Finite Group Databasebeta

← #24993914

Subgroups — #24993914

Order 11008.

640 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143617C211yesmaximal, characteristic, complemented
2#19139557C211yesmaximal, characteristic
3#19134580C211yesmaximal, characteristic, complemented
4#19133163C211yesmaximal, characteristic, complemented
5#19132475C211yesmaximal, characteristic, complemented
6#19132473C211yesmaximal, characteristic, complemented
7C43×#1519C211yesmaximal, characteristic, complemented
8C2×#13063297—21no—
9C2×C4×C22⋊D43C2211yescharacteristic
10C8×C22⋊D43—22no—
11(C22⋊D43)⋊C8—22no—
12#14582949—21no—
13C2×#13063239—21no—
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C22⋊C8×D43—21no—
16#14582830C411yescharacteristic, complemented
17#14582825C411yescharacteristic, complemented
18#14582813C411yescharacteristic, complemented
19#14582807C411yescharacteristic, complemented
20#14582787—21no—
21#14582779—21no—
22#14582775—21no—
23#14582759C2211yescharacteristic
24C2×C43⋊#95C2211yescharacteristic
25#14582665—21no—
26#14582633—22no—
27C2×#121×C43C2211yescharacteristic
28C2×C22⋊C8×C43C2211yescharacteristic
29C43×#380C2211yescharacteristic
30C43×#327—22no—
31C22×C22⋊D43—21no—
32C22×C22⋊D43D411yescharacteristic
33C23×Dic43—21no—
34C22×C4×D43D411yescharacteristic
35C22×C43⋊C8—21no—
36C2×C8×D43—22no—
37#13063297—42no—
38#13063297—42no—
39C4×C22⋊D43—21no—
40C4×C22⋊D43—21no—
41C4×C22⋊D43—21no—
42C4×C22⋊D43—21no—
43C2×C4⋊Dic43—21no—
44C2×Dic43⋊C4—21no—
45C2×Dic43⋊C4C2×C411yescharacteristic
46C2×C22⋊Dic43—21no—
47C2×C22⋊Dic43—21no—
48C2×C22⋊Dic43—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43D411yescharacteristic
51C2×(C2×D43)⋊C4—21no—
52C2×(C2×D43)⋊C4C2×C411yescharacteristic
53C2×C4×Dic43D411yescharacteristic
54Dic43⋊C8—22no—
55#13063239—42no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)D412yescomplemented
58(C2×D43)⋊C8—22no—
59C8×Dic43—22no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95C2×C411yescharacteristic
65C43⋊#95C2×C411yescharacteristic
66C22×D4×C43—21no—
67C22×D4×C43C2×C411yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C22×C8×C43—21no—
70#121×C43—21no—
71#121×C43—21no—
72#121×C43—21no—
73#121×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43C2×C411yescharacteristic
76C2×C22⋊C4×C43—21no—
77C2×C22⋊C4×C43—21no—
78C22⋊C8×C43—21no—
79C22⋊C8×C43D412yescomplemented
80#95×C43—21no—
81C24×C43—21no—
82C24×C43C2×D411yescharacteristic
83C23×D43C22⋊C411yescharacteristic
84C2×D4×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—41no—
92C2×D4×C43—81no—
93C22×C4×C43—21no—
94C22×C4×C43—41no—
95C22×C4×C43—81no—
96C22×C4×C43C22×C411yescharacteristic
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43#4111yescharacteristic
101C22×C4×C43#4111yescharacteristic
102C2×C22⋊D43—21no—
103C2×C22⋊D43—21no—
104C2×C22⋊D43—21no—
105C2×C22⋊D43—21no—
106C2×C22⋊D43—42no—
107C2×C22⋊D43—42no—
108C2×C22⋊D43—81no—
109C2×C22⋊D43D812yes—
110C2×C22⋊D43SD1612yes—
111C22×Dic43—21no—
112C22×Dic43—21no—
113C22×Dic43—42no—
114C22×Dic43—41no—
115C22×Dic43—41no—
116C22×Dic43—41no—
117C22×Dic43—81no—
118C22×Dic43C22⋊C411yescharacteristic
119C22×Dic43C22⋊C411yescharacteristic
120C22×Dic43C22⋊C411yescharacteristic
121C2×C4×D43—21no—
122C2×C4×D43—21no—
123C2×C4×D43—81no—
124C2×C8×C43—22no—
125C2×C8×C43—81no—
126C4⋊C4×C43—21no—
127C4⋊C4×C43—21no—
128C4⋊C4×C43—81no—
129C22⋊C4×C43—41no—
130C22⋊C4×C43—41no—
131C22⋊C4×C43—41no—
132C22⋊C4×C43—41no—
133C22⋊Dic43—21no—
134C22⋊Dic43—21no—
135C22⋊Dic43—42no—
136C22⋊Dic43—42no—
137C22⋊Dic43—41no—
138C22⋊Dic43—41no—
139C22⋊Dic43—81no—
140(C2×D43)⋊C4—21no—
141(C2×D43)⋊C4—21no—
142(C2×D43)⋊C4—42no—
143C4⋊Dic43—81no—
144Dic43⋊C4—21no—
145Dic43⋊C4—21no—
146Dic43⋊C4—42no—
147C4×Dic43—21no—
148C4×Dic43—21no—
149C2×C43⋊C8—22no—
150C2×C43⋊C8—81no—
