Finite Group Databasebeta

← #25138059

Subgroups — #25138059

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
1#19144410C211yesmaximal, characteristic, complemented
2C2×#14583190C211yesmaximal, characteristic, complemented
3C4×#13063350C211yesmaximal, characteristic
4#19136040C212yesmaximal, complemented
5#19135886C212yesmaximal
6#19135583C211yesmaximal, characteristic, complemented
7#19135375C212yesmaximal, complemented
8#19135371C211yesmaximal, characteristic, complemented
9#19135257C212yesmaximal, complemented
10#19134584C211yesmaximal, characteristic, complemented
11C43×#2925C211yesmaximal, characteristic, complemented
12C2×#13063350C2211yescharacteristic
13C2×#13063325C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15#14583194—21no—
16#14583190—21no—
17#14583190—21no—
18#14583190—22no—
19#14583189—21no—
20#14583184—21no—
21#14583179—21no—
22#14583009—21no—
23#14582997—21no—
24C4×#10621884—21no—
25C4×#10621882—21no—
26C2×#13063261C2212yes—
27#14582942C2212yes—
28#14582942C2211yescharacteristic
29C2×#13063257C2212yes—
30#14582923C2211yescharacteristic
31#14582903C2211yescharacteristic
32#14582900C2211yescharacteristic
33#14582900C2212yes—
34C2×#13063247C2212yes—
35C2×#13063241C2212yes—
36C4×#10621877C2211yescharacteristic
37#14582667C2212yes—
38#14582667C2212yes—
39#14582667C2212yes—
40#14582664C2212yes—
41C4×#41×C43C2211yescharacteristic
42C43×#433—22no—
43C43×#432—21no—
44C43×#431—21no—
45C43×#423C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C43×#408C2212yes—
48C43×#405C2212yes—
49C22×Dic86—21no—
50C22×D172C2311yescharacteristic
51C22×C4×D43—21no—
52#13063350—22no—
53#13063350—22no—
54C2×#10621884—21no—
55C2×#10621882—21no—
56C2×#10621877C2311yescharacteristic
57C2×#10621877C2312yes—
58C2×#10621877C2311yescharacteristic
59#13063325—21no—
60#13063325—21no—
61#13063325—21no—
62#13063325—21no—
63C4×D172—21no—
64C4×D172—21no—
65C4×D172—21no—
66C4×D172—21no—
67C2×C4⋊Dic43—21no—
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2312yes—
70C2×(C2×D43)⋊C4—21no—
71#13063261—24no—
72#13063258—22no—
73#13063258—21no—
74#13063257—22no—
75#13063257—22no—
76#13063256—22no—
77#13063256—21no—
78C4⋊(C43⋊C8)—21no—
79C4⋊(C43⋊C8)—21no—
80#13063249—22no—
81#13063249—21no—
82#13063247—22no—
83#13063247—22no—
84#13063246—22no—
85#13063246—21no—
86#13063245—21no—
87#13063245—21no—
88#13063241—24no—
89#13063236—21no—
90C4×C43⋊C8—21no—
91C2×#41×C43C2311yescharacteristic
92C2×M16×C43C2312yes—
93C22×C8×C43C2312yes—
94C4×Q8×C43D411yescharacteristic
95C4×Q8×C43D411yescharacteristic
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43D411yescharacteristic
99C4×D4×C43D411yescharacteristic
100#117×C43—21no—
101#117×C43C2311yescharacteristic
102C2×C42×C43—21no—
103C2×C42×C43C2311yescharacteristic
104C4⋊C8×C43—21no—
105C4⋊C8×C43—21no—
106C4⋊C8×C43D411yescharacteristic
107C4⋊C8×C43D411yescharacteristic
108C4⋊C8×C43D412yes—
109C22⋊C8×C43—22no—
110C22⋊C8×C43—22no—
111#97×C43—22no—
112C4×C8×C43—22no—
113C23×D43—21no—
114#41×C43—21no—
115#41×C43—21no—
116#41×C43—21no—
117#41×C43—21no—
118C2×Q8×C43C2×D411yescharacteristic
119C2×D4×C43—21no—
120C2×D4×C43C2×D411yescharacteristic
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43#4111yescharacteristic
125C22×C4×C43#4111yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C22×Dic43—21no—
128C22×Dic43—22no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172—21no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172#4112yes—
