Finite Group Databasebeta

← #25146972

Subgroups — #25146972

Order 11008.

764 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#19144059C211yesmaximal, characteristic
3#19143338C211yesmaximal, characteristic, complemented
4#19136036C212yesmaximal, complemented
5#19135888C212yesmaximal, complemented
6#19135585C211yesmaximal, characteristic, complemented
7#19135371C211yesmaximal, characteristic, complemented
8#19135106C212yesmaximal, complemented
9#19134660C212yesmaximal, complemented
10C4×#13063242C211yesmaximal, characteristic, complemented
11C2×C43×#474C211yesmaximal, characteristic, complemented
12C2×#13063351C2212yes—
13C2×#13063331C2212yes—
14#14583449C2211yescharacteristic
15#14583261—22no—
16#14583251—21no—
17#14583247—21no—
18#14583114—22no—
19#14583104—21no—
20#14583094—21no—
21#14582976—21no—
22#14582969—22no—
23#14582964—21no—
24C2×#13063261C2212yes—
25#14582923C2211yescharacteristic
26#14582898C2212yes—
27#14582898C2212yes—
28#14582898C2212yes—
29C2×#13063242C2211yescharacteristic
30C2×#13063242C2211yescharacteristic
31#14582865C2212yes—
32C4×#10621877C2211yescharacteristic
33C4×#10621877C2211yescharacteristic
34#14582668C2211yescharacteristic
35#14582668C2212yes—
36#14582668C2212yes—
37#14582668C2211yescharacteristic
38#14582664C2212yes—
39C2×C4⋊Q8×C43C2211yescharacteristic
40C2×C4×D4×C43C2211yescharacteristic
41C43×#474—21no—
42C43×#474—22no—
43C43×#474—21no—
44C2×#107×C43C2212yes—
45C2×C4⋊C8×C43C2211yescharacteristic
46C2×#102×C43C2212yes—
47C2×#10621898C2312yes—
48#13063351—24no—
49#13063351—42no—
50C2×#10621883—22no—
51C2×#10621882—22no—
52#13063331—24no—
53#13063331—42no—
54C2×#10621877C2311yescharacteristic
55C2×#10621877C2311yescharacteristic
56C2×#10621877C2311yescharacteristic
57C2×#10621877C2312yes—
58C2×#10621877C2311yescharacteristic
59C2×#10621872—22no—
60C2×C8×D43—22no—
61#13063325D411yescharacteristic
62#13063322D411yescharacteristic
63#13063313D412yes—
64#13063299—21no—
65#13063299—21no—
66C4×D172—21no—
67C4×D172—21no—
68#13063261—42no—
69C4⋊(C43⋊C8)—21no—
70C4⋊(C43⋊C8)—21no—
71#13063248—22no—
72#13063248—22no—
73#13063248—22no—
74#13063245—22no—
75#13063245—22no—
76#13063245—22no—
77#13063242—22no—
78#13063242—22no—
79(C2×D43)⋊C8—22no—
80(C2×D43)⋊C8—22no—
81#13063236—21no—
82#13063236—21no—
83C4×C43⋊C8—21no—
84C4×C43⋊C8—21no—
85C22×Q8×C43—21no—
86C22×D4×C43C2311yescharacteristic
87C23×C4×C43—21no—
88C22×C8×C43C2312yes—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43—21no—
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2312yes—
100C2×C22⋊C4×C43—21no—
101C2×C42×C43C2311yescharacteristic
102#107×C43—22no—
103#107×C43—22no—
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43D412yes—
106C4⋊C8×C43D411yescharacteristic
107#102×C43—22no—
108#102×C43—22no—
109C24×C43—21no—
110C2×Q8×C43—41no—
111C2×Q8×C43—41no—
112C2×Q8×C43—82no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43#4112yes—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
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—22no—
128#10621898—22no—
129#10621898—22no—
130#10621898—22no—
131#10621898—22no—
132C2×D172—21no—
133C2×D172—21no—
134C2×D172C2×D412yes—
135C2×C4×D43—22no—
136C2×Dic86C2×D412yes—
137C2×C8×C43—22no—
138C2×C8×C43—22no—
139C2×C8×C43C2×D412yes—
140C2×C8×C43C2×D412yes—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—41no—
146C4⋊C4×C43—41no—
147C22⋊C4×C43—41no—
148C22⋊C4×C43—41no—
149C42×C43C2×D411yescharacteristic
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152C42×C43C2×D411yescharacteristic
153#10621883—44no—
154#10621882—44no—
155(C2×D43)⋊C4—22no—
156(C2×D43)⋊C4—22no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159#10621877—21no—
160#10621877—21no—
161#10621877—21no—
162#10621877—21no—
163#10621877—22no—
