Finite Group Databasebeta

← #14685043

Subgroups — #14685043

Order 2816.

2134 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×#10622552C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic
3C2×#10622552C211yesmaximal, characteristic
4C2×#10622541C211yesmaximal, characteristic, complemented
5C2×#10622553C214yesmaximal, complemented
6#13066854C214yesmaximal, complemented
7#13066846C211yesmaximal, characteristic, complemented
8#13066846C211yesmaximal, characteristic, complemented
9C2×C43×C11C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C22×C42×C11C2212yes—
12C22×C42×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C42×C11C2212yes—
16C22×(C2×D11)⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2214yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2214yes—
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C43×C11—24no—
25C2×C11⋊#95C2214yes—
26C2×C11⋊#95C2214yes—
27C2×C11⋊#95C2212yes—
28#10622553—216no—
29#10622552—24no—
30#10622552—24no—
31#10622552C418yescomplemented
32#10622541—24no—
33C24×D11C2312yes—
34C23×C4×C11C2312yes—
35C23×C4×C11C2311yescharacteristic
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44—22no—
45C22×D44—22no—
46C22×D44—22no—
47C22×D44—22no—
48C22×D44C2×C414yes—
49C2×C42×C11—24no—
50C2×C42×C11—22no—
51C2×C42×C11—22no—
52C2×C42×C11—24no—
53C2×C42×C11—24no—
54C2×C42×C11—24no—
55C2×C42×C11—22no—
56C2×C42×C11—22no—
57C2×C42×C11—24no—
58C2×C42×C11—22no—
59C2×C42×C11—22no—
60C2×C42×C11C2×C414yes—
61C2×C42×C11D414yes—
62C2×C42×C11D414yes—
63C2×C42×C11D418yescomplemented
64C2×(C2×D11)⋊C4—28no—
65C2×(C2×D11)⋊C4—28no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—24no—
68C2×(C2×D11)⋊C4—28no—
69C2×(C2×D11)⋊C4—28no—
70C2×(C2×D11)⋊C4—28no—
71C2×(C2×D11)⋊C4—28no—
72C2×(C2×D11)⋊C4—28no—
73C2×(C2×D11)⋊C4C2×C4116yes—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—22no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11C2×C414yes—
83C2×Dic11⋊C4—24no—
84C2×Dic11⋊C4—28no—
85C11⋊#95—24no—
86C11⋊#95—28no—
87C11⋊#95—28no—
88#14700—111nomaximal, Sylow
89C24×C11C2411yescharacteristic
90C23×D11—24no—
91C23×D11—22no—
92C23×D11—22no—
93C23×D11—24no—
94C23×D11—24no—
95C23×D11—24no—
96C23×D11—22no—
97C23×D11—22no—
98C23×D11—22no—
99C23×D11—22no—
100C23×D11C22×C414yes—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11C22×C414yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C2×D414yes—
118C22×C4×C11C2×D414yes—
119C22×C4×C11C2×D414yes—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11#4114yes—
126C22×C4×C11#4114yes—
127C22×C4×C11#4114yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×C4×C11#4112yes—
131C22×C4×C11#4112yes—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11—24no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11C22×C414yes—
147C2×D44—28no—
148C2×D44—28no—
149C2×D44—28no—
150C2×D44—44no—
151C2×D44—44no—
152C2×D44—44no—
153C2×D44—44no—
154C42×C11—216no—
155C42×C11—28no—
156C42×C11—28no—
157C42×C11—216no—
