Finite Group Databasebeta

← #25027727

Subgroups — #25027727

Order 11008.

1486 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×#14582761C211yesmaximal, characteristic
2C2×#14582758C211yesmaximal, characteristic
3C2×#14582756C211yesmaximal, characteristic
4#19132858C211yesmaximal, characteristic, complemented
5#19132858C212yesmaximal, complemented
6#19132852C211yesmaximal, characteristic, complemented
7#19132851C211yesmaximal, characteristic, complemented
8#19132850C212yesmaximal, complemented
9#19132839C212yesmaximal
10#19132837C212yesmaximal
11C43×#1444C211yesmaximal, characteristic, complemented
12C23×C4×D43C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×Dic43⋊C4C2211yescharacteristic
15C22×Dic43⋊C4C2211yescharacteristic
16C22×Dic43⋊C4C2212yes—
17C22×(C2×D43)⋊C4C2211yescharacteristic
18C22×(C2×D43)⋊C4C2212yes—
19C22×(C2×D43)⋊C4C2211yescharacteristic
20C22×(C2×D43)⋊C4C2212yes—
21#14582761C418yescomplemented
22#14582758—24no—
23#14582756—24no—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2211yescharacteristic
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2212yes—
29C2×C43⋊#95C2212yes—
30C2×C43⋊#95C2212yes—
31C2×C43⋊#95C2212yes—
32C2×C43⋊#95C2211yescharacteristic
33C22×C4⋊C4×C43C2211yescharacteristic
34C22×C4⋊C4×C43C2212yes—
35C2×#95×C43C2211yescharacteristic
36C2×#95×C43C2212yes—
37C2×#95×C43C2211yescharacteristic
38C24×D43C2311yescharacteristic
39C23×Dic43C2311yescharacteristic
40C23×Dic43C2311yescharacteristic
41C23×Dic43C2312yes—
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—42no—
51C2×Dic43⋊C4—22no—
52C2×Dic43⋊C4—22no—
53C2×Dic43⋊C4—42no—
54C2×Dic43⋊C4—42no—
55C2×Dic43⋊C4—42no—
56C2×Dic43⋊C4—42no—
57C2×Dic43⋊C4—42no—
58C2×(C2×D43)⋊C4—24no—
59C2×(C2×D43)⋊C4—22no—
60C2×(C2×D43)⋊C4—22no—
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)⋊C4—42no—
67C2×(C2×D43)⋊C4C2×C418yes—
68C43⋊#95—22no—
69C43⋊#95—24no—
70C43⋊#95—42no—
71C43⋊#95—42no—
72C43⋊#95—42no—
73C43⋊#95—42no—
74C43⋊#95—42no—
75C43⋊#95C2×C414yes—
76C43⋊#95C2×C418yes—
77C23×C4×C43C2311yescharacteristic
78C23×C4×C43C2312yes—
79C23×C4×C43C2311yescharacteristic
80C23×C4×C43C2312yes—
81C23×C4×C43C2311yescharacteristic
82C2×C4⋊C4×C43—22no—
83C2×C4⋊C4×C43—42no—
84C2×C4⋊C4×C43—42no—
85C2×C4⋊C4×C43—42no—
86C2×C4⋊C4×C43—42no—
87#95×C43—22no—
88#95×C43—42no—
89#95×C43C2×C414yes—
90C24×C43C2411yescharacteristic
91C23×D43—21no—
92C23×D43—22no—
93C23×D43—21no—
94C23×D43—22no—
95C23×D43—22no—
96C23×D43—21no—
97C23×D43—22no—
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—21no—
115C22×C4×C43—22no—
116C22×C4×C43—22no—
117C22×C4×C43—22no—
118C22×C4×C43—22no—
119C22×C4×C43—22no—
120C22×C4×C43—21no—
121C22×C4×C43—22no—
122C22×C4×C43—22no—
123C22×C4×C43—22no—
124C22×C4×C43—22no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43C22×C414yes—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43C2×Q812yes—
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—21no—
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—21no—
