Finite Group Databasebeta

← #25026694

Subgroups — #25026694

Order 11008.

1706 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582811C211yesmaximal, characteristic
2C2×#14582803C212yesmaximal, complemented
3C2×#14582771C212yesmaximal
4#19132858C212yesmaximal, complemented
5#19132850C212yesmaximal, complemented
6#19132832C212yesmaximal
7#19132819C212yesmaximal, complemented
8#19132817C211yesmaximal, characteristic
9C43×#1439C211yesmaximal, characteristic
10C23×Dic86C2211yescharacteristic
11C24×Dic43C2211yescharacteristic
12C22×Dic43⋊C4C2212yes—
13C22×Dic43⋊C4C2212yes—
14C22×C22⋊Dic43C2212yes—
15C22×C22⋊Dic43C2211yescharacteristic
16C22×C4×Dic43C2212yes—
17#14582811C418yescomplemented
18#14582803—28no—
19#14582771—28no—
20C2×C43⋊#95C2212yes—
21C2×C43⋊#95C2212yes—
22C2×C43⋊#95C2212yes—
23C2×C43⋊#95C2212yes—
24C2×C43⋊#95C2212yes—
25C2×C43⋊#95C2212yes—
26C2×C43⋊#95C2212yes—
27C2×C43⋊#95C2211yescharacteristic
28C2×C43⋊#95C2212yes—
29C22×C4⋊C4×C43C2211yescharacteristic
30C22×C22⋊C4×C43C2212yes—
31C22×C22⋊C4×C43C2211yescharacteristic
32C2×#95×C43C2212yes—
33C2×#95×C43C2211yescharacteristic
34C22×Dic86—24no—
35C22×Dic86—24no—
36C22×Dic86—41no—
37C22×Dic86—41no—
38C22×Dic86C2×C414yescomplemented
39C23×Dic43—22no—
40C23×Dic43—24no—
41C23×Dic43—42no—
42C23×Dic43—41no—
43C23×Dic43—41no—
44C23×Dic43C2312yes—
45C23×Dic43C2312yes—
46C23×Dic43C2312yes—
47C23×Dic43C2312yes—
48C2×Dic43⋊C4—24no—
49C2×Dic43⋊C4—24no—
50C2×Dic43⋊C4—24no—
51C2×Dic43⋊C4—42no—
52C2×Dic43⋊C4—42no—
53C2×Dic43⋊C4—42no—
54C2×C22⋊Dic43—24no—
55C2×C22⋊Dic43—24no—
56C2×C22⋊Dic43—41no—
57C2×C22⋊Dic43—41no—
58C2×C22⋊Dic43C2×C418yes—
59C2×C22⋊Dic43Q814yescomplemented
60C2×C4×Dic43—24no—
61C2×C4×Dic43—24no—
62C2×C4×Dic43—42no—
63C43⋊#95—24no—
64C43⋊#95—24no—
65C43⋊#95—24no—
66C43⋊#95—42no—
67C43⋊#95—42no—
68C43⋊#95—42no—
69C43⋊#95C2×C414yescomplemented
70C43⋊#95C2×C418yescomplemented
71C43⋊#95D418yes—
72C25×C43C2311yescharacteristic
73C23×C4×C43C2312yes—
74C23×C4×C43C2311yescharacteristic
75C23×C4×C43C2311yescharacteristic
76C23×C4×C43C2312yes—
77C2×C4⋊C4×C43—41no—
78C2×C4⋊C4×C43—42no—
79C2×C22⋊C4×C43—24no—
80C2×C22⋊C4×C43—24no—
81C2×C22⋊C4×C43—41no—
82C2×C22⋊C4×C43—41no—
83C2×C22⋊C4×C43—42no—
84C2×C22⋊C4×C43C2×C414yes—
85#95×C43—24no—
86#95×C43—41no—
87C24×C43—22no—
88C24×C43—22no—
89C24×C43—21no—
90C24×C43—21no—
91C24×C43—22no—
92C24×C43—21no—
93C24×C43—21no—
94C24×C43—22no—
95C24×C43C22×C412yes—
96C24×C43C2×Q812yes—
97C24×C43#4112yes—
98C24×C43C2411yescharacteristic
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—22no—
104C22×C4×C43—22no—
105C22×C4×C43—22no—
106C22×C4×C43—21no—
107C22×C4×C43—22no—
108C22×C4×C43—21no—
109C22×C4×C43—22no—
110C22×C4×C43—21no—
111C22×C4×C43—21no—
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×C43C22×C412yes—
121C22×C4×C43C22×C412yes—
122C22×C4×C43C2×D414yes—
123C22×Dic43—22no—
124C22×Dic43—22no—
125C22×Dic43—22no—
126C22×Dic43—22no—
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—22no—
130C22×Dic43—22no—
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—48no—
