Finite Group Databasebeta

← #24988549

Subgroups — #24988549

Order 11008.

836 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135523C211yesmaximal, characteristic, complemented
2#19134615C211yesmaximal, characteristic, complemented
3#19133285C211yesmaximal, characteristic, complemented
4#19133263C211yesmaximal, characteristic, complemented
5#19133094C211yesmaximal, characteristic, complemented
6#19132982C211yesmaximal, characteristic, complemented
7C43×#3508C211yesmaximal, characteristic
8#14582952C2211yescharacteristic
9#14582923C2211yescharacteristic
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×#13063252—21no—
12C2×#13063246—22no—
13C4×C4⋊Dic43C2211yescharacteristic
14#14582658—21no—
15#14582648—21no—
16#14582645—21no—
17#14582643—22no—
18#14582636—22no—
19Q8⋊(C43⋊C8)—21no—
20D4⋊(C43⋊C8)—21no—
21C43×#559—21no—
22C43×#559C412yescomplemented
23C43×#550—21no—
24C43×#550C412yescomplemented
25C43×#546—22no—
26C43×#546—22no—
27C43×#540—22no—
28C43×#535—21no—
29C43×#533C2211yescharacteristic
30C43×#532—21no—
31C43×#532—21no—
32C2×#127×C43C2211yescharacteristic
33C43×#518—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#13063246—44no—
46C22⋊(C43⋊C8)—21no—
47C4×C43⋊C8—21no—
48C43⋊#95—21no—
49C2×#41×C43—22no—
50C2×#41×C43—22no—
51C2×#41×C43D411yescharacteristic
52C22×D4×C43—21no—
53C22×D4×C43—21no—
54C22×D4×C43D412yes—
55C4⋊Q8×C43D411yescharacteristic
56C4⋊Q8×C43D411yescharacteristic
57#127×C43—22no—
58#127×C43—21no—
59#127×C43—21no—
60#127×C43C2×C412yes—
61#127×C43D412yes—
62#125×C43—21no—
63#124×C43—22no—
64#124×C43—22no—
65#124×C43—22no—
66#123×C43—24no—
67#123×C43—24no—
68C22⋊Q8×C43—21no—
69C22⋊Q8×C43D412yes—
70#121×C43—22no—
71#121×C43—22no—
72#121×C43—22no—
73#121×C43—24no—
74#121×C43—24no—
75#121×C43—22no—
76#120×C43—24no—
77C4×Q8×C43—21no—
78C4×Q8×C43C2×C411yescharacteristic
79C4×Q8×C43C2×C412yes—
80C4×Q8×C43D411yescharacteristic
81C4×D4×C43—22no—
82C4×D4×C43—22no—
83C4×D4×C43—22no—
84C4×D4×C43—21no—
85C4×D4×C43—21no—
86C4×D4×C43—22no—
87C4×D4×C43—22no—
88C4×D4×C43—22no—
89C4×D4×C43C2×C411yescharacteristic
90C4×D4×C43D411yescharacteristic
91#117×C43—21no—
92#117×C43—21no—
93#117×C43D411yescharacteristic
94C2×C22⋊C4×C43—24no—
95C2×C42×C43—21no—
96C2×C42×C43C2311yescharacteristic
97C24×C43—22no—
98#41×C43—21no—
99#41×C43—21no—
100#41×C43—21no—
101#41×C43—21no—
102#41×C43—84no—
103#41×C43—82no—
104#41×C43—82no—
105C2×Q8×C43—21no—
106C2×Q8×C43C22⋊C411yescharacteristic
107C2×Q8×C43C22⋊C412yes—
108C2×D4×C43—24no—
109C2×D4×C43—24no—
110C2×D4×C43—22no—
111C2×D4×C43—22no—
112C2×D4×C43—22no—
113C2×D4×C43—22no—
114C2×D4×C43—22no—
115C2×D4×C43—21no—
116C2×D4×C43—41no—
117C2×D4×C43—41no—
118C2×D4×C43—41no—
119C2×D4×C43—41no—
120C2×D4×C43—42no—
121C2×D4×C43—42no—
122C2×D4×C43—82no—
