Finite Group Databasebeta

← #24998911

Subgroups — #24998911

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583176C211yesmaximal, characteristic, complemented
2C2×#14583101C211yesmaximal, characteristic, complemented
3#19139511C211yesmaximal, characteristic
4C2×#14582628C211yesmaximal, characteristic, complemented
5C2×#14582628C211yesmaximal, characteristic, complemented
6#19132478C211yesmaximal, characteristic, complemented
7C43×#1990C211yesmaximal, characteristic, complemented
8C22×#10621884—21no—
9C2×#13063300—21no—
10C2×#13063300—21no—
11C2×C4×D172C2211yescharacteristic
12C2×C4×D172C2211yescharacteristic
13#14583176—22no—
14#14583176—22no—
15#14583101—22no—
16#14583101—22no—
17C2×#13063258—21no—
18C2×C4⋊(C43⋊C8)C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063249—21no—
21C2×#13063245—21no—
22#14582816—22no—
23#14582756—21no—
24#14582756—21no—
25#14582628—22no—
26#14582628—22no—
27C2×C4⋊Q8×C43C2211yescharacteristic
28C2×C4×C8×C43C2211yescharacteristic
29C43×#384C2211yescharacteristic
30C43×#340—22no—
31C22×D172—22no—
32C22×D172D411yescharacteristic
33C22×D172D411yescharacteristic
34C22×C4×D43—21no—
35C22×C4×D43—21no—
36C2×#10621884—24no—
37C2×#10621884—42no—
38C2×#10621884—42no—
39C22×C43⋊C8—21no—
40C22×C43⋊C8—21no—
41#13063300—42no—
42#13063300—42no—
43#13063300—42no—
44#13063300—42no—
45C4×D172—21no—
46C4×D172—21no—
47C4×D172—21no—
48C4×D172—21no—
49C4×D172—21no—
50C4×D172—21no—
51C4×D172—21no—
52C4×D172—21no—
53C2×C4⋊Dic43D411yescharacteristic
54C2×C4⋊Dic43D411yescharacteristic
55C2×(C2×D43)⋊C4—22no—
56C2×(C2×D43)⋊C4—22no—
57C2×(C2×D43)⋊C4—21no—
58C2×(C2×D43)⋊C4—21no—
59#13063258—24no—
60C4⋊(C43⋊C8)—21no—
61C4⋊(C43⋊C8)—21no—
62C4⋊(C43⋊C8)D412yescomplemented
63C4⋊(C43⋊C8)D412yescomplemented
64#13063249—24no—
65#13063245—24no—
66C43⋊#95—22no—
67C22×Q8×C43—21no—
68C22×C8×C43—21no—
69C4⋊Q8×C43—21no—
70C4⋊Q8×C43—21no—
71C4⋊Q8×C43—21no—
72C4⋊Q8×C43D412yescomplemented
73C2×C4⋊C4×C43—21no—
74C2×C4⋊C4×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43—21no—
77C2×C4⋊C4×C43D412yes—
78C2×C42×C43C2311yescharacteristic
79C4×C8×C43—21no—
80C4×C8×C43—21no—
81C23×D43—21no—
82C23×D43—21no—
83C2×Q8×C43—22no—
84C2×Q8×C43—41no—
85C2×Q8×C43—41no—
86C2×Q8×C43—41no—
87C2×Q8×C43—41no—
88C2×Q8×C43—41no—
89C22×C4×C43—22no—
90C22×C4×C43—41no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C22×Dic43—21no—
95C22×Dic43—21no—
96C2×D172—21no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172—21no—
100C2×D172—21no—
101C2×D172—21no—
102C2×D172—21no—
103C2×D172—21no—
104C2×D172—21no—
105C2×D172—21no—
106C2×D172—44no—
107C2×D172—44no—
108C2×D172—82no—
109C2×D172D812yes—
110C2×D172SD1612yescomplemented
111C2×C4×D43—41no—
112C2×C4×D43—41no—
113C2×C4×D43—41no—
114C2×C4×D43—41no—
115C2×C4×D43—41no—
116C2×C4×D43—41no—
117C2×C4×D43—41no—
118C2×C4×D43—41no—
119C2×C4×D43—41no—
120C2×C4×D43—41no—
121C2×C4×D43—41no—
122C2×C4×D43—41no—
123C2×C8×C43—22no—
124C2×C8×C43—41no—
125C2×C8×C43—41no—
126C4⋊C4×C43—22no—
127C4⋊C4×C43—22no—
128C4⋊C4×C43—42no—
