Finite Group Databasebeta

← #25024639

Subgroups — #25024639

Order 11008.

1866 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582787C212yesmaximal, complemented
2C2×#14582779C211yesmaximal, characteristic
3C2×#14582757C212yesmaximal, complemented
4#19132853C212yesmaximal, complemented
5#19132838C212yesmaximal, complemented
6#19132836C211yesmaximal, characteristic
7#19132832C212yesmaximal, complemented
8#19132830C212yesmaximal, complemented
9C43×#1438C211yesmaximal, characteristic
10C24×Dic43C2211yescharacteristic
11C22×Dic43⋊C4C2212yes—
12C22×Dic43⋊C4C2212yes—
13C22×C22⋊Dic43C2211yescharacteristic
14C22×C22⋊Dic43C2212yes—
15C22×C22⋊Dic43C2212yes—
16C22×C22⋊Dic43C2211yescharacteristic
17C22×C22⋊Dic43C2211yescharacteristic
18C22×C4×Dic43C2212yes—
19#14582787—28no—
20#14582779C418yescomplemented
21#14582757—28no—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C23×D4×C43C2211yescharacteristic
30C22×C22⋊C4×C43C2212yes—
31C22×C22⋊C4×C43C2212yes—
32C2×#95×C43C2211yescharacteristic
33C2×#95×C43C2211yescharacteristic
34C23×Dic43—24no—
35C23×Dic43—24no—
36C23×Dic43—41no—
37C23×Dic43—41no—
38C23×Dic43C2×C414yes—
39C23×Dic43C2312yes—
40C23×Dic43C2312yes—
41C23×Dic43C2312yes—
42C23×Dic43C2312yes—
43C2×Dic43⋊C4—24no—
44C2×Dic43⋊C4—24no—
45C2×Dic43⋊C4—24no—
46C2×Dic43⋊C4—24no—
47C2×Dic43⋊C4—42no—
48C2×Dic43⋊C4—42no—
49C2×C22⋊Dic43—24no—
50C2×C22⋊Dic43—24no—
51C2×C22⋊Dic43—24no—
52C2×C22⋊Dic43—24no—
53C2×C22⋊Dic43—24no—
54C2×C22⋊Dic43—42no—
55C2×C22⋊Dic43—42no—
56C2×C22⋊Dic43—41no—
57C2×C22⋊Dic43—42no—
58C2×C22⋊Dic43—41no—
59C2×C22⋊Dic43C2×C418yes—
60C2×C22⋊Dic43C2×C414yes—
61C2×C4×Dic43—24no—
62C2×C4×Dic43—42no—
63C2×C4×Dic43—42no—
64C43⋊#95—24no—
65C43⋊#95—24no—
66C43⋊#95—42no—
67C43⋊#95—42no—
68C43⋊#95—42no—
69C43⋊#95C2×C418yes—
70C43⋊#95D418yescomplemented
71C25×C43C2311yescharacteristic
72C25×C43C2311yescharacteristic
73C22×D4×C43—24no—
74C22×D4×C43—41no—
75C22×D4×C43—41no—
76C22×D4×C43—42no—
77C22×D4×C43C2×C414yes—
78C23×C4×C43C2312yes—
79C23×C4×C43C2311yescharacteristic
80C23×C4×C43C2312yes—
81C2×C22⋊C4×C43—24no—
82C2×C22⋊C4×C43—24no—
83C2×C22⋊C4×C43—24no—
84C2×C22⋊C4×C43—42no—
85C2×C22⋊C4×C43—42no—
86C2×C22⋊C4×C43—42no—
87#95×C43—41no—
88#95×C43—41no—
89C24×C43—22no—
90C24×C43—22no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—21no—
94C24×C43—21no—
95C24×C43—22no—
96C24×C43—22no—
97C24×C43—22no—
98C24×C43—22no—
99C24×C43—22no—
100C24×C43—22no—
101C24×C43—21no—
102C24×C43—21no—
103C24×C43—22no—
104C24×C43C22×C412yes—
105C24×C43C22×C412yes—
106C24×C43#4114yes—
107C24×C43C2411yescharacteristic
108C2×D4×C43—28no—
109C2×D4×C43—44no—
110C2×D4×C43—44no—
111C2×D4×C43—48no—
112C2×D4×C43—48no—
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—21no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—22no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C2×D414yes—
132C22×Dic43—216no—
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—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—44no—
157C22×Dic43—44no—
158C22×Dic43—48no—
159C22×Dic43—44no—
160C22×Dic43C22×C414yes—
161C22×Dic43C22×C414yes—
162C22×Dic43C2×D414yes—
