Finite Group Databasebeta

← #24996821

Subgroups — #24996821

Order 11008.

812 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583212C211yesmaximal, characteristic, complemented
2#19140329C211yesmaximal, characteristic
3#19134681C211yesmaximal, characteristic, complemented
4C2×#14582632C211yesmaximal, characteristic, complemented
5C2×#14582623C211yesmaximal, characteristic, complemented
6#19132474C211yesmaximal, characteristic, complemented
7C2×C43×#397C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×#13063294—21no—
10#14583212—22no—
11#14583212—22no—
12C2×#13063258—21no—
13C2×#13063245—21no—
14C2×C22⋊(C43⋊C8)C2211yescharacteristic
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16#14582824—21no—
17#14582815—22no—
18#14582808—21no—
19#14582778—21no—
20#14582759C2211yescharacteristic
21#14582661—22no—
22#14582632—22no—
23#14582623—22no—
24C22×C4⋊C4×C43C2211yescharacteristic
25C22×C22⋊C4×C43—21no—
26C22×C22⋊C4×C43C2211yescharacteristic
27C43×#397—22no—
28C43×#397—22no—
29C2×#95×C43—21no—
30C2×#95×C43C2211yescharacteristic
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C22×C22⋊D43—22no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8—21no—
36#13063299—21no—
37#13063299—21no—
38#13063299—21no—
39#13063299—21no—
40#13063294—42no—
41#13063294—42no—
42C2×C4⋊Dic43D411yescharacteristic
43C2×C4⋊Dic43D412yes—
44C2×C22⋊Dic43—22no—
45C2×C22⋊Dic43—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—22no—
48#13063258—24no—
49#13063245—24no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C22⋊(C43⋊C8)D412yescomplemented
54C43⋊#95—22no—
55C43⋊#95—21no—
56C25×C43D411yescharacteristic
57C23×C4×C43—21no—
58C23×C4×C43—21no—
59C23×C4×C43D411yescharacteristic
60C23×C4×C43C2311yescharacteristic
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43—21no—
65C2×C4⋊C4×C43—21no—
66C2×C4⋊C4×C43D412yescomplemented
67C2×C22⋊C4×C43—24no—
68C2×C22⋊C4×C43—21no—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—21no—
71C2×C22⋊C4×C43—21no—
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43—42no—
75C2×C22⋊C4×C43—42no—
76#95×C43—24no—
77#95×C43—21no—
78#95×C43D412yescomplemented
79C24×C43—21no—
80C24×C43—21no—
81C24×C43—21no—
82C24×C43—21no—
83C24×C43—21no—
84C24×C43—21no—
85C24×C43—42no—
86C24×C43—42no—
87C24×C43D812yes—
88C24×C43C2×D411yescharacteristic
89C23×D43—21no—
90C22×C4×C43—21no—
91C22×C4×C43—22no—
92C22×C4×C43—22no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—42no—
96C22×C4×C43—42no—
97C22×C4×C43—42no—
98C22×C4×C43—42no—
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×C43—41no—
106C22×C4×C43—41no—
107C22×C4×C43C2×D411yescharacteristic
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D411yescharacteristic
112C22×C4×C43#4111yescharacteristic
113C2×C22⋊D43—44no—
114C2×C22⋊D43—41no—
115C2×C22⋊D43—41no—
116C2×C22⋊D43—41no—
117C2×C22⋊D43—41no—
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—82no—
121C2×C22⋊D43—82no—
122C22×Dic43—21no—
123C22×Dic43—22no—
124C2×D172—21no—
125C2×D172—21no—
126C2×D172—42no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43—22no—
129C4⋊C4×C43—41no—
130C4⋊C4×C43—41no—
131C22⋊C4×C43—48no—
132C22⋊C4×C43—41no—
133C22⋊C4×C43—41no—
134C22⋊C4×C43—41no—
135C22⋊C4×C43—41no—
136C22⋊Dic43—44no—
137C22⋊Dic43—41no—
138C22⋊Dic43—41no—
139(C2×D43)⋊C4—41no—
140(C2×D43)⋊C4—41no—
141(C2×D43)⋊C4—82no—
142C4⋊Dic43—21no—
143C4⋊Dic43—21no—
144C4⋊Dic43—42no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8—42no—
147C2×C43⋊C8—42no—
148C2×C43⋊C8—41no—
149C23×C43—22no—
150C23×C43—22no—
151C23×C43—22no—
152C23×C43—22no—
153C23×C43—22no—
154C23×C43—44no—
155C23×C43—44no—
156C23×C43—42no—
157C23×C43—42no—
158C23×C43—41no—
159C23×C43—41no—
160C23×C43—41no—
161C23×C43—42no—
162C23×C43—42no—
163C23×C43—41no—
