Finite Group Databasebeta

← #25000103

Subgroups — #25000103

Order 11008.

614 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134722C211yesmaximal, characteristic, complemented
2#19134595C211yesmaximal, characteristic, complemented
3#19134595C211yesmaximal, characteristic, complemented
4C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
5C2×D4⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
6#19132478C211yesmaximal, characteristic, complemented
7C43×#2537C211yesmaximal, characteristic
8C2×C4⋊(C43⋊C8)C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×#13063246—21no—
11C2×#13063246—21no—
12C2×C4×C43⋊C8C2211yescharacteristic
13#14582769C2211yescharacteristic
14#14582661—22no—
15#14582661—21no—
16#14582661—21no—
17D4⋊(C43⋊C8)—22no—
18D4⋊(C43⋊C8)—22no—
19C2×#121×C43—21no—
20C2×#121×C43—21no—
21C2×C4×D4×C43C2211yescharacteristic
22C2×C4×D4×C43C2211yescharacteristic
23C43×#394—22no—
24C43×#384C2211yescharacteristic
25C43×#380—21no—
26C43×#380—21no—
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29C22×C43⋊C8—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C4⋊(C43⋊C8)—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37#13063246—42no—
38#13063246—42no—
39C4×C43⋊C8—21no—
40C4×C43⋊C8D412yescomplemented
41C22×D4×C43—22no—
42C22×D4×C43D411yescharacteristic
43C22×D4×C43D411yescharacteristic
44C23×C4×C43—21no—
45C23×C4×C43—21no—
46#121×C43—42no—
47#121×C43—42no—
48#121×C43—42no—
49#121×C43—42no—
50C4×D4×C43—21no—
51C4×D4×C43—21no—
52C4×D4×C43—21no—
53C4×D4×C43—21no—
54C4×D4×C43—21no—
55C4×D4×C43—21no—
56C4×D4×C43—21no—
57C4×D4×C43—21no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43D411yescharacteristic
61C2×C4⋊C4×C43D411yescharacteristic
62C2×C4⋊C4×C43D412yes—
63C2×C22⋊C4×C43—22no—
64C2×C22⋊C4×C43—22no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C42×C43C2311yescharacteristic
68#95×C43—22no—
69C24×C43—21no—
70C24×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—21no—
78C2×D4×C43—21no—
79C2×D4×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—44no—
82C2×D4×C43—44no—
83C2×D4×C43—82no—
84C2×D4×C43D812yes—
85C2×D4×C43SD1612yes—
86C22×C4×C43—21no—
87C22×C4×C43—21no—
88C22×C4×C43—22no—
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×C43C2×D411yescharacteristic
102C22×C4×C43C2×D411yescharacteristic
103C22×C4×C43C2×D411yescharacteristic
104C22×Dic43—41no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C4⋊C4×C43—42no—
110C4⋊C4×C43—41no—
111C4⋊C4×C43—41no—
112C4⋊C4×C43—41no—
113C4⋊C4×C43—41no—
114C22⋊C4×C43—44no—
115C22⋊C4×C43—44no—
116C22⋊C4×C43—41no—
117C22⋊C4×C43—41no—
118C22⋊C4×C43—41no—
119C22⋊C4×C43—41no—
120C42×C43C2×D411yescharacteristic
121C42×C43#4111yescharacteristic
122C42×C43#4111yescharacteristic
123C42×C43#4111yescharacteristic
124C4⋊Dic43—42no—
125C4⋊Dic43—41no—
126C4⋊Dic43—41no—
127C4⋊Dic43—41no—
128C4⋊Dic43—41no—
129C2×C43⋊C8—22no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8—41no—
134C2×C43⋊C8—41no—
135C2×C43⋊C8—41no—
136C2×C43⋊C8—41no—
137C2×C43⋊C8—41no—
138C23×C43—22no—
139C23×C43—22no—
140C23×C43—41no—
141C23×C43—41no—
142C23×C43—41no—
143C23×C43—41no—
144C23×C43—41no—
145C23×C43—41no—
146C23×C43—41no—
147C23×C43—41no—
148C23×C43—41no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43#12011yescharacteristic
153D4×C43—22no—
154D4×C43—22no—
155D4×C43—22no—
156D4×C43—22no—
157D4×C43—41no—
158D4×C43—41no—
159D4×C43—41no—
160D4×C43—41no—
161D4×C43—88no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—41no—
167C2×C4×C43—42no—
