Finite Group Databasebeta

← #25079433

Subgroups — #25079433

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144991C211yesmaximal, characteristic, complemented
2#19144595C211yesmaximal, characteristic
3D4×#10621877C211yesmaximal, characteristic, complemented
4#19134172C212yesmaximal, complemented
5#19134130C212yesmaximal, complemented
6#19134048C212yesmaximal, complemented
7#19134006C212yesmaximal, complemented
8#19133345C211yesmaximal, characteristic, complemented
9#19133276C211yesmaximal, characteristic, complemented
10#19133270C211yesmaximal, characteristic, complemented
11C2×C43×#476C211yesmaximal, characteristic, complemented
12C22×#10621877—21no—
13#14583449C2211yescharacteristic
14#14583261—22no—
15#14583251C2212yescomplemented
16#14583247C2212yescomplemented
17#14583212—21no—
18#14583179C2211yescharacteristic
19#14583179C2211yescharacteristic
20#14583094C2211yescharacteristic
21#14583094C2211yescharacteristic
22#14583033—21no—
23C4×#10621882—21no—
24C4×#10621882—21no—
25#14582977C2212yes—
26#14582971—22no—
27D4×C43⋊C8C2212yes—
28#14582952C2211yescharacteristic
29#14582923C2211yescharacteristic
30#14582898—21no—
31#14582898—21no—
32#14582863—21no—
33C4×#10621877C2211yescharacteristic
34#14582651C2212yescomplemented
35#14582649C2212yescomplemented
36#14582648C2212yescomplemented
37#14582648C2212yescomplemented
38#14582644C2212yescomplemented
39#14582642C2212yescomplemented
40C2×C4⋊Q8×C43C2211yescharacteristic
41C2×C4×D4×C43C2211yescharacteristic
42C43×#476—21no—
43C43×#476—21no—
44C43×#476C2212yes—
45C43×#476C2212yes—
46C2×#106×C43—21no—
47C2×C4⋊C8×C43C2211yescharacteristic
48C2×#102×C43—21no—
49C2×#10621898—21no—
50C2×#10621882—21no—
51C2×#10621882—21no—
52C2×#10621877—21no—
53C2×#10621877—22no—
54C2×#10621877—44no—
55C2×#10621877D411yescharacteristic
56C2×#10621877D411yescharacteristic
57C22×C43⋊C8—22no—
58#13063325C2311yescharacteristic
59#13063322C2311yescharacteristic
60#13063313—21no—
61#13063299—21no—
62#13063299—21no—
63C4×D172—21no—
64C4×D172—21no—
65#13063258—21no—
66#13063258—21no—
67C4⋊(C43⋊C8)—21no—
68C4⋊(C43⋊C8)C2311yescharacteristic
69C4⋊(C43⋊C8)C2311yescharacteristic
70C4⋊(C43⋊C8)C2312yes—
71#13063248—22no—
72#13063248—22no—
73#13063246—21no—
74#13063246—21no—
75#13063245—21no—
76#13063245—21no—
77#13063245—22no—
78#13063245—22no—
79C22⋊(C43⋊C8)—21no—
80C22⋊(C43⋊C8)—22no—
81C22⋊(C43⋊C8)—22no—
82#13063236D412yes—
83C4×C43⋊C8—21no—
84C4×C43⋊C8C2312yes—
85C22×Q8×C43—21no—
86C22×D4×C43D411yescharacteristic
87C23×C4×C43—21no—
88C22×C8×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43C2312yes—
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43D411yescharacteristic
96C4×D4×C43D411yescharacteristic
97C4×D4×C43C2311yescharacteristic
98C4×D4×C43C2311yescharacteristic
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C22⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104#106×C43—22no—
105#106×C43—22no—
106C4⋊C8×C43—21no—
107C4⋊C8×C43C2312yes—
108#102×C43—22no—
109#102×C43—22no—
110C24×C43—21no—
111C2×Q8×C43—22no—
112C2×Q8×C43—41no—
113C2×Q8×C43—82no—
114C2×D4×C43—21no—
115C2×D4×C43—22no—
116C2×D4×C43—41no—
117C2×D4×C43C2×D411yescharacteristic
118C2×D4×C43C2×D411yescharacteristic
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—42no—
125C22×C4×C43—42no—
126C22×C4×C43—41no—
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43#4111yescharacteristic
130C2×C22⋊D43—41no—
131#10621898—42no—
132#10621898—42no—
133C2×D172—21no—
134C2×D172—21no—
135C2×D172—21no—
136C2×C4×D43—41no—
137C2×Dic86—21no—
138C2×C8×C43—22no—
139C2×C8×C43—42no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43C2×D411yescharacteristic
146C4⋊C4×C43C2×D411yescharacteristic
147C22⋊C4×C43—21no—
148C22⋊C4×C43—21no—
149C22⋊C4×C43—21no—
150C22⋊C4×C43—21no—
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153C42×C43#4111yescharacteristic
