Finite Group Databasebeta

← #25023867

Subgroups — #25023867

Order 11008.

1566 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582761C211yesmaximal, characteristic
2C2×#14582756C211yesmaximal, characteristic
3C2×#14582746C211yesmaximal, characteristic
4#19132860C211yesmaximal, characteristic, complemented
5#19132854C211yesmaximal, characteristic, complemented
6#19132851C211yesmaximal, characteristic, complemented
7#19132841C212yesmaximal
8#19132837C212yesmaximal
9#19132824C212yesmaximal, complemented
10#19132820C212yesmaximal, complemented
11C43×#1444C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×C4⋊Dic43C2212yes—
14C22×C4⋊Dic43C2211yescharacteristic
15C22×(C2×D43)⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2211yescharacteristic
17C22×(C2×D43)⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2211yescharacteristic
19C22×C4×Dic43C2212yes—
20#14582761—24no—
21#14582756—24no—
22#14582746C418yescomplemented
23C2×C43⋊#95C2211yescharacteristic
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2211yescharacteristic
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C22×C4⋊C4×C43C2212yes—
34C22×C4⋊C4×C43C2211yescharacteristic
35C2×#95×C43C2212yes—
36C2×#95×C43C2211yescharacteristic
37C2×#95×C43C2211yescharacteristic
38C24×D43C2311yescharacteristic
39C23×Dic43C2311yescharacteristic
40C23×Dic43C2312yes—
41C23×Dic43C2311yescharacteristic
42C23×Dic43C2312yes—
43C23×Dic43C2311yescharacteristic
44C22×C4×D43—42no—
45C22×C4×D43—42no—
46C22×C4×D43C2×C414yes—
47C22×C4×D43D414yes—
48C22×C4×D43Q814yes—
49C2×C4⋊Dic43—22no—
50C2×C4⋊Dic43—24no—
51C2×C4⋊Dic43—42no—
52C2×C4⋊Dic43—42no—
53C2×C4⋊Dic43—42no—
54C2×(C2×D43)⋊C4—24no—
55C2×(C2×D43)⋊C4—24no—
56C2×(C2×D43)⋊C4—24no—
57C2×(C2×D43)⋊C4—22no—
58C2×(C2×D43)⋊C4—22no—
59C2×(C2×D43)⋊C4—42no—
60C2×(C2×D43)⋊C4—42no—
61C2×(C2×D43)⋊C4—42no—
62C2×(C2×D43)⋊C4—42no—
63C2×(C2×D43)⋊C4C2×C418yes—
64C2×C4×Dic43—42no—
65C2×C4×Dic43—42no—
66C2×C4×Dic43C2×C418yes—
67C43⋊#95—22no—
68C43⋊#95—24no—
69C43⋊#95—24no—
70C43⋊#95—22no—
71C43⋊#95—22no—
72C43⋊#95—42no—
73C43⋊#95—42no—
74C43⋊#95—42no—
75C43⋊#95—42no—
76C43⋊#95C2×C414yes—
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2312yes—
79C23×C4×C43C2311yescharacteristic
80C23×C4×C43C2311yescharacteristic
81C23×C4×C43C2312yes—
82C2×C4⋊C4×C43—22no—
83C2×C4⋊C4×C43—24no—
84C2×C4⋊C4×C43—42no—
85C2×C4⋊C4×C43—42no—
86C2×C4⋊C4×C43—42no—
87#95×C43—22no—
88#95×C43—24no—
89#95×C43C2×C414yes—
90C24×C43C2411yescharacteristic
91C23×D43—22no—
92C23×D43—22no—
93C23×D43—21no—
94C23×D43—21no—
95C23×D43—22no—
96C23×D43—22no—
97C23×D43—21no—
98C23×D43—21no—
99C23×D43C22×C412yes—
100C23×D43C2×D412yes—
101C23×D43C2×Q812yes—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—22no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—21no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C22×C412yes—
126C22×C4×C43C22×C414yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×Q812yes—
129C22×C4×C43#4114yes—
130C22×C4×C43#4114yes—
131C22×Dic43—21no—
132C22×Dic43—21no—
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—21no—
146C22×Dic43—22no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—22no—
