Finite Group Databasebeta

← #24999940

Subgroups — #24999940

Order 11008.

646 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140523C211yesmaximal, characteristic
2#19134912C211yesmaximal, characteristic
3#19134902C211yesmaximal, characteristic, complemented
4C2×#14582635C211yesmaximal, characteristic, complemented
5C2×#14582632C211yesmaximal, characteristic
6#19132438C211yesmaximal, characteristic, complemented
7C43×#1444C211yesmaximal, characteristic, complemented
8C2×#13063304C2211yescharacteristic
9C2×#13063299C2211yescharacteristic
10C2×#13063248—21no—
11C2×#13063245—21no—
12C2×C22⋊(C43⋊C8)C2211yescharacteristic
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14#14582839—21no—
15#14582826—21no—
16#14582817—21no—
17#14582812—21no—
18#14582778—21no—
19#14582778—21no—
20#14582661—21no—
21#14582661—21no—
22#14582635—22no—
23#14582632—22no—
24C22×C4⋊C4×C43—21no—
25C22×C4⋊C4×C43C2211yescharacteristic
26C2×#95×C43—21no—
27C2×#95×C43C2211yescharacteristic
28C2×#95×C43C2211yescharacteristic
29C22×Dic86D411yescharacteristic
30C22×D172D411yescharacteristic
31C22×C22⋊D43—21no—
32C22×C43⋊C8—21no—
33C22×C43⋊C8—21no—
34#13063304—21no—
35#13063304—21no—
36#13063304—21no—
37#13063304—21no—
38#13063299—21no—
39#13063299—21no—
40#13063299—21no—
41#13063299—21no—
42C2×C4⋊Dic43D411yescharacteristic
43C2×C4⋊Dic43D411yescharacteristic
44C2×Dic43⋊C4—21no—
45C2×C22⋊Dic43—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×(C2×D43)⋊C4—21no—
51#13063248—42no—
52#13063245—42no—
53C22⋊(C43⋊C8)—21no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C43⋊#95—21no—
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C23×C4×C43—21no—
62C23×C4×C43—21no—
63C23×C4×C43D411yescharacteristic
64C23×C4×C43D411yescharacteristic
65C23×C4×C43C2311yescharacteristic
66C2×C4⋊C4×C43—21no—
67C2×C4⋊C4×C43—21no—
68C2×C4⋊C4×C43—42no—
69C2×C4⋊C4×C43—42no—
70C2×C4⋊C4×C43—42no—
71C2×C4⋊C4×C43—42no—
72#95×C43—21no—
73#95×C43—21no—
74#95×C43—21no—
75#95×C43—42no—
76#95×C43D412yes—
77C24×C43C2×D411yescharacteristic
78C23×D43—21no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—22no—
82C22×C4×C43—21no—
83C22×C4×C43—21no—
84C22×C4×C43—22no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—21no—
89C22×C4×C43—41no—
90C22×C4×C43—41no—
91C22×C4×C43—41no—
92C22×C4×C43—41no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43—41no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43—41no—
105C22×C4×C43C2×D411yescharacteristic
106C22×C4×C43C2×D411yescharacteristic
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43#4111yescharacteristic
109C22×C4×C43#4111yescharacteristic
110C22×C4×C43#4111yescharacteristic
111C2×C22⋊D43—41no—
112C2×C22⋊D43—41no—
113C2×C22⋊D43—41no—
114C2×C22⋊D43—41no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C22×Dic43—21no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C2×D172—21no—
121C2×D172—21no—
122C2×D172—41no—
123C2×D172—41no—
124C2×Dic86—21no—
125C2×Dic86—21no—
126C2×Dic86—41no—
127C2×Dic86—41no—
128C4⋊C4×C43—22no—
129C4⋊C4×C43—22no—
130C4⋊C4×C43—41no—
131C4⋊C4×C43—41no—
132C4⋊C4×C43—48no—
133C22⋊Dic43—41no—
134C22⋊Dic43—41no—
135(C2×D43)⋊C4—41no—
136(C2×D43)⋊C4—41no—
137(C2×D43)⋊C4—81no—
138(C2×D43)⋊C4—81no—
139(C2×D43)⋊C4—81no—
140(C2×D43)⋊C4—81no—
141C4⋊Dic43—21no—
142C4⋊Dic43—21no—
143C4⋊Dic43—21no—
144C4⋊Dic43—21no—
145Dic43⋊C4—41no—
146Dic43⋊C4—41no—
147C2×C43⋊C8—41no—
148C2×C43⋊C8—41no—
149C2×C43⋊C8—41no—
150C2×C43⋊C8—41no—
151C2×C43⋊C8—41no—
152C2×C43⋊C8—41no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43#12011yescharacteristic
158C23×C43#12111yescharacteristic
159C23×C43#12411yescharacteristic
160C23×C43#13511yescharacteristic
