Finite Group Databasebeta

← #25027663

Subgroups — #25027663

Order 11008.

1602 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582779C211yesmaximal, characteristic
2#19132856C212yesmaximal, complemented
3#19132850C212yesmaximal, complemented
4#19132842C212yesmaximal, complemented
5#19132838C212yesmaximal, complemented
6#19132838C212yesmaximal, complemented
7#19132836C211yesmaximal, characteristic
8#19132817C212yesmaximal, complemented
9C43×#1438C211yesmaximal, characteristic
10C24×Dic43C2211yescharacteristic
11C22×Dic43⋊C4C2212yes—
12C22×C22⋊Dic43C2212yes—
13C22×C22⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43C2211yescharacteristic
15C22×C22⋊Dic43C2211yescharacteristic
16C22×C22⋊Dic43C2212yes—
17#14582779C418yescomplemented
18C2×C43⋊#95C2212yes—
19C2×C43⋊#95C2212yes—
20C2×C43⋊#95C2212yes—
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C23×D4×C43C2211yescharacteristic
28C22×C22⋊C4×C43C2212yes—
29C22×C22⋊C4×C43C2212yes—
30C2×#95×C43C2211yescharacteristic
31C2×#95×C43C2211yescharacteristic
32C23×Dic43—41no—
33C23×Dic43—41no—
34C23×Dic43—42no—
35C23×Dic43—42no—
36C23×Dic43C2×C414yes—
37C23×Dic43C2312yes—
38C23×Dic43C2312yes—
39C23×Dic43C2312yes—
40C23×Dic43C2312yes—
41C2×Dic43⋊C4—42no—
42C2×Dic43⋊C4—42no—
43C2×Dic43⋊C4—42no—
44C2×C22⋊Dic43—24no—
45C2×C22⋊Dic43—42no—
46C2×C22⋊Dic43—42no—
47C2×C22⋊Dic43—42no—
48C2×C22⋊Dic43—42no—
49C2×C22⋊Dic43—42no—
50C2×C22⋊Dic43—41no—
51C2×C22⋊Dic43—41no—
52C2×C22⋊Dic43—42no—
53C2×C22⋊Dic43—42no—
54C2×C22⋊Dic43C2×C414yes—
55C2×C22⋊Dic43C2×C418yes—
56C43⋊#95—42no—
57C43⋊#95—42no—
58C43⋊#95—42no—
59C43⋊#95—42no—
60C43⋊#95—42no—
61C43⋊#95—42no—
62C43⋊#95—42no—
63C43⋊#95—42no—
64C43⋊#95C2×C418yes—
65C25×C43C2311yescharacteristic
66C25×C43C2311yescharacteristic
67C22×D4×C43—24no—
68C22×D4×C43—41no—
69C22×D4×C43—41no—
70C22×D4×C43—42no—
71C22×D4×C43C2×C414yes—
72C23×C4×C43C2312yes—
73C23×C4×C43C2312yes—
74C23×C4×C43C2311yescharacteristic
75C2×C22⋊C4×C43—24no—
76C2×C22⋊C4×C43—42no—
77C2×C22⋊C4×C43—42no—
78C2×C22⋊C4×C43—42no—
79C2×C22⋊C4×C43—42no—
80C2×C22⋊C4×C43—42no—
81#95×C43—41no—
82#95×C43—41no—
83C24×C43—22no—
84C24×C43—22no—
85C24×C43—22no—
86C24×C43—21no—
87C24×C43—21no—
88C24×C43—22no—
89C24×C43—22no—
90C24×C43—22no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—22no—
94C24×C43—21no—
95C24×C43—21no—
96C24×C43—22no—
97C24×C43—22no—
98C24×C43C22×C412yes—
99C24×C43C22×C412yes—
100C24×C43#4114yes—
101C24×C43C2411yescharacteristic
102C2×D4×C43—28no—
103C2×D4×C43—44no—
104C2×D4×C43—44no—
105C2×D4×C43—48no—
106C2×D4×C43—48no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43C22×C412yes—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—22no—
144C22×Dic43—22no—
145C22×Dic43—22no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—44no—
153C22×Dic43—48no—
154C22×Dic43—44no—
155C22×Dic43—48no—
156C22×Dic43—44no—
157C22×Dic43C22×C414yes—
158C22×Dic43C22×C414yes—
159C22⋊C4×C43—48no—
160C22⋊C4×C43—48no—
161C22⋊Dic43—44no—
162C22⋊Dic43—48no—
163C22⋊Dic43—48no—
164C22⋊Dic43—44no—
165C22⋊Dic43—44no—
166Dic43⋊C4—48no—
167C23×C43—22no—
168C23×C43—22no—
169C23×C43—24no—
170C23×C43—24no—
171C23×C43—24no—
172C23×C43—24no—
173C23×C43—24no—
174C23×C43—24no—
175C23×C43—24no—
176C23×C43—24no—
177C23×C43—22no—
178C23×C43—24no—
179C23×C43—22no—
180C23×C43—22no—
181C23×C43—24no—
182C23×C43—41no—
183C23×C43—42no—
184C23×C43—41no—
185C23×C43—42no—
186C23×C43—42no—
187C23×C43—41no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—41no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43—42no—
197C23×C43—42no—
198C23×C43—41no—
199C23×C43—42no—
200C23×C43—41no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—41no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—42no—
