Finite Group Databasebeta

← #24988528

Subgroups — #24988528

Order 11008.

772 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#19135519C211yesmaximal, characteristic, complemented
2#19134615C211yesmaximal, characteristic, complemented
3#19133276C211yesmaximal, characteristic, complemented
4#19133272C211yesmaximal, characteristic, complemented
5#19133090C211yesmaximal, characteristic, complemented
6#19132982C211yesmaximal, characteristic, complemented
7C43×#3511C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9#14582923C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×#13063252—21no—
12C2×#13063249—22no—
13C4×C4⋊Dic43C2211yescharacteristic
14#14582658—21no—
15#14582648—22no—
16#14582645—21no—
17#14582643—21no—
18#14582633—22no—
19Q8⋊(C43⋊C8)—21no—
20D4⋊(C43⋊C8)—21no—
21C43×#556—21no—
22C43×#555C412yescomplemented
23C43×#554C412yescomplemented
24C43×#553—22no—
25C43×#548—22no—
26C43×#547—21no—
27C43×#542—22no—
28C43×#537—21no—
29C43×#533—21no—
30C43×#532—21no—
31C43×#532C2211yescharacteristic
32C2×C4⋊Q8×C43C2211yescharacteristic
33C43×#520—21no—
34C4×#41×C43C2211yescharacteristic
35C2×#10621877—21no—
36C22×C43⋊C8—21no—
37C2×C4⋊Dic43—21no—
38C2×C4×Dic43—21no—
39C4⋊(C43⋊C8)—21no—
40C4⋊(C43⋊C8)—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44#13063252—42no—
45#13063249—44no—
46C22⋊(C43⋊C8)—21no—
47C4×C43⋊C8—21no—
48C43⋊#95—21no—
49C2×#41×C43—22no—
50C2×#41×C43—21no—
51C2×#41×C43D411yescharacteristic
52C22×Q8×C43D412yes—
53C4⋊Q8×C43—21no—
54C4⋊Q8×C43—21no—
55C4⋊Q8×C43C2×C412yes—
56C4⋊Q8×C43D412yes—
57C4⋊Q8×C43D411yescharacteristic
58#127×C43D411yescharacteristic
59#126×C43—24no—
60#125×C43—22no—
61#124×C43—22no—
62#124×C43—24no—
63#124×C43—21no—
64#123×C43—24no—
65C22⋊Q8×C43—22no—
66C22⋊Q8×C43—22no—
67C22⋊Q8×C43—22no—
68C22⋊Q8×C43—24no—
69#121×C43—22no—
70#121×C43—24no—
71#121×C43—22no—
72#121×C43—22no—
73#121×C43—21no—
74#121×C43D412yes—
75C4×Q8×C43—22no—
76C4×Q8×C43—22no—
77C4×Q8×C43C2×C411yescharacteristic
78C4×Q8×C43D411yescharacteristic
79C4×D4×C43—22no—
80C4×D4×C43—24no—
81C4×D4×C43—22no—
82C4×D4×C43—21no—
83C4×D4×C43—21no—
84C4×D4×C43—21no—
85C4×D4×C43C2×C411yescharacteristic
86C4×D4×C43C2×C412yes—
87C4×D4×C43D411yescharacteristic
88#117×C43—22no—
89#117×C43—22no—
90#117×C43—21no—
91#117×C43D411yescharacteristic
92C2×C4⋊C4×C43—21no—
93C2×C4⋊C4×C43—21no—
94C2×C4⋊C4×C43—22no—
95C2×C42×C43—21no—
96C2×C42×C43C2311yescharacteristic
97#41×C43—21no—
98#41×C43—21no—
99#41×C43—21no—
100#41×C43—21no—
101#41×C43—41no—
102#41×C43—41no—
103#41×C43—41no—
104#41×C43—41no—
105#41×C43—82no—
106#41×C43—82no—
107C2×Q8×C43—21no—
108C2×Q8×C43—22no—
109C2×Q8×C43—42no—
110C2×Q8×C43—42no—
111C2×Q8×C43C22⋊C411yescharacteristic
112C2×Q8×C43C22⋊C414yes—
113C2×D4×C43—24no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—21no—
117C2×D4×C43—22no—
118C2×D4×C43C22⋊C411yescharacteristic
