Finite Group Databasebeta

← #14755407

Subgroups — #14755407

Order 2816.

2126 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623329C211yesmaximal, characteristic, complemented
2C22×#66898C211yesmaximal, characteristic, complemented
3#13071194C212yesmaximal, complemented
4#13069030C214yesmaximal, complemented
5#13069025C214yesmaximal, complemented
6C2×#10622165C212yesmaximal, complemented
7C2×C11×#534C211yesmaximal, characteristic
8C23×D4×C11C2211yescharacteristic
9C23×D4×C11C2211yescharacteristic
10C11×#534—24no—
11C11×#534C418yescomplemented
12C2×C11×#123—21no—
13C2×C11×#123C2212yes—
14C2×C11×#121—22no—
15C2×C11×#120—21no—
16C2×C11×#120C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11—21no—
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2212yes—
21#10623329—22no—
22#10623329—24no—
23#10623329C2214yes—
24C2×D4×Dic11—24no—
25C2×#66979—21no—
26#10622860C2214yescomplemented
27#10622833—24no—
28#10622833—24no—
29C2×#66898—24no—
30C2×#66898C2214yes—
31#10622824C2214yescomplemented
32#10622165C2218yescomplemented
33C25×C11D411yescharacteristic
34C25×C11C2311yescharacteristic
35C25×C11C2311yescharacteristic
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—24no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×D4×C11—22no—
44C22×D4×C11—24no—
45C22×D4×C11—22no—
46C22×D4×C11C2×C414yes—
47C22×D4×C11C2×C414yescomplemented
48C22×D4×C11D414yes—
49C22×D4×C11D412yes—
50C22×D4×C11C2312yes—
51C23×C4×C11—21no—
52C23×C4×C11D411yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11—22no—
55C23×Dic11—22no—
56C23×Dic11D414yescomplemented
57C11×#123—24no—
58C11×#123—28no—
59C11×#123C2×C418yescomplemented
60C11×#121—216no—
61C11×#120—28no—
62C11×#120—24no—
63C11×#120C2×C418yescomplemented
64C2×C11×C4⋊C4—22no—
65C2×C11×C22⋊C4—21no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4C2×C414yescomplemented
70C2×C11×C22⋊C4C2312yes—
71C2×C22⋊Dic11—22no—
72C2×C22⋊Dic11—24no—
73C2×C22⋊Dic11—22no—
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—24no—
80C2×C22⋊Dic11—22no—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11D414yescomplemented
83C2×C22⋊Dic11C2314yes—
84C2×C22⋊Dic11C2314yes—
85D4×Dic11—216no—
86D4×Dic11—216no—
87#66979—24no—
88#66979—24no—
89C2×C4⋊Dic11—22no—
90C2×C4×Dic11—22no—
91#66898—28no—
92C11⋊#95—28no—
93#20960—111nomaximal, Sylow
94C24×C11—21no—
95C24×C11—21no—
96C24×C11—22no—
97C24×C11—22no—
98C24×C11—21no—
99C24×C11—21no—
100C24×C11—22no—
101C24×C11—82no—
102C24×C11—82no—
103C24×C11—82no—
104C24×C11C22⋊C414yescomplemented
105C24×C11C22×C412yes—
106C24×C11C22×C412yescomplemented
107C24×C11C2×D412yes—
108C24×C11C2×D411yescharacteristic
109C24×C11C2×D411yescharacteristic
110C24×C11C2×D412yes—
111C24×C11C2×D412yes—
112C24×C11C2×D412yes—
113C24×C11#4114yes—
114C24×C11C2411yescharacteristic
115C2×D4×C11—28no—
116C2×D4×C11—28no—
117C2×D4×C11—24no—
118C2×D4×C11—28no—
119C2×D4×C11—28no—
120C2×D4×C11—24no—
121C2×D4×C11—24no—
122C2×D4×C11—24no—
123C2×D4×C11—24no—
124C2×D4×C11—24no—
125C2×D4×C11—28no—
126C2×D4×C11—28no—
127C2×D4×C11—28no—
128C2×D4×C11—41no—
129C2×D4×C11—42no—
130C2×D4×C11—41no—
131C2×D4×C11—44no—
132C2×D4×C11—44no—
133C2×D4×C11—42no—
134C2×D4×C11—42no—
135C2×D4×C11—84no—
136C2×D4×C11C22⋊C418yescomplemented
137C2×D4×C11C22×C414yes—
