Finite Group Databasebeta

← #25027317

Subgroups — #25027317

Order 11008.

1326 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582836C211yesmaximal, characteristic
2C2×#14582795C211yesmaximal, characteristic, complemented
3C2×#14582788C211yesmaximal, characteristic
4#19132864C211yesmaximal, characteristic, complemented
5#19132847C212yesmaximal, complemented
6#19132847C212yesmaximal, complemented
7#19132843C212yesmaximal
8#19132839C212yesmaximal
9#19132837C211yesmaximal, characteristic
10#19132820C211yesmaximal, characteristic, complemented
11C43×#1442C211yesmaximal, characteristic, complemented
12C22×C4⋊Dic43C2211yescharacteristic
13C22×C4⋊Dic43C2212yes—
14C22×Dic43⋊C4C2211yescharacteristic
15C22×Dic43⋊C4C2212yes—
16C22×(C2×D43)⋊C4C2211yescharacteristic
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2211yescharacteristic
19C22×(C2×D43)⋊C4C2212yes—
20C22×(C2×D43)⋊C4C2212yes—
21C22×C4×Dic43C2211yescharacteristic
22#14582836C418yescomplemented
23#14582795—24no—
24#14582788—24no—
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2212yes—
33C22×C4⋊C4×C43C2211yescharacteristic
34C2×#95×C43C2211yescharacteristic
35C2×#95×C43C2212yes—
36C2×#95×C43C2212yes—
37C2×#95×C43C2211yescharacteristic
38C24×D43C2311yescharacteristic
39C23×Dic43C2312yes—
40C23×Dic43C2311yescharacteristic
41C23×Dic43C2312yes—
42C23×Dic43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C2×C4⋊Dic43—22no—
45C2×C4⋊Dic43—22no—
46C2×C4⋊Dic43—42no—
47C2×C4⋊Dic43—42no—
48C2×C4⋊Dic43C2×C414yes—
49C2×C4⋊Dic43C2×C418yes—
50C2×Dic43⋊C4—22no—
51C2×Dic43⋊C4—24no—
52C2×Dic43⋊C4—42no—
53C2×Dic43⋊C4—42no—
54C2×Dic43⋊C4—42no—
55C2×(C2×D43)⋊C4—22no—
56C2×(C2×D43)⋊C4—22no—
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)⋊C4—42no—
64C2×(C2×D43)⋊C4—42no—
65C2×(C2×D43)⋊C4—42no—
66C2×(C2×D43)⋊C4C2×C414yes—
67C2×(C2×D43)⋊C4C2×C418yes—
68C2×C4×Dic43—42no—
69C2×C4×Dic43D414yes—
70C43⋊#95—22no—
71C43⋊#95—22no—
72C43⋊#95—24no—
73C43⋊#95—42no—
74C43⋊#95—42no—
75C43⋊#95—42no—
76C43⋊#95—42no—
77C43⋊#95—42no—
78C23×C4×C43C2312yes—
79C23×C4×C43C2311yescharacteristic
80C23×C4×C43C2311yescharacteristic
81C23×C4×C43C2312yes—
82C23×C4×C43C2311yescharacteristic
83C2×C4⋊C4×C43—22no—
84C2×C4⋊C4×C43—42no—
85#95×C43—22no—
86#95×C43—42no—
87#95×C43—42no—
88#95×C43C2×C414yes—
89C24×C43C2411yescharacteristic
90C23×D43—21no—
91C23×D43—21no—
92C23×D43—22no—
93C23×D43—22no—
94C23×D43—22no—
95C23×D43—21no—
96C23×D43—21no—
97C23×D43—21no—
98C23×D43—22no—
99C23×D43—21no—
100C23×D43C22×C412yes—
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—22no—
107C22×C4×C43—22no—
108C22×C4×C43—22no—
109C22×C4×C43—21no—
110C22×C4×C43—22no—
111C22×C4×C43—22no—
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—21no—
123C22×C4×C43—22no—
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43C22×C414yes—
127C22×C4×C43C22×C412yes—
128C22×C4×C43C2×D412yes—
129C22×C4×C43#4112yes—
130C22×Dic43—21no—
131C22×Dic43—22no—
