Finite Group Databasebeta

← #24999869

Subgroups — #24999869

Order 11008.

772 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134913C211yesmaximal, characteristic, complemented
2#19134787C211yesmaximal, characteristic, complemented
3C2×#14582633C211yesmaximal, characteristic, complemented
4C2×#14582623C211yesmaximal, characteristic, complemented
5#19132840C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#2617C211yesmaximal, characteristic
8C22×C4⋊Dic43C2211yescharacteristic
9C22×C22⋊Dic43—21no—
10C2×#13063256—21no—
11C2×#13063246—21no—
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14C2×C43⋊#95—21no—
15C2×C43⋊#95C2211yescharacteristic
16#14582661—21no—
17#14582661—21no—
18#14582633—22no—
19#14582623—22no—
20C2×#121×C43C2211yescharacteristic
21C2×#120×C43—21no—
22C22×C22⋊C4×C43C2211yescharacteristic
23C43×#397—21no—
24C43×#394—21no—
25C43×#394—21no—
26C43×#392—21no—
27C43×#386—21no—
28C43×#380C2211yescharacteristic
29C23×Dic43—21no—
30C23×Dic43—21no—
31C22×C43⋊C8—21no—
32C22×C43⋊C8—21no—
33C2×C4⋊Dic43—21no—
34C2×C4⋊Dic43—21no—
35C2×C4⋊Dic43—42no—
36C2×C22⋊Dic43—42no—
37C2×C22⋊Dic43—42no—
38C2×C22⋊Dic43—42no—
39#13063256—42no—
40#13063246—42no—
41C22⋊(C43⋊C8)—21no—
42C22⋊(C43⋊C8)—21no—
43C22⋊(C43⋊C8)—21no—
44C22⋊(C43⋊C8)D412yescomplemented
45C43⋊#95—21no—
46C43⋊#95—21no—
47C43⋊#95—42no—
48C25×C43D411yescharacteristic
49C22×D4×C43—21no—
50C22×D4×C43—21no—
51C22×D4×C43—21no—
52C22×D4×C43D411yescharacteristic
53C23×C4×C43D411yescharacteristic
54C23×C4×C43C2311yescharacteristic
55#121×C43—21no—
56#121×C43—21no—
57#121×C43—21no—
58#121×C43—21no—
59#120×C43—42no—
60#120×C43—42no—
61C2×C4⋊C4×C43D411yescharacteristic
62C2×C4⋊C4×C43D411yescharacteristic
63C2×C4⋊C4×C43D411yescharacteristic
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43—21no—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—21no—
75C2×C22⋊C4×C43—21no—
76#95×C43—21no—
77#95×C43—21no—
78#95×C43—21no—
79C24×C43—21no—
80C24×C43—21no—
81C24×C43—21no—
82C24×C43—21no—
83C24×C43—21no—
84C24×C43—21no—
85C24×C43—21no—
86C24×C43—41no—
87C24×C43—41no—
88C24×C43—41no—
89C24×C43—41no—
90C24×C43SD1612yes—
91C24×C43C2×D411yescharacteristic
92C2×D4×C43—21no—
93C2×D4×C43—21no—
94C2×D4×C43—42no—
95C2×D4×C43—42no—
96C2×D4×C43—41no—
97C2×D4×C43—41no—
98C2×D4×C43—41no—
99C2×D4×C43—41no—
100C2×D4×C43—41no—
101C2×D4×C43—41no—
102C2×D4×C43—41no—
103C2×D4×C43—41no—
104C2×D4×C43—81no—
105C2×D4×C43—81no—
106C2×D4×C43—81no—
107C2×D4×C43—81no—
108C22×C4×C43—21no—
109C22×C4×C43—21no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—41no—
115C22×C4×C43—41no—
116C22×C4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43#4111yescharacteristic
122C22×C4×C43#4111yescharacteristic
123C22×C4×C43#4111yescharacteristic
124C22×Dic43—22no—
125C22×Dic43—22no—
126C22×Dic43—41no—
127C22×Dic43—41no—
128C22×Dic43—41no—
129C22×Dic43—41no—
130C22×Dic43—41no—
131C22×Dic43—41no—
132C22×Dic43—41no—
133C22×Dic43—41no—
134C22×Dic43—41no—
135C22×Dic43—41no—
136C22×Dic43—41no—
137C22×Dic43—41no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—41no—
141C4⋊C4×C43—41no—
142C22⋊C4×C43—42no—
143C22⋊C4×C43—42no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C22⋊C4×C43—41no—
147C22⋊C4×C43—41no—
148C22⋊C4×C43—41no—
149C22⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C22⋊C4×C43—81no—
153C22⋊C4×C43—81no—
154C22⋊Dic43—48no—
155C4⋊Dic43—22no—
156C4⋊Dic43—22no—
157C4⋊Dic43—41no—
158C4⋊Dic43—41no—
159C2×C43⋊C8—22no—
160C2×C43⋊C8—41no—
161C2×C43⋊C8—41no—
162C2×C43⋊C8—41no—
163C2×C43⋊C8—41no—
164C2×C43⋊C8—41no—
165C23×C43—21no—
166C23×C43—21no—
167C23×C43—21no—