129C4⋊C4×C43—41no—
130C4⋊C4×C43—41no—
131C4⋊C4×C43—41no—
132C4⋊C4×C43—41no—
133C4⋊C4×C43—41no—
134C4⋊C4×C43—41no—
135C42×C43C2×D411yescharacteristic
136C42×C43C2×D411yescharacteristic
137C42×C43C2×D411yescharacteristic
138C42×C43#4111yescharacteristic
139#10621884—48no—
140(C2×D43)⋊C4—44no—
141(C2×D43)⋊C4—44no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—41no—
144(C2×D43)⋊C4—41no—
145(C2×D43)⋊C4—41no—
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—21no—
149C4⋊Dic43—21no—
150C2×C43⋊C8—22no—
151C2×C43⋊C8—22no—
152C2×C43⋊C8—41no—
153C2×C43⋊C8—41no—
154C2×C43⋊C8—41no—
155C2×C43⋊C8—41no—
156C23×C43#12011yescharacteristic
157C22×D43—22no—
158C22×D43—22no—
159C22×D43—41no—
160C22×D43—41no—
161C22×D43—41no—
162C22×D43—41no—
163C22×D43—41no—
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171Q8×C43—42no—
172Q8×C43—42no—
173Q8×C43—81no—
174Q8×C43—81no—
175C2×C4×C43—21no—
176C2×C4×C43—21no—
177C2×C4×C43—42no—
178C2×C4×C43—42no—
179C2×C4×C43—42no—
180C2×C4×C43—42no—
181C2×C4×C43—81no—
182C2×C4×C43—81no—
183C2×C4×C43#12011yescharacteristic
184C2×C4×C43#12011yescharacteristic
185C2×C4×C43#12111yescharacteristic
186C2×C4×C43#12111yescharacteristic
187C2×C4×C43#12111yescharacteristic
188C2×C4×C43#12711yescharacteristic
189C2×C4×C43C2×D811yescharacteristic
190C2×C4×C43C2×SD1611yescharacteristic
191C2×C4×C43#13511yescharacteristic
192C2×C4×C43#13511yescharacteristic
193C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
195C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C43#13711yescharacteristic
197C2×Dic43—41no—
198C2×Dic43—41no—
199C2×Dic43—41no—
200C2×Dic43—41no—
201C2×Dic43—41no—
202C2×Dic43—41no—
203D172—22no—
204D172—22no—
205D172—22no—
206D172—22no—
207D172—41no—
208D172—41no—
209D172—41no—
210D172—41no—
211D172—88no—
212C4×D43—81no—
213C4×D43—81no—
214C4×D43—81no—
215C4×D43—81no—
216C4×D43—81no—
217C4×D43—81no—
218C4×D43—81no—
219C4×D43—81no—
220C8×C43—42no—
221C43⋊C8—42no—
222C43⋊C8—42no—
223#10231—431nomaximal, Sylow
224C22×C43#39211yescharacteristic
225C22×C43#44711yescharacteristic
226C22×C43#44911yescharacteristic
227C22×C43#45011yescharacteristic
228C22×C43#45211yescharacteristic
229C22×C43#45511yescharacteristic
230C22×C43#45611yescharacteristic
231C2×D43—42no—
232C2×D43—42no—
233C2×D43—42no—
234C2×D43—42no—
235C2×D43—42no—
236C2×D43—42no—
237C2×D43—81no—
238C2×D43—81no—
239C2×D43—81no—
240C2×D43—81no—
241C2×D43—81no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—81no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—82no—
248C4×C43—82no—
249C4×C43#44711yescharacteristic
250C4×C43#44811yescharacteristic
251C4×C43#44911yescharacteristic
252C4×C43#44911yescharacteristic
253C4×C43#46511yescharacteristic
254C4×C43#46611yescharacteristic
255C4×C43#46811yescharacteristic
256C4×C43#46911yescharacteristic
257Dic43—81no—
258Dic43—81no—
259C2×#474—431no—
260C2×#461—431no—
261#2537—431no—
262#1990D4311yescharacteristic, complemented
263C2×D4⋊C8—431no—
264C2×D4⋊C8—431no—
265#1296—431no—
