Finite Group Databasebeta

← #24989003

Subgroups — #24989003

Order 11008.

736 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19133300C211yesmaximal, characteristic, complemented
2#19133226C211yesmaximal, characteristic, complemented
3#19133172C211yesmaximal, characteristic, complemented
4#19133142C211yesmaximal, characteristic, complemented
5#19133142C211yesmaximal, characteristic, complemented
6#19133064C211yesmaximal, characteristic, complemented
7C43×#3546C211yesmaximal, characteristic
8#14582956C2211yescharacteristic, complemented
9#14582956C2211yescharacteristic, complemented
10#14582952C2211yescharacteristic, complemented
11#14582767C2211yescharacteristic, complemented
12#14582645—21no—
13#14582643—21no—
14#14582641—21no—
15#14582639—21no—
16#14582636—21no—
17#14582633—21no—
18#14582633—21no—
19#14582633—22no—
20#14582633—21no—
21D4⋊(C43⋊C8)—22no—
22C43×#560—22no—
23C43×#556C411yescharacteristic, complemented
24C43×#553—21no—
25C43×#550—21no—
26C43×#550C411yescharacteristic, complemented
27C43×#547C411yescharacteristic, complemented
28C43×#546—21no—
29C43×#546—21no—
30D42×C43C411yescharacteristic, complemented
31C43×#542—21no—
32C43×#538—22no—
33C43×#537—21no—
34C43×#535—21no—
35C43×#535—21no—
36C43×#532C2211yescharacteristic
37C43×#532C2211yescharacteristic
38C43×#529C2211yescharacteristic
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C22⋊(C43⋊C8)—21no—
43C22⋊(C43⋊C8)—21no—
44C22⋊(C43⋊C8)—21no—
45#13063236—21no—
46#13063236—21no—
47C4×C43⋊C8—21no—
48C43⋊#95—21no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C2×#41×C43—21no—
52C2×#41×C43—21no—
53C2×#41×C43—21no—
54C2×#41×C43—21no—
55C22×D4×C43—21no—
56C22×D4×C43—21no—
57C4⋊Q8×C43C2×C411yescharacteristic
58C4⋊Q8×C43D411yescharacteristic
59#127×C43—22no—
60#127×C43—21no—
61#127×C43C2×C411yescharacteristic
62#127×C43D411yescharacteristic
63#126×C43—22no—
64#126×C43—22no—
65#126×C43—21no—
66#125×C43D411yescharacteristic
67#124×C43—22no—
68#124×C43—21no—
69#124×C43—21no—
70#124×C43—21no—
71#124×C43D411yescharacteristic
72#123×C43—22no—
73#123×C43—22no—
74#123×C43—21no—
75#123×C43—22no—
76C22⋊Q8×C43—22no—
77C22⋊Q8×C43—21no—
78C22⋊Q8×C43—21no—
79C22⋊Q8×C43D411yescharacteristic
80#121×C43—22no—
81#121×C43—22no—
82#121×C43—22no—
83#121×C43—22no—
84#121×C43—22no—
85#121×C43—21no—
86#121×C43—22no—
87#121×C43—21no—
88#121×C43—21no—
89#121×C43—21no—
90#121×C43—21no—
91#121×C43—21no—
92#121×C43D411yescharacteristic
93#121×C43D411yescharacteristic
94#121×C43D411yescharacteristic
95#121×C43D412yes—
96#120×C43—22no—
97#120×C43—22no—
98#120×C43—22no—
99#120×C43—22no—
100C4×Q8×C43—21no—
101C4×Q8×C43C2×C411yescharacteristic
102C4×D4×C43—22no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43—21no—
107C4×D4×C43C2×C411yescharacteristic
108C4×D4×C43C2×C411yescharacteristic
109C4×D4×C43C2×C411yescharacteristic
110C4×D4×C43D412yes—
111#117×C43—21no—
112#117×C43—21no—
113C2×C4⋊C4×C43—21no—
114C2×C22⋊C4×C43—22no—
115C2×C42×C43C2311yescharacteristic
116C24×C43—22no—
117#41×C43—82no—
118#41×C43—82no—
119#41×C43—82no—
120#41×C43—82no—
121C2×Q8×C43—21no—
122C2×Q8×C43—21no—
123C2×Q8×C43C22⋊C411yescharacteristic
124C2×D4×C43—22no—
125C2×D4×C43—22no—
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—22no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—22no—
136C2×D4×C43—21no—
137C2×D4×C43—82no—
138C2×D4×C43—82no—
139C2×D4×C43C22⋊C411yescharacteristic
140C2×D4×C43C22⋊C411yescharacteristic
141C2×D4×C43C22⋊C411yescharacteristic
142C2×D4×C43C22⋊C412yes—
143C22×C4×C43—22no—
144C22×C4×C43—22no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—22no—
149C22×C4×C43C2×D411yescharacteristic
150C22×C4×C43C2×D411yescharacteristic
151C22×C4×C43C2×D411yescharacteristic
152C22×Dic43—41no—
153C4⋊C4×C43—22no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43C22⋊C411yescharacteristic
162C4⋊C4×C43C22⋊C411yescharacteristic
