Finite Group Databasebeta

← #14856995

Subgroups — #14856995

Order 2816.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074577C211yesmaximal, characteristic
2#13071261C211yesmaximal, characteristic, complemented
3#13070114C211yesmaximal, characteristic, complemented
4#13069997C211yesmaximal, characteristic, complemented
5#13069990C211yesmaximal, characteristic
6#13069472C211yesmaximal, characteristic
7#13069343C211yesmaximal, characteristic, complemented
8#13069310C211yesmaximal, characteristic
9#13069308C211yesmaximal, characteristic, complemented
10#13069246C211yesmaximal, characteristic
11#13069200C211yesmaximal, characteristic, complemented
12#13068973C211yesmaximal, characteristic
13#13068882C211yesmaximal, characteristic, complemented
14#13068475C211yesmaximal, characteristic, complemented
15C11×#2055C211yesmaximal, characteristic
16C22×C11×SD16C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×#103C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C11×#391C2211yescharacteristic
22C11×#390C2211yescharacteristic
23#10622843C2211yescharacteristic
24C2×#66899C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26#10622834C2211yescharacteristic
27#10622834C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66881C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622598C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622586C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39#10622566—21no—
40#10622565—21no—
41#10622565—21no—
42#10622561—21no—
43#10622545C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622541C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622267—21no—
48#10622266—21no—
49#10622264—21no—
50#10622263—21no—
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C2×C11×SD16—22no—
62C2×C11×SD16—22no—
63C2×C11×SD16—41no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C22⋊C4—21no—
69C2×C11×C22⋊C4—21no—
70C2×C42×C11C2311yescharacteristic
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75Q8×Dic11—22no—
76Q8×Dic11—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11—21no—
89C2×C4×Dic11C2311yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C11×C4⋊C8—22no—
94C11×#103—22no—
95C11×#102—41no—
96C11×#95—21no—
97C11×#95—21no—
98#66899—22no—
99#66899—41no—
100#66896—22no—
101#66896—22no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95D411yescharacteristic
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114#66881—22no—
115#66879—41no—
116C8×Dic11—41no—
117#66872—22no—
118#66872—41no—
119C4⋊(C11⋊C8)—22no—
120#29442—111nomaximal, Sylow
121C24×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11#4112yes—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11C2×D411yescharacteristic
145C22×Dic11C2×D411yescharacteristic
146C22×Dic11C2×D411yescharacteristic
147C22×Dic11C2×D411yescharacteristic
148C11×SD16—44no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11#4112yes—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C22⋊C4—81no—
160C11×C22⋊C4—81no—
161C42×C11—21no—
162C42×C11—21no—
163C22⋊Dic11—81no—
164C22⋊Dic11—81no—
165C22⋊Dic11—81no—
166C22⋊Dic11—81no—
167C4⋊Dic11—24no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—81no—
176C4⋊Dic11#4112yes—
177Dic11⋊C4—81no—
178Dic11⋊C4—81no—
179Dic11⋊C4—81no—
180Dic11⋊C4—81no—
181C4×Dic11—24no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—81no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8#4112yes—
193#2644—111no—
194#2320—111no—
195#2088—111no—
196#2066—111no—
197#2065—111no—
198#2055D1111yescharacteristic
199#1968—111no—
200#1941—111no—
201#1936—111no—
202#1935—111no—
203#1926—111no—
204#1920—111no—
205#1880—111no—
206#1865—111no—
207#1768—111no—
208C23×C11—41no—
209C23×C11—41no—
210C23×C11—41no—
211C23×C11—41no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11C22×D411yescharacteristic
216Q8×C11—22no—
217Q8×C11—22no—
218Q8×C11—41no—
219Q8×C11—41no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—41no—
223D4×C11—41no—
224C2×C4×C11—22no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C112−1+411yescharacteristic
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—22no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C8×C11—22no—
270C8×C11—41no—
271C11⋊C8—22no—
272C11⋊C8—41no—
273C22×SD16C2×D1111yescharacteristic
274C2×C4×Q8—111no—
275C2×#106—111no—
276C2×#106—111no—
277C2×#106—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8C2×D1111yescharacteristic
280C2×#103—111no—
281C2×#103—111no—
282C2×#103C2×D1111yescharacteristic
283C2×#102—111no—
284C2×#102—111no—
285C2×#102C2×D1111yescharacteristic
286C2×#97—111no—
287C2×C4×C8—111no—
288#397—221no—
289#397—221no—
290#397—221no—
291#396—221no—
292#391—111no—
293#391C2×D1111yescharacteristic
294#390—111no—
295#390—111no—
296#390C2×D1111yescharacteristic
