Finite Group Databasebeta

← #24988486

Subgroups — #24988486

Order 11008.

706 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#19135540C211yesmaximal, characteristic, complemented
2#19134425C211yesmaximal, characteristic, complemented
3#19133210C211yesmaximal, characteristic, complemented
4#19133183C211yesmaximal, characteristic
5#19133120C211yesmaximal, characteristic
6#19133042C211yesmaximal, characteristic, complemented
7C43×#3523C211yesmaximal, characteristic
8#14582956C2211yescharacteristic
9C2×#13063249—21no—
10C4×#10621877C2211yescharacteristic
11C2×#13063236C2211yescharacteristic
12C4×C4⋊Dic43C2211yescharacteristic
13#14582661—21no—
14#14582658—22no—
15#14582641—22no—
16#14582641—21no—
17#14582639—21no—
18#14582636—21no—
19#14582633—21no—
20Q8⋊(C43⋊C8)—21no—
21Q8⋊(C43⋊C8)—21no—
22C43×#557—21no—
23C43×#557C411yescharacteristic, complemented
24C43×#557C411yescharacteristic, complemented
25C43×#556—21no—
26C43×#556C411yescharacteristic, complemented
27C43×#552—22no—
28C43×#552—21no—
29D4×Q8×C43—21no—
30D4×Q8×C43C411yescharacteristic, complemented
31C43×#541—22no—
32C43×#541—21no—
33C43×#533—21no—
34C43×#533C2211yescharacteristic
35C43×#529—21no—
36C43×#529C2211yescharacteristic
37C43×#519—21no—
38C2×C4×Q8×C43C2211yescharacteristic
39C2×#10621877—21no—
40C22×C43⋊C8—21no—
41C2×C4⋊Dic43—21no—
42C2×C4×Dic43—21no—
43C4⋊(C43⋊C8)—21no—
44#13063249—24no—
45C22⋊(C43⋊C8)—21no—
46#13063236—21no—
47#13063236—21no—
48#13063236—21no—
49#13063236—21no—
50C4×C43⋊C8—21no—
51C43⋊#95—21no—
52C22×Q8×C43—21no—
53C22×Q8×C43D411yescharacteristic
54C4⋊Q8×C43—22no—
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43—21no—
57C4⋊Q8×C43—21no—
58C4⋊Q8×C43C2×C411yescharacteristic
59C4⋊Q8×C43C2×C411yescharacteristic
60#126×C43—22no—
61#126×C43—22no—
62#126×C43—22no—
63#126×C43—22no—
64#126×C43—21no—
65#125×C43—22no—
66#125×C43—22no—
67#125×C43—22no—
68#125×C43—21no—
69#125×C43—22no—
70#125×C43—22no—
71#125×C43—21no—
72#125×C43D411yescharacteristic
73#125×C43D412yes—
74#124×C43—21no—
75#124×C43D411yescharacteristic
76#123×C43—22no—
77#123×C43—21no—
78C22⋊Q8×C43—22no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43—21no—
81C22⋊Q8×C43—21no—
82C22⋊Q8×C43—21no—
83C22⋊Q8×C43—21no—
84C22⋊Q8×C43—22no—
85C22⋊Q8×C43D411yescharacteristic
86#121×C43D411yescharacteristic
87C4×Q8×C43—22no—
88C4×Q8×C43—22no—
89C4×Q8×C43—21no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43—21no—
98C4×Q8×C43C2×C411yescharacteristic
99C4×Q8×C43C2×C411yescharacteristic
100C4×Q8×C43C2×C411yescharacteristic
101C4×Q8×C43D411yescharacteristic
102C4×Q8×C43D411yescharacteristic
103C4×D4×C43—22no—
104C4×D4×C43—21no—
105C4×D4×C43—21no—
106C4×D4×C43C2×C411yescharacteristic
107#117×C43—22no—
108#117×C43—22no—
109#117×C43—22no—
110#117×C43—21no—
111#117×C43—21no—
112#117×C43D412yes—
113C2×C4⋊C4×C43—21no—
114C2×C4⋊C4×C43D411yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117C2×Q8×C43—22no—
118C2×Q8×C43—21no—
119C2×Q8×C43—21no—
120C2×Q8×C43—21no—
121C2×Q8×C43—22no—
122C2×Q8×C43—41no—
123C2×Q8×C43—42no—
124C2×Q8×C43—42no—
125C2×Q8×C43C22⋊C411yescharacteristic
126C2×Q8×C43C22⋊C411yescharacteristic
127C2×Q8×C43C22⋊C411yescharacteristic
128C2×D4×C43—21no—
129C2×D4×C43C22⋊C411yescharacteristic
130C22×C4×C43—22no—
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×Dic43—41no—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—22no—
146C4⋊C4×C43—21no—
147C4⋊C4×C43—21no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43—21no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—22no—
159C4⋊C4×C43C22⋊C411yescharacteristic
160C4⋊C4×C43C22⋊C411yescharacteristic
161C4⋊C4×C43C22⋊C412yes—
162C4⋊C4×C43C22⋊C412yes—
163C4⋊C4×C43C22⋊C411yescharacteristic
164C4⋊C4×C43C22⋊C411yescharacteristic
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—22no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—21no—