150C22×Dic43—22no—
151C22×Dic43—21no—
152C22×Dic43—22no—
153C22×Dic43—22no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43C22×C414yes—
157C22×Dic43C22×C412yes—
158C22×Dic43C2×D412yes—
159C22×Dic43C2×Q812yes—
160C2×C4×D43—48no—
161C2×C4×D43—44no—
162C2×C4×D43—44no—
163C2×C4×D43—48no—
164C2×C4×D43C4⋊C4116yescomplemented
165C4⋊C4×C43—44no—
166C4⋊C4×C43—48no—
167(C2×D43)⋊C4—216no—
168(C2×D43)⋊C4—44no—
169(C2×D43)⋊C4—44no—
170(C2×D43)⋊C4—48no—
171C4⋊Dic43—44no—
172C4⋊Dic43—48no—
173C4×Dic43—48no—
174C23×C43C23×C411yescharacteristic
175C23×C43C22×D411yescharacteristic
176C23×C43C22×Q811yescharacteristic
177C23×C43C2×#4112yes—
178C23×C43C2×#4112yes—
179C23×C43H(5,𝔽2)12yes—
180C23×C43H(5,𝔽2)11yescharacteristic
181C23×C43H(5,𝔽2)12yes—
182C23×C43H(5,𝔽2)11yescharacteristic
183C23×C432−1+411yescharacteristic
184C23×C432−1+411yescharacteristic
185C22×D43—24no—
186C22×D43—24no—
187C22×D43—22no—
188C22×D43—22no—
189C22×D43—22no—
190C22×D43—22no—
191C22×D43—24no—
192C22×D43—22no—
193C22×D43—22no—
194C22×D43—22no—
195C22×D43—22no—
196C22×D43—24no—
197C22×D43—22no—
198C22×D43—22no—
199C22×D43—42no—
200C22×D43—42no—
201C22×D43—42no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43C2×C4⋊C414yes—
208C2×C4×C43—24no—
209C2×C4×C43—24no—
210C2×C4×C43—24no—
211C2×C4×C43—22no—
212C2×C4×C43—22no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—24no—
217C2×C4×C43—24no—
218C2×C4×C43—41no—
219C2×C4×C43—42no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
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×C43C2×C4⋊C414yes—
236C2×C4×C43#11718yes—
237C2×Dic43—24no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—24no—
241C2×Dic43—24no—
242C2×Dic43—24no—
243C2×Dic43—24no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—41no—
249C2×Dic43—42no—
250C2×Dic43—41no—
251C2×Dic43—42no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—42no—
255C2×Dic43—41no—
256C2×Dic43—41no—
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×Dic43C2×C4⋊C414yes—
266C4×D43—416no—
267#14355—431nomaximal, Sylow
268C22×C43C22×C4⋊C411yescharacteristic
269C22×C43C2×#11712yes—
270C22×C43#51812yes—
271C22×C43#52011yescharacteristic
272C22×C43#52011yescharacteristic
273C22×C43#53211yescharacteristic
274C22×C43#53211yescharacteristic
275C22×C43#53312yes—
276C22×C43#53411yescharacteristic
277C22×C43#53411yescharacteristic
278C22×C43#53511yescharacteristic
279C22×C43#53611yescharacteristic
280C22×C43#53812yes—
281C22×C43#53812yes—
282C22×C43#53912yes—
283C22×C43#53912yes—
284C22×C43#54012yes—
285C22×C43#54012yes—
286C22×C43#54212yes—
287C22×C43#54212yes—
288C22×C43#54312yes—
289C22×C43#54411yescharacteristic
290C22×C43#54411yescharacteristic
291C2×D43—24no—
292C2×D43—24no—
293C2×D43—24no—
294C2×D43—44no—
295C2×D43—44no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—44no—
301C2×D43—44no—
302C4×C43—24no—
303C4×C43—28no—
304C4×C43—81no—
305C4×C43—82no—
306C4×C43—81no—
307Dic43—24no—
308Dic43—44no—
309Dic43—82no—
310Dic43—81no—
311Dic43—81no—
312C2×#381—431no—
313C2×#380—431no—
314C2×C4×C22⋊C4—431no—
315#1444—431no—
316#1444D4311yescharacteristic, complemented
