Finite Group Databasebeta

← #14822308

Subgroups — #14822308

Order 2816.

812 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#13073143C211yesmaximal, characteristic, complemented
2#13070019C211yesmaximal, characteristic, complemented
3#13069990C211yesmaximal, characteristic, complemented
4#13069847C211yesmaximal, characteristic
5#13069847C211yesmaximal, characteristic
6#13069302C211yesmaximal, characteristic, complemented
7#13069240C211yesmaximal, characteristic, complemented
8#13069201C211yesmaximal, characteristic, complemented
9#13069201C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068877C211yesmaximal, characteristic, complemented
12#13068877C211yesmaximal, characteristic, complemented
13#13068616C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2366C211yesmaximal, characteristic
16C2×C11×#127C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C11×#390—21no—
21C11×#390C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#386—21no—
24C11×#386—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622597—21no—
36#10622594—21no—
37C2×#66872C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39#10622548C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622270—21no—
48#10622260—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C11×#127—22no—
66C11×#127—22no—
67C4×D4×C11—22no—
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C4×D4×C11—41no—
71C4×D4×C11—44no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C11×#95—21no—
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104#66896—22no—
105#66896—22no—
106#66896—22no—
107#66896—22no—
108#66896—22no—
109#66896—22no—
110#66896—41no—
111#66896—41no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117#66872—22no—
118#66872—22no—
119C4⋊(C11⋊C8)—41no—
120C4×C11⋊C8—41no—
121#26754—111nomaximal, Sylow
122C24×C11—21no—
123C24×C11—21no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11—81no—
139C2×D4×C11—81no—
140C2×D4×C11#4112yes—
141C2×D4×C11#4112yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—42no—
148C22×C4×C11—81no—
149C22×C4×C11—81no—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—41no—
165C11×C4⋊C4SD1614yes—
166C11×C4⋊C4#4112yes—
167C11×C22⋊C4—42no—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—81no—
172C11×C22⋊C4—81no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—42no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—81no—
188C4⋊Dic11—81no—
189C4⋊Dic11#4112yes—
190Dic11⋊C4—42no—
191Dic11⋊C4—81no—
192Dic11⋊C4—81no—
193Dic11⋊C4—81no—
194C4×Dic11—81no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207#2507—111no—
208#2366D1111yescharacteristic
209#2071—111no—
210#2065—111no—
211#2041—111no—
212#2041—111no—
213#1934—111no—
214#1926—111no—
215#1920—111no—
216#1920—111no—
217#1916—111no—
218#1864—111no—
219#1864—111no—
220#1802—111no—
221C4×#102—111no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—41no—
225C23×C11—41no—
226C23×C11—41no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11C22×D411yescharacteristic
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—22no—
241D4×C11—48no—
242D4×C11—41no—
243D4×C11—41no—
244D4×C11—41no—
245D4×C11—41no—
246D4×C11—84no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—84no—
269C2×C4×C11—84no—
270C2×C4×C11C2×SD1612yes—
271C2×C4×C11C2×SD1612yes—
272C2×C4×C11C2×SD1612yes—
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11H(5,𝔽2)11yescharacteristic
278C2×C4×C112−1+411yescharacteristic
279C2×Dic11—22no—
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—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C11⋊C8—41no—
292C11⋊C8—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C2×#127C2×D1111yescharacteristic
296C2×C4×D4—21no—
297C2×C4×D4C2×D1111yescharacteristic
298C2×C4×D4C2×D1111yescharacteristic
299C2×#106—111no—
300C2×#106—111no—
301C2×C4⋊C8—111no—
302C2×#102—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×#102—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×C4×C8—111no—
311#398—221no—
312#398—221no—
313#390—21no—
314#390C2×D1111yescharacteristic
315#390C2×D1111yescharacteristic
316#389—111no—
317#389—111no—
318#389—111no—
319#389—111no—
320#389—221no—
321#387—221no—
322#386—21no—
323#386—21no—
324#384—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4C2×D1111yescharacteristic
327C4×C4⋊C4C2×D1111yescharacteristic
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338C22×C11—42no—
339C22×C11—42no—
340C22×C11—42no—
341C22×C11—42no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—81no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11—81no—
350C22×C11—81no—
351C22×C11—81no—
352C22×C11#52511yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11#54811yescharacteristic