138C2×D4×C11C2×D414yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—22no—
147C22×C4×C11—24no—
148C22×C4×C11—82no—
149C22×C4×C11C22⋊C414yescomplemented
150C22×C4×C11C22×C412yescomplemented
151C22×C4×C11C2×D412yes—
152C22×Dic11—28no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—44no—
157C22×Dic11—84no—
158C22×Dic11—84no—
159C22×Dic11—84no—
160C22×Dic11C2×D418yes—
161C11×C4⋊C4—28no—
162C11×C22⋊C4—24no—
163C11×C22⋊C4—28no—
164C11×C22⋊C4—22no—
165C11×C22⋊C4—28no—
166C11×C22⋊C4C22×C414yescomplemented
167C22⋊Dic11—28no—
168C22⋊Dic11—24no—
169C22⋊Dic11—24no—
170C22⋊Dic11—24no—
171C22⋊Dic11—24no—
172C22⋊Dic11—24no—
173C22⋊Dic11—24no—
174C22⋊Dic11—44no—
175C22⋊Dic11—88no—
176C4⋊Dic11—28no—
177C4×Dic11—28no—
178C2×#534D1111yescharacteristic
179C2×#518—111no—
180C22×#99—111no—
181#2308—112no—
182#1890—114no—
183#1889—114no—
184C2×#342—112no—
185C23×C11—22no—
186C23×C11—24no—
187C23×C11—22no—
188C23×C11—24no—
189C23×C11—22no—
190C23×C11—24no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—44no—
197C23×C11—44no—
198C23×C11—48no—
199C23×C11—44no—
200C23×C11—41no—
201C23×C11—42no—
202C23×C11—41no—
203C23×C11—82no—
204C23×C11—82no—
205C23×C11—82no—
206C23×C11—82no—
207C23×C11—84no—
208C23×C11—84no—
209C23×C11—84no—
210C23×C11—82no—
211C23×C11—84no—
212C23×C11C2×C22⋊C414yes—
213C23×C11C2×C22⋊C412yes—
214C23×C11C2×C22⋊C412yes—
215C23×C11C4×D414yes—
216C23×C11C4×D414yes—
217C23×C11#12011yescharacteristic
218C23×C11#12012yes—
219C23×C11#12011yescharacteristic
220C23×C11#12114yes—
221C23×C11#12114yes—
222C23×C11#12312yes—
223C23×C11#12312yes—
224C23×C11C23×C411yescharacteristic
225C23×C11C22×D412yes—
226C23×C11C22×D411yescharacteristic
227C23×C11C22×D411yescharacteristic
228C23×C11C2×#4112yes—
229D4×C11—28no—
230D4×C11—28no—
231D4×C11—216no—
232D4×C11—44no—
233D4×C11—44no—
234D4×C11—48no—
235D4×C11—88no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—22no—
242C2×C4×C11—24no—
243C2×C4×C11—44no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—41no—
247C2×C4×C11—84no—
248C2×C4×C11C2×C22⋊C414yes—
249C2×Dic11—28no—
250C2×Dic11—48no—
251C2×Dic11—48no—
252C2×Dic11—48no—
253C2×Dic11—44no—
254C2×Dic11—84no—
255C2×Dic11—88no—
256C2×Dic11—88no—
257C23×D4C2×D1111yescharacteristic
258C23×D4C2×D1111yescharacteristic
259#534—24no—
260#534Dic1118yescomplemented
261C2×#123—21no—
262C2×#123C2×D1112yes—
263C2×#121—22no—
264C2×#120—21no—
265C2×#120C2×D1112yes—
266#518—114no—
267#518—224no—
268#518—222no—
269C2×C4×D4—224no—
270C2×#117—221no—
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—221no—
274C22×C22⋊C4C2×D1111yescharacteristic
275C2×#99—114no—
276C2×#99—224no—
277#386—224no—
278#386—224no—
279#381—114no—
280#379—114no—
281#342—118no—
282C22×C11—22no—
283C22×C11—22no—
284C22×C11—24no—
285C22×C11—22no—
286C22×C11—24no—
287C22×C11—24no—
288C22×C11—42no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11—41no—
292C22×C11—41no—
293C22×C11—42no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—44no—
300C22×C11—48no—
301C22×C11—44no—
302C22×C11—48no—
303C22×C11—44no—
304C22×C11—42no—
305C22×C11—82no—
306C22×C11—84no—
307C22×C11—84no—
308C22×C11—82no—
309C22×C11—82no—
310C22×C11#38612yes—
311C22×C11#38612yes—
312C22×C11#38614yes—
313C22×C11C22×C22⋊C411yescharacteristic
314C22×C11C2×C4×D412yes—
315C22×C11C2×#12011yescharacteristic
