Finite Group Databasebeta

← #25250987

Subgroups — #25250987

Order 11008.

696 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147729C211yesmaximal, characteristic, complemented
2#19145019C211yesmaximal, characteristic, complemented
3C2×#14583016C211yesmaximal, characteristic, complemented
4#19136674C212yesmaximal, complemented
5#19136669C212yesmaximal, complemented
6#19136666C212yesmaximal, complemented
7#19136662C212yesmaximal, complemented
8C2×#14582719C211yesmaximal, characteristic, complemented
9#19136345C211yesmaximal, characteristic, complemented
10#19136344C211yesmaximal, characteristic, complemented
11C43×#3414C211yesmaximal, characteristic, complemented
12C2×#13063347C2211yescharacteristic
13C2×#13063345—21no—
14C2×#13063332—21no—
15#14583445—21no—
16#14583340—21no—
17#14583339C2212yes—
18#14583335—21no—
19#14583334C2212yes—
20#14583329—22no—
21C2×#13063265C2211yescharacteristic
22#14583284C2211yescharacteristic, complemented
23#14583282C2211yescharacteristic, complemented
24#14583280—21no—
25#14583277C2211yescharacteristic, complemented
26#14583274C2211yescharacteristic, complemented
27#14583270—21no—
28#14583016—21no—
29#14583016—21no—
30#14583016C2212yes—
31#14583016C2212yes—
32C2×#13063261C2211yescharacteristic
33C2×#13063252—21no—
34C2×C8×Dic43C2211yescharacteristic
35#14582719C2212yescomplemented
36#14582719C2212yescomplemented
37#14582716C2212yescomplemented
38#14582715C2212yescomplemented
39#14582713C2212yescomplemented
40#14582712C2212yescomplemented
41C2×#135×C43C2211yescharacteristic
42C2×#135×C43C2211yescharacteristic
43C43×#510—21no—
44C43×#510C2212yes—
45C43×#509—21no—
46C43×#509C2212yes—
47C43×#508—22no—
48C2×M32×C43C2211yescharacteristic
49C2×#10621898—21no—
50#13063347—21no—
51#13063347—21no—
52#13063347—21no—
53#13063347—21no—
54#13063345—41no—
55#13063345—41no—
56#13063345—41no—
57#13063345—41no—
58C2×Dic172C2311yescharacteristic
59C2×#10621885—21no—
60C2×#10621873—21no—
61C2×#10621883—21no—
62C2×#10621884—21no—
63C2×D344C2311yescharacteristic
64C2×#10621882—21no—
65#13063332—22no—
66#13063332—22no—
67#13063332—41no—
68#13063332—41no—
69C2×#10621877—21no—
70C2×#10621877—41no—
71C22×C43⋊C8—41no—
72C22×C43⋊C8D411yescharacteristic
73#13063323—21no—
74#13063321—21no—
75#13063314—21no—
76#13063312—21no—
77#13063297—42no—
78C4×C22⋊D43—42no—
79C2×C4×Dic43D411yescharacteristic
80#13063271—22no—
81#13063269—22no—
82#13063268—22no—
83#13063266—22no—
84#13063265—21no—
85#13063265C2312yes—
86C2×C43⋊C16—21no—
87#13063261—21no—
88#13063261C2312yes—
89#13063252—22no—
90#13063252—22no—
91C8×Dic43D411yescharacteristic
92C8×Dic43D411yescharacteristic
93C8×Dic43C2311yescharacteristic
94C8×Dic43C2311yescharacteristic
95C2×#41×C43—21no—
96C2×#41×C43—21no—
97#135×C43—21no—
98#135×C43—21no—
99#135×C43—21no—
100#135×C43—21no—
101#135×C43—21no—
102#135×C43—21no—
103#135×C43D412yescomplemented
104#135×C43C2312yes—
105C2×Q16×C43D411yescharacteristic, complemented
106C2×Q16×C43C2311yescharacteristic
107C2×SD16×C43—21no—
108C2×SD16×C43—21no—
109C2×D8×C43D411yescharacteristic, complemented
110C2×D8×C43C2311yescharacteristic
111C22×C8×C43C2311yescharacteristic
112Q32×C43—22no—
113SD32×C43—22no—
114SD32×C43—22no—
115D16×C43—22no—
116M32×C43—21no—
117M32×C43C2312yes—
