Finite Group Databasebeta

← #25137899

Subgroups — #25137899

Order 11008.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583180C211yesmaximal, characteristic, complemented
2C2×#14582955C211yesmaximal, characteristic, complemented
3#19142948C211yesmaximal, characteristic, complemented
4C4×#13063300C211yesmaximal, characteristic
5#19136025C212yesmaximal, complemented
6#19135786C212yesmaximal
7#19135547C211yesmaximal, characteristic, complemented
8#19135339C212yesmaximal, complemented
9#19135293C212yesmaximal, complemented
10#19134592C211yesmaximal, characteristic, complemented
11C43×#1948C211yesmaximal, characteristic, complemented
12C2×#13063325C2211yescharacteristic
13C2×#13063305—21no—
14C2×#13063300C2211yescharacteristic
15C2×C4×D172—21no—
16C2×C4×D172C2211yescharacteristic
17C2×C42×D43C2211yescharacteristic
18#14583180—24no—
19#14582955—24no—
20C2×#13063259C2212yes—
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063247C2212yes—
23C2×#13063245C2212yes—
24C2×(C2×D43)⋊C8C2212yes—
25C2×#13063235C2212yes—
26#14582804—21no—
27#14582800C2211yescharacteristic
28#14582798—21no—
29#14582798C2212yes—
30#14582798C2211yescharacteristic
31#14582791—21no—
32#14582777—21no—
33#14582756—21no—
34#14582756C2211yescharacteristic
35#14582756C2212yes—
36C4×(C2×D43)⋊C4—21no—
37#14582661C2212yes—
38#14582661C2212yes—
39#14582661C2212yes—
40C2×#106×C43C2212yes—
41C2×C4⋊C8×C43C2211yescharacteristic
42C43×#384C2211yescharacteristic
43C4×C4⋊C4×C43C2211yescharacteristic
44C43×#340C2212yes—
45C22×Dic86—21no—
46C22×D172—21no—
47C22×D172C2311yescharacteristic
48C22×C4×D43—21no—
49C22×C4×D43D411yescharacteristic
50C22×C4×D43D411yescharacteristic
51C22×C4×D43C2311yescharacteristic
52C22×C43⋊C8C2312yes—
53#13063325—22no—
54#13063325—22no—
55#13063305—44no—
56#13063300—22no—
57#13063300—22no—
58C4×D172—22no—
59C4×D172—22no—
60C4×D172—44no—
61C2×C4⋊Dic43—21no—
62C2×C4⋊Dic43—21no—
63C2×C4⋊Dic43—22no—
64C2×C4⋊Dic43C2311yescharacteristic
65C2×C4⋊Dic43C2312yes—
66C2×(C2×D43)⋊C4—21no—
67C2×(C2×D43)⋊C4—21no—
68C2×(C2×D43)⋊C4—22no—
69C2×(C2×D43)⋊C4—21no—
70C2×(C2×D43)⋊C4—21no—
71C2×(C2×D43)⋊C4—21no—
72C2×C4×Dic43D411yescharacteristic
73C2×C4×Dic43D411yescharacteristic
74C2×C4×Dic43C2311yescharacteristic
75C42×D43—22no—
76C42×D43—22no—
77#13063259—24no—
78C4⋊(C43⋊C8)—22no—
79#13063247—24no—
80#13063245—24no—
81(C2×D43)⋊C8—24no—
82#13063235—24no—
83C43⋊#95—21no—
84C43⋊#95—22no—
85C43⋊#95—22no—
86C43⋊#95—21no—
87C22×C8×C43C2312yes—
88C2×C4⋊C4×C43—21no—
89C2×C4⋊C4×C43—21no—
90C2×C4⋊C4×C43C2312yes—
91C2×C4⋊C4×C43C2311yescharacteristic
92C2×C4⋊C4×C43C2311yescharacteristic
93C2×C42×C43—21no—
94C2×C42×C43C2311yescharacteristic
95#106×C43—24no—
96C4⋊C8×C43D414yescomplemented
97#95×C43—21no—
98C23×D43—21no—
99C23×D43C2×D411yescharacteristic
100C22×C4×C43—21no—
101C22×C4×C43—21no—
102C22×C4×C43—22no—
103C22×C4×C43C2×D411yescharacteristic
104C22×C4×C43C2×D411yescharacteristic
105C22×C4×C43C2411yescharacteristic
106C22×Dic43—21no—
107C22×Dic43—22no—
108C22×Dic43C2×D411yescharacteristic
109C22×Dic43C2×D411yescharacteristic
110C22×Dic43C2×D411yescharacteristic
111C2×D172—24no—
112C2×D172—21no—
113C2×D172—21no—