132C22×Dic43—21no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—21no—
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—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43C22×C414yes—
156C22×Dic43C22×C412yes—
157C22×Dic43C2×D412yes—
158C22×Dic43C2×D412yes—
159C4⋊C4×C43—44no—
160(C2×D43)⋊C4—28no—
161(C2×D43)⋊C4—48no—
162(C2×D43)⋊C4—44no—
163(C2×D43)⋊C4—44no—
164(C2×D43)⋊C4—48no—
165C4⋊Dic43—28no—
166C4⋊Dic43—48no—
167Dic43⋊C4—48no—
168Dic43⋊C4—44no—
169C4×Dic43—44no—
170C23×C43C23×C411yescharacteristic
171C23×C43C22×D411yescharacteristic
172C23×C43C2×#4111yescharacteristic
173C23×C43H(5,𝔽2)12yes—
174C23×C43H(5,𝔽2)11yescharacteristic
175C23×C43H(5,𝔽2)12yes—
176C23×C43H(5,𝔽2)12yes—
177C23×C432−1+411yescharacteristic
178C23×C432−1+412yes—
179C23×C432−1+411yescharacteristic
180C23×C432−1+411yescharacteristic
181C22×D43—22no—
182C22×D43—24no—
183C22×D43—22no—
184C22×D43—24no—
185C22×D43—22no—
186C22×D43—41no—
187C22×D43—41no—
188C22×D43—41no—
189C22×D43—41no—
190C22×D43—41no—
191C22×D43—41no—
192C22×D43—42no—
193C22×D43—42no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—42no—
197C22×D43—42no—
198C22×D43—42no—
199C22×D43—42no—
200C22×D43—42no—
201C22×D43—42no—
202C22×D43—42no—
203C22×D43—42no—
204C2×C4×C43—24no—
205C2×C4×C43—22no—
206C2×C4×C43—22no—
207C2×C4×C43—24no—
208C2×C4×C43—24no—
209C2×C4×C43—24no—
210C2×C4×C43—24no—
211C2×C4×C43—42no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
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×C43C4×D414yes—
233C2×Dic43—24no—
234C2×Dic43—22no—
235C2×Dic43—24no—
236C2×Dic43—24no—
237C2×Dic43—24no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—41no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—41no—
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—
262#14628—431nomaximal, Sylow
263C22×C43C2×C4×D411yescharacteristic
264C22×C43#51812yes—
265C22×C43#51911yescharacteristic
266C22×C43#52012yes—
267C22×C43#52011yescharacteristic
268C22×C43#53411yescharacteristic
269C22×C43#53511yescharacteristic
270C22×C43#53511yescharacteristic
271C22×C43#53611yescharacteristic
272C22×C43#53611yescharacteristic
273C22×C43#53711yescharacteristic
274C22×C43#53912yes—
275C22×C43#54012yes—
276C22×C43#54111yescharacteristic
277C22×C43#54211yescharacteristic
278C22×C43#56012yes—
279C22×C43#56212yes—
280C22×C43#56212yes—
281C22×C43#56212yes—
282C22×C43#56212yes—
283C22×C43#56312yes—
284C22×C43#56312yes—
285C22×C43#56312yes—
286C2×D43—42no—
287C2×D43—42no—
288C2×D43—42no—
289C2×D43—44no—
290C2×D43—44no—
291C2×D43—81no—
292C2×D43—81no—
293C2×D43—81no—
294C2×D43—82no—
295C2×D43—82no—
296C2×D43—81no—
297C4×C43—24no—
298C4×C43—44no—
299C4×C43—81no—
300C4×C43—81no—
301C4×C43—82no—
302Dic43—42no—
303Dic43—44no—
304Dic43—42no—
305Dic43—42no—
306Dic43—82no—
307C2×#399—431no—
308C2×#389—431no—
309C2×#388—431no—
310#1445—431no—
311#1442D4311yescharacteristic, complemented
312#1441—432no—
313#1441—432no—
