Finite Group Databasebeta

← #25138056

Subgroups — #25138056

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#19144411C211yesmaximal, characteristic, complemented
2C2×#14583179C211yesmaximal, characteristic, complemented
3C4×#13063351C211yesmaximal, characteristic
4#19143263C211yesmaximal, characteristic, complemented
5#19136039C212yesmaximal, complemented
6#19135887C212yesmaximal
7#19135583C211yesmaximal, characteristic, complemented
8#19135379C212yesmaximal, complemented
9#19135368C211yesmaximal, characteristic, complemented
10#19135259C212yesmaximal, complemented
11C43×#1800C211yesmaximal, characteristic, complemented
12C2×#13063351C2211yescharacteristic
13C2×#13063325C2211yescharacteristic
14C4×#10621898C2211yescharacteristic
15#14583195—21no—
16#14583190—21no—
17#14583185—21no—
18#14583180—21no—
19#14583179—21no—
20#14583179—21no—
21#14583179—22no—
22#14583009—21no—
23#14582999—21no—
24C4×#10621883—21no—
25C4×#10621882—21no—
26#14582959—22no—
27#14582955—21no—
28#14582951—21no—
29C2×#13063260C2212yes—
30#14582941C2212yes—
31#14582939C2211yescharacteristic
32C2×#13063258C2212yes—
33C2×C4⋊(C43⋊C8)C2211yescharacteristic
34#14582904C2211yescharacteristic
35#14582901C2212yes—
36#14582898C2211yescharacteristic
37C2×#13063246C2212yes—
38#14582867C2212yes—
39#14582857C2212yes—
40C4×#10621877C2211yescharacteristic
41#14582667C2212yes—
42#14582667C2212yes—
43#14582663C2212yes—
44C2×C4×D4×C43C2211yescharacteristic
45C43×#423C2211yescharacteristic
46C43×#423C2211yescharacteristic
47C2×#100×C43C2212yes—
48C43×#343C2212yes—
49C2×#10621898C2311yescharacteristic
50C22×Dic86—21no—
51#13063351—22no—
52#13063351—22no—
53C2×#10621883—21no—
54C2×#10621882—21no—
55C2×#10621877C2311yescharacteristic
56C2×#10621877C2311yescharacteristic
57C22×C43⋊C8C2312yes—
58#13063325—21no—
59#13063325—21no—
60#13063325—21no—
61#13063325—21no—
62C4×Dic86D411yescharacteristic
63C4×Dic86D411yescharacteristic
64C4×D172D411yescharacteristic
65C4×D172D411yescharacteristic
66C4×C22⋊D43—21no—
67C4×C22⋊D43—21no—
68#13063284C2311yescharacteristic
69#13063282—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2312yes—
72C42×D43—21no—
73#13063260—24no—
74#13063259—22no—
75#13063258—21no—
76#13063258—22no—
77#13063258—22no—
78#13063257—22no—
79#13063256—21no—
80C4⋊(C43⋊C8)D411yescharacteristic
81C4⋊(C43⋊C8)D411yescharacteristic
82C4⋊(C43⋊C8)D412yes—
83#13063250—22no—
84#13063248—21no—
85#13063247—22no—
86#13063246—21no—
87#13063246—21no—
88#13063246—22no—
89#13063246—22no—
90#13063245—21no—
91(C2×D43)⋊C8—22no—
92(C2×D43)⋊C8—22no—
93#13063236—21no—
94#13063235—22no—
95C4×C43⋊C8—21no—
96C8×Dic43—22no—
97C22×D4×C43C2311yescharacteristic
98C23×C4×C43—21no—
99C2×M16×C43C2312yes—
100C2×M16×C43C2312yes—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C22⋊C4×C43—21no—
107C2×C42×C43C2311yescharacteristic
108C4⋊C8×C43—21no—
109C4⋊C8×C43—21no—
110C4⋊C8×C43—21no—
111C4⋊C8×C43—21no—