114C2×D172—21no—
115C2×D172—21no—
116C2×D172—21no—
117C2×D172—42no—
118C2×D172—42no—
119C2×D172#4112yes—
120C2×C4×D43—22no—
121C2×C4×D43—22no—
122C2×C4×D43—22no—
123C2×C4×D43—22no—
124C2×C4×D43—21no—
125C2×C4×D43—21no—
126C2×C4×D43—21no—
127C2×C4×D43—21no—
128C2×C4×D43—21no—
129C2×C4×D43—21no—
130C2×C4×D43—22no—
131C2×C4×D43—41no—
132C2×C4×D43—42no—
133C2×C4×D43—42no—
134C2×C4×D43—42no—
135C2×Dic86—42no—
136C2×Dic86—42no—
137C2×Dic86—42no—
138C2×C8×C43—22no—
139C2×C8×C43—22no—
140C2×C8×C43C2×D414yes—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—42no—
147C4⋊C4×C43—42no—
148C4⋊C4×C43#4112yes—
149C42×C43—42no—
150C42×C43C2×D412yes—
151C42×C43#4112yes—
152(C2×D43)⋊C4—24no—
153(C2×D43)⋊C4—42no—
154(C2×D43)⋊C4—44no—
155(C2×D43)⋊C4—42no—
156(C2×D43)⋊C4—42no—
157(C2×D43)⋊C4—42no—
158C4⋊Dic43—22no—
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161C4⋊Dic43—22no—
162C4⋊Dic43—42no—
163C4⋊Dic43—44no—
164C4⋊Dic43—42no—
165C4×Dic43—22no—
166C4×Dic43—22no—
167C4×Dic43—21no—
168C4×Dic43—21no—
169C2×C43⋊C8—22no—
170C2×C43⋊C8—22no—
171C2×C43⋊C8—22no—
172C23×C43C22×D411yescharacteristic
173C22×D43—21no—
174C22×D43—21no—
175C22×D43—21no—
176C22×D43—21no—
177C22×D43—21no—
178C22×D43—21no—
179C22×D43—22no—
180C22×D43—41no—
181C22×D43—41no—
182C22×D43—41no—
183C22×D43—41no—
184C22×D43—41no—
185C22×D43—41no—
186C22×D43#13712yes—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—22no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—42no—
193C2×C4×C43—41no—
194C2×C4×C43—42no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—42no—
198C2×C4×C43#12112yes—
199C2×C4×C43#12112yes—
200C2×C4×C43AGL(1,ℤ/8)12yes—
201C2×C4×C43AGL(1,ℤ/8)12yes—
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C2×#4111yescharacteristic
204C2×C4×C43C2×#4111yescharacteristic
205C2×C4×C43C2×#4111yescharacteristic
206C2×C4×C432−1+411yescharacteristic
207C2×C4×C432−1+411yescharacteristic
208C2×Dic43—21no—
209C2×Dic43—21no—
210C2×Dic43—21no—
211C2×Dic43—21no—
212C2×Dic43—21no—
213C2×Dic43—21no—
214C2×Dic43—21no—
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—42no—
218C2×Dic43—41no—
219C2×Dic43—42no—
220C2×Dic43—41no—
221C2×Dic43—42no—
222C2×Dic43—41no—
223D172—22no—
224D172—22no—
225D172—48no—
226D172—41no—
227D172—41no—
228C4×D43—44no—
229C4×D43—41no—
230C4×D43—41no—
231C4×D43—41no—
232C4×D43—41no—
233C4×D43—44no—
234C4×D43—84no—
235Dic86—84no—
236C8×C43—24no—
237C43⋊C8—42no—
238#24709—431nomaximal, Sylow
239C22×C43C2×#12111yescharacteristic
240C22×C43#52511yescharacteristic
241C22×C43#53611yescharacteristic
242C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
243C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
244C22×C43C2×#13711yescharacteristic
245C22×C43#57511yescharacteristic
246C2×D43—22no—
247C2×D43—22no—
248C2×D43—22no—
249C2×D43—41no—
250C2×D43—41no—
251C2×D43—41no—
252C2×D43—41no—
253C2×D43—42no—
254C2×D43—42no—
255C2×D43—42no—
256C2×D43—81no—
257C2×D43—81no—
258C2×D43—81no—
259C2×D43—81no—
260C4×C43—22no—
261C4×C43—42no—
262C4×C43—82no—
263C4×C43—81no—
264C4×C43#46914yes—
265C4×C43#54711yescharacteristic
266C4×C43#54811yescharacteristic
267C4×C43#55211yescharacteristic