146C22×Dic43—44no—
147C22×Dic43—44no—
148C22×Dic43—48no—
149C22×Dic43—44no—
150C22×Dic43C22×C414yes—
151C22×Dic43C22×C414yes—
152C22×Dic43C2×D414yes—
153C22×Dic43C2×D414yes—
154C22×Dic43C2×Q814yes—
155C22×Dic43#4114yes—
156C2×Dic86—216no—
157C2×Dic86—44no—
158C2×Dic86—44no—
159C2×Dic86—48no—
160C2×Dic86—44no—
161C4⋊C4×C43—44no—
162C22⋊C4×C43—44no—
163C22⋊C4×C43—48no—
164C22⋊Dic43—216no—
165C22⋊Dic43—44no—
166Dic43⋊C4—48no—
167Dic43⋊C4—48no—
168C4×Dic43—48no—
169C23×C43—24no—
170C23×C43—22no—
171C23×C43—24no—
172C23×C43—22no—
173C23×C43—22no—
174C23×C43—22no—
175C23×C43—22no—
176C23×C43—22no—
177C23×C43—24no—
178C23×C43—24no—
179C23×C43—24no—
180C23×C43—24no—
181C23×C43—42no—
182C23×C43—42no—
183C23×C43—42no—
184C23×C43—42no—
185C23×C43—41no—
186C23×C43—42no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43—42no—
190C23×C43—41no—
191C23×C43C4×Q814yes—
192C23×C43C23×C411yescharacteristic
193C23×C43C22×D412yes—
194C23×C43C22×Q811yescharacteristic
195C23×C43C2×#4112yes—
196C23×C43C2×#4111yescharacteristic
197C23×C43H(5,𝔽2)11yescharacteristic
198C23×C43H(5,𝔽2)11yescharacteristic
199C23×C43H(5,𝔽2)12yes—
200C23×C43H(5,𝔽2)11yescharacteristic
201C23×C432−1+411yescharacteristic
202C23×C432−1+412yes—
203C2×C4×C43—24no—
204C2×C4×C43—22no—
205C2×C4×C43—22no—
206C2×C4×C43—24no—
207C2×C4×C43—24no—
208C2×C4×C43—24no—
209C2×C4×C43—24no—
210C2×C4×C43—42no—
211C2×C4×C43—42no—
212C2×C4×C43—41no—
213C2×C4×C43—42no—
214C2×C4×C43—41no—
215C2×C4×C43—42no—
216C2×C4×C43—41no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—41no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×Dic43—24no—
228C2×Dic43—24no—
229C2×Dic43—24no—
230C2×Dic43—24no—
231C2×Dic43—24no—
232C2×Dic43—24no—
233C2×Dic43—24no—
234C2×Dic43—24no—
235C2×Dic43—24no—
236C2×Dic43—24no—
237C2×Dic43—24no—
238C2×Dic43—24no—
239C2×Dic43—24no—
240C2×Dic43—24no—
241C2×Dic43—24no—
242C2×Dic43—416no—
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×Dic43C4×D418yes—
256Dic86—416no—
257#14575—431nomaximal, Sylow
258C22×C43—24no—
259C22×C43—28no—
260C22×C43—44no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—44no—
266C22×C43—44no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43C2×C4×D412yes—
270C22×C43C2×C4×Q811yescharacteristic
271C22×C43#51811yescharacteristic
272C22×C43#52012yes—
273C22×C43#52011yescharacteristic
274C22×C43#53512yes—
275C22×C43#53612yes—
276C22×C43#53811yescharacteristic
277C22×C43#53911yescharacteristic
278C22×C43#54212yes—
279C22×C43#54212yes—
280C22×C43#54311yescharacteristic
281C22×C43#54411yescharacteristic
282C22×C43D4211yescharacteristic
283C22×C43#54612yes—
284C22×C43#54612yes—
285C22×C43D4×Q812yes—
286C22×C43#55111yescharacteristic
287C22×C43#55212yes—
288C22×C43#55412yes—
289C22×C43H(3,𝔽4)11yescharacteristic
290C22×C43#56212yes—
291C22×C43#56311yescharacteristic
292C4×C43—42no—
293C4×C43—42no—
294C4×C43—44no—
295C4×C43—82no—
296Dic43—28no—
297Dic43—44no—
298Dic43—44no—
299Dic43—44no—
300C2×#393—431no—
301C2×#391—432no—
302C2×#385—432no—
