Finite Group Databasebeta

← #24988451

Subgroups — #24988451

Order 11008.

768 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134405C211yesmaximal, characteristic, complemented
2#19133202C211yesmaximal, characteristic, complemented
3#19133103C211yesmaximal, characteristic, complemented
4#19133081C211yesmaximal, characteristic, complemented
5#19133029C211yesmaximal, characteristic, complemented
6#19133012C211yesmaximal, characteristic, complemented
7C43×#3514C211yesmaximal, characteristic
8#14582956C2211yescharacteristic, complemented
9#14582952C2211yescharacteristic, complemented
10C2×#13063252—21no—
11C4×#10621877C2211yescharacteristic, complemented
12#14582745C2211yescharacteristic, complemented
13#14582658—21no—
14#14582641—21no—
15#14582639—21no—
16#14582636—21no—
17#14582633—21no—
18#14582633—22no—
19Q8⋊(C43⋊C8)—21no—
20D4⋊(C43⋊C8)—22no—
21D4⋊(C43⋊C8)—21no—
22C43×#559C411yescharacteristic, complemented
23C43×#556C411yescharacteristic, complemented
24C43×#555—21no—
25C43×#551—22no—
26D4×Q8×C43C411yescharacteristic, complemented
27C43×#548—21no—
28C43×#546—21no—
29C43×#546—21no—
30D42×C43C411yescharacteristic, complemented
31C43×#542—21no—
32C43×#538—22no—
33C43×#532C2211yescharacteristic
34C43×#529—21no—
35C43×#529C2211yescharacteristic
36C2×#124×C43—21no—
37C43×#518—21no—
38C4×#41×C43C2211yescharacteristic
39C2×#10621877—21no—
40C2×C4×Dic43—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43#13063252—24no—
44C22⋊(C43⋊C8)—21no—
45C22⋊(C43⋊C8)—21no—
46#13063236—21no—
47#13063236—21no—
48C4×C43⋊C8—21no—
49C4×C43⋊C8—21no—
50C43⋊#95—21no—
51C43⋊#95—21no—
52C2×#41×C43—21no—
53C2×#41×C43D411yescharacteristic
54C22×Q8×C43—21no—
55C22×D4×C43—21no—
56C22×D4×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43C2×C411yescharacteristic
59#127×C43C2×C411yescharacteristic
60#126×C43—22no—
61#126×C43—22no—
62#126×C43—21no—
63#125×C43D411yescharacteristic
64#124×C43—22no—
65#124×C43—22no—
66#124×C43—22no—
67#124×C43—21no—
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—22no—
75#123×C43—21no—
76C22⋊Q8×C43—22no—
77C22⋊Q8×C43—21no—
78C22⋊Q8×C43—21no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43D411yescharacteristic
81#121×C43—22no—
82#121×C43—22no—
83#121×C43—21no—
84#121×C43—21no—
85#121×C43—21no—
86#121×C43D411yescharacteristic
87#121×C43D412yes—
88#120×C43—22no—
89#120×C43—22no—
90C4×Q8×C43—21no—
91C4×Q8×C43C2×C411yescharacteristic
92C4×Q8×C43C2×C411yescharacteristic
93C4×Q8×C43D411yescharacteristic
94C4×D4×C43—22no—
95C4×D4×C43—22no—
96C4×D4×C43—21no—
97C4×D4×C43—21no—
98C4×D4×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C4×D4×C43—21no—
102C4×D4×C43—21no—
103C4×D4×C43C2×C411yescharacteristic
104C4×D4×C43C2×C411yescharacteristic
105C4×D4×C43D411yescharacteristic
106C4×D4×C43D412yes—
107#117×C43—22no—
108#117×C43—21no—
109#117×C43—21no—
110#117×C43—21no—
111#117×C43D411yescharacteristic
112C2×C22⋊C4×C43—22no—
113C2×C22⋊C4×C43—22no—
114C2×C22⋊C4×C43—22no—
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117C24×C43—22no—
118#41×C43—22no—
119#41×C43—41no—
120#41×C43—82no—
121C2×Q8×C43—22no—
122C2×Q8×C43—21no—
123C2×Q8×C43—82no—
124C2×Q8×C43C22⋊C411yescharacteristic
125C2×Q8×C43C22⋊C411yescharacteristic
126C2×D4×C43—22no—
127C2×D4×C43—22no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—22no—
133C2×D4×C43—42no—
134C2×D4×C43—42no—
135C2×D4×C43—82no—
136C2×D4×C43C22⋊C411yescharacteristic
137C2×D4×C43C22⋊C411yescharacteristic
138C2×D4×C43C22⋊C412yes—
139C22×C4×C43—22no—
140C22×C4×C43—22no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—22no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×Dic43—41no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43C22⋊C411yescharacteristic
160C4⋊C4×C43C22⋊C411yescharacteristic
161C4⋊C4×C43C22⋊C411yescharacteristic
162C4⋊C4×C43C22⋊C411yescharacteristic