268C4×C43#55611yescharacteristic
269Dic43—41no—
270Dic43—41no—
271Dic43—41no—
272Dic43—82no—
273Dic43—81no—
274C2×#474—431no—
275C2×#432—431no—
276#2857—431no—
277C4×#121—431no—
278#2076—432no—
279#2034—432no—
280#1988—431no—
281#1948D4311yescharacteristic, complemented
282#1944—432no—
283#1936—432no—
284#1802—431no—
285C2×C43#241511yescharacteristic
286C2×C43C2×#46911yescharacteristic
287C2×C43#305611yescharacteristic
288C2×C43#311011yescharacteristic
289C2×C43#311511yescharacteristic
290C2×C43#323511yescharacteristic
291C2×C43#323911yescharacteristic
292D43—42no—
293D43—82no—
294C2×C4⋊Q8—431no—
295C2×C22⋊Q8—861no—
296C2×#121—431no—
297C2×C4×D4—431no—
298C2×C4×D4—861no—
299C22×C42—431no—
300#474—864no—
301#432—864no—
302C2×#107—432no—
303C2×#106C2×D4312yes—
304C2×C4⋊C8—431no—
305C2×C4⋊C8C2×D4311yescharacteristic
306C2×#102—432no—
307C2×#102—432no—
308C2×C22⋊C8—432no—
309C2×#97—432no—
310#391—861no—
311#390—431no—
312#389—432no—
313#389—431no—
314#389—861no—
315#388—861no—
316#386—861no—
317#384C2×D4311yescharacteristic
318#380—431no—
319#380—432no—
320#380—861no—
321C4×C4⋊C4C2×D4311yescharacteristic
322C4×C22⋊C4—861no—
323#340—432no—
324#340—432no—
325#340—432no—
326#340C2×D4312yes—
327C43#2470911yescharacteristic, complemented, Sylow
328C22×Q8—861no—
329C22×D4—431no—
330C22×D4—861no—
331C23×C4—431no—
332C23×C4—431no—
333C23×C4—431no—
334C23×C4—861no—
335C22×C8—432no—
336C22×C8C22×D4312yes—
337C4⋊Q8—862no—
338C4⋊Q8—862no—
339C22⋊Q8—1724no—
340#121—862no—
341#121—862no—
342C4×D4—862no—
343C4×D4—862no—
344C4×D4—1724no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—431no—
348C2×C4⋊C4—432no—
349C2×C4⋊C4—861no—
350C2×C4⋊C4—862no—
351C2×C4⋊C4—861no—
352C2×C4⋊C4C22×D4311yescharacteristic
353C2×C4⋊C4C22×D4312yes—
354C2×C4⋊C4C22×D4311yescharacteristic
355C2×C22⋊C4—861no—
356C2×C22⋊C4—861no—
357C2×C22⋊C4—861no—
358C2×C22⋊C4—861no—
359C2×C22⋊C4—862no—
360C2×C22⋊C4—861no—
361C2×C42—21no—
362C2×C42—431no—
363C2×C42—431no—
364C2×C42—431no—
365C2×C42—862no—
366C2×C42—862no—
367C2×C42C22×D4311yescharacteristic
368#107—864no—
369#106—24no—
370C4⋊C8—862no—
371C4⋊C8D17214yescomplemented
372#102—864no—
373#102—864no—
374C22⋊C8—864no—
375#97—864no—
376#95—21no—
377#95—861no—
378#95—861no—
379#95—862no—
380#95—862no—
381C24—431no—
382C24—861no—
383C2×Q8—1722no—
384C2×Q8—1722no—
385C2×Q8—1722no—
386C2×D4—432no—
387C2×D4—864no—
388C2×D4—861no—
389C2×D4—861no—
390C2×D4—861no—
391C2×D4—861no—
392C2×D4—861no—
393C2×D4—1722no—
394C2×D4—1722no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—431no—
399C22×C4—431no—
400C22×C4—431no—
401C22×C4—862no—
402C22×C4—862no—
403C22×C4—862no—
404C22×C4—862no—
405C22×C4—862no—
406C22×C4—861no—
407C22×C4—861no—
408C22×C4—861no—
409C22×C4—861no—
410C22×C4—861no—
411C22×C4—861no—
412C22×C4—861no—
413C22×C4—862no—
414C22×C4—1721no—
415C22×C4—1722no—
416C22×C4—1722no—
417C22×C4—1722no—
418C22×C4D4×D4311yescharacteristic
419C22×C4D4×D4311yescharacteristic
420C22×C4C23×D4311yescharacteristic
421C2×C8—22no—
422C2×C8—22no—
423C2×C8—862no—
424C2×C8—862no—
425C2×C8—862no—
426C2×C8C2×D17214yes—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—42no—
433C4⋊C4—42no—
434C4⋊C4—862no—
