Finite Group Databasebeta

← #14788880

Subgroups — #14788880

Order 2816.

1482 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622667C212yesmaximal, complemented
2C2×#10622852C212yesmaximal, complemented
3C4×#66977C211yesmaximal, characteristic, complemented
4#13069859C211yesmaximal, characteristic, complemented
5#13069847C211yesmaximal, characteristic, complemented
6#13069716C211yesmaximal, characteristic, complemented
7#13069704C211yesmaximal, characteristic, complemented
8#13069549C212yesmaximal, complemented
9#13068596C211yesmaximal, characteristic, complemented
10#13068556C212yesmaximal, complemented
11C2×C11×#532C211yesmaximal, characteristic
12C22×C11×#41C2212yes—
13C11×#532—28no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#127C2211yescharacteristic
16C2×C11×#124C2212yes—
17C2×C11×#121—21no—
18C2×C11×#121—21no—
19C2×C4×D4×C11—21no—
20C2×C4×D4×C11—21no—
21C22×C42×C11C2211yescharacteristic
22C22×#4326C2212yes—
23C22×#4324C2212yes—
24C2×#66977C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic
26#10622852—28no—
27C2×#66899C2212yes—
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×#66896C2212yes—
31C2×#66896C2212yes—
32C2×#66896C2212yes—
33#10622825C2211yescharacteristic
34#10622823—21no—
35C4×C22⋊Dic11—21no—
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622667—28no—
38C4×C4⋊Dic11C2211yescharacteristic
39#10622546—21no—
40C4×Dic11⋊C4—21no—
41#10622542C2211yescharacteristic
42#10622541C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2212yes—
44#10622162C2211yescharacteristic
45#10622162C2211yescharacteristic
46C2×C11×#41—24no—
47C2×C11×#41—24no—
48C2×C11×#41—24no—
49C2×C11×#41—24no—
50C2×C11×#41—42no—
51C2×C11×#41—42no—
52C22×Q8×C11C2312yes—
53C22×D4×C11—22no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11C2312yes—
57C23×C4×C11—22no—
58C23×C4×C11D411yescharacteristic
59C23×C4×C11D411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C11×C4⋊Q8—24no—
63C11×#127—24no—
64C11×#124—24no—
65C11×#124D418yes—
66C11×#121—28no—
67C11×#121—28no—
68C4×D4×C11—28no—
69C4×D4×C11—28no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C22⋊C4—22no—
73C2×C11×C22⋊C4—22no—
74C2×C42×C11—24no—
75C2×C42×C11D411yescharacteristic
76C2×C42×C11D411yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×#4326—24no—
82C2×#4326—24no—
83C2×#4326—42no—
84C2×#4324—24no—
85C2×#4324—24no—
86C2×#4324—42no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90#66977—22no—
91#66977D414yescomplemented
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2312yes—
98C22×C11⋊C8C2312yes—
99C4×Dic22—24no—
100#66899—24no—
101#66899—24no—
102#66899—42no—
103#66896—24no—
104#66896—24no—
105#66896—42no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C22⋊(C11⋊C8)—24no—
112C4⋊(C11⋊C8)—24no—
113#24216—111nomaximal, Sylow
114C24×C11—22no—
115C24×C11C2×D411yescharacteristic
116C11×#41—48no—
117C11×#41—48no—
118C11×#41—48no—
119C11×#41—48no—
120C2×Q8×C11—22no—
121C2×Q8×C11—22no—
122C2×Q8×C11—22no—
123C2×Q8×C11—22no—
124C2×Q8×C11—22no—
125C2×Q8×C11C2×D414yes—
126C2×D4×C11—24no—
127C2×D4×C11—24no—
128C2×D4×C11—28no—
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—42no—
135C2×D4×C11—42no—
136C2×D4×C11—44no—
137C2×D4×C11—44no—
138C2×D4×C11—42no—
139C2×D4×C11—42no—
140C2×D4×C11C2×D414yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—28no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—41no—
150C22×C4×C11—41no—
151C22×C4×C11—44no—
152C22×C4×C11—44no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11#4112yes—
160C22×C4×C11C2411yescharacteristic
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C2×Dic22—22no—
166C2×Dic22—21no—
167C2×Dic22—22no—
168C2×Dic22C2×D412yes—
169C11×C4⋊C4—24no—
170C11×C4⋊C4—24no—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—28no—
173C42×C11—22no—
174C42×C11—22no—
175C42×C11—22no—
176C42×C11C2×D414yes—
