Finite Group Databasebeta

← #25129584

Subgroups — #25129584

Order 11008.

1344 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583560C211yesmaximal, characteristic
2C2×#14583217C211yesmaximal, characteristic, complemented
3#19138906C211yesmaximal, characteristic, complemented
4#19135832C212yesmaximal, complemented
5#19135789C212yesmaximal, complemented
6#19135023C211yesmaximal, characteristic, complemented
7#19134887C211yesmaximal, characteristic, complemented
8#19134861C212yesmaximal, complemented
9#19134534C212yesmaximal, complemented
10#19134530C211yesmaximal, characteristic, complemented
11C22×#103×C43C211yesmaximal, characteristic, complemented
12C22×#10621902C2211yescharacteristic
13#14583560—24no—
14#14583560—24no—
15C2×#13063314—21no—
16C2×#13063314C2211yescharacteristic
17C2×#13063301—21no—
18C2×#13063301C2211yescharacteristic
19C2×#13063299—21no—
20C2×#13063299C2211yescharacteristic
21C2×Q8×Dic43C2211yescharacteristic
22C2×C4×C22⋊D43—21no—
23C2×C4×C22⋊D43C2211yescharacteristic
24#14583217—24no—
25C2×#13063256C2212yes—
26C2×#13063249C2212yes—
27C2×#13063249C2212yes—
28C2×#13063247C2212yes—
29C2×#13063245C2212yes—
30C2×C22⋊(C43⋊C8)C2211yescharacteristic
31C2×(C2×D43)⋊C8C2212yes—
32#14582837—21no—
33#14582834—21no—
34#14582795C2212yes—
35#14582778—21no—
36#14582772—21no—
37#14582759C2211yescharacteristic
38#14582756C2212yes—
39#14582662C2212yes—
40#14582653C2212yes—
41C23×Q8×C43C2211yescharacteristic
42C23×C8×C43C2211yescharacteristic
43C22×C4⋊C4×C43C2211yescharacteristic
44C2×#103×C43—24no—
45C2×#103×C43C2212yes—
46C2×#103×C43C2212yes—
47C2×#10621902—22no—
48C2×#10621902—22no—
49C2×#10621902—24no—
50C2×#10621902—42no—
51C22×D172—21no—
52C22×D172C2311yescharacteristic
53C22×C22⋊D43—21no—
54C22×C22⋊D43D411yescharacteristic
55C22×C4×D43—21no—
56C22×C4×D43C2311yescharacteristic
57C22×C43⋊C8C2312yes—
58#13063314—28no—
59#13063314—22no—
60#13063314—22no—
61#13063301—28no—
62#13063301—22no—
63#13063301—22no—
64#13063299—28no—
65#13063299—22no—
66#13063299D414yes—
67Q8×Dic43—22no—
68Q8×Dic43—22no—
69C4×C22⋊D43—28no—
70C4×C22⋊D43—22no—
71C4×C22⋊D43—22no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2312yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4D411yescharacteristic
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43D411yescharacteristic
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—22no—
85C2×(C2×D43)⋊C4D411yescharacteristic
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88#13063256—24no—
89#13063249—24no—
90#13063249—42no—
91#13063247—42no—
92#13063245—24no—
93C22⋊(C43⋊C8)—22no—
94(C2×D43)⋊C8—42no—
95C43⋊#95—21no—
96C43⋊#95—22no—
97C43⋊#95—22no—
98C22×Q8×C43—22no—
99C22×Q8×C43—21no—
100C22×Q8×C43—24no—
101C22×Q8×C43—42no—
102C22×Q8×C43D414yes—
103C22×Q8×C43C2311yescharacteristic
104C22×Q8×C43C2311yescharacteristic
105C23×C4×C43—21no—
106C23×C4×C43—21no—
107C23×C4×C43C2311yescharacteristic
108C22×C8×C43—22no—
109C22×C8×C43—42no—
110C22×C8×C43C2312yes—
111C2×C4⋊C4×C43—22no—
112C2×C4⋊C4×C43—22no—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43C2312yes—
115#103×C43—24no—
116#103×C43—24no—
117C24×C43C2×D411yescharacteristic
118C23×D43—21no—
119C23×D43C2×D411yescharacteristic
120C2×Q8×C43—24no—
