Finite Group Databasebeta

← #14756990

Subgroups — #14756990

Order 2816.

800 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077384C211yesmaximal, characteristic
2#13077259C211yesmaximal, characteristic, complemented
3#131×Dic11C211yesmaximal, characteristic, complemented
4#13069265C211yesmaximal, characteristic, complemented
5#13069263C211yesmaximal, characteristic, complemented
6#13069218C211yesmaximal, characteristic, complemented
7#13069212C211yesmaximal, characteristic, complemented
8#13068943C211yesmaximal, characteristic
9#13068941C211yesmaximal, characteristic
10#13068893C211yesmaximal, characteristic, complemented
11#108×Dic11C211yesmaximal, characteristic, complemented
12#104×Dic11C211yesmaximal, characteristic, complemented
13#13068420C211yesmaximal, characteristic, complemented
14#13068360C211yesmaximal, characteristic, complemented
15C11×#1866C211yesmaximal, characteristic, complemented
16C2×C11×#131C2211yescharacteristic
17#41×Dic11C2211yescharacteristic
18C2×#67003C2211yescharacteristic
19C2×#67001C2211yescharacteristic
20#10623053C2211yescharacteristic
21C2×C11×#108C2211yescharacteristic
22C11×#424C2211yescharacteristic
23C2×C11×#104C2211yescharacteristic
24C11×#416C2211yescharacteristic
25C2×#66901C2211yescharacteristic
26C2×#66889C2211yescharacteristic
27#10622742C2211yescharacteristic
28#10622735—21no—
29#10622735C2211yescharacteristic
30M16×Dic11—21no—
31M16×Dic11C2211yescharacteristic
32M16×Dic11C2211yescharacteristic
33#10622726C2211yescharacteristic
34#10622723C2211yescharacteristic
35C2×#66883C2211yescharacteristic
36#10622714—21no—
37#10622714C2211yescharacteristic
38C2×C8×Dic11—21no—
39C2×C8×Dic11C2211yescharacteristic
40C2×C8×Dic11C2211yescharacteristic
41#10622612C2211yescharacteristic
42#10622611C2211yescharacteristic
43C42×Dic11C2211yescharacteristic
44C2×#66869C2211yescharacteristic
45#10622453—21no—
46#10622453—21no—
47#10622446—21no—
48#10622446—21no—
49#10622403C411yescharacteristic, complemented
50#10622403C411yescharacteristic, complemented
51#10622401C411yescharacteristic, complemented
52#10622401C411yescharacteristic, complemented
53#10622371C411yescharacteristic, complemented
54#10622371C411yescharacteristic, complemented
55#10622369C411yescharacteristic, complemented
56#10622369C411yescharacteristic, complemented
57C11×#339C2211yescharacteristic
58C11×#336C2211yescharacteristic
59#10622196C2211yescharacteristic
60#10622196C2211yescharacteristic
61#10622193C2211yescharacteristic
62#10622188C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622162C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×C11×#41C2311yescharacteristic
68C2×#4339C2311yescharacteristic
69C11×#131—22no—
70C11×#131—22no—
71C2×C11×M16—21no—
72C2×C11×M16C2311yescharacteristic
73C2×C11×M16C2311yescharacteristic
74C22×C8×C11—21no—
75C22×C8×C11C2311yescharacteristic
76C22×C8×C11C2311yescharacteristic
77C11×#117C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79#67003—22no—
80#67003—22no—
81#67001—22no—
82#67001—22no—
83Q8×Dic11C2×C411yescharacteristic
84Q8×Dic11C2×C411yescharacteristic
85C2×#4326C2×C411yescharacteristic
