic11—21no—
68#66979—22no—
69#66979C2×C414yes—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11Q814yescomplemented
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2312yes—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×C4×Dic11—21no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—44no—
86C2×C4×Dic11C2×C414yes—
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11D411yescharacteristic
89C2×C4×Dic11D414yes—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×#4318—22no—
93C2×#4318—22no—
94C2×#4318—22no—
95C22×C11⋊C8C2312yes—
96#66943—22no—
97#66943—22no—
98#66943C2×C414yescomplemented
99#66943C2×C414yescomplemented
100#66941—22no—
101#66941—22no—
102#66941C2×C414yescomplemented
103#66941C2×C414yescomplemented
104#66931—28no—
105#66931—28no—
106C4×Dic22—28no—
107C4×Dic22—28no—
108C11⋊#95—22no—
109C11⋊#95—22no—
110Dic11⋊C8—24no—
111Dic11⋊C8—24no—
112#21312—111nomaximal, Sylow
113C24×C11C2×D411yescharacteristic
114C22×C4×C11—24no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—42no—
119C22×C4×C11—42no—
120C22×C4×C11C22×C412yes—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×Q812yes—
124C22×C4×C11C2×Q812yes—
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—24no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—41no—
135C22×Dic11—41no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C22×Dic11C22⋊C414yes—
139C22×Dic11C22⋊C414yes—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C2×Dic22—24no—
145C2×Dic22—24no—
146C2×Dic22—42no—
147C2×Dic22—42no—
148C2×Dic22—42no—
149C2×Dic22—42no—
150C11×M16—44no—
151C2×C8×C11—22no—
152C2×C8×C11—22no—
153C2×C8×C11—22no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4C22×C412yes—
159C11×C4⋊C4C22×C412yes—
160C11×C4⋊C4C2×Q814yes—
161C11×C22⋊C4—24no—
162C42×C11—24no—
163C22⋊Dic11—24no—
164C4⋊Dic11—24no—
165C4⋊Dic11—24no—
166C4⋊Dic11—24no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—22no—
170C4⋊Dic11C22×C412yes—
171C4⋊Dic11C22×C412yes—
172C4⋊Dic11C2×Q814yes—
173Dic11⋊C4—24no—
174Dic11⋊C4—24no—
175Dic11⋊C4—24no—
176Dic11⋊C4—24no—
177C4×Dic11—24no—
178C4×Dic11—44no—
179C4×Dic11—44no—
180C4×Dic11C22⋊C414yes—
181C4×Dic11C22⋊C414yes—
182C4×Dic11C22×C412yes—
183C4×Dic11C22×C412yes—
184C4×Dic11C2×D412yes—
185C4×Dic11C2×D412yes—
186#4318—44no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×#533—111no—
191C2×#423—111no—
192C2×C4×C4⋊C4—111no—
193#1989—112no—
194#1989—112no—
195#1988—112no—
196#1987—112no—
197#1736—111no—
198#1736—111no—
199#1736—111no—
200#1736D1111yescharacteristic
201C23×C11—21no—
202C23×C11—21no—
203C23×C11—21no—
204C23×C11—21no—
205C23×C11C2×C22⋊C412yes—
206C23×C11C22⋊Q812yes—
207C23×C11C22⋊Q812yes—
208C23×C11C22×D411yescharacteristic
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—24no—
212C2×C4×C11—48no—
213C2×C4×C11—42no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—42no—
219C2×C4×C11C2×C22⋊C412yes—
220C2×C4×C11C4×Q814yes—
221C2×C4×C11C4×Q814yes—
222C2×C4×C11C22⋊Q812yes—
223C2×C4×C11C22⋊Q812yes—
224C2×C4×C11#12414yes—
225C2×C4×C11C4⋊Q814yes—
226C2×C4×C11C23×C411yescharacteristic
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×Q811yescharacteristic
229C2×C4×C11C22×Q811yescharacteristic
230C2×C4×C11C2×#4111yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×Dic11—21no—
233C2×Dic11—21no—
234C2×Dic11—21no—
235C2×Dic11—21no—
236C2×Dic11—21no—
237C2×Dic11—21no—
238C2×Dic11—28no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—44no—
243C2×Dic11—48no—
244C2×Dic11—42no—
245C2×Dic11—41no—
