Finite Group Databasebeta

← #14771124

Subgroups — #14771124

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077276C211yesmaximal, characteristic, complemented
2C2×#10622846C211yesmaximal, characteristic
3#13077065C211yesmaximal, characteristic
4#13069324C212yesmaximal, complemented
5#13069267C212yesmaximal, complemented
6#13068889C212yesmaximal, complemented
7#13068716C211yesmaximal, characteristic, complemented
8#13068652C211yesmaximal, characteristic, complemented
9#13068461C212yesmaximal, complemented
10#13068394C211yesmaximal, characteristic, complemented
11C11×#1789C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C2×#67001C2212yes—
14C2×#66979C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×C11×#104C2212yes—
17C2×C11×#104C2212yes—
18C11×#407C2211yescharacteristic
19C4×C11×C22⋊C4C2211yescharacteristic
20#10622847—22no—
21#10622847C2212yes—
22#10622846C411yescharacteristic, complemented
23#10622846C411yescharacteristic, complemented
24#10622846C411yescharacteristic, complemented
25#10622846C411yescharacteristic, complemented
26#10622846C2211yescharacteristic
27#10622846C2211yescharacteristic
28#10622846C2211yescharacteristic
29#10622846C2211yescharacteristic
30C2×#66899C411yescharacteristic, complemented
31C2×#66899C411yescharacteristic, complemented
32C2×#66896C411yescharacteristic, complemented
33C2×#66896C411yescharacteristic, complemented
34#10622820—21no—
35#10622820C2211yescharacteristic
36C2×C22⋊(C11⋊C8)—21no—
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×#66886C2212yescomplemented
39#10622735C2212yescomplemented
40#10622732C2212yescomplemented
41C2×#66867C2212yescomplemented
42#10622333—22no—
43#10622332—21no—
44#10622331—21no—
45#10622196C2212yescomplemented
46#10622162C2212yescomplemented
47#10622161C2212yescomplemented
48#10622161C2212yescomplemented
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—24no—
52C2×C11×#41—42no—
53C2×C11×#41C2×C411yescharacteristic
54C2×C11×#41C2×C411yescharacteristic
55C2×C11×#41C2311yescharacteristic
56C2×C11×#41C2311yescharacteristic
57C22×Q8×C11C2×C411yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2×C411yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C2×C11×M16C2312yes—
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2312yes—
65C2×C22⋊Dic11—21no—
66#67001—24no—
67#67001—42no—
68#66979—21no—
69#66979—21no—
70#66979C2×C411yescharacteristic
71#66979C2×C411yescharacteristic
72#66979C2311yescharacteristic
73#66979C2311yescharacteristic
74C2×C4⋊Dic11C2×C411yescharacteristic
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×C4×Dic11—21no—
77C2×#4318—22no—
78C2×#4318C2312yes—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—42no—
81C22×C11⋊C8C2×C411yescharacteristic
82C22×C11⋊C8C2×C411yescharacteristic
83C22×C11⋊C8C2×C411yescharacteristic
84C22×C11⋊C8C2×C411yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2312yes—
88C11×#104—24no—
89C11×#104—42no—
90C11×C22⋊C8—21no—
91C11×C22⋊C8—21no—
92C11×#95—21no—
93#66899C2×C411yescharacteristic
94#66899C2×C411yescharacteristic
95#66899C2×C411yescharacteristic
96#66899C2×C411yescharacteristic
97#66899C2×C411yescharacteristic
98#66899C2×C411yescharacteristic
99#66899C2×C411yescharacteristic
100#66899C2×C411yescharacteristic
101#66896C2×C411yescharacteristic
102#66896C2×C411yescharacteristic
103#66896C2×C411yescharacteristic
104#66896C2×C411yescharacteristic
105#66896C2×C411yescharacteristic
106#66896C2×C411yescharacteristic
107#66896C2×C411yescharacteristic
108#66896C2×C411yescharacteristic
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—22no—
112C22⋊(C11⋊C8)—22no—
113C22⋊(C11⋊C8)D411yescharacteristic
114C22⋊(C11⋊C8)D411yescharacteristic
115C22⋊(C11⋊C8)D412yes—
116#66886—42no—
117#66879—22no—
118Dic11⋊C8—22no—
119Dic11⋊C8—22no—
120C8×Dic11—22no—
121#66867—42no—
122#22586—111nomaximal, Sylow
123C24×C11—21no—
124C24×C11#4111yescharacteristic
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—22no—
128C11×#41—22no—
129C11×#41—22no—
130C11×#41—44no—
131C11×#41—41no—
132C11×#41—41no—
133C11×#41—44no—
134C11×#41#4114yes—
135C2×Q8×C11—21no—
136C2×Q8×C11—22no—
137C2×Q8×C11—41no—
138C2×Q8×C11C22×C411yescharacteristic
139C2×Q8×C11C22×C411yescharacteristic
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—41no—
147C2×D4×C11—44no—
148C2×D4×C11C22×C411yescharacteristic
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—22no—
