Finite Group Databasebeta

← #25165247

Subgroups — #25165247

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139105C211yesmaximal, characteristic, complemented
2#19137671C211yesmaximal, characteristic
3#19136002C211yesmaximal, characteristic
4#19135964C211yesmaximal, characteristic
5#19135833C211yesmaximal, characteristic
6#19135832C211yesmaximal, characteristic
7#19135274C211yesmaximal, characteristic, complemented
8#19135186C211yesmaximal, characteristic, complemented
9#19135182C211yesmaximal, characteristic, complemented
10#19135150C211yesmaximal, characteristic, complemented
11#19134851C211yesmaximal, characteristic, complemented
12#19134845C211yesmaximal, characteristic
13#19134598C211yesmaximal, characteristic, complemented
14C4×#13063245C211yesmaximal, characteristic
15C43×#1927C211yesmaximal, characteristic, complemented
16C2×#13063317—21no—
17C2×#13063314C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×C4×C43⋊C8C2211yescharacteristic
29#14582841—21no—
30#14582833—21no—
31#14582800C2211yescharacteristic
32#14582798C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582797C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582791—21no—
37#14582788—21no—
38#14582783—21no—
39#14582773—21no—
40#14582768C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×Dic43⋊C4C2211yescharacteristic
43#14582746—21no—
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#106×C43C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C4×D43—21no—
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063317—44no—
64#13063314—22no—
65#13063314—22no—
66Q8×Dic43—22no—
67Q8×Dic43—41no—
68C4×D172—22no—
69C4×D172—41no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×C4×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92Dic43⋊C8—41no—
93#13063249—22no—
94#13063249—41no—
95#13063247—22no—
96#13063247—41no—
97#13063245—22no—
98#13063245—22no—
99C4×C43⋊C8—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C22×Q8×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115#106×C43—22no—
116#103×C43—22no—
117#103×C43—22no—
118#95×C43—21no—
119#95×C43—21no—
120#95×C43—21no—
121C23×D43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—21no—
124C2×Q8×C43—21no—
125C2×Q8×C43—21no—
126C2×Q8×C43—21no—
127C2×Q8×C43#4112yes—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C22×Dic43C2×D411yescharacteristic
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172—21no—
147C2×D172#4112yes—
148C2×C4×D43—42no—
149C2×C4×D43—42no—
150C2×C4×D43—81no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43#4112yes—
163C42×C43—21no—
164C42×C43—21no—
165C42×C43—42no—
166(C2×D43)⋊C4—24no—
167(C2×D43)⋊C4—24no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4—81no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—42no—
177C4⋊Dic43—42no—
178C4⋊Dic43—42no—
179C4⋊Dic43#4112yes—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182Dic43⋊C4—42no—
183Dic43⋊C4—42no—
184Dic43⋊C4—42no—
185Dic43⋊C4—42no—
186C4×Dic43—21no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—21no—
190C4×Dic43—42no—
191C4×Dic43—81no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C23×C43C22×D411yescharacteristic
199C22×D43—22no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206Q8×C43—22no—
207Q8×C43—22no—
208Q8×C43—41no—
209Q8×C43—41no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—22no—
213C2×C4×C43—21no—
214C2×C4×C43—22no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43AGL(1,ℤ/8)12yes—
228C2×C4×C43C2×#4111yescharacteristic
229C2×C4×C43C2×#4111yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C2×C4×C432−1+411yescharacteristic