168C23×C43—21no—
169C23×C43—22no—
170C23×C43—22no—
171C23×C43—22no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43—42no—
177C23×C43—42no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—41no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—41no—
193C23×C43—81no—
194C23×C43—81no—
195C23×C43—81no—
196C23×C43—81no—
197C23×C43—81no—
198C23×C43—81no—
199C23×C43#12011yescharacteristic
200C23×C43#12111yescharacteristic
201C23×C43#12311yescharacteristic
202C23×C43C2×SD1611yescharacteristic
203C23×C43#13511yescharacteristic
204C23×C43AGL(1,ℤ/8)11yescharacteristic
205C23×C43AGL(1,ℤ/8)11yescharacteristic
206D4×C43—42no—
207D4×C43—81no—
208D4×C43—84no—
209D4×C43—84no—
210D4×C43—81no—
211D4×C43—81no—
212D4×C43—81no—
213D4×C43—81no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—42no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—81no—
236C2×C4×C43#12111yescharacteristic
237C2×C4×C43#12111yescharacteristic
238C2×C4×C43#12311yescharacteristic
239C2×C4×C43#12411yescharacteristic
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—81no—
247C2×Dic43—81no—
248C2×Dic43—81no—
249C2×Dic43—81no—
250C2×Dic43—81no—
251C2×Dic43—81no—
252C2×Dic43—81no—
253C2×Dic43—81no—
254C43⋊C8—42no—
255C43⋊C8—81no—
256#10395—431nomaximal, Sylow
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—21no—
266C22×C43—21no—
267C22×C43—21no—
268C22×C43—21no—
269C22×C43—44no—
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—82no—
274C22×C43—82no—
275C22×C43—82no—
276C22×C43—81no—
277C22×C43—81no—
278C22×C43—81no—
279C22×C43—81no—
280C22×C43—81no—
281C22×C43—81no—
282C22×C43—81no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43#39411yescharacteristic
288C22×C43#44911yescharacteristic
289C22×C43#45011yescharacteristic
290C22×C43#45311yescharacteristic
291C22×C43#45511yescharacteristic
292C22×C43B(4,𝔽2)11yescharacteristic
293C22×C43#45811yescharacteristic
294C22×C43#46511yescharacteristic
295C22×C43#46911yescharacteristic
296C22×C43#48111yescharacteristic
297C22×C43#48211yescharacteristic
298C4×C43—21no—
299C4×C43—21no—
300C4×C43—21no—
301C4×C43—21no—
302C4×C43—81no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43—81no—
306Dic43—82no—
307Dic43—82no—
308#2617D4311yescharacteristic
309#1874—431no—
310#1853—431no—
311C2×#327—431no—
312C2×#323—431no—
313#1439—431no—
314#1294—431no—
315C2×C43—21no—
316C2×C43—21no—
317C2×C43—21no—
318C2×C43—21no—
319C2×C43—82no—
320C2×C43—161no—
321C2×C43#160011yescharacteristic
322C2×C43#160111yescharacteristic
323C2×C43#161211yescharacteristic
324C2×C43#161311yescharacteristic
325C2×C43#203411yescharacteristic
326C2×C43#203711yescharacteristic
327C2×C43#204411yescharacteristic
328C2×#121C2×D4311yescharacteristic
329C2×#120—21no—
330C22×C4⋊C4—431no—
331C22×C22⋊C4—861no—
332C22×C22⋊C4C2×D4311yescharacteristic
333C2×#106—861no—
334C2×#102—861no—
335C2×C22⋊C8—431no—
336C2×C22⋊C8—431no—
337#397—21no—
338#394—21no—
339#394—21no—
340#392—21no—
341#386—21no—
342#380C2×D4311yescharacteristic
343C2×#95—431no—
344C2×#95—861no—
345#340—861no—
346#340—861no—
347#327—862no—
348#323—862no—
349C43#1039511yescharacteristic, complemented, Sylow
350C25C22⋊D4311yescharacteristic
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4C22⋊D4311yescharacteristic
355C23×C4—861no—
356C23×C4—861no—
357C23×C4C22⋊D4311yescharacteristic
358C23×C4C22×D4311yescharacteristic
359C22×C8—861no—
360C22×C8—861no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#120—42no—
366#120—42no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—1722no—
370C2×C4⋊C4C22⋊D4311yescharacteristic
371C2×C4⋊C4C22⋊D4311yescharacteristic