154C42×C43C2411yescharacteristic
155#10621882—42no—
156#10621882—42no—
157(C2×D43)⋊C4—41no—
158(C2×D43)⋊C4—41no—
159C4⋊Dic43—21no—
160C4⋊Dic43—21no—
161#10621877—22no—
162#10621877—22no—
163#10621877—44no—
164#10621877—42no—
165C2×C43⋊C8—21no—
166C2×C43⋊C8—21no—
167C2×C43⋊C8—22no—
168C2×C43⋊C8—44no—
169C2×C43⋊C8C2×D412yes—
170C2×C43⋊C8C2×D412yes—
171C23×C43—21no—
172C23×C43—21no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—81no—
176C23×C43#12111yescharacteristic
177C22×D43—41no—
178Q8×C43—82no—
179Q8×C43—82no—
180D4×C43—21no—
181D4×C43—21no—
182D4×C43—21no—
183D4×C43—42no—
184D4×C43#13712yes—
185C2×C4×C43—21no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—21no—
189C2×C4×C43—41no—
190C2×C4×C43—42no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—42no—
196C2×C4×C43—42no—
197C2×C4×C43—42no—
198C2×C4×C43—82no—
199C2×C4×C43#12111yescharacteristic
200C2×C4×C43#12111yescharacteristic
201C2×C4×C43#12111yescharacteristic
202C2×C4×C43#13512yes—
203C2×C4×C43AGL(1,ℤ/8)12yes—
204C2×C4×C43C22×D411yescharacteristic
205C2×C4×C43C22×D411yescharacteristic
206C2×C4×C43C2×#4111yescharacteristic
207C22⋊D43—82no—
208C2×Dic43—41no—
209D172—41no—
210D172—41no—
211D172—41no—
212D172—41no—
213D172—81no—
214C4×D43—82no—
215Dic86—41no—
216Dic86—41no—
217C8×C43—42no—
218C43⋊C8—22no—
219C43⋊C8—22no—
220C43⋊C8—42no—
221C43⋊C8—41no—
222C43⋊C8—41no—
223#19168—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—22no—
227C22×C43—41no—
228C22×C43—41no—
229C22×C43—41no—
230C22×C43—41no—
231C22×C43—41no—
232C22×C43—84no—
233C22×C43#46312yes—
234C22×C43C2×#12111yescharacteristic
235C2×D43—81no—
236C2×D43—81no—
237C2×D43—81no—
238C4×C43—21no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—41no—
242C4×C43—41no—
243C4×C43—82no—
244C4×C43#46312yes—
245C4×C43C2×#13511yescharacteristic
246C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
247C4×C43C2×#13711yescharacteristic
248C4×C43#57511yescharacteristic
249Dic43—81no—
250#3141—431no—
251#3100—431no—
252C2×#476D4311yescharacteristic, complemented
253D4×M16—431no—
254#1703—432no—
255#1697—432no—
256#1683—432no—
257#1677—432no—
258#1565—431no—
259#1548—431no—
260#1547—431no—
261C2×C43—22no—
262C2×C43—42no—
263C2×C43—81no—
264C2×C43C2×#46311yescharacteristic
265C2×C43#305611yescharacteristic
266C2×C43#306811yescharacteristic
267D43—161no—
268C22×M16—861no—
269#532—431no—
270C2×C4⋊Q8C2×D4311yescharacteristic
271C2×C4×D4C2×D4311yescharacteristic
272#489—862no—
273#487—432no—
274#486—432no—
275#480—861no—
276#476—21no—
277#476—21no—
278#476C2×D4312yes—
279#476C2×D4312yes—
280#474—431no—
281#474—431no—
282#459—431no—
283#459—431no—
284#447—861no—
285C4×D8—861no—
286C4×D8—861no—
287#436—432no—
288#435—862no—
289C8×D4—432no—
290#431—431no—
291C2×#106—21no—
292#423—431no—
293C2×C4⋊C8C2×D4311yescharacteristic
294#417—861no—
295#417—861no—
296C2×#102—21no—
297#407—861no—
298C4×M16—431no—
299#335—432no—
300#334—432no—
301#333—432no—
302#333—432no—
303#332—432no—
304#331—432no—
305C43#1916811yescharacteristic, complemented, Sylow
306C2×#41—861no—
307C22×Q8—21no—
308C22×D4C22⋊D4311yescharacteristic
309C23×C4—21no—
310C2×D8—861no—
311C2×D8—861no—
312C2×M16—431no—
313C2×M16—431no—
314C2×M16—862no—
315C2×M16—861no—
316C2×M16—1724no—
317C22×C8—21no—
318C22×C8—862no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—431no—
323C4⋊Q8C22×D4312yes—
324#127—431no—
325#124—861no—
326#121—861no—
327#121—861no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—861no—
331C4×D4—861no—
332C4×D4C22⋊D4311yescharacteristic
333C4×D4C22⋊D4311yescharacteristic
334C4×D4C22×D4311yescharacteristic
335C4×D4C22×D4311yescharacteristic
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4C22⋊D4311yescharacteristic
339C2×C22⋊C4—21no—
340C2×C42C22×D4311yescharacteristic
341#107—861no—
342#107—861no—