168C2×C4×C43—41no—
169C2×C4×C43—41no—
170C2×C4×C43—42no—
171C2×C4×C43—41no—
172C2×C4×C43—42no—
173C2×C4×C43—81no—
174C2×C4×C43—81no—
175C2×C4×C43—81no—
176C2×C4×C43—81no—
177C2×C4×C43—81no—
178C2×C4×C43—81no—
179C2×C4×C43—81no—
180C2×C4×C43—81no—
181C2×C4×C43#12111yescharacteristic
182C2×C4×C43#12111yescharacteristic
183C2×C4×C43#12111yescharacteristic
184C2×C4×C43#12311yescharacteristic
185C2×C4×C43#12311yescharacteristic
186C2×C4×C43#12411yescharacteristic
187C2×C4×C43C2×D811yescharacteristic
188C2×C4×C43C2×SD1611yescharacteristic
189C2×C4×C43#13511yescharacteristic
190C2×C4×C43#13511yescharacteristic
191C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C43#13711yescharacteristic
195C2×Dic43—81no—
196C2×Dic43—81no—
197C2×Dic43—81no—
198C43⋊C8—42no—
199C43⋊C8—81no—
200C43⋊C8—81no—
201#10431—431nomaximal, Sylow
202C22×C43—42no—
203C22×C43—42no—
204C22×C43—42no—
205C22×C43—42no—
206C22×C43—42no—
207C22×C43—42no—
208C22×C43—81no—
209C22×C43—81no—
210C22×C43—81no—
211C22×C43—81no—
212C22×C43—81no—
213C22×C43—81no—
214C22×C43—81no—
215C22×C43—81no—
216C22×C43#39411yescharacteristic
217C22×C43#44711yescharacteristic
218C22×C43#44911yescharacteristic
219C22×C43#45011yescharacteristic
220C22×C43#45211yescharacteristic
221C22×C43#45411yescharacteristic
222C22×C43#45511yescharacteristic
223C4×C43—21no—
224C4×C43—21no—
225C4×C43—82no—
226C4×C43—81no—
227C4×C43—81no—
228C4×C43#46511yescharacteristic
229C4×C43#46611yescharacteristic
230C4×C43#46811yescharacteristic
231C4×C43#46911yescharacteristic
232C4×C43#48011yescharacteristic
233C4×C43#48111yescharacteristic
234C4×C43#48211yescharacteristic
235C4×C43#48211yescharacteristic
236Dic43—161no—
237#2537D4311yescharacteristic
238#1834—431no—
239#1802—431no—
240#1802—431no—
241C2×D4⋊C8—431no—
242C2×D4⋊C8—431no—
243#1296—431no—
244C2×C43—82no—
245C2×C43—82no—
246C2×C43#162511yescharacteristic
247C2×C43#163511yescharacteristic
248C2×C43#163911yescharacteristic
249C2×C43#164611yescharacteristic
250C2×C43#203311yescharacteristic
251C2×C43#203411yescharacteristic
252C2×C43#204011yescharacteristic
253C2×#121—21no—
254C2×#121—21no—
255C2×C4×D4C2×D4311yescharacteristic
256C2×C4×D4C2×D4311yescharacteristic
257C2×C4⋊C8—431no—
258C2×C4⋊C8—431no—
259C2×#102—861no—
260C2×#102—861no—
261C2×C4×C8—431no—
262#394—22no—
263#384—431no—
264#384C2×D4311yescharacteristic
265#380—21no—
266#380—21no—
267#340—861no—
268#340—861no—
269#340—862no—
270D4⋊C8—862no—
271D4⋊C8—862no—
272C43#1043111yescharacteristic, complemented, Sylow
273C22×D4—22no—
274C22×D4C22⋊D4311yescharacteristic
275C22×D4C22⋊D4311yescharacteristic
276C23×C4—21no—
277C23×C4—21no—
278C22×C8—861no—
279C22×C8—861no—
280C22×C8—861no—
281#121—42no—
282#121—42no—
283#121—42no—
284#121—42no—
285C4×D4—21no—
286C4×D4—21no—
287C4×D4—21no—
288C4×D4—21no—
289C4×D4—21no—
290C4×D4—21no—
291C4×D4—21no—
292C4×D4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—861no—
296C2×C4⋊C4—861no—
297C2×C4⋊C4—861no—
298C2×C4⋊C4C22⋊D4311yescharacteristic
299C2×C4⋊C4C22⋊D4311yescharacteristic
300C2×C4⋊C4C22⋊D4312yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C42C22×D4311yescharacteristic
306C4⋊C8—861no—
307C4⋊C8—861no—
308C4⋊C8—861no—
309C4⋊C8—861no—
310#102—1722no—
311#102—1722no—
312C4×C8—432no—
313C4×C8—861no—
314#95—22no—
315C24—21no—
316C24—21no—
317C2×D4—21no—
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—21no—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—21no—
326C2×D4—21no—
327C2×D4—44no—
328C2×D4—44no—
329C2×D4—82no—
330C2×D4#1062188212yes—