86C2×#4325C2×C411yescharacteristic
87D4×Dic11—21no—
88D4×Dic11—21no—
89D4×Dic11C2×C411yescharacteristic
90D4×Dic11C2×C411yescharacteristic
91C2×#4324C2×C411yescharacteristic
92C2×#4323C2×C411yescharacteristic
93#66979—21no—
94#66979C2311yescharacteristic
95C2×C4×Dic11—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C2×C4×Dic11C2311yescharacteristic
100C2×#4318—21no—
101C2×#4318C2311yescharacteristic
102C2×#4318C2311yescharacteristic
103C22×C11⋊C8—21no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66946C2×C411yescharacteristic
107#66946C2×C411yescharacteristic
108#66940C2×C411yescharacteristic
109#66940C2×C411yescharacteristic
110(C22⋊D11)⋊C4—21no—
111(C22⋊D11)⋊C4—21no—
112#66925—21no—
113C42×D11—21no—
114C11×#108—22no—
115C11×C4⋊C8—21no—
116C11×C4⋊C8—21no—
117C11×#104—22no—
118C11×#103C2×C411yescharacteristic
119C11×#103C2×C411yescharacteristic
120C11×#102C2×C411yescharacteristic
121C11×#102C2×C411yescharacteristic
122#66901—22no—
123#66889—22no—
124#66885C2×C411yescharacteristic
125#66885C2×C411yescharacteristic
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128(C2×D11)⋊C8—21no—
129(C2×D11)⋊C8—21no—
130#66883—22no—
131#66880C2×C411yescharacteristic
132#66880C2×C411yescharacteristic
133#66879—21no—
134#66879—21no—
135#66879—21no—
136#66879—21no—
137C8×Dic11—21no—
138C8×Dic11—21no—
139C8×Dic11—21no—
140C8×Dic11—21no—
141C8×Dic11C2×C411yescharacteristic
142C8×Dic11C2×C411yescharacteristic
143C8×Dic11C2×C411yescharacteristic
144C8×Dic11C2×C411yescharacteristic
145C8×Dic11D411yescharacteristic
146C8×Dic11D411yescharacteristic
147C8×Dic11D411yescharacteristic
148C8×Dic11D411yescharacteristic
149#66872C2×C411yescharacteristic
150#66872C2×C411yescharacteristic
151#66871C2×C411yescharacteristic
152#66871C2×C411yescharacteristic
153#66869—22no—
154C4⋊(C11⋊C8)—21no—
155C4⋊(C11⋊C8)—21no—
156#21137—111nomaximal, Sylow
157C11×#41—21no—
158C11×#41—21no—
159C11×#41#4112yes—
160C11×#41#4112yes—
161C2×Q8×C11C22×C411yescharacteristic
162C2×D4×C11—21no—
163C2×D4×C11C22×C411yescharacteristic
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11C2411yescharacteristic
167C2×C22⋊D11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11#4111yescharacteristic
172C22×Dic11#4111yescharacteristic
173#4339—21no—
174#4339—21no—
175#4339—21no—
176#4339—21no—
177C2×D44C22×C411yescharacteristic
178C2×C4×D11—21no—
179C2×C4×D11—21no—
180C2×C4×D11—21no—
181C2×Dic22C22×C411yescharacteristic
182C11×M16—24no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—21no—
186C11×M16#4112yes—
187C2×C8×C11—24no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11C22×C411yescharacteristic
195C2×C8×C11C22×C411yescharacteristic
196C2×C8×C11C2×D411yescharacteristic
197C2×C8×C11C2×D411yescharacteristic
198C11×C4⋊C4C22×C411yescharacteristic
199C11×C4⋊C4C22×C411yescharacteristic
200C11×C22⋊C4—21no—
201C42×C11—21no—
202C42×C11—21no—
203C42×C11—21no—
204C22⋊Dic11—21no—
205C22⋊Dic11—21no—
206C22⋊Dic11—21no—
207#4326—22no—
208#4325—22no—
209#4324—22no—
210#4323—22no—
211(C2×D11)⋊C4—21no—
212(C2×D11)⋊C4—21no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11C22×C411yescharacteristic