177C22⋊Dic11—24no—
178C22⋊Dic11—42no—
179#4326—48no—
180#4324—48no—
181C4⋊Dic11—22no—
182C4⋊Dic11—21no—
183C4⋊Dic11—22no—
184C4⋊Dic11C2×D412yes—
185Dic11⋊C4—24no—
186Dic11⋊C4—42no—
187Dic11⋊C4—42no—
188C4×Dic11—42no—
189C4×Dic11—42no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—22no—
196C2×#532D1111yescharacteristic
197C2×#464—112no—
198C2×#452—112no—
199C4×C22⋊Q8—111no—
200#2043—111no—
201#2041—111no—
202#2016—111no—
203#2014—111no—
204#1983—112no—
205#1797—111no—
206#1788—112no—
207C23×C11—21no—
208C23×C11—21no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—24no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11#12112yes—
221C23×C11C22×D411yescharacteristic
222Q8×C11—24no—
223Q8×C11—24no—
224Q8×C11—42no—
225Q8×C11—42no—
226D4×C11—24no—
227D4×C11—24no—
228D4×C11—48no—
229D4×C11—48no—
230D4×C11—416no—
231D4×C11—42no—
232D4×C11—42no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—44no—
247C2×C4×C11—44no—
248C2×C4×C11—416no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11#12012yes—
252C2×C4×C11#12012yes—
253C2×C4×C11#12112yes—
254C2×C4×C11#13512yes—
255C2×C4×C11#13712yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D412yes—
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)12yes—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272Dic22—24no—
273Dic22—42no—
274C11⋊C8—42no—
275C11⋊C8—42no—
276C22×#41C2×D1112yes—
277C22×Q16—112no—
278C22×SD16—112no—
279#532—28no—
280C2×C4⋊Q8C2×D1111yescharacteristic
281C2×#127C2×D1111yescharacteristic
282C2×#124C2×D1112yes—
283C2×C22⋊Q8—111no—
284C2×#121—21no—
285C2×#121—21no—
286C2×C4×Q8—111no—
287C2×C4×D4—21no—
288C2×C4×D4—21no—
289C22×C42C2×D1111yescharacteristic
290#464—228no—
291#452—228no—
292C2×C4⋊C8—112no—
293C2×#103—112no—
294C2×#103—112no—
295C2×#103—112no—
296C2×#102—112no—
297C2×#102—112no—
298C2×#102—112no—
299C2×C22⋊C8—112no—
300#391—111no—
301#389—111no—
302#387—221no—
303#385—221no—
304#380—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—221no—
307C4×C22⋊C4—221no—
308#336—111no—
309#336—111no—
310C22×C11—22no—
311C22×C11—22no—
312C22×C11—22no—
313C22×C11—41no—
314C22×C11—41no—
315C22×C11—41no—
316C22×C11—41no—
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—82no—
321C22×C11—82no—
322C22×C11—82no—
323C22×C11—82no—
324C22×C11C2×#12011yescharacteristic
325C22×C11C2×#12111yescharacteristic
326C22×C11#53511yescharacteristic
327C22×C11C2×#13511yescharacteristic
328C22×C11C2×#13711yescharacteristic
329C22×C11#57511yescharacteristic
330C22×C11#57511yescharacteristic
331C4×C11—22no—
332C4×C11—22no—
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—44no—
337C4×C11D4212yes—
338C4×C11#54612yes—
339Dic11—42no—
340Dic11—42no—
341Dic11—81no—
342Dic11—81no—
343C2×#41—24no—
344C2×#41—24no—
345C2×#41—24no—
346C2×#41—24no—
347C2×#41—42no—
348C2×#41—42no—
349C22×Q8—111no—
350C22×Q8C22×D1112yes—
351C22×D4—22no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4C22×D1112yes—
355C23×C4—22no—
356C23×C4C22⋊D1111yescharacteristic
357C23×C4C22⋊D1111yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C2×Q16—224no—
360C2×Q16—224no—
361C2×Q16—442no—
362C2×SD16—224no—
363C2×SD16—224no—
364C2×SD16—442no—
365C22×C8—112no—
366C22×C8—112no—
367C4⋊Q8—24no—
368#127—24no—
369#124—24no—
370#124C22⋊D1118yes—
371C22⋊Q8—114no—
372C22⋊Q8—222no—
373#121—28no—
374#121—28no—
375C4×Q8—224no—
376C4×D4—28no—
377C4×D4—28no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C42—24no—
391C2×C42—221no—
392C2×C42—221no—
393C2×C42C22⋊D1111yescharacteristic
394C2×C42C22⋊D1111yescharacteristic
395C2×C42C22×D1111yescharacteristic
396C2×C42C22×D1111yescharacteristic
397C4⋊C8—224no—
398#103—224no—
399#103—224no—
400#103—442no—
401#102—224no—
402#102—224no—
403#102—442no—
404C22⋊C8—224no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410C2×C11—42no—
411C2×C11—84no—
