Finite Group Databasebeta

← #14817346

Subgroups — #14817346

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072310C211yesmaximal, characteristic, complemented
2#13071650C211yesmaximal, characteristic
3#13070183C211yesmaximal, characteristic, complemented
4#13070114C211yesmaximal, characteristic, complemented
5#13069988C211yesmaximal, characteristic, complemented
6#13069750C211yesmaximal, characteristic, complemented
7#13069566C211yesmaximal, characteristic, complemented
8#13069206C211yesmaximal, characteristic, complemented
9#13069041C211yesmaximal, characteristic
10#13068935C211yesmaximal, characteristic
11#13068863C211yesmaximal, characteristic, complemented
12#13068816C211yesmaximal, characteristic, complemented
13#13068792C211yesmaximal, characteristic, complemented
14#13068331C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66991C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×#66941C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C11×#382C2211yescharacteristic
26#10622834C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29#10622826—21no—
30C4×C22⋊Dic11—21no—
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34#10622600C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622586C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38#10622570—21no—
39#10622557—21no—
40C4×(C2×D11)⋊C4C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622289—21no—
44#10622286—21no—
45#10622265—21no—
46#10622259—21no—
47C11×#340C2211yescharacteristic
48C11×#340C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C22×C22⋊D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×Dic22—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×D4×C11—22no—
67C4×D4×C11—41no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76#66991—22no—
77#66991Q814yescomplemented
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4D411yescharacteristic
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×C8×D11—22no—
98C2×C8×D11—41no—
99C2×C8×D11—41no—
100#66945—22no—
101#66945—22no—
102#66945—41no—
103#66945—41no—
104#66941—22no—
105#66941—41no—
106C11×C4⋊C8—41no—
107C11×#102—41no—
108C11×#102—41no—
109C11×#95—21no—
110C11×#95—21no—
111#66896—22no—
112#66896—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95D411yescharacteristic
119C11⋊#95D411yescharacteristic
120(C2×D11)⋊C8—22no—
121#66881—41no—
122Dic11⋊C8—41no—
123#66871—22no—
124#26409—111nomaximal, Sylow
125C24×C11—21no—
126C23×D11C2×D411yescharacteristic
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11C2×Q812yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—42no—
137C22×C4×C11—42no—
138C22×C4×C11—81no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C2×C22⋊D11—24no—
143C2×C22⋊D11—81no—
144C2×C22⋊D11—81no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11C2×Q812yes—
157C2×C4×D11#4112yes—
158C2×Dic22—42no—
159C2×Dic22—42no—
160C2×Dic22—81no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4#4112yes—
173C11×C22⋊C4—42no—
174C42×C11—21no—
175C42×C11—21no—
176C22⋊Dic11—24no—
177C22⋊Dic11—42no—
178C22⋊Dic11—81no—
179(C2×D11)⋊C4—22no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—81no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11C2×Q812yes—
191C4⋊Dic11#4112yes—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—42no—
199C4×Dic11—42no—
200C4×Dic11—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C8×D11—44no—
208#2439—111no—
209#2363—111no—
210#2101—111no—
211#2088—111no—
212#2065—111no—
213#2023—111no—
214#1988—111no—
215#1921—111no—
216#1893—111no—
217#1875—111no—
218#1862—111no—
219#1854—111no—
220#1850—111no—
221#1804D1111yescharacteristic, complemented
222#1735—111no—
223C23×C11—22no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11C22×D411yescharacteristic
231C22×D11—21no—
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11C22⋊Q812yes—
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—41no—
241D4×C11—41no—
242C2×C4×C11—22no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—84no—
258C2×C4×C11C22×Q811yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C22⋊D11—84no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—22no—
270C2×Dic11—21no—
271C2×Dic11—22no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11C22⋊Q812yes—
285C2×Dic11#13512yes—
286C4×D11—22no—
287C4×D11—22no—
288C4×D11—22no—
289C4×D11—22no—
290Dic22—84no—
291C8×C11—41no—
292C8×C11—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C23×C8—111no—
296C2×C4⋊Q8—111no—
297C2×#121—111no—
298C2×C4×D4C2×D1111yescharacteristic
299C2×#117—111no—
300C2×#117—111no—
301C2×#107—111no—
302C2×#106—111no—
303C2×C4⋊C8—111no—
304C2×C4⋊C8C2×D1111yescharacteristic
305C2×#102—111no—
306C2×#102—111no—
307C2×#102C2×D1111yescharacteristic
308C2×#102C2×D1111yescharacteristic
309C2×C22⋊C8—111no—
310#396—221no—
311#393—221no—
312#391—221no—
313#390—111no—
314#390—221no—
315#389—111no—
316#389—111no—
317#389—111no—
318#388—221no—
319#387—221no—
320#386—221no—
321#382C2×D1111yescharacteristic
322#380—111no—
323C4×C4⋊C4—111no—
324C4×C22⋊C4—111no—
325C4×C22⋊C4—221no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340C2×D1111yescharacteristic
335#340C2×D1111yescharacteristic
336#336—111no—
337#336—111no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—81no—