135C2×C4×D43—41no—
136C2×C4×D43—41no—
137C2×C4×D43—82no—
138C2×Dic86—41no—
139C2×Dic86—41no—
140C2×Dic86—82no—
141M16×C43—22no—
142M16×C43—22no—
143C2×C8×C43—22no—
144C2×C8×C43—22no—
145C2×C8×C43—22no—
146C2×C8×C43C2×D412yes—
147C2×C8×C43C2×D412yes—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
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—22no—
168C4⋊Dic43—22no—
169C4⋊Dic43—21no—
170C4⋊Dic43—41no—
171C4⋊Dic43—41no—
172#10621877—21no—
173#10621877—22no—
174#10621877—22no—
175#10621877—21no—
176#10621877—21no—
177#10621877#4112yes—
178C2×C43⋊C8—21no—
179C2×C43⋊C8—21no—
180C2×C43⋊C8—22no—
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—
190D4×C43—21no—
191D4×C43—21no—
192D4×C43—41no—
193D4×C43—41no—
194C2×C4×C43—22no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—21no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—42no—
202C2×C4×C43—81no—
203C2×C4×C43#12111yescharacteristic
204C2×C4×C43#12111yescharacteristic
205C2×C4×C43#12111yescharacteristic
206C2×C4×C43#12111yescharacteristic
207C2×C4×C43C22×D411yescharacteristic
208C2×C4×C43C22×D411yescharacteristic
209C2×C4×C43C2×#4111yescharacteristic
210C2×C4×C43C2×#4111yescharacteristic
211C2×C4×C432−1+411yescharacteristic
212C2×C4×C432−1+411yescharacteristic
213C2×Dic43—42no—
214C2×Dic43—41no—
215C2×Dic43—82no—
216C2×Dic43—81no—
217D172—22no—
218D172—22no—
219D172—41no—
220D172—41no—
221C4×D43—82no—
222C4×D43—82no—
223Dic86—82no—
224Dic86—82no—
225C8×C43—22no—
226C8×C43—22no—
227C8×C43—42no—
228C43⋊C8—22no—
229C43⋊C8—42no—
230C43⋊C8—41no—
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#47112yes—
252C4×C43#52511yescharacteristic
253C4×C43#53611yescharacteristic
254C4×C43#54711yescharacteristic
255C4×C43#54811yescharacteristic
256Dic43—81no—
257Dic43—82no—
258#3079—431no—
259C2×#476—431no—
260C4×AGL(1,ℤ/8)—431no—
261#2925D4311yescharacteristic, complemented
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⋊Q8—431no—
278C4×#41C2×D4311yescharacteristic
279C2×C4×D4—431no—
280#477—861no—
281#476—861no—
282#476—861no—
283#476—861no—
284#476—862no—
285#475—861no—
286#474—861no—
287#442—861no—
288#440—861no—
289C4×SD16—861no—
290C4×D8—861no—
291#433—22no—
292#432—21no—
293#431—21no—
294C2×#108—432no—
295#428—432no—
296#428—431no—
297C2×#106—432no—
298#423—431no—
299#423C2×D4311yescharacteristic
300C2×C4⋊C8C2×D4311yescharacteristic
301#418—431no—
302#417—432no—
303#417—431no—
304C2×#102—432no—
305C2×#100—432no—
306#408C2×D4312yes—
307#405C2×D4312yes—
308C4×M16—431no—
309#343—432no—
310#343—432no—
311#343—432no—
312#341—432no—
313C43#2472111yescharacteristic, complemented, Sylow
314C2×#41C22×D4311yescharacteristic
315C22×Q8—861no—
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×C8C22×D4312yes—
327C4⋊Q8—861no—
328C4⋊Q8—861no—
329C4⋊Q8—861no—
330C4⋊Q8—861no—
331C4×Q8D17211yescharacteristic
332C4×Q8D17211yescharacteristic
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—861no—
336C4×D4—861no—
337C4×D4—861no—
338C4×D4—861no—
339C4×D4D17211yescharacteristic
340C4×D4D17211yescharacteristic
341#117—21no—
342#117C22×D4311yescharacteristic
343C2×C4⋊C4—431no—
344C2×C4⋊C4—432no—
345C2×C4⋊C4—861no—
346C2×C22⋊C4—861no—
347C2×C42—21no—
348C2×C42C22×D4311yescharacteristic
349#108—864no—
350#107—861no—
351#107—862no—
352#106—862no—
353#106—862no—
354#106—861no—
355#106—862no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—861no—
359C4⋊C8—861no—
360C4⋊C8C22⋊D4311yescharacteristic
361C4⋊C8C22⋊D4311yescharacteristic
