Finite Group Databasebeta

← #24998897

Subgroups — #24998897

Order 11008.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583091C211yesmaximal, characteristic
2#19139513C211yesmaximal, characteristic, complemented
3#19135402C211yesmaximal, characteristic, complemented
4C2×Q8⋊(C43⋊C8)C211yesmaximal, characteristic, complemented
5C2×#14582626C211yesmaximal, characteristic, complemented
6#19132479C211yesmaximal, characteristic, complemented
7C2×C43×#460C211yesmaximal, characteristic, complemented
8C22×#10621882—21no—
9C2×#13063301—21no—
10C2×C4×D172C2211yescharacteristic
11#14583091—22no—
12#14583091—22no—
13C2×C4⋊(C43⋊C8)C2211yescharacteristic
14C2×#13063246—21no—
15C2×#13063246—22no—
16C2×C4×C43⋊C8C2211yescharacteristic
17#14582821—22no—
18#14582801—21no—
19#14582797—21no—
20#14582769C2211yescharacteristic
21#14582756—21no—
22Q8⋊(C43⋊C8)—22no—
23#14582626—22no—
24C22×SD16×C43—21no—
25C2×#127×C43C2211yescharacteristic
26C2×C4×Q8×C43C2211yescharacteristic
27C43×#460—22no—
28C43×#460—22no—
29C2×C4⋊C8×C43C2211yescharacteristic
30C2×#102×C43—21no—
31C22×D172D411yescharacteristic
32C22×C4×D43—21no—
33C2×#10621882—24no—
34C2×#10621882—42no—
35C2×#10621882—42no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38#13063301—42no—
39#13063301—42no—
40C4×D172—21no—
41C4×D172—21no—
42C4×D172—21no—
43C4×D172—21no—
44C2×C4⋊Dic43—21no—
45C2×C4⋊Dic43—21no—
46C2×C4⋊Dic43D411yescharacteristic
47C2×C4⋊Dic43D412yes—
48C2×Dic43⋊C4—22no—
49C2×(C2×D43)⋊C4—22no—
50C2×(C2×D43)⋊C4—21no—
51C2×(C2×D43)⋊C4—22no—
52C4⋊(C43⋊C8)—21no—
53C4⋊(C43⋊C8)D412yes—
54#13063246—24no—
55#13063246—44no—
56C4×C43⋊C8—21no—
57C4×C43⋊C8—21no—
58C43⋊#95—22no—
59C22×Q8×C43D411yescharacteristic
60C22×D4×C43—21no—
61C22×D4×C43—21no—
62C22×D4×C43—21no—
63C2×SD16×C43—24no—
64C2×SD16×C43—42no—
65C2×SD16×C43—42no—
66C22×C8×C43—21no—
67#127×C43—21no—
68#127×C43—21no—
69#127×C43—21no—
70#127×C43D412yes—
71C4×Q8×C43—21no—
72C4×Q8×C43—21no—
73C4×Q8×C43—21no—
74C4×Q8×C43—21no—
75C2×C4⋊C4×C43—21no—
76C2×C4⋊C4×C43D411yescharacteristic
77C2×C42×C43—21no—
78C2×C42×C43C2311yescharacteristic
79C4⋊C8×C43—21no—
80C4⋊C8×C43D412yes—
81#102×C43—24no—
82C24×C43—41no—
83C23×D43—21no—
84C2×Q8×C43—21no—
85C2×Q8×C43—21no—
86C2×Q8×C43—21no—
87C2×Q8×C43—21no—
88C2×Q8×C43—21no—
89C2×Q8×C43D812yescomplemented
90C2×D4×C43—22no—
91C2×D4×C43—22no—
92C2×D4×C43—22no—
93C2×D4×C43—41no—
94C2×D4×C43—41no—
95C2×D4×C43—41no—
96C2×D4×C43—42no—
97C2×D4×C43—42no—
98C2×D4×C43—41no—
99C2×D4×C43—41no—
100C2×D4×C43—41no—
101C2×D4×C43—41no—
102C2×D4×C43—41no—
103C2×D4×C43—41no—
104C2×D4×C43—41no—
105C2×D4×C43—41no—
106C22×C4×C43—21no—
107C22×C4×C43—21no—
108C22×C4×C43C2×D411yescharacteristic
109C22×C4×C43C2×D411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×Dic43—21no—
112C22×Dic43—22no—
113C2×D172—21no—
114C2×D172—21no—
115C2×D172—21no—
116C2×D172—21no—
117C2×D172—21no—
118C2×D172SD1612yescomplemented
119C2×C4×D43—41no—
120C2×C4×D43—41no—
121C2×C4×D43—41no—
122C2×C4×D43—41no—
123C2×C4×D43—41no—
124C2×C4×D43—41no—