119C2×D4×C43C22⋊C412yes—
120C22×C4×C43—24no—
121C22×C4×C43—21no—
122C22×C4×C43—22no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—22no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×Dic43—41no—
130C4⋊C4×C43—24no—
131C4⋊C4×C43—24no—
132C4⋊C4×C43—22no—
133C4⋊C4×C43—22no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—22no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43C22⋊C411yescharacteristic
140C4⋊C4×C43C22⋊C411yescharacteristic
141C4⋊C4×C43C22⋊C412yes—
142C22⋊C4×C43—24no—
143C22⋊C4×C43—24no—
144C22⋊C4×C43—24no—
145C22⋊C4×C43—21no—
146C22⋊C4×C43—22no—
147C22⋊C4×C43—21no—
148C22⋊C4×C43—22no—
149C22⋊C4×C43—21no—
150C42×C43—24no—
151C42×C43—21no—
152C42×C43—21no—
153C42×C43—21no—
154C42×C43C22×C411yescharacteristic
155C42×C43C2×D411yescharacteristic
156C42×C43C2×D411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C4⋊Dic43—22no—
159C4⋊Dic43—41no—
160C4×Dic43—41no—
161C4×Dic43—41no—
162#10621877—41no—
163#10621877—41no—
164C2×C43⋊C8—42no—
165C2×C43⋊C8—41no—
166C2×C43⋊C8—41no—
167C2×C43⋊C8—41no—
168C23×C43—21no—
169C23×C43—22no—
170C23×C43#12011yescharacteristic
171Q8×C43—21no—
172Q8×C43—21no—
173Q8×C43—44no—
174Q8×C43—41no—
175Q8×C43—41no—
176Q8×C43—42no—
177Q8×C43—42no—
178D4×C43—21no—
179D4×C43—21no—
180D4×C43—42no—
181D4×C43—41no—
182D4×C43—42no—
183D4×C43—41no—
184D4×C43—42no—
185D4×C43—41no—
186D4×C43—41no—
187D4×C43—41no—
188D4×C43—41no—
189D4×C43—84no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—22no—
195C2×C4×C43—21no—
196C2×C4×C43—24no—
197C2×C4×C43—41no—
198C2×C4×C43—42no—
199C2×C4×C43—42no—
200C2×C4×C43—42no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—82no—
206C2×C4×C43—84no—
207C2×C4×C43C2×C22⋊C411yescharacteristic
208C2×C4×C43C2×C22⋊C411yescharacteristic
209C2×C4×C43C2×C22⋊C411yescharacteristic
210C2×C4×C43#12011yescharacteristic
211C2×C4×C43#12011yescharacteristic
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43#13511yescharacteristic
214C2×C4×C43#13511yescharacteristic
215C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
216C2×C4×C43#13711yescharacteristic
217C2×Dic43—42no—
218C2×Dic43—81no—
219C2×Dic43—81no—
220C43⋊C8—81no—
221C43⋊C8—81no—
222C43⋊C8—81no—
223#8423—431nomaximal, Sylow
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—41no—
227C22×C43—42no—
228C22×C43—41no—
229C22×C43—42no—
230C22×C43—41no—
231C22×C43—42no—
232C22×C43#37911yescharacteristic
233C22×C43#44911yescharacteristic
234C22×C43#45211yescharacteristic
235C4×C43—21no—
236C4×C43—21no—
237C4×C43—21no—
238C4×C43—41no—
239C4×C43—44no—
240C4×C43—41no—
241C4×C43—41no—
242C4×C43—42no—
243C4×C43#41611yescharacteristic
244C4×C43#41711yescharacteristic
245C4×C43#44911yescharacteristic
246C4×C43#45211yescharacteristic
247C4×C43#45311yescharacteristic
248C4×C43#45511yescharacteristic
249Dic43—82no—
250#3511D4311yescharacteristic
