Finite Group Databasebeta

← #14771126

Subgroups — #14771126

Order 2816.

906 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#13077274C211yesmaximal, characteristic, complemented
2C2×#10622615C211yesmaximal, characteristic
3#13077066C211yesmaximal, characteristic
4#13069321C212yesmaximal, complemented
5#13069262C212yesmaximal, complemented
6#13068892C212yesmaximal, complemented
7#13068652C211yesmaximal, characteristic, complemented
8#13068561C211yesmaximal, characteristic
9#13068450C212yesmaximal, complemented
10C22⋊C4×C11⋊C8C211yesmaximal, characteristic, complemented
11C11×#1826C211yesmaximal, characteristic, complemented
12C22×#4339C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C23×C11⋊C8C2211yescharacteristic
15C2×#66960C2212yes—
16C11×#407C2211yescharacteristic
17C4×C11×C22⋊C4C2211yescharacteristic
18#10622820C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20#10622742C2212yes—
21C2×#66886C2212yescomplemented
22#10622615C411yescharacteristic, complemented
23#10622615C411yescharacteristic, complemented
24#10622615C411yescharacteristic, complemented
25#10622615C411yescharacteristic, complemented
26#10622615C2211yescharacteristic
27#10622615C2211yescharacteristic
28#10622615C2211yescharacteristic
29#10622615C2211yescharacteristic
30#10622613—22no—
31#10622612C2212yescomplemented
32#10622610C2212yescomplemented
33C2×#66874C411yescharacteristic, complemented
34C2×#66874C411yescharacteristic, complemented
35C2×#66873C411yescharacteristic, complemented
36C2×#66873C411yescharacteristic, complemented
37C2×#66869C2212yes—
38C2×#66869C2212yes—
39#10622539—21no—
40#10622538—21no—
41C2×C4×C11⋊C8C2212yescomplemented
42#10622340—22no—
43#10622339—21no—
44D11×C22⋊C8—21no—
45C11×#339C2212yescomplemented
46C11×#339C2212yescomplemented
47#10622196C2212yescomplemented
48#10622162C2212yescomplemented
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C2×#4339—21no—
52C2×#4339—21no—
53C2×#4339—24no—
54C2×#4339—42no—
55C2×#4339C2×C411yescharacteristic
56C2×#4339C2×C411yescharacteristic
57C2×#4339C2311yescharacteristic
58C2×#4339C2311yescharacteristic
59C22×D44C2×C411yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22C2×C411yescharacteristic
62C2×C11×M16C2312yes—
63C11×#117—21no—
64C11×#117—21no—
65C11×#117C2×C411yescharacteristic
66C11×#117C2×C411yescharacteristic
67C11×#117C2311yescharacteristic
68C11×#117C2311yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C4⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C42×C11C2312yes—
75C2×#4318C2312yes—
76C22×C11⋊C8—42no—
77C22×C11⋊C8C2×C411yescharacteristic
78C22×C11⋊C8C2×C411yescharacteristic
79C22×C11⋊C8C2×C411yescharacteristic
80C22×C11⋊C8C2×C411yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2312yes—
84#66960—24no—
85#66960—42no—
86C2×#4313—22no—
87C2×C8×D11—22no—
88C11×C22⋊C8—21no—
89C11×C22⋊C8—21no—
90C11×#95—21no—
91C22⋊(C11⋊C8)—21no—
92C22⋊(C11⋊C8)—21no—
93C22⋊(C11⋊C8)D411yescharacteristic
94C22⋊(C11⋊C8)D411yescharacteristic
95C22⋊(C11⋊C8)D412yes—
96#66886—42no—
97(C2×D11)⋊C8—22no—
98(C2×D11)⋊C8—22no—
99#66874C2×C411yescharacteristic
100#66874C2×C411yescharacteristic
101#66874C2×C411yescharacteristic
102#66874C2×C411yescharacteristic
103#66874C2×C411yescharacteristic
104#66874C2×C411yescharacteristic
105#66874C2×C411yescharacteristic
106#66874C2×C411yescharacteristic
107#66873C2×C411yescharacteristic
108#66873C2×C411yescharacteristic
109#66873C2×C411yescharacteristic
110#66873C2×C411yescharacteristic
111#66873C2×C411yescharacteristic
112#66873C2×C411yescharacteristic
113#66873C2×C411yescharacteristic
114#66873C2×C411yescharacteristic
115#66869—24no—
116#66869—42no—
117C4⋊(C11⋊C8)—22no—
118C4⋊(C11⋊C8)—22no—
119#66867—22no—
120C4×C11⋊C8—22no—
121C4×C11⋊C8—42no—
122#22587—111nomaximal, Sylow
123C24×C11#4111yescharacteristic
124C23×D11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—22no—
129C22×C4×C11—21no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11#4111yescharacteristic