216C4⋊Dic11C22×C411yescharacteristic
217Dic11⋊C4—21no—
218Dic11⋊C4—21no—
219C4×Dic11—24no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225C4×Dic11—21no—
226C4×Dic11—21no—
227C4×Dic11—42no—
228C4×Dic11C22×C411yescharacteristic
229C4×Dic11C22×C411yescharacteristic
230C4×Dic11C2×D411yescharacteristic
231C4×Dic11C2×D411yescharacteristic
232#4318—24no—
233#4318—21no—
234#4318—21no—
235#4318—21no—
236#4318#4112yes—
237C2×C11⋊C8—24no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8C22×C411yescharacteristic
245C2×C11⋊C8C22×C411yescharacteristic
246C2×C11⋊C8C2×D411yescharacteristic
247C2×C11⋊C8C2×D411yescharacteristic
248C4×#135—111no—
249#2922—111no—
250C4×#131—111no—
251#1929—111no—
252#1929—111no—
253#1922—111no—
254#1922—111no—
255#1876—111no—
256#1876—111no—
257#1866—111no—
258#1866D1111yescharacteristic, complemented
259C4×#108—111no—
260C4×#104—111no—
261C4×#104—111no—
262#1744—111no—
263C23×C11—21no—
264C23×C11C2×#4111yescharacteristic
265C22×D11—21no—
266Q8×C11—21no—
267Q8×C11#11712yes—
268D4×C11—22no—
269D4×C11—22no—
270D4×C11—21no—
271D4×C11#11712yes—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11C23×C411yescharacteristic
281C2×C4×C11C22×D411yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C22⋊D11—41no—
287C22⋊D11—41no—
288C2×Dic11—22no—
289C2×Dic11—22no—
290C2×Dic11—22no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—21no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11C4×D411yescharacteristic
299C2×Dic11C4×D411yescharacteristic
300C2×Dic11C4×D411yescharacteristic
301C2×Dic11C4×D411yescharacteristic
302D44—21no—
303D44—21no—
304C4×D11—41no—
305C4×D11—41no—
306C4×D11—42no—
307C4×D11—42no—
308Dic22—21no—
309Dic22—21no—
310C8×C11—21no—
311C8×C11—21no—
312C8×C11—21no—
313C8×C11—22no—
314C8×C11—21no—
315C8×C11—41no—
316C11⋊C8—21no—
317C11⋊C8—21no—
318C11⋊C8—21no—
319C11⋊C8—22no—
320C11⋊C8—21no—
321C11⋊C8—41no—
322C2×#135—111no—
323C2×#131—111no—
324C2×#131C2×D1111yescharacteristic
325C4×#41—111no—
326C4×#41—111no—
327C4×Q16—111no—
328C4×Q16—111no—
329C4×SD16—111no—
330C4×SD16—111no—
331C4×SD16—111no—
332C4×SD16—111no—
333C4×D8—111no—
334C4×D8—111no—
335#433—221no—
336#433—221no—
337#431—221no—
338#431—221no—
339C2×#108—111no—
340C2×#108C2×D1111yescharacteristic
341#427—111no—
342#424—111no—
343#424C2×D1111yescharacteristic
344C2×#104—111no—
345C2×#104—111no—
346C2×#104—111no—
347C2×#104C2×D1111yescharacteristic
348#416—111no—
349#416C2×D1111yescharacteristic
350#408—111no—
351#408—111no—
352#405—111no—
353#405—111no—
354#405—221no—
355#405—221no—
356C4×M16—111no—
357C4×M16—111no—
358C4×M16—221no—
359C2×C4×C8—111no—
360C2×C4×C8—111no—
361C2×C4×C8—221no—
362C43—111no—
363#341—111no—
364#341—111no—
365#339—111no—
366#339—111no—
367#339—111no—
368#339C2×D1111yescharacteristic
369#336—111no—
370#336—111no—
371#336—111no—
372#336C2×D1111yescharacteristic
373C22×C11—21no—
374C22×C11—21no—
375C22×C11—22no—
376C22×C11—41no—
377C22×C11—41no—
378C22×C11C2×C4×D411yescharacteristic
379C22×C11#52911yescharacteristic
380C22×C11#52911yescharacteristic
381C2×D11—41no—
382C2×D11—41no—
383C2×D11—41no—
384C4×C11—22no—