118C2×C16×C43—21no—
119#41×C43—22no—
120#41×C43—22no—
121#41×C43—41no—
122#41×C43—41no—
123#41×C43—41no—
124#41×C43—41no—
125#41×C43—41no—
126#41×C43—41no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—41no—
132C2×D4×C43—41no—
133C22×C4×C43—41no—
134C22×C4×C43—41no—
135C22×C4×C43C2×D411yescharacteristic
136C2×C22⋊D43—42no—
137C2×C22⋊D43—41no—
138C22×Dic43—21no—
139#10621898—41no—
140#10621898—41no—
141#10621898—41no—
142#10621898—41no—
143C2×D172—21no—
144C2×C4×D43—41no—
145C2×Dic86—21no—
146Q16×C43—21no—
147Q16×C43—21no—
148Q16×C43—21no—
149Q16×C43C2×D412yes—
150SD16×C43—22no—
151SD16×C43—22no—
152SD16×C43—41no—
153SD16×C43—41no—
154D8×C43—21no—
155D8×C43—21no—
156D8×C43—21no—
157D8×C43C2×D412yes—
158C2×C8×C43C2×D411yescharacteristic
159C2×C8×C43C2×D411yescharacteristic
160C2×C8×C43C2×D411yescharacteristic
161C2×C8×C43#4111yescharacteristic
162C2×C8×C43#4111yescharacteristic
163C2×C8×C43C2411yescharacteristic
164C22⋊Dic43—42no—
165#10621885—41no—
166#10621885—41no—
167#10621884—41no—
168#10621884—41no—
169#10621883—41no—
170#10621883—41no—
171#10621882—41no—
172#10621882—41no—
173(C2×D43)⋊C4—42no—
174Dic43⋊C4—42no—
175C4×Dic43—21no—
176C4×Dic43C2×D411yescharacteristic
177C4×Dic43C2×D411yescharacteristic
178#10621877—22no—
179#10621877—41no—
180#10621877—42no—
181#10621877—42no—
182C2×C43⋊C8—41no—
183C2×C43⋊C8—42no—
184C2×C43⋊C8—42no—
185C2×C43⋊C8D811yescharacteristic
186C2×C43⋊C8D811yescharacteristic
187C2×C43⋊C8D811yescharacteristic
188C2×C43⋊C8D811yescharacteristic
189C2×C43⋊C8C2×D411yescharacteristic
190C2×C43⋊C8C2×D411yescharacteristic
191Dic172—21no—
192Dic172—21no—
193D344—21no—
194D344—21no—
195#10621873—41no—
196#10621873—41no—
197C16×C43—22no—
198C43⋊C16—22no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43AGL(1,ℤ/8)11yescharacteristic
202C22×D43—41no—
203Q8×C43—22no—
204Q8×C43—41no—
205Q8×C43—41no—
206Q8×C43—41no—
207D4×C43—22no—
208D4×C43—42no—
209D4×C43—42no—
210D4×C43—41no—
211D4×C43—41no—
212D4×C43—41no—
213D4×C43—81no—
214D4×C43—81no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—41no—
219C2×C4×C43—81no—
220C2×C4×C43—81no—
221C2×C4×C43#12111yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C2×C4×C43C2×D811yescharacteristic
224C2×C4×C43C2×D811yescharacteristic
225C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
226C2×C4×C43C22×D411yescharacteristic
227C22⋊D43—84no—
228C22⋊D43—81no—
229C22⋊D43—81no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—42no—
233C2×Dic43—41no—
234D172—41no—
235D172—41no—
236C4×D43—81no—
237C4×D43—81no—
238Dic86—41no—
239Dic86—41no—
240C8×C43#12111yescharacteristic
241C8×C43#12111yescharacteristic
242C8×C43C22×D411yescharacteristic
243C8×C43C2×#4111yescharacteristic
244C43⋊C8—42no—
245C43⋊C8C2×D811yescharacteristic
246C43⋊C8C2×D811yescharacteristic
247C43⋊C8C2×D811yescharacteristic
248C43⋊C8C2×D811yescharacteristic
249#33594—431nomaximal, Sylow
250C22×C43—41no—
251C22×C43—42no—
252C22×C43—82no—
253C22×C43—82no—
254C22×C43—81no—
255C22×C43#45911yescharacteristic
256C22×C43#45911yescharacteristic
257C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
258C2×D43—82no—
259C2×D43—81no—
260C4×C43—42no—
261C4×C43—81no—
262C4×C43#45911yescharacteristic
263C4×C43#45911yescharacteristic
