Finite Group Databasebeta

← #14823585

Subgroups — #14823585

Order 2816.

784 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622402C211yesmaximal, characteristic, complemented
2#13072473C211yesmaximal, characteristic, complemented
3#13072410C211yesmaximal, characteristic
4#13069986C211yesmaximal, characteristic
5#13069951C211yesmaximal, characteristic, complemented
6#13069937C211yesmaximal, characteristic, complemented
7#13069710C211yesmaximal, characteristic
8#13069498C211yesmaximal, characteristic
9#13069310C211yesmaximal, characteristic
10#13069308C211yesmaximal, characteristic, complemented
11#13069292C211yesmaximal, characteristic, complemented
12#13068968C211yesmaximal, characteristic
13#13068868C211yesmaximal, characteristic, complemented
14#13068490C211yesmaximal, characteristic, complemented
15C2×C11×#488C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C11×#124C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C11×#488—24no—
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C4×C8×C11C2211yescharacteristic
28#10622843C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30#10622834C2211yescharacteristic
31#10622834C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×#66880C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×#66879C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38#10622598C2211yescharacteristic
39#10622597—21no—
40#10622595—21no—
41#10622591—21no—
42#10622587C2211yescharacteristic
43#10622586—21no—
44#10622586C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622566—21no—
48#10622562—21no—
49#10622557—21no—
50#10622557—21no—
51C4×Dic11⋊C4C2211yescharacteristic
52#10622542C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622402—24no—
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#125—22no—
67C11×#125—41no—
68C11×#124—22no—
69C11×#124—41no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81Q8×Dic11—22no—
82Q8×Dic11—41no—
83C2×#4326—22no—
84C2×#4326—22no—
85C2×#4326—22no—
86C2×#4324—22no—
87C2×#4324—22no—
88C2×#4324—41no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4D411yescharacteristic
98C2×Dic11⋊C4D411yescharacteristic
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11C2311yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66940—22no—
106#66940—41no—
107C11×#103—22no—
108C11×#103D414yes—
109C11×#102—22no—
110C11×#102—22no—
111C4×C8×C11—22no—
112#66899—22no—
113#66896—22no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66880—22no—
126#66880—22no—
127#66879—22no—
128#66879—22no—
129Dic11⋊C8—22no—
130#66872—22no—
131#66871—41no—
132#26839—111nomaximal, Sylow
133C24×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C2×D412yes—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×Dic22—21no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22#4112yes—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11C2×D412yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4—42no—
177C11×C4⋊C4C2×D412yes—
178C11×C22⋊C4—42no—
179C11×C22⋊C4—42no—
180C42×C11—21no—
181C42×C11—21no—
182C22⋊Dic11—42no—
183C22⋊Dic11—42no—
184C22⋊Dic11—81no—
185C22⋊Dic11—81no—
186#4326—28no—
187#4324—44no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—42no—
195C4⋊Dic11—42no—
196Dic11⋊C4—41no—
197Dic11⋊C4—41no—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—81no—
201C4×Dic11—21no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8#4112yes—
212C2×C11⋊C8#4112yes—
213C2×#488D1111yescharacteristic
214C2×#441—111no—
215#2453—111no—
216#2448—111no—
217#2065—111no—
218#2059—111no—
219#2056—111no—
220#2015—111no—
221#1973—111no—
222#1936—111no—
223#1935—111no—
224#1933—111no—
225#1880—111no—
226#1863—111no—
227#1771—111no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11C22×D411yescharacteristic
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—41no—
239Q8×C11—41no—
240D4×C11—41no—
241D4×C11—41no—
242D4×C11—41no—
243D4×C11—41no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11C22×D411yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289Dic22—22no—
290Dic22—22no—
291Dic22—41no—
292Dic22—41no—
293C8×C11—22no—
294C8×C11—41no—
295C11⋊C8—22no—
296C11⋊C8—22no—
297C22×Q16—111no—
298C22×SD16—111no—
299C2×#125C2×D1111yescharacteristic
300C2×#124C2×D1111yescharacteristic
301C2×C4×Q8—111no—
302C2×C4×Q8—111no—
303#488—24no—
304#441—224no—
305C2×#107—111no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×#103C2×D1111yescharacteristic
312C2×#103C2×D1111yescharacteristic
313C2×#102—111no—
314C2×#102C2×D1111yescharacteristic
315C2×#102C2×D1111yescharacteristic
316C2×#97—111no—
317C2×#97—111no—
318C2×C4×C8C2×D1111yescharacteristic
319#400—221no—
320#399—221no—
321#398—221no—
322#397—221no—
323#391—111no—
324#391—111no—
325#391—111no—
326#390—111no—
327#390—111no—
328#389—111no—
329#389—111no—
330#389—111no—