151C8×D43—82no—
152C23×C43—41no—
153C23×C43—41no—
154C23×C43—41no—
155C23×C43—41no—
156C23×C43—41no—
157C23×C43—41no—
158C23×C43—41no—
159C23×C43—41no—
160C23×C43—41no—
161C23×C43C2×C22⋊C411yescharacteristic
162C23×C43#12111yescharacteristic
163C23×C43#12111yescharacteristic
164C23×C43C2×D811yescharacteristic
165C23×C43C2×SD1611yescharacteristic
166C23×C43#13511yescharacteristic
167C23×C43#13511yescharacteristic
168C22×D43—21no—
169C22×D43—21no—
170C22×D43—41no—
171C22×D43—41no—
172C22×D43#10212yes—
173D4×C43—81no—
174D4×C43—81no—
175D4×C43—81no—
176D4×C43—81no—
177D4×C43—81no—
178D4×C43—81no—
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—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—81no—
189C2×C4×C43—81no—
190C2×C4×C43—81no—
191C2×C4×C43C4×D411yescharacteristic
192C2×C4×C43C4×D411yescharacteristic
193C2×C4×C43#12011yescharacteristic
194C2×C4×C43#12311yescharacteristic
195C22⋊D43—22no—
196C22⋊D43—22no—
197C22⋊D43—22no—
198C22⋊D43—22no—
199C22⋊D43—84no—
200C2×Dic43—21no—
201C2×Dic43—21no—
202C2×Dic43—22no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—41no—
212C2×Dic43—82no—
213C2×Dic43—82no—
214C2×Dic43—81no—
215C2×Dic43—81no—
216C2×Dic43—81no—
217C2×Dic43#10212yes—
218C4×D43—42no—
219C4×D43—81no—
220C8×C43—42no—
221C43⋊C8—42no—
222#9384—431nomaximal, Sylow
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—41no—
230C22×C43—41no—
231C22×C43—41no—
232C22×C43—41no—
233C22×C43—81no—
234C22×C43—81no—
235C22×C43—81no—
236C22×C43—81no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43—81no—
240C22×C43#38611yescharacteristic
241C22×C43C2×#10211yescharacteristic
242C22×C43#41611yescharacteristic
243C22×C43#46511yescharacteristic
244C22×C43#46511yescharacteristic
245C22×C43#46611yescharacteristic
246C22×C43#46611yescharacteristic
247C2×D43—22no—
248C2×D43—41no—
249C2×D43—41no—
250C2×D43—42no—
251C2×D43—81no—
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—81no—
257C4×C43—161no—
258Dic43—22no—
259Dic43—42no—
260Dic43—41no—
261Dic43—41no—
262Dic43—81no—
263Dic43—161no—
264#2972—431no—
265#2543—431no—
266#1799—431no—
267#1519—431no—
268#1519D4311yescharacteristic, complemented
269#1294—431no—
270#1294—431no—
271C2×C43—21no—
272C2×C43—21no—
273C2×C43—21no—
274C2×C43—21no—
275C2×C43—21no—
276C2×C43—21no—
277C2×C43—161no—
278C2×C43#188411yescharacteristic
279C2×C43#189311yescharacteristic
280C2×C43#191311yescharacteristic
281D43—42no—
282C2×#121—861no—
283C2×#121C2×D4311yescharacteristic
284C2×C4×D4—431no—
285C8×D4—862no—
286C8×D4—862no—
287#431—861no—
288C2×#99—861no—
289C2×C22⋊C8—431no—
290C2×C22⋊C8—861no—
291C2×C22⋊C8C2×D4311yescharacteristic
292#398—431no—
293#397—431no—
294#394—431no—
295#392—431no—
296#388—861no—
297#386—861no—
298#386—861no—
299#380—431no—
300#380C2×D4311yescharacteristic
301C2×#95—431no—
302#342—861no—
303#327—22no—
304#327—862no—
305C43#938411yescharacteristic, complemented, Sylow
306C22×D4—21no—
307C22×D4—431no—
308C22×D4—861no—
309C22×D4C4×D4311yescharacteristic
310C23×C4—431no—
311C23×C4—861no—
312C23×C4C22×D4311yescharacteristic
313C22×C8—21no—
314C22×C8—862no—
315C22×C8—861no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—21no—
320#121—1722no—
321#121—1722no—
322C4×D4—861no—
323C4×D4—861no—
324C4×D4—861no—
325C4×D4—861no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—431no—
328C2×C4⋊C4—861no—
329C2×C4⋊C4—861no—
330C2×C4⋊C4C4×D4311yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—431no—
334C2×C22⋊C4—431no—
335C2×C22⋊C4—861no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C22⋊C4—861no—
339C2×C22⋊C4—861no—
340C2×C42—431no—
341C4⋊C8—862no—
342#99—1722no—
343C22⋊C8—21no—
344C22⋊C8—432no—
345C22⋊C8—862no—
346C22⋊C8—861no—
347C22⋊C8C22⋊D4312yescomplemented
348C4×C8—862no—
349#95—21no—
350#95—431no—
351#95—431no—
