Finite Group Databasebeta

← #14652897

Subgroups — #14652897

Order 2816.

856 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076959C211yesmaximal, characteristic
2#13068594C211yesmaximal, characteristic, complemented
3C2×#10622108C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic, complemented
5C2×#10622089C211yesmaximal, characteristic, complemented
6#95×Dic11C211yesmaximal, characteristic, complemented
7C2×C11×#327C211yesmaximal, characteristic, complemented
8C2×C11×#121C2211yescharacteristic
9C2×#66993C411yescharacteristic, complemented
10C2×#66992—21no—
11C2×#66992—21no—
12C2×#66983C2211yescharacteristic
13C22×C4×Dic11—21no—
14C22×C4×Dic11C2211yescharacteristic
15C2×C11×C22⋊C8C2211yescharacteristic
16C2×C11×#95C2211yescharacteristic
17#10622834C411yescharacteristic, complemented
18C2×C11⋊#95—21no—
19C2×C11⋊#95C2211yescharacteristic
20C2×C22⋊(C11⋊C8)C2211yescharacteristic
21C2×Dic11⋊C8—21no—
22#10622601C411yescharacteristic, complemented
23#10622589C411yescharacteristic, complemented
24#10622570—21no—
25#10622570—21no—
26C11×#327—22no—
27#10622188—21no—
28#10622175—22no—
29#10622108—22no—
30#10622089—22no—
31C22×D4×C11—21no—
32C22×D4×C11C2×C411yescharacteristic
33C23×C4×C11—21no—
34C23×C4×C11C2311yescharacteristic
35C22×C22⋊D11—21no—
36C22×C22⋊D11—21no—
37C22×C22⋊D11—21no—
38C23×Dic11—21no—
39C23×Dic11D411yescharacteristic
40C23×Dic11D411yescharacteristic
41C22×D44C2×C411yescharacteristic
42C22×C8×C11—21no—
43C11×#121—21no—
44C11×#121—21no—
45C11×#121—21no—
46C11×#121—21no—
47C2×C11×C4⋊C4C2×C411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C22⋊Dic11—21no—
50C2×C22⋊Dic11—21no—
51#66993—42no—
52#66992—42no—
53#66992—42no—
54#66992—42no—
55#66992—42no—
56#66983—21no—
57#66983—21no—
58#66983—21no—
59#66983—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—21no—
63C2×C4⋊Dic11C2×C411yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—21no—
66C2×C4×Dic11—24no—
67C2×C4×Dic11—42no—
68C2×C4×Dic11—42no—
69C2×C4×Dic11—42no—
70C2×C4×Dic11C2×C411yescharacteristic
71C2×C4×Dic11C2×C411yescharacteristic
72C2×C4×Dic11D411yescharacteristic
73C2×C4×Dic11D411yescharacteristic
74C22×C11⋊C8—21no—
75C11×C22⋊C8—21no—
76C11×C22⋊C8—21no—
77C11×#95—21no—
78C11×#95D412yescomplemented
79C11⋊#95—24no—
80C11⋊#95—21no—
81C11⋊#95D412yescomplemented
82C22⋊(C11⋊C8)—21no—
83C22⋊(C11⋊C8)—21no—
84Dic11⋊C8—42no—
85#9712—111nomaximal, Sylow
86C24×C11—21no—
87C24×C11C2×D411yescharacteristic
88C23×D11—21no—
89C2×D4×C11—21no—
90C2×D4×C11—21no—
91C2×D4×C11—41no—
92C2×D4×C11—41no—
93C2×D4×C11—41no—
94C2×D4×C11—41no—
95C2×D4×C11—41no—
96C2×D4×C11—41no—
97C2×D4×C11—41no—
98C2×D4×C11—41no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11—41no—
104C22×C4×C11—41no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—41no—
108C22×C4×C11—41no—
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11#4111yescharacteristic
115C2×C22⋊D11—42no—
116C2×C22⋊D11—42no—
117C2×C22⋊D11—42no—
118C2×C22⋊D11—42no—
119C2×C22⋊D11—42no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—41no—
122C2×C22⋊D11—41no—
123C2×C22⋊D11—41no—
124C2×C22⋊D11—41no—
125C2×C22⋊D11—41no—
126C2×C22⋊D11—41no—
127C22×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—41no—
137C22×Dic11—41no—
138C22×Dic11—41no—
139C22×Dic11—41no—
140C22×Dic11—41no—
141C22×Dic11C22⋊C411yescharacteristic
142C22×Dic11C22⋊C411yescharacteristic
143C22×Dic11C22⋊C411yescharacteristic
144C22×Dic11C22⋊C411yescharacteristic
145C22×Dic11D812yes—
146C22×Dic11SD1612yes—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—41no—
150C2×D44—41no—
151C2×C8×C11—41no—
152C2×C8×C11—41no—
153C2×C8×C11—41no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C22⋊C4—41no—
157C11×C22⋊C4—41no—
158C22⋊Dic11—42no—
159C22⋊Dic11—42no—
160(C2×D11)⋊C4—42no—
161(C2×D11)⋊C4—42no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4—41no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166Dic11⋊C4—42no—
167Dic11⋊C4—42no—
168C4×Dic11—22no—
169C4×Dic11—22no—
170C4×Dic11—41no—
171C4×Dic11—41no—
172C4×Dic11—48no—
173C2×C11⋊C8—41no—
174C2×C11⋊C8—41no—
175C2×C11⋊C8—41no—
176#2856—111no—
177#1797—111no—
178C2×#327—111no—
179C2×#327—111no—
180C2×#327—111no—