251#1981—431no—
252#1806—431no—
253#1548—431no—
254#1547—431no—
255#1502—431no—
256#1477—431no—
257C2×C43—21no—
258C2×C43—21no—
259C2×C43—81no—
260C2×C43—82no—
261C2×C43#178811yescharacteristic
262C2×C43#179211yescharacteristic
263C2×C43#179611yescharacteristic
264#556—21no—
265#555Dic4312yescomplemented
266#554Dic4312yescomplemented
267#553—22no—
268#548—22no—
269#547—21no—
270#542—22no—
271#537—21no—
272#533—21no—
273#532—21no—
274#532C2×D4311yescharacteristic
275C2×C4⋊Q8C2×D4311yescharacteristic
276#520—21no—
277C4×#41C2×D4311yescharacteristic
278#431—431no—
279#423—431no—
280C2×C4⋊C8—431no—
281C2×#104—861no—
282C2×#103—862no—
283C4×C4⋊C4—431no—
284#339—861no—
285#333—862no—
286#332—861no—
287#331—861no—
288#327—862no—
289Q8⋊C8—861no—
290D4⋊C8—861no—
291C43#842311yescharacteristic, complemented, Sylow
292C2×#41—22no—
293C2×#41—21no—
294C2×#41C22⋊D4311yescharacteristic
295C22×Q8C22⋊D4312yes—
296C2×M16—861no—
297C22×C8—861no—
298C4⋊Q8—21no—
299C4⋊Q8—21no—
300C4⋊Q8C2×Dic4312yes—
301C4⋊Q8C22⋊D4312yes—
302C4⋊Q8C22⋊D4311yescharacteristic
303#127C22⋊D4311yescharacteristic
304#126—24no—
305#125—22no—
306#124—22no—
307#124—24no—
308#124—21no—
309#123—24no—
310C22⋊Q8—22no—
311C22⋊Q8—22no—
312C22⋊Q8—22no—
313C22⋊Q8—24no—
314#121—22no—
315#121—24no—
316#121—22no—
317#121—22no—
318#121—21no—
319#121C22⋊D4312yes—
320C4×Q8—22no—
321C4×Q8—22no—
322C4×Q8C2×Dic4311yescharacteristic
323C4×Q8C22⋊D4311yescharacteristic
324C4×D4—22no—
325C4×D4—24no—
326C4×D4—22no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4C2×Dic4311yescharacteristic
331C4×D4C2×Dic4312yes—
332C4×D4C22⋊D4311yescharacteristic
333#117—22no—
334#117—22no—
335#117—21no—
336#117C22⋊D4311yescharacteristic
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—22no—
340C2×C4⋊C4—861no—
341C2×C42—21no—
342C2×C42—861no—
343C2×C42C22×D4311yescharacteristic
344C4⋊C8—861no—
345C4⋊C8—861no—
346C4⋊C8—861no—
347C4⋊C8—861no—
348C4⋊C8—861no—
349#104—1722no—
350#103—1724no—
351C22⋊C8—861no—
352C4×C8—861no—
353#95—861no—
354#41—21no—
355#41—21no—
356#41—21no—
357#41—21no—
358#41—41no—
359#41—41no—
360#41—41no—
361#41—41no—
362#41—82no—
363#41—82no—
364C2×Q8—21no—
365C2×Q8—22no—
366C2×Q8—42no—
367C2×Q8—42no—
368C2×Q8C22⋊Dic4311yescharacteristic
369C2×Q8C22⋊Dic4314yes—
370C2×D4—21no—
371C2×D4—22no—
372C2×D4—24no—
373C2×D4—21no—
374C2×D4—21no—
375C2×D4C22⋊Dic4311yescharacteristic
376C2×D4C22⋊Dic4312yes—
377C22×C4—24no—
378C22×C4—22no—
379C22×C4—21no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—1721no—
384C22×C4C2×C22⋊D4311yescharacteristic
385C22×C4C2×C22⋊D4311yescharacteristic
386C22×C4C2×C22⋊D4311yescharacteristic
387M16—1721no—
388M16—1721no—
389C2×C8—1722no—
390C2×C8—1721no—
391C2×C8—1721no—
392C2×C8—1721no—
393C4⋊C4—24no—
394C4⋊C4—24no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—21no—
398C4⋊C4—22no—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—862no—