207C23×C43—41no—
208C23×C43#11714yes—
209C23×C43C23×C411yescharacteristic
210C23×C43C2×#4112yes—
211C23×C43H(5,𝔽2)11yescharacteristic
212C23×C43H(5,𝔽2)12yes—
213C23×C43H(5,𝔽2)11yescharacteristic
214C23×C43H(5,𝔽2)12yes—
215C23×C43H(5,𝔽2)12yes—
216C23×C43H(5,𝔽2)12yes—
217C23×C432−1+412yes—
218D4×C43—416no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×Dic43—24no—
239C2×Dic43—24no—
240C2×Dic43—24no—
241C2×Dic43—24no—
242C2×Dic43—24no—
243C2×Dic43—24no—
244C2×Dic43—416no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43—42no—
252C2×Dic43—42no—
253C2×Dic43—42no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257C2×Dic43—42no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267#14666—431nomaximal, Sylow
268C22×C43—24no—
269C22×C43—28no—
270C22×C43—44no—
271C22×C43—44no—
272C22×C43—44no—
273C22×C43—44no—
274C22×C43—42no—
275C22×C43—42no—
276C22×C43—44no—
277C22×C43—42no—
278C22×C43—44no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—44no—
282C22×C43—82no—
283C22×C43—82no—
284C22×C43—82no—
285C22×C43—82no—
286C22×C43C2×#11711yescharacteristic
287C22×C43#51812yes—
288C22×C43#51811yescharacteristic
289C22×C43#51811yescharacteristic
290C22×C43#52012yes—
291C22×C43#53812yes—
292C22×C43#53812yes—
293C22×C43#53812yes—
294C22×C43#53812yes—
295C22×C43#53912yes—
296C22×C43#53912yes—
297C22×C43#56011yescharacteristic
298C22×C43#56011yescharacteristic
299C22×C43#56012yes—
300C22×C43#56012yes—
301C22×C43#56012yes—
302C22×C43H(3,𝔽4)11yescharacteristic
303C22×C43#56212yes—
304C22×C43#56212yes—
305C22×C43#56212yes—
306C22×C43#56311yescharacteristic
307C4×C43—42no—
308C4×C43—82no—
309C4×C43—82no—
310Dic43—44no—
311Dic43—44no—
312Dic43—82no—
313Dic43—82no—
314C2×#386—431no—
315#1443—432no—
316#1442—432no—
317#1440—432no—
318#1439—432no—
319#1439—432no—
320#1438—431no—
321#1438D4311yescharacteristic
322C22⋊#95—432no—
323C2×C43—44no—
324C2×C43—82no—
325C2×C43#231211yescharacteristic
326C2×C43#231812yes—
327C2×C43#237511yescharacteristic
328C2×C43#237611yescharacteristic
329C2×C43#237712yes—
330C2×C43#282412yes—
331C2×C43#282512yes—
332C2×C43#282612yes—
333C2×C43#282712yes—
334C23×D4C2×D4311yescharacteristic
335C24×C4—431no—
336C22×C4⋊C4—432no—
337C22×C22⋊C4—431no—
338C22×C22⋊C4—432no—
339C22×C22⋊C4—432no—
340C22×C22⋊C4—431no—
341C22×C22⋊C4—431no—
342C22×C22⋊C4C2×D4312yes—
343C22×C22⋊C4C2×D4312yes—
344#386—438no—
345C2×#95—432no—
346C2×#95—432no—
347C2×#95—432no—
348C2×#95—432no—
349C2×#95—432no—
350C2×#95—432no—
351C2×#95—432no—
352C2×#95—432no—
353C2×#95—432no—
354C2×#95C2×D4311yescharacteristic
355C2×#95C2×D4311yescharacteristic
356C43#1466611yescharacteristic, complemented, Sylow
357C25C22×D4311yescharacteristic
358C25C22×D4311yescharacteristic
359C22×D4—24no—
360C22×D4—41no—
361C22×D4—41no—
362C22×D4—42no—
363C22×D4C4×D4314yes—
364C23×C4—432no—
365C23×C4—432no—
366C23×C4—434no—
367C23×C4—432no—
368C23×C4—432no—
369C23×C4—1721no—
370C23×C4—1721no—
371C23×C4—1722no—
372C23×C4—1722no—
373C23×C4C22×D4312yes—
374C23×C4C22×D4312yes—
375C23×C4C22×D4311yescharacteristic
376C2×C4⋊C4—1722no—
377C2×C4⋊C4—1722no—
378C2×C4⋊C4—1722no—
379C2×C22⋊C4—24no—
380C2×C22⋊C4—42no—
381C2×C22⋊C4—42no—
382C2×C22⋊C4—42no—
383C2×C22⋊C4—42no—
384C2×C22⋊C4—42no—
385C2×C22⋊C4—434no—
386C2×C22⋊C4—438no—
387C2×C22⋊C4—864no—
388C2×C22⋊C4—1722no—
389C2×C22⋊C4—1722no—
390C2×C22⋊C4—1722no—
391C2×C22⋊C4—1722no—
392C2×C22⋊C4—1722no—
393C2×C22⋊C4—1721no—
394C2×C22⋊C4—1721no—
395C2×C22⋊C4—1722no—
396C2×C22⋊C4—1722no—
397#95—41no—
398#95—41no—
399#95—438no—
400#95—1722no—
401#95—1722no—
402#95—1722no—
403#95—1722no—
404#95—1722no—
405#95—1722no—
406#95—1722no—
407#95—1722no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—21no—
412C24—21no—