163C4⋊C4×C43C22⋊C411yescharacteristic
164C4⋊C4×C43C22⋊C411yescharacteristic
165C4⋊C4×C43C22⋊C412yes—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—22no—
169C22⋊C4×C43—22no—
170C22⋊C4×C43—22no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C22⋊C4×C43—21no—
176C22⋊C4×C43—21no—
177C22⋊C4×C43—21no—
178C22⋊C4×C43—21no—
179C22⋊C4×C43—22no—
180C22⋊C4×C43—22no—
181C22⋊C4×C43—21no—
182C42×C43—22no—
183C42×C43—21no—
184C42×C43C22×C411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C2×C43⋊C8—41no—
189C2×C43⋊C8—41no—
190C2×C43⋊C8—41no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—22no—
194C23×C43—21no—
195C23×C43—82no—
196C23×C43—82no—
197C23×C43—82no—
198C23×C43#12011yescharacteristic
199Q8×C43—41no—
200Q8×C43—42no—
201Q8×C43—81no—
202D4×C43—41no—
203D4×C43—41no—
204D4×C43—42no—
205D4×C43—41no—
206D4×C43—42no—
207D4×C43—42no—
208D4×C43—81no—
209D4×C43—81no—
210D4×C43—81no—
211D4×C43—81no—
212D4×C43—81no—
213D4×C43—82no—
214D4×C43—82no—
215D4×C43—82no—
216D4×C43—82no—
217D4×C43—82no—
218D4×C43—82no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—22no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—82no—
232C2×C4×C43—82no—
233C2×C4×C43—82no—
234C2×C4×C43C2×C22⋊C411yescharacteristic
235C2×C4×C43C2×C22⋊C411yescharacteristic
236C2×C4×C43C2×C22⋊C411yescharacteristic
237C2×C4×C43#12011yescharacteristic
238C2×C4×C43#12011yescharacteristic
239C2×C4×C43#12011yescharacteristic
240C2×Dic43—81no—
241C2×Dic43—81no—
242C2×Dic43—81no—
243C43⋊C8—81no—
244C43⋊C8—81no—
245C43⋊C8—81no—
246#8500—431nomaximal, Sylow
247C22×C43—21no—
248C22×C43—21no—
249C22×C43—21no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—42no—
253C22×C43—41no—
254C22×C43—41no—
255C22×C43—41no—
256C22×C43—41no—
257C22×C43—41no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43—164no—
263C22×C43#37911yescharacteristic
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—21no—
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—41no—
271C4×C43—41no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—42no—
276Dic43—161no—
277#3546D4311yescharacteristic
278#1553—431no—
279#1535—431no—
280#1521—431no—
281#1514—431no—
282#1514—431no—
283#1496—431no—
284C2×C43—41no—
285C2×C43—81no—
286C2×C43—82no—
287C2×C43—81no—
288C2×C43—81no—
289C2×C43#179411yescharacteristic
290C2×C43#179511yescharacteristic
291C2×C43#179511yescharacteristic
292#560—22no—
293#556Dic4311yescharacteristic, complemented
294#553—21no—
295#550—21no—
296#550Dic4311yescharacteristic, complemented
297#547Dic4311yescharacteristic, complemented
298#546—21no—
299#546—21no—
300D42Dic4311yescharacteristic, complemented
301#542—21no—
302#538—22no—
303#537—21no—
304#535—21no—
305#535—21no—
306#532C2×D4311yescharacteristic
307#532C2×D4311yescharacteristic
308#529C2×D4311yescharacteristic
309#432—431no—
310#432—431no—
311#431—431no—
312#383—431no—
313#332—861no—
314#331—861no—
315#330—861no—
316#329—861no—
317#328—861no—
318#327—861no—
319#327—861no—
320#327—862no—
321#327—861no—
322D4⋊C8—862no—
323C43#850011yescharacteristic, complemented, Sylow
324C2×#41—21no—
325C2×#41—21no—
326C2×#41—21no—
327C2×#41—21no—
328C22×D4—21no—
329C22×D4—21no—
330C4⋊Q8C2×Dic4311yescharacteristic
331C4⋊Q8C22⋊D4311yescharacteristic
332#127—22no—
333#127—21no—
334#127C2×Dic4311yescharacteristic
335#127C22⋊D4311yescharacteristic
336#126—22no—
337#126—22no—
338#126—21no—
339#125C22⋊D4311yescharacteristic
340#124—22no—
341#124—21no—
342#124—21no—
343#124—21no—
344#124C22⋊D4311yescharacteristic
345#123—22no—
346#123—22no—
347#123—21no—
348#123—22no—
349C22⋊Q8—22no—
350C22⋊Q8—21no—
351C22⋊Q8—21no—
352C22⋊Q8C22⋊D4311yescharacteristic
353#121—22no—
354#121—22no—
355#121—22no—
356#121—22no—
357#121—22no—
358#121—21no—
359#121—22no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121C22⋊D4311yescharacteristic
366#121C22⋊D4311yescharacteristic
367#121C22⋊D4311yescharacteristic