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—21no—
173C22⋊C4×C43—22no—
174C42×C43—22no—
175C42×C43—22no—
176C42×C43—22no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—21no—
182C42×C43—22no—
183C42×C43C22×C411yescharacteristic
184C42×C43C2×D411yescharacteristic
185C42×C43C2×D411yescharacteristic
186C42×C43C2×D411yescharacteristic
187C4⋊Dic43—22no—
188C4⋊Dic43—41no—
189C4×Dic43—42no—
190#10621877—22no—
191#10621877—41no—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—41no—
194C2×C43⋊C8—41no—
195C2×C43⋊C8—41no—
196C2×C43⋊C8—41no—
197C23×C43—21no—
198C23×C43#12011yescharacteristic
199Q8×C43—21no—
200Q8×C43—21no—
201Q8×C43—21no—
202Q8×C43—42no—
203Q8×C43—41no—
204Q8×C43—42no—
205Q8×C43—44no—
206Q8×C43—41no—
207Q8×C43—41no—
208Q8×C43#10412yes—
209D4×C43—41no—
210D4×C43—41no—
211D4×C43—41no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—22no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—41no—
226C2×C4×C43—42no—
227C2×C4×C43—44no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43C2×C22⋊C411yescharacteristic
233C2×C4×C43C2×C22⋊C411yescharacteristic
234C2×C4×C43C2×C22⋊C411yescharacteristic
235C2×C4×C43#12011yescharacteristic
236C2×C4×C43#12011yescharacteristic
237C2×C4×C43#12011yescharacteristic
238C2×Dic43—42no—
239C2×Dic43—81no—
240C2×Dic43—81no—
241C43⋊C8—42no—
242C43⋊C8—42no—
243C43⋊C8—81no—
244#8417—431nomaximal, Sylow
245C22×C43—21no—
246C22×C43—21no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43#37911yescharacteristic
251C22×C43#45411yescharacteristic
252C22×C43#45611yescharacteristic
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—22no—
259C4×C43—41no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—42no—
264C4×C43—41no—
265C4×C43—42no—
266C4×C43—41no—
267C4×C43C2×#10411yescharacteristic
268C4×C43#42111yescharacteristic
269Dic43—82no—
270#3523D4311yescharacteristic
271#1986—431no—
272#1763—431no—
273#1531—431no—
274#1524—431no—
275#1509—431no—
276#1491—431no—
277C2×C43—21no—
278C2×C43—21no—
279C2×C43—81no—
280C2×C43#178911yescharacteristic
281C2×C43#179311yescharacteristic
282C2×C43#179611yescharacteristic
283#557—21no—
284#557Dic4311yescharacteristic, complemented
285#557Dic4311yescharacteristic, complemented
286#556—21no—
287#556Dic4311yescharacteristic, complemented
288#552—22no—
289#552—21no—
290D4×Q8—21no—
291D4×Q8Dic4311yescharacteristic, complemented
292#541—22no—
293#541—21no—
294#533—21no—
295#533C2×D4311yescharacteristic
296#529—21no—
297#529C2×D4311yescharacteristic
298#519—21no—
299C2×C4×Q8C2×D4311yescharacteristic
300#432—431no—
301C2×#103—861no—
302C4×M16—431no—
303C2×#97—431no—
304C4×C4⋊C4—431no—
305#340—861no—
306#339—862no—
307#330—861no—
308#330—862no—
309#329—861no—
310#328—861no—
311#327—861no—
312Q8⋊C8—861no—
313Q8⋊C8—861no—
314C43#841711yescharacteristic, complemented, Sylow
315C22×Q8—21no—
316C22×Q8C22⋊D4311yescharacteristic
317C2×M16—861no—
318C22×C8—861no—
319C4⋊Q8—22no—
320C4⋊Q8—21no—
321C4⋊Q8—21no—
322C4⋊Q8—21no—
323C4⋊Q8C2×Dic4311yescharacteristic
324C4⋊Q8C2×Dic4311yescharacteristic
325#126—22no—
326#126—22no—
327#126—22no—
328#126—22no—
329#126—21no—
330#125—22no—
331#125—22no—
332#125—22no—
333#125—21no—
334#125—22no—
335#125—22no—
336#125—21no—
337#125C22⋊D4311yescharacteristic
338#125C22⋊D4312yes—
339#124—21no—
340#124C22⋊D4311yescharacteristic
341#123—22no—
342#123—21no—
343C22⋊Q8—22no—
344C22⋊Q8—22no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—22no—
350C22⋊Q8C22⋊D4311yescharacteristic
351#121C22⋊D4311yescharacteristic
352C4×Q8—22no—
353C4×Q8—22no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8—21no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8C2×Dic4311yescharacteristic
364C4×Q8C2×Dic4311yescharacteristic
365C4×Q8C2×Dic4311yescharacteristic