164#10621877—21no—
165#10621877—22no—
166#10621877—21no—
167#10621877—21no—
168#10621877#4112yes—
169C2×C43⋊C8—21no—
170C2×C43⋊C8—21no—
171C2×C43⋊C8—21no—
172C2×C43⋊C8—21no—
173C2×C43⋊C8—22no—
174#10621872—44no—
175C8×D43—44no—
176C23×C43—22no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—81no—
180C23×C43—81no—
181C23×C43C2×#4111yescharacteristic
182C22×D43—22no—
183Q8×C43—82no—
184Q8×C43—82no—
185D4×C43—22no—
186D4×C43—22no—
187D4×C43—41no—
188D4×C43—41no—
189C2×C4×C43—22no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—42no—
193C2×C4×C43—82no—
194C2×C4×C43—82no—
195C2×C4×C43—81no—
196C2×C4×C43—82no—
197C2×C4×C43#12111yescharacteristic
198C2×C4×C43#12111yescharacteristic
199C2×C4×C43#12111yescharacteristic
200C2×C4×C43#12111yescharacteristic
201C2×C4×C43C22×D411yescharacteristic
202C2×C4×C43C22×D411yescharacteristic
203C2×C4×C43C2×#4111yescharacteristic
204C2×C4×C43C2×#4111yescharacteristic
205C2×C4×C43H(5,𝔽2)11yescharacteristic
206C2×C4×C432−1+411yescharacteristic
207C22⋊D43—42no—
208C22⋊D43—42no—
209C2×Dic43—22no—
210D172—22no—
211D172—22no—
212D172—42no—
213D172—81no—
214C4×D43—42no—
215C4×D43—42no—
216Dic86—22no—
217Dic86—22no—
218C8×C43—22no—
219C8×C43—22no—
220C43⋊C8—22no—
221C43⋊C8—41no—
222C43⋊C8—42no—
223C43⋊C8—41no—
224C43⋊C8—41no—
225#25358—431nomaximal, Sylow
226C22×C43—21no—
227C22×C43—21no—
228C22×C43—42no—
229C22×C43—82no—
230C22×C43—82no—
231C22×C43—81no—
232C22×C43—81no—
233C22×C43C2×#12111yescharacteristic
234C22×C43#52911yescharacteristic
235C22×C43#54211yescharacteristic
236C2×D43—42no—
237C2×D43—42no—
238C2×D43—42no—
239C4×C43—21no—
240C4×C43—21no—
241C4×C43—21no—
242C4×C43—81no—
243C4×C43—82no—
244C4×C43#47212yes—
245C4×C43#54611yescharacteristic
246C4×C43#54611yescharacteristic
247C4×C43#54711yescharacteristic
248C4×C43#54811yescharacteristic
249Dic43—42no—
250#3141—431no—
251C2×#474D4311yescharacteristic, complemented
252#3036—431no—
253#2935—431no—
254#2078—432no—
255#2051—432no—
256#1997—431no—
257#1950—431no—
258#1907—432no—
259#1816—432no—
260C4×#100—431no—
261C2×C43—21no—
262C2×C43—21no—
263C2×C43—82no—
264C2×C43#242711yescharacteristic
265C2×C43C2×#47211yescharacteristic
266C2×C43#306911yescharacteristic
267D43—82no—
268C2×AGL(1,ℤ/8)—432no—
269C2×#131—432no—
270#532—431no—
271C2×C4⋊Q8C2×D4311yescharacteristic
272C2×C4×D4C2×D4311yescharacteristic
273#489—862no—
274#487—861no—
275#486—861no—
276#474—21no—
277#474—22no—
278#474—21no—
279#463—862no—
280#461—861no—
281#459—861no—
282#436—861no—
283#435—862no—
284C8×D4—861no—
285C2×#108—432no—
286C2×#107C2×D4312yes—
287#423—431no—
288C2×C4⋊C8C2×D4311yescharacteristic
289#417—432no—
290#417—432no—
291#417—432no—
292C2×#102C2×D4312yes—
293C2×#100—431no—
294C2×#100—431no—
295#408—432no—
296C4×M16—431no—
297C4×M16—431no—
298#343—432no—
299#343—431no—
300#343—432no—
301#343—431no—
302#341—432no—
303C43#2535811yescharacteristic, complemented, Sylow
304C2×#41—432no—
305C22×Q8—21no—
306C22×D4C22×D4311yescharacteristic
307C23×C4—21no—
308AGL(1,ℤ/8)—864no—
309AGL(1,ℤ/8)—1722no—
310C2×SD16—862no—
311C2×D8—862no—
312#131—864no—
313#131—1722no—
314C2×M16—431no—
315C2×M16—432no—
316C2×M16—431no—
317C2×M16—431no—
318C2×M16—431no—
319C2×M16—862no—
320C22×C8—862no—
321C22×C8C22×D4312yes—
322C4⋊Q8—21no—
323C4⋊Q8—21no—
324C4⋊Q8—21no—
325C4⋊Q8—21no—
326C4⋊Q8—431no—
327#127—431no—
328#124—432no—
329#121—861no—
330#121—861no—
331C4×D4—21no—
332C4×D4—21no—
333C4×D4—21no—
334C4×D4—21no—
335C4×D4—861no—
336C4×D4—861no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4C22×D4311yescharacteristic
339C2×C4⋊C4C22×D4312yes—
340C2×C22⋊C4—21no—
341C2×C42C22×D4311yescharacteristic
342#108—1722no—
343#107—22no—
344#107—22no—
345C4⋊C8—861no—
346C4⋊C8—861no—
347C4⋊C8C22⋊D4311yescharacteristic
348C4⋊C8C22⋊D4312yes—
