Finite Group Databasebeta

← #24989329

Subgroups — #24989329

Order 11008.

698 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137101C211yesmaximal, characteristic
2#19134573C211yesmaximal, characteristic, complemented
3C2×#14582634C211yesmaximal, characteristic
4C2×#14582632C211yesmaximal, characteristic
5#19132821C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1294C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×#13063287C411yescharacteristic, complemented
10C2×(C22⋊D43)⋊C4—21no—
11C22×C4×Dic43C2211yescharacteristic
12C2×Dic43⋊C8—21no—
13C2×C22⋊(C43⋊C8)C2211yescharacteristic
14#14582800C411yescharacteristic, complemented
15#14582795C411yescharacteristic, complemented
16#14582788—21no—
17#14582776—21no—
18C4⋊C4×Dic43C411yescharacteristic, complemented
19#14582746—21no—
20C2×C43⋊#95—21no—
21C2×C43⋊#95—21no—
22C2×C43⋊#95C2211yescharacteristic
23#14582653—21no—
24#14582634—22no—
25#14582632—22no—
26C2×C22⋊C8×C43C2211yescharacteristic
27C43×#380C2211yescharacteristic
28C2×#95×C43C2211yescharacteristic
29C22×D172C2×C411yescharacteristic
30C22×C22⋊D43—21no—
31C23×Dic43—21no—
32C23×Dic43D411yescharacteristic
33C23×Dic43D411yescharacteristic
34C22×C4×D43—21no—
35C22×C43⋊C8—21no—
36#13063299—21no—
37#13063299—21no—
38#13063299D412yes—
39#13063299Q812yes—
40#13063287—42no—
41(C22⋊D43)⋊C4—42no—
42(C22⋊D43)⋊C4—42no—
43C2×C4⋊Dic43C2×C411yescharacteristic
44C2×Dic43⋊C4—21no—
45C2×(C2×D43)⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×C4×Dic43—21no—
50C2×C4×Dic43—42no—
51C2×C4×Dic43C2×C411yescharacteristic
52C2×C4×Dic43C2×C411yescharacteristic
53C2×C4×Dic43D411yescharacteristic
54C2×C4×Dic43D411yescharacteristic
55Dic43⋊C8—42no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)—21no—
58C43⋊#95—24no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—42no—
64C23×C4×C43—21no—
65C23×C4×C43C2311yescharacteristic
66C22×C8×C43—21no—
67C2×C4⋊C4×C43C2×C411yescharacteristic
68C2×C4⋊C4×C43C2×C411yescharacteristic
69C2×C22⋊C4×C43—21no—
70C22⋊C8×C43—21no—
71C22⋊C8×C43—21no—
72#95×C43—21no—
73#95×C43—21no—
74#95×C43—21no—
75C24×C43C2×D411yescharacteristic
76C23×D43—21no—
77C22×C4×C43—22no—
78C22×C4×C43—21no—
79C22×C4×C43—21no—
80C22×C4×C43—41no—
81C22×C4×C43—41no—
82C22×C4×C43—41no—
83C22×C4×C43—41no—
84C22×C4×C43—41no—
85C22×C4×C43—41no—
86C22×C4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43C22×C411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43C2×Q811yescharacteristic
92C22×C4×C43#4111yescharacteristic
93C22×C4×C43#4111yescharacteristic
94C2×C22⋊D43—22no—
95C2×C22⋊D43—22no—
96C2×C22⋊D43—41no—
97C2×C22⋊D43—41no—
98C2×C22⋊D43—41no—
99C2×C22⋊D43—41no—
100C22×Dic43—22no—
101C22×Dic43—22no—
102C22×Dic43—22no—
103C22×Dic43—21no—
104C22×Dic43—21no—
105C22×Dic43—21no—
106C22×Dic43—21no—
107C22×Dic43—21no—
108C22×Dic43—41no—
109C22×Dic43—41no—
110C22×Dic43—41no—
111C22×Dic43—41no—
112C22×Dic43—41no—
113C22×Dic43—41no—
114C22×Dic43—41no—