246C2×Dic11—41no—
247C2×Dic11—41no—
248C2×Dic11—41no—
249C2×Dic11—42no—
250C2×Dic11C2×C22⋊C412yes—
251C2×Dic11C2×C22⋊C412yes—
252C2×Dic11C2×C22⋊C412yes—
253C2×Dic11C2×C22⋊C412yes—
254C2×Dic11AGL(1,ℤ/8)12yes—
255C2×Dic11#13712yes—
256Dic22—48no—
257Dic22—48no—
258C8×C11—42no—
259C11⋊C8—42no—
260C22×M16—111no—
261C22×M16C2×D1111yescharacteristic
262#533—118no—
263#533—224no—
264C2×C4⋊Q8—111no—
265C2×C4⋊Q8—111no—
266C2×#125—111no—
267C2×#125—111no—
268C2×C22⋊Q8—221no—
269C2×C22⋊Q8—221no—
270C2×C4×Q8—221no—
271C2×C4×Q8—221no—
272C2×#117—111no—
273C2×#117C2×D1111yescharacteristic
274C22×C4⋊C4—111no—
275C22×C4⋊C4C2×D1111yescharacteristic
276C22×C42—111no—
277C22×C42—221no—
278#423—224no—
279C2×C4⋊C8—112no—
280C2×C4⋊C8—112no—
281C4×C4⋊C4—112no—
282C4×C4⋊C4—112no—
283C4×C4⋊C4—221no—
284C4×C4⋊C4—221no—
285C2×#95—221no—
286#340—112no—
287#340—112no—
288#340—112no—
289#340—112no—
290#340—112no—
291#340—112no—
292#340C2×D1112yes—
293#340C2×D1112yes—
294C22×C11—22no—
295C22×C11—22no—
296C22×C11—22no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11#39114yes—
301C22×C11C22×C22⋊C411yescharacteristic
302C22×C11C2×C22⋊Q811yescharacteristic
303C22×C11C2×C22⋊Q811yescharacteristic
304C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
305C22×C11C2×#13711yescharacteristic
306C22×C11#57511yescharacteristic
307C22×C11#57511yescharacteristic
308C4×C11—44no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11#39114yes—
312C4×C11C2×C4×Q811yescharacteristic
313C4×C11C2×C4×Q811yescharacteristic
314C4×C11C2×#12411yescharacteristic
315C4×C11C2×C4⋊Q811yescharacteristic
316Dic11—22no—
317Dic11—22no—
318Dic11—22no—
319Dic11—44no—
320Dic11—42no—
321Dic11—42no—
322Dic11#41714yes—
323C22×Q8—221no—
324C22×Q8—221no—
325C23×C4—21no—
326C23×C4—111no—
327C23×C4—111no—
328C23×C4—221no—
329C23×C4C22×D1111yescharacteristic
330C2×M16—22no—
331C2×M16—22no—
332C2×M16—22no—
333C2×M16—222no—
334C2×M16—222no—
335C2×M16—222no—
336C22×C8—112no—
337C22×C8C22×D1112yes—
338C4⋊Q8—114no—
339C4⋊Q8—114no—
340C4⋊Q8—222no—
341C4⋊Q8—222no—
342#125—114no—
343#125—114no—
344#125—222no—
345#125—222no—
346C22⋊Q8—228no—
347C22⋊Q8—228no—
348C4×Q8—228no—
349C4×Q8—228no—
350#117—22no—
351#117—114no—
352#117—222no—
353#117C4×D1114yes—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4Dic2214yescomplemented
369C2×C4⋊C4C22×D1112yes—
370C2×C4⋊C4C22×D1111yescharacteristic
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C22⋊C4—21no—
373C2×C22⋊C4—221no—
374C2×C42—21no—
375C2×C42—114no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—114no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—221no—
382C2×C42—222no—
383C2×C42—222no—
384C2×C42—444no—
385C4⋊C8—224no—
386C4⋊C8—224no—
387#95—222no—
388#95—222no—
389C2×C11—24no—
390C2×C11C2×#39111yescharacteristic
391C2×C11C2×#41711yescharacteristic
392C2×C11#289611yescharacteristic
393C2×C11#307711yescharacteristic
394C2×C11#307711yescharacteristic
395C2×C11#307811yescharacteristic
396C2×C11#307811yescharacteristic
397C24D4×D1111yescharacteristic
398C2×Q8—224no—
399C2×Q8—224no—
400C2×Q8—442no—
401C2×Q8—442no—
402C2×Q8—442no—
403C2×Q8—442no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—42no—
409C22×C4—42no—
410C22×C4—111no—
411C22×C4—114no—
412C22×C4—111no—
413C22×C4—111no—
414C22×C4—111no—
415C22×C4—114no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—441no—
423C22×C4—441no—
424C22×C4—442no—
425C22×C4—442no—
426C22×C4C2×Dic2212yes—
427C22×C4C2×C4×D1112yes—
428C22×C4#433912yes—