314#1440—432no—
315#1439—432no—
316#1439—431no—
317#1434—431no—
318C2×C43#232211yescharacteristic
319C2×C43#232311yescharacteristic
320C2×C43#232811yescharacteristic
321C2×C43#237612yes—
322C2×C43#237812yes—
323C2×C43#281311yescharacteristic
324C2×C43#281611yescharacteristic
325C2×C43#282011yescharacteristic
326C2×C43#282111yescharacteristic
327C2×C43#283612yes—
328C2×C43#283712yes—
329D43—82no—
330C22×C4⋊C4—431no—
331C22×C4⋊C4—432no—
332C22×C4⋊C4—432no—
333C22×C4⋊C4—431no—
334C22×C4⋊C4C2×D4311yescharacteristic
335C22×C22⋊C4—431no—
336C22×C22⋊C4—432no—
337C22×C22⋊C4—431no—
338C22×C22⋊C4—431no—
339C22×C22⋊C4—432no—
340C22×C42—431no—
341#399—438no—
342#389—864no—
343#388—864no—
344C2×#95—431no—
345C2×#95—432no—
346C2×#95—431no—
347C2×#95—432no—
348C2×#95—432no—
349C2×#95—432no—
350C2×#95—432no—
351C2×#95—432no—
352C2×#95C2×D4311yescharacteristic
353C2×#95C2×D4312yes—
354C2×#95C2×D4312yes—
355C2×#95C2×D4311yescharacteristic
356C43#1462811yescharacteristic, complemented, Sylow
357C25—431no—
358C23×C4—431no—
359C23×C4—432no—
360C23×C4—431no—
361C23×C4—431no—
362C23×C4—432no—
363C23×C4C22×D4312yes—
364C23×C4C22×D4311yescharacteristic
365C23×C4C22×D4311yescharacteristic
366C23×C4C22×D4312yes—
367C23×C4C22×D4311yescharacteristic
368C2×C4⋊C4—22no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4—434no—
371C2×C4⋊C4—438no—
372C2×C4⋊C4—862no—
373C2×C4⋊C4—862no—
374C2×C4⋊C4—862no—
375C2×C4⋊C4—864no—
376C2×C4⋊C4—1722no—
377C2×C4⋊C4—1722no—
378C2×C4⋊C4—1722no—
379C2×C4⋊C4—1722no—
380C2×C4⋊C4—1722no—
381C2×C22⋊C4—434no—
382C2×C22⋊C4—438no—
383C2×C22⋊C4—862no—
384C2×C22⋊C4—862no—
385C2×C22⋊C4—862no—
386C2×C22⋊C4—862no—
387C2×C22⋊C4—1722no—
388C2×C22⋊C4—1722no—
389C2×C22⋊C4—1722no—
390C2×C22⋊C4—1722no—
391C2×C22⋊C4—1722no—
392C2×C22⋊C4—1722no—
393C2×C22⋊C4—1722no—
394C2×C42—434no—
395C2×C42—1722no—
396#95—22no—
397#95—42no—
398#95—42no—
399#95—862no—
400#95—864no—
401#95—862no—
402#95—1722no—
403#95—1722no—
404#95—1722no—
405#95—1722no—
406#95—1722no—
407#95C4×D4314yes—
408C24—432no—
409C24—861no—
410C24—861no—
411C24—861no—
412C24—862no—
413C24—862no—
414C24—862no—
415C24—861no—
416C24—861no—
417C24—862no—
418C24—861no—
419C24C23×D4311yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—432no—
446C22×C4—434no—
447C22×C4—432no—
448C22×C4—432no—
449C22×C4—861no—
450C22×C4—862no—
451C22×C4—861no—
452C22×C4—862no—
453C22×C4—861no—
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—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—862no—
470C22×C4—862no—
471C22×C4—862no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4C2×C4×D4314yes—
475C22×C4C2×C4×D4312yes—
476C22×C4D4×D4312yes—
477C22×C4#1062190212yes—
478C4⋊C4—44no—
479C4⋊C4—868no—
480C4⋊C4—1728no—
481C4⋊C4—1724no—
482C4⋊C4—1728no—
483C22⋊C4—868no—
484C22⋊C4—1728no—
485C22⋊C4—1724no—
486C22⋊C4—1724no—
487C22⋊C4—1728no—
488C42—1724no—
489C23—862no—
490C23—864no—
491C23—862no—
492C23—862no—
493C23—864no—