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43—22no—
124C2×Q8×C43—28no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—44no—
128C2×Q8×C43—44no—
129C2×Q8×C43—48no—
130C2×Q8×C43C2×D412yes—
131C2×Q8×C43C2×D412yes—
132C2×Q8×C43#4114yes—
133C22×C4×C43—22no—
134C22×C4×C43—22no—
135C22×C4×C43—24no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—22no—
139C22×C4×C43—44no—
140C22×C4×C43—42no—
141C22×C4×C43—82no—
142C22×C4×C43C2×D412yes—
143C22×C4×C43C2×D412yes—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—22no—
147C2×C22⋊D43—24no—
148C2×C22⋊D43—22no—
149C2×C22⋊D43—22no—
150C2×C22⋊D43—42no—
151C2×C22⋊D43—42no—
152C22×Dic43—21no—
153C22×Dic43—22no—
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C22×Dic43C2×D411yescharacteristic
157#10621902—48no—
158#10621902—44no—
159#10621902—44no—
160C2×D172—24no—
161C2×D172—21no—
162C2×D172—22no—
163C2×D172—22no—
164C2×D172—44no—
165C2×D172C2×D412yes—
166C2×C4×D43—24no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—22no—
170C2×C4×D43—22no—
171C2×C4×D43—44no—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C2×C8×C43—22no—
175C2×C8×C43—44no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—42no—
179C22⋊Dic43—22no—
180C22⋊Dic43—42no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—24no—
184(C2×D43)⋊C4—24no—
185(C2×D43)⋊C4—22no—
186(C2×D43)⋊C4—82no—
187C4⋊Dic43—24no—
188C4⋊Dic43—21no—
189C4⋊Dic43—22no—
190C4⋊Dic43—22no—
191C4⋊Dic43C2×D412yes—
192Dic43⋊C4—24no—
193Dic43⋊C4—22no—
194Dic43⋊C4—82no—
195C4×Dic43—24no—
196C4×Dic43—21no—
197C4×Dic43—21no—
198C2×C43⋊C8—22no—
199C2×C43⋊C8—22no—
200C2×C43⋊C8—22no—
201C23×C43—22no—
202C23×C43—22no—
203C23×C43#12012yes—
204C23×C43#13512yes—
205C23×C43#13712yes—
206C23×C43C22×D411yescharacteristic
207C22×D43—21no—
208C22×D43—22no—
209C22×D43—22no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—22no—
213C22×D43—42no—
214C22×D43—41no—
215C22×D43—41no—
216C22×D43—42no—
217Q8×C43—22no—
218Q8×C43—24no—
219Q8×C43—22no—
220Q8×C43—22no—
221Q8×C43—48no—
222Q8×C43—42no—
223Q8×C43#12314yes—
224C2×C4×C43—22no—
225C2×C4×C43—24no—
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—24no—
230C2×C4×C43—22no—
231C2×C4×C43—48no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43—84no—
237C2×C4×C43#12012yes—
238C2×C4×C43C22×D411yescharacteristic
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C2×#4112yes—
241C2×C4×C43H(5,𝔽2)12yes—
242C22⋊D43—44no—
243C22⋊D43—48no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—22no—
247C2×Dic43—21no—
248C2×Dic43—22no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—42no—
255C2×Dic43—42no—
256C2×Dic43—42no—
257D172—24no—
258D172—48no—
259D172—41no—
260D172—41no—
261C4×D43—48no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—42no—
265C8×C43—42no—
266C43⋊C8—42no—
267#24036—431nomaximal, Sylow
268C22×C43—22no—
269C22×C43—22no—
270C22×C43—24no—
271C22×C43—24no—
272C22×C43#45214yes—
273C22×C43C2×#12011yescharacteristic
274C22×C43#54612yes—
275C22×C43C2×#13511yescharacteristic
276C22×C43C2×#13711yescharacteristic
277C22×C43#57712yes—
278C2×D43—41no—
279C2×D43—42no—
280C2×D43—41no—
281C2×D43—42no—
282C2×D43—41no—
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—82no—
287C2×D43—82no—
288C4×C43—24no—