372C2×C4⋊C4C22⋊D4311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—1722no—
386C2×C22⋊C4—1722no—
387C2×C22⋊C4—1722no—
388#106—1722no—
389#102—1722no—
390C22⋊C8—432no—
391C22⋊C8—861no—
392C22⋊C8—861no—
393C22⋊C8—861no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—861no—
398#95—861no—
399#95—1722no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24#1062188312yes—
412C24C2×C22⋊D4311yescharacteristic
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C2×D4—81no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—1721no—
442C22×C4—1721no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4—1721no—
446C22×C4—1721no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1721no—
450C22×C4—1721no—
451C22×C4—1721no—
452C22×C4—1721no—
453C22×C4D4×D4311yescharacteristic
454C22×C4#1062190011yescharacteristic
455C22×C4#1062190011yescharacteristic
456C22×C4#1062190011yescharacteristic
457C22×C4C2×C22⋊D4311yescharacteristic
458C22×C4C2×C22⋊D4311yescharacteristic
459C2×C8—862no—
460C2×C8—1721no—
461C2×C8—1721no—
462C2×C8—1721no—
463C2×C8—1721no—
464C2×C8—1721no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—862no—
470C4⋊C4—862no—
471C4⋊C4—1721no—
472C4⋊C4—1721no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—81no—
484C22⋊C4—81no—
485C22⋊C4—1728no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—81no—
515C23—81no—
516C23—81no—
517C23—81no—
518C23—81no—
519C23—81no—
520C23#1306329411yescharacteristic
521C23#1306329711yescharacteristic
522C23#1306330611yescharacteristic
523C23C2×#1062188311yescharacteristic
524C23#1306334511yescharacteristic
525C23#1306335011yescharacteristic
526C23#1306335111yescharacteristic
527D4—42no—
528D4—81no—
529D4—84no—
530D4—84no—
531D4—81no—
532D4—81no—
533D4—81no—
534D4—81no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—81no—
557C2×C4—3441no—
558C2×C4—3441no—
559C2×C4—3441no—
560C2×C4—3441no—
561C2×C4—3441no—
562C2×C4—3441no—
563C2×C4—3441no—
564C2×C4—3441no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4#1306329611yescharacteristic
572C2×C4#1306329711yescharacteristic
573C2×C4#1306330611yescharacteristic
574C2×C4#1306331211yescharacteristic
575C8—3441no—
576C8—1722no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#1458281311yescharacteristic
608C22#1458304411yescharacteristic
609C22#1458305011yescharacteristic
610C22#1458306711yescharacteristic
611C22#1458307711yescharacteristic
612C22#1458308611yescharacteristic
613C22#1458308911yescharacteristic
614C22#1458312611yescharacteristic
615C22#1458315011yescharacteristic
616C22#1458321511yescharacteristic
617C22#1458322011yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—81no—
623C4—81no—
624C4—81no—
625C4—81no—
626C4—3442no—
627C4—3442no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—161no—
634C2#1913354111yescharacteristic
635C2#1913354711yescharacteristic
636C2#1913360911yescharacteristic
637C2#1913361511yescharacteristic
638C2#1913578111yescharacteristic
639C2#1913580211yescharacteristic
640C2#1913584311yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
Fitting, prime radicalC43×#2617C2
socleC23×C43#120
hypercenter#2617D43
hypocenterC43#10395
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. #19134913C2semidirect
2. #19134787C2semidirect
3. C2×#14582633C2semidirect
4. C2×#14582623C2semidirect
5. #19132840C2semidirect
6. #19132473C2semidirect
44. C22⋊(C43⋊C8)D4semidirect
349. C43#10395semidirect

Maximal subgroups

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

subgroupindex
#191349132
#191347872
C2×#145826332
C2×#145826232
#191328402
#191324732
C43×#26172
#1039543