181C2×#327D1111yescharacteristic, complemented
182C4×#95—111no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—41no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—41no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11C2×C22⋊C411yescharacteristic
195C23×C11#12111yescharacteristic
196C23×C11#12111yescharacteristic
197C23×C11C2×D811yescharacteristic
198C23×C11C2×SD1611yescharacteristic
199C23×C11AGL(1,ℤ/8)11yescharacteristic
200C23×C11AGL(1,ℤ/8)11yescharacteristic
201C22×D11—41no—
202C22×D11—41no—
203C22×D11—41no—
204C22×D11—41no—
205C22×D11—41no—
206C22×D11—41no—
207C22×D11—41no—
208D4×C11—81no—
209D4×C11—81no—
210D4×C11—81no—
211D4×C11—81no—
212D4×C11—81no—
213D4×C11—81no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—24no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—42no—
227C2×C4×C11—42no—
228C2×C4×C11—42no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11C4×D411yescharacteristic
233C2×C4×C11C4×D411yescharacteristic
234C2×C4×C11#12411yescharacteristic
235C2×C4×C11#12711yescharacteristic
236C22⋊D11—84no—
237C22⋊D11—81no—
238C22⋊D11—81no—
239C22⋊D11—81no—
240C22⋊D11—81no—
241C22⋊D11—84no—
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—42no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11#9912yes—
264C2×Dic11#10212yes—
265C2×Dic11#10212yes—
266C2×Dic11#10412yes—
267C2×Dic11#10412yes—
268D44—81no—
269D44—81no—
270C8×C11—81no—
271C11⋊C8—81no—
272C2×#127—111no—
273C2×#121—111no—
274C2×#121—221no—
275C2×#121—221no—
276C2×#121C2×D1111yescharacteristic
277C22×C42—111no—
278C22×C42—221no—
279C2×C4⋊C8—221no—
280C2×C22⋊C8—111no—
281C2×C22⋊C8C2×D1111yescharacteristic
282#390—111no—
283#390—111no—
284#390—221no—
285#390—221no—
286#384—111no—
287C2×#95—111no—
288C2×#95—221no—
289C2×#95C2×D1111yescharacteristic
290#336—221no—
291#327—22no—
292#327—222no—
293#327—222no—
294#327—222no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—21no—
307C22×C11—81no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11—81no—
313C22×C11—81no—
314C22×C11#39011yescharacteristic
315C22×C11C2×#9911yescharacteristic
316C22×C11#41011yescharacteristic
317C22×C11C2×#10211yescharacteristic
318C22×C11#41811yescharacteristic
319C22×C11C2×#10411yescharacteristic
320C22×C11C2×#10411yescharacteristic
321C22×C11#45911yescharacteristic
322C22×C11#45911yescharacteristic
323C22×C11#46011yescharacteristic
324C22×C11#46011yescharacteristic
325C2×D11—81no—
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—81no—
332C4×C11—21no—
333C4×C11—21no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—44no—
337C4×C11—81no—
338Dic11—22no—
339Dic11—22no—
340Dic11—44no—
341Dic11—41no—
342Dic11—81no—
343Dic11#32714yescomplemented
344C22×D4—21no—
345C22×D4—111no—
346C22×D4—221no—
347C22×D4—221no—
348C22×D4—221no—
349C22×D4C4×D1111yescharacteristic
350C23×C4—21no—
351C23×C4—111no—
352C23×C4—111no—
353C23×C4—221no—
354C23×C4C22×D1111yescharacteristic
355C22×C8—21no—
356C22×C8—221no—
357#127—442no—
358#121—21no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121—221no—
363#121—221no—
364#121—221no—
365#121—221no—
366#121—442no—
367#121—442no—
368#121—442no—
369#121—442no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C4×D1111yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—221no—
376C2×C22⋊C4—221no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42—111no—
383C2×C42—111no—
384C2×C42—224no—
385C2×C42—442no—
386C2×C42—442no—
387C2×C42—442no—
388C4⋊C8—442no—
389C22⋊C8—21no—
390C22⋊C8—21no—
391C22⋊C8—221no—
392C22⋊C8—221no—
393#95—21no—
394#95—112no—
395#95—224no—
396#95—221no—
397#95C22⋊D1112yescomplemented
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—21no—
401C2×C11—21no—
402C2×C11—161no—
403C2×C11C2×#32711yescharacteristic
404C2×C11#150211yescharacteristic
405C2×C11#150511yescharacteristic
406C2×C11#150711yescharacteristic
407C2×C11#196211yescharacteristic
408C2×C11#196411yescharacteristic
409C2×C11#198211yescharacteristic
410D11—161no—
411C24—21no—
412C24—221no—
413C24D4×D1111yescharacteristic
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—41no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—221no—
425C2×D4—221no—
426C2×D4—441no—
427C2×D4—441no—