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—22no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43#13512yes—
255D172—22no—
256D172—22no—
257D172—41no—
258D172—41no—
259C4×D43—84no—
260C8×C43—41no—
261C8×C43—41no—
262C43⋊C8—41no—
263C43⋊C8—41no—
264#26761—431nomaximal, Sylow
265C22×C43#52511yescharacteristic
266C22×C43#54611yescharacteristic
267C22×C43#54811yescharacteristic
268C22×C43C2×#13511yescharacteristic
269C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57811yescharacteristic
272C2×D43—42no—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—81no—
276C2×D43—81no—
277C2×D43—81no—
278C2×D43—81no—
279C4×C43—22no—
280C4×C43—42no—
281C4×C43—42no—
282C4×C43—41no—
283C4×C43—81no—
284C4×C43—81no—
285C4×C43#52911yescharacteristic
286C4×C43#53911yescharacteristic
287C4×C43#55211yescharacteristic
288C4×C43#55311yescharacteristic
289Dic43—22no—
290Dic43—41no—
291Dic43—41no—
292Dic43—42no—
293Dic43—41no—
294Dic43—81no—
295Dic43—81no—
296#2506—431no—
297#2367—431no—
298#2071—431no—
299#2065—431no—
300#2042—431no—
301#2042—431no—
302#1933—431no—
303#1927D4311yescharacteristic, complemented
304#1921—431no—
305#1920—431no—
306#1916—431no—
307#1863—431no—
308#1862—431no—
309#1803—431no—
310C4×#102—431no—
311C2×C43#246011yescharacteristic
312C2×C43#310611yescharacteristic
313C2×C43#312011yescharacteristic
314C2×C43#330011yescharacteristic
315C2×C43#330611yescharacteristic
316C2×C43#336511yescharacteristic
317C2×C43#336711yescharacteristic
318D43—82no—
319C2×#125—861no—
320C2×#124—431no—
321C2×C4×Q8—431no—
322C2×C4×D4—431no—
323C2×#107—431no—
324C2×#106C2×D4311yescharacteristic
325C2×C4⋊C8—431no—
326C2×#103—431no—
327C2×#103—431no—
328C2×#103C2×D4311yescharacteristic
329C2×#103C2×D4311yescharacteristic
330C2×#102—431no—
331C2×#102—431no—
332C2×#102—431no—
333C2×#102—431no—
334C2×C4×C8—431no—
335#400—861no—
336#398—861no—
337#391C2×D4311yescharacteristic
338#390—431no—
339#389—431no—
340#389—431no—
341#389—431no—
342#389—431no—
343#388—861no—
344#388—861no—
345#387—861no—
346#385—861no—
347#384—431no—
348C4×C4⋊C4—431no—
349C4×C4⋊C4—431no—
350C4×C4⋊C4C2×D4311yescharacteristic
351C4×C22⋊C4—861no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340—431no—
357#340C2×D4311yescharacteristic
358#336—431no—
359#336—431no—
360#336—431no—
361#336C2×D4311yescharacteristic
362C43#2676111yescharacteristic, complemented, Sylow
363C22×Q8C22×D4311yescharacteristic
364C22×D4—431no—
365C23×C4—861no—
366C22×C8—431no—
367C22×C8—431no—
368C22×C8C22×D4311yescharacteristic
369C22×C8C22×D4311yescharacteristic
370#125—1724no—
371#124—862no—
372#124—862no—
373C4×Q8—862no—
374C4×Q8—1721no—
375C4×D4—862no—
376C4×D4—1721no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4—861no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—861no—
386C2×C4⋊C4—861no—
387C2×C4⋊C4—861no—
388C2×C4⋊C4—861no—
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C4⋊C4C22×D4311yescharacteristic
392C2×C22⋊C4—861no—
393C2×C22⋊C4—861no—
394C2×C22⋊C4—861no—
395C2×C22⋊C4—861no—
396C2×C22⋊C4—861no—
397C2×C42—21no—
398C2×C42—431no—
399C2×C42—431no—
400C2×C42—861no—
401C2×C42—861no—
402C2×C42C22×D4311yescharacteristic
403#107—862no—
404#106—22no—
405C4⋊C8—1721no—
406#103—22no—
407#103—22no—
408#103—862no—
409#103—1721no—
410#102—862no—
411#102—862no—
412#102—862no—
413#102—1721no—
414C4×C8—1721no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—431no—
419#95—431no—
420#95—861no—
421#95—861no—
422#95—861no—
423#95—861no—
424#95—861no—
425C24—861no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8#1062189812yes—