112#100×C43—24no—
113C24×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43#4112yes—
120C22×C4×C43—21no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43—82no—
124C22×C4×C43#4111yescharacteristic
125C22×C4×C43#4111yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C2×C22⋊D43—21no—
128C22×Dic43—22no—
129#10621898—21no—
130#10621898—21no—
131#10621898—21no—
132#10621898—21no—
133C2×D172C2×D411yescharacteristic
134C2×C4×D43—21no—
135C2×C4×D43—21no—
136C2×C4×D43—21no—
137C2×Dic86—41no—
138C2×Dic86—41no—
139C2×Dic86—82no—
140C2×Dic86C2×D411yescharacteristic
141M16×C43—22no—
142M16×C43—22no—
143M16×C43—22no—
144M16×C43—22no—
145C2×C8×C43—22no—
146C2×C8×C43—22no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C22⋊C4×C43—41no—
150C22⋊C4×C43—41no—
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153C42×C43C2×D411yescharacteristic
154C42×C43C2×D411yescharacteristic
155C22⋊Dic43—21no—
156#10621883—24no—
157#10621882—24no—
158(C2×D43)⋊C4—21no—
159(C2×D43)⋊C4—21no—
160C4⋊Dic43—22no—
161C4⋊Dic43—22no—
162C4⋊Dic43—41no—
163C4⋊Dic43—41no—
164C4⋊Dic43C2×D411yescharacteristic
165C4⋊Dic43C2×D411yescharacteristic
166Dic43⋊C4—21no—
167Dic43⋊C4—21no—
168C4×Dic43—21no—
169C4×Dic43—21no—
170C4×Dic43—21no—
171#10621877—21no—
172#10621877—21no—
173#10621877—21no—
174#10621877#4112yes—
175C2×C43⋊C8—21no—
176C2×C43⋊C8—22no—
177C2×C43⋊C8—22no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8C2×D412yes—
180C2×C43⋊C8C2×D412yes—
181C23×C43—22no—
182C23×C43—41no—
183C23×C43—41no—
184C23×C43—81no—
185C23×C43—81no—
186C23×C43C2×#4111yescharacteristic
187C22×D43—21no—
188D4×C43—22no—
189D4×C43—22no—
190D4×C43—41no—
191D4×C43—41no—
192C2×C4×C43—22no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—82no—
196C2×C4×C43—82no—
197C2×C4×C43—81no—
198C2×C4×C43#12111yescharacteristic
199C2×C4×C43#12111yescharacteristic
200C2×C4×C43#12111yescharacteristic
201C2×C4×C43#12111yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C22×D411yescharacteristic
204C2×C4×C43C2×#4111yescharacteristic
205C2×C4×C43C2×#4111yescharacteristic
206C2×C4×C432−1+411yescharacteristic
207C2×C4×C432−1+411yescharacteristic
208C22⋊D43—41no—
209C22⋊D43—41no—
210C2×Dic43—21no—
211C2×Dic43—21no—
212C2×Dic43—21no—
213C2×Dic43—42no—
214C2×Dic43—82no—
215D172—21no—
216D172—21no—
217C4×D43—41no—
218C4×D43—41no—
219C4×D43—42no—
220C4×D43—81no—
221Dic86—21no—
222Dic86—21no—
223Dic86—82no—
224Dic86—82no—
225C8×C43—42no—
226C8×C43—42no—
227C43⋊C8—22no—
228C43⋊C8—22no—
229C43⋊C8—22no—
230C43⋊C8—41no—
231#24720—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—42no—
235C22×C43—82no—
236C22×C43—82no—
237C22×C43—81no—
238C22×C43—81no—
239C22×C43C2×#12111yescharacteristic
240C22×C43#55211yescharacteristic
241C22×C43#55611yescharacteristic
242C2×D43—41no—
243C2×D43—41no—
244C2×D43—41no—
245C4×C43—21no—
246C4×C43—21no—
247C4×C43—21no—
248C4×C43—81no—
249C4×C43#47212yes—
250C4×C43#52511yescharacteristic