428C2×D4—442no—
429C2×D4—442no—
430C2×D4—442no—
431C2×D4—442no—
432C2×D4—442no—
433C2×D4—442no—
434C2×D4—441no—
435C2×D4—441no—
436C2×D4—441no—
437C2×D4—441no—
438C2×D4—441no—
439C2×D4—441no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—111no—
451C22×C4—111no—
452C22×C4—111no—
453C22×C4—112no—
454C22×C4—112no—
455C22×C4—111no—
456C22×C4—222no—
457C22×C4—222no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4—441no—
466C22×C4—441no—
467C22×C4—441no—
468C22×C4—441no—
469C22×C4—441no—
470C22×C4C2×C4×D1111yescharacteristic
471C22×C4#433911yescharacteristic
472C22×C4D4×D1111yescharacteristic
473C22×C4D4×D1111yescharacteristic
474C22×C4#434111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—441no—
480C2×C8—441no—
481C2×C8—441no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—442no—
487C4⋊C4—442no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—442no—
491C22⋊C4—442no—
492C22⋊C4—442no—
493C22⋊C4—442no—
494C22⋊C4—441no—
495C22⋊C4—441no—
496C42—222no—
497C42—222no—
498C42—441no—
499C42—441no—
500C42—448no—
501C11#971211yescharacteristic, complemented, Sylow
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—441no—
514C23—441no—
515C23—441no—
516C23—441no—
517C23—441no—
518C23—441no—
519C23—441no—
520C23C22⋊C4×D1111yescharacteristic
521C23#6693711yescharacteristic
522C23D8×D1111yescharacteristic
523C23#6696411yescharacteristic
524C23SD16×D1111yescharacteristic
525C23#6696711yescharacteristic
526C23#6699211yescharacteristic
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4—81no—
532D4—81no—
533D4—881no—
534D4—881no—
535D4—884no—
536D4—884no—
537D4—881no—
538D4—881no—
539D4—881no—
540D4—881no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—24no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—112no—
560C2×C4—112no—
561C2×C4—112no—
562C2×C4—112no—
563C2×C4—112no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—221no—
570C2×C4—224no—
571C2×C4—221no—
572C2×C4—221no—
573C2×C4—221no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4(C22⋊D11)⋊C411yescharacteristic
586C2×C4#6693811yescharacteristic
587C2×C4C4×C22⋊D1111yescharacteristic
588C2×C4#6699311yescharacteristic
589C8—81no—
590C8—881no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—21no—
598C22—21no—
599C22—21no—
600C22—21no—
601C22—21no—
602C22—21no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—881no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22—881no—
616C22—881no—
617C22#1062235311yescharacteristic
618C22D11×#9911yescharacteristic
619C22#1062237511yescharacteristic
620C22D11×#10211yescharacteristic
621C22#1062238311yescharacteristic
622C22#1062239911yescharacteristic
623C22D11×#10411yescharacteristic
624C22D11×#10411yescharacteristic
625C22#1062257011yescharacteristic
626C22#1062276311yescharacteristic
627C22#1062277611yescharacteristic
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—44no—
633C4—81no—
634C4—114no—
635C4—222no—
636C4—222no—
637C4—444no—
638C4—441no—
639C4—881no—
640C2—21no—
641C2—21no—
642C2—21no—
643C2—21no—
644C2—161no—
645C2—1761no—
646C2D11×#32711yescharacteristic
647C2#1306710911yescharacteristic
648C2#1306712211yescharacteristic
649C2#1306713011yescharacteristic
650C2#1306944211yescharacteristic
651C2#1306945011yescharacteristic
652C2#1306954111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#327C2
socleC23×C11C2×C22⋊C4
prime radical#13076959C2
cosocleC23×C4×C11C23
hypercenterC2×#327D11
hypocenterC11#9712
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#327

Complements

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

NH ≅ G/Ntype
2. #13068594C2semidirect
3. C2×#10622108C2semidirect
4. C2×#10622175C2semidirect
5. C2×#10622089C2semidirect
6. #95×Dic11C2semidirect
7. C2×C11×#327C2semidirect
9. C2×#66993C4semidirect
17. #10622834C4semidirect
22. #10622601C4semidirect
23. #10622589C4semidirect
78. C11×#95D4semidirect
81. C11⋊#95D4semidirect
181. C2×#327D11semidirect
343. Dic11#327semidirect
397. #95C22⋊D11semidirect
501. C11#9712semidirect

Maximal subgroups

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

subgroupindex
#130769592
#130685942
C2×#106221082
C2×#106221752
C2×#106220892
#95×Dic112
C2×C11×#3272
#971211