150C22×Dic43—22no—
151C22×Dic43—22no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—22no—
155C22×Dic43—22no—
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—48no—
168(C2×D43)⋊C4—48no—
169(C2×D43)⋊C4—44no—
170(C2×D43)⋊C4—44no—
171C4⋊Dic43—44no—
172Dic43⋊C4—44no—
173Dic43⋊C4—44no—
174Dic43⋊C4—48no—
175C23×C43C23×C411yescharacteristic
176C23×C43C22×D411yescharacteristic
177C23×C43C22×Q811yescharacteristic
178C23×C43H(5,𝔽2)12yes—
179C23×C43H(5,𝔽2)11yescharacteristic
180C23×C43H(5,𝔽2)12yes—
181C23×C43H(5,𝔽2)12yes—
182C23×C43H(5,𝔽2)11yescharacteristic
183C23×C432−1+411yescharacteristic
184C23×C432−1+412yes—
185C23×C432−1+411yescharacteristic
186C22×D43—24no—
187C22×D43—22no—
188C22×D43—24no—
189C22×D43—22no—
190C22×D43—22no—
191C22×D43—22no—
192C22×D43—22no—
193C22×D43—22no—
194C22×D43—22no—
195C22×D43—22no—
196C22×D43—24no—
197C22×D43—24no—
198C22×D43—22no—
199C22×D43—22no—
200C22×D43—42no—
201C22×D43—42no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43C2×C4⋊C414yes—
209C2×C4×C43—24no—
210C2×C4×C43—22no—
211C2×C4×C43—22no—
212C2×C4×C43—24no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—24no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—42no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
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×C43C2×C4⋊C414yes—
238C2×Dic43—24no—
239C2×Dic43—22no—
240C2×Dic43—22no—
241C2×Dic43—24no—
242C2×Dic43—24no—
243C2×Dic43—24no—
244C2×Dic43—24no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—41no—
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×Dic43—42no—
266C2×Dic43C2×C4⋊C414yes—
267C4×D43—416no—
268#14674—431nomaximal, Sylow
269C22×C43C22×C4⋊C411yescharacteristic
270C22×C43#51812yes—
271C22×C43#52011yescharacteristic
272C22×C43#52012yes—
273C22×C43#52011yescharacteristic
274C22×C43#53411yescharacteristic
275C22×C43#53411yescharacteristic
276C22×C43#53511yescharacteristic
277C22×C43#53511yescharacteristic
278C22×C43#53611yescharacteristic
279C22×C43#53611yescharacteristic
280C22×C43#54312yes—
281C22×C43#54412yes—
282C22×C43#54411yescharacteristic
283C22×C43#54411yescharacteristic
284C22×C43#56012yes—
285C22×C43#56012yes—
286C22×C43#56212yes—
287C22×C43#56212yes—
288C22×C43#56212yes—
289C22×C43#56212yes—
290C22×C43#56312yes—
291C22×C43#56312yes—
292C2×D43—24no—
293C2×D43—24no—
294C2×D43—24no—
295C2×D43—42no—
296C2×D43—42no—
297C2×D43—42no—
298C2×D43—44no—
299C2×D43—44no—
300C2×D43—44no—
301C2×D43—44no—
302C2×D43—42no—
303C4×C43—24no—
304C4×C43—44no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43—82no—
308Dic43—24no—
309Dic43—44no—
310Dic43—81no—
311Dic43—82no—
312Dic43—81no—
313C2×#381—431no—
314C2×#380—431no—
315C2×#380—431no—
316#1444—432no—
317#1444—431no—
318#1444D4311yescharacteristic, complemented
319#1442—432no—
320#1442—431no—
321#1442—431no—
322#1439—432no—
323#1439—432no—
324C2×C43#231511yescharacteristic
325C2×C43#231711yescharacteristic
326C2×C43#231711yescharacteristic
327C2×C43#237612yes—
328C2×C43#237612yes—