403C4⋊C4—1721no—
404C4⋊C4C22⋊Dic4311yescharacteristic
405C4⋊C4C22⋊Dic4311yescharacteristic
406C4⋊C4C22⋊Dic4312yes—
407C22⋊C4—24no—
408C22⋊C4—24no—
409C22⋊C4—24no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—22no—
413C22⋊C4—21no—
414C22⋊C4—22no—
415C42—24no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42—1721no—
420C42—1721no—
421C42C22×Dic4311yescharacteristic
422C42C2×C22⋊D4311yescharacteristic
423C42C2×C22⋊D4311yescharacteristic
424C42C2×C22⋊D4311yescharacteristic
425C23—21no—
426C23—22no—
427C23#1306329411yescharacteristic
428Q8—21no—
429Q8—21no—
430Q8—44no—
431Q8—41no—
432Q8—41no—
433Q8—42no—
434Q8—42no—
435D4—21no—
436D4—21no—
437D4—42no—
438D4—41no—
439D4—42no—
440D4—41no—
441D4—42no—
442D4—41no—
443D4—41no—
444D4—41no—
445D4—41no—
446D4—84no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—21no—
453C2×C4—24no—
454C2×C4—41no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—82no—
463C2×C4—84no—
464C2×C4—3441no—
465C2×C4—3441no—
466C2×C4—1722no—
467C2×C4C2×C22⋊Dic4311yescharacteristic
468C2×C4C2×C22⋊Dic4311yescharacteristic
469C2×C4C2×C22⋊Dic4311yescharacteristic
470C2×C4#1306329411yescharacteristic
471C2×C4#1306329411yescharacteristic
472C2×C4#1306329411yescharacteristic
473C2×C4#1306334511yescharacteristic
474C2×C4#1306334511yescharacteristic
475C2×C4#1306335011yescharacteristic
476C2×C4#1306335511yescharacteristic
477C8—3441no—
478C8—3441no—
479C8—3441no—
480C22—21no—
481C22—21no—
482C22—41no—
483C22—42no—
484C22—41no—
485C22—42no—
486C22—41no—
487C22—42no—
488C22#1458275511yescharacteristic
489C22#1458304411yescharacteristic
490C22#1458306111yescharacteristic
491C4—21no—
492C4—21no—
493C4—21no—
494C4—41no—
495C4—42no—
496C4—41no—
497C4—44no—
498C4—41no—
499C4—3442no—
500C4#1458289511yescharacteristic
501C4#1458290011yescharacteristic
502C4#1458304411yescharacteristic
503C4#1458306111yescharacteristic
504C4#1458306711yescharacteristic
505C4#1458307711yescharacteristic
506C2—21no—
507C2—21no—
508C2—81no—
509C2—82no—
510C2#1913453511yescharacteristic
511C2#1913454911yescharacteristic
512C2#1913457011yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3511C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3511D43
hypocenterC43#8423
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3511

Complements

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

NH ≅ G/Ntype
1. #19135519C2semidirect
2. #19134615C2semidirect
3. #19133276C2semidirect
4. #19133272C2semidirect
5. #19133090C2semidirect
6. #19132982C2semidirect
22. C43×#555C4semidirect
23. C43×#554C4semidirect
265. #555Dic43semidirect
266. #554Dic43semidirect
291. C43#8423semidirect

Maximal subgroups

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

subgroupindex
#191355192
#191346152
#191332762
#191332722
#191330902
#191329822
C43×#35112
#842343