352#95—861no—
353#95—861no—
354#95—861no—
355#95—861no—
356C24—21no—
357C24—431no—
358C24D4×D4311yescharacteristic
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—81no—
368C2×D4—432no—
369C2×D4—432no—
370C2×D4—861no—
371C2×D4—861no—
372C2×D4—861no—
373C2×D4—861no—
374C2×D4—3441no—
375C2×D4—1722no—
376C2×D4—1722no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—81no—
380C22×C4—431no—
381C22×C4—431no—
382C22×C4—431no—
383C22×C4—861no—
384C22×C4—861no—
385C22×C4—861no—
386C22×C4—861no—
387C22×C4—3441no—
388C22×C4—3441no—
389C22×C4—1722no—
390C22×C4—1721no—
391C22×C4—1721no—
392C22×C4—1721no—
393C22×C4C2×C4×D4311yescharacteristic
394C22×C4#1062189811yescharacteristic
395C22×C4D4×D4311yescharacteristic
396C22×C4D4×D4311yescharacteristic
397C22×C4#1062190011yescharacteristic
398C22×C4C2×C22⋊D4311yescharacteristic
399C2×C8—22no—
400C2×C8—81no—
401C2×C8—862no—
402C2×C8—3442no—
403C2×C8—3441no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—81no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C4⋊C4—3441no—
410C4⋊C4—1722no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—861no—
416C22⋊C4—861no—
417C22⋊C4—861no—
418C22⋊C4—861no—
419C22⋊C4—3441no—
420C22⋊C4—1722no—
421C22⋊C4—1722no—
422C22⋊C4—1722no—
423C22⋊C4—1721no—
424C22⋊C4—1721no—
425C42—861no—
426C42—861no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—432no—
437C23—861no—
438C23—861no—
439C23—1721no—
440C23—1721no—
441C23C22⋊C4×D4311yescharacteristic
442C23#1306329611yescharacteristic
443C23#1306329811yescharacteristic
444C23D8×D4311yescharacteristic
445C23SD16×D4311yescharacteristic
446C23#1306334411yescharacteristic
447C23#1306334611yescharacteristic
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452D4—81no—
453D4—81no—
454D4—862no—
455D4—862no—
456D4—862no—
457D4—862no—
458D4—3444no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—432no—
472C2×C4—861no—
473C2×C4—861no—
474C2×C4—862no—
475C2×C4—861no—
476C2×C4—861no—
477C2×C4—3441no—
478C2×C4—3442no—
479C2×C4—3442no—
480C2×C4—3441no—
481C2×C4—3441no—
482C2×C4—3441no—
483C2×C4—1722no—
484C2×C4—1721no—
485C2×C4—1721no—
486C2×C4—1721no—
487C2×C4—1721no—
488C2×C4—1721no—
489C2×C4—1721no—
490C2×C4—1721no—
491C2×C4(C22⋊D43)⋊C411yescharacteristic
492C2×C4C4×C22⋊D4311yescharacteristic
493C2×C4#1306329311yescharacteristic
494C2×C4#1306330711yescharacteristic
495C8—42no—
496C8—1722no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—862no—
515C22—3441no—
516C22—1722no—
517C22—1721no—
518C22—1721no—
519C22#1458277511yescharacteristic
520C22#102×D4311yescharacteristic
521C22#1458289211yescharacteristic
522C22#1458312511yescharacteristic
523C22#1458312711yescharacteristic
524C22#1458313211yescharacteristic
525C22#1458313411yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—81no—
531C4—161no—
532C4—862no—
533C4—3441no—
534C4—1722no—
535C4—1721no—
536C4—1721no—
537C4—6881no—
538C2—21no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—161no—
545C2—1722no—
546C2#1913497511yescharacteristic
547C2#1913502011yescharacteristic
548C2#1913513411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1519C2
socleC22×C43#386
prime radical#19139557C2
cosocleC23×C4×C43C23
hypercenter#1519D43
hypocenterC43#9384
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
1. #19143617C2semidirect
3. #19134580C2semidirect
4. #19133163C2semidirect
5. #19132475C2semidirect
6. #19132473C2semidirect
7. C43×#1519C2semidirect
16. #14582830C4semidirect
17. #14582825C4semidirect
18. #14582813C4semidirect
19. #14582807C4semidirect
57. C22⋊(C43⋊C8)D4semidirect
79. C22⋊C8×C43D4semidirect
268. #1519D43semidirect
305. C43#9384semidirect
347. C22⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191436172
#191395572
#191345802
#191331632
#191324752
#191324732
C43×#15192
#938443