329C2×C43#281511yescharacteristic
330C2×C43#281611yescharacteristic
331C2×C43#281611yescharacteristic
332C2×C43#281711yescharacteristic
333C2×C43#284112yes—
334C2×C43#284112yes—
335D43—44no—
336C24×C4—431no—
337C22×C4⋊C4—431no—
338C22×C4⋊C4—431no—
339C22×C4⋊C4—431no—
340C22×C4⋊C4—432no—
341C22×C4⋊C4C2×D4311yescharacteristic
342C22×C4⋊C4C2×D4312yes—
343C22×C22⋊C4—432no—
344C22×C22⋊C4—431no—
345C22×C22⋊C4—431no—
346C22×C22⋊C4—432no—
347#381—438no—
348#380—864no—
349#380—864no—
350C2×#95—432no—
351C2×#95—431no—
352C2×#95—432no—
353C2×#95—431no—
354C2×#95—432no—
355C2×#95—432no—
356C2×#95—432no—
357C2×#95—432no—
358C2×#95—432no—
359C2×#95C2×D4311yescharacteristic
360C2×#95C2×D4312yes—
361C2×#95C2×D4311yescharacteristic
362C43#1467411yescharacteristic, complemented, Sylow
363C25—431no—
364C23×C4—431no—
365C23×C4—434no—
366C23×C4—434no—
367C23×C4—434no—
368C23×C4—432no—
369C23×C4—431no—
370C23×C4—431no—
371C23×C4—432no—
372C23×C4—1722no—
373C23×C4—1722no—
374C23×C4C22×D4311yescharacteristic
375C23×C4C22×D4312yes—
376C23×C4C22×D4311yescharacteristic
377C23×C4C22×D4312yes—
378C23×C4C22×D4311yescharacteristic
379C2×C4⋊C4—22no—
380C2×C4⋊C4—42no—
381C2×C4⋊C4—42no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—862no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—862no—
387C2×C4⋊C4—1722no—
388C2×C4⋊C4—1722no—
389C2×C4⋊C4—1722no—
390C2×C4⋊C4—1722no—
391C2×C4⋊C4—1722no—
392C2×C4⋊C4—1722no—
393C2×C22⋊C4—438no—
394C2×C22⋊C4—862no—
395C2×C22⋊C4—862no—
396C2×C22⋊C4—864no—
397C2×C22⋊C4—1722no—
398C2×C22⋊C4—1722no—
399C2×C22⋊C4—1722no—
400C2×C22⋊C4—1722no—
401C2×C22⋊C4—1722no—
402C2×C22⋊C4—1722no—
403#95—22no—
404#95—42no—
405#95—438no—
406#95—434no—
407#95—864no—
408#95—862no—
409#95—1722no—
410#95—1722no—
411#95—1722no—
412#95—1722no—
413#95—1722no—
414#95C4×D4314yes—
415C24—432no—
416C24—432no—
417C24—432no—
418C24—861no—
419C24—862no—
420C24—862no—
421C24—861no—
422C24—862no—
423C24—861no—
424C24—862no—
425C24—861no—
426C24C23×D4311yescharacteristic
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—21no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—432no—
455C22×C4—4316no—
456C22×C4—434no—
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—861no—
466C22×C4—861no—
467C22×C4—862no—
468C22×C4—861no—
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—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—862no—
481C22×C4—862no—
482C22×C4—1728no—
483C22×C4—1724no—
484C22×C4—1724no—
485C22×C4—1728no—
486C22×C4C2×C4×D4314yes—
487C22×C4C2×C4×D4312yes—
488C22×C4D4×D4312yes—
489C22×C4Q8×D4312yes—
490C4⋊C4—44no—
491C4⋊C4—48no—
492C4⋊C4—1724no—
493C4⋊C4—1724no—
494C4⋊C4—1724no—
495C4⋊C4—1728no—
496C22⋊C4—1728no—
497C22⋊C4—1724no—
498C22⋊C4—1724no—
499C22⋊C4—1728no—
500C23—434no—
501C23—864no—
502C23—862no—
503C23—864no—
504C23—862no—
505C23—862no—
506C23—862no—
507C23—862no—
508C23—862no—
509C23—862no—
510C23—862no—
511C23—864no—
512C23—864no—
513C23—862no—
514C23—862no—
515C23—1722no—
516C23—1722no—
517C23—1722no—