317#1442—431no—
318#1442—431no—
319#1439—432no—
320#1439—432no—
321C4⋊#95—432no—
322#1434—432no—
323C2×C43#228511yescharacteristic
324C2×C43#231511yescharacteristic
325C2×C43#231711yescharacteristic
326C2×C43#231812yes—
327C2×C43#231912yes—
328C2×C43#266111yescharacteristic
329C2×C43#266111yescharacteristic
330C2×C43#266311yescharacteristic
331C2×C43#266311yescharacteristic
332C2×C43#266512yes—
333C2×C43#266712yes—
334D43—44no—
335C24×C4—431no—
336C22×C4⋊C4—432no—
337C22×C4⋊C4—431no—
338C22×C4⋊C4C2×D4312yes—
339C22×C4⋊C4C2×D4311yescharacteristic
340C22×C22⋊C4—432no—
341C22×C22⋊C4—432no—
342C22×C22⋊C4—431no—
343C22×C22⋊C4—431no—
344C22×C42—432no—
345#381—864no—
346#380—864no—
347C4×C22⋊C4—438no—
348C2×#95—431no—
349C2×#95—431no—
350C2×#95—432no—
351C2×#95—432no—
352C2×#95—431no—
353C2×#95—431no—
354C2×#95—432no—
355C2×#95—432no—
356C2×#95—432no—
357C2×#95—432no—
358C2×#95C2×D4312yes—
359C2×#95C2×D4311yescharacteristic
360C2×#95C2×D4311yescharacteristic
361C43#1435511yescharacteristic, complemented, Sylow
362C25—431no—
363C23×C4—431no—
364C23×C4—434no—
365C23×C4—434no—
366C23×C4—434no—
367C23×C4—432no—
368C23×C4—431no—
369C23×C4—432no—
370C23×C4—431no—
371C23×C4—1722no—
372C23×C4—1722no—
373C23×C4C22×D4311yescharacteristic
374C23×C4C22×D4312yes—
375C23×C4C22×D4311yescharacteristic
376C23×C4C22×D4311yescharacteristic
377C23×C4C22×D4312yes—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—862no—
384C2×C4⋊C4—864no—
385C2×C4⋊C4—1722no—
386C2×C4⋊C4—1722no—
387C2×C4⋊C4—1722no—
388C2×C22⋊C4—438no—
389C2×C22⋊C4—864no—
390C2×C22⋊C4—864no—
391C2×C22⋊C4—864no—
392C2×C22⋊C4—862no—
393C2×C22⋊C4—862no—
394C2×C22⋊C4—1722no—
395C2×C22⋊C4—1722no—
396C2×C22⋊C4—1722no—
397C2×C22⋊C4—1722no—
398C2×C42—438no—
399C2×C42—1722no—
400C2×C42—1722no—
401#95—22no—
402#95—24no—
403#95—434no—
404#95—864no—
405#95—862no—
406#95—862no—
407#95—862no—
408#95—864no—
409#95—1722no—
410#95—1722no—
411#95—1722no—
412#95—1722no—
413#95C4×D4314yes—
414C24—432no—
415C24—432no—
416C24—432no—
417C24—862no—
418C24—862no—
419C24—861no—
420C24—862no—
421C24—861no—
422C24—862no—
423C24—861no—
424C24—861no—
425C24C23×D4311yescharacteristic
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
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—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—432no—
450C22×C4—432no—
451C22×C4—432no—
452C22×C4—4316no—
453C22×C4—434no—
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—861no—
463C22×C4—861no—
464C22×C4—862no—
465C22×C4—862no—
466C22×C4—862no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—861no—
472C22×C4—861no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—862no—
476C22×C4—862no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—1728no—
480C22×C4—1724no—
481C22×C4—1724no—
482C22×C4—1728no—
483C22×C4C2×C4×D4312yes—
484C22×C4C2×C4×D4314yes—
485C22×C4D4×D4312yes—
486C22×C4#1062190014yes—
487C22×C4Q8×D4312yes—
488C22×C4#1062190214yes—
489C4⋊C4—44no—
490C4⋊C4—48no—
491C4⋊C4—1724no—
492C4⋊C4—1728no—
493C22⋊C4—8616no—
494C22⋊C4—1724no—
495C22⋊C4—1724no—
496C22⋊C4—1728no—
497C42—1728no—
498C23—434no—