123C2×D4×C43C22⋊C411yescharacteristic
124C2×D4×C43C22⋊C414yes—
125C22×C4×C43—24no—
126C22×C4×C43—24no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×Dic43—41no—
134C4⋊C4×C43—21no—
135C4⋊C4×C43—22no—
136C4⋊C4×C43—21no—
137C4⋊C4×C43—21no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43C22⋊C411yescharacteristic
142C4⋊C4×C43C22⋊C411yescharacteristic
143C4⋊C4×C43C22⋊C412yes—
144C22⋊C4×C43—24no—
145C22⋊C4×C43—24no—
146C22⋊C4×C43—24no—
147C22⋊C4×C43—24no—
148C22⋊C4×C43—21no—
149C22⋊C4×C43—21no—
150C22⋊C4×C43—21no—
151C22⋊C4×C43—22no—
152C42×C43—21no—
153C42×C43—22no—
154C42×C43—21no—
155C42×C43—21no—
156C42×C43C22×C411yescharacteristic
157C42×C43C2×D411yescharacteristic
158C42×C43C2×D411yescharacteristic
159C42×C43C2×D411yescharacteristic
160C4⋊Dic43—22no—
161C4⋊Dic43—41no—
162C4×Dic43—41no—
163C4×Dic43—41no—
164#10621877—41no—
165#10621877—41no—
166C2×C43⋊C8—42no—
167C2×C43⋊C8—41no—
168C2×C43⋊C8—41no—
169C2×C43⋊C8—41no—
170C23×C43—24no—
171C23×C43—21no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—82no—
175C23×C43—82no—
176C23×C43#12011yescharacteristic
177Q8×C43—21no—
178Q8×C43—21no—
179Q8×C43—42no—
180Q8×C43—41no—
181Q8×C43—41no—
182D4×C43—21no—
183D4×C43—21no—
184D4×C43—44no—
185D4×C43—44no—
186D4×C43—41no—
187D4×C43—41no—
188D4×C43—42no—
189D4×C43—42no—
190D4×C43—42no—
191D4×C43—42no—
192D4×C43—42no—
193D4×C43—42no—
194D4×C43—82no—
195D4×C43—84no—
196D4×C43—84no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—41no—
205C2×C4×C43—42no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—84no—
211C2×C4×C43—84no—
212C2×C4×C43C2×C22⋊C411yescharacteristic
213C2×C4×C43C2×C22⋊C411yescharacteristic
214C2×C4×C43C2×C22⋊C411yescharacteristic
215C2×C4×C43#12011yescharacteristic
216C2×C4×C43#12011yescharacteristic
217C2×C4×C43#12011yescharacteristic
218C2×C4×C43#13511yescharacteristic
219C2×C4×C43#13511yescharacteristic
220C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
221C2×C4×C43#13711yescharacteristic
222C2×Dic43—42no—
223C2×Dic43—81no—
224C2×Dic43—81no—
225C43⋊C8—81no—
226C43⋊C8—81no—
227C43⋊C8—81no—
228#8426—431nomaximal, Sylow
229C22×C43—21no—
230C22×C43—21no—
231C22×C43—44no—
232C22×C43—41no—
233C22×C43—44no—
234C22×C43—41no—
235C22×C43—44no—
236C22×C43—41no—
237C22×C43—162no—
238C22×C43—162no—
239C22×C43#37911yescharacteristic
240C22×C43#44911yescharacteristic
241C22×C43#45211yescharacteristic
242C4×C43—21no—
243C4×C43—21no—
244C4×C43—21no—
245C4×C43—41no—
246C4×C43—42no—
247C4×C43—41no—
248C4×C43—42no—
249C4×C43—41no—
250C4×C43#41611yescharacteristic
251C4×C43#41711yescharacteristic
252C4×C43#44911yescharacteristic
253C4×C43#45211yescharacteristic
254C4×C43#45311yescharacteristic
255C4×C43#45511yescharacteristic
256Dic43—82no—
257#3508D4311yescharacteristic
258#1982—431no—