163C4⋊C4×C43C22⋊C412yes—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
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—22no—
178C22⋊C4×C43—22no—
179C22⋊C4×C43—21no—
180C22⋊C4×C43—21no—
181C42×C43—22no—
182C42×C43—21no—
183C42×C43—21no—
184C42×C43—21no—
185C42×C43—21no—
186C42×C43C22×C411yescharacteristic
187C42×C43C2×D411yescharacteristic
188C42×C43C2×D411yescharacteristic
189C42×C43C2×D411yescharacteristic
190C4×Dic43—22no—
191C4×Dic43—41no—
192#10621877—22no—
193#10621877—41no—
194C2×C43⋊C8—41no—
195C2×C43⋊C8—41no—
196C2×C43⋊C8—41no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—22no—
200C23×C43—44no—
201C23×C43—82no—
202C23×C43—82no—
203C23×C43#12011yescharacteristic
204Q8×C43—21no—
205Q8×C43—21no—
206Q8×C43—41no—
207Q8×C43—42no—
208Q8×C43—82no—
209D4×C43—21no—
210D4×C43—41no—
211D4×C43—42no—
212D4×C43—42no—
213D4×C43—42no—
214D4×C43—44no—
215D4×C43—41no—
216D4×C43—41no—
217D4×C43—81no—
218D4×C43—82no—
219D4×C43—82no—
220D4×C43#10412yes—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—81no—
237C2×C4×C43—82no—
238C2×C4×C43—82no—
239C2×C4×C43—82no—
240C2×C4×C43C2×C22⋊C411yescharacteristic
241C2×C4×C43C2×C22⋊C411yescharacteristic
242C2×C4×C43C2×C22⋊C411yescharacteristic
243C2×C4×C43#12011yescharacteristic
244C2×C4×C43#12011yescharacteristic
245C2×C4×C43#12011yescharacteristic
246C2×Dic43—42no—
247C2×Dic43—81no—
248C2×Dic43—81no—
249C43⋊C8—42no—
250C43⋊C8—81no—
251C43⋊C8—81no—
252#8412—431nomaximal, Sylow
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—22no—
256C22×C43—21no—
257C22×C43—41no—
258C22×C43—41no—
259C22×C43—41no—
260C22×C43—42no—
261C22×C43—41no—
262C22×C43—42no—
263C22×C43—41no—
264C22×C43—42no—
265C22×C43—164no—
266C22×C43#37911yescharacteristic
267C4×C43—21no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—21no—
272C4×C43—41no—
273C4×C43—41no—
274C4×C43—41no—
275C4×C43—42no—
276C4×C43—41no—
277C4×C43—41no—
278C4×C43—41no—
279C4×C43C2×#10411yescharacteristic
280C4×C43#42111yescharacteristic
281Dic43—82no—
282#3514D4311yescharacteristic
283#1759—431no—
284#1529—431no—
285#1505—431no—
286#1500—431no—
287#1488—431no—
288#1484—431no—
289C2×C43—41no—
290C2×C43—42no—
291C2×C43—82no—
292C2×C43—81no—
293C2×C43#178911yescharacteristic
294C2×C43#179411yescharacteristic
295C2×C43#179511yescharacteristic
296#559Dic4311yescharacteristic, complemented
297#556Dic4311yescharacteristic, complemented
298#555—21no—
299#551—22no—
300D4×Q8Dic4311yescharacteristic, complemented
301#548—21no—
302#546—21no—
303#546—21no—
304D42Dic4311yescharacteristic, complemented
305#542—21no—
306#538—22no—
307#532C2×D4311yescharacteristic
308#529—21no—
309#529C2×D4311yescharacteristic
310C2×#124—21no—
311#518—21no—
312C4×#41C2×D4311yescharacteristic
313#432—431no—
314#431—431no—
315C2×#104—861no—
316C4×M16—431no—
317#376—431no—
318#339—861no—
319#330—861no—
320#329—861no—
321#328—861no—
322#327—861no—
323#327—862no—
324Q8⋊C8—861no—
325D4⋊C8—862no—
326D4⋊C8—861no—
327C43#841211yescharacteristic, complemented, Sylow
328C2×#41—21no—
329C2×#41C22⋊D4311yescharacteristic
330C22×Q8—21no—
331C22×D4—21no—
332C22×D4—21no—
333C2×M16—861no—
334C4⋊Q8—21no—
335C4⋊Q8C2×Dic4311yescharacteristic
336#127C2×Dic4311yescharacteristic
337#126—22no—
338#126—22no—
339#126—21no—
340#125C22⋊D4311yescharacteristic
341#124—22no—
342#124—22no—
343#124—22no—
344#124—21no—
345#124—21no—
346#124—21no—
347#124—21no—
348#124C22⋊D4311yescharacteristic
349#123—22no—
350#123—22no—
351#123—22no—
352#123—21no—
353C22⋊Q8—22no—
354C22⋊Q8—21no—
355C22⋊Q8—21no—
356C22⋊Q8—22no—
357C22⋊Q8C22⋊D4311yescharacteristic
358#121—22no—
359#121—22no—
360#121—21no—
361#121—21no—
362#121—21no—
363#121C22⋊D4311yescharacteristic
364#121C22⋊D4312yes—
365#120—22no—
366#120—22no—
367C4×Q8—21no—
368C4×Q8C2×Dic4311yescharacteristic
369C4×Q8C2×Dic4311yescharacteristic
370C4×Q8C22⋊D4311yescharacteristic
371C4×D4—22no—
372C4×D4—22no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—21no—
