Finite Group Databasebeta

← #25000111

Subgroups — #25000111

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139508C211yesmaximal, characteristic
2#19134751C211yesmaximal, characteristic, complemented
3#19134592C211yesmaximal, characteristic, complemented
4C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
5C2×#14582626C211yesmaximal, characteristic, complemented
6#19132479C211yesmaximal, characteristic, complemented
7C43×#1802C211yesmaximal, characteristic, complemented
8C2×#13063299—21no—
9C2×#13063296—21no—
10C2×C4×D172C2211yescharacteristic
11C2×#13063256—22no—
12C2×C4⋊(C43⋊C8)C2211yescharacteristic
13C2×#13063245—21no—
14C2×C4×C43⋊C8C2211yescharacteristic
15#14582815—22no—
16#14582769C2211yescharacteristic
17#14582759—21no—
18#14582756—21no—
19#14582661—21no—
20D4⋊(C43⋊C8)—22no—
21#14582626—22no—
22C2×C4×D4×C43C2211yescharacteristic
23C2×C4⋊C8×C43C2211yescharacteristic
24C2×#102×C43—21no—
25C43×#384C2211yescharacteristic
26C43×#340—21no—
27C22×D172D411yescharacteristic
28C22×C22⋊D43—22no—
29C22×C4×D43—21no—
30C22×C43⋊C8—21no—
31C22×C43⋊C8—21no—
32#13063299—42no—
33#13063299—42no—
34#13063296—42no—
35#13063296—42no—
36C4×D172—21no—
37C4×D172—21no—
38C4×D172—21no—
39C4×D172—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43—21no—
42C2×C4⋊Dic43D411yescharacteristic
43C2×C4⋊Dic43D412yes—
44C2×C22⋊Dic43—22no—
45C2×(C2×D43)⋊C4—22no—
46C2×(C2×D43)⋊C4—21no—
47#13063256—44no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50#13063245—42no—
51C4×C43⋊C8—21no—
52C4×C43⋊C8D412yescomplemented
53C43⋊#95—22no—
54C22×D4×C43D411yescharacteristic
55C23×C4×C43—21no—
56C22×C8×C43—21no—
57C4×D4×C43—21no—
58C4×D4×C43—21no—
59C4×D4×C43—21no—
60C4×D4×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—21no—
64C2×C4⋊C4×C43D411yescharacteristic
65C2×C22⋊C4×C43—21no—
66C2×C42×C43C2311yescharacteristic
67C4⋊C8×C43—21no—
68C4⋊C8×C43—21no—
69#102×C43—42no—
70C24×C43—21no—
71C23×D43—21no—
72C2×D4×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43SD1612yes—
78C22×C4×C43—21no—
79C22×C4×C43—41no—
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×C43C2×D411yescharacteristic
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C2×C22⋊D43—44no—
90C2×C22⋊D43—44no—
91C2×C22⋊D43—82no—
92C22×Dic43—21no—
93C22×Dic43—22no—
94C2×D172—21no—
95C2×D172—21no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172SD1612yes—
100C2×C4×D43—41no—
101C2×C4×D43—41no—
102C2×C4×D43—41no—
103C2×C4×D43—41no—
104C2×C4×D43—41no—
105C2×C4×D43—41no—
106C2×C8×C43—41no—
107C2×C8×C43—41no—
108C2×C8×C43—41no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—42no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C4⋊C4×C43—41no—
115C4⋊C4×C43—41no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120C42×C43#4111yescharacteristic
121C42×C43#4111yescharacteristic
122C22⋊Dic43—44no—
123(C2×D43)⋊C4—44no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4—41no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43—41no—
129C4⋊Dic43—41no—
130C4⋊Dic43—41no—
131C4⋊Dic43—41no—
132C4⋊Dic43—42no—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138C2×C43⋊C8—41no—
139C23×C43—22no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43#12011yescharacteristic
147C22×D43—22no—
148C22×D43—41no—
149C22×D43—41no—
150C22×D43—41no—
151C22×D43—41no—
152C22×D43—41no—
153C22×D43—41no—
154D4×C43—22no—
155D4×C43—22no—
156D4×C43—41no—
157D4×C43—41no—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—41no—
161C2×C4×C43—41no—
162C2×C4×C43—41no—
163C2×C4×C43—81no—
164C2×C4×C43—81no—
165C2×C4×C43—81no—
166C2×C4×C43—81no—
167C2×C4×C43—81no—