115C22×Dic43—41no—
116C22×Dic43C22⋊C411yescharacteristic
117C22×Dic43C22⋊C411yescharacteristic
118C22×Dic43C22⋊C411yescharacteristic
119C22×Dic43C22⋊C411yescharacteristic
120C2×D172—21no—
121C2×D172—41no—
122C2×D172—41no—
123C2×D172C4⋊C412yes—
124C2×C4×D43—42no—
125C2×C4×D43—42no—
126C2×C4×D43—42no—
127C2×C8×C43—41no—
128C2×C8×C43—41no—
129C2×C8×C43—41no—
130C4⋊C4×C43—41no—
131C4⋊C4×C43—41no—
132C22⋊C4×C43—41no—
133C22⋊C4×C43—41no—
134(C2×D43)⋊C4—22no—
135(C2×D43)⋊C4—22no—
136(C2×D43)⋊C4—42no—
137(C2×D43)⋊C4—42no—
138(C2×D43)⋊C4—42no—
139C4⋊Dic43—21no—
140C4⋊Dic43C4⋊C412yes—
141Dic43⋊C4—42no—
142C4×Dic43—22no—
143C4×Dic43—22no—
144C4×Dic43—41no—
145C4×Dic43—41no—
146C4×Dic43—42no—
147C2×C43⋊C8—41no—
148C2×C43⋊C8—41no—
149C2×C43⋊C8—41no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43C2×C22⋊C411yescharacteristic
155C23×C43#12111yescharacteristic
156C23×C43C22⋊Q811yescharacteristic
157C23×C43#13511yescharacteristic
158C23×C43#13511yescharacteristic
159C23×C43AGL(1,ℤ/8)11yescharacteristic
160C23×C43AGL(1,ℤ/8)11yescharacteristic
161C22×D43—22no—
162C22×D43—41no—
163C22×D43—41no—
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—41no—
173C2×C4×C43—41no—
174C2×C4×C43—41no—
175C2×C4×C43—41no—
176C2×C4×C43—42no—
177C2×C4×C43—42no—
178C2×C4×C43—42no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—81no—
186C2×C4×C43—81no—
187C2×C4×C43—81no—
188C2×C4×C43—81no—
189C2×C4×C43C2×C4⋊C411yescharacteristic
190C2×C4×C43#11711yescharacteristic
191C2×C4×C43#12111yescharacteristic
192C2×C4×C43C22⋊Q811yescharacteristic
193C22⋊D43—42no—
194C22⋊D43—42no—
195C22⋊D43—42no—
196C22⋊D43—42no—
197C2×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43—22no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—21no—
208C2×Dic43—42no—
209C2×Dic43—42no—
210C2×Dic43—42no—
211C2×Dic43—42no—
212C2×Dic43—41no—
213C2×Dic43—41no—
214C2×Dic43—42no—
215C2×Dic43—42no—
216C2×Dic43—42no—
217C2×Dic43—81no—
218C2×Dic43—81no—
219C2×Dic43—81no—
220C2×Dic43—81no—
221C2×Dic43#9912yes—
222C2×Dic43#10412yes—
223D172—42no—
224D172—42no—
225C4×D43—84no—
226C8×C43—81no—
227C43⋊C8—81no—
228#8573—431nomaximal, Sylow
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—21no—
240C22×C43—21no—
241C22×C43#38011yescharacteristic
242C22×C43C2×#9911yescharacteristic
243C22×C43#41011yescharacteristic
244C22×C43#41611yescharacteristic
245C22×C43#41811yescharacteristic
246C22×C43C2×#10411yescharacteristic
247C22×C43#42111yescharacteristic
248C22×C43#46311yescharacteristic
249C22×C43#46311yescharacteristic
250C22×C43#47811yescharacteristic
251C22×C43#47811yescharacteristic
252C2×D43—42no—
253C2×D43—42no—
254C2×D43—42no—
255C2×D43—81no—
256C2×D43—81no—
257C2×D43—81no—
258C2×D43—81no—
259C4×C43—21no—
260C4×C43—21no—
261C4×C43—21no—
262C4×C43—21no—
263C4×C43—82no—
264C4×C43—81no—
265C4×C43—81no—
266Dic43—22no—
267Dic43—22no—
268Dic43—42no—
269Dic43—41no—
270Dic43—41no—
271Dic43—82no—