342C22×C11—81no—
343C22×C11—81no—
344C22×C11—81no—
345C22×C11C2×C22⋊Q811yescharacteristic
346C22×C11#54611yescharacteristic
347C22×C11#54611yescharacteristic
348C22×C11C2×#13511yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57611yescharacteristic
351C22×C11#57711yescharacteristic
352C2×D11—22no—
353C2×D11—22no—
354C2×D11—22no—
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—81no—
363C4×C11—81no—
364C4×C11#52911yescharacteristic
365C4×C11#53811yescharacteristic
366C4×C11#55411yescharacteristic
367C4×C11#55411yescharacteristic
368Dic11—22no—
369Dic11—22no—
370Dic11—42no—
371Dic11—42no—
372Dic11—41no—
373Dic11—81no—
374Dic11—81no—
375C22×Q8—221no—
376C22×D4—221no—
377C22×D4C22×D1111yescharacteristic
378C23×C4—21no—
379C23×C4—111no—
380C22×C8—111no—
381C22×C8—111no—
382C22×C8—222no—
383C22×C8—441no—
384C22×C8—441no—
385C22×C8C22×D1111yescharacteristic
386C22×C8C22×D1111yescharacteristic
387C4⋊Q8—222no—
388C4⋊Q8—441no—
389#121—114no—
390#121—222no—
391C4×D4—22no—
392C4×D4—41no—
393#117—222no—
394#117—222no—
395#117—441no—
396#117—441no—
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⋊C4C22×D1111yescharacteristic
406C2×C4⋊C4C22×D1111yescharacteristic
407C2×C4⋊C4C22×D1111yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—111no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4—221no—
416C2×C22⋊C4—221no—
417C2×C42—111no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42—221no—
421C2×C42C22×D1111yescharacteristic
422#107—222no—
423#106—441no—
424C4⋊C8—41no—
425C4⋊C8—441no—
426#102—41no—
427#102—41no—
428#102—222no—
429#102—441no—
430C22⋊C8—222no—
431#95—21no—
432#95—21no—
433#95—111no—
434#95—111no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440C2×C11—82no—
441C2×C11#245011yescharacteristic
442C2×C11#307611yescharacteristic
443C2×C11#308111yescharacteristic
444C2×C11#329711yescharacteristic
445C2×C11#330411yescharacteristic
446C2×C11#331911yescharacteristic
447C2×C11#332111yescharacteristic
448D11—42no—
449C24—21no—
450C24—111no—
451C2×Q8—442no—
452C2×Q8—442no—
453C2×Q8—881no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—224no—
460C2×D4—881no—
461C2×D4—881no—
462C2×D4Q8×D1112yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—112no—
472C22×C4—112no—
473C22×C4—111no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—444no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—112no—
504C4⋊C4—112no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—442no—
512C4⋊C4—442no—
513C4⋊C4—881no—
514C4⋊C4—881no—
515C4⋊C4#433912yes—
516C22⋊C4—42no—
517C22⋊C4—222no—
518C22⋊C4—224no—
519C22⋊C4—441no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C42—21no—
526C42—21no—
527C42—221no—
528C42—221no—
529C42—442no—
530C42—442no—
531C42—881no—
532C11#2640911yescharacteristic, complemented, Sylow
533C23—22no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—112no—
541C23—221no—
542C23—221no—
543C23—221no—
544C23—221no—
545C23—221no—
546C23—221no—
547C23C2×D4×D1111yescharacteristic
548Q8—884no—
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—884no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—84no—
570C2×C4—112no—
571C2×C4—112no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—222no—
584C2×C4—222no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4C2×#433911yescharacteristic
596C2×C4#6703711yescharacteristic
597C2×C4#6703711yescharacteristic
598C2×C4C2×Q8×D1111yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C2×C4#41×D1111yescharacteristic
601C8—41no—
602C8—41no—
603C8—441no—
604C8—441no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—222no—
613C22—222no—
614C22—222no—
615C22—441no—
616C22—441no—
617C22—441no—
618C22—441no—
619C22#1062302111yescharacteristic
620C22#1062314311yescharacteristic
621C22D11×C22⋊Q811yescharacteristic
622C22D11×#13511yescharacteristic
623C22#1062330111yescharacteristic
624C22#1062330411yescharacteristic
625C22#1062330511yescharacteristic
626C4—41no—
627C4—42no—
628C4—41no—
629C4—81no—
630C4—81no—
631C4—222no—
632C4—222no—
633C4—442no—
634C4—442no—
635C4—441no—
636C4—881no—
637C4—881no—
638C4#1062304211yescharacteristic
639C4#1062305911yescharacteristic
640C4#1062314411yescharacteristic
641C4#1062316711yescharacteristic
642C2—82no—
643C2—442no—
644C2#1307244711yescharacteristic
645C2#1307840111yescharacteristic
646C2#1307844611yescharacteristic
647C2#1308047311yescharacteristic
648C2#1308055111yescharacteristic
649C2#1308077311yescharacteristic
650C2#1308080911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#1804D11
hypocenterC11#26409
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
1. #13072310C2semidirect
3. #13070183C2semidirect
4. #13070114C2semidirect
5. #13069988C2semidirect
6. #13069750C2semidirect
7. #13069566C2semidirect
8. #13069206C2semidirect
11. #13068863C2semidirect
12. #13068816C2semidirect
13. #13068792C2semidirect
14. #13068331C2semidirect
15. C11×#1804C2semidirect
77. #66991Q8semidirect
221. #1804D11semidirect
532. C11#26409semidirect

Maximal subgroups

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

subgroupindex
#130723102
#130716502
#130701832
#130701142
#130699882
#130697502
#130695662
#130692062
#130690412
#130689352
#130688632
#130688162
#130687922
#130683312
C11×#18042
#2640911