355C22×C11C22×SD1611yescharacteristic
356C22×C11#57511yescharacteristic
357C22×C11#57611yescharacteristic
358C22×C11#57611yescharacteristic
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—22no—
362C4×C11—41no—
363C4×C11—42no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11#52911yescharacteristic
368C4×C11#53911yescharacteristic
369C4×C11#55211yescharacteristic
370C4×C11#55311yescharacteristic
371Dic11—42no—
372Dic11—81no—
373Dic11—81no—
374Dic11—81no—
375C22×D4—21no—
376C22×D4—21no—
377C22×D4C22×D1111yescharacteristic
378C22×D4C22×D1111yescharacteristic
379C23×C4—21no—
380C23×C4—21no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8—111no—
384C22×C8—111no—
385#127—22no—
386#127—22no—
387C4×D4—22no—
388C4×D4—22no—
389C4×D4—41no—
390C4×D4—41no—
391C4×D4—44no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22⋊D1111yescharacteristic
403C2×C4⋊C4C22⋊D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C22⋊C4—21no—
407C2×C22⋊C4—21no—
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C42—21no—
413C2×C42—221no—
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416C2×C42C22×D1111yescharacteristic
417#106—222no—
418#106—222no—
419C4⋊C8—441no—
420#102—222no—
421#102—222no—
422#102—222no—
423#102—222no—
424#102—222no—
425#102—222no—
426#102—441no—
427#102—441no—
428C4×C8—441no—
429#95—21no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95C22⋊D1111yescharacteristic
436#95C22⋊D1111yescharacteristic
437C2×C11—82no—
438C2×C11—82no—
439C2×C11#246011yescharacteristic
440C2×C11#310111yescharacteristic
441C2×C11#312211yescharacteristic
442C2×C11#329511yescharacteristic
443C2×C11#330911yescharacteristic
444C2×C11#336211yescharacteristic
445C2×C11#337011yescharacteristic
446C24—21no—
447C24—21no—
448C2×D4—24no—
449C2×D4—24no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—81no—
463C2×D4—81no—
464C2×D4#433912yes—
465C2×D4#433912yes—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—81no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—112no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—442no—
510C4⋊C4—881no—
511C4⋊C4—881no—
512C4⋊C4—881no—
513C4⋊C4—881no—
514C4⋊C4—881no—
515C4⋊C4#432414yes—
516C4⋊C4#434112yes—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—81no—
522C22⋊C4—81no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—42no—
530C42—881no—
531C11#2675411yescharacteristic, complemented, Sylow
532C23—22no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23C22×C22⋊D1111yescharacteristic
547D4—22no—
548D4—22no—
549D4—22no—
550D4—22no—
551D4—48no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—84no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—84no—
579C2×C4—84no—
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×C4C2×#432412yes—
593C2×C4C2×#432412yes—
594C2×C4C2×#432412yes—
595C2×C4C2×#433911yescharacteristic
596C2×C4C2×#433911yescharacteristic
597C2×C4C2×#434111yescharacteristic
598C2×C4#6703711yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C2×C4#6704311yescharacteristic
601C8—441no—
602C8—441no—
603C8—441no—
604C8—441no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22#1062332211yescharacteristic
620C22C22×#432411yescharacteristic
621C22#1062333711yescharacteristic
622C22#1062335311yescharacteristic
623C22#1062336211yescharacteristic
624C22#1062336611yescharacteristic
625C22#1062336611yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—41no—
630C4—41no—
631C4—41no—
632C4—42no—
633C4—81no—
634C4—442no—
635C4—881no—
636C4—881no—
637C4—881no—
638C4#1062306911yescharacteristic
639C4#1062307111yescharacteristic
640C4#1062307211yescharacteristic
641C4#1062309511yescharacteristic
642C2—82no—
643C2—82no—
644C2#1307256211yescharacteristic
645C2#1307862411yescharacteristic
646C2#1307885911yescharacteristic
647C2#1308044011yescharacteristic
648C2#1308062211yescharacteristic
649C2#1308128311yescharacteristic
650C2#1308136311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2366C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2366D11
hypocenterC11#26754
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. #13073143C2semidirect
2. #13070019C2semidirect
3. #13069990C2semidirect
6. #13069302C2semidirect
7. #13069240C2semidirect
8. #13069201C2semidirect
9. #13069201C2semidirect
10. #13069175C2semidirect
11. #13068877C2semidirect
12. #13068877C2semidirect
13. #13068616C2semidirect
14. C4×#66896C2semidirect
531. C11#26754semidirect

Maximal subgroups

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

subgroupindex
#130731432
#130700192
#130699902
#130698472
#130693022
#130692402
#130692012
#130691752
#130688772
#130686162
C4×#668962
C11×#23662
#2675411