297#389—111no—
298#389—111no—
299#389—111no—
300#389—111no—
301#389—111no—
302#387—221no—
303#387—221no—
304#383—221no—
305#382—221no—
306C4×C4⋊C4—111no—
307#376—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340C2×D1111yescharacteristic
314#336—111no—
315#336—111no—
316C22×C11—81no—
317C22×C11—81no—
318C22×C11—81no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11#52511yescharacteristic
324C22×C11#53211yescharacteristic
325C22×C11#53711yescharacteristic
326C22×C11#57711yescharacteristic
327C22×C11#57711yescharacteristic
328C22×C11#57711yescharacteristic
329C22×C11#57711yescharacteristic
330C4×C11—42no—
331C4×C11—41no—
332C4×C11—41no—
333C4×C11—81no—
334C4×C11—81no—
335C4×C11#55111yescharacteristic
336C4×C11#55211yescharacteristic
337C4×C11#55311yescharacteristic
338C4×C11#55611yescharacteristic
339Dic11—41no—
340Dic11—42no—
341Dic11—41no—
342Dic11—41no—
343Dic11—41no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347C22×Q8C22×D1111yescharacteristic
348C22×D4C22×D1111yescharacteristic
349C2×SD16—22no—
350C2×SD16—22no—
351C2×SD16—41no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C4×Q8—222no—
357C4×Q8—222no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4C22×D1111yescharacteristic
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—221no—
373C2×C22⋊C4—221no—
374C2×C22⋊C4—221no—
375C2×C22⋊C4—221no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—221no—
379C2×C42—221no—
380C2×C42C22×D1111yescharacteristic
381#106—222no—
382#106—222no—
383#106—441no—
384C4⋊C8—22no—
385C4⋊C8—222no—
386#103—22no—
387#103—222no—
388#103—441no—
389#102—41no—
390#102—222no—
391#102—222no—
392#97—441no—
393C4×C8—441no—
394#95—21no—
395#95—21no—
396#95—111no—
397#95—111no—
398#95—111no—
399#95—111no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408C2×C11—161no—
409C2×C11#260111yescharacteristic
410C2×C11#312511yescharacteristic
411C2×C11#312611yescharacteristic
412C2×C11#317311yescharacteristic
413C2×C11#317411yescharacteristic
414C2×C11#326011yescharacteristic
415C2×C11#326311yescharacteristic
416C24—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8#434112yes—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4—111no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443SD16—44no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—112no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8#434112yes—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—112no—
461C4⋊C4—224no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—881no—
470C4⋊C4—881no—
471C4⋊C4—881no—
472C4⋊C4—881no—
473C4⋊C4—881no—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C22⋊C4—881no—
477C22⋊C4—881no—
478C22⋊C4—881no—
479C22⋊C4—881no—
480C42—21no—
481C42—21no—
482C42—224no—
483C42—221no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42—881no—
488C11#2944211yescharacteristic, complemented, Sylow
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23C2×D4×D1111yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—222no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4C2×#434111yescharacteristic
545C2×C4C2×#434111yescharacteristic
546C2×C4#6703711yescharacteristic
547C2×C4#41×D1111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#6704311yescharacteristic
550C8—22no—
551C8—41no—
552C8—222no—
553C8—441no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22#1062312711yescharacteristic
562C22#1062313711yescharacteristic
563C22#1062313911yescharacteristic
564C22#1062329311yescharacteristic
565C22#1062330111yescharacteristic
566C22#1062330611yescharacteristic
567C22#1062330911yescharacteristic
568C4—42no—
569C4—41no—
570C4—41no—
571C4—81no—
572C4—81no—
573C4—441no—
574C4—441no—
575C4—442no—
576C4—441no—
577C4—441no—
578C4—881no—
579C4—881no—
580C4—881no—
581C4#1062311811yescharacteristic
582C4#1062318111yescharacteristic
583C4#1062319211yescharacteristic
584C4#1062320211yescharacteristic
585C2—161no—
586C2#1307420611yescharacteristic
587C2#1307889211yescharacteristic
588C2#1307890511yescharacteristic
589C2#1307922611yescharacteristic
590C2#1307923911yescharacteristic
591C2#1308005911yescharacteristic
592C2#1308008311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2055C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2055D11
hypocenterC11#29442
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
2. #13071261C2semidirect
3. #13070114C2semidirect
4. #13069997C2semidirect
7. #13069343C2semidirect
9. #13069308C2semidirect
11. #13069200C2semidirect
13. #13068882C2semidirect
14. #13068475C2semidirect
488. C11#29442semidirect

Maximal subgroups

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

subgroupindex
#130745772
#130712612
#130701142
#130699972
#130699902
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