164C23×C43—82no—
165C23×C43—82no—
166C23×C43—81no—
167C23×C43—81no—
168C23×C43#12011yescharacteristic
169C23×C43#12011yescharacteristic
170C23×C43#12111yescharacteristic
171C23×C43C2×D811yescharacteristic
172C23×C43#13511yescharacteristic
173C23×C43AGL(1,ℤ/8)11yescharacteristic
174C23×C43AGL(1,ℤ/8)11yescharacteristic
175C22×D43—41no—
176C22×D43—41no—
177C22×D43—41no—
178C22×D43—42no—
179C22×D43—42no—
180C2×C4×C43—22no—
181C2×C4×C43—22no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—42no—
187C2×C4×C43—42no—
188C2×C4×C43—42no—
189C2×C4×C43—41no—
190C2×C4×C43—42no—
191C2×C4×C43—42no—
192C2×C4×C43—42no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43—82no—
196C2×C4×C43—82no—
197C2×C4×C43—81no—
198C2×C4×C43—81no—
199C2×C4×C43—81no—
200C2×C4×C43—81no—
201C2×C4×C43—81no—
202C2×C4×C43#12011yescharacteristic
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43#12111yescharacteristic
205C2×C4×C43#12711yescharacteristic
206C22⋊D43—88no—
207C22⋊D43—81no—
208C22⋊D43—81no—
209C22⋊D43—81no—
210C22⋊D43—81no—
211C2×Dic43—41no—
212C2×Dic43—42no—
213C2×Dic43—41no—
214C2×Dic43—41no—
215C2×Dic43—42no—
216C2×Dic43—42no—
217D172—42no—
218D172—81no—
219C43⋊C8—42no—
220C43⋊C8—81no—
221#9918—431nomaximal, Sylow
222C22×C43—22no—
223C22×C43—22no—
224C22×C43—22no—
225C22×C43—22no—
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—21no—
229C22×C43—21no—
230C22×C43—44no—
231C22×C43—44no—
232C22×C43—42no—
233C22×C43—82no—
234C22×C43—82no—
235C22×C43—82no—
236C22×C43—82no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43#39211yescharacteristic
240C22×C43#44711yescharacteristic
241C22×C43#44711yescharacteristic
242C22×C43#44911yescharacteristic
243C22×C43#44911yescharacteristic
244C22×C43#45512yes—
245C22×C43#45812yes—
246C22×C43#46611yescharacteristic
247C22×C43#46911yescharacteristic
248C2×D43—82no—
249C2×D43—82no—
250C2×D43—81no—
251C2×D43—81no—
252C2×D43—81no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—82no—
258C4×C43—82no—
259C4×C43—81no—
260Dic43—82no—
261Dic43—81no—
262C2×#480—431no—
263#2617—431no—
264C2×#397D4311yescharacteristic, complemented
265#1823—431no—
266C2×#327—431no—
267C2×#323—431no—
268#1294—431no—
269C2×C43—21no—
270C2×C43—21no—
271C2×C43—21no—
272C2×C43—21no—
273C2×C43—82no—
274C2×C43#160712yes—
275C2×C43#161212yes—
276C2×C43#199911yescharacteristic
277C2×C43#200411yescharacteristic
278C2×C43#202211yescharacteristic
279D43—161no—
280C2×#121—431no—
281C2×#120—861no—
282C22×C4⋊C4C2×D4311yescharacteristic
283C22×C22⋊C4—21no—
284C22×C22⋊C4C2×D4311yescharacteristic
285#480—862no—
286#480—862no—
287C2×#107—861no—
288C2×#102—861no—
289C2×C22⋊C8—431no—
290C2×C22⋊C8—431no—
291#397—22no—
292#397—22no—
293#397—861no—
294#394—862no—
295#392—861no—
296#386—861no—
297#380—431no—
298C2×#95—21no—
299C2×#95C2×D4311yescharacteristic
300#340—862no—
301#327—862no—
302#323—862no—
303C43#991811yescharacteristic, complemented, Sylow
304C25C22⋊D4311yescharacteristic
305C22×D4—431no—
306C22×D4—862no—
307C22×D4—861no—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4C22⋊D4311yescharacteristic
311C23×C4C22×D4311yescharacteristic
312C22×C8—861no—
313C22×C8—861no—
314#121—861no—
315#121—861no—
316#121—861no—
317#121—861no—
318#120—1722no—
319#120—1722no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—431no—
326C2×C4⋊C4—432no—
327C2×C4⋊C4C22⋊D4312yescomplemented
328C2×C22⋊C4—24no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—21no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—42no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—862no—
338C2×C22⋊C4—862no—
339C2×C22⋊C4—861no—
340C2×C22⋊C4—861no—
341#107—864no—
342#102—864no—
343C22⋊C8—432no—
344C22⋊C8—861no—
345C22⋊C8—861no—
346C22⋊C8—861no—
347#95—24no—
348#95—21no—
349#95—862no—
350#95—861no—
