Finite Group Databasebeta

← #14856931

Subgroups — #14856931

Order 2816.

708 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074579C211yesmaximal, characteristic, complemented
2#13071259C211yesmaximal, characteristic, complemented
3#13070108C211yesmaximal, characteristic, complemented
4#13069988C211yesmaximal, characteristic, complemented
5#13069985C211yesmaximal, characteristic, complemented
6#13069925C211yesmaximal, characteristic
7#13069479C211yesmaximal, characteristic
8#13069345C211yesmaximal, characteristic, complemented
9#13069315C211yesmaximal, characteristic, complemented
10#13069314C211yesmaximal, characteristic, complemented
11#13069244C211yesmaximal, characteristic, complemented
12#13069184C211yesmaximal, characteristic, complemented
13#13068964C211yesmaximal, characteristic
14#13068472C211yesmaximal, characteristic, complemented
15C11×#1864C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C22×#4323C2211yescharacteristic
18C2×C11×#106C2211yescharacteristic
19C2×C11×#102C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C11×#389C2211yescharacteristic
22#10622834C2211yescharacteristic
23#10622834C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25#10622825—21no—
26#10622824—21no—
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622607—21no—
35#10622606—21no—
36#10622601C2211yescharacteristic
37#10622601C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622586C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622564—21no—
45#10622564—21no—
46#10622552C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622545C2211yescharacteristic
49#10622288—21no—
50#10622287—21no—
51C11×#340C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×D44C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C4×D4×C11—22no—
65C4×D4×C11—22no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C22⋊C4—21no—
71C2×C42×C11C2311yescharacteristic
72C2×C22⋊Dic11—21no—
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×#4323—22no—
77C2×#4323—22no—
78C2×#4323—41no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C11×#106—22no—
98C11×#102—22no—
99C11×#102—22no—
100C11×#95—21no—
101#66896—41no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110C11⋊#95D411yescharacteristic
111#66885—22no—
112#66885—41no—
113#66881—41no—
114#66879—41no—
115Dic11⋊C8—22no—
116Dic11⋊C8—22no—
117C8×Dic11—41no—
118#66873—22no—
119#66871—22no—
120#29437—111nomaximal, Sylow
121C24×C11—21no—
122C23×D11—21no—
123C2×D4×C11—21no—
124C2×D4×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11#4112yes—
129C22×C4×C11—21no—
130C22×C4×C11—24no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—81no—
134C22×C4×C11—81no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11#4112yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—81no—
163C11×C4⋊C4#4112yes—
164C11×C22⋊C4—24no—
165C42×C11—21no—
166C42×C11—21no—
167C22⋊Dic11—81no—
168C22⋊Dic11—81no—
169C22⋊Dic11—81no—
170C22⋊Dic11—81no—
171#4323—44no—
172(C2×D11)⋊C4—81no—
173(C2×D11)⋊C4—81no—
174(C2×D11)⋊C4—81no—
175(C2×D11)⋊C4—81no—
176(C2×D11)⋊C4—81no—
177(C2×D11)⋊C4—81no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—81no—
185C4⋊Dic11—81no—
186C4⋊Dic11—81no—
187Dic11⋊C4—81no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—81no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8#4112yes—
199#2644—111no—
200#2319—111no—
201#2086—111no—
202#2065—111no—
203#2065—111no—
204#2054—111no—
205#1970—111no—
206#1941—111no—
207#1936—111no—
208#1936—111no—
209#1926—111no—
210#1918—111no—
211#1879—111no—
212#1864D1111yescharacteristic, complemented
213#1768—111no—
214C23×C11—22no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11C22×D411yescharacteristic
222C22×D11—41no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229D4×C11—22no—
230D4×C11—22no—
231D4×C11—41no—
232D4×C11—41no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—84no—
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276D44—41no—
277D44—41no—
278D44—41no—
279D44—41no—
280C8×C11—22no—
281C8×C11—41no—
282C11⋊C8—22no—
283C11⋊C8—41no—
284C22×D8—111no—
285C2×C4×D4C2×D1111yescharacteristic
286C2×#107—111no—
287C2×#106—111no—
288C2×#106C2×D1111yescharacteristic
289C2×C4⋊C8—111no—
290C2×C4⋊C8—111no—
291C2×#102—111no—
292C2×#102—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×#102C2×D1111yescharacteristic
296C2×#102C2×D1111yescharacteristic
297C2×#97—111no—
298C2×C4×C8—111no—
299#397—221no—
300#397—221no—
301#397—221no—
302#396—221no—
303#390—111no—
304#390—111no—
305#390—111no—
306#390—111no—
307#390—111no—
308#389—111no—
309#389—111no—
310#389—111no—
311#389—111no—
312#389C2×D1111yescharacteristic
313#388—221no—
314#388—221no—
315#381—221no—
316#380—221no—
317C4×C4⋊C4—111no—
318#376—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340—111no—
323#340—111no—
324#340C2×D1111yescharacteristic
325#336—111no—
326#336C2×D1111yescharacteristic
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11#52511yescharacteristic
335C22×C11#53211yescharacteristic
336C22×C11#53711yescharacteristic
337C22×C11#57611yescharacteristic
338C22×C11#57611yescharacteristic
339C22×C11#57711yescharacteristic