518C23—1722no—
519C23—1722no—
520C23—1722no—
521C23—1722no—
522C23—1722no—
523C23C22×C4×D4311yescharacteristic
524C23C2×D4×D4311yescharacteristic
525C23C2×Q8×D4311yescharacteristic
526C23#1306337012yes—
527C23#1306337011yescharacteristic
528C23#1306337012yes—
529C23#1306337112yes—
530C23#1306337111yescharacteristic
531C23#1306337211yescharacteristic
532C23#1306337312yes—
533C23#1306337311yescharacteristic
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—24no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—42no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—434no—
563C2×C4—864no—
564C2×C4—862no—
565C2×C4—862no—
566C2×C4—864no—
567C2×C4—864no—
568C2×C4—864no—
569C2×C4—864no—
570C2×C4—17216no—
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—1721no—
580C2×C4—1721no—
581C2×C4—1722no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1722no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1722no—
588C2×C4—1722no—
589C2×C4—1722no—
590C2×C4—1722no—
591C2×C4—1722no—
592C2×C4C4⋊C4×D4314yes—
593C22—864no—
594C22—864no—
595C22—864no—
596C22—1724no—
597C22—1724no—
598C22—1724no—
599C22—1724no—
600C22—1722no—
601C22—1722no—
602C22—1722no—
603C22—1722no—
604C22C2×C4⋊C4×D4311yescharacteristic
605C22#1458337112yes—
606C22#1458337811yescharacteristic
607C22#1458338012yes—
608C22#1458338111yescharacteristic
609C22#1458345911yescharacteristic
610C22#1458346011yescharacteristic
611C22#1458346211yescharacteristic
612C22#1458346511yescharacteristic
613C22#1458347211yescharacteristic
614C22#1458347411yescharacteristic
615C22#1458352412yes—
616C22#1458352612yes—
617C22#1458352611yescharacteristic
618C22#1458352911yescharacteristic
619C22#1458363712yes—
620C22#1458363812yes—
621C22#1458364512yes—
622C22#1458364512yes—
623C22#1458364612yes—
624C22#1458364712yes—
625C22#1458364812yes—
626C22#1458365012yes—
627C4—24no—
628C4—44no—
629C4—82no—
630C4—81no—
631C4—81no—
632C4—864no—
633C4—3441no—
634C4—3441no—
635C4—3442no—
636C4—1724no—
637C2—1724no—
638C2#1913720611yescharacteristic
639C2#1913721611yescharacteristic
640C2#1913721711yescharacteristic
641C2#1913774012yes—
642C2#1913774412yes—
643C2#1914261611yescharacteristic
644C2#1914262411yescharacteristic
645C2#1914262811yescharacteristic
646C2#1914262911yescharacteristic
647C2#1914284912yes—
648C2#1914285112yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1444C2
socle, cosocleC24×C43C24
prime radicalC24×D43C23
hypercenter#1444D43
hypocenterC43#14674
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
4. #19132858C2semidirect
5. #19132858C2semidirect
6. #19132852C2semidirect
7. #19132851C2semidirect
8. #19132850C2semidirect
11. C43×#1444C2semidirect
21. #14582761C4semidirect
164. C2×C4×D43C4⋊C4semidirect
318. #1444D43semidirect
362. C43#14674semidirect

Maximal subgroups

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

subgroupindex
C2×#145827612
C2×#145827582
C2×#145827562
#191328582
#191328522
#191328512
#191328502
#191328392
#191328372
C43×#14442
#1467443