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1112yes—
431C22×C4#434112yes—
432C22×C4Q8×D1112yes—
433C22×C4C23×D1111yescharacteristic
434M16—44no—
435M16—444no—
436C2×C8—22no—
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—222no—
440C2×C8—222no—
441C2×C8—222no—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—112no—
447C4⋊C4—112no—
448C4⋊C4—114no—
449C4⋊C4—224no—
450C4⋊C4—224no—
451C4⋊C4—224no—
452C4⋊C4—224no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4—222no—
457C4⋊C4—221no—
458C4⋊C4—221no—
459C4⋊C4C2×Dic2214yes—
460C4⋊C4C2×C4×D1112yes—
461C4⋊C4C2×C4×D1112yes—
462C22⋊C4—24no—
463C22⋊C4—224no—
464C42—24no—
465C42—114no—
466C42—114no—
467C42—112no—
468C42—112no—
469C42—112no—
470C42—112no—
471C42—224no—
472C42—444no—
473C42—444no—
474C11#2131211yescharacteristic, complemented, Sylow
475C23—21no—
476C23—21no—
477C23—21no—
478C23—21no—
479C23#6693112yes—
480C23C22⋊C4×D1112yes—
481C23#6694912yes—
482C23C2×D4×D1111yescharacteristic
483Q8—448no—
484Q8—448no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—48no—
489C2×C4—42no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—112no—
496C2×C4—112no—
497C2×C4—112no—
498C2×C4—112no—
499C2×C4—112no—
500C2×C4—112no—
501C2×C4—228no—
502C2×C4—221no—
503C2×C4—221no—
504C2×C4—221no—
505C2×C4—221no—
506C2×C4—221no—
507C2×C4—221no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—224no—
511C2×C4—444no—
512C2×C4—448no—
513C2×C4—442no—
514C2×C4—441no—
515C2×C4—441no—
516C2×C4—441no—
517C2×C4—442no—
518C2×C4—441no—
519C2×C4C4×Dic2214yes—
520C2×C4#6693112yes—
521C2×C4C22⋊C4×D1112yes—
522C2×C4#6693814yes—
523C2×C4#6694014yes—
524C2×C4#6694114yes—
525C2×C4#6694912yes—
526C2×C4C22×Dic2211yescharacteristic
527C2×C4C22×C4×D1111yescharacteristic
528C2×C4C2×#433911yescharacteristic
529C2×C4C2×D4×D1111yescharacteristic
530C2×C4C2×#434111yescharacteristic
531C2×C4C2×Q8×D1111yescharacteristic
532C8—42no—
533C8—442no—
534C22—22no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—22no—
539C22—22no—
540C22#1062225914yes—
541C22C2×#6693111yescharacteristic
542C22C2×C22⋊C4×D1111yescharacteristic
543C22C2×#6694911yescharacteristic
544C22D11×AGL(1,ℤ/8)11yescharacteristic
545C22#1062330411yescharacteristic
546C22D11×#13711yescharacteristic
547C22#1062330811yescharacteristic
548C4—42no—
549C4—44no—
550C4—42no—
551C4—114no—
552C4—222no—
553C4—222no—
554C4—222no—
555C4—442no—
556C4—442no—
557C4—444no—
558C4#1062225914yes—
559C4C2×C4×Dic2211yescharacteristic
560C4C2×#6693811yescharacteristic
561C4C2×#6694011yescharacteristic
562C4C2×#6694111yescharacteristic
563C2—24no—
564C2C2×#1062225911yescharacteristic
565C2D11×#41711yescharacteristic
566C2#1307713211yescharacteristic
567C2#1307841011yescharacteristic
568C2#1307841211yescharacteristic
569C2#1307841811yescharacteristic
570C2#1307842011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1736C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1736D11
hypocenterC11#21312
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #13069572C2semidirect
5. #13069570C2semidirect
6. #13069566C2semidirect
7. #13069562C2semidirect
21. #10623048C4semidirect
61. C2×C11×C4⋊C4Q8semidirect
74. C2×C4⋊Dic11Q8semidirect
98. #66943C2×C4semidirect
99. #66943C2×C4semidirect
102. #66941C2×C4semidirect
103. #66941C2×C4semidirect
368. C2×C4⋊C4Dic22semidirect
474. C11#21312semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#106227312
C2×C4⋊C4×Dic112
#130695722
#130695702
#130695662
#130695622
#130683372
#130683362
#130683352
C11×#17362
#2131211