Finite Group Databasebeta

← #25138066

Subgroups — #25138066

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583186C211yesmaximal, characteristic, complemented
2C4×#13063350C211yesmaximal, characteristic
3#19143261C211yesmaximal, characteristic, complemented
4#19136043C212yesmaximal, complemented
5#19135885C212yesmaximal
6#19135585C211yesmaximal, characteristic, complemented
7#19135372C212yesmaximal, complemented
8#19135368C211yesmaximal, characteristic, complemented
9#19135256C212yesmaximal, complemented
10#19134584C211yesmaximal, characteristic, complemented
11C43×#3079C211yesmaximal, characteristic, complemented
12C2×#13063350C2211yescharacteristic
13C2×C4×D172C2211yescharacteristic
14#14583186—21no—
15#14583186—21no—
16#14583186—22no—
17#14583009—21no—
18#14582997—21no—
19C4×#10621884—21no—
20C4×#10621882—21no—
21#14582960—22no—
22#14582956—21no—
23#14582952—21no—
24C2×#13063260C2212yes—
25#14582942C2211yescharacteristic
26C2×#13063256C2212yes—
27#14582923C2211yescharacteristic
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29#14582903C2211yescharacteristic
30#14582900C2211yescharacteristic
31C2×#13063245C2212yes—
32C2×#13063241C2212yes—
33#14582866C2212yes—
34#14582855C2212yes—
35C4×#10621877C2211yescharacteristic
36#14582668C2212yes—
37#14582668C2212yes—
38#14582667C2212yes—
39#14582663C2212yes—
40C2×C4⋊Q8×C43C2211yescharacteristic
41C4×#41×C43C2211yescharacteristic
42C43×#477—21no—
43C43×#476—21no—
44C43×#475—21no—
45C43×#474—21no—
46C43×#428C2212yes—
47C43×#423C2211yescharacteristic
48C43×#417C2212yes—
49C22×D172C2311yescharacteristic
50C22×C4×D43—21no—
51#13063350—22no—
52#13063350—22no—
53C2×#10621884—21no—
54C2×#10621882—21no—
55C2×#10621877C2311yescharacteristic
56C2×#10621877C2312yes—
57C2×#10621877C2311yescharacteristic
58C22×C43⋊C8C2312yes—
59C4×D172—21no—
60C4×D172—21no—
61C4×D172—21no—
62C4×D172—21no—
63C2×C4⋊Dic43C2311yescharacteristic
64C2×(C2×D43)⋊C4—21no—
65#13063260—24no—
66#13063258—21no—
67#13063256—21no—
68#13063256—22no—
69#13063256—22no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)D411yescharacteristic
73C4⋊(C43⋊C8)D411yescharacteristic
74C4⋊(C43⋊C8)D412yes—
75#13063249—21no—
76#13063246—21no—
77#13063245—21no—
78#13063245—21no—
79#13063245—22no—
80#13063245—22no—
81#13063241—24no—
82C22⋊(C43⋊C8)—22no—
83C22⋊(C43⋊C8)—22no—
84#13063236—21no—
85#13063236—22no—
86C4×C43⋊C8—21no—
87C4×C43⋊C8—22no—
88C2×#41×C43C2311yescharacteristic
89C22×Q8×C43—21no—
90C2×M16×C43C2312yes—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43—21no—
93C4⋊Q8×C43—21no—
94C4⋊Q8×C43—21no—
95C4×Q8×C43D411yescharacteristic
96C4×Q8×C43D411yescharacteristic
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43D411yescharacteristic
100C4×D4×C43D411yescharacteristic
101#117×C43—21no—
102#117×C43C2311yescharacteristic
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43C2312yes—