168C2×C4×C43—81no—
169C2×C4×C43—81no—
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12311yescharacteristic
174C2×C4×C43#12311yescharacteristic
175C2×C4×C43#12411yescharacteristic
176C2×C4×C43C2×SD1611yescharacteristic
177C2×C4×C43C2×SD1611yescharacteristic
178C2×C4×C43#13511yescharacteristic
179C2×C4×C43#13511yescharacteristic
180C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
184C22⋊D43—88no—
185C2×Dic43—41no—
186C2×Dic43—41no—
187C2×Dic43—42no—
188C2×Dic43—42no—
189C2×Dic43—41no—
190C2×Dic43—42no—
191D172—22no—
192D172—22no—
193D172—41no—
194D172—41no—
195C4×D43—81no—
196C4×D43—81no—
197C4×D43—81no—
198C4×D43—81no—
199C8×C43—81no—
200C43⋊C8—24no—
201C43⋊C8—81no—
202#10432—431nomaximal, Sylow
203C22×C43—42no—
204C22×C43—42no—
205C22×C43—42no—
206C22×C43—81no—
207C22×C43—81no—
208C22×C43—81no—
209C22×C43—81no—
210C22×C43#39411yescharacteristic
211C22×C43#44911yescharacteristic
212C22×C43#44911yescharacteristic
213C22×C43#45011yescharacteristic
214C22×C43#45011yescharacteristic
215C22×C43#45311yescharacteristic
216C22×C43#45611yescharacteristic
217C2×D43—42no—
218C2×D43—42no—
219C2×D43—42no—
220C2×D43—81no—
221C2×D43—81no—
222C2×D43—81no—
223C2×D43—81no—
224C4×C43—21no—
225C4×C43—21no—
226C4×C43—81no—
227C4×C43—161no—
228C4×C43#46511yescharacteristic
229C4×C43#46511yescharacteristic
230C4×C43#46911yescharacteristic
231C4×C43#46911yescharacteristic
232C4×C43#48111yescharacteristic
233C4×C43#48111yescharacteristic
234C4×C43#48211yescharacteristic
235C4×C43#48211yescharacteristic
236Dic43—82no—
237Dic43—81no—
238#2537—431no—
239#1844—431no—
240#1802—431no—
241#1802D4311yescharacteristic, complemented
242C2×D4⋊C8—431no—
243C2×D4⋊C8—431no—
244#1296—431no—
245C2×C43—82no—
246C2×C43#162411yescharacteristic
247C2×C43#162911yescharacteristic
248C2×C43#165411yescharacteristic
249C2×C43#165411yescharacteristic
250C2×C43#203411yescharacteristic
251C2×C43#203411yescharacteristic
252C2×C43#203911yescharacteristic
253D43—82no—
254C2×#121—861no—
255C2×#121—861no—
256C2×C4×D4—431no—
257C2×C4×D4C2×D4311yescharacteristic
258C2×#106—862no—
259C2×C4⋊C8—431no—
260C2×C4⋊C8C2×D4311yescharacteristic
261C2×#102—21no—
262C2×#102—861no—
263C2×C4×C8—431no—
264#394—862no—
265#384—431no—
266#384C2×D4311yescharacteristic
267#380—861no—
268#380—861no—
269#340—21no—
270#340—861no—
271D4⋊C8—862no—
272D4⋊C8—862no—
273C43#1043211yescharacteristic, complemented, Sylow
274C22×D4—431no—
275C22×D4—862no—
276C22×D4C22⋊D4311yescharacteristic
277C23×C4—21no—
278C23×C4—861no—
279C22×C8—21no—
280C22×C8—861no—
281C22×C8—861no—
282#121—1722no—
283#121—1722no—
284#121—1722no—
285#121—1722no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—861no—
291C4×D4—861no—
292C4×D4—861no—
293C4×D4—861no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—431no—
298C2×C4⋊C4—432no—
299C2×C4⋊C4—861no—
300C2×C4⋊C4—861no—
301C2×C4⋊C4C22⋊D4311yescharacteristic
302C2×C22⋊C4—21no—
303C2×C22⋊C4—862no—
304C2×C22⋊C4—862no—
305C2×C22⋊C4—861no—
306C2×C42C22×D4311yescharacteristic
307#106—1724no—
308C4⋊C8—21no—
309C4⋊C8—21no—
310C4⋊C8—861no—
311C4⋊C8—861no—
312#102—42no—
313#102—1722no—
314C4×C8—432no—
315C4×C8—861no—
316#95—862no—
317C24—21no—
318C24—861no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—432no—
325C2×D4—861no—
326C2×D4—861no—
327C2×D4—861no—
328C2×D4—861no—
329C2×D4—861no—
330C2×D4—3442no—
331C2×D4—1724no—
332C2×D4—1724no—
333C2×D4#1062188412yes—
334C22×C4—21no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—861no—
343C22×C4—862no—
344C22×C4—1721no—
345C22×C4—1721no—
346C22×C4—1721no—
347C22×C4—1721no—