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—21no—
137C2×C22⋊D11—21no—
138C2×C22⋊D11—21no—
139C2×C22⋊D11—21no—
140C2×C22⋊D11—44no—
141C22×Dic11—21no—
142#4339—22no—
143#4339—22no—
144#4339—22no—
145#4339—22no—
146#4339—22no—
147#4339—41no—
148#4339—41no—
149#4339—44no—
150#4339—44no—
151#4339#4114yes—
152C2×D44—22no—
153C2×D44—21no—
154C2×D44—41no—
155C2×D44C22×C411yescharacteristic
156C2×D44C22×C411yescharacteristic
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—44no—
162C2×Dic22—22no—
163C2×Dic22—21no—
164C2×Dic22—41no—
165C2×Dic22C22×C411yescharacteristic
166C2×Dic22C22×C411yescharacteristic
167C11×M16—22no—
168C11×M16—22no—
169C2×C8×C11—22no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4C22×C411yescharacteristic
173C11×C4⋊C4C22×C411yescharacteristic
174C11×C4⋊C4C22×C411yescharacteristic
175C11×C4⋊C4C22×C411yescharacteristic
176C11×C22⋊C4—24no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—21no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—22no—
186C42×C11—22no—
187#4318—22no—
188#4318—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—41no—
195C2×C11⋊C8—41no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C2×C11⋊C8C22×C411yescharacteristic
199C2×C11⋊C8C22×C411yescharacteristic
200C2×C11⋊C8C22×C411yescharacteristic
201C2×C11⋊C8C22×C411yescharacteristic
202C2×C11⋊C8C2×D412yes—
203C2×C11⋊C8C2×D412yes—
204#4313—44no—
205C8×D11—44no—
206#2924—111no—
207C2×#416—111no—
208#2880—111no—
209#1937—112no—
210#1929—112no—
211#1866—112no—
212#1826D1111yescharacteristic, complemented
213#1810—111no—
214#1789—111no—
215#1764—112no—
216C8×C22⋊C4—111no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—41no—
220C23×C11C4×D411yescharacteristic
221C23×C11C4×D411yescharacteristic
222C23×C11C2×#4111yescharacteristic
223C22×D11—21no—
224C22×D11—21no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—81no—
228C2×C4×C11—22no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11—81no—
244C2×C4×C11C4×D411yescharacteristic
245C2×C4×C11C4×D411yescharacteristic
246C2×C4×C11C23×C411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4112yes—
249C2×C4×C11H(5,𝔽2)12yes—
250C22⋊D11—24no—
251C22⋊D11—42no—
252C22⋊D11—42no—
253C22⋊D11—42no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—42no—
257D44—21no—
258D44—21no—
259D44—21no—
260D44—42no—
261D44#11712yes—
262C4×D11—24no—
263C4×D11—42no—
264C4×D11—42no—
265C4×D11—42no—
266Dic22—21no—
267Dic22—21no—
268Dic22—21no—
269Dic22—42no—
270Dic22#11712yes—
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×#41—111no—
280C2×#131—112no—
281C23×C8—111no—
282C2×#117C2×D1111yescharacteristic
283#433—222no—
284#432—221no—
285#431—221no—
286C2×#108—112no—
287#424—112no—
288C2×#104—112no—
289C2×#104—112no—
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×C4×C8—112no—
311C4×C22⋊C4C2×D1111yescharacteristic
312#341—112no—
313#339C2×D1112yescomplemented
314#339C2×D1112yescomplemented
315#336—112no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—21no—
322C22×C11—21no—
323C22×C11—44no—
324C22×C11#44312yes—
325C22×C11C2×C4×D411yescharacteristic
326C22×C11#55112yes—
327C2×D11—22no—
328C2×D11—41no—
329C2×D11—41no—
330C2×D11—41no—
331C2×D11—41no—
332C2×D11—41no—
333C2×D11—84no—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—44no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11C2×#11711yescharacteristic
342C4×C11#51811yescharacteristic
343C4×C11#54612yes—
344Dic11—22no—
345Dic11—41no—
346C2×#41—111no—
347C2×#41—111no—
348C2×#41—111no—
349C2×#41—111no—
350C2×#41—224no—
351C2×#41—221no—
352C2×#41—221no—
353C2×#41—442no—
354C22×Q8—111no—
355C22×D4—111no—
356C22×D4—221no—
357C23×C4—221no—
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—21no—
374#117—21no—
375#117C4×D1111yescharacteristic
376#117C4×D1111yescharacteristic
377#117C22×D1111yescharacteristic
378#117C22×D1111yescharacteristic
379C2×C4⋊C4C4×D1111yescharacteristic