340C22×C11#57711yescharacteristic
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C4×C11—41no—
349C4×C11—42no—
350C4×C11—41no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11#55111yescharacteristic
354C4×C11#55211yescharacteristic
355C4×C11#55311yescharacteristic
356C4×C11#55611yescharacteristic
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360Dic11—41no—
361Dic11—81no—
362Dic11—81no—
363Dic11—81no—
364C22×D4—111no—
365C22×D4C22×D1111yescharacteristic
366C23×C4—21no—
367C2×D8—222no—
368C2×D8—222no—
369C2×D8—441no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8C22×D1111yescharacteristic
373C22×C8C22×D1111yescharacteristic
374C4×D4—22no—
375C4×D4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—221no—
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C42—111no—
399C2×C42—111no—
400C2×C42—221no—
401C2×C42C22×D1111yescharacteristic
402#107—222no—
403#106—22no—
404#106—441no—
405C4⋊C8—222no—
406C4⋊C8—222no—
407#102—22no—
408#102—22no—
409#102—222no—
410#102—222no—
411#102—441no—
412#102—441no—
413#97—441no—
414C4×C8—441no—
415#95—21no—
416#95—111no—
417#95—111no—
418#95—111no—
419#95—111no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425C2×C11—82no—
426C2×C11#260111yescharacteristic
427C2×C11#311811yescharacteristic
428C2×C11#311911yescharacteristic
429C2×C11#317311yescharacteristic
430C2×C11#317611yescharacteristic
431C2×C11#325711yescharacteristic
432C2×C11#325711yescharacteristic
433D11—161no—
434C24—21no—
435C24—221no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—221no—
445C2×D4—221no—
446C2×D4—221no—
447C2×D4#434112yes—
448C22×C4—21no—
449C22×C4—24no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—81no—
453C22×C4—81no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—221no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4D4×D1111yescharacteristic
462C22×C4D4×D1111yescharacteristic
463C22×C4C23×D1111yescharacteristic
464D8—444no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—112no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C2×C8—221no—
476C2×C8#433912yes—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—81no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—881no—
490C4⋊C4—881no—
491C4⋊C4—881no—
492C4⋊C4—881no—
493C4⋊C4#434112yes—
494C22⋊C4—24no—
495C22⋊C4—881no—
496C22⋊C4—881no—
497C22⋊C4—881no—
498C22⋊C4—881no—
499C22⋊C4—881no—
500C22⋊C4—881no—
501C22⋊C4—881no—
502C22⋊C4—881no—
503C22⋊C4—881no—
504C22⋊C4—881no—
505C42—21no—
506C42—21no—
507C42—221no—
508C42—221no—
509C42—221no—
510C42—221no—
511C42—881no—
512C11#2943711yescharacteristic, complemented, Sylow
513C23—22no—
514C23—41no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—441no—
521C23—441no—
522C23—441no—
523C23—441no—
524C23—441no—
525C23—441no—
526C23—441no—
527C23C2×D4×D1111yescharacteristic
528D4—22no—
529D4—22no—
530D4—41no—
531D4—41no—
532D4—441no—
533D4—441no—
534D4—441no—
535D4—441no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—84no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—441no—
565C2×C4—441no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4C2×#433911yescharacteristic
574C2×C4C2×#434111yescharacteristic
575C2×C4C2×#434111yescharacteristic
576C2×C4#6704011yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C2×C4#6704211yescharacteristic
579C8—22no—
580C8—41no—
581C8—222no—
582C8—441no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—881no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22—881no—
595C22—881no—
596C22—881no—
597C22#1062307911yescharacteristic
598C22#1062311711yescharacteristic
599C22#1062316011yescharacteristic
600C22#1062329311yescharacteristic
601C22#1062330111yescharacteristic
602C22#1062330511yescharacteristic
603C22#1062330511yescharacteristic
604C4—41no—
605C4—42no—
606C4—41no—
607C4—81no—
608C4—81no—
609C4—441no—
610C4—441no—
611C4—441no—
612C4—441no—
613C4—881no—
614C4—881no—
615C4—881no—
616C4#1062304411yescharacteristic
617C4#1062309611yescharacteristic
618C4#1062317211yescharacteristic
619C4#1062318911yescharacteristic
620C2—82no—
621C2—1761no—
622C2#1307421711yescharacteristic
623C2#1307880111yescharacteristic
624C2#1307881611yescharacteristic
625C2#1307922911yescharacteristic
626C2#1307926411yescharacteristic
627C2#1308002611yescharacteristic
628C2#1308003111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1864C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#1864D11
hypocenterC11#29437
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
1. #13074579C2semidirect
2. #13071259C2semidirect
3. #13070108C2semidirect
4. #13069988C2semidirect
5. #13069985C2semidirect
8. #13069345C2semidirect
9. #13069315C2semidirect
10. #13069314C2semidirect
11. #13069244C2semidirect
12. #13069184C2semidirect
14. #13068472C2semidirect
15. C11×#1864C2semidirect
212. #1864D11semidirect
512. C11#29437semidirect

Maximal subgroups

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

subgroupindex
#130745792
#130712592
#130701082
#130699882
#130699852
#130699252
#130694792
#130693452
#130693152
#130693142
#130692442
#130691842
#130689642
#130684722
C11×#18642
#2943711