125SD16×C43—48no—
126C2×C8×C43—22no—
127C2×C8×C43—41no—
128C2×C8×C43—41no—
129C4⋊C4×C43—21no—
130C4⋊C4×C43—21no—
131C4⋊C4×C43—41no—
132C4⋊C4×C43—41no—
133C42×C43—41no—
134C42×C43—41no—
135C42×C43C2×D411yescharacteristic
136C42×C43C2×D411yescharacteristic
137C42×C43C2×D411yescharacteristic
138C42×C43#4111yescharacteristic
139#10621882—48no—
140(C2×D43)⋊C4—44no—
141(C2×D43)⋊C4—41no—
142(C2×D43)⋊C4—41no—
143(C2×D43)⋊C4—82no—
144C4⋊Dic43—21no—
145C4⋊Dic43—21no—
146C4⋊Dic43—41no—
147C4⋊Dic43—41no—
148C4⋊Dic43—41no—
149C4⋊Dic43—41no—
150C4⋊Dic43—42no—
151Dic43⋊C4—44no—
152C2×C43⋊C8—22no—
153C2×C43⋊C8—22no—
154C2×C43⋊C8—41no—
155C2×C43⋊C8—41no—
156C2×C43⋊C8—41no—
157C2×C43⋊C8—41no—
158C23×C43—42no—
159C23×C43—81no—
160C23×C43—81no—
161C23×C43—81no—
162C23×C43—81no—
163C23×C43—81no—
164C23×C43—81no—
165C23×C43#12011yescharacteristic
166C22×D43—22no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170C22×D43—41no—
171C22×D43—41no—
172C22×D43—41no—
173Q8×C43—22no—
174Q8×C43—22no—
175Q8×C43—41no—
176Q8×C43—41no—
177D4×C43—44no—
178D4×C43—42no—
179D4×C43—42no—
180D4×C43—42no—
181D4×C43—42no—
182D4×C43—82no—
183D4×C43—81no—
184D4×C43—81no—
185D4×C43—81no—
186D4×C43—81no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—22no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43#12011yescharacteristic
196C2×C4×C43#12011yescharacteristic
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43#12111yescharacteristic
199C2×C4×C43#12111yescharacteristic
200C2×C4×C43#12711yescharacteristic
201C2×C4×C43C2×D811yescharacteristic
202C2×C4×C43C2×SD1611yescharacteristic
203C2×C4×C43#13511yescharacteristic
204C2×C4×C43#13511yescharacteristic
205C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
207C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
208C2×C4×C43#13711yescharacteristic
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—42no—
212C2×Dic43—42no—
213C2×Dic43—41no—
214C2×Dic43—42no—
215D172—22no—
216D172—22no—
217D172—41no—
218D172—41no—
219C4×D43—81no—
220C4×D43—81no—
221C4×D43—81no—
222C4×D43—81no—
223C8×C43—42no—
224C43⋊C8—42no—
225C43⋊C8—42no—
226#10229—431nomaximal, Sylow
227C22×C43—82no—
228C22×C43—82no—
229C22×C43—82no—
230C22×C43—161no—
231C22×C43—161no—
232C22×C43—161no—
233C22×C43—161no—
234C22×C43#39211yescharacteristic
235C22×C43#44711yescharacteristic
236C22×C43#44811yescharacteristic
237C22×C43#44911yescharacteristic
238C22×C43#44911yescharacteristic
239C22×C43#45311yescharacteristic
240C22×C43#45411yescharacteristic
241C2×D43—42no—
242C2×D43—42no—
243C2×D43—42no—
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—81no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—42no—
251C4×C43—81no—
252C4×C43#44711yescharacteristic
253C4×C43#44911yescharacteristic
254C4×C43#45011yescharacteristic
255C4×C43#45211yescharacteristic
256C4×C43#46511yescharacteristic
257C4×C43#46611yescharacteristic
258C4×C43#46811yescharacteristic
259C4×C43#46911yescharacteristic
260Dic43—82no—
261Dic43—81no—
262C2×#460D4311yescharacteristic, complemented