289C4×C43—22no—
290C4×C43—42no—
291C4×C43—82no—
292C4×C43C2×#12311yescharacteristic
293C4×C43#53411yescharacteristic
294C4×C43#54612yes—
295Dic43—41no—
296Dic43—41no—
297Dic43—42no—
298Dic43—41no—
299Dic43—82no—
300C2×#548—431no—
301C2×#481—431no—
302C22×#103D4311yescharacteristic, complemented
303#2487—431no—
304#2042—432no—
305#2035—432no—
306#1893—431no—
307#1869—431no—
308#1865—432no—
309#1788—432no—
310#1787—431no—
311C2×C43—24no—
312C2×C43#240511yescharacteristic
313C2×C43C2×#45211yescharacteristic
314C2×C43#301011yescharacteristic
315C2×C43#330112yes—
316C2×C43#331612yes—
317D43—81no—
318D43—82no—
319C22×#41—431no—
320C23×Q8C2×D4311yescharacteristic
321C23×C8C2×D4311yescharacteristic
322#548—864no—
323#548—864no—
324C2×#124—431no—
325C2×#124—861no—
326C2×C22⋊Q8—431no—
327C2×C22⋊Q8—861no—
328C2×#121—431no—
329C2×#121—861no—
330C2×C4×Q8—431no—
331C2×C4×D4—431no—
332C2×C4×D4—861no—
333C22×C4⋊C4C2×D4311yescharacteristic
334#481—864no—
335C2×#106—432no—
336C2×#103—24no—
337C2×#103—432no—
338C2×#103—432no—
339C2×#103C2×D4312yes—
340C2×#103C2×D4312yes—
341C2×#102—432no—
342C2×#102—432no—
343C2×C22⋊C8—431no—
344C2×C22⋊C8—432no—
345#400—861no—
346#399—861no—
347#389—432no—
348#386—861no—
349#385—861no—
350#380—431no—
351#380—432no—
352#340—432no—
353#336—432no—
354C43#2403611yescharacteristic, complemented, Sylow
355C2×#41—862no—
356C2×#41—862no—
357C2×#41—864no—
358C2×#41—1722no—
359C22×Q8—21no—
360C22×Q8—22no—
361C22×Q8—24no—
362C22×Q8—42no—
363C22×Q8C22⋊D4314yes—
364C22×Q8C22×D4311yescharacteristic
365C22×Q8C22×D4311yescharacteristic
366C22×D4—431no—
367C22×D4—431no—
368C22×D4—861no—
369C22×D4—861no—
370C23×C4—21no—
371C23×C4—21no—
372C23×C4—431no—
373C23×C4—861no—
374C23×C4C22×D4311yescharacteristic
375C22×C8—22no—
376C22×C8—42no—
377C22×C8—432no—
378C22×C8C22×D4312yes—
379#124—862no—
380#124—868no—
381#124—862no—
382C22⋊Q8—862no—
383C22⋊Q8—868no—
384C22⋊Q8—862no—
385#121—434no—
386#121—868no—
387#121—862no—
388C4×Q8—862no—
389C4×Q8—862no—
390C4×D4—868no—
391C4×D4—862no—
392C4×D4—862no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—432no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—862no—
402C2×C4⋊C4C22×D4312yes—
403C2×C22⋊C4—431no—
404C2×C22⋊C4—431no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—862no—
410C2×C22⋊C4—861no—
411C2×C42—431no—
412C2×C42—861no—
413#106—864no—
414#103—24no—
415#103—24no—
416#103—864no—
417#103—1722no—
418#102—864no—
419#102—1722no—
420C22⋊C8—862no—
421C22⋊C8—1722no—
422#95—862no—
423#95—862no—
424#95—861no—
425C24—431no—
426C24—861no—
427C24D4×D4311yescharacteristic
428#41—1728no—
429#41—1724no—
430#41—1724no—
431C2×Q8—24no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—28no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—44no—
439C2×Q8—44no—
440C2×Q8—48no—
441C2×Q8#1062189814yes—
442C2×Q8C2×C22⋊D4312yes—
443C2×Q8C2×C22⋊D4312yes—
444C2×D4—432no—
445C2×D4—864no—
446C2×D4—864no—
447C2×D4—862no—
448C2×D4—862no—
449C2×D4—862no—
450C2×D4—861no—
451C2×D4—862no—
452C2×D4—862no—
453C2×D4—1724no—
454C2×D4—1722no—
455C2×D4—1722no—
456C22×C4—21no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—44no—
463C22×C4—42no—
464C22×C4—82no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—864no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—862no—