331#389—221no—
332#388—221no—
333#388—221no—
334#387—221no—
335C4×C4⋊C4—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#336—111no—
341#336—111no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11#53211yescharacteristic
350C22×C11D4211yescharacteristic
351C22×C11#54811yescharacteristic
352C22×C11#57511yescharacteristic
353C22×C11#57511yescharacteristic
354C22×C11#57711yescharacteristic
355C22×C11#57811yescharacteristic
356C4×C11—42no—
357C4×C11—41no—
358C4×C11—42no—
359C4×C11—41no—
360C4×C11—81no—
361C4×C11#52511yescharacteristic
362C4×C11#54211yescharacteristic
363C4×C11#54711yescharacteristic
364C4×C11#55111yescharacteristic
365Dic11—41no—
366Dic11—41no—
367Dic11—42no—
368Dic11—41no—
369Dic11—41no—
370Dic11—81no—
371Dic11—81no—
372Dic11—81no—
373C22×Q8—111no—
374C22×Q8C22×D1111yescharacteristic
375C22×D4C22×D1111yescharacteristic
376C2×Q16—222no—
377C2×Q16—222no—
378C2×Q16—222no—
379C2×SD16—222no—
380C2×SD16—222no—
381C2×SD16—441no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386#125—22no—
387#125—41no—
388#124—22no—
389#124—41no—
390C4×Q8—222no—
391C4×Q8—222no—
392C4×Q8—441no—
393C4×Q8—441no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—221no—
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419#107—441no—
420#106—222no—
421C4⋊C8—222no—
422#103—22no—
423#103—222no—
424#103—222no—
425#103—222no—
426#103C22⋊D1114yes—
427#102—22no—
428#102—22no—
429#102—222no—
430#97—222no—
431#97—222no—
432C4×C8—22no—
433#95—111no—
434#95—111no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443#95—221no—
444C2×C11—161no—
445C2×C11#246111yescharacteristic
446C2×C11#317811yescharacteristic
447C2×C11#318311yescharacteristic
448C2×C11#326911yescharacteristic
449C2×C11#327111yescharacteristic
450C2×C11#337111yescharacteristic
451C2×C11#337711yescharacteristic
452C24—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—112no—
459C2×Q8—221no—
460C2×Q8—221no—
461C2×Q8—221no—
462C2×Q8—221no—
463C2×Q8—221no—
464C2×Q8C2×C22⋊D1112yes—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485Q16—228no—
486SD16—444no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—112no—
493C2×C8—112no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8C2×C22⋊D1112yes—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—441no—
511C4⋊C4—441no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—442no—
515C4⋊C4—442no—
516C4⋊C4—881no—
517C4⋊C4C2×C22⋊D1112yes—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—881no—
523C22⋊C4—881no—
524C42—21no—
525C42—21no—
526C42—221no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42—442no—
531C42—442no—
532C11#2683911yescharacteristic, complemented, Sylow
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23C2×D4×D1111yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—41no—
544Q8—41no—
545Q8—222no—
546Q8—222no—
547Q8—441no—
548Q8—441no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—221no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—222no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4#6703711yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C2×C4#41×D1111yescharacteristic
595C2×C4#41×D1111yescharacteristic
596C2×C4#6704311yescharacteristic
597C2×C4C22×C22⋊D1111yescharacteristic
598C8—22no—
599C8—41no—
600C8—222no—
601C8—222no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22#1062319911yescharacteristic
610C22#1062320811yescharacteristic
611C22#1062329911yescharacteristic
612C22#1062329911yescharacteristic
613C22#1062330111yescharacteristic
614C22#1062330211yescharacteristic
615C22D4×C22⋊D1111yescharacteristic
616C4—41no—
617C4—42no—
618C4—41no—
619C4—42no—
620C4—81no—
621C4—441no—
622C4—441no—
623C4—441no—
624C4—442no—
625C4—441no—
626C4—881no—
627C4—881no—
628C4—881no—
629C4#1062320011yescharacteristic
630C4#1062321011yescharacteristic
631C4#1062335511yescharacteristic
632C4#1062335911yescharacteristic
633C2—161no—
634C2#1307257911yescharacteristic
635C2#1307928311yescharacteristic
636C2#1307934411yescharacteristic
637C2#1308017111yescharacteristic
638C2#1308020111yescharacteristic
639C2#1308139011yescharacteristic
640C2#1308146411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#488C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#488D11
hypocenterC11#26839
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#10622402C2semidirect
2. #13072473C2semidirect
5. #13069951C2semidirect
6. #13069937C2semidirect
10. #13069308C2semidirect
11. #13069292C2semidirect
13. #13068868C2semidirect
14. #13068490C2semidirect
532. C11#26839semidirect

Maximal subgroups

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

subgroupindex
C2×#106224022
#130724732
#130724102
#130699862
#130699512
#130699372
#130697102
#130694982
#130693102
#130693082
#130692922
#130689682
#130688682
#130684902
C2×C11×#4882
#2683911