316C22×C11C2×#12112yes—
317C22×C11C2×#12311yescharacteristic
318C4×C11—24no—
319C4×C11—44no—
320C4×C11—42no—
321Dic11—48no—
322Dic11—84no—
323C25C22⋊D1111yescharacteristic
324C25C22×D1111yescharacteristic
325C25C22×D1111yescharacteristic
326C22×D4—22no—
327C22×D4—22no—
328C22×D4—24no—
329C22×D4—22no—
330C22×D4—22no—
331C22×D4—24no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—22no—
335C22×D4—22no—
336C22×D4C2×Dic1114yes—
337C22×D4C2×Dic1114yescomplemented
338C22×D4C22⋊D1114yes—
339C22×D4C22⋊D1112yes—
340C22×D4C22×D1112yes—
341C23×C4—21no—
342C23×C4—114no—
343C23×C4—222no—
344C23×C4—222no—
345C23×C4C22⋊D1111yescharacteristic
346C23×C4C22×D1111yescharacteristic
347#123—24no—
348#123—28no—
349#123C2×Dic1118yescomplemented
350#121—216no—
351#120—28no—
352#120—24no—
353#120C2×Dic1118yescomplemented
354C4×D4—2216no—
355C4×D4—2216no—
356#117—224no—
357#117—224no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—222no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—22no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4—114no—
365C2×C22⋊C4—114no—
366C2×C22⋊C4—114no—
367C2×C22⋊C4—222no—
368C2×C22⋊C4—224no—
369C2×C22⋊C4—222no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—222no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—222no—
377C2×C22⋊C4—228no—
378C2×C22⋊C4C2×Dic1114yescomplemented
379C2×C22⋊C4C22×D1112yes—
380C2×C42—222no—
381#99—228no—
382#95—228no—
383C2×C11—22no—
384C2×C11—21no—
385C2×C11—22no—
386C2×C11—22no—
387C2×C11—21no—
388C2×C11—22no—
389C2×C11—24no—
390C2×C11—44no—
391C2×C11—82no—
392C2×C11C2×#38611yescharacteristic
393C2×C11#302612yes—
394C24—21no—
395C24—22no—
396C24—21no—
397C24—22no—
398C24—21no—
399C24—22no—
400C24—21no—
401C24—82no—
402C24—82no—
403C24—82no—
404C24C22⋊Dic1114yescomplemented
405C24D4×D1112yes—
406C24D4×D1112yes—
407C24#434114yes—
408C24C22×Dic1112yes—
409C24C22×Dic1112yescomplemented
410C24C2×C22⋊D1112yes—
411C24C2×C22⋊D1111yescharacteristic
412C24C2×C22⋊D1111yescharacteristic
413C24C2×C22⋊D1112yes—
414C24C23×D1111yescharacteristic
415C2×D4—28no—
416C2×D4—28no—
417C2×D4—24no—
418C2×D4—24no—
419C2×D4—28no—
420C2×D4—28no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—28no—
424C2×D4—28no—
425C2×D4—24no—
426C2×D4—24no—
427C2×D4—28no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4—41no—
431C2×D4—42no—
432C2×D4—41no—
433C2×D4—44no—
434C2×D4—44no—
435C2×D4—84no—
436C2×D4C22⋊Dic1118yescomplemented
437C2×D4C22×Dic1114yes—
438C2×D4C2×C22⋊D1114yes—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—82no—
449C22×C4—118no—
450C22×C4—224no—
451C22×C4—228no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4—444no—
455C22×C4—884no—
456C22×C4—884no—
457C22×C4—884no—
458C22×C4C22⋊Dic1114yescomplemented
459C22×C4C22×Dic1112yescomplemented
460C22×C4C2×C22⋊D1112yes—
461C4⋊C4—28no—
462C4⋊C4—228no—
463C22⋊C4—24no—
464C22⋊C4—28no—
465C22⋊C4—22no—
466C22⋊C4—28no—
467C22⋊C4—228no—
468C22⋊C4—224no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C22⋊C4—224no—
472C22⋊C4—224no—
473C22⋊C4—224no—
474C22⋊C4—444no—
475C22⋊C4—888no—
476C22⋊C4C22×Dic1114yescomplemented
477C42—228no—
478C11#2096011yescharacteristic, complemented, Sylow
479C23—22no—
480C23—24no—
481C23—22no—
482C23—24no—
483C23—24no—
484C23—22no—
485C23—42no—
486C23—44no—
487C23—44no—
488C23—42no—
