Finite Group Databasebeta

← #14765175

Subgroups — #14765175

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077311C211yesmaximal, characteristic, complemented
2C2×#10622847C211yesmaximal, characteristic, complemented
3#13069505C212yesmaximal, complemented
4#13069322C212yesmaximal, complemented
5#13069266C212yesmaximal, complemented
6#13068945C212yesmaximal, complemented
7#13068919C211yesmaximal, characteristic, complemented
8#13068823C211yesmaximal, characteristic, complemented
9#13068560C211yesmaximal, characteristic, complemented
10#13068390C211yesmaximal, characteristic, complemented
11C11×#3002C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C2×C11×#135C2212yes—
14C11×#525C2211yescharacteristic
15C2×#67001C2211yescharacteristic, complemented
16C22×#4318C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C11×#452C412yescomplemented
19C11×#451C411yescharacteristic, complemented
20C11×#450C411yescharacteristic, complemented
21C11×#449C412yescomplemented
22C11×#448C411yescharacteristic, complemented
23C11×#447C411yescharacteristic, complemented
24C11×#416C2212yes—
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×#66901C2212yes—
27C2×#66901C2212yes—
28C2×#66901C2212yescomplemented
29#10622847—21no—
30#10622847—21no—
31#10622847C2212yes—
32#10622847C2212yes—
33#10622847C2211yescharacteristic, complemented
34C4×C22⋊Dic11C2211yescharacteristic
35#10622820C2211yescharacteristic
36C2×C22⋊(C11⋊C8)—21no—
37C2×C22⋊(C11⋊C8)—21no—
38C2×#66883C2212yescomplemented
39C2×C8×Dic11C2212yescomplemented
40#10622624—21no—
41#10622624—21no—
42D4×C11⋊C8—21no—
43D4×C11⋊C8—21no—
44#10622612C2211yescharacteristic, complemented
45#10622610C2211yescharacteristic, complemented
46#10622190C2212yescomplemented
47#10622188C2212yescomplemented
48#10622170C2212yescomplemented
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—42no—
52C2×C11×#41—42no—
53C2×C11×#41C2×C412yes—
54C2×C11×#41C2311yescharacteristic
55C2×C11×#41C2312yes—
56C22×Q8×C11C2×C411yescharacteristic
57C22×D4×C11—21no—
58C22×D4×C11C2×C411yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C11×#135—42no—
62C11×#135—42no—
63C2×C11×Q16C2×C412yes—
64C2×C11×SD16C2×C412yes—
65C2×C11×SD16C2×C412yes—
66C2×C11×D8C2×C412yes—
67C22×C8×C11C2312yes—
68C11×#123—21no—
69C11×C22⋊Q8C2×C411yescharacteristic
70C11×C22⋊Q8C2×C411yescharacteristic
71C11×#121C2×C411yescharacteristic
72C11×#121C2×C411yescharacteristic
73C11×#120—21no—
74C4×D4×C11—21no—
75C4×D4×C11—21no—
76C11×#117C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78#67001—42no—
79C2×C4×Dic11C2312yes—
80C2×#4318—21no—
81C2×#4318—21no—
82C2×#4318—42no—
83C2×#4318C2311yescharacteristic
84C2×#4318C2312yes—
85C2×#4318C2311yescharacteristic
86C22×C11⋊C8—21no—
87C22×C11⋊C8—21no—
88C22×C11⋊C8—42no—
89C22×C11⋊C8D411yescharacteristic
90C22×C11⋊C8D411yescharacteristic
91C22×C11⋊C8D411yescharacteristic
92C22×C11⋊C8D411yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C11×#103C2×C412yes—
96C11×#103C2×C412yes—
97C11×#102C2×C412yes—
98C11×#102C2×C412yes—
99C11×C22⋊C8C2×C411yescharacteristic
100C11×C22⋊C8C2×C411yescharacteristic
101C11×C22⋊C8C2×C412yes—
102#66901—42no—
103#66901—42no—
104#66901—42no—
105C11⋊#95—21no—
106C22⋊(C11⋊C8)—21no—
107C22⋊(C11⋊C8)—21no—
108C22⋊(C11⋊C8)—22no—
109C22⋊(C11⋊C8)—22no—
110C22⋊(C11⋊C8)—22no—
111C22⋊(C11⋊C8)—22no—
112C22⋊(C11⋊C8)—21no—