105C2×C42×C43—21no—
106C2×C42×C43C2311yescharacteristic
107#107×C43—22no—
108#106×C43—22no—
109C4⋊C8×C43—21no—
110C4⋊C8×C43—21no—
111#103×C43—22no—
112#102×C43—22no—
113C23×D43—21no—
114#41×C43—21no—
115#41×C43—21no—
116#41×C43—21no—
117#41×C43—21no—
118C2×Q8×C43—41no—
119C2×Q8×C43—41no—
120C2×Q8×C43—82no—
121C2×Q8×C43C2×D411yescharacteristic
122C2×D4×C43—21no—
123C2×D4×C43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—22no—
128C22×C4×C43#4111yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×D172—21no—
137C2×D172#4112yes—
138C2×C4×D43—41no—
139C2×C4×D43—41no—
140C2×C4×D43—82no—
141M16×C43—22no—
142M16×C43—22no—
143C2×C8×C43—22no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—41no—
149C4⋊C4×C43—41no—
150C4⋊C4×C43C2×D411yescharacteristic
151C4⋊C4×C43C2×D411yescharacteristic
152C22⋊C4×C43—21no—
153C22⋊C4×C43—21no—
154C22⋊C4×C43—21no—
155C42×C43—21no—
156C42×C43—21no—
157C42×C43—21no—
158C42×C43C2×D411yescharacteristic
159C42×C43C2×D411yescharacteristic
160C42×C43C2×D411yescharacteristic
161C42×C43C2×D411yescharacteristic
162#10621884—24no—
163#10621882—24no—
164(C2×D43)⋊C4—41no—
165(C2×D43)⋊C4—41no—
166C4⋊Dic43—21no—
167C4⋊Dic43—21no—
168#10621877—21no—
169#10621877—22no—
170#10621877—21no—
171#10621877—21no—
172#10621877—22no—
173#10621877#4112yes—
174C2×C43⋊C8—21no—
175C2×C43⋊C8—22no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8C2×D412yes—
180C2×C43⋊C8C2×D412yes—
181C23×C43—21no—
182C23×C43C2×#4111yescharacteristic
183C22×D43—22no—
184C22×D43—41no—
185C22×D43—41no—
186C22×D43—81no—
187C22×D43—81no—
188Q8×C43—21no—
189Q8×C43—21no—
190Q8×C43—82no—
191Q8×C43—82no—
192D4×C43—21no—
193D4×C43—21no—
194D4×C43—41no—
195D4×C43—41no—
196C2×C4×C43—22no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—42no—
204C2×C4×C43—42no—
205C2×C4×C43—81no—
206C2×C4×C43—82no—
207C2×C4×C43#12111yescharacteristic
208C2×C4×C43#12111yescharacteristic
209C2×C4×C43#12111yescharacteristic
210C2×C4×C43#12111yescharacteristic
211C2×C4×C43C22×D411yescharacteristic
212C2×C4×C43C22×D411yescharacteristic
213C2×C4×C43C2×#4111yescharacteristic
214C2×C4×C43C2×#4111yescharacteristic
215C2×C4×C432−1+411yescharacteristic
216C2×C4×C432−1+411yescharacteristic
217C2×Dic43—41no—
218C2×Dic43—81no—
219D172—22no—
220D172—22no—
221D172—41no—
222D172—41no—
223C4×D43—82no—
224C4×D43—82no—
225C8×C43—42no—
226C43⋊C8—22no—
227C43⋊C8—22no—
228C43⋊C8—22no—
229C43⋊C8—41no—
230C43⋊C8—42no—
231#24721—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—41no—
235C22×C43—41no—
236C22×C43—41no—
237C22×C43C2×#12111yescharacteristic
238C22×C43#55211yescharacteristic
239C22×C43#55611yescharacteristic
240C2×D43—42no—
241C2×D43—82no—
242C2×D43—81no—
243C2×D43—81no—
244C2×D43—82no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—41no—
249C4×C43—41no—
250C4×C43—41no—
251C4×C43—82no—
252C4×C43#47112yes—
253C4×C43#52511yescharacteristic