263C2×#459—431no—
264#2538—431no—
265#1957—431no—
266C2×Q8⋊C8—431no—
267C2×D4⋊C8—431no—
268#1296—431no—
269C2×C43—162no—
270C2×C43#162111yescharacteristic
271C2×C43#162211yescharacteristic
272C2×C43#162711yescharacteristic
273C2×C43#162811yescharacteristic
274C2×C43#199911yescharacteristic
275C2×C43#200011yescharacteristic
276C2×C43#200611yescharacteristic
277D43—82no—
278C22×SD16—21no—
279C22×D8—861no—
280C2×#127C2×D4311yescharacteristic
281C2×C22⋊Q8—861no—
282C2×C4×Q8C2×D4311yescharacteristic
283C2×C4×D4—431no—
284#460—22no—
285#460—22no—
286#459—862no—
287#459—862no—
288C2×C4⋊C8—431no—
289C2×C4⋊C8C2×D4311yescharacteristic
290C2×#102—21no—
291C2×#102—861no—
292C2×#102—862no—
293C2×C4×C8—431no—
294#396—862no—
295#390—861no—
296#389—861no—
297#384—431no—
298#380—861no—
299Q8⋊C8—862no—
300D4⋊C8—862no—
301C43#1022911yescharacteristic, complemented, Sylow
302C22×Q8C22⋊D4311yescharacteristic
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—431no—
307C23×C4—861no—
308C2×SD16—24no—
309C2×SD16—42no—
310C2×SD16—42no—
311C2×D8—864no—
312C2×D8—1722no—
313C2×D8—1722no—
314C22×C8—21no—
315C22×C8—861no—
316C22×C8—861no—
317#127—21no—
318#127—21no—
319#127—21no—
320#127C22⋊D4312yes—
321C22⋊Q8—1722no—
322C22⋊Q8—1722no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×D4—861no—
328C4×D4—861no—
329C4×D4—861no—
330C4×D4—861no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—431no—
333C2×C4⋊C4—432no—
334C2×C4⋊C4—862no—
335C2×C4⋊C4—861no—
336C2×C4⋊C4—861no—
337C2×C4⋊C4C22⋊D4311yescharacteristic
338C2×C22⋊C4—862no—
339C2×C22⋊C4—862no—
340C2×C22⋊C4—861no—
341C2×C42—21no—
342C2×C42C22×D4311yescharacteristic
343C4⋊C8—21no—
344C4⋊C8—432no—
345C4⋊C8—861no—
346C4⋊C8C22⋊D4312yes—
347#102—24no—
348#102—864no—
349#102—1724no—
350C4×C8—861no—
351C4×C8—861no—
352#95—862no—
353C24—41no—
354C24—861no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8#1062188212yescomplemented
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—432no—
378C2×D4—861no—
379C2×D4—861no—
380C2×D4—861no—
381C2×D4—861no—
382C2×D4—861no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—861no—
386C22×C4—862no—
387C22×C4—1721no—
388C22×C4—1721no—
389C22×C4—1721no—
390C22×C4—1721no—
391C22×C4—1721no—
392C22×C4—1721no—
393C22×C4D4×D4311yescharacteristic
394C22×C4D4×D4311yescharacteristic
395C22×C4C2×C22⋊D4311yescharacteristic
396SD16—48no—
397D8—1728no—
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—862no—
402C2×C8—862no—
403C2×C8—1721no—
404C2×C8—1721no—
405C2×C8—1721no—
406C2×C8—1721no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—861no—
412C4⋊C4—861no—
413C4⋊C4—1722no—
414C4⋊C4—1724no—
415C4⋊C4—1721no—
416C4⋊C4—1721no—
417C4⋊C4—1721no—
418C4⋊C4—1721no—
419C22⋊C4—3442no—
420C22⋊C4—1724no—
421C22⋊C4—1721no—
422C22⋊C4—1721no—
423C42—41no—
424C42—41no—
425C42D4×D4311yescharacteristic
426C42#1062190011yescharacteristic
427C42C2×C22⋊D4311yescharacteristic
428C42C2×C22⋊D4311yescharacteristic
429C23—42no—
430C23—81no—
431C23—81no—
432C23—81no—
433C23—81no—