412C2×C11#240811yescharacteristic
413C2×C11#300211yescharacteristic
414C2×C11#300711yescharacteristic
415C2×C11#303511yescharacteristic
416C2×C11#303711yescharacteristic
417C2×C11#321011yescharacteristic
418C2×C11#321911yescharacteristic
419C24—22no—
420C24C2×C22⋊D1111yescharacteristic
421#41—48no—
422#41—48no—
423#41—48no—
424#41—48no—
425C2×Q8—22no—
426C2×Q8—22no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—22no—
430C2×Q8—112no—
431C2×Q8—221no—
432C2×Q8—222no—
433C2×Q8—222no—
434C2×Q8C2×C22⋊D1114yes—
435C2×D4—24no—
436C2×D4—24no—
437C2×D4—28no—
438C2×D4—22no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—42no—
444C2×D4—42no—
445C2×D4—44no—
446C2×D4—44no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4C2×C22⋊D1114yes—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—44no—
461C22×C4—44no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4D4×D1112yes—
467C22×C4#434112yes—
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C23×D1111yescharacteristic
474Q16—448no—
475SD16—448no—
476C2×C8—222no—
477C2×C8—222no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—222no—
481C2×C8—222no—
482C4⋊C4—24no—
483C4⋊C4—24no—
484C4⋊C4—112no—
485C4⋊C4—224no—
486C4⋊C4—221no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—442no—
490C4⋊C4—442no—
491C22⋊C4—28no—
492C22⋊C4—28no—
493C22⋊C4—224no—
494C22⋊C4—442no—
495C42—22no—
496C42—22no—
497C42—22no—
498C42—442no—
499C42—442no—
500C42C2×C22⋊D1114yes—
501C11#2421611yescharacteristic, complemented, Sylow
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—21no—
507C23—21no—
508C23—24no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23—42no—
514C23—42no—
515C23#6699112yes—
516C23C22×C22⋊D1111yescharacteristic
517Q8—24no—
518Q8—24no—
519Q8—42no—
520Q8—42no—
521Q8—224no—
522Q8—442no—
523D4—24no—
524D4—24no—
525D4—48no—
526D4—48no—
527D4—416no—
528D4—42no—
529D4—42no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—416no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—222no—
549C2×C4—222no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4#6699112yes—
561C2×C4#6700312yes—
562C2×C4#6700412yes—
563C2×C4#6700612yes—
564C2×C4#6700612yes—
565C2×C4C2×D4×D1111yescharacteristic
566C2×C4C2×#434111yescharacteristic
567C2×C4#6703712yes—
568C2×C4C22×C22⋊D1112yes—
569C8—442no—
570C8—442no—
571C22—22no—
572C22—22no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—44no—
579C22—44no—
580C22—44no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22—82no—
585C22C2×#6699111yescharacteristic
586C22#1062333611yescharacteristic
587C22C2×#6700311yescharacteristic
588C22#1062335311yescharacteristic
589C22#1062335311yescharacteristic
590C22C2×#6700411yescharacteristic
591C22C2×#6700611yescharacteristic
592C4—22no—
593C4—22no—
594C4—22no—
595C4—22no—
596C4—22no—
597C4—44no—
598C4—442no—
599C4—442no—
600C4—881no—
601C4—881no—
602C4D4×C22⋊D1112yes—
603C4#1062333712yes—
604C2—42no—
605C2—84no—
606C2#1307196611yescharacteristic
607C2#1307783411yescharacteristic
608C2#1307787611yescharacteristic
609C2#1307806511yescharacteristic
610C2#1307808411yescharacteristic
611C2#1307957211yescharacteristic
612C2#1307965311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#532C2
socleC23×C11C22×D4
hypercenterC2×#532D11
hypocenterC11#24216
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. C2×#10622667C2semidirect
2. C2×#10622852C2semidirect
3. C4×#66977C2semidirect
4. #13069859C2semidirect
5. #13069847C2semidirect
6. #13069716C2semidirect
7. #13069704C2semidirect
8. #13069549C2semidirect
9. #13068596C2semidirect
10. #13068556C2semidirect
91. #66977D4semidirect
501. C11#24216semidirect

Maximal subgroups

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

subgroupindex
C2×#106226672
C2×#106228522
C4×#669772
#130698592
#130698472
#130697162
#130697042
#130695492
#130685962
#130685562
C2×C11×#5322
#2421611