266C2×C43#163911yescharacteristic
267C2×C43#164611yescharacteristic
268C2×C43#164711yescharacteristic
269C2×C43#165411yescharacteristic
270C2×C43#199911yescharacteristic
271C2×C43#200011yescharacteristic
272C2×C43#200711yescharacteristic
273D43—82no—
274D43—82no—
275C22×SD16—861no—
276C2×C4⋊Q8C2×D4311yescharacteristic
277C2×#121—861no—
278C2×#121—861no—
279C2×C4×D4—431no—
280C2×C4×D4—431no—
281#474—862no—
282#474—862no—
283#461—862no—
284#461—862no—
285C2×#107—861no—
286C2×C4⋊C8—431no—
287C2×C4⋊C8—431no—
288C2×#103—861no—
289C2×#102—861no—
290C2×C4×C8C2×D4311yescharacteristic
291#394—862no—
292#384C2×D4311yescharacteristic
293#380—861no—
294#380—861no—
295#340—22no—
296D4⋊C8—862no—
297D4⋊C8—862no—
298C43#1023111yescharacteristic, complemented, Sylow
299C22×Q8—21no—
300C22×D4—431no—
301C22×D4—431no—
302C22×D4—862no—
303C23×C4—861no—
304C23×C4—861no—
305C2×SD16—864no—
306C2×SD16—1722no—
307C2×SD16—1722no—
308C22×C8—21no—
309C22×C8—861no—
310C22×C8—861no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8D17212yescomplemented
315#121—1722no—
316#121—1722no—
317#121—1722no—
318#121—1722no—
319C4×D4—861no—
320C4×D4—861no—
321C4×D4—861no—
322C4×D4—861no—
323C4×D4—861no—
324C4×D4—861no—
325C4×D4—861no—
326C4×D4—861no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—431no—
332C2×C4⋊C4—431no—
333C2×C4⋊C4C22⋊D4312yes—
334C2×C22⋊C4—862no—
335C2×C22⋊C4—862no—
336C2×C22⋊C4—861no—
337C2×C22⋊C4—861no—
338C2×C42C22×D4311yescharacteristic
339#107—864no—
340C4⋊C8—432no—
341C4⋊C8—432no—
342C4⋊C8—861no—
343C4⋊C8—861no—
344#103—864no—
345#102—864no—
346C4×C8—21no—
347C4×C8—21no—
348#95—862no—
349C24—861no—
350C24—861no—
351C2×Q8—22no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×D4—432no—
358C2×D4—432no—
359C2×D4—861no—
360C2×D4—861no—
361C2×D4—861no—
362C2×D4—861no—
363C2×D4—861no—
364C2×D4—861no—
365C2×D4—861no—
366C2×D4—861no—
367C2×D4—861no—
368C2×D4—861no—
369C2×D4—3442no—
370C2×D4—1724no—
371C2×D4—1724no—
372C22×C4—22no—
373C22×C4—41no—
374C22×C4—861no—
375C22×C4—861no—
376C22×C4—1721no—
377C22×C4—1721no—
378C22×C4—1721no—
379C22×C4—1721no—
380C22×C4—1721no—
381C22×C4—1721no—
382C22×C4—1721no—
383C22×C4—1721no—
384C22×C4—1721no—
385C22×C4—1721no—
386C22×C4—1721no—
387C22×C4—1721no—
388C22×C4D4×D4311yescharacteristic
389C22×C4D4×D4311yescharacteristic
390C22×C4C2×C22⋊D4311yescharacteristic
391SD16—1728no—
392C2×C8—22no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—862no—
396C2×C8—862no—
397C2×C8—1721no—
398C2×C8—1721no—
399C2×C8—1721no—
400C2×C8—1721no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—42no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—41no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—861no—
411C4⋊C4—861no—
412C4⋊C4—861no—
413C4⋊C4—861no—
414C22⋊C4—1724no—
415C22⋊C4—1724no—
416C22⋊C4—1721no—
417C22⋊C4—1721no—
418C22⋊C4—1721no—
419C22⋊C4—1721no—
420C42C2×D17211yescharacteristic
421C42#1062189811yescharacteristic
422C42D4×D4311yescharacteristic
423C42D4×D4311yescharacteristic
424C23—862no—
425C23—862no—