434C23—81no—
435C23—81no—
436C23—862no—
437C23—1721no—
438C23—1721no—
439C23—1721no—
440C23—1721no—
441C23—1721no—
442C23—1721no—
443C23#1306329311yescharacteristic
444Q8—22no—
445Q8—22no—
446Q8—41no—
447Q8—41no—
448D4—44no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—82no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—862no—
459D4—862no—
460D4—1721no—
461D4—1721no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—3441no—
471C2×C4—3441no—
472C2×C4—3441no—
473C2×C4—3441no—
474C2×C4—1721no—
475C2×C4—1722no—
476C2×C4—1721no—
477C2×C4—1722no—
478C2×C4—1722no—
479C2×C4—1721no—
480C2×C4#1306329311yescharacteristic
481C2×C4#1306329411yescharacteristic
482C2×C4#1306329611yescharacteristic
483C2×C4#1306329711yescharacteristic
484C2×C4#1306329711yescharacteristic
485C2×C4#1306332111yescharacteristic
486C2×C4C2×#1062188211yescharacteristic
487C2×C4SD16×D4311yescharacteristic
488C2×C4#1306334511yescharacteristic
489C2×C4#1306334611yescharacteristic
490C2×C4#1306335011yescharacteristic
491C2×C4#1306335111yescharacteristic
492C2×C4#1306335211yescharacteristic
493C2×C4#1306335411yescharacteristic
494C8—42no—
495C8—1722no—
496C8—1722no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—161no—
501C22—161no—
502C22—161no—
503C22—161no—
504C22—3441no—
505C22—3441no—
506C22—3441no—
507C22—3441no—
508C22—1722no—
509C22—1722no—
510C22—1722no—
511C22#1458280711yescharacteristic
512C22#1458303211yescharacteristic
513C22#1458303611yescharacteristic
514C22#1458304211yescharacteristic
515C22#1458304311yescharacteristic
516C22#1458306511yescharacteristic
517C22#1458307011yescharacteristic
518C4—21no—
519C4—21no—
520C4—42no—
521C4—81no—
522C4—3441no—
523C4—3442no—
524C4#1458303311yescharacteristic
525C4#1458304411yescharacteristic
526C4#1458304811yescharacteristic
527C4#1458305811yescharacteristic
528C4#1458312511yescharacteristic
529C4#1458313311yescharacteristic
530C4#1458314211yescharacteristic
531C4#1458315011yescharacteristic
532C2—162no—
533C2—3442no—
534C2#1913365811yescharacteristic
535C2#1913366611yescharacteristic
536C2#1913369611yescharacteristic
537C2#1913370411yescharacteristic
538C2#1913559111yescharacteristic
539C2#1913559511yescharacteristic
540C2#1913563511yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC2×C43×#460C2
socleC23×C43#120
prime radicalC2×#14583091C2
hypercenterC2×#460D43
hypocenterC43#10229
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#460

Complements

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

NH ≅ G/Ntype
2. #19139513C2semidirect
3. #19135402C2semidirect
4. C2×Q8⋊(C43⋊C8)C2semidirect
5. C2×#14582626C2semidirect
6. #19132479C2semidirect
7. C2×C43×#460C2semidirect
89. C2×Q8×C43D8semidirect
118. C2×D172SD16semidirect
262. C2×#460D43semidirect
301. C43#10229semidirect
360. C2×Q8#10621882semidirect

Maximal subgroups

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

subgroupindex
C2×#145830912
#191395132
#191354022
C2×Q8⋊(C43⋊C8)2
C2×#145826262
#191324792
C2×C43×#4602
#1022943