473C22×C4—862no—
474C22×C4—862no—
475C22×C4—1724no—
476C22×C4D4×D4311yescharacteristic
477C22×C4D4×D4312yes—
478C22×C4C2×C22⋊D4312yes—
479C22×C4C23×D4311yescharacteristic
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—44no—
484C2×C8—862no—
485C2×C8—862no—
486C2×C8—862no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—42no—
490C4⋊C4—432no—
491C4⋊C4—864no—
492C4⋊C4—864no—
493C4⋊C4—862no—
494C4⋊C4—861no—
495C4⋊C4—862no—
496C4⋊C4—862no—
497C4⋊C4—3442no—
498C22⋊C4—864no—
499C22⋊C4—864no—
500C22⋊C4—864no—
501C22⋊C4—862no—
502C22⋊C4—862no—
503C22⋊C4—864no—
504C22⋊C4—3442no—
505C22⋊C4—1722no—
506C42—864no—
507C42—861no—
508C42—861no—
509C23—22no—
510C23—22no—
511C23—862no—
512C23—861no—
513C23—861no—
514C23—861no—
515C23—862no—
516C23—862no—
517C23—1721no—
518C23—1721no—
519C23—1722no—
520C23—1722no—
521C23#1306329312yes—
522C23#1306334812yes—
523C23#1306335712yes—
524C23C2×D4×D4311yescharacteristic
525Q8—22no—
526Q8—24no—
527Q8—22no—
528Q8—22no—
529Q8—48no—
530Q8—42no—
531Q8#1306330814yes—
532D4—864no—
533D4—1728no—
534D4—1724no—
535D4—1728no—
536D4—1721no—
537D4—1721no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—48no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—84no—
551C2×C4—861no—
552C2×C4—862no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—862no—
558C2×C4—862no—
559C2×C4—1728no—
560C2×C4—1722no—
561C2×C4—1722no—
562C2×C4—1722no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1722no—
568C2×C4#1306329312yes—
569C2×C4C2×D4×D4311yescharacteristic
570C2×C4C22×C22⋊D4311yescharacteristic
571C2×C4C2×#1062189812yes—
572C2×C4#1306337012yes—
573C8—42no—
574C8—1722no—
575C22—22no—
576C22—22no—
577C22—24no—
578C22—24no—
579C22—3442no—
580C22—3442no—
581C22—1721no—
582C22—1722no—
583C22—1722no—
584C22—1721no—
585C22—1721no—
586C22—1722no—
587C22—1722no—
588C22—1722no—
589C22#1458306014yes—
590C22C2×#1306329311yescharacteristic
591C22#1458353912yes—
592C22C2×#1306334811yescharacteristic
593C22C2×#1306335711yescharacteristic
594C22#1458370512yes—
595C4—22no—
596C4—24no—
597C4—42no—
598C4—82no—
599C4—3442no—
600C4—1721no—
601C4—1722no—
602C4—1721no—
603C4—1721no—
604C4C2×#1306330811yescharacteristic
605C4#1458345811yescharacteristic
606C4#1458353912yes—
607C2—24no—
608C2—3442no—
609C2—3441no—
610C2#1913792211yescharacteristic
611C2C2×#1458306011yescharacteristic
612C2#1914387711yescharacteristic
613C2#1914649312yes—
614C2#1914670212yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC22×#103×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583560C2
hypercenterC22×#103D43
hypocenterC43#24036
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C2×#14583217C2semidirect
3. #19138906C2semidirect
4. #19135832C2semidirect
5. #19135789C2semidirect
6. #19135023C2semidirect
7. #19134887C2semidirect
8. #19134861C2semidirect
9. #19134534C2semidirect
10. #19134530C2semidirect
11. C22×#103×C43C2semidirect
302. C22×#103D43semidirect
354. C43#24036semidirect

Maximal subgroups

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

subgroupindex
C2×#145835602
C2×#145832172
#191389062
#191358322
#191357892
#191350232
#191348872
#191348612
#191345342
#191345302
C22×#103×C432
#2403643