251C4×C43#53611yescharacteristic
252C4×C43#54711yescharacteristic
253C4×C43#54811yescharacteristic
254Dic43—41no—
255Dic43—41no—
256Dic43—41no—
257Dic43—82no—
258#3079—431no—
259C2×#474—431no—
260C4×AGL(1,ℤ/8)—431no—
261#2925—431no—
262#2078—432no—
263#2051—432no—
264#1997—431no—
265#1952—432no—
266#1950—431no—
267#1931—432no—
268#1800D4311yescharacteristic, complemented
269C2×C43—21no—
270C2×C43—21no—
271C2×C43—82no—
272C2×C43#241511yescharacteristic
273C2×C43C2×#47211yescharacteristic
274C2×C43#306911yescharacteristic
275D43—81no—
276C2×AGL(1,ℤ/8)—431no—
277C2×C4⋊Q8—431no—
278C4×#41—431no—
279C2×C4×D4C2×D4311yescharacteristic
280#477—861no—
281#476—861no—
282#475—861no—
283#474—861no—
284#474—861no—
285#474—861no—
286#474—862no—
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—432no—
296#428—431no—
297C2×#107—432no—
298#423C2×D4311yescharacteristic
299#423C2×D4311yescharacteristic
300C2×C4⋊C8—431no—
301#418—431no—
302#417—432no—
303#417—431no—
304C2×#102—432no—
305C2×#100C2×D4312yes—
306#408—432no—
307#405—432no—
308C4×M16—431no—
309#343—432no—
310#343—432no—
311#343C2×D4312yes—
312#341—432no—
313C43#2472011yescharacteristic, complemented, Sylow
314C2×#41—431no—
315C22×Q8—861no—
316C22×D4C22×D4311yescharacteristic
317C23×C4—21no—
318AGL(1,ℤ/8)—862no—
319AGL(1,ℤ/8)—862no—
320C2×SD16—861no—
321C2×D8—861no—
322C2×M16—431no—
323C2×M16—431no—
324C2×M16C22×D4312yes—
325C2×M16C22×D4312yes—
326C22×C8—432no—
327C4⋊Q8—861no—
328C4⋊Q8—861no—
329C4⋊Q8—861no—
330C4⋊Q8—861no—
331C4×Q8—431no—
332C4×Q8—431no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—21no—
336C4×D4—21no—
337C4×D4—431no—
338C4×D4—431no—
339C4×D4—861no—
340C4×D4—861no—
341#117—431no—
342#117—861no—
343C2×C4⋊C4—432no—
344C2×C4⋊C4—861no—
345C2×C4⋊C4C22×D4311yescharacteristic
346C2×C22⋊C4—21no—
347C2×C42—861no—
348C2×C42C22×D4311yescharacteristic
349#108—864no—
350#107—861no—
351#107—862no—
352#107—862no—
353#107—862no—
354#106—861no—
355#106—862no—
356C4⋊C8—21no—
357C4⋊C8—21no—
358C4⋊C8—21no—
359C4⋊C8—21no—
360C4⋊C8—431no—
361C4⋊C8—431no—
362C4⋊C8—432no—
363#103—861no—
364#103—862no—
365#102—861no—
366#102—861no—
367#102—861no—
368#102—862no—
369#102—862no—
370#102—862no—
371#100—24no—
372C22⋊C8—862no—
373C22⋊C8—862no—
374#97—862no—
375#97—861no—
376C4×C8—862no—
377C4×C8—861no—
378C24—21no—
379#41—861no—
380#41—861no—
381#41—861no—
382#41—861no—
383C2×Q8—431no—
384C2×Q8—3442no—
385C2×Q8—1721no—
386C2×Q8—1721no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—431no—
393C2×D4—861no—
394C2×D4#1062190012yes—
395C22×C4—21no—
396C22×C4—41no—
397C22×C4—41no—
398C22×C4—82no—
399C22×C4—861no—
400C22×C4—861no—
401C22×C4—861no—
402C22×C4—862no—
403C22×C4#1062189811yescharacteristic
404C22×C4#1062189811yescharacteristic
405C22×C4C23×D4311yescharacteristic
406SD16—864no—
407D8—864no—
408M16—22no—
409M16—22no—
410M16—22no—
411M16—22no—
412M16—432no—
413M16—861no—
414M16—861no—