158C42×C11—28no—
159(C2×D11)⋊C4—232no—
160(C2×D11)⋊C4—416no—
161(C2×D11)⋊C4—48no—
162(C2×D11)⋊C4—48no—
163C4⋊Dic11—28no—
164C4⋊Dic11—44no—
165C4⋊Dic11—44no—
166Dic11⋊C4—48no—
167C2×#390—111no—
168C2×#390—111no—
169C2×#390—111no—
170C2×#389—111no—
171C2×#388—114no—
172C2×C43D1111yescharacteristic, complemented
173#1437—114no—
174C4⋊#95—111no—
175C4⋊#95—111no—
176C23×C11C23×C411yescharacteristic
177C23×C11C22×D411yescharacteristic
178C23×C11C22×D412yes—
179C23×C11C22×D411yescharacteristic
180C23×C11C2×#4111yescharacteristic
181C23×C11C2×#4111yescharacteristic
182C23×C11C2×#4111yescharacteristic
183C23×C11C2×#4112yes—
184C23×C11C2×#4111yescharacteristic
185C23×C11C2×#4112yes—
186C23×C11C2×#4112yes—
187C22×D11—24no—
188C22×D11—28no—
189C22×D11—24no—
190C22×D11—24no—
191C22×D11—28no—
192C22×D11—44no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—44no—
196C22×D11—42no—
197C22×D11—42no—
198C22×D11—42no—
199C22×D11—44no—
200C22×D11—44no—
201C22×D11—44no—
202C22×D11—44no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—44no—
206C22×D11—44no—
207C22×D11—44no—
208C22×D11—44no—
209C22×D11—42no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11#11714yes—
231C2×C4×C11C4×D418yes—
232C2×C4×C11C4×D414yes—
233C2×C4×C11C4×D414yes—
234C2×C4×C11#12118yes—
235C2×C4×C11#12114yes—
236C2×C4×C11#12314yes—
237C2×C4×C11#12414yes—
238C2×C4×C11#12414yes—
239C2×C4×C11#12614yes—
240C2×C4×C11#12714yes—
241C2×Dic11—24no—
242C2×Dic11—28no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—44no—
246C2×Dic11—42no—
247C2×Dic11—44no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—44no—
253C2×Dic11—42no—
254C2×Dic11—44no—
255C2×Dic11—44no—
256D44—416no—
257C23×D4—111no—
258C22×C4⋊C4—111no—
259C22×C4⋊C4—112no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—111no—
262C22×C22⋊C4—114no—
263C22×C22⋊C4—112no—
264C22×C22⋊C4—114no—
265C22×C22⋊C4—112no—
266C22×C42C2×D1112yes—
267C22×C42C2×D1111yescharacteristic
268C22×C42C2×D1111yescharacteristic
269C22×C42C2×D1112yes—
270C22×C42C2×D1111yescharacteristic
271#390—118no—
272#390—224no—
273#390—224no—
274#389—224no—
275#388—2216no—
276C2×#95—114no—
277C2×#95—114no—
278C2×#95—112no—
279C43—24no—
280C22×C11C2×#11711yescharacteristic
281C22×C11C2×C4×D411yescharacteristic
282C22×C11C2×C4×D412yes—
283C22×C11C2×C4×D411yescharacteristic
284C22×C11C4×#4112yes—
285C22×C11C2×#12111yescharacteristic
286C22×C11C2×#12112yes—
287C22×C11C2×#12311yescharacteristic
288C22×C11#52512yes—
289C22×C11C2×#12411yescharacteristic
290C22×C11C2×#12411yescharacteristic
291C22×C11C2×#12611yescharacteristic
292C22×C11#52912yes—
293C22×C11#52912yes—
294C22×C11#52912yes—
295C22×C11#52912yes—
296C22×C11C2×#12711yescharacteristic
297C22×C11#53211yescharacteristic
298C22×C11#53212yes—
299C22×C11#53212yes—
300C22×C11#53212yes—
301C22×C11#53211yescharacteristic
302C22×C11#53212yes—
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—48no—
306C2×D11—48no—
307C2×D11—44no—
308C2×D11—82no—
309C2×D11—84no—