161C23×C43#13511yescharacteristic
162C23×C43AGL(1,ℤ/8)11yescharacteristic
163C23×C43#13711yescharacteristic
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—24no—
176C2×C4×C43—41no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—42no—
181C2×C4×C43—42no—
182C2×C4×C43—42no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—42no—
186C2×C4×C43—42no—
187C2×C4×C43—42no—
188C2×C4×C43—42no—
189C2×C4×C43—42no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—42no—
196C2×C4×C43—41no—
197C2×C4×C43—81no—
198C2×C4×C43—81no—
199C2×C4×C43—81no—
200C2×C4×C43—81no—
201C2×C4×C43—81no—
202C2×C4×C43—81no—
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43#12111yescharacteristic
205C2×C4×C43#12311yescharacteristic
206C2×C4×C43#12311yescharacteristic
207C22⋊D43—81no—
208C22⋊D43—81no—
209C22⋊D43—81no—
210C22⋊D43—81no—
211C2×Dic43—41no—
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43—41no—
216C2×Dic43—41no—
217C2×Dic43—41no—
218C2×Dic43—41no—
219C2×Dic43—41no—
220D172—42no—
221D172—81no—
222Dic86—42no—
223Dic86—81no—
224C43⋊C8—81no—
225C43⋊C8—81no—
226#10405—431nomaximal, Sylow
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—21no—
239C22×C43#39411yescharacteristic
240C22×C43#44911yescharacteristic
241C22×C43#45211yescharacteristic
242C22×C43#45311yescharacteristic
243C22×C43#45611yescharacteristic
244C22×C43B(4,𝔽2)11yescharacteristic
245C22×C43#45811yescharacteristic
246C22×C43#46311yescharacteristic
247C22×C43#46411yescharacteristic
248C22×C43#48811yescharacteristic
249C22×C43#48911yescharacteristic
250C2×D43—81no—
251C2×D43—81no—
252C2×D43—81no—
253C2×D43—81no—
254C2×D43—81no—
255C2×D43—81no—
256C2×D43—81no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—44no—
262C4×C43—81no—
263C4×C43—82no—
264C4×C43—81no—
265Dic43—81no—
266Dic43—81no—
267Dic43—81no—
268#2639—431no—
269#1874—431no—
270#1872—431no—
271C2×#328—431no—
272C2×#327—431no—
273#1444D4311yescharacteristic, complemented
274#1280—431no—
275C2×C43—21no—
276C2×C43—21no—
277C2×C43—21no—
278C2×C43—21no—
279C2×C43#160011yescharacteristic
280C2×C43#160311yescharacteristic
281C2×C43#160911yescharacteristic
282C2×C43#161811yescharacteristic
283C2×C43#203911yescharacteristic
284C2×C43#204211yescharacteristic
285C2×C43#204411yescharacteristic
286D43—161no—
287C2×C22⋊Q8—431no—
288C2×#121—431no—
289C22×C4⋊C4—21no—
290C22×C4⋊C4C2×D4311yescharacteristic
291C2×#103—861no—
292C2×#102—861no—
293C2×C22⋊C8—431no—
294C2×C22⋊C8—431no—
295#400—861no—
296#397—861no—
297#394—861no—
298#393—861no—
299#386—861no—
300#386—861no—
301C2×#95—21no—
302C2×#95C2×D4311yescharacteristic
303C2×#95C2×D4311yescharacteristic
304#340—861no—
305#340—861no—
306#328—862no—
307#327—862no—
308C43#1040511yescharacteristic, complemented, Sylow
309C22×Q8—431no—
310C22×D4—431no—
311C22×D4—861no—
312C23×C4—21no—
313C23×C4—21no—
314C23×C4C22⋊D4311yescharacteristic
315C23×C4C22⋊D4311yescharacteristic
316C23×C4C22×D4311yescharacteristic
317C22×C8—861no—
318C22×C8—861no—
319C22⋊Q8—861no—
320C22⋊Q8—861no—
321C22⋊Q8—861no—
322C22⋊Q8—861no—
323#121—861no—
324#121—861no—
325#121—861no—
326#121—861no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—42no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—42no—
332C2×C4⋊C4—42no—
333C2×C4⋊C4—431no—
334C2×C4⋊C4—431no—
335C2×C4⋊C4—861no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—861no—
340C2×C22⋊C4—861no—
341C2×C22⋊C4—861no—
342#103—1722no—
343#102—1722no—
344C22⋊C8—861no—
345C22⋊C8—861no—
346C22⋊C8—861no—
347C22⋊C8—861no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—42no—
352#95—861no—
353#95—861no—
354#95—861no—
355#95—861no—
356#95D17212yes—
357C24—861no—