380C4×D4C2×Dic4311yescharacteristic
381C4×D4C2×Dic4311yescharacteristic
382C4×D4C22⋊D4311yescharacteristic
383C4×D4C22⋊D4312yes—
384#117—22no—
385#117—21no—
386#117—21no—
387#117—21no—
388#117C22⋊D4311yescharacteristic
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C42—21no—
393C2×C42—861no—
394C2×C42C22×D4311yescharacteristic
395C4⋊C8—861no—
396C4⋊C8—861no—
397#104—864no—
398C22⋊C8—861no—
399C22⋊C8—861no—
400#97—861no—
401#97—861no—
402C4×C8—861no—
403C4×C8—861no—
404#95—861no—
405#95—861no—
406C24—22no—
407#41—22no—
408#41—41no—
409#41—82no—
410C2×Q8—22no—
411C2×Q8—21no—
412C2×Q8—82no—
413C2×Q8C22⋊Dic4311yescharacteristic
414C2×Q8C22⋊Dic4311yescharacteristic
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—21no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—42no—
423C2×D4—42no—
424C2×D4—82no—
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—21no—
434C22×C4—22no—
435C22×C4—1721no—
436C22×C4C2×C22⋊D4311yescharacteristic
437C22×C4C2×C22⋊D4311yescharacteristic
438C22×C4C2×C22⋊D4311yescharacteristic
439M16—862no—
440M16—1721no—
441C2×C8—1721no—
442C2×C8—1721no—
443C2×C8—1721no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4C22⋊Dic4311yescharacteristic
454C4⋊C4C22⋊Dic4311yescharacteristic
455C4⋊C4C22⋊Dic4311yescharacteristic
456C4⋊C4C22⋊Dic4311yescharacteristic
457C4⋊C4C22⋊Dic4312yes—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C42—22no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—862no—
481C42—1721no—
482C42C22×Dic4311yescharacteristic
483C42C2×C22⋊D4311yescharacteristic
484C42C2×C22⋊D4311yescharacteristic
485C42C2×C22⋊D4311yescharacteristic
486C23—21no—
487C23—21no—
488C23—22no—
489C23—44no—
490C23—82no—
491C23—82no—
492C23#1306329411yescharacteristic
493Q8—21no—
494Q8—21no—
495Q8—41no—
496Q8—42no—
497Q8—82no—
498D4—21no—
499D4—41no—
500D4—42no—
501D4—42no—
502D4—42no—
503D4—44no—
504D4—41no—
505D4—41no—
506D4—82no—
507D4—81no—
508D4—82no—
509D4#1306325212yes—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4—81no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4—3441no—
530C2×C4—3441no—
531C2×C4—1722no—
532C2×C4C2×C22⋊Dic4311yescharacteristic
533C2×C4C2×C22⋊Dic4311yescharacteristic
534C2×C4C2×C22⋊Dic4311yescharacteristic
535C2×C4#1306329411yescharacteristic
536C2×C4#1306329411yescharacteristic
537C2×C4#1306329411yescharacteristic
538C8—3441no—
539C8—3441no—
540C8—1722no—
541C22—21no—
542C22—22no—
543C22—21no—
544C22—21no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—42no—
549C22—42no—
550C22—41no—
551C22—42no—
552C22—41no—
553C22—164no—
554C22#1458275511yescharacteristic
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—42no—
566C4—41no—
567C4—3442no—
568C4C2×#1306325211yescharacteristic
569C4#1458291611yescharacteristic
570C2—41no—
571C2—42no—
572C2—81no—
573C2—82no—
574C2#1913453911yescharacteristic
575C2#1913455911yescharacteristic
576C2#1913456511yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3514C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3514D43
hypocenterC43#8412
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3514

Complements

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

NH ≅ G/Ntype
1. #19134405C2semidirect
2. #19133202C2semidirect
3. #19133103C2semidirect
4. #19133081C2semidirect
5. #19133029C2semidirect
6. #19133012C2semidirect
8. #14582956C22semidirect
9. #14582952C22semidirect
11. C4×#10621877C22semidirect
12. #14582745C22semidirect
22. C43×#559C4semidirect
23. C43×#556C4semidirect
26. D4×Q8×C43C4semidirect
30. D42×C43C4semidirect
296. #559Dic43semidirect
297. #556Dic43semidirect
300. D4×Q8Dic43semidirect
304. D42Dic43semidirect
327. C43#8412semidirect

Maximal subgroups

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

subgroupindex
#191344052
#191332022
#191331032
#191330812
#191330292
#191330122
C43×#35142
#841243