254C4×C43#53611yescharacteristic
255C4×C43#54711yescharacteristic
256C4×C43#54811yescharacteristic
257Dic43—81no—
258#3079D4311yescharacteristic, complemented
259C2×#476—431no—
260C4×AGL(1,ℤ/8)—431no—
261#2925—431no—
262#2079—432no—
263#2051—432no—
264#1997—431no—
265#1951—432no—
266#1950—431no—
267#1931—432no—
268#1800—431no—
269C2×C43—21no—
270C2×C43—21no—
271C2×C43—81no—
272C2×C43#241511yescharacteristic
273C2×C43C2×#47111yescharacteristic
274C2×C43#306811yescharacteristic
275D43—82no—
276C2×AGL(1,ℤ/8)—431no—
277C2×C4⋊Q8C2×D4311yescharacteristic
278C4×#41C2×D4311yescharacteristic
279C2×C4×D4—431no—
280#477—21no—
281#476—21no—
282#476—861no—
283#476—861no—
284#476—862no—
285#475—21no—
286#474—21no—
287#442—861no—
288#440—861no—
289C4×SD16—861no—
290C4×D8—861no—
291#433—862no—
292#432—861no—
293#431—861no—
294C2×#108—432no—
295#428—431no—
296#428C2×D4312yes—
297C2×#106—432no—
298#423—431no—
299#423C2×D4311yescharacteristic
300C2×C4⋊C8—431no—
301#418—431no—
302#417—431no—
303#417C2×D4312yes—
304C2×#102—432no—
305C2×#100—432no—
306#408—432no—
307#405—432no—
308C4×M16—431no—
309#343—432no—
310#343—432no—
311#343—432no—
312#341—432no—
313C43#2472111yescharacteristic, complemented, Sylow
314C2×#41C22×D4311yescharacteristic
315C22×Q8—21no—
316C22×D4—431no—
317C23×C4—861no—
318AGL(1,ℤ/8)—862no—
319AGL(1,ℤ/8)—862no—
320C2×SD16—861no—
321C2×D8—861no—
322C2×M16—431no—
323C2×M16—431no—
324C2×M16—432no—
325C2×M16C22×D4312yes—
326C22×C8—432no—
327C4⋊Q8—21no—
328C4⋊Q8—21no—
329C4⋊Q8—21no—
330C4⋊Q8—21no—
331C4×Q8C22⋊D4311yescharacteristic
332C4×Q8C22⋊D4311yescharacteristic
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—861no—
336C4×D4—861no—
337C4×D4—861no—
338C4×D4—861no—
339C4×D4C22⋊D4311yescharacteristic
340C4×D4C22⋊D4311yescharacteristic
341#117—21no—
342#117C22×D4311yescharacteristic
343C2×C4⋊C4—21no—
344C2×C4⋊C4—431no—
345C2×C4⋊C4C22×D4312yes—
346C2×C22⋊C4—861no—
347C2×C42—21no—
348C2×C42C22×D4311yescharacteristic
349#108—864no—
350#107—22no—
351#107—861no—
352#106—22no—
353#106—862no—
354#106—862no—
355#106—861no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—431no—
359C4⋊C8—431no—
360C4⋊C8—432no—
361C4⋊C8—861no—
362C4⋊C8—861no—
363#103—22no—
364#103—861no—
365#102—22no—
366#102—862no—
367#102—862no—
368#102—861no—
369#102—861no—
370#102—861no—
371#100—864no—
372C22⋊C8—862no—
373C22⋊C8—862no—
374#97—862no—
375#97—861no—
376C4×C8—862no—
377C4×C8—861no—
378C24—861no—
379#41—21no—
380#41—21no—
381#41—21no—
382#41—21no—
383C2×Q8—41no—
384C2×Q8—41no—
385C2×Q8—82no—
386C2×Q8C2×C22⋊D4311yescharacteristic
387C2×D4—21no—
388C2×D4—432no—
389C2×D4—861no—
390C2×D4—861no—
391C2×D4—861no—
392C2×D4—861no—
393C2×D4—861no—
394C2×D4C2×C22⋊D4311yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—861no—
400C22×C4—3442no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4#1062190011yescharacteristic
404C22×C4#1062190011yescharacteristic