413C24—22no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—22no—
418C24—22no—
419C24—21no—
420C24—21no—
421C24—22no—
422C24—22no—
423C24C2×C4×D4312yes—
424C24C2×C4×D4312yes—
425C24#1062190014yes—
426C24C23×D4311yescharacteristic
427C2×D4—28no—
428C2×D4—44no—
429C2×D4—44no—
430C2×D4—48no—
431C2×D4—48no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—434no—
451C22×C4—434no—
452C22×C4—862no—
453C22×C4—862no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—862no—
458C22×C4—862no—
459C22×C4—862no—
460C22×C4—862no—
461C22×C4—862no—
462C22×C4—862no—
463C22×C4—862no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—862no—
478C22×C4—1728no—
479C22×C4—1724no—
480C22×C4—1724no—
481C22×C4—1728no—
482C22×C4—1724no—
483C22×C4C2×C4×D4312yes—
484C4⋊C4—1728no—
485C22⋊C4—48no—
486C22⋊C4—48no—
487C22⋊C4—1728no—
488C22⋊C4—1724no—
489C22⋊C4—1728no—
490C22⋊C4—1724no—
491C22⋊C4—1724no—
492C23—24no—
493C23—22no—
494C23—22no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—24no—
499C23—24no—
500C23—24no—
501C23—24no—
502C23—22no—
503C23—24no—
504C23—22no—
505C23—22no—
506C23—24no—
507C23—41no—
508C23—41no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—41no—
513C23—42no—
514C23—42no—
515C23—42no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—42no—
520C23—42no—
521C23—42no—
522C23—41no—
523C23—42no—
524C23—42no—
525C23—42no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—42no—
532C23—42no—
533C23#1306328114yes—
534C23C22×C4×D4311yescharacteristic
535C23C2×#1062190012yes—
536C23#1306337012yes—
537C23#1306337011yescharacteristic
538C23#1306337011yescharacteristic
539C23#1306337012yes—
540C23#1306337012yes—
541C23#1306337112yes—
542C23#1306337212yes—
543D4—416no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—864no—
564C2×C4—864no—
565C2×C4—864no—
566C2×C4—864no—
567C2×C4—864no—
568C2×C4—864no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—17216no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C22—24no—
593C22—28no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—44no—
598C22—42no—
599C22—42no—
600C22—44no—
601C22—42no—
602C22—42no—
603C22—44no—
604C22—42no—
605C22—44no—
606C22—82no—
607C22—82no—
608C22—82no—
609C22—82no—
610C22C2×#1306328111yescharacteristic
611C22#1458337112yes—
612C22#1458337211yescharacteristic
613C22#1458337211yescharacteristic
614C22#1458337812yes—
615C22#1458348412yes—
616C22#1458348412yes—
617C22#1458348412yes—
618C22#1458348612yes—
619C22#1458349312yes—
620C22#1458349412yes—
621C22#1458363611yescharacteristic
622C22#1458363611yescharacteristic
623C22#1458363712yes—
624C22#1458363712yes—
625C22#1458363812yes—
626C22#1458364111yescharacteristic
627C22#1458364412yes—
628C22#1458364412yes—
629C22#1458364612yes—
630C22#1458364911yescharacteristic
631C4—42no—
632C4—82no—
633C4—82no—
634C4—3442no—
635C4—3442no—
636C4—1724no—
637C4—1724no—
638C2—44no—
639C2—82no—
640C2#1913719111yescharacteristic
641C2#1913722112yes—
642C2#1913773211yescharacteristic
643C2#1913774511yescharacteristic
644C2#1913775312yes—
645C2#1914267812yes—
646C2#1914268312yes—
647C2#1914269412yes—
648C2#1914270712yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1438C2
socle, cosocleC24×C43C24
prime radicalC23×D4×C43C22
hypercenter#1438D43
hypocenterC43#14666
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. #19132856C2semidirect
3. #19132850C2semidirect
4. #19132842C2semidirect
5. #19132838C2semidirect
6. #19132838C2semidirect
8. #19132817C2semidirect
17. #14582779C4semidirect
356. C43#14666semidirect

Maximal subgroups

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

subgroupindex
C2×#145827792
#191328562
#191328502
#191328422
#191328382
#191328362
#191328172
C43×#14382
#1466643