113C22⋊(C11⋊C8)—21no—
114#66883—42no—
115C8×Dic11—42no—
116C4⋊(C11⋊C8)—21no—
117C4⋊(C11⋊C8)—21no—
118#66867—21no—
119C4×C11⋊C8—21no—
120#22060—111nomaximal, Sylow
121C24×C11—21no—
122C24×C11#4111yescharacteristic
123C11×#41—22no—
124C11×#41—22no—
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—22no—
128C11×#41—22no—
129C11×#41—42no—
130C11×#41—42no—
131C11×#41—44no—
132C11×#41—42no—
133C11×#41—42no—
134C2×Q8×C11—21no—
135C2×Q8×C11—42no—
136C2×Q8×C11C22×C412yes—
137C2×Q8×C11C22×C411yescharacteristic
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—22no—
141C2×D4×C11—21no—
142C2×D4×C11—22no—
143C2×D4×C11—21no—
144C2×D4×C11—42no—
145C2×D4×C11—44no—
146C2×D4×C11C22×C412yes—
147C2×D4×C11C22×C411yescharacteristic
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11C22×C411yescharacteristic
157C22×C4×C11C22×C411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11#4111yescharacteristic
161C22×C4×C11C2411yescharacteristic
162C22×Dic11—22no—
163C11×Q16—42no—
164C11×SD16—42no—
165C11×SD16—42no—
166C11×D8—42no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11C22×C412yes—
170C2×C8×C11C22×C412yes—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C42×C11—21no—
181C22⋊Dic11—24no—
182C4×Dic11—22no—
183C4×Dic11—22no—
184#4318—22no—
185#4318—22no—
186#4318—22no—
187#4318—22no—
188#4318—42no—
189#4318—42no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—22no—
195C2×C11⋊C8—41no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C2×C11⋊C8—41no—
199C2×C11⋊C8—42no—
200C2×C11⋊C8—42no—
201C2×C11⋊C8C2×D411yescharacteristic
202C2×C11⋊C8C2×D411yescharacteristic
203C2×C11⋊C8C2×D411yescharacteristic
204C2×C11⋊C8C2×D411yescharacteristic
205#3002D1111yescharacteristic
206#2929—111no—
207C2×#408—111no—
208#1974—112no—
209#1937—112no—
210#1929—112no—
211#1876—112no—
212#1871—111no—
213#1855—111no—
214#1789—111no—
215C8×C22⋊C4—111no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—21no—
219C23×C11—22no—
220C23×C11—41no—
221C23×C11—42no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11C4×D411yescharacteristic
225C23×C11C4×D411yescharacteristic
226C23×C11C2×#4111yescharacteristic
227Q8×C11—22no—
228Q8×C11—22no—
229Q8×C11—22no—
230Q8×C11—42no—
231D4×C11—22no—
232D4×C11—22no—
233D4×C11—22no—
234D4×C11—42no—
235D4×C11—42no—
236D4×C11—44no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—42no—
240D4×C11—42no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—44no—
253C2×C4×C11—42no—
254C2×C4×C11—41no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—41no—
258C2×C4×C11C4×D411yescharacteristic
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C23×C411yescharacteristic
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11H(5,𝔽2)12yes—
263C2×C4×C11H(5,𝔽2)12yes—
264C2×Dic11—24no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C8×C11—22no—
268C8×C11—22no—
269C11⋊C8—21no—
270C11⋊C8—21no—
271C11⋊C8—21no—
272C11⋊C8—21no—
273C11⋊C8—41no—
274C11⋊C8—42no—
275C11⋊C8—41no—
276C22×#41C2×D1111yescharacteristic
277C2×#135C2×D1112yes—
278C2×#131—111no—
279C22×M16—111no—
280C23×C8—111no—
281#525C2×D1111yescharacteristic
282#452Dic1112yescomplemented
283#451Dic1111yescharacteristic, complemented
284#450Dic1111yescharacteristic, complemented
285#449Dic1112yescomplemented
286#448Dic1111yescharacteristic, complemented
287#447Dic1111yescharacteristic, complemented