259#1806—431no—
260#1550—431no—
261#1545—431no—
262#1503—431no—
263#1477—431no—
264C2×C43—21no—
265C2×C43—21no—
266C2×C43—81no—
267C2×C43—84no—
268C2×C43#178811yescharacteristic
269C2×C43#179211yescharacteristic
270C2×C43#179511yescharacteristic
271#559—21no—
272#559Dic4312yescomplemented
273#550—21no—
274#550Dic4312yescomplemented
275#546—22no—
276#546—22no—
277#540—22no—
278#535—21no—
279#533C2×D4311yescharacteristic
280#532—21no—
281#532—21no—
282C2×#127C2×D4311yescharacteristic
283#518—21no—
284C4×#41C2×D4311yescharacteristic
285#431—431no—
286#423—431no—
287C2×C4⋊C8—431no—
288C2×#104—861no—
289C2×#102—862no—
290C4×C4⋊C4—431no—
291#339—861no—
292#333—861no—
293#332—861no—
294#331—862no—
295#328—862no—
296Q8⋊C8—861no—
297D4⋊C8—861no—
298C43#842611yescharacteristic, complemented, Sylow
299C2×#41—22no—
300C2×#41—22no—
301C2×#41C22⋊D4311yescharacteristic
302C22×D4—21no—
303C22×D4—21no—
304C22×D4C22⋊D4312yes—
305C2×M16—861no—
306C22×C8—861no—
307C4⋊Q8C22⋊D4311yescharacteristic
308C4⋊Q8C22⋊D4311yescharacteristic
309#127—22no—
310#127—21no—
311#127—21no—
312#127C2×Dic4312yes—
313#127C22⋊D4312yes—
314#125—21no—
315#124—22no—
316#124—22no—
317#124—22no—
318#123—24no—
319#123—24no—
320C22⋊Q8—21no—
321C22⋊Q8C22⋊D4312yes—
322#121—22no—
323#121—22no—
324#121—22no—
325#121—24no—
326#121—24no—
327#121—22no—
328#120—24no—
329C4×Q8—21no—
330C4×Q8C2×Dic4311yescharacteristic
331C4×Q8C2×Dic4312yes—
332C4×Q8C22⋊D4311yescharacteristic
333C4×D4—22no—
334C4×D4—22no—
335C4×D4—22no—
336C4×D4—21no—
337C4×D4—21no—
338C4×D4—22no—
339C4×D4—22no—
340C4×D4—22no—
341C4×D4C2×Dic4311yescharacteristic
342C4×D4C22⋊D4311yescharacteristic
343#117—21no—
344#117—21no—
345#117C22⋊D4311yescharacteristic
346C2×C4⋊C4—861no—
347C2×C22⋊C4—24no—
348C2×C42—21no—
349C2×C42—861no—
350C2×C42C22×D4311yescharacteristic
351C4⋊C8—861no—
352C4⋊C8—861no—
353C4⋊C8—861no—
354C4⋊C8—861no—
355C4⋊C8—861no—
356#104—1722no—
357#102—1724no—
358C22⋊C8—861no—
359C4×C8—861no—
360#95—861no—
361C24—22no—
362#41—21no—
363#41—21no—
364#41—21no—
365#41—21no—
366#41—84no—
367#41—82no—
368#41—82no—
369C2×Q8—21no—
370C2×Q8C22⋊Dic4311yescharacteristic
371C2×Q8C22⋊Dic4312yes—
372C2×D4—21no—
373C2×D4—24no—
374C2×D4—24no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—42no—
381C2×D4—42no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—82no—
387C2×D4C22⋊Dic4311yescharacteristic
388C2×D4C22⋊Dic4314yes—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—1721no—
395C22×C4C2×C22⋊D4311yescharacteristic
396C22×C4C2×C22⋊D4311yescharacteristic
397C22×C4C2×C22⋊D4311yescharacteristic
398M16—1721no—
399M16—1721no—
400C2×C8—1722no—
401C2×C8—1721no—
402C2×C8—1721no—
403C2×C8—1721no—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—21no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—21no—