158C22×C4×C11—44no—
159C22×C4×C11C22×C411yescharacteristic
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11#4111yescharacteristic
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—21no—
166C22×Dic11—21no—
167C11×M16—22no—
168C11×M16—22no—
169C2×C8×C11—22no—
170C11×C22⋊C4—42no—
171C42×C11—22no—
172C42×C11—22no—
173C22⋊Dic11—21no—
174C22⋊Dic11—21no—
175C22⋊Dic11—21no—
176C22⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11C22×C411yescharacteristic
180C4⋊Dic11C22×C411yescharacteristic
181C4⋊Dic11C22×C411yescharacteristic
182C4⋊Dic11C22×C411yescharacteristic
183C4×Dic11—21no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187#4318—22no—
188#4318—22no—
189#4318—44no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
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—44no—
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C22×C411yescharacteristic
203C2×C11⋊C8C22×C411yescharacteristic
204C2×C11⋊C8C2×D412yes—
205C2×C11⋊C8C2×D412yes—
206#2924—111no—
207C2×#416—111no—
208#2880—111no—
209#1938—112no—
210#1929—112no—
211#1866—112no—
212#1826—111no—
213#1810—111no—
214#1789D1111yescharacteristic
215#1765—112no—
216#1752—111no—
217C23×C11—21no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—21no—
221C23×C11—41no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—81no—
225C23×C11C4×D411yescharacteristic
226C23×C11C4×D411yescharacteristic
227C23×C11C2×#4111yescharacteristic
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—42no—
232Q8×C11#11712yes—
233D4×C11—24no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11#11712yes—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—42no—
253C2×C4×C11—42no—
254C2×C4×C11—42no—
255C2×C4×C11—42no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11C4×D411yescharacteristic
260C2×C4×C11C4×D411yescharacteristic
261C2×C4×C11C23×C411yescharacteristic
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C2×#4112yes—
264C2×C4×C11H(5,𝔽2)12yes—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—42no—
270C2×Dic11—81no—
271C8×C11—42no—
272C11⋊C8—21no—
273C11⋊C8—21no—
274C11⋊C8—21no—
275C11⋊C8—21no—
276C11⋊C8—22no—
277C11⋊C8—22no—
278C11⋊C8—42no—
279C22×#41C2×D1111yescharacteristic
280C2×#131—112no—
281C23×C8—111no—
282C2×#117—111no—
283#433—222no—
284#432—221no—
285#431—221no—
286C2×#108—112no—
287#424—112no—
288C2×#104C2×D1112yes—
289C2×#104C2×D1112yes—
290#416—111no—
291#416—111no—
292#416—111no—
293#416—111no—
294#416—111no—
295#416—111no—
296#416—111no—
297#416—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×#102—111no—
301C2×#102—111no—
302#408—112no—
303#408—222no—
304#407—111no—
305#407—221no—
306#407C2×D1111yescharacteristic
307C2×C22⋊C8—111no—
308C2×C22⋊C8—221no—
309#405—112no—
310C2×#97—112no—
311C4×C22⋊C4C2×D1111yescharacteristic
312#341—112no—
313#339—112no—
314#339—112no—
315#336—112no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—22no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—44no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—84no—
331C22×C11#44412yes—
332C22×C11C2×C4×D411yescharacteristic
333C22×C11#55112yes—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—41no—
338C4×C11—82no—
339C4×C11C2×#11711yescharacteristic
340C4×C11#51811yescharacteristic
341C4×C11#54612yes—
342Dic11—41no—
343Dic11—41no—
344Dic11—41no—
345Dic11—41no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—24no—
349C2×#41—42no—
350C2×#41C4×D1111yescharacteristic
351C2×#41C4×D1111yescharacteristic
352C2×#41C22×D1111yescharacteristic
353C2×#41C22×D1111yescharacteristic
354C22×Q8C4×D1111yescharacteristic
355C22×D4—21no—
356C22×D4C4×D1111yescharacteristic
357C23×C4—21no—
358C23×C4C22×D1111yescharacteristic
359#131—224no—
360#131—442no—
361C2×M16—112no—
362C2×M16—222no—
363C2×M16C22×D1112yes—
364C22×C8—111no—
365C22×C8—111no—
366C22×C8—112no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8—111no—
370C22×C8—111no—
371C22×C8—222no—
372C22×C8—442no—
373#117—111no—
374#117—111no—
375#117—111no—
376#117—111no—
377#117—221no—
378#117—221no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—221no—
383C2×C42—221no—
384C2×C42C22×D1112yes—
385#108—442no—
386C4⋊C8—222no—
387C4⋊C8—222no—
388#104—24no—
389#104—42no—
390#103—111no—
391#103—111no—
392#103—111no—
393#103—111no—
394#103—111no—
395#103—111no—
396#103—111no—
397#103—111no—
398#102—111no—
399#102—111no—
400#102—111no—
401#102—111no—
402#102—111no—