264C4×C43C2×#12111yescharacteristic
265C4×C43C22×D811yescharacteristic
266Dic43—22no—
267Dic43—41no—
268Dic43—81no—
269#3414—431no—
270#3414D4311yescharacteristic, complemented
271#3147—431no—
272C2×#443—431no—
273#2214—432no—
274#2213—432no—
275#2212—432no—
276#2212—432no—
277C2×#364—431no—
278#2148—431no—
279#2148—431no—
280C2×C43—21no—
281C2×C43—21no—
282C2×C43—21no—
283C2×C43—82no—
284C2×C43—161no—
285C2×C43C2×#45911yescharacteristic
286D43—161no—
287C2×#135—431no—
288C2×#135—861no—
289C2×#135C2×D4311yescharacteristic
290C2×#135C2×D4311yescharacteristic
291C2×#131—861no—
292#532—861no—
293#510—21no—
294#510—432no—
295#510—861no—
296#510C2×D4312yes—
297#509—21no—
298#509—432no—
299#509—861no—
300#509C2×D4312yes—
301#508—22no—
302#508—862no—
303C2×M32—431no—
304C2×M32C2×D4311yescharacteristic
305#495—431no—
306#495—431no—
307#495—861no—
308#494—431no—
309#493—431no—
310#492—861no—
311#443—432no—
312#443—432no—
313#443—861no—
314#443—861no—
315C2×#108—431no—
316C2×#104—861no—
317C2×C4×C8—431no—
318#364—432no—
319#364—432no—
320#362—432no—
321#362—432no—
322#361—432no—
323#361—432no—
324C43#3359411yescharacteristic, complemented, Sylow
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—861no—
328#135—21no—
329#135—21no—
330#135—21no—
331#135—21no—
332#135—21no—
333#135—21no—
334#135—861no—
335#135—861no—
336#135—861no—
337#135—861no—
338#135—1721no—
339#135—1721no—
340#135—1721no—
341#135—1721no—
342#135C22⋊D4312yescomplemented
343#135C22×D4312yes—
344C2×Q16—431no—
345C2×Q16—861no—
346C2×Q16C22⋊D4311yescharacteristic, complemented
347C2×Q16C22×D4311yescharacteristic
348C2×SD16—21no—
349C2×SD16—21no—
350C2×SD16—861no—
351C2×SD16—861no—
352C2×SD16—861no—
353C2×D8—431no—
354C2×D8—861no—
355C2×D8C22⋊D4311yescharacteristic, complemented
356C2×D8C22×D4311yescharacteristic
357#131—862no—
358#131—862no—
359#131—1721no—
360#131—1721no—
361C2×M16—861no—
362C2×M16—1721no—
363C22×C8—431no—
364C22×C8—1721no—
365C22×C8C22×D4311yescharacteristic
366C4⋊Q8—861no—
367#127—861no—
368#124—861no—
369#124—861no—
370#121—1722no—
371C4×D4—1722no—
372C2×C42—431no—
373Q32—22no—
374Q32—862no—
375SD32—22no—
376SD32—22no—
377SD32—862no—
378SD32—862no—
379D16—22no—
380D16—862no—
381M32—21no—
382M32—432no—
383M32—861no—
384M32C22×D4312yes—
385C2×C16—21no—
386C2×C16—861no—
387#108—432no—
388#108—861no—
389#104—862no—
390#104—862no—
391C4×C8—431no—
392C4×C8—431no—
393C4×C8—431no—
394C4×C8—431no—
395#41—22no—
396#41—22no—
397#41—41no—
398#41—41no—
399#41—41no—
400#41—41no—
401#41—41no—
402#41—41no—
403#41—1721no—
404#41—1721no—
405#41—1721no—
406#41—1721no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—861no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—41no—
413C2×D4—41no—
414C2×D4—861no—
415C2×D4—1722no—
416C2×D4—1721no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—861no—
420C22×C4—1721no—
421C22×C4D4×D4311yescharacteristic
422Q16—21no—
423Q16—21no—
424Q16—21no—
425Q16—861no—
426Q16—861no—
427Q16—1721no—
428Q16—1721no—
429Q16C2×C22⋊D4312yes—
430SD16—22no—
431SD16—22no—
432SD16—41no—
433SD16—41no—
434SD16—1721no—
435SD16—1721no—
436SD16—1721no—
437SD16—1721no—
438SD16—1721no—
439SD16—1721no—
440D8—21no—
441D8—21no—
442D8—21no—
443D8—861no—
444D8—861no—
445D8—1721no—
446D8—1721no—