426C23—1721no—
427C23—1721no—
428C23—1721no—
429C23—1721no—
430C23—1721no—
431C23—1721no—
432C23—1721no—
433C23—1721no—
434C23—1721no—
435C23—1721no—
436C23—1721no—
437C23—1721no—
438C23#1306329311yescharacteristic
439Q8—42no—
440Q8—42no—
441Q8—81no—
442Q8—81no—
443D4—862no—
444D4—862no—
445D4—862no—
446D4—862no—
447D4—3448no—
448D4—1721no—
449D4—1721no—
450D4—1721no—
451D4—1721no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—3441no—
461C2×C4—3441no—
462C2×C4—3441no—
463C2×C4—3441no—
464C2×C4—3441no—
465C2×C4—3441no—
466C2×C4—3441no—
467C2×C4—3441no—
468C2×C4—1721no—
469C2×C4—1721no—
470C2×C4—1721no—
471C2×C4—1721no—
472C2×C4—1721no—
473C2×C4—1721no—
474C2×C4#1306329511yescharacteristic
475C2×C4#1306329511yescharacteristic
476C2×C4#1306329811yescharacteristic
477C2×C4#1306329811yescharacteristic
478C2×C4#1306329911yescharacteristic
479C2×C4#1306332111yescharacteristic
480C2×C4D8×D4311yescharacteristic
481C2×C4SD16×D4311yescharacteristic
482C2×C4#1306334611yescharacteristic
483C2×C4#1306334811yescharacteristic
484C2×C4#1306334911yescharacteristic
485C2×C4#1306335211yescharacteristic
486C2×C4#1306335211yescharacteristic
487C2×C4#1306335711yescharacteristic
488C8—42no—
489C8—1722no—
490C8—1722no—
491C22—3441no—
492C22—3441no—
493C22—3441no—
494C22—3441no—
495C22—3441no—
496C22—3441no—
497C22—3441no—
498C22—3441no—
499C22—1722no—
500C22—1722no—
501C22—1722no—
502C22—1722no—
503C22—1722no—
504C22—1722no—
505C22#1458280811yescharacteristic
506C22#1458303111yescharacteristic
507C22#1458304311yescharacteristic
508C22#1458304811yescharacteristic
509C22#1458306011yescharacteristic
510C22#1458307611yescharacteristic
511C22#1458308111yescharacteristic
512C4—21no—
513C4—21no—
514C4—82no—
515C4—82no—
516C4—3441no—
517C4—3441no—
518C4#1458303411yescharacteristic
519C4#1458303911yescharacteristic
520C4#1458304511yescharacteristic
521C4#1458304711yescharacteristic
522C4#1458313111yescharacteristic
523C4#1458313411yescharacteristic
524C4#1458314811yescharacteristic
525C4#1458315111yescharacteristic
526C2—3442no—
527C2—3442no—
528C2#1913377111yescharacteristic
529C2#1913382011yescharacteristic
530C2#1913382711yescharacteristic
531C2#1913387611yescharacteristic
532C2#1913559211yescharacteristic
533C2#1913559711yescharacteristic
534C2#1913564111yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1990C2
socleC23×C43#120
prime radical#19139511C2
hypercenter#1990D43
hypocenterC43#10231
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
1. C2×#14583176C2semidirect
2. C2×#14583101C2semidirect
4. C2×#14582628C2semidirect
5. C2×#14582628C2semidirect
6. #19132478C2semidirect
7. C43×#1990C2semidirect
62. C4⋊(C43⋊C8)D4semidirect
63. C4⋊(C43⋊C8)D4semidirect
72. C4⋊Q8×C43D4semidirect
110. C2×D172SD16semidirect
262. #1990D43semidirect
298. C43#10231semidirect
314. C4⋊Q8D172semidirect

Maximal subgroups

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

subgroupindex
C2×#145831762
C2×#145831012
#191395112
C2×#145826282
#191324782
C43×#19902
#1023143