303#1444—432no—
304#1442—432no—
305#1439D4311yescharacteristic
306#1437—432no—
307#1434—432no—
308C22⋊#95—431no—
309C2×C43—44no—
310C2×C43#232612yes—
311C2×C43#232911yescharacteristic
312C2×C43#235811yescharacteristic
313C2×C43#236012yes—
314C2×C43#237911yescharacteristic
315C2×C43#267011yescharacteristic
316C2×C43#267711yescharacteristic
317C2×C43#268712yes—
318C2×C43#269212yes—
319C2×C43#276311yescharacteristic
320C2×C43#276411yescharacteristic
321C23×Q8—431no—
322C24×C4—431no—
323C22×C4⋊C4—432no—
324C22×C4⋊C4—432no—
325C22×C4⋊C4C2×D4311yescharacteristic
326C22×C22⋊C4—432no—
327C22×C22⋊C4—431no—
328C22×C22⋊C4C2×D4312yes—
329C22×C22⋊C4C2×D4311yescharacteristic
330C22×C42—432no—
331#393—438no—
332#391—868no—
333#385—868no—
334C2×#95—432no—
335C2×#95—431no—
336C2×#95—432no—
337C2×#95—432no—
338C2×#95—432no—
339C2×#95—432no—
340C2×#95—432no—
341C2×#95—432no—
342C2×#95—432no—
343C2×#95C2×D4312yes—
344C2×#95C2×D4311yescharacteristic
345C43#1457511yescharacteristic, complemented, Sylow
346C25C22×D4311yescharacteristic
347C22×Q8—434no—
348C22×Q8—864no—
349C22×Q8—864no—
350C22×Q8—1721no—
351C22×Q8—1721no—
352C23×C4—432no—
353C23×C4—432no—
354C23×C4—432no—
355C23×C4—432no—
356C23×C4—864no—
357C23×C4—862no—
358C23×C4—1722no—
359C23×C4—1721no—
360C23×C4—1721no—
361C23×C4C22×D4312yes—
362C23×C4C22×D4311yescharacteristic
363C23×C4C22×D4311yescharacteristic
364C23×C4C22×D4312yes—
365C2×C4⋊C4—42no—
366C2×C4⋊C4—41no—
367C2×C4⋊C4—864no—
368C2×C4⋊C4—864no—
369C2×C4⋊C4—864no—
370C2×C4⋊C4—1722no—
371C2×C4⋊C4—1722no—
372C2×C4⋊C4—1722no—
373C2×C22⋊C4—24no—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—41no—
376C2×C22⋊C4—41no—
377C2×C22⋊C4—42no—
378C2×C22⋊C4—438no—
379C2×C22⋊C4—434no—
380C2×C22⋊C4—864no—
381C2×C22⋊C4—864no—
382C2×C22⋊C4—1721no—
383C2×C22⋊C4—1721no—
384C2×C22⋊C4C4×D4314yes—
385C2×C42—864no—
386C2×C42—864no—
387C2×C42—1722no—
388#95—24no—
389#95—41no—
390#95—438no—
391#95—434no—
392#95—438no—
393#95—864no—
394#95—864no—
395#95—864no—
396#95—1722no—
397#95—1722no—
398#95—1722no—
399C24—22no—
400C24—22no—
401C24—21no—
402C24—22no—
403C24—21no—
404C24—21no—
405C24—22no—
406C24—21no—
407C24C2×C4×D4312yes—
408C24#1062190012yes—
409C24Q8×D4312yes—
410C24C23×D4311yescharacteristic
411C2×Q8—8616no—
412C2×Q8—1724no—
413C2×Q8—1724no—
414C2×Q8—1724no—
415C2×Q8—1728no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
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—22no—
436C22×C4—22no—
437C22×C4—434no—
438C22×C4—434no—
439C22×C4—434no—
440C22×C4—434no—
441C22×C4—434no—
442C22×C4—434no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—862no—
453C22×C4—862no—
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—862no—
465C22×C4—1724no—
466C22×C4—1728no—
467C22×C4—1728no—
468C22×C4—1724no—
469C22×C4—1724no—
470C22×C4C2×C4×D4312yes—
471C22×C4C2×C4×D4312yes—
472C22×C4D4×D4314yes—
473C4⋊C4—44no—
474C4⋊C4—1728no—
475C4⋊C4—1728no—
476C22⋊C4—44no—
477C22⋊C4—48no—
478C22⋊C4—8616no—
479C22⋊C4—1724no—
480C42—1728no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—24no—