447D8C2×C22⋊D4312yes—
448M16—862no—
449M16—1722no—
450M16—1722no—
451M16—1721no—
452C2×C8—431no—
453C2×C8—431no—
454C2×C8—431no—
455C2×C8—431no—
456C2×C8—431no—
457C2×C8—431no—
458C2×C8—1722no—
459C2×C8—1722no—
460C2×C8—1721no—
461C2×C8D4×D4311yescharacteristic
462C2×C8#1062190011yescharacteristic
463C2×C8#1062190011yescharacteristic
464C2×C8C2×C22⋊D4311yescharacteristic
465C2×C8C2×C22⋊D4311yescharacteristic
466C2×C8C23×D4311yescharacteristic
467C4⋊C4—1722no—
468C22⋊C4—1722no—
469C22⋊C4—1722no—
470C42—431no—
471C42—431no—
472C42—861no—
473C16—22no—
474C16—862no—
475C23—41no—
476C23—41no—
477C23—1721no—
478C23#1306334911yescharacteristic
479Q8—22no—
480Q8—41no—
481Q8—41no—
482Q8—41no—
483Q8—1721no—
484Q8—1721no—
485D4—22no—
486D4—42no—
487D4—42no—
488D4—41no—
489D4—41no—
490D4—41no—
491D4—81no—
492D4—81no—
493D4—3444no—
494D4—3441no—
495D4—3441no—
496D4—1721no—
497D4—1721no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—41no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—3441no—
507C2×C4—3441no—
508C2×C4—1722no—
509C2×C4—1721no—
510C2×C4#1306329711yescharacteristic
511C2×C4#1306329711yescharacteristic
512C2×C4D8×D4311yescharacteristic
513C2×C4D8×D4311yescharacteristic
514C2×C4#1306334911yescharacteristic
515C2×C4C2×D4×D4311yescharacteristic
516C8—431no—
517C8—431no—
518C8—431no—
519C8—431no—
520C8—1722no—
521C8#1306329711yescharacteristic
522C8#1306329711yescharacteristic
523C8C22×C22⋊D4311yescharacteristic
524C8C2×#1062190011yescharacteristic
525C22—41no—
526C22—42no—
527C22—82no—
528C22—82no—
529C22—81no—
530C22—3442no—
531C22—3441no—
532C22#1458309211yescharacteristic
533C22#1458309211yescharacteristic
534C22C2×#1306334911yescharacteristic
535C4—42no—
536C4—81no—
537C4—862no—
538C4—3441no—
539C4—1721no—
540C4#1458309211yescharacteristic
541C4#1458309211yescharacteristic
542C4C2×#1306329711yescharacteristic
543C4C2×D8×D4311yescharacteristic
544C2—21no—
545C2—21no—
546C2—21no—
547C2—82no—
548C2—161no—
549C2—6881no—
550C2C2×#1458309211yescharacteristic
subgroupG/H
centerC4#14583092
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3414C2
socleC2×C43C2×#459
hypercenter#3414D43
hypocenterC43#33594
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #3414

Complements

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

NH ≅ G/Ntype
1. #19147729C2semidirect
2. #19145019C2semidirect
3. C2×#14583016C2semidirect
4. #19136674C2semidirect
5. #19136669C2semidirect
6. #19136666C2semidirect
7. #19136662C2semidirect
8. C2×#14582719C2semidirect
9. #19136345C2semidirect
10. #19136344C2semidirect
11. C43×#3414C2semidirect
22. #14583284C22semidirect
23. #14583282C22semidirect
25. #14583277C22semidirect
26. #14583274C22semidirect
35. #14582719C22semidirect
36. #14582719C22semidirect
37. #14582716C22semidirect
38. #14582715C22semidirect
39. #14582713C22semidirect
40. #14582712C22semidirect
103. #135×C43D4semidirect
105. C2×Q16×C43D4semidirect
109. C2×D8×C43D4semidirect
270. #3414D43semidirect
324. C43#33594semidirect
342. #135C22⋊D43semidirect
346. C2×Q16C22⋊D43semidirect
355. C2×D8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191477292
#191450192
C2×#145830162
#191366742
#191366692
#191366662
#191366622
C2×#145827192
#191363452
#191363442
C43×#34142
#3359443