Finite Group Databasebeta

← #25027277

Subgroups — #25027277

Order 11008.

1390 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582811C211yesmaximal, characteristic
2C2×#14582805C211yesmaximal, characteristic, complemented
3#19132865C211yesmaximal, characteristic, complemented
4#19132859C211yesmaximal, characteristic, complemented
5#19132854C212yesmaximal, complemented
6#19132850C212yesmaximal, complemented
7#19132842C212yesmaximal
8#19132840C211yesmaximal, characteristic
9#19132838C212yesmaximal
10#19132822C211yesmaximal, characteristic, complemented
11C2×C43×#388C211yesmaximal, characteristic
12C23×Dic86C2211yescharacteristic
13C22×C4⋊Dic43C2211yescharacteristic
14C22×Dic43⋊C4C2212yes—
15C22×C22⋊Dic43C2212yes—
16C22×C22⋊Dic43C2212yes—
17#14582811C418yescomplemented
18#14582805—24no—
19C2×C43⋊#95C2212yes—
20C2×C43⋊#95C2212yes—
21C2×C43⋊#95C2211yescharacteristic
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2212yes—
28C2×C43⋊#95C2211yescharacteristic
29C2×C43⋊#95C2212yes—
30C22×C4⋊C4×C43C2211yescharacteristic
31C22×C22⋊C4×C43C2211yescharacteristic
32C22×C22⋊C4×C43C2211yescharacteristic
33C22×C22⋊C4×C43C2211yescharacteristic
34C22×C42×C43C2211yescharacteristic
35C43×#388—24no—
36C2×#95×C43C2211yescharacteristic
37C2×#95×C43C2211yescharacteristic
38C22×Dic86—22no—
39C22×Dic86—22no—
40C22×Dic86—42no—
41C22×Dic86—42no—
42C22×Dic86C2×C414yes—
43C23×Dic43C2312yes—
44C23×Dic43C2312yes—
45C23×Dic43C2312yes—
46C23×Dic43C2312yes—
47C2×C4⋊Dic43—22no—
48C2×C4⋊Dic43—42no—
49C2×Dic43⋊C4—42no—
50C2×Dic43⋊C4—42no—
51C2×Dic43⋊C4—42no—
52C2×C22⋊Dic43—42no—
53C2×C22⋊Dic43—42no—
54C2×C22⋊Dic43—42no—
55C2×C22⋊Dic43—42no—
56C2×C22⋊Dic43—42no—
57C2×C22⋊Dic43C2×C418yes—
58C43⋊#95—24no—
59C43⋊#95—24no—
60C43⋊#95—22no—
61C43⋊#95—42no—
62C43⋊#95—42no—
63C43⋊#95—42no—
64C43⋊#95—42no—
65C43⋊#95—42no—
66C43⋊#95—42no—
67C43⋊#95C2×C414yes—
68C43⋊#95C2×C418yes—
69C25×C43C2311yescharacteristic
70C23×C4×C43C2311yescharacteristic
71C23×C4×C43C2311yescharacteristic
72C23×C4×C43C2311yescharacteristic
73C23×C4×C43C2311yescharacteristic
74C23×C4×C43C2311yescharacteristic
75C23×C4×C43C2311yescharacteristic
76C2×C4⋊C4×C43—22no—
77C2×C4⋊C4×C43—42no—
78C2×C22⋊C4×C43—22no—
79C2×C22⋊C4×C43—22no—
80C2×C22⋊C4×C43—22no—
81C2×C22⋊C4×C43—22no—
82C2×C22⋊C4×C43—42no—
83C2×C22⋊C4×C43—42no—
84C2×C22⋊C4×C43C2×C414yes—
85C2×C42×C43—42no—
86C2×C42×C43D414yes—
87#95×C43—22no—
88#95×C43—22no—
89C24×C43—21no—
90C24×C43—21no—
91C24×C43—22no—
92C24×C43—22no—
93C24×C43—22no—
94C24×C43—21no—
95C24×C43—21no—
96C24×C43—21no—
97C24×C43—21no—
98C24×C43—22no—
99C24×C43C22×C412yes—
100C24×C43C2411yescharacteristic
101C22×C4×C43—21no—
102C22×C4×C43—21no—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
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—21no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43—22no—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43—22no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43C22×C412yes—
126C22×C4×C43C22×C412yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2×D412yes—
129C22×C4×C43C2×D412yes—
130C22×C4×C43#4112yes—
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—22no—
153C22×Dic43—22no—
154C22×Dic43—22no—
155C22×Dic43—22no—
156C22×Dic43—22no—
157C22×Dic43C22×C414yes—
158C22×Dic43C22×C414yes—
159C2×Dic86—28no—
160C2×Dic86—48no—
161C2×Dic86—44no—
162C2×Dic86—44no—
163C2×Dic86—48no—
164C4⋊C4×C43—44no—
165C22⋊C4×C43—28no—
166C22⋊C4×C43—44no—
167C22⋊C4×C43—44no—
168C42×C43—44no—
169C22⋊Dic43—48no—
170C22⋊Dic43—48no—
171C4⋊Dic43—44no—
172Dic43⋊C4—48no—
173C23×C43—22no—
174C23×C43—24no—
175C23×C43—22no—
176C23×C43—24no—
177C23×C43—22no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—41no—
181C23×C43—41no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—42no—
185C23×C43—41no—
186C23×C43—42no—
187C23×C43—41no—