163C22×Dic43C2×D414yes—
164C22×Dic43#4114yes—
165C22⋊C4×C43—48no—
166C22⋊C4×C43—48no—
167C22⋊Dic43—216no—
168C22⋊Dic43—44no—
169C22⋊Dic43—48no—
170C22⋊Dic43—44no—
171C22⋊Dic43—44no—
172Dic43⋊C4—48no—
173Dic43⋊C4—48no—
174C4×Dic43—48no—
175C23×C43—24no—
176C23×C43—22no—
177C23×C43—22no—
178C23×C43—24no—
179C23×C43—24no—
180C23×C43—24no—
181C23×C43—24no—
182C23×C43—24no—
183C23×C43—24no—
184C23×C43—24no—
185C23×C43—22no—
186C23×C43—24no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—24no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—41no—
195C23×C43—42no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—42no—
199C23×C43—41no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—42no—
205C23×C43—42no—
206C23×C43—41no—
207C23×C43—42no—
208C23×C43—42no—
209C23×C43—42no—
210C23×C43—41no—
211C23×C43—42no—
212C23×C43—42no—
213C23×C43—41no—
214C23×C43—42no—
215C23×C43—41no—
216C23×C43#11714yes—
217C23×C43C23×C411yescharacteristic
218C23×C43C22×D412yes—
219C23×C43C2×#4112yes—
220C23×C43C2×#4112yes—
221C23×C43H(5,𝔽2)12yes—
222C23×C43H(5,𝔽2)11yescharacteristic
223C23×C43H(5,𝔽2)11yescharacteristic
224C23×C43H(5,𝔽2)12yes—
225C23×C432−1+412yes—
226D4×C43—416no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—22no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—42no—
238C2×C4×C43—42no—
239C2×C4×C43—42no—
240C2×C4×C43—42no—
241C2×C4×C43—42no—
242C2×C4×C43—42no—
243C2×C4×C43—42no—
244C2×C4×C43—42no—
245C2×C4×C43—42no—
246C2×Dic43—24no—
247C2×Dic43—24no—
248C2×Dic43—24no—
249C2×Dic43—24no—
250C2×Dic43—24no—
251C2×Dic43—24no—
252C2×Dic43—24no—
253C2×Dic43—24no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—24no—
257C2×Dic43—24no—
258C2×Dic43—416no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43—42no—
265C2×Dic43—42no—
266C2×Dic43—42no—
267C2×Dic43—42no—
268C2×Dic43—42no—
269C2×Dic43—42no—
270C2×Dic43—42no—
271C2×Dic43—42no—
272C2×Dic43—42no—
273C2×Dic43—42no—
274C2×Dic43C4×D418yes—
275#14410—431nomaximal, Sylow
276C22×C43—24no—
277C22×C43—28no—
278C22×C43—44no—
279C22×C43—42no—
280C22×C43—42no—
281C22×C43—44no—
282C22×C43—44no—
283C22×C43—44no—
284C22×C43—44no—
285C22×C43—42no—
286C22×C43—44no—
287C22×C43—44no—
288C22×C43—42no—
289C22×C43—42no—
290C22×C43—82no—
291C22×C43—82no—
292C22×C43—82no—
293C22×C43—82no—
294C22×C43C2×#11711yescharacteristic
295C22×C43C2×C4×D412yes—
296C22×C43#51811yescharacteristic
297C22×C43#51811yescharacteristic
298C22×C43#52012yes—
299C22×C43#53512yes—
300C22×C43#53712yes—
301C22×C43#53812yes—
302C22×C43#53812yes—
303C22×C43#54012yes—
304C22×C43#54212yes—
305C22×C43D4211yescharacteristic
306C22×C43#54612yes—
307C22×C43#54612yes—
308C22×C43#54812yes—
309C22×C43#55111yescharacteristic
310C22×C43#55212yes—
311C22×C43#55312yes—
312C22×C43#56011yescharacteristic
313C22×C43#56212yes—
314C22×C43#56311yescharacteristic
315C4×C43—42no—
316C4×C43—44no—
317C4×C43—82no—
318Dic43—28no—
319Dic43—44no—
320Dic43—44no—
321Dic43—82no—
322C2×#388—432no—
323C2×#386—431no—
324C2×#380—432no—
325#1442—432no—
326#1439—432no—
327#1438—431no—
328#1438D4311yescharacteristic
329#1437—432no—
330#1436—432no—