485C23—22no—
486C23—24no—
487C23—22no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—24no—
493C23—41no—
494C23—41no—
495C23—42no—
496C23—41no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—41no—
502C23—42no—
503C23#1306329014yes—
504C23C22×C4×D4311yescharacteristic
505C23C2×D4×D4312yes—
506C23C2×Q8×D4311yescharacteristic
507C23#41×D4312yes—
508C23C2×#1062190011yescharacteristic
509C23#1306337011yescharacteristic
510C23#1306337012yes—
511C23#1306337011yescharacteristic
512C23#1306337111yescharacteristic
513C23#1306337212yes—
514C23#1306337211yescharacteristic
515Q8—17216no—
516C2×C4—24no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—41no—
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—438no—
541C2×C4—864no—
542C2×C4—864no—
543C2×C4—864no—
544C2×C4—864no—
545C2×C4—864no—
546C2×C4—864no—
547C2×C4—864no—
548C2×C4—864no—
549C2×C4—864no—
550C2×C4—864no—
551C2×C4—864no—
552C2×C4—864no—
553C2×C4—864no—
554C2×C4—864no—
555C2×C4—864no—
556C2×C4—17216no—
557C2×C4—1722no—
558C2×C4—1722no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1722no—
569C22—24no—
570C22—28no—
571C22—44no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—44no—
577C22—42no—
578C22—42no—
579C22—44no—
580C22C4×D4×D4312yes—
581C22C2×#1306329011yescharacteristic
582C22#1458337211yescharacteristic
583C22#1458337812yes—
584C22#1458337911yescharacteristic
585C22#1458346512yes—
586C22#1458347112yes—
587C22#1458348611yescharacteristic
588C22#1458349411yescharacteristic
589C22#1458351312yes—
590C22#1458351512yes—
591C22#1458352411yescharacteristic
592C22#1458352811yescharacteristic
593C22#1458353411yescharacteristic
594C22#1458353612yes—
595C22#1458353812yes—
596C22#1458356212yes—
597C22#1458357911yescharacteristic
598C22#1458358612yes—
599C22#1458360312yes—
600C22#1458364211yescharacteristic
601C22#1458364412yes—
602C22#1458365211yescharacteristic
603C4—42no—
604C4—44no—
605C4—42no—
606C4—82no—
607C4—868no—
608C4—1724no—
609C4—1724no—
610C4—1724no—
611C2—44no—
612C2#1913730412yes—
613C2#1913732511yescharacteristic
614C2#1913757611yescharacteristic
615C2#1913759512yes—
616C2#1913776511yescharacteristic
617C2#1914082211yescharacteristic
618C2#1914091111yescharacteristic
619C2#1914102212yes—
620C2#1914109712yes—
621C2#1914201311yescharacteristic
622C2#1914202211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D43
commutatorC23×C43C23×C4
FittingC43×#1439C2
socle, cosocleC24×C43C24
prime radicalC25×C43C23
hypercenter#1439D43
hypocenterC43#14575
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C2×#14582803C2semidirect
4. #19132858C2semidirect
5. #19132850C2semidirect
7. #19132819C2semidirect
17. #14582811C4semidirect
38. C22×Dic86C2×C4semidirect
59. C2×C22⋊Dic43Q8semidirect
69. C43⋊#95C2×C4semidirect
70. C43⋊#95C2×C4semidirect
345. C43#14575semidirect

Maximal subgroups

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

subgroupindex
C2×#145828112
C2×#145828032
C2×#145827712
#191328582
#191328502
#191328322
#191328192
#191328172
C43×#14392
#1457543