188C23×C43—42no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—42no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43C23×C411yescharacteristic
197C23×C43C22×D411yescharacteristic
198C23×C43C2×#4111yescharacteristic
199C23×C43H(5,𝔽2)12yes—
200C23×C43H(5,𝔽2)12yes—
201C23×C43H(5,𝔽2)12yes—
202C23×C43H(5,𝔽2)11yescharacteristic
203C23×C432−1+411yescharacteristic
204C23×C432−1+411yescharacteristic
205C23×C432−1+411yescharacteristic
206C23×C432−1+412yes—
207C2×C4×C43—24no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
210C2×C4×C43—24no—
211C2×C4×C43—22no—
212C2×C4×C43—24no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43C4×D414yes—
237C2×Dic43—24no—
238C2×Dic43—24no—
239C2×Dic43—24no—
240C2×Dic43—24no—
241C2×Dic43—24no—
242C2×Dic43—24no—
243C2×Dic43—42no—
244C2×Dic43—42no—
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—
265Dic86—416no—
266#14625—431nomaximal, Sylow
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43—44no—
271C22×C43—44no—
272C22×C43—81no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—82no—
276C22×C43—82no—
277C22×C43—81no—
278C22×C43C2×C4×D411yescharacteristic
279C22×C43#51812yes—
280C22×C43#51911yescharacteristic
281C22×C43#52012yes—
282C22×C43#52011yescharacteristic
283C22×C43#53411yescharacteristic
284C22×C43#53511yescharacteristic
285C22×C43#53511yescharacteristic
286C22×C43#53611yescharacteristic
287C22×C43#53611yescharacteristic
288C22×C43#53711yescharacteristic
289C22×C43#53812yes—
290C22×C43#54111yescharacteristic
291C22×C43#54212yes—
292C22×C43#54211yescharacteristic
293C22×C43H(3,𝔽4)12yes—
294C22×C43#56212yes—
295C22×C43#56212yes—
296C22×C43#56212yes—
297C22×C43#56212yes—
298C22×C43#56312yes—
299C22×C43#56312yes—
300C22×C43#56312yes—
301C4×C43—24no—
302C4×C43—42no—
303C4×C43—42no—
304C4×C43—42no—
305C4×C43—81no—
306C4×C43—81no—
307Dic43—44no—
308Dic43—44no—
309Dic43—82no—
310Dic43—82no—
311C2×#393—431no—
312C2×#391—431no—
313C2×#388D4311yescharacteristic
314#1446—431no—
315#1444—431no—
316#1442—432no—
317#1442—432no—
318#1440—432no—
319#1439—432no—
320#1439—431no—
321#1434—431no—
322C2×C43—82no—
323C2×C43#232111yescharacteristic
324C2×C43#232311yescharacteristic
325C2×C43#232611yescharacteristic
326C2×C43#237812yes—
327C2×C43#237912yes—
328C2×C43#281411yescharacteristic
329C2×C43#281611yescharacteristic
330C2×C43#281911yescharacteristic
331C2×C43#282111yescharacteristic
332C2×C43#283112yes—
333C2×C43#283212yes—
334C23×Q8—431no—
335C22×C4⋊C4—431no—
336C22×C4⋊C4—432no—
337C22×C4⋊C4C2×D4311yescharacteristic
338C22×C22⋊C4—432no—
339C22×C22⋊C4—432no—
340C22×C22⋊C4C2×D4311yescharacteristic
341C22×C22⋊C4C2×D4311yescharacteristic
342C22×C22⋊C4C2×D4311yescharacteristic
343C22×C42C2×D4311yescharacteristic
344#393—438no—
345#391—864no—
346#388—24no—
347C2×#95—431no—
348C2×#95—432no—
349C2×#95—431no—
350C2×#95—432no—
351C2×#95—432no—
352C2×#95—432no—
353C2×#95—432no—
354C2×#95—432no—
355C2×#95—432no—
356C2×#95—432no—
357C2×#95—432no—
358C2×#95C2×D4311yescharacteristic
359C2×#95C2×D4311yescharacteristic
360C43#1462511yescharacteristic, complemented, Sylow
361C25C22×D4311yescharacteristic
362C22×Q8—434no—
363C22×Q8—862no—
364C22×Q8—862no—
365C22×Q8—1722no—
366C22×Q8—1722no—
367C23×C4—432no—
368C23×C4—432no—
369C23×C4—432no—
370C23×C4—432no—
371C23×C4C22×D4311yescharacteristic
372C23×C4C22×D4311yescharacteristic
373C23×C4C22×D4311yescharacteristic
374C23×C4C22×D4311yescharacteristic
375C23×C4C22×D4311yescharacteristic
376C23×C4C22×D4311yescharacteristic
377C2×C4⋊C4—22no—
378C2×C4⋊C4—42no—
379C2×C4⋊C4—862no—
380C2×C4⋊C4—1722no—
381C2×C4⋊C4—1722no—
382C2×C4⋊C4—1722no—
383C2×C4⋊C4—1722no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—42no—
389C2×C22⋊C4—42no—
390C2×C22⋊C4—438no—
391C2×C22⋊C4—1722no—
392C2×C22⋊C4—1722no—
393C2×C22⋊C4—1722no—
394C2×C22⋊C4—1722no—
395C2×C22⋊C4—1722no—
396C2×C22⋊C4C4×D4314yes—
397C2×C42—42no—
398C2×C42C22⋊D4314yes—