331C2×C43—44no—
332C2×C43—82no—
333C2×C43#231211yescharacteristic
334C2×C43#232412yes—
335C2×C43#235212yes—
336C2×C43#235811yescharacteristic
337C2×C43#237611yescharacteristic
338C2×C43#267612yes—
339C2×C43#270212yes—
340C2×C43#270312yes—
341C2×C43#274112yes—
342C23×D4C2×D4311yescharacteristic
343C24×C4—431no—
344C22×C4⋊C4—432no—
345C22×C4⋊C4—432no—
346C22×C22⋊C4—432no—
347C22×C22⋊C4—431no—
348C22×C22⋊C4—432no—
349C22×C22⋊C4—431no—
350C22×C22⋊C4—431no—
351C22×C22⋊C4C2×D4312yes—
352C22×C22⋊C4C2×D4312yes—
353C22×C42—432no—
354#388—868no—
355#386—438no—
356#380—868no—
357C2×#95—432no—
358C2×#95—432no—
359C2×#95—432no—
360C2×#95—432no—
361C2×#95—432no—
362C2×#95—432no—
363C2×#95—432no—
364C2×#95C2×D4311yescharacteristic
365C2×#95C2×D4311yescharacteristic
366C43#1441011yescharacteristic, complemented, Sylow
367C25C22×D4311yescharacteristic
368C25C22×D4311yescharacteristic
369C22×D4—24no—
370C22×D4—41no—
371C22×D4—41no—
372C22×D4—42no—
373C22×D4C4×D4314yes—
374C23×C4—432no—
375C23×C4—432no—
376C23×C4—432no—
377C23×C4—434no—
378C23×C4—432no—
379C23×C4—864no—
380C23×C4—864no—
381C23×C4—1721no—
382C23×C4—1721no—
383C23×C4C22×D4312yes—
384C23×C4C22×D4311yescharacteristic
385C23×C4C22×D4312yes—
386C2×C4⋊C4—864no—
387C2×C4⋊C4—864no—
388C2×C4⋊C4—864no—
389C2×C4⋊C4—864no—
390C2×C4⋊C4—1722no—
391C2×C4⋊C4—1722no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—24no—
394C2×C22⋊C4—24no—
395C2×C22⋊C4—42no—
396C2×C22⋊C4—42no—
397C2×C22⋊C4—42no—
398C2×C22⋊C4—438no—
399C2×C22⋊C4—434no—
400C2×C22⋊C4—864no—
401C2×C22⋊C4—864no—
402C2×C22⋊C4—864no—
403C2×C22⋊C4—864no—
404C2×C22⋊C4—864no—
405C2×C22⋊C4—1722no—
406C2×C22⋊C4—1721no—
407C2×C22⋊C4—1722no—
408C2×C22⋊C4—1722no—
409C2×C22⋊C4—1721no—
410C2×C42—864no—
411C2×C42—1722no—
412C2×C42—1722no—
413#95—41no—
414#95—41no—
415#95—438no—
416#95—438no—
417#95—864no—
418#95—864no—
419#95—1722no—
420#95—1722no—
421#95—1722no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—21no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24—21no—
435C24—21no—
436C24—22no—
437C24C2×C4×D4312yes—
438C24C2×C4×D4312yes—
439C24#1062190014yes—
440C24C23×D4311yescharacteristic
441C2×D4—28no—
442C2×D4—44no—
443C2×D4—44no—
444C2×D4—48no—
445C2×D4—48no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—434no—
464C22×C4—434no—
465C22×C4—434no—
466C22×C4—434no—
467C22×C4—434no—
468C22×C4—8616no—
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—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—862no—
483C22×C4—862no—
484C22×C4—862no—
485C22×C4—862no—
486C22×C4—862no—
487C22×C4—862no—
488C22×C4—862no—
489C22×C4—862no—
490C22×C4—862no—
491C22×C4—862no—
492C22×C4—1724no—
493C22×C4—1724no—
494C22×C4—1724no—
495C22×C4—1728no—
496C22×C4C2×C4×D4312yes—
497C22×C4D4×D4314yes—
498C4⋊C4—1728no—
499C4⋊C4—1728no—
500C22⋊C4—48no—
501C22⋊C4—48no—
502C22⋊C4—8616no—
503C22⋊C4—1724no—
504C22⋊C4—1724no—
505C22⋊C4—1728no—
506C22⋊C4—1724no—
507C42—1728no—
508C23—24no—
509C23—24no—
510C23—24no—
511C23—24no—
512C23—22no—
513C23—22no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—24no—
520C23—22no—
521C23—22no—
522C23—24no—
523C23—41no—