358C24C2×C22⋊D4311yescharacteristic
359C2×Q8—861no—
360C2×Q8—861no—
361C2×Q8—1721no—
362C2×Q8—1721no—
363C2×D4—861no—
364C2×D4—861no—
365C2×D4—1721no—
366C2×D4—1721no—
367C2×D4—1721no—
368C2×D4—1721no—
369C2×D4—1721no—
370C2×D4—1721no—
371C2×D4—1721no—
372C2×D4—1721no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—41no—
395C22×C4—41no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—861no—
400C22×C4—861no—
401C22×C4—861no—
402C22×C4C2×D17211yescharacteristic
403C22×C4#1062189811yescharacteristic
404C22×C4D4×D4311yescharacteristic
405C22×C4D4×D4311yescharacteristic
406C22×C4#1062190211yescharacteristic
407C22×C4#1062190211yescharacteristic
408C2×C8—1721no—
409C2×C8—1721no—
410C2×C8—1721no—
411C2×C8—1721no—
412C2×C8—1721no—
413C2×C8—1721no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—48no—
419C4⋊C4—861no—
420C4⋊C4—861no—
421C4⋊C4—861no—
422C4⋊C4—861no—
423C4⋊C4—1721no—
424C4⋊C4—1721no—
425C22⋊C4—3441no—
426C22⋊C4—3441no—
427C22⋊C4—3441no—
428C22⋊C4—3441no—
429C22⋊C4—1721no—
430C22⋊C4—1721no—
431C22⋊C4—1721no—
432C22⋊C4—1721no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—1721no—
438C23—1721no—
439C23—1721no—
440C23—1721no—
441C23—1721no—
442C23—1721no—
443C23—1721no—
444C23#1306329311yescharacteristic
445C23#1306329911yescharacteristic
446C23#1306331411yescharacteristic
447C23#1306334511yescharacteristic
448C23#1306334511yescharacteristic
449C23#1306335111yescharacteristic
450C23#1306335611yescharacteristic
451Q8—3441no—
452Q8—1722no—
453D4—3441no—
454D4—3441no—
455D4—3441no—
456D4—3441no—
457D4—3441no—
458D4—1722no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—24no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—81no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—81no—
490C2×C4—81no—
491C2×C4—1721no—
492C2×C4—1721no—
493C2×C4—1721no—
494C2×C4—1721no—
495C2×C4—1721no—
496C2×C4—1721no—
497C2×C4—1721no—
498C2×C4—1721no—
499C2×C4—1721no—
500C2×C4#1306330011yescharacteristic
501C2×C4#1306330011yescharacteristic
502C2×C4#1306331011yescharacteristic
503C2×C4#1306331011yescharacteristic
504C8—3441no—
505C8—3441no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—3441no—
519C22—3441no—
520C22—3441no—
521C22—3441no—
522C22—3441no—
523C22—3441no—
524C22—3441no—
525C22#1458281611yescharacteristic
526C22#1458304211yescharacteristic
527C22#1458305911yescharacteristic
528C22#1458306611yescharacteristic
529C22#1458308111yescharacteristic
530C22#1458308511yescharacteristic
531C22#1458308811yescharacteristic
532C22#1458311411yescharacteristic
533C22#1458312111yescharacteristic
534C22#1458325611yescharacteristic
535C22#1458326111yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—44no—
541C4—81no—
542C4—82no—
543C4—81no—
544C4—3441no—
545C4—3441no—
546C4—3441no—
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—6881no—
552C2#1913353911yescharacteristic
553C2#1913355611yescharacteristic
554C2#1913359011yescharacteristic
555C2#1913364111yescharacteristic
556C2#1913581911yescharacteristic
557C2#1913583611yescharacteristic
558C2#1913584611yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1444C2
socleC23×C43#120
prime radicalC2×#13063299C22
hypercenter#1444D43
hypocenterC43#10405
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1444

Complements

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

NH ≅ G/Ntype
3. #19134902C2semidirect
4. C2×#14582635C2semidirect
6. #19132438C2semidirect
7. C43×#1444C2semidirect
273. #1444D43semidirect
308. C43#10405semidirect

Maximal subgroups

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

subgroupindex
#191405232
#191349122
#191349022
C2×#145826352
C2×#145826322
#191324382
C43×#14442
#1040543