399#95—22no—
400#95—22no—
401#95—434no—
402#95—438no—
403#95—862no—
404#95—864no—
405#95—864no—
406#95—1722no—
407#95—1722no—
408#95—1722no—
409#95—1722no—
410#95—1722no—
411#95—1722no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—22no—
416C24—22no—
417C24—21no—
418C24—21no—
419C24—21no—
420C24—22no—
421C24—21no—
422C24C2×C4×D4312yes—
423C24C23×D4311yescharacteristic
424C2×Q8—868no—
425C2×Q8—1728no—
426C2×Q8—1724no—
427C2×Q8—1724no—
428C2×Q8—1728no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—434no—
454C22×C4—434no—
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—862no—
479C22×C4—862no—
480C22×C4—862no—
481C22×C4C2×C4×D4312yes—
482C22×C4C2×C4×D4312yes—
483C22×C4#1062189812yes—
484C22×C4C2×C22⋊D4312yes—
485C22×C4C2×C22⋊D4312yes—
486C22×C4C2×C22⋊D4312yes—
487C4⋊C4—44no—
488C4⋊C4—1724no—
489C4⋊C4—1728no—
490C22⋊C4—28no—
491C22⋊C4—44no—
492C22⋊C4—44no—
493C22⋊C4—1728no—
494C22⋊C4—1728no—
495C42—44no—
496C23—22no—
497C23—24no—
498C23—22no—
499C23—24no—
500C23—22no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—41no—
515C23—42no—
516C23—41no—
517C23—42no—
518C23—41no—
519C23C22×C4×D4311yescharacteristic
520C23C22×C22⋊D4311yescharacteristic
521C23C2×#1062189811yescharacteristic
522C23#1306337012yes—
523C23#1306337012yes—
524C23#1306337112yes—
525C23#1306337111yescharacteristic
526C23#1306337211yescharacteristic
527C23#1306337211yescharacteristic
528C23#1306337212yes—
529C23#1306337211yescharacteristic
530Q8—17216no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—22no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
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—41no—
559C2×C4—41no—
560C2×C4—864no—
561C2×C4—864no—
562C2×C4—864no—
563C2×C4—864no—
564C2×C4—864no—
565C2×C4—864no—
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—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—1722no—
584C2×C4—1722no—
585C2×C4—1722no—
586C2×C4—1722no—
587C2×C4—1722no—
588C2×C4C4×C22⋊D4314yes—
589C22—42no—
590C22—42no—
591C22—44no—
592C22—44no—
593C22—42no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22C2×C4×C22⋊D4311yescharacteristic
601C22#1458337112yes—
602C22#1458337611yescharacteristic
603C22#1458337812yes—
604C22#1458337911yescharacteristic
605C22#1458345811yescharacteristic
606C22#1458346311yescharacteristic
607C22#1458346611yescharacteristic
608C22#1458347011yescharacteristic
609C22#1458347011yescharacteristic
610C22#1458347711yescharacteristic
611C22#1458348212yes—
612C22#1458351111yescharacteristic
613C22#1458351412yes—
614C22#1458352011yescharacteristic
615C22#1458364112yes—
616C22#1458364312yes—
617C22#1458364412yes—
618C22#1458364412yes—
619C22#1458364612yes—
620C22#1458365112yes—
621C22#1458365112yes—
622C22#1458365212yes—
623C4—24no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—81no—
628C4—81no—
629C4—3442no—
630C4—3442no—
631C4—1724no—
632C4—1724no—
633C2—82no—
634C2#1913724911yescharacteristic
635C2#1913727711yescharacteristic
636C2#1913730711yescharacteristic
637C2#1913776212yes—
638C2#1913776412yes—
639C2#1914260811yescharacteristic
640C2#1914262311yescharacteristic
641C2#1914264011yescharacteristic
642C2#1914265311yescharacteristic
643C2#1914274512yes—
644C2#1914276012yes—
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC2×C43×#388C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenterC2×#388D43
hypocenterC43#14625
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#14582805C2semidirect
3. #19132865C2semidirect
4. #19132859C2semidirect
5. #19132854C2semidirect
6. #19132850C2semidirect
10. #19132822C2semidirect
17. #14582811C4semidirect
360. C43#14625semidirect

Maximal subgroups

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

subgroupindex
C2×#145828112
C2×#145828052
#191328652
#191328592
#191328542
#191328502
#191328422
#191328402
#191328382
#191328222
C2×C43×#3882
#1462543