272C4×#121—431no—
273#1797—431no—
274C2×#327—431no—
275C2×#327—431no—
276#1434—431no—
277#1294—431no—
278#1294D4311yescharacteristic, complemented
279C2×C43—21no—
280C2×C43—21no—
281C2×C43—21no—
282C2×C43—21no—
283C2×C43#150011yescharacteristic
284C2×C43#150711yescharacteristic
285C2×C43#151411yescharacteristic
286C2×C43#151611yescharacteristic
287C2×C43#179911yescharacteristic
288C2×C43#180411yescharacteristic
289C2×C43#180611yescharacteristic
290D43—82no—
291C2×#121—431no—
292C2×C4×D4—431no—
293C2×C4×D4—861no—
294C22×C42—431no—
295C2×C4⋊C8—861no—
296C2×C22⋊C8—431no—
297C2×C22⋊C8C2×D4311yescharacteristic
298#390—431no—
299#389—431no—
300#388—861no—
301#386—861no—
302#380C2×D4311yescharacteristic
303C4×C4⋊C4—431no—
304C4×C22⋊C4—861no—
305C2×#95—431no—
306C2×#95—861no—
307C2×#95—861no—
308C2×#95C2×D4311yescharacteristic
309#336—861no—
310#327—862no—
311#327—862no—
312C43#857311yescharacteristic, complemented, Sylow
313C22×D4—431no—
314C22×D4—861no—
315C23×C4—21no—
316C23×C4—431no—
317C23×C4—431no—
318C23×C4—861no—
319C23×C4—861no—
320C23×C4C22×D4311yescharacteristic
321C22×C8—21no—
322C22×C8—861no—
323#121—432no—
324#121—432no—
325#121—861no—
326#121—861no—
327C4×D4—1722no—
328C4×D4—1722no—
329C4×D4—1722no—
330C2×C4⋊C4—431no—
331C2×C4⋊C4—861no—
332C2×C4⋊C4C4×D4311yescharacteristic
333C2×C4⋊C4C4×D4311yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—861no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C42—431no—
340C2×C42—431no—
341C2×C42—431no—
342C2×C42—431no—
343C2×C42—861no—
344C2×C42—1722no—
345C4⋊C8—1722no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8—861no—
349C22⋊C8—861no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—861no—
354#95—861no—
355#95—864no—
356#95—861no—
357#95—861no—
358#95—1722no—
359C24—861no—
360C24D4×D4311yescharacteristic
361C2×D4—432no—
362C2×D4—862no—
363C2×D4—862no—
364C2×D4—861no—
365C2×D4—1721no—
366C2×D4—1721no—
367C2×D4—1721no—
368C2×D4—1721no—
369C2×D4—1721no—
370C2×D4—1721no—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—431no—
383C22×C4—431no—
384C22×C4—431no—
385C22×C4—431no—
386C22×C4—862no—
387C22×C4—862no—
388C22×C4—861no—
389C22×C4—861no—
390C22×C4—861no—
391C22×C4—861no—
392C22×C4—861no—
393C22×C4—862no—
394C22×C4—1722no—
395C22×C4—1722no—
396C22×C4—1722no—
397C22×C4—1721no—
398C22×C4—1721no—
399C22×C4—1721no—
400C22×C4—1721no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4—1721no—
404C22×C4—1721no—
405C22×C4C2×C4×D4311yescharacteristic
406C22×C4#1062189811yescharacteristic
407C22×C4#1062189811yescharacteristic
408C22×C4D4×D4311yescharacteristic
409C22×C4D4×D4311yescharacteristic
410C22×C4Q8×D4311yescharacteristic
411C2×C8—41no—
412C2×C8—41no—
413C2×C8—41no—
414C2×C8—1721no—
415C2×C8—1721no—
416C2×C8—1721no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—432no—
420C4⋊C4—861no—
421C4⋊C4—1722no—
422C22⋊C4—41no—
423C22⋊C4—41no—
424C22⋊C4—862no—
425C22⋊C4—862no—
426C22⋊C4—1722no—