403#102—111no—
404#102—111no—
405#102—111no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—111no—
409C22⋊C8—111no—
410C22⋊C8—112no—
411C22⋊C8—222no—
412C22⋊C8—222no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415#97—222no—
416#97—442no—
417C4×C8—222no—
418#95—21no—
419C2×C11—22no—
420C2×C11—22no—
421C2×C11—41no—
422C2×C11—42no—
423C2×C11—81no—
424C2×C11#234211yescharacteristic
425C2×C11C2×#44411yescharacteristic
426C2×C11#295711yescharacteristic
427C24—21no—
428C24#434111yescharacteristic
429#41—22no—
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—44no—
435#41—41no—
436#41—41no—
437#41—44no—
438#41#434114yes—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—41no—
442C2×Q8C2×C4×D1111yescharacteristic
443C2×Q8C2×C4×D1111yescharacteristic
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—44no—
452C2×D4C2×C4×D1111yescharacteristic
453C2×D4C2×C4×D1111yescharacteristic
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—44no—
463C22×C4—221no—
464C22×C4—221no—
465C22×C4C2×C4×D1111yescharacteristic
466C22×C4C2×C4×D1111yescharacteristic
467C22×C4D4×D1111yescharacteristic
468C22×C4D4×D1111yescharacteristic
469C22×C4#434111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471M16—22no—
472M16—22no—
473M16—222no—
474M16—222no—
475M16—444no—
476C2×C8—22no—
477C2×C8—111no—
478C2×C8—111no—
479C2×C8—111no—
480C2×C8—111no—
481C2×C8—112no—
482C2×C8—112no—
483C2×C8—222no—
484C2×C8—222no—
485C2×C8—222no—
486C2×C8—222no—
487C2×C8—222no—
488C2×C8—441no—
489C2×C8—441no—
490C2×C8—441no—
491C2×C8—441no—
492C2×C8—444no—
493C4⋊C4—111no—
494C4⋊C4—111no—
495C4⋊C4—111no—
496C4⋊C4—111no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C22⋊C4—42no—
500C22⋊C4—221no—
501C22⋊C4—221no—
502C22⋊C4—221no—
503C22⋊C4—221no—
504C42—22no—
505C42—22no—
506C42—221no—
507C42—221no—
508C42—221no—
509C42—221no—
510C11#2258611yescharacteristic, complemented, Sylow
511C23—21no—
512C23—22no—
513C23—22no—
514C23—21no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—81no—
519C23(C22⋊D11)⋊C411yescharacteristic
520C23(C22⋊D11)⋊C411yescharacteristic
521C23C2×#434111yescharacteristic
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—42no—
526Q8#6693012yes—
527D4—24no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—42no—
535D4#6693012yes—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—24no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—442no—
558C2×C4—881no—
559C2×C4(C22⋊D11)⋊C411yescharacteristic
560C2×C4(C22⋊D11)⋊C411yescharacteristic
561C2×C4C22×C4×D1111yescharacteristic
562C2×C4C2×D4×D1111yescharacteristic
563C2×C4C2×#434112yes—
564C2×C4#6703712yes—
565C8—42no—
566C8—221no—
567C8—221no—
568C8—221no—
569C8—221no—
570C8—222no—
571C8—222no—
572C8—442no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—22no—
581C22—44no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—84no—
588C22#1062243612yes—
589C22C2×(C22⋊D11)⋊C411yescharacteristic
590C22#1062311812yes—
591C4—21no—
592C4—21no—
593C4—22no—
594C4—41no—
595C4—82no—
596C4—441no—
597C4—441no—
598C4—441no—
599C4—441no—
600C4C2×#6693011yescharacteristic
601C4#1062301711yescharacteristic
602C4#1062312212yes—
603C2—22no—
604C2—22no—
605C2—41no—
606C2—42no—
607C2—81no—
608C2#1307146711yescharacteristic
609C2C2×#1062243611yescharacteristic
610C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1789C2
socleC22×C11C2×C4×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenter#1789D11
hypocenterC11#22586
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
1. #13077276C2semidirect
4. #13069324C2semidirect
5. #13069267C2semidirect
6. #13068889C2semidirect
7. #13068716C2semidirect
8. #13068652C2semidirect
9. #13068461C2semidirect
10. #13068394C2semidirect
22. #10622846C4semidirect
23. #10622846C4semidirect
24. #10622846C4semidirect
25. #10622846C4semidirect
30. C2×#66899C4semidirect
31. C2×#66899C4semidirect
32. C2×#66896C4semidirect
33. C2×#66896C4semidirect
38. C2×#66886C22semidirect
39. #10622735C22semidirect
40. #10622732C22semidirect
41. C2×#66867C22semidirect
45. #10622196C22semidirect
46. #10622162C22semidirect
47. #10622161C22semidirect
48. #10622161C22semidirect
510. C11#22586semidirect

Maximal subgroups

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

subgroupindex
#130772762
C2×#106228462
#130770652
#130693242
#130692672
#130688892
#130687162
#130686522
#130684612
#130683942
C11×#17892
#2258611