348C22×C4—1721no—
349C22×C4—1721no—
350C22×C4D4×D4311yescharacteristic
351C22×C4D4×D4311yescharacteristic
352C22×C4C2×C22⋊D4311yescharacteristic
353C2×C8—41no—
354C2×C8—41no—
355C2×C8—41no—
356C2×C8—862no—
357C2×C8—862no—
358C2×C8—862no—
359C2×C8—1721no—
360C2×C8—1721no—
361C2×C8—1721no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—42no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—861no—
370C4⋊C4—861no—
371C4⋊C4—1722no—
372C4⋊C4—1721no—
373C4⋊C4—1721no—
374C4⋊C4—1721no—
375C4⋊C4—1721no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—1724no—
379C22⋊C4—1724no—
380C22⋊C4—1721no—
381C22⋊C4—1721no—
382C42#1062189811yescharacteristic
383C42#1062189811yescharacteristic
384C42D4×D4311yescharacteristic
385C42#1062190011yescharacteristic
386C23—22no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—862no—
394C23—1721no—
395C23—1721no—
396C23—1721no—
397C23—1721no—
398C23—1721no—
399C23—1721no—
400C23#1306329311yescharacteristic
401D4—22no—
402D4—22no—
403D4—41no—
404D4—41no—
405D4—862no—
406D4—862no—
407D4—3448no—
408D4—1721no—
409D4—1721no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—81no—
416C2×C4—81no—
417C2×C4—81no—
418C2×C4—81no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—3441no—
423C2×C4—3441no—
424C2×C4—3441no—
425C2×C4—3441no—
426C2×C4—1721no—
427C2×C4—1722no—
428C2×C4—1721no—
429C2×C4—1722no—
430C2×C4—1722no—
431C2×C4—1721no—
432C2×C4#1306329711yescharacteristic
433C2×C4#1306329811yescharacteristic
434C2×C4#1306329811yescharacteristic
435C2×C4#1306330711yescharacteristic
436C2×C4#1306330811yescharacteristic
437C2×C4#1306331111yescharacteristic
438C2×C4SD16×D4311yescharacteristic
439C2×C4C2×#1062188411yescharacteristic
440C2×C4#1306334411yescharacteristic
441C2×C4#1306334511yescharacteristic
442C2×C4#1306334911yescharacteristic
443C2×C4#1306335011yescharacteristic
444C2×C4#1306335111yescharacteristic
445C2×C4#1306335211yescharacteristic
446C8—81no—
447C8—864no—
448C8—3441no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—3441no—
457C22—3441no—
458C22—3441no—
459C22—3441no—
460C22—1722no—
461C22—1722no—
462C22—1722no—
463C22#1458281411yescharacteristic
464C22#1458304111yescharacteristic
465C22#1458304211yescharacteristic
466C22#1458304811yescharacteristic
467C22#1458304911yescharacteristic
468C22#1458306511yescharacteristic
469C22#1458308011yescharacteristic
470C4—21no—
471C4—21no—
472C4—81no—
473C4—161no—
474C4—3442no—
475C4—3441no—
476C4#1458312711yescharacteristic
477C4#1458313011yescharacteristic
478C4#1458315011yescharacteristic
479C4#1458315111yescharacteristic
480C4#1458321611yescharacteristic
481C4#1458321711yescharacteristic
482C4#1458322111yescharacteristic
483C4#1458322311yescharacteristic
484C2—82no—
485C2—3442no—
486C2#1913367711yescharacteristic
487C2#1913371011yescharacteristic
488C2#1913387711yescharacteristic
489C2#1913387811yescharacteristic
490C2#1913578211yescharacteristic
491C2#1913578411yescharacteristic
492C2#1913581711yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1802C2
socleC23×C43#120
prime radical#19139508C2
hypercenter#1802D43
hypocenterC43#10432
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
2. #19134751C2semidirect
3. #19134592C2semidirect
4. C2×D4⋊(C43⋊C8)C2semidirect
5. C2×#14582626C2semidirect
6. #19132479C2semidirect
7. C43×#1802C2semidirect
52. C4×C43⋊C8D4semidirect
241. #1802D43semidirect
273. C43#10432semidirect

Maximal subgroups

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

subgroupindex
#191395082
#191347512
#191345922
C2×D4⋊(C43⋊C8)2
C2×#145826262
#191324792
C43×#18022
#1043243