385C4×C11—42no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11C2×#11711yescharacteristic
389C4×C11C4×#4111yescharacteristic
390C4×C11#52511yescharacteristic
391C4×C11#52511yescharacteristic
392Dic11—21no—
393Dic11—21no—
394Dic11—42no—
395Dic11—41no—
396Dic11—41no—
397Dic11—41no—
398Dic11#44312yes—
399Dic11#44412yes—
400C2×#41—111no—
401C2×#41C22×D1111yescharacteristic
402#135—222no—
403#135—222no—
404C2×Q16—111no—
405C2×SD16—111no—
406C2×SD16—111no—
407C2×D8—111no—
408#131—22no—
409#131—22no—
410#131—222no—
411#131—222no—
412C2×M16—21no—
413C2×M16—111no—
414C2×M16—111no—
415C2×M16—221no—
416C2×M16C22×D1111yescharacteristic
417C2×M16C22×D1111yescharacteristic
418C22×C8—21no—
419C22×C8—111no—
420C22×C8—111no—
421C22×C8—221no—
422C22×C8C22×D1111yescharacteristic
423C22×C8C22×D1111yescharacteristic
424C4×Q8—111no—
425C4×Q8—111no—
426C4×Q8—111no—
427C4×Q8—111no—
428C4×D4—111no—
429C4×D4—111no—
430C4×D4—111no—
431C4×D4—111no—
432C4×D4—221no—
433C4×D4—221no—
434C4×D4—221no—
435C4×D4—221no—
436#117—111no—
437#117—221no—
438#117—221no—
439#117C22×D1111yescharacteristic
440C2×C42—111no—
441C2×C42—111no—
442C2×C42—221no—
443C2×C42—221no—
444C2×C42—221no—
445C2×C42—221no—
446C2×C42C22×D1111yescharacteristic
447#108—22no—
448#108—222no—
449#107—111no—
450#107—111no—
451#106—111no—
452#106—111no—
453C4⋊C8—21no—
454C4⋊C8—21no—
455C4⋊C8—221no—
456C4⋊C8—221no—
457#104—22no—
458#104—222no—
459#104—222no—
460#104—222no—
461#103—111no—
462#103—111no—
463#103C4×D1111yescharacteristic
464#103C4×D1111yescharacteristic
465#102—111no—
466#102—111no—
467#102C4×D1111yescharacteristic
468#102C4×D1111yescharacteristic
469C22⋊C8—221no—
470C22⋊C8—221no—
471C22⋊C8—221no—
472C22⋊C8—221no—
473#97—221no—
474#97—221no—
475#97—221no—
476#97—221no—
477C4×C8—111no—
478C4×C8—111no—
479C4×C8—111no—
480C4×C8—111no—
481C4×C8—111no—
482C4×C8—111no—
483C4×C8—111no—
484C4×C8—111no—
485C4×C8—221no—
486C4×C8—221no—
487C4×C8—221no—
488C4×C8—221no—
489C2×C11—21no—
490C2×C11—21no—
491C2×C11—42no—
492C2×C11#229011yescharacteristic
493C2×C11C2×#44311yescharacteristic
494C2×C11C2×#44411yescharacteristic
495D11—81no—
496#41—21no—
497#41—21no—
498#41—221no—
499#41—221no—
500#41—221no—
501#41—221no—
502#41#434112yes—
503#41#434312yes—
504C2×Q8—111no—
505C2×Q8C2×C4×D1111yescharacteristic
506C2×D4—21no—
507C2×D4—111no—
508C2×D4—221no—
509C2×D4C2×C4×D1111yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—111no—
513C22×C4—111no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4C23×D1111yescharacteristic
521Q16—222no—
522SD16—222no—
523SD16—222no—
524D8—222no—
525M16—24no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—112no—
530M16—224no—
531M16—221no—
532M16—221no—
533M16—221no—
534M16#434112yes—
535C2×C8—24no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—111no—
543C2×C8—111no—
544C2×C8—111no—
545C2×C8—111no—
546C2×C8—224no—
547C2×C8—221no—
548C2×C8—221no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8C2×C4×D1111yescharacteristic
554C2×C8C2×C4×D1111yescharacteristic
555C2×C8D4×D1111yescharacteristic
556C2×C8D4×D1111yescharacteristic
557C4⋊C4—111no—