366C4×Q8C22⋊D4311yescharacteristic
367C4×Q8C22⋊D4311yescharacteristic
368C4×D4—22no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4C2×Dic4311yescharacteristic
372#117—22no—
373#117—22no—
374#117—22no—
375#117—21no—
376#117—21no—
377#117C22⋊D4312yes—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4C22⋊D4311yescharacteristic
381C2×C42—21no—
382C2×C42—861no—
383C2×C42C22×D4311yescharacteristic
384C4⋊C8—861no—
385#103—864no—
386C22⋊C8—861no—
387#97—861no—
388#97—861no—
389#97—861no—
390#97—861no—
391C4×C8—861no—
392#95—861no—
393C2×Q8—22no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—21no—
397C2×Q8—22no—
398C2×Q8—41no—
399C2×Q8—42no—
400C2×Q8—42no—
401C2×Q8C22⋊Dic4311yescharacteristic
402C2×Q8C22⋊Dic4311yescharacteristic
403C2×Q8C22⋊Dic4311yescharacteristic
404C2×D4—21no—
405C2×D4C22⋊Dic4311yescharacteristic
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—1721no—
411C22×C4C2×C22⋊D4311yescharacteristic
412C22×C4C2×C22⋊D4311yescharacteristic
413C22×C4C2×C22⋊D4311yescharacteristic
414M16—862no—
415M16—1721no—
416C2×C8—862no—
417C2×C8—1721no—
418C2×C8—1721no—
419C2×C8—1721no—
420C2×C8—1721no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—22no—
442C4⋊C4—862no—
443C4⋊C4—1721no—
444C4⋊C4C22⋊Dic4311yescharacteristic
445C4⋊C4C22⋊Dic4311yescharacteristic
446C4⋊C4C22⋊Dic4312yes—
447C4⋊C4C22⋊Dic4312yes—
448C4⋊C4C22⋊Dic4311yescharacteristic
449C4⋊C4C22⋊Dic4311yescharacteristic
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—21no—
454C22⋊C4—22no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C22⋊C4—21no—
458C22⋊C4—21no—
459C42—22no—
460C42—22no—
461C42—22no—
462C42—21no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—21no—
467C42—22no—
468C42—1722no—
469C42C22×Dic4311yescharacteristic
470C42C2×C22⋊D4311yescharacteristic
471C42C2×C22⋊D4311yescharacteristic
472C42C2×C22⋊D4311yescharacteristic
473C23—21no—
474C23#1306329411yescharacteristic
475Q8—21no—
476Q8—21no—
477Q8—21no—
478Q8—42no—
479Q8—41no—
480Q8—44no—
481Q8—42no—
482Q8—41no—
483Q8—41no—
484Q8#1306325212yes—
485D4—41no—
486D4—41no—
487D4—41no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—3441no—
509C2×C4—3441no—
510C2×C4—1722no—
511C2×C4C2×C22⋊Dic4311yescharacteristic
512C2×C4C2×C22⋊Dic4311yescharacteristic
513C2×C4C2×C22⋊Dic4311yescharacteristic
514C2×C4#1306329411yescharacteristic
515C2×C4#1306329411yescharacteristic
516C2×C4#1306329411yescharacteristic
517C8—3441no—
518C8—1722no—
519C8—1722no—
520C22—21no—
521C22—21no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22#1458275511yescharacteristic
526C22#1458307211yescharacteristic
527C22#1458308211yescharacteristic
528C4—21no—
529C4—22no—
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—42no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—42no—
541C4—41no—
542C4—3442no—
543C4C2×#1306325211yescharacteristic
544C4#1458291611yescharacteristic
545C2—21no—
546C2—21no—
547C2—81no—
548C2#1913453911yescharacteristic
549C2#1913455411yescharacteristic
550C2#1913457011yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3523C2
socleC22×C43#379
prime radical#121×C43D4
cosocleC2×C42×C43C23
hypercenter#3523D43
hypocenterC43#8417
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3523

Complements

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

NH ≅ G/Ntype
1. #19135540C2semidirect
2. #19134425C2semidirect
3. #19133210C2semidirect
6. #19133042C2semidirect
23. C43×#557C4semidirect
24. C43×#557C4semidirect
26. C43×#556C4semidirect
30. D4×Q8×C43C4semidirect
284. #557Dic43semidirect
285. #557Dic43semidirect
287. #556Dic43semidirect
291. D4×Q8Dic43semidirect
314. C43#8417semidirect

Maximal subgroups

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

subgroupindex
#191355402
#191344252
#191332102
#191331832
#191331202
#191330422
C43×#35232
#841743