489C23—42no—
490C23—44no—
491C23—44no—
492C23—48no—
493C23—44no—
494C23—41no—
495C23—41no—
496C23—42no—
497C23—82no—
498C23—84no—
499C23—82no—
500C23—82no—
501C23—82no—
502C23—84no—
503C23—84no—
504C23—84no—
505C23—82no—
506C23D4×Dic1114yes—
507C23D4×Dic1114yes—
508C23#6698812yes—
509C23#6698812yes—
510C23#6699011yescharacteristic
511C23#6699012yes—
512C23#6699011yescharacteristic
513C23#6699214yes—
514C23#6699214yes—
515C23C2×C22⋊Dic1114yes—
516C23C2×C22⋊Dic1112yes—
517C23C2×C22⋊Dic1112yes—
518C23C2×D4×D1112yes—
519C23C2×#434112yes—
520C23C23×Dic1111yescharacteristic
521C23C22×C22⋊D1111yescharacteristic
522C23C22×C22⋊D1111yescharacteristic
523D4—28no—
524D4—28no—
525D4—216no—
526D4—44no—
527D4—44no—
528D4—48no—
529D4—88no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—44no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—228no—
543C2×C4—448no—
544C2×C4—448no—
545C2×C4—448no—
546C2×C4—444no—
547C2×C4—884no—
548C2×C4—888no—
549C2×C4—888no—
550C2×C4C2×C22⋊Dic1114yes—
551C22—22no—
552C22—22no—
553C22—24no—
554C22—24no—
555C22—22no—
556C22—24no—
557C22—42no—
558C22—44no—
559C22—42no—
560C22—42no—
561C22—42no—
562C22—41no—
563C22—41no—
564C22—44no—
565C22—44no—
566C22—42no—
567C22—44no—
568C22—44no—
569C22—48no—
570C22—44no—
571C22—48no—
572C22—44no—
573C22—42no—
574C22—82no—
575C22—84no—
576C22—84no—
577C22—82no—
578C22—82no—
579C22#1062283312yes—
580C22#1062283312yes—
581C22#1062283314yes—
582C22C2×D4×Dic1112yes—
583C22C2×#6698811yescharacteristic
584C22C2×#6699011yescharacteristic
585C22C2×#6699212yes—
586C22C22×C22⋊Dic1111yescharacteristic
587C4—24no—
588C4—44no—
589C4—42no—
590C4—448no—
591C4—884no—
592C2—21no—
593C2—22no—
594C2—22no—
595C2—22no—
596C2—21no—
597C2—22no—
598C2—24no—
599C2—44no—
600C2—82no—
601C2C2×#1062283311yescharacteristic
602C2#1307801212yes—
subgroupG/H
centerC22C2×#66990
commutatorC23×C11C23×C4
FrattiniC24C23×D11
Fitting, prime radicalC2×C11×#534C2
socleC22×C11C2×#120
cosocleC24×C11C24
hypercenterC2×#534D11
hypocenterC11#20960
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C25 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C2×#10623329C2semidirect
2. C22×#66898C2semidirect
3. #13071194C2semidirect
4. #13069030C2semidirect
5. #13069025C2semidirect
6. C2×#10622165C2semidirect
11. C11×#534C4semidirect
26. #10622860C22semidirect
31. #10622824C22semidirect
32. #10622165C22semidirect
47. C22×D4×C11C2×C4semidirect
56. C23×Dic11D4semidirect
59. C11×#123C2×C4semidirect
63. C11×#120C2×C4semidirect
69. C2×C11×C22⋊C4C2×C4semidirect
82. C2×C22⋊Dic11D4semidirect
104. C24×C11C22⋊C4semidirect
106. C24×C11C22×C4semidirect
136. C2×D4×C11C22⋊C4semidirect
149. C22×C4×C11C22⋊C4semidirect
150. C22×C4×C11C22×C4semidirect
166. C11×C22⋊C4C22×C4semidirect
260. #534Dic11semidirect
337. C22×D4C2×Dic11semidirect
349. #123C2×Dic11semidirect
353. #120C2×Dic11semidirect
378. C2×C22⋊C4C2×Dic11semidirect
404. C24C22⋊Dic11semidirect
409. C24C22×Dic11semidirect
436. C2×D4C22⋊Dic11semidirect
458. C22×C4C22⋊Dic11semidirect
459. C22×C4C22×Dic11semidirect
476. C22⋊C4C22×Dic11semidirect
478. C11#20960semidirect

Maximal subgroups

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

subgroupindex
C2×#106233292
C22×#668982
#130711942
#130690302
#130690252
C2×#106221652
C2×C11×#5342
#2096011