558C4⋊C4—111no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4C2×C4×D1111yescharacteristic
564C4⋊C4C2×C4×D1111yescharacteristic
565C22⋊C4—21no—
566C22⋊C4—221no—
567C22⋊C4—221no—
568C22⋊C4—221no—
569C22⋊C4—221no—
570C22⋊C4—221no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—111no—
575C42—111no—
576C42—111no—
577C42—111no—
578C42—221no—
579C42—221no—
580C42—221no—
581C42—221no—
582C42—224no—
583C42—221no—
584C42—221no—
585C42—221no—
586C42—442no—
587C11#2113711yescharacteristic, complemented, Sylow
588C23—21no—
589C23—221no—
590C23#41×D1111yescharacteristic
591Q8—21no—
592Q8—221no—
593Q8—221no—
594Q8#6694512yes—
595D4—22no—
596D4—22no—
597D4—21no—
598D4—221no—
599D4—221no—
600D4—441no—
601D4—441no—
602D4#6694512yes—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—111no—
612C2×C4—111no—
613C2×C4—111no—
614C2×C4—111no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—222no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—221no—
621C2×C4—442no—
622C2×C4—442no—
623C2×C4—442no—
624C2×C4—442no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4C22×C4×D1111yescharacteristic
630C2×C4C2×D4×D1111yescharacteristic
631C2×C4C2×#434111yescharacteristic
632C2×C4C2×#434111yescharacteristic
633C2×C4C2×#434311yescharacteristic
634C2×C4#41×D1111yescharacteristic
635C8—21no—
636C8—21no—
637C8—21no—
638C8—22no—
639C8—21no—
640C8—41no—
641C8—221no—
642C8—221no—
643C8—221no—
644C8—221no—
645C8—222no—
646C8—441no—
647C22—21no—
648C22—21no—
649C22—22no—
650C22—41no—
651C22—41no—
652C22—441no—
653C22—441no—
654C22—441no—
655C22C4×D4×D1111yescharacteristic
656C22#1062315511yescharacteristic
657C22#1062318011yescharacteristic
658C4—22no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—112no—
663C4—112no—
664C4—221no—
665C4—221no—
666C4—442no—
667C4—441no—
668C4—441no—
669C4—441no—
670C4C2×#6694511yescharacteristic
671C4C4×#434111yescharacteristic
672C4#1062311711yescharacteristic
673C4#1062315811yescharacteristic
674C2—21no—
675C2—21no—
676C2—42no—
677C2—881no—
678C2#1307105211yescharacteristic
679C2D11×#44311yescharacteristic
680C2D11×#44411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1866C2
socleC22×C11C2×C4×D4
prime radicalC2×#67003C22
cosocleC22×C4×C11C24
hypercenter#1866D11
hypocenterC11#21137
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
2. #13077259C2semidirect
3. #131×Dic11C2semidirect
4. #13069265C2semidirect
5. #13069263C2semidirect
6. #13069218C2semidirect
7. #13069212C2semidirect
10. #13068893C2semidirect
11. #108×Dic11C2semidirect
12. #104×Dic11C2semidirect
13. #13068420C2semidirect
14. #13068360C2semidirect
15. C11×#1866C2semidirect
49. #10622403C4semidirect
50. #10622403C4semidirect
51. #10622401C4semidirect
52. #10622401C4semidirect
53. #10622371C4semidirect
54. #10622371C4semidirect
55. #10622369C4semidirect
56. #10622369C4semidirect
258. #1866D11semidirect
587. C11#21137semidirect

Maximal subgroups

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

subgroupindex
#130773842
#130772592
#131×Dic112
#130692652
#130692632
#130692182
#130692122
#130689432
#130689412
#130688932
#108×Dic112
#104×Dic112
#130684202
#130683602
C11×#18662
#2113711