331C2×D4#1062188312yes—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—1721no—
348C22×C4C2×C22⋊D4311yescharacteristic
349C22×C4C2×C22⋊D4311yescharacteristic
350C22×C4C2×C22⋊D4311yescharacteristic
351C2×C8—862no—
352C2×C8—1721no—
353C2×C8—1721no—
354C2×C8—1721no—
355C2×C8—1721no—
356C2×C8—1721no—
357C2×C8—1721no—
358C2×C8—1721no—
359C2×C8—1721no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—42no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—1722no—
370C4⋊C4—1721no—
371C4⋊C4—1721no—
372C4⋊C4—1721no—
373C4⋊C4—1721no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C42D4×D4311yescharacteristic
381C42#1062190011yescharacteristic
382C42#1062190011yescharacteristic
383C42#1062190011yescharacteristic
384C23—22no—
385C23—22no—
386C23—41no—
387C23—41no—
388C23—41no—
389C23—41no—
390C23—41no—
391C23—41no—
392C23—41no—
393C23—41no—
394C23—41no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23#1306329411yescharacteristic
399D4—22no—
400D4—22no—
401D4—22no—
402D4—22no—
403D4—41no—
404D4—41no—
405D4—41no—
406D4—41no—
407D4—88no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—81no—
420C2×C4—81no—
421C2×C4—81no—
422C2×C4—81no—
423C2×C4—81no—
424C2×C4—81no—
425C2×C4—81no—
426C2×C4—81no—
427C2×C4—3441no—
428C2×C4—3441no—
429C2×C4—3441no—
430C2×C4#1306329611yescharacteristic
431C2×C4#1306329711yescharacteristic
432C2×C4#1306329711yescharacteristic
433C2×C4#1306330611yescharacteristic
434C2×C4#1306330611yescharacteristic
435C2×C4#1306331211yescharacteristic
436C2×C4C2×#1062188211yescharacteristic
437C2×C4C2×#1062188311yescharacteristic
438C2×C4#1306334511yescharacteristic
439C2×C4#1306334511yescharacteristic
440C2×C4#1306335011yescharacteristic
441C2×C4#1306335111yescharacteristic
442C2×C4#1306335111yescharacteristic
443C2×C4#1306335511yescharacteristic
444C8—3441no—
445C8—3441no—
446C8—1722no—
447C22—42no—
448C22—42no—
449C22—42no—
450C22—42no—
451C22—42no—
452C22—42no—
453C22—81no—
454C22—81no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—81no—
461C22#1458281311yescharacteristic
462C22#1458303311yescharacteristic
463C22#1458304411yescharacteristic
464C22#1458305011yescharacteristic
465C22#1458306111yescharacteristic
466C22#1458307211yescharacteristic
467C22#1458307711yescharacteristic
468C4—21no—
469C4—21no—
470C4—81no—
471C4—81no—
472C4—82no—
473C4—6881no—
474C4#1458312611yescharacteristic
475C4#1458313311yescharacteristic
476C4#1458314311yescharacteristic
477C4#1458315011yescharacteristic
478C4#1458321011yescharacteristic
479C4#1458321511yescharacteristic
480C4#1458322011yescharacteristic
481C4#1458322011yescharacteristic
482C2—82no—
483C2—82no—
484C2#1913368411yescharacteristic
485C2#1913374611yescharacteristic
486C2#1913377411yescharacteristic
487C2#1913382311yescharacteristic
488C2#1913577411yescharacteristic
489C2#1913578111yescharacteristic
490C2#1913582111yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#2537C2
socleC23×C43#120
hypercenter#2537D43
hypocenterC43#10431
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2537

Complements

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

NH ≅ G/Ntype
1. #19134722C2semidirect
2. #19134595C2semidirect
3. #19134595C2semidirect
4. C2×D4⋊(C43⋊C8)C2semidirect
5. C2×D4⋊(C43⋊C8)C2semidirect
6. #19132478C2semidirect
40. C4×C43⋊C8D4semidirect
272. C43#10431semidirect

Maximal subgroups

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

subgroupindex
#191347222
#191345952
C2×D4⋊(C43⋊C8)2
#191324782
C43×#25372
#1043143