349C4⋊C8C22⋊D4311yescharacteristic
350#103—862no—
351#103—862no—
352#103—862no—
353#102—22no—
354#102—22no—
355#102—862no—
356#102—862no—
357#102—862no—
358#100—862no—
359#100—862no—
360C22⋊C8—862no—
361C22⋊C8—862no—
362#97—861no—
363#97—861no—
364C4×C8—861no—
365C4×C8—861no—
366C24—21no—
367#41—862no—
368#41—862no—
369#41—862no—
370#41—862no—
371C2×Q8—41no—
372C2×Q8—41no—
373C2×Q8—82no—
374C2×Q8—432no—
375C2×D4—21no—
376C2×D4—21no—
377C2×D4—21no—
378C2×D4—21no—
379C2×D4—21no—
380C2×D4—432no—
381C2×D4—862no—
382C2×D4—861no—
383C2×D4—861no—
384C2×D4#1062190212yes—
385C22×C4—21no—
386C22×C4—22no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—82no—
390C22×C4—862no—
391C22×C4#1062190011yescharacteristic
392C22×C4#1062190011yescharacteristic
393C22×C4C23×D4311yescharacteristic
394SD16—1724no—
395D8—1724no—
396M16—432no—
397M16—861no—
398M16—861no—
399M16—861no—
400M16—861no—
401M16—862no—
402M16—861no—
403M16—862no—
404M16—861no—
405M16—861no—
406M16—1724no—
407C2×C8—22no—
408C2×C8—22no—
409C2×C8—861no—
410C2×C8—861no—
411C2×C8—861no—
412C2×C8—862no—
413C2×C8—861no—
414C2×C8—1724no—
415C2×C8C2×C22⋊D4312yes—
416C2×C8C2×C22⋊D4312yes—
417C4⋊C4—21no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—21no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—861no—
424C4⋊C4—861no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—862no—
428C22⋊C4—862no—
429C42D4×D4311yescharacteristic
430C42D4×D4311yescharacteristic
431C42C2×C22⋊D4311yescharacteristic
432C42C2×C22⋊D4311yescharacteristic
433C23—22no—
434C23—41no—
435C23—41no—
436C23—81no—
437C23—81no—
438C23—862no—
439C23C2×#1062190011yescharacteristic
440Q8—82no—
441Q8—82no—
442Q8—862no—
443Q8—862no—
444D4—22no—
445D4—22no—
446D4—41no—
447D4—41no—
448D4—862no—
449D4—862no—
450D4—3441no—
451D4—1722no—
452D4—1722no—
453D4—1722no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4—81no—
461C2×C4—82no—
462C2×C4—862no—
463C2×C4—1722no—
464C2×C4—1722no—
465C2×C4#1306329611yescharacteristic
466C2×C4#1306329611yescharacteristic
467C2×C4#1306329611yescharacteristic
468C2×C4#1306329611yescharacteristic
469C2×C4C2×D4×D4311yescharacteristic
470C2×C4C22×C22⋊D4311yescharacteristic
471C2×C4#41×D4311yescharacteristic
472C2×C4C2×#1062190211yescharacteristic
473C2×C4#1306337111yescharacteristic
474C2×C4#1306337311yescharacteristic
475C8—22no—
476C8—22no—
477C8—862no—
478C8—1721no—
479C8—1722no—
480C8—1721no—
481C8—1721no—
482C22—21no—
483C22—21no—
484C22—42no—
485C22—82no—
486C22—82no—
487C22—81no—
488C22—81no—
489C22—1722no—
490C22—1722no—
491C22—1722no—
492C22C2×#1306329611yescharacteristic
493C22#1458343511yescharacteristic
494C22#1458352211yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—81no—
499C4—82no—
500C4—1722no—
501C4#1458316612yes—
502C4#1458353711yescharacteristic
503C4#1458354011yescharacteristic
504C4#1458355111yescharacteristic
505C4#1458356011yescharacteristic
506C2—21no—
507C2—21no—
508C2—82no—
509C2—3442no—
510C2#1913816811yescharacteristic
511C2C2×#1458316611yescharacteristic
512C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#474C2
socleC22×C43C2×#121
prime radical#19144059C2
hypercenterC2×#474D43
hypocenterC43#25358
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. #19144991C2semidirect
3. #19143338C2semidirect
4. #19136036C2semidirect
5. #19135888C2semidirect
6. #19135585C2semidirect
7. #19135371C2semidirect
8. #19135106C2semidirect
9. #19134660C2semidirect
10. C4×#13063242C2semidirect
11. C2×C43×#474C2semidirect
251. C2×#474D43semidirect
303. C43#25358semidirect

Maximal subgroups

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

subgroupindex
#191449912
#191440592
#191433382
#191360362
#191358882
#191355852
#191353712
#191351062
#191346602
C4×#130632422
C2×C43×#4742
#2535843