524C23—41no—
525C23—42no—
526C23—41no—
527C23—42no—
528C23—42no—
529C23—42no—
530C23—42no—
531C23—41no—
532C23—42no—
533C23—42no—
534C23—41no—
535C23—42no—
536C23—42no—
537C23—41no—
538C23—42no—
539C23—41no—
540C23—42no—
541C23—42no—
542C23—42no—
543C23—42no—
544C23—42no—
545C23—42no—
546C23—41no—
547C23—42no—
548C23—42no—
549C23#1306328114yes—
550C23C22×C4×D4311yescharacteristic
551C23C2×D4×D4312yes—
552C23#41×D4312yes—
553C23C2×#1062190012yes—
554C23#1306337011yescharacteristic
555C23#1306337012yes—
556C23#1306337011yescharacteristic
557C23#1306337012yes—
558C23#1306337212yes—
559D4—416no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—42no—
567C2×C4—42no—
568C2×C4—42no—
569C2×C4—42no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—42no—
573C2×C4—42no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—42no—
579C2×C4—438no—
580C2×C4—864no—
581C2×C4—864no—
582C2×C4—864no—
583C2×C4—864no—
584C2×C4—864no—
585C2×C4—864no—
586C2×C4—864no—
587C2×C4—864no—
588C2×C4—864no—
589C2×C4—864no—
590C2×C4—864no—
591C2×C4—864no—
592C2×C4—17216no—
593C2×C4—1722no—
594C2×C4—1722no—
595C2×C4—1722no—
596C2×C4—1722no—
597C2×C4—1722no—
598C2×C4—1722no—
599C2×C4—1722no—
600C2×C4—1722no—
601C2×C4—1722no—
602C2×C4—1722no—
603C2×C4—1722no—
604C2×C4—1722no—
605C2×C4—1722no—
606C2×C4—1722no—
607C2×C4—1722no—
608C22—24no—
609C22—28no—
610C22—44no—
611C22—44no—
612C22—42no—
613C22—44no—
614C22—44no—
615C22—44no—
616C22—42no—
617C22—44no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—44no—
622C22—82no—
623C22—82no—
624C22—82no—
625C22—82no—
626C22C2×#1306328111yescharacteristic
627C22C4×D4×D4312yes—
628C22#1458337211yescharacteristic
629C22#1458337211yescharacteristic
630C22#1458337812yes—
631C22#1458346412yes—
632C22#1458347812yes—
633C22#1458348412yes—
634C22#1458348412yes—
635C22#1458349912yes—
636C22#1458351712yes—
637C22#1458353411yescharacteristic
638C22#1458353612yes—
639C22#1458353812yes—
640C22#1458355512yes—
641C22#1458357911yescharacteristic
642C22#1458358612yes—
643C22#1458359212yes—
644C22#1458363611yescharacteristic
645C22#1458364412yes—
646C22#1458364911yescharacteristic
647C4—44no—
648C4—42no—
649C4—82no—
650C4—868no—
651C4—3442no—
652C4—1724no—
653C4—1724no—
654C2—44no—
655C2—82no—
656C2#1913719111yescharacteristic
657C2#1913728512yes—
658C2#1913752212yes—
659C2#1913757611yescharacteristic
660C2#1913774511yescharacteristic
661C2#1914090112yes—
662C2#1914122812yes—
663C2#1914124312yes—
664C2#1914170312yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1438C2
socle, cosocleC24×C43C24
prime radicalC23×D4×C43C22
hypercenter#1438D43
hypocenterC43#14410
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C2×#14582787C2semidirect
3. C2×#14582757C2semidirect
4. #19132853C2semidirect
5. #19132838C2semidirect
7. #19132832C2semidirect
8. #19132830C2semidirect
20. #14582779C4semidirect
70. C43⋊#95D4semidirect
366. C43#14410semidirect

Maximal subgroups

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

subgroupindex
C2×#145827872
C2×#145827792
C2×#145827572
#191328532
#191328382
#191328362
#191328322
#191328302
C43×#14382
#1441043