288#435—221no—
289#435—221no—
290C8×D4—221no—
291C8×D4—221no—
292C2×#108—112no—
293#424—111no—
294C2×#104—112no—
295C2×#104—112no—
296C2×#104—112no—
297#416C2×D1112yes—
298#408—112no—
299#408—112no—
300#408—111no—
301#408—221no—
302#408—221no—
303#407—111no—
304C2×C22⋊C8—221no—
305C2×C22⋊C8—221no—
306C2×C22⋊C8C2×D1111yescharacteristic
307#405—111no—
308C2×C4×C8—112no—
309C4×C22⋊C4—111no—
310#341—112no—
311#339—112no—
312#336—112no—
313C22×C11—21no—
314C22×C11—21no—
315C22×C11—21no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—44no—
321C22×C11—42no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—42no—
325C22×C11—41no—
326C22×C11—42no—
327C22×C11—84no—
328C22×C11#44312yes—
329C22×C11C2×C4×D411yescharacteristic
330C22×C11#53812yes—
331C4×C11—21no—
332C4×C11—21no—
333C4×C11—42no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11#51812yes—
338C4×C11#53411yescharacteristic
339C4×C11#53511yescharacteristic
340Dic11—44no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—42no—
344C2×#41—42no—
345C2×#41C2×Dic1112yes—
346C2×#41C22×D1111yescharacteristic
347C2×#41C22×D1112yes—
348C22×Q8C2×Dic1111yescharacteristic
349C22×D4—21no—
350C22×D4C2×Dic1111yescharacteristic
351C23×C4—21no—
352C23×C4C22×D1111yescharacteristic
353#135—42no—
354#135—42no—
355C2×Q16C2×Dic1112yes—
356C2×SD16C2×Dic1112yes—
357C2×SD16C2×Dic1112yes—
358C2×D8C2×Dic1112yes—
359#131—442no—
360C2×M16—112no—
361C2×M16—111no—
362C2×M16—111no—
363C2×M16—221no—
364C2×M16—221no—
365C2×M16—442no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—111no—
372C22×C8—221no—
373C22×C8—221no—
374C22×C8—442no—
375C22×C8C22×D1112yes—
376#123—21no—
377C22⋊Q8C2×Dic1111yescharacteristic
378C22⋊Q8C2×Dic1111yescharacteristic
379#121C2×Dic1111yescharacteristic
380#121C2×Dic1111yescharacteristic
381#120—21no—
382C4×D4—21no—
383C4×D4—21no—
384#117C22×D1111yescharacteristic
385C2×C22⋊C4—221no—
386C2×C42—112no—
387#108—442no—
388C4⋊C8—221no—
389C4⋊C8—221no—
390#104—442no—
391#104—442no—
392#104—442no—
393#103C2×Dic1112yes—
394#103C2×Dic1112yes—
395#102C2×Dic1112yes—
396#102C2×Dic1112yes—
397C22⋊C8—222no—
398C22⋊C8—222no—
399C22⋊C8—222no—
400C22⋊C8—222no—
401C22⋊C8—221no—
402C22⋊C8—221no—
403C22⋊C8—221no—
404C22⋊C8—221no—
405C22⋊C8C2×Dic1111yescharacteristic
406C22⋊C8C2×Dic1111yescharacteristic
407C22⋊C8C2×Dic1112yes—
408#97—221no—
409C4×C8—221no—
410C4×C8—442no—
411#95—221no—
412C2×C11—22no—
413C2×C11—22no—
414C2×C11—41no—
415C2×C11—81no—
416C2×C11—82no—
417C2×C11#232111yescharacteristic
418C2×C11C2×#44311yescharacteristic
419C2×C11#295511yescharacteristic
420C24—21no—
421C24#434111yescharacteristic
422#41—22no—
423#41—22no—
424#41—22no—
425#41—22no—
426#41—22no—
427#41—22no—
428#41—42no—
429#41—42no—
430#41—44no—
431#41—42no—
432#41—42no—
433C2×Q8—21no—
434C2×Q8—42no—
435C2×Q8C22×Dic1112yes—
436C2×Q8C22×Dic1111yescharacteristic
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—22no—
442C2×D4—21no—
443C2×D4—42no—
444C2×D4—44no—
445C2×D4C22×Dic1112yes—
446C2×D4C22×Dic1111yescharacteristic
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—222no—
456C22×C4D4×D1111yescharacteristic
457C22×C4D4×D1111yescharacteristic
458C22×C4#434111yescharacteristic
459C22×C4C22×Dic1111yescharacteristic
460C22×C4C22×Dic1111yescharacteristic
461C22×C4C23×D1111yescharacteristic
462Q16—42no—
463SD16—42no—
464SD16—42no—