362C4⋊C8C22⋊D4312yes—
363#103—861no—
364#103—862no—
365#102—861no—
366#102—862no—
367#102—862no—
368#102—862no—
369#102—861no—
370#102—861no—
371#100—864no—
372C22⋊C8—22no—
373C22⋊C8—22no—
374#97—22no—
375#97—861no—
376C4×C8—22no—
377C4×C8—861no—
378C24—861no—
379#41—21no—
380#41—21no—
381#41—21no—
382#41—21no—
383C2×Q8—3442no—
384C2×Q8—1721no—
385C2×Q8—1721no—
386C2×Q8C2×D17211yescharacteristic
387C2×D4—21no—
388C2×D4—432no—
389C2×D4—861no—
390C2×D4—861no—
391C2×D4—861no—
392C2×D4—861no—
393C2×D4—861no—
394C2×D4C2×D17211yescharacteristic
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—861no—
399C22×C4—862no—
400C22×C4—3442no—
401C22×C4—1721no—
402C22×C4—1721no—
403C22×C4#1062189811yescharacteristic
404C22×C4#1062189811yescharacteristic
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—22no—
418C2×C8—22no—
419C2×C8—861no—
420C2×C8—861no—
421C2×C8—862no—
422C2×C8C2×C22⋊D4312yes—
423C2×C8C2×C22⋊D4312yes—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—862no—
427C4⋊C4—861no—
428C4⋊C4—861no—
429C4⋊C4—862no—
430C4⋊C4—1721no—
431C4⋊C4—1721no—
432C4⋊C4C2×D17211yescharacteristic
433C4⋊C4C2×D17211yescharacteristic
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C42—21no—
440C42—21no—
441C42—21no—
442C42C2×D17211yescharacteristic
443C42C2×D17211yescharacteristic
444C42C2×C22⋊D4311yescharacteristic
445C42C2×C22⋊D4311yescharacteristic
446C23—21no—
447C23—862no—
448C23—3441no—
449C23—3441no—
450C23—1721no—
451C23—1721no—
452C23C2×#1062189811yescharacteristic
453Q8—21no—
454Q8—21no—
455Q8—3442no—
456Q8—3442no—
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—81no—
474C2×C4—3442no—
475C2×C4—3442no—
476C2×C4—3441no—
477C2×C4—3442no—
478C2×C4—1721no—
479C2×C4—1722no—
480C2×C4#1306329911yescharacteristic
481C2×C4#1306329911yescharacteristic
482C2×C4#1306329911yescharacteristic
483C2×C4#1306329911yescharacteristic
484C2×C4C22×C22⋊D4311yescharacteristic
485C2×C4C22×D17211yescharacteristic
486C2×C4#41×D4311yescharacteristic
487C2×C4#41×D4311yescharacteristic
488C2×C4#1306337211yescharacteristic
489C2×C4#1306337211yescharacteristic
490C8—22no—
491C8—22no—
492C8—42no—
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×#1306329911yescharacteristic
507C22#1458358811yescharacteristic
508C22#1458361711yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—41no—
513C4—41no—
514C4—41no—
515C4—3441no—
516C4—3442no—
517C4#1458316212yes—
518C4#1458341111yescharacteristic
519C4#1458347511yescharacteristic
520C4#1458354811yescharacteristic
521C4#1458355611yescharacteristic
522C2—21no—
523C2—21no—
524C2—81no—
525C2—3442no—
526C2#1913801811yescharacteristic
527C2C2×#1458316211yescharacteristic
528C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2925C2
socleC22×C43C2×#121
prime radicalC2×#13063350C22
hypercenter#2925D43
hypocenterC43#24721
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2925

Complements

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

NH ≅ G/Ntype
1. #19144410C2semidirect
2. C2×#14583190C2semidirect
4. #19136040C2semidirect
6. #19135583C2semidirect
7. #19135375C2semidirect
8. #19135371C2semidirect
9. #19135257C2semidirect
10. #19134584C2semidirect
11. C43×#2925C2semidirect
261. #2925D43semidirect
313. C43#24721semidirect

Maximal subgroups

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

subgroupindex
#191444102
C2×#145831902
C4×#130633502
#191360402
#191358862
#191355832
#191353752
#191353712
#191352572
#191345842
C43×#29252
#2472143