310C2×D11—82no—
311C2×D11—82no—
312C2×D11—84no—
313C2×D11—82no—
314C4×C11—24no—
315C4×C11—28no—
316C4×C11—24no—
317C4×C11—28no—
318C4×C11#38818yescomplemented
319Dic11—44no—
320Dic11—82no—
321Dic11—82no—
322C25—112no—
323C22×D4—114no—
324C22×D4—222no—
325C22×D4—222no—
326C22×D4—222no—
327C22×D4—222no—
328C22×D4—222no—
329C22×D4—222no—
330C23×C4—112no—
331C23×C4—112no—
332C23×C4—112no—
333C23×C4C22×D1112yes—
334C23×C4C22×D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1112yes—
337C23×C4C22×D1111yescharacteristic
338C2×C4⋊C4—114no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—222no—
341C2×C4⋊C4—228no—
342C2×C4⋊C4—224no—
343C2×C4⋊C4—222no—
344C2×C4⋊C4—222no—
345C2×C4⋊C4—222no—
346C2×C4⋊C4—222no—
347C2×C4⋊C4—222no—
348C2×C4⋊C4—222no—
349C2×C22⋊C4—1116no—
350C2×C22⋊C4—228no—
351C2×C22⋊C4—228no—
352C2×C22⋊C4—228no—
353C2×C22⋊C4—228no—
354C2×C22⋊C4—224no—
355C2×C22⋊C4—224no—
356C2×C22⋊C4—228no—
357C2×C22⋊C4—228no—
358C2×C22⋊C4—228no—
359C2×C42—24no—
360C2×C42—24no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—24no—
366C2×C42—24no—
367C2×C42—22no—
368C2×C42—22no—
369C2×C42—24no—
370C2×C42C4×D1114yes—
371C2×C42D4414yes—
372C2×C42D4418yescomplemented
373C2×C42C22⋊D1114yes—
374#95—228no—
375#95—228no—
376#95—224no—
377C2×C11C2×#38811yescharacteristic
378C2×C11#229312yes—
379C2×C11C4×#12112yes—
380C2×C11C4×#12411yescharacteristic
381C2×C11C4×#12711yescharacteristic
382C2×C11#285011yescharacteristic
383C2×C11#285412yes—
384C2×C11#285611yescharacteristic
385C2×C11#285811yescharacteristic
386C2×C11#286012yes—
387C2×C11#286111yescharacteristic
388D11—84no—
389C24—114no—
390C24—224no—
391C24—222no—
392C24—224no—
393C24—224no—
394C24—224no—
395C24—222no—
396C24—222no—
397C24—222no—
398C24—222no—
399C24—222no—
400C24C23×D1111yescharacteristic
401C2×D4—228no—
402C2×D4—228no—
403C2×D4—228no—
404C2×D4—444no—
405C2×D4—444no—
406C2×D4—444no—
407C2×D4—444no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—114no—
423C22×C4—224no—
424C22×C4—222no—
425C22×C4—224no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—222no—
437C22×C4C2×C4×D1114yes—
438C22×C4C2×C4×D1112yes—
439C22×C4C2×D4414yes—
440C22×C4C2×D4412yes—
441C22×C4C2×D4414yes—
442C22×C4C2×D4412yes—
443C22×C4C2×D4414yes—
444C22×C4C2×D4412yes—
445C22×C4#433914yes—
446C22×C4#433914yes—
447C22×C4#433914yes—
448C22×C4#433912yes—
449C22×C4#433912yes—
450C22×C4#433912yes—
451C22×C4#433912yes—
452C22×C4C2×C22⋊D1114yes—
453C22×C4C2×C22⋊D1112yes—
454C4⋊C4—228no—
455C4⋊C4—448no—
456C4⋊C4—444no—
457C4⋊C4—444no—
458C22⋊C4—2232no—
459C22⋊C4—448no—
460C22⋊C4—448no—
461C22⋊C4—4416no—
462C42—216no—
463C42—28no—
464C42—28no—
465C42—28no—
466C42—216no—
467C11#1470011yescharacteristic, complemented, Sylow
468C23—224no—
469C23—228no—
470C23—224no—
471C23—228no—
472C23—224no—
473C23—442no—
474C23—442no—
475C23—442no—
476C23—444no—
477C23—442no—
478C23—442no—
479C23—444no—
480C23—444no—
481C23—444no—
482C23—442no—
483C23—444no—
484C23—444no—
485C23—444no—