415M16—861no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—432no—
419C2×C8—432no—
420C2×C8—861no—
421C2×C8—862no—
422C2×C8—862no—
423C2×C8—861no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—431no—
427C4⋊C4—431no—
428C4⋊C4—861no—
429C4⋊C4—861no—
430C4⋊C4—862no—
431C4⋊C4—862no—
432C4⋊C4—1721no—
433C4⋊C4—1721no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—861no—
437C22⋊C4—861no—
438C22⋊C4—861no—
439C42—861no—
440C42—861no—
441C42—861no—
442C42D4×D4311yescharacteristic
443C42D4×D4311yescharacteristic
444C42D4×D4311yescharacteristic
445C42D4×D4311yescharacteristic
446C23—22no—
447C23—41no—
448C23—41no—
449C23—81no—
450C23—81no—
451C23—861no—
452C23C2×#1062189811yescharacteristic
453Q8—861no—
454Q8—861no—
455Q8—3442no—
456Q8—3442no—
457D4—22no—
458D4—22no—
459D4—41no—
460D4—41no—
461D4—861no—
462D4—861no—
463D4—1721no—
464D4—1721no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—82no—
469C2×C4—82no—
470C2×C4—81no—
471C2×C4—861no—
472C2×C4—861no—
473C2×C4—861no—
474C2×C4—3441no—
475C2×C4—3442no—
476C2×C4—1722no—
477C2×C4—1721no—
478C2×C4—1722no—
479C2×C4—1721no—
480C2×C4#1306329811yescharacteristic
481C2×C4#1306329811yescharacteristic
482C2×C4#1306329811yescharacteristic
483C2×C4#1306329811yescharacteristic
484C2×C4C2×D4×D4311yescharacteristic
485C2×C4C2×D4×D4311yescharacteristic
486C2×C4#41×D4311yescharacteristic
487C2×C4C2×#1062190011yescharacteristic
488C2×C4#1306337211yescharacteristic
489C2×C4#1306337311yescharacteristic
490C8—42no—
491C8—42no—
492C8—862no—
493C8—862no—
494C8—862no—
495C8—1721no—
496C22—21no—
497C22—21no—
498C22—42no—
499C22—82no—
500C22—82no—
501C22—81no—
502C22—81no—
503C22—1721no—
504C22—1721no—
505C22—1721no—
506C22C2×#1306329811yescharacteristic
507C22#1458358411yescharacteristic
508C22#1458361711yescharacteristic
509C4—21no—
510C4—21no—
511C4—21no—
512C4—81no—
513C4—3442no—
514C4—1721no—
515C4—1721no—
516C4—1721no—
517C4#1458316812yes—
518C4#1458340911yescharacteristic
519C4#1458347211yescharacteristic
520C4#1458355111yescharacteristic
521C4#1458355511yescharacteristic
522C2—21no—
523C2—21no—
524C2—82no—
525C2—3441no—
526C2#1913802611yescharacteristic
527C2C2×#1458316811yescharacteristic
528C2#1914433511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1800C2
socleC22×C43C2×#121
prime radicalC2×#13063351C22
hypercenter#1800D43
hypocenterC43#24720
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
1. #19144411C2semidirect
2. C2×#14583179C2semidirect
4. #19143263C2semidirect
5. #19136039C2semidirect
7. #19135583C2semidirect
8. #19135379C2semidirect
9. #19135368C2semidirect
10. #19135259C2semidirect
11. C43×#1800C2semidirect
268. #1800D43semidirect
313. C43#24720semidirect

Maximal subgroups

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

subgroupindex
#191444112
C2×#145831792
C4×#130633512
#191432632
#191360392
#191358872
#191355832
#191353792
#191353682
#191352592
C43×#18002
#2472043