343#106—22no—
344#106—22no—
345C4⋊C8—21no—
346C4⋊C8—432no—
347C4⋊C8—431no—
348C4⋊C8—431no—
349C4⋊C8—861no—
350C4⋊C8C22×D4312yes—
351#103—862no—
352#103—862no—
353#102—22no—
354#102—22no—
355#102—862no—
356#102—862no—
357#102—861no—
358#102—861no—
359#102—861no—
360#102—861no—
361C22⋊C8—862no—
362C22⋊C8—862no—
363C22⋊C8—861no—
364#97—432no—
365C4×C8—432no—
366C4×C8—861no—
367C24—21no—
368#41—1722no—
369#41—1722no—
370C2×Q8—22no—
371C2×Q8—41no—
372C2×Q8—82no—
373C2×Q8—861no—
374C2×D4—22no—
375C2×D4—21no—
376C2×D4—41no—
377C2×D4—861no—
378C2×D4—861no—
379C2×D4—861no—
380C2×D4—1721no—
381C2×D4C2×C22⋊D4311yescharacteristic
382C2×D4C2×C22⋊D4311yescharacteristic
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—41no—
391C22×C4—1721no—
392C22×C4D4×D4311yescharacteristic
393C22×C4#1062190011yescharacteristic
394C22×C4C2×C22⋊D4311yescharacteristic
395D8—1722no—
396D8—1722no—
397M16—862no—
398M16—862no—
399M16—1724no—
400M16—1722no—
401C2×C8—22no—
402C2×C8—42no—
403C2×C8—432no—
404C2×C8—432no—
405C2×C8—862no—
406C2×C8—861no—
407C2×C8—861no—
408C2×C8—1724no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—22no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—861no—
415C4⋊C4—861no—
416C4⋊C4C2×C22⋊D4311yescharacteristic
417C4⋊C4C2×C22⋊D4311yescharacteristic
418C22⋊C4—21no—
419C22⋊C4—21no—
420C22⋊C4—21no—
421C22⋊C4—21no—
422C22⋊C4—1721no—
423C22⋊C4—1721no—
424C42D4×D4311yescharacteristic
425C42#1062190011yescharacteristic
426C42C2×C22⋊D4311yescharacteristic
427C42C23×D4311yescharacteristic
428C23—21no—
429C23—21no—
430C23—42no—
431C23—42no—
432C23—81no—
433C23—1721no—
434C23#1306329711yescharacteristic
435Q8—82no—
436Q8—82no—
437Q8—1721no—
438Q8—1721no—
439D4—21no—
440D4—21no—
441D4—21no—
442D4—42no—
443D4—3441no—
444D4—3442no—
445D4—1721no—
446D4—1721no—
447D4—1721no—
448D4—1721no—
449D4#1306335612yes—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—82no—
464C2×C4—3442no—
465C2×C4—1721no—
466C2×C4#1306329711yescharacteristic
467C2×C4#1306329711yescharacteristic
468C2×C4#1306329711yescharacteristic
469C2×C4#1306334612yes—
470C2×C4#1306335212yes—
471C2×C4C2×D4×D4311yescharacteristic
472C2×C4C22×C22⋊D4311yescharacteristic
473C2×C4C2×#1062190011yescharacteristic
474C8—42no—
475C8—862no—
476C8—862no—
477C8—1722no—
478C8—1721no—
479C8—1721no—
480C22—21no—
481C22—21no—
482C22—22no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—84no—
489C22—3441no—
490C22—3441no—
491C22—3441no—
492C22#1458311612yes—
493C22C2×#1306329711yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—41no—
498C4—41no—
499C4—82no—
500C4—3441no—
501C4#1458311612yes—
502C4C2×#1306334611yescharacteristic
503C4C2×#1306335211yescharacteristic
504C4C2×#1306335611yescharacteristic
505C4#1458369711yescharacteristic
506C2—22no—
507C2—42no—
508C2—81no—
509C2—6881no—
510C2C2×#1458311611yescharacteristic
511C2#1914422111yescharacteristic
512C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#476C2
socleC22×C43C2×#121
prime radical#19144595C2
hypercenterC2×#476D43
hypocenterC43#19168
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. #19144991C2semidirect
3. D4×#10621877C2semidirect
4. #19134172C2semidirect
5. #19134130C2semidirect
6. #19134048C2semidirect
7. #19134006C2semidirect
8. #19133345C2semidirect
9. #19133276C2semidirect
10. #19133270C2semidirect
11. C2×C43×#476C2semidirect
15. #14583251C22semidirect
16. #14583247C22semidirect
34. #14582651C22semidirect
35. #14582649C22semidirect
36. #14582648C22semidirect
37. #14582648C22semidirect
38. #14582644C22semidirect
39. #14582642C22semidirect
252. C2×#476D43semidirect
305. C43#19168semidirect

Maximal subgroups

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

subgroupindex
#191449912
#191445952
D4×#106218772
#191341722
#191341302
#191340482
#191340062
#191333452
#191332762
#191332702
C2×C43×#4762
#1916843