351#95C22⋊D4312yescomplemented
352C24—21no—
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—21no—
358C24—42no—
359C24—42no—
360C24—861no—
361C24#1062188212yes—
362C24C2×C22⋊D4311yescharacteristic
363C2×D4—861no—
364C2×D4—861no—
365C2×D4—3442no—
366C2×D4—3442no—
367C2×D4—1722no—
368C2×D4—1724no—
369C2×D4—1721no—
370C2×D4—1721no—
371C2×D4—1721no—
372C2×D4—1721no—
373C2×D4—1721no—
374C2×D4—1721no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
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—861no—
393C22×C4—862no—
394C22×C4D4×D4311yescharacteristic
395C22×C4D4×D4311yescharacteristic
396C22×C4D4×D4311yescharacteristic
397C22×C4#1062190011yescharacteristic
398C22×C4C2×C22⋊D4311yescharacteristic
399C22×C4C2×C22⋊D4311yescharacteristic
400C2×C8—862no—
401C2×C8—1722no—
402C2×C8—1721no—
403C2×C8—1722no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—861no—
409C4⋊C4—861no—
410C4⋊C4—1722no—
411C22⋊C4—48no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—3442no—
417C22⋊C4—1724no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C22⋊C4—1721no—
421C22⋊C4—1721no—
422C23—22no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—44no—
428C23—42no—
429C23—44no—
430C23—42no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—42no—
435C23—42no—
436C23—41no—
437C23—82no—
438C23—81no—
439C23—82no—
440C23—81no—
441C23—1721no—
442C23—1721no—
443C23—1722no—
444C23—1722no—
445C23—1721no—
446C23#1306329311yescharacteristic
447C23#1306329411yescharacteristic
448C23#1306329711yescharacteristic
449C23C2×#1062188211yescharacteristic
450C23#1306334511yescharacteristic
451C23#1306335011yescharacteristic
452C23#1306335111yescharacteristic
453D4—3441no—
454D4—3448no—
455D4—3441no—
456D4—3441no—
457D4—3441no—
458D4—3441no—
459D4—1722no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—42no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—1721no—
483C2×C4—1721no—
484C2×C4—1722no—
485C2×C4—1722no—
486C2×C4—1721no—
487C2×C4—1722no—
488C2×C4#1306329311yescharacteristic
489C2×C4#1306329611yescharacteristic
490C2×C4#1306329711yescharacteristic
491C2×C4#1306332111yescharacteristic
492C8—3441no—
493C8—1722no—
494C22—21no—
495C22—21no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—21no—
501C22—21no—
502C22—44no—
503C22—42no—
504C22—44no—
505C22—82no—
506C22—82no—
507C22—82no—
508C22—81no—
509C22—82no—
510C22—81no—
511C22—3441no—
512C22—3441no—
513C22—3442no—
514C22—3442no—
515C22—3441no—
516C22#1458280711yescharacteristic
517C22#1458303211yescharacteristic
518C22#1458303311yescharacteristic
519C22#1458304211yescharacteristic
520C22#1458304411yescharacteristic
521C22#1458307612yes—
522C22#1458308812yes—
523C22#1458313311yescharacteristic
524C22#1458315011yescharacteristic
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—82no—
530C4—82no—
531C4—81no—
532C4—3441no—
533C4—3442no—
534C2—21no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—82no—
539C2—6881no—
540C2#1913358012yes—
541C2#1913360712yes—
542C2#1913559111yescharacteristic
543C2#1913562411yescharacteristic
544C2#1913572311yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC2×C43×#397C2
socleC23×C43#120
prime radical#19140329C2
hypercenterC2×#397D43
hypocenterC43#9918
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C2×#14583212C2semidirect
3. #19134681C2semidirect
4. C2×#14582632C2semidirect
5. C2×#14582623C2semidirect
6. #19132474C2semidirect
7. C2×C43×#397C2semidirect
53. C22⋊(C43⋊C8)D4semidirect
66. C2×C4⋊C4×C43D4semidirect
78. #95×C43D4semidirect
264. C2×#397D43semidirect
303. C43#9918semidirect
327. C2×C4⋊C4C22⋊D43semidirect
351. #95C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145832122
#191403292
#191346812
C2×#145826322
C2×#145826232
#191324742
C2×C43×#3972
#991843