427C22⋊C4—1722no—
428C22⋊C4—1722no—
429C42—862no—
430C42—862no—
431C42—1721no—
432C42—1721no—
433C42—1722no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—862no—
439C23—1721no—
440C23—1721no—
441C23—1721no—
442C23—1721no—
443C23—1721no—
444C23—1721no—
445C23C22⋊C4×D4311yescharacteristic
446C23#1306329811yescharacteristic
447C23#1306330311yescharacteristic
448C23#1306334611yescharacteristic
449C23#1306334811yescharacteristic
450C23#1306334911yescharacteristic
451C23#1306335211yescharacteristic
452D4—1722no—
453D4—1722no—
454D4—1722no—
455D4—1722no—
456D4—1722no—
457D4—1722no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—432no—
480C2×C4—432no—
481C2×C4—861no—
482C2×C4—861no—
483C2×C4—861no—
484C2×C4—861no—
485C2×C4—861no—
486C2×C4—861no—
487C2×C4—861no—
488C2×C4—861no—
489C2×C4—861no—
490C2×C4—861no—
491C2×C4—862no—
492C2×C4—3444no—
493C2×C4—3441no—
494C2×C4—3441no—
495C2×C4—3441no—
496C2×C4—3441no—
497C2×C4—1722no—
498C2×C4—1722no—
499C2×C4—1722no—
500C2×C4—1722no—
501C2×C4—1722no—
502C2×C4—1722no—
503C2×C4—1722no—
504C2×C4—1721no—
505C2×C4—1721no—
506C2×C4C4⋊C4×D4311yescharacteristic
507C2×C4#1306328211yescharacteristic
508C2×C4#1306329811yescharacteristic
509C2×C4#1306330311yescharacteristic
510C8—81no—
511C8—3441no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—3441no—
525C22—3441no—
526C22—3441no—
527C22—3441no—
528C22—1722no—
529C22—1722no—
530C22—1722no—
531C22#1458275811yescharacteristic
532C22#99×D4311yescharacteristic
533C22#1458287111yescharacteristic
534C22#1458289411yescharacteristic
535C22#1458290211yescharacteristic
536C22#104×D4311yescharacteristic
537C22#1458291411yescharacteristic
538C22#1458311311yescharacteristic
539C22#1458311711yescharacteristic
540C22#1458319811yescharacteristic
541C22#1458320211yescharacteristic
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—82no—
547C4—81no—
548C4—81no—
549C4—862no—
550C4—862no—
551C4—3442no—
552C4—1722no—
553C4—1721no—
554C4—1721no—
555C2—21no—
556C2—21no—
557C2—21no—
558C2—21no—
559C2—3442no—
560C2#1913308011yescharacteristic
561C2#1913310911yescharacteristic
562C2#1913314011yescharacteristic
563C2#1913315011yescharacteristic
564C2#1913458211yescharacteristic
565C2#1913460411yescharacteristic
566C2#1913461411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1294C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C22
cosocleC23×C4×C43C23
hypercenter#1294D43
hypocenterC43#8573
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. #19134573C2semidirect
5. #19132821C2semidirect
6. #19132473C2semidirect
7. C43×#1294C2semidirect
9. C2×#13063287C4semidirect
14. #14582800C4semidirect
15. #14582795C4semidirect
18. C4⋊C4×Dic43C4semidirect
278. #1294D43semidirect
312. C43#8573semidirect

Maximal subgroups

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

subgroupindex
#191371012
#191345732
C2×#145826342
C2×#145826322
#191328212
#191324732
C43×#12942
#857343