486C23—444no—
487C23—442no—
488C23—444no—
489C23—442no—
490C23—444no—
491C23C22×C4×D1111yescharacteristic
492C23C22×D4411yescharacteristic
493C23C22×D4412yes—
494C23C2×#433911yescharacteristic
495C23C2×#433911yescharacteristic
496C23C2×#433911yescharacteristic
497C23C2×#433912yes—
498C23C2×#433912yes—
499C23C2×#433912yes—
500C23C2×#433911yescharacteristic
501C23C22×C22⋊D1111yescharacteristic
502D4—4416no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—228no—
524C2×C4—224no—
525C2×C4—442no—
526C2×C4—442no—
527C2×C4—444no—
528C2×C4—442no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—444no—
534C2×C4—444no—
535C2×C4—444no—
536C2×C4—444no—
537C2×C4—442no—
538C2×C4#6692514yes—
539C2×C4C4×D4418yes—
540C2×C4C4×D4414yes—
541C2×C4#6692714yes—
542C2×C4#6692814yes—
543C2×C4#6692814yes—
544C2×C4#6692914yes—
545C2×C4C4×C22⋊D1114yes—
546C2×C4#6698214yes—
547C2×C4#6698318yes—
548C2×C4#6698314yes—
549C22—448no—
550C22—444no—
551C22—444no—
552C22—444no—
553C22—448no—
554C22—882no—
555C22—884no—
556C22—882no—
557C22—882no—
558C22—884no—
559C22—882no—
560C22C2×#6692511yescharacteristic
561C22C2×C4×D4412yes—
562C22C2×C4×D4411yescharacteristic
563C22C4×#433912yes—
564C22C2×#6692711yescharacteristic
565C22C2×#6692811yescharacteristic
566C22C2×#6692811yescharacteristic
567C22#1062300812yes—
568C22#1062300811yescharacteristic
569C22#1062300811yescharacteristic
570C22#1062300812yes—
571C22#1062300812yes—
572C22#1062300812yes—
573C22C2×#6692911yescharacteristic
574C22#1062301012yes—
575C22#1062301012yes—
576C22#1062301012yes—
577C22#1062301012yes—
578C22C2×C4×C22⋊D1111yescharacteristic
579C22C2×#6698211yescharacteristic
580C22C2×#6698312yes—
581C22C2×#6698311yescharacteristic
582C22#1062332212yes—
583C4—28no—
584C4—24no—
585C4—28no—
586C4—24no—
587C4—444no—
588C4—882no—
589C4—882no—
590C4#1062255318yescomplemented
591C2—884no—
592C2C2×#1062255311yescharacteristic
593C2#1307108012yes—
594C2C4×#6698312yes—
595C2C4×#6692811yescharacteristic
596C2C4×#6692711yescharacteristic
597C2#1307691711yescharacteristic
598C2#1307694712yes—
599C2#1307696111yescharacteristic
600C2#1307697311yescharacteristic
601C2#1307698312yes—
602C2#1307698811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C43×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×C43D11
hypocenterC11#14700
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C43

Complements

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

NH ≅ G/Ntype
4. C2×#10622541C2semidirect
5. C2×#10622553C2semidirect
6. #13066854C2semidirect
7. #13066846C2semidirect
8. #13066846C2semidirect
9. C2×C43×C11C2semidirect
31. #10622552C4semidirect
63. C2×C42×C11D4semidirect
172. C2×C43D11semidirect
318. C4×C11#388semidirect
372. C2×C42D44semidirect
467. C11#14700semidirect
590. C4#10622553semidirect

Maximal subgroups

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

subgroupindex
C2×#106225522
C2×#106225412
C2×#106225532
#130668542
#130668462
C2×C43×C112
#1470011