410C4⋊C4—22no—
411C4⋊C4—862no—
412C4⋊C4—1721no—
413C4⋊C4C22⋊Dic4311yescharacteristic
414C4⋊C4C22⋊Dic4311yescharacteristic
415C4⋊C4C22⋊Dic4312yes—
416C22⋊C4—24no—
417C22⋊C4—24no—
418C22⋊C4—24no—
419C22⋊C4—24no—
420C22⋊C4—21no—
421C22⋊C4—22no—
422C22⋊C4—21no—
423C22⋊C4—21no—
424C42—21no—
425C42—22no—
426C42—21no—
427C42—21no—
428C42—1721no—
429C42—1721no—
430C42C22×Dic4311yescharacteristic
431C42C2×C22⋊D4311yescharacteristic
432C42C2×C22⋊D4311yescharacteristic
433C42C2×C22⋊D4311yescharacteristic
434C23—24no—
435C23—21no—
436C23—42no—
437C23—42no—
438C23—82no—
439C23—82no—
440C23#1306329411yescharacteristic
441Q8—21no—
442Q8—21no—
443Q8—42no—
444Q8—41no—
445Q8—41no—
446D4—21no—
447D4—21no—
448D4—44no—
449D4—44no—
450D4—41no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—42no—
456D4—42no—
457D4—42no—
458D4—82no—
459D4—84no—
460D4—84no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—84no—
475C2×C4—84no—
476C2×C4—3441no—
477C2×C4—3441no—
478C2×C4—1722no—
479C2×C4C2×C22⋊Dic4311yescharacteristic
480C2×C4C2×C22⋊Dic4311yescharacteristic
481C2×C4C2×C22⋊Dic4311yescharacteristic
482C2×C4#1306329411yescharacteristic
483C2×C4#1306329411yescharacteristic
484C2×C4#1306329411yescharacteristic
485C2×C4#1306334511yescharacteristic
486C2×C4#1306334511yescharacteristic
487C2×C4#1306335011yescharacteristic
488C2×C4#1306335511yescharacteristic
489C8—3441no—
490C8—3441no—
491C8—3441no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—44no—
496C22—41no—
497C22—44no—
498C22—41no—
499C22—44no—
500C22—162no—
501C22—162no—
502C22#1458275511yescharacteristic
503C22#1458304411yescharacteristic
504C22#1458306111yescharacteristic
505C4—21no—
506C4—21no—
507C4—21no—
508C4—41no—
509C4—41no—
510C4—42no—
511C4—41no—
512C4—42no—
513C4—3442no—
514C4#1458289511yescharacteristic
515C4#1458290011yescharacteristic
516C4#1458304411yescharacteristic
517C4#1458306111yescharacteristic
518C4#1458306711yescharacteristic
519C4#1458307711yescharacteristic
520C2—21no—
521C2—21no—
522C2—84no—
523C2—81no—
524C2#1913453511yescharacteristic
525C2#1913454911yescharacteristic
526C2#1913456511yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3508C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3508D43
hypocenterC43#8426
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #19135523C2semidirect
2. #19134615C2semidirect
3. #19133285C2semidirect
4. #19133263C2semidirect
5. #19133094C2semidirect
6. #19132982C2semidirect
22. C43×#559C4semidirect
24. C43×#550C4semidirect
272. #559Dic43semidirect
274. #550Dic43semidirect
298. C43#8426semidirect

Maximal subgroups

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

subgroupindex
#191355232
#191346152
#191332852
#191332632
#191330942
#191329822
C43×#35082
#842643