405C22×C4C23×D4311yescharacteristic
406SD16—864no—
407D8—864no—
408M16—22no—
409M16—22no—
410M16—432no—
411M16—861no—
412M16—862no—
413M16—862no—
414M16—861no—
415M16—861no—
416C2×C8—22no—
417C2×C8—432no—
418C2×C8—432no—
419C2×C8—861no—
420C2×C8—862no—
421C2×C8—862no—
422C2×C8—862no—
423C2×C8—861no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—861no—
431C4⋊C4—861no—
432C4⋊C4C2×C22⋊D4311yescharacteristic
433C4⋊C4C2×C22⋊D4311yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C42—21no—
440C42—21no—
441C42—21no—
442C42D4×D4311yescharacteristic
443C42D4×D4311yescharacteristic
444C42C2×C22⋊D4311yescharacteristic
445C42C2×C22⋊D4311yescharacteristic
446C23—21no—
447C23—862no—
448C23—3441no—
449C23—3441no—
450C23—1721no—
451C23—1721no—
452C23C2×#1062190011yescharacteristic
453Q8—21no—
454Q8—21no—
455Q8—82no—
456Q8—82no—
457D4—21no—
458D4—21no—
459D4—41no—
460D4—41no—
461D4—862no—
462D4—862no—
463D4—1721no—
464D4—1721no—
465C2×C4—22no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—81no—
475C2×C4—82no—
476C2×C4—3442no—
477C2×C4—3442no—
478C2×C4—3441no—
479C2×C4—1721no—
480C2×C4#1306329711yescharacteristic
481C2×C4#1306329711yescharacteristic
482C2×C4#1306329711yescharacteristic
483C2×C4#1306329711yescharacteristic
484C2×C4C2×D4×D4311yescharacteristic
485C2×C4C22×C22⋊D4311yescharacteristic
486C2×C4#41×D4311yescharacteristic
487C2×C4#41×D4311yescharacteristic
488C2×C4#1306337311yescharacteristic
489C2×C4#1306337311yescharacteristic
490C8—42no—
491C8—862no—
492C8—862no—
493C8—862no—
494C8—1722no—
495C8—1721no—
496C22—21no—
497C22—21no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—3442no—
502C22—3442no—
503C22—3441no—
504C22—3441no—
505C22—1722no—
506C22C2×#1306329711yescharacteristic
507C22#1458358311yescharacteristic
508C22#1458362011yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—82no—
516C4—3441no—
517C4#1458316412yes—
518C4#1458340611yescharacteristic
519C4#1458347311yescharacteristic
520C4#1458355111yescharacteristic
521C4#1458355911yescharacteristic
522C2—21no—
523C2—21no—
524C2—81no—
525C2—3442no—
526C2#1913802511yescharacteristic
527C2C2×#1458316411yescharacteristic
528C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3079C2
socleC22×C43C2×#121
prime radicalC2×#13063350C22
hypercenter#3079D43
hypocenterC43#24721
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. C2×#14583186C2semidirect
3. #19143261C2semidirect
4. #19136043C2semidirect
6. #19135585C2semidirect
7. #19135372C2semidirect
8. #19135368C2semidirect
9. #19135256C2semidirect
10. #19134584C2semidirect
11. C43×#3079C2semidirect
258. #3079D43semidirect
313. C43#24721semidirect

Maximal subgroups

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

subgroupindex
C2×#145831862
C4×#130633502
#191432612
#191360432
#191358852
#191355852
#191353722
#191353682
#191352562
#191345842
C43×#30792
#2472143