368#121C22⋊D4312yes—
369#120—22no—
370#120—22no—
371#120—22no—
372#120—22no—
373C4×Q8—21no—
374C4×Q8C2×Dic4311yescharacteristic
375C4×D4—22no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C2×Dic4311yescharacteristic
381C4×D4C2×Dic4311yescharacteristic
382C4×D4C2×Dic4311yescharacteristic
383C4×D4C22⋊D4312yes—
384#117—21no—
385#117—21no—
386C2×C4⋊C4—21no—
387C2×C22⋊C4—22no—
388C2×C42C22×D4311yescharacteristic
389C4⋊C8—861no—
390C4⋊C8—861no—
391C4⋊C8—861no—
392C22⋊C8—861no—
393C22⋊C8—861no—
394C22⋊C8—861no—
395#97—861no—
396#97—861no—
397C4×C8—861no—
398#95—861no—
399#95—861no—
400#95—861no—
401C24—22no—
402#41—82no—
403#41—82no—
404#41—82no—
405#41—82no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8C22⋊Dic4311yescharacteristic
409C2×D4—22no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4C22⋊Dic4311yescharacteristic
425C2×D4C22⋊Dic4311yescharacteristic
426C2×D4C22⋊Dic4311yescharacteristic
427C2×D4C22⋊Dic4312yes—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—1721no—
435C22×C4C2×C22⋊D4311yescharacteristic
436C22×C4C2×C22⋊D4311yescharacteristic
437C22×C4C2×C22⋊D4311yescharacteristic
438C2×C8—1721no—
439C2×C8—1721no—
440C2×C8—1721no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4C22⋊Dic4311yescharacteristic
450C4⋊C4C22⋊Dic4311yescharacteristic
451C4⋊C4C22⋊Dic4311yescharacteristic
452C4⋊C4C22⋊Dic4311yescharacteristic
453C4⋊C4C22⋊Dic4312yes—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—21no—
460C22⋊C4—21no—
461C22⋊C4—21no—
462C22⋊C4—21no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C42—22no—
471C42—21no—
472C42C22×Dic4311yescharacteristic
473C42C2×C22⋊D4311yescharacteristic
474C42C2×C22⋊D4311yescharacteristic
475C42C2×C22⋊D4311yescharacteristic
476C23—21no—
477C23—21no—
478C23—22no—
479C23—21no—
480C23—82no—
481C23—82no—
482C23—82no—
483C23#1306329411yescharacteristic
484Q8—41no—
485Q8—42no—
486Q8—81no—
487D4—41no—
488D4—41no—
489D4—41no—
490D4—42no—
491D4—42no—
492D4—42no—
493D4—81no—
494D4—81no—
495D4—81no—
496D4—81no—
497D4—82no—
498D4—81no—
499D4—82no—
500D4—82no—
501D4—82no—
502D4—82no—
503D4—82no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—3441no—
520C2×C4—3441no—
521C2×C4—3441no—
522C2×C4C2×C22⋊Dic4311yescharacteristic
523C2×C4C2×C22⋊Dic4311yescharacteristic
524C2×C4C2×C22⋊Dic4311yescharacteristic
525C2×C4#1306329411yescharacteristic
526C2×C4#1306329411yescharacteristic
527C2×C4#1306329411yescharacteristic
528C8—3441no—
529C8—3441no—
530C8—3441no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—42no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—42no—
544C22—41no—
545C22—41no—
546C22—164no—
547C22#1458275511yescharacteristic
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—21no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—42no—
559C4—41no—
560C4—6881no—
561C2—41no—
562C2—81no—
563C2—81no—
564C2—82no—
565C2—81no—
566C2#1913455911yescharacteristic
567C2#1913456511yescharacteristic
568C2#1913456511yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3546C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3546D43
hypocenterC43#8500
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3546

Complements

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

NH ≅ G/Ntype
1. #19133300C2semidirect
2. #19133226C2semidirect
3. #19133172C2semidirect
4. #19133142C2semidirect
5. #19133142C2semidirect
6. #19133064C2semidirect
8. #14582956C22semidirect
9. #14582956C22semidirect
10. #14582952C22semidirect
11. #14582767C22semidirect
23. C43×#556C4semidirect
26. C43×#550C4semidirect
27. C43×#547C4semidirect
30. D42×C43C4semidirect
293. #556Dic43semidirect
296. #550Dic43semidirect
297. #547Dic43semidirect
300. D42Dic43semidirect
323. C43#8500semidirect

Maximal subgroups

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

subgroupindex
#191333002
#191332262
#191331722
#191331422
#191330642
C43×#35462
#850043