432C2×D4—432no—
433C2×D4—861no—
434C2×D4—861no—
435C2×D4—861no—
436C2×D4—861no—
437C2×D4—861no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—431no—
443C22×C4—431no—
444C22×C4—431no—
445C22×C4—431no—
446C22×C4—861no—
447C22×C4—861no—
448C22×C4—861no—
449C22×C4—3441no—
450C22×C4—1722no—
451C22×C4—1722no—
452C22×C4D4×D4311yescharacteristic
453C22×C4D4×D4311yescharacteristic
454C22×C4C23×D4311yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—861no—
462C2×C8—861no—
463C2×C8—861no—
464C2×C8—861no—
465C2×C8—861no—
466C2×C8—861no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—432no—
473C4⋊C4—862no—
474C4⋊C4—862no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—1722no—
481C4⋊C4—1722no—
482C4⋊C4—1722no—
483C4⋊C4—1722no—
484C4⋊C4—1722no—
485C4⋊C4—1722no—
486C4⋊C4—1722no—
487C4⋊C4#1062190012yes—
488C22⋊C4—864no—
489C22⋊C4—864no—
490C22⋊C4—3441no—
491C22⋊C4—1722no—
492C22⋊C4—1722no—
493C42—21no—
494C42—21no—
495C42—42no—
496C42—861no—
497C42—861no—
498C42—861no—
499C42—861no—
500C42—3441no—
501C42—1722no—
502C23—862no—
503C23—1721no—
504C23—1721no—
505C23—1721no—
506C23—1721no—
507C23—1721no—
508C23—1721no—
509C23C2×D4×D4311yescharacteristic
510Q8—22no—
511Q8—22no—
512Q8—41no—
513Q8—41no—
514D4—862no—
515D4—862no—
516D4—1721no—
517D4—1721no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—432no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—861no—
546C2×C4—861no—
547C2×C4—862no—
548C2×C4—3444no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4—1721no—
554C2×C4—1721no—
555C2×C4—1721no—
556C2×C4—1721no—
557C2×C4#1306335212yes—
558C2×C4#41×D4311yescharacteristic
559C2×C4#41×D4311yescharacteristic
560C2×C4C2×#1062190011yescharacteristic
561C2×C4C2×#1062189811yescharacteristic
562C2×C4#1306337111yescharacteristic
563C2×C4#1306337211yescharacteristic
564C8—41no—
565C8—41no—
566C8—1721no—
567C8—1721no—
568C22—3441no—
569C22—3441no—
570C22—3441no—
571C22—3441no—
572C22—1722no—
573C22—1722no—
574C22—1722no—
575C22#1458340811yescharacteristic
576C22#1458354111yescharacteristic
577C22#1458355511yescharacteristic
578C22#135×D4311yescharacteristic
579C22C2×#1306335211yescharacteristic
580C22#1458370811yescharacteristic
581C22#1458371511yescharacteristic
582C4—22no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—81no—
587C4—81no—
588C4—862no—
589C4—3441no—
590C4—3441no—
591C4—1721no—
592C4—1722no—
593C4—1721no—
594C4—1721no—
595C4#1458342811yescharacteristic
596C4#1458349011yescharacteristic
597C4#1458358211yescharacteristic
598C4#1458359511yescharacteristic
599C2—3442no—
600C2#1913855111yescharacteristic
601C2#1914465311yescharacteristic
602C2#1914480711yescharacteristic
603C2#1914648511yescharacteristic
604C2#1914655411yescharacteristic
605C2#1914728611yescharacteristic
606C2#1914731711yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1927C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1927D43
hypocenterC43#26761
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1927

Complements

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

NH ≅ G/Ntype
1. #19139105C2semidirect
7. #19135274C2semidirect
8. #19135186C2semidirect
9. #19135182C2semidirect
10. #19135150C2semidirect
11. #19134851C2semidirect
13. #19134598C2semidirect
15. C43×#1927C2semidirect
303. #1927D43semidirect
362. C43#26761semidirect

Maximal subgroups

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

subgroupindex
#191391052
#191376712
#191360022
#191359642
#191358332
#191358322
#191352742
#191351862
#191351822
#191351502
#191348512
#191348452
#191345982
C4×#130632452
C43×#19272
#2676143