499C23—864no—
500C23—864no—
501C23—862no—
502C23—862no—
503C23—862no—
504C23—862no—
505C23—864no—
506C23—862no—
507C23—862no—
508C23—862no—
509C23—862no—
510C23—864no—
511C23—862no—
512C23—862no—
513C23—1722no—
514C23—1722no—
515C23—1722no—
516C23—1722no—
517C23—1722no—
518C23—1722no—
519C23—1722no—
520C23—1722no—
521C23C22×C4×D4311yescharacteristic
522C23C2×D4×D4311yescharacteristic
523C23C2×Q8×D4311yescharacteristic
524C23C2×#1062190012yes—
525C23C2×#1062190212yes—
526C23#1306337012yes—
527C23#1306337011yescharacteristic
528C23#1306337112yes—
529C23#1306337111yescharacteristic
530C23#1306337211yescharacteristic
531C23#1306337311yescharacteristic
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
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—434no—
560C2×C4—864no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—864no—
564C2×C4—864no—
565C2×C4—864no—
566C2×C4—864no—
567C2×C4—17216no—
568C2×C4—1721no—
569C2×C4—1722no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4—1722no—
581C2×C4—1722no—
582C2×C4—1722no—
583C2×C4—1722no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4C4⋊C4×D4314yes—
590C2×C4#1306328318yes—
591C22—864no—
592C22—864no—
593C22—864no—
594C22—1722no—
595C22—1722no—
596C22—1722no—
597C22—1722no—
598C22—1724no—
599C22—1724no—
600C22—1724no—
601C22—1724no—
602C22C2×C4⋊C4×D4311yescharacteristic
603C22C2×#1306328312yes—
604C22#1458337112yes—
605C22#1458337811yescharacteristic
606C22#1458338111yescharacteristic
607C22#1458344711yescharacteristic
608C22#1458345011yescharacteristic
609C22#1458345412yes—
610C22#1458345911yescharacteristic
611C22#1458346011yescharacteristic
612C22#1458346511yescharacteristic
613C22#1458347211yescharacteristic
614C22#1458348412yes—
615C22#1458348912yes—
616C22#1458349312yes—
617C22#1458349812yes—
618C22#1458350212yes—
619C22#1458350512yes—
620C22#1458352212yes—
621C22#1458352312yes—
622C22#1458352412yes—
623C22#1458352611yescharacteristic
624C22#1458352911yescharacteristic
625C4—24no—
626C4—28no—
627C4—81no—
628C4—82no—
629C4—81no—
630C4—864no—
631C4—3441no—
632C4—3442no—
633C4—3441no—
634C4—1724no—
635C2—1724no—
636C2#1913700011yescharacteristic
637C2#1913720611yescharacteristic
638C2#1913721711yescharacteristic
639C2#1913722312yes—
640C2#1913723412yes—
641C2#1914072611yescharacteristic
642C2#1914072811yescharacteristic
643C2#1914074811yescharacteristic
644C2#1914075011yescharacteristic
645C2#1914077012yes—
646C2#1914079412yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1444C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1444D43
hypocenterC43#14355
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. #19132860C2semidirect
5. #19132854C2semidirect
6. #19132851C2semidirect
9. #19132824C2semidirect
10. #19132820C2semidirect
11. C43×#1444C2semidirect
22. #14582746C4semidirect
164. C2×C4×D43C4⋊C4semidirect
316. #1444D43semidirect
361. C43#14355semidirect

Maximal subgroups

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

subgroupindex
C2×#145827612
C2×#145827562
C2×#145827462
#191328602
#191328542
#191328512
#191328412
#191328372
#191328242
#191328202
C43×#14442
#1435543