465D8—42no—
466M16—222no—
467M16—222no—
468M16—222no—
469M16—222no—
470M16—442no—
471M16—442no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—111no—
475C2×C8—111no—
476C2×C8—111no—
477C2×C8—111no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—221no—
481C2×C8—222no—
482C2×C8—221no—
483C2×C8—441no—
484C2×C8—441no—
485C2×C8—441no—
486C2×C8—441no—
487C2×C8—442no—
488C2×C8—442no—
489C2×C8C22×Dic1112yes—
490C2×C8C22×Dic1112yes—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4C22×Dic1111yescharacteristic
494C4⋊C4C22×Dic1111yescharacteristic
495C22⋊C4—21no—
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—224no—
501C42—21no—
502C42—222no—
503C42—222no—
504C11#2206011yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—21no—
508C23—22no—
509C23—41no—
510C23—42no—
511C23—42no—
512C23—42no—
513C23D4×Dic1111yescharacteristic
514C23D4×Dic1111yescharacteristic
515C23C2×#434111yescharacteristic
516Q8—22no—
517Q8—22no—
518Q8—22no—
519Q8—42no—
520D4—22no—
521D4—22no—
522D4—22no—
523D4—42no—
524D4—42no—
525D4—44no—
526D4—42no—
527D4—42no—
528D4—42no—
529D4—42no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—224no—
548C2×C4—442no—
549C2×C4—442no—
550C2×C4D4×Dic1111yescharacteristic
551C2×C4D4×Dic1111yescharacteristic
552C2×C4C2×D4×D1111yescharacteristic
553C2×C4#6703712yes—
554C2×C4#6703712yes—
555C2×C4C23×Dic1111yescharacteristic
556C8—22no—
557C8—22no—
558C8—221no—
559C8—221no—
560C8—221no—
561C8—221no—
562C8—441no—
563C8—442no—
564C8—441no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—21no—
572C22—44no—
573C22—41no—
574C22—42no—
575C22—41no—
576C22—42no—
577C22—42no—
578C22—41no—
579C22—84no—
580C22#1062280912yes—
581C22#1062312412yes—
582C22C2×D4×Dic1111yescharacteristic
583C4—21no—
584C4—21no—
585C4—41no—
586C4—41no—
587C4—42no—
588C4—41no—
589C4—444no—
590C4#1062312011yescharacteristic
591C4#1062312311yescharacteristic
592C4#1062332912yes—
593C2—22no—
594C2—22no—
595C2—41no—
596C2—82no—
597C2—81no—
598C2#1307127711yescharacteristic
599C2C2×#1062280911yescharacteristic
600C2#1307751911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3002C2
socleC22×C11C2×C4×D4
cosocleC22×C4×C11C24
hypercenter#3002D11
hypocenterC11#22060
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. #13077311C2semidirect
2. C2×#10622847C2semidirect
3. #13069505C2semidirect
4. #13069322C2semidirect
5. #13069266C2semidirect
6. #13068945C2semidirect
7. #13068919C2semidirect
8. #13068823C2semidirect
9. #13068560C2semidirect
10. #13068390C2semidirect
15. C2×#67001C22semidirect
18. C11×#452C4semidirect
19. C11×#451C4semidirect
20. C11×#450C4semidirect
21. C11×#449C4semidirect
22. C11×#448C4semidirect
23. C11×#447C4semidirect
28. C2×#66901C22semidirect
33. #10622847C22semidirect
38. C2×#66883C22semidirect
39. C2×C8×Dic11C22semidirect
44. #10622612C22semidirect
45. #10622610C22semidirect
46. #10622190C22semidirect
47. #10622188C22semidirect
48. #10622170C22semidirect
282. #452Dic11semidirect
283. #451Dic11semidirect
284. #450Dic11semidirect
285. #449Dic11semidirect
286. #448Dic11semidirect
287. #447Dic11semidirect
504. C11#22060semidirect

Maximal subgroups

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

subgroupindex
#130773112
C2×#106228472
#130695052
#130693222
#130692662
#130689452
#130689192
#130688232
#130685602
#130683902
C11×#30022
#2206011