494C23—1722no—
495C23—1722no—
496C23—1722no—
497C23—1722no—
498C23—1722no—
499C23—1722no—
500C23—1722no—
501C23—1722no—
502C23—1721no—
503C23—1721no—
504C23—1721no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1722no—
509C23—1722no—
510C23—1721no—
511C23—1721no—
512C23C22×C4×D4311yescharacteristic
513C23C2×D4×D4311yescharacteristic
514C23C2×#1062190211yescharacteristic
515C23#1306337011yescharacteristic
516C23#1306337012yes—
517C23#1306337112yes—
518C23#1306337112yes—
519C23#1306337211yescharacteristic
520C23#1306337211yescharacteristic
521C23#1306337212yes—
522C23#1306337311yescharacteristic
523C2×C4—24no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—862no—
552C2×C4—864no—
553C2×C4—864no—
554C2×C4—864no—
555C2×C4—864no—
556C2×C4—862no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4—1722no—
573C2×C4—1722no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1722no—
577C2×C4—1722no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4#1306328714yes—
581C22—3441no—
582C22—3442no—
583C22—3442no—
584C22—3441no—
585C22—3441no—
586C22—3441no—
587C22—1722no—
588C22—1724no—
589C22—1724no—
590C22—1722no—
591C22—1722no—
592C22C2×#1306328711yescharacteristic
593C22#1458337312yes—
594C22#1458337511yescharacteristic
595C22#1458337811yescharacteristic
596C22#1458337812yes—
597C22#1458345911yescharacteristic
598C22#1458346711yescharacteristic
599C22#1458346711yescharacteristic
600C22#1458347111yescharacteristic
601C22#1458347211yescharacteristic
602C22#1458347811yescharacteristic
603C22#1458349812yes—
604C22#1458350512yes—
605C22#1458351211yescharacteristic
606C22#1458352311yescharacteristic
607C22#1458363712yes—
608C22#1458364312yes—
609C22#1458364512yes—
610C22#1458364612yes—
611C22#1458364612yes—
612C22#1458365112yes—
613C22#1458365112yes—
614C22#1458365312yes—
615C4—24no—
616C4—44no—
617C4—82no—
618C4—81no—
619C4—81no—
620C4—3442no—
621C4—1722no—
622C4—1724no—
623C4—1722no—
624C4—1722no—
625C2—3442no—
626C2#1913726311yescharacteristic
627C2#1913727511yescharacteristic
628C2#1913731811yescharacteristic
629C2#1913774112yes—
630C2#1913775912yes—
631C2#1914259611yescharacteristic
632C2#1914262111yescharacteristic
633C2#1914265111yescharacteristic
634C2#1914266011yescharacteristic
635C2#1914280012yes—
636C2#1914281512yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1442C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1442D43
hypocenterC43#14628
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. C2×#14582795C2semidirect
4. #19132864C2semidirect
5. #19132847C2semidirect
6. #19132847C2semidirect
10. #19132820C2semidirect
11. C43×#1442C2semidirect
22. #14582836C4semidirect
311. #1442D43semidirect
356. C43#14628semidirect

Maximal subgroups

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

subgroupindex
C2×#145828362
C2×#145827952
C2×#145827882
#191328642
#191328472
#191328432
#191328392
#191328372
#191328202
C43×#14422
#1462843