435C4⋊C4—861no—
436C4⋊C4—861no—
437C4⋊C4—862no—
438C4⋊C4—1722no—
439C4⋊C4—1724no—
440C4⋊C4—1722no—
441C4⋊C4#1062190012yes—
442C22⋊C4—864no—
443C22⋊C4—1722no—
444C22⋊C4—1722no—
445C22⋊C4—1722no—
446C22⋊C4—1724no—
447C22⋊C4—1722no—
448C42—42no—
449C42—862no—
450C42—862no—
451C42—861no—
452C42—861no—
453C42C2×D17212yes—
454C42#1062190212yes—
455C23—432no—
456C23—861no—
457C23—861no—
458C23—861no—
459C23—861no—
460C23—861no—
461C23—861no—
462C23—862no—
463C23—1721no—
464C23—1721no—
465C23—1721no—
466C23—1721no—
467C23—1721no—
468C23—1721no—
469C23C2×D4×D4311yescharacteristic
470Q8—3444no—
471D4—862no—
472D4—862no—
473D4—1728no—
474D4—1721no—
475D4—1721no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—861no—
488C2×C4—861no—
489C2×C4—861no—
490C2×C4—861no—
491C2×C4—861no—
492C2×C4—861no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—861no—
496C2×C4—3444no—
497C2×C4—1724no—
498C2×C4—1721no—
499C2×C4—1722no—
500C2×C4—1721no—
501C2×C4—1722no—
502C2×C4—1721no—
503C2×C4—1722no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4—1721no—
507C2×C4—1721no—
508C2×C4—1724no—
509C2×C4#1306330012yes—
510C2×C4#1306330012yes—
511C2×C4#1306335212yes—
512C2×C4#1306335212yes—
513C2×C4C22×D17211yescharacteristic
514C2×C4#41×D4311yescharacteristic
515C2×C4C2×#1062190011yescharacteristic
516C2×C4C2×#1062190211yescharacteristic
517C2×C4#1306337211yescharacteristic
518C2×C4#1306337311yescharacteristic
519C8—24no—
520C8—1722no—
521C22—862no—
522C22—862no—
523C22—862no—
524C22—3441no—
525C22—3441no—
526C22—3441no—
527C22—3441no—
528C22—1722no—
529C22—1722no—
530C22—1722no—
531C22—1721no—
532C22—1721no—
533C22—1721no—
534C22—1721no—
535C22C2×#1306330011yescharacteristic
536C22#1458340911yescharacteristic
537C22#1458347211yescharacteristic
538C22C2×#1306335211yescharacteristic
539C22C2×#1306335211yescharacteristic
540C22#137×D4311yescharacteristic
541C22#1458369511yescharacteristic
542C4—22no—
543C4—42no—
544C4—82no—
545C4—81no—
546C4—3441no—
547C4—3442no—
548C4—1721no—
549C4—1721no—
550C4—1721no—
551C4#1458315314yes—
552C4#1458355311yescharacteristic
553C4#1458356111yescharacteristic
554C4#1458358711yescharacteristic
555C4#1458362311yescharacteristic
556C2—3442no—
557C2—1722no—
558C2#1913802211yescharacteristic
559C2C2×#1458315311yescharacteristic
560C2#1914422611yescharacteristic
561C2#1914469311yescharacteristic
562C2#1914474511yescharacteristic
563C2#1914579111yescharacteristic
564C2#1914582911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1948C2
socleC23×C43C22×D4
prime radicalC2×#13063300C22
hypercenter#1948D43
hypocenterC43#24709
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
1. C2×#14583180C2semidirect
2. C2×#14582955C2semidirect
3. #19142948C2semidirect
5. #19136025C2semidirect
7. #19135547C2semidirect
8. #19135339C2semidirect
9. #19135293C2semidirect
10. #19134592C2semidirect
11. C43×#1948C2semidirect
96. C4⋊C8×C43D4semidirect
281. #1948D43semidirect
327. C43#24709semidirect
371. C4⋊C8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145831802
C2×#145829552
#191429482
C4×#130633002
#191360252
#191357862
#191355472
#191353392
#191352932
#191345922
C43×#19482
#2470943