380C2×C4⋊C4C4×D1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C42—21no—
384C2×C42C22×D1112yes—
385#108—442no—
386C4⋊C8—222no—
387C4⋊C8—222no—
388#104—224no—
389#104—442no—
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—
416C4×C8—222no—
417C4×C8—442no—
418#95—21no—
419C2×C11—22no—
420C2×C11—22no—
421C2×C11—41no—
422C2×C11#234211yescharacteristic
423C2×C11C2×#44311yescharacteristic
424C2×C11#295711yescharacteristic
425D11—42no—
426D11—81no—
427C24—221no—
428C24#434111yescharacteristic
429#41—114no—
430#41—222no—
431#41—222no—
432#41—222no—
433#41—222no—
434#41—222no—
435#41—444no—
436#41—441no—
437#41—441no—
438#41—444no—
439C2×Q8—111no—
440C2×Q8—111no—
441C2×Q8—222no—
442C2×Q8—221no—
443C2×Q8—441no—
444C2×D4—111no—
445C2×D4—111no—
446C2×D4—222no—
447C2×D4—221no—
448C2×D4—221no—
449C2×D4—221no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—441no—
453C2×D4—444no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—444no—
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—444no—
489C2×C8—441no—
490C2×C8—441no—
491C2×C8—441no—
492C2×C8—441no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4C2×C4×D1111yescharacteristic
496C4⋊C4C2×C4×D1111yescharacteristic
497C4⋊C4C2×C4×D1111yescharacteristic
498C4⋊C4C2×C4×D1111yescharacteristic
499C22⋊C4—24no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—22no—
509C42—22no—
510C11#2258711yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23—41no—
514C23—221no—
515C23—221no—
516C23—442no—
517C23—442no—
518C23—881no—
519C23(C22⋊D11)⋊C411yescharacteristic
520C23(C22⋊D11)⋊C411yescharacteristic
521C23C2×#434111yescharacteristic
522Q8—112no—
523Q8—221no—
524Q8—221no—
525Q8—221no—
526Q8—442no—
527D4—112no—
528D4—224no—
529D4—221no—
530D4—221no—
531D4—221no—
532D4—442no—
533D4—442no—
534D4—442no—
535D4—442no—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—81no—
552C2×C4—221no—
553C2×C4—224no—
554C2×C4—221no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4(C22⋊D11)⋊C411yescharacteristic
560C2×C4(C22⋊D11)⋊C411yescharacteristic
561C2×C4C22×C4×D1111yescharacteristic
562C2×C4C2×D4×D1111yescharacteristic
563C2×C4#41×D1112yes—
564C2×C4#6704212yes—
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—44no—
581C22—222no—
582C22—441no—
583C22—441no—
584C22—441no—
585C22—441no—
586C22—441no—
587C22—884no—
588C22#1062243712yes—
589C22C2×(C22⋊D11)⋊C411yescharacteristic
590C22#1062318912yes—
591C4—21no—
592C4—21no—
593C4—44no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—222no—
599C4—441no—
600C4D11×#11711yescharacteristic
601C4#1062305211yescharacteristic
602C4#1062318512yes—
603C2—22no—
604C2—22no—
605C2—41no—
606C2—442no—
607C2—881no—
608C2#1307145811yescharacteristic
609C2C2×#1062243711yescharacteristic
610C2#1307752911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1826C2
socleC22×C11C2×C4×D4
prime radicalC22×#4339C22
cosocleC22×C4×C11C24
hypercenter#1826D11
hypocenterC11#22587
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
1. #13077274C2semidirect
4. #13069321C2semidirect
5. #13069262C2semidirect
6. #13068892C2semidirect
7. #13068652C2semidirect
9. #13068450C2semidirect
10. C22⋊C4×C11⋊C8C2semidirect
11. C11×#1826C2semidirect
21. C2×#66886C22semidirect
22. #10622615C4semidirect
23. #10622615C4semidirect
24. #10622615C4semidirect
25. #10622615C4semidirect
31. #10622612C22semidirect
32. #10622610C22semidirect
33. C2×#66874C4semidirect
34. C2×#66874C4semidirect
35. C2×#66873C4semidirect
36. C2×#66873C4semidirect
41. C2×C4×C11⋊C8C22semidirect
45. C11×#339C22semidirect
46. C11×#339C22semidirect
47. #10622196C22semidirect
48. #10622162C22semidirect
212. #1826D11semidirect
313. #339C2×D11semidirect
314. #339C2×D11semidirect
510. C11#22587semidirect

Maximal subgroups

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

subgroupindex
#130772742
C2×#106226152
#130770662
#130693212
#130692622
#130688922
#130686522
#130685612
#130684502
C22⋊C4×C11⋊C82
C11×#18262
#2258711