Finite Group Databasebeta

← #24989064

Subgroups — #24989064

Order 11008.

728 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135540C211yesmaximal, characteristic, complemented
2#19135528C211yesmaximal, characteristic, complemented
3#19133295C211yesmaximal, characteristic, complemented
4#19133193C211yesmaximal, characteristic, complemented
5#19133120C211yesmaximal, characteristic, complemented
6#19133008C211yesmaximal, characteristic, complemented
7C43×#3561C211yesmaximal, characteristic
8#14582956C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×#13063249—21no—
11C2×#13063246—21no—
12C4×#10621877C2211yescharacteristic
13C4×C4⋊Dic43C2211yescharacteristic
14#14582658—22no—
15#14582645—21no—
16#14582645—21no—
17#14582639—22no—
18#14582636—21no—
19#14582633—21no—
20Q8⋊(C43⋊C8)—21no—
21D4⋊(C43⋊C8)—21no—
22C43×#563C412yescomplemented
23C43×#562C412yescomplemented
24C43×#556—21no—
25C43×#551—22no—
26D4×Q8×C43—21no—
27C43×#548—21no—
28C43×#546—21no—
29C43×#543—21no—
30C43×#542—21no—
31C43×#542—22no—
32C43×#538—21no—
33C43×#536—21no—
34C43×#533C2211yescharacteristic
35C43×#529C2211yescharacteristic
36C2×#124×C43C2211yescharacteristic
37C2×#10621877—21no—
38C22×C43⋊C8—21no—
39C2×C4⋊Dic43—21no—
40C2×C4×Dic43—21no—
41C4⋊(C43⋊C8)—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44#13063249—42no—
45#13063246—42no—
46C22⋊(C43⋊C8)—21no—
47#13063236—21no—
48#13063236—21no—
49C4×C43⋊C8—21no—
50C43⋊#95—21no—
51C2×#41×C43—21no—
52C22×Q8×C43—21no—
53C22×Q8×C43D411yescharacteristic
54C22×D4×C43D411yescharacteristic
55C4⋊Q8×C43—21no—
56C4⋊Q8×C43—22no—
57C4⋊Q8×C43D411yescharacteristic
58C4⋊Q8×C43D411yescharacteristic
59#126×C43—22no—
60#126×C43—22no—
61#126×C43—22no—
62#126×C43—21no—
63#125×C43C2×C411yescharacteristic
64#125×C43C2×C412yes—
65#124×C43—21no—
66#124×C43—22no—
67#124×C43—22no—
68#124×C43—21no—
69#124×C43—21no—
70#124×C43C2×C412yes—
71#124×C43C2×C411yescharacteristic
72#124×C43D412yes—
73#123×C43—22no—
74#123×C43—22no—
75#123×C43—21no—
76#123×C43—22no—
77#123×C43—22no—
78C22⋊Q8×C43—22no—
79C22⋊Q8×C43—22no—
80C22⋊Q8×C43—21no—
81C22⋊Q8×C43—22no—
82C22⋊Q8×C43—22no—
83C22⋊Q8×C43—22no—
84C22⋊Q8×C43—21no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43—22no—
87C22⋊Q8×C43—22no—
88C22⋊Q8×C43D411yescharacteristic
89#121×C43—21no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43D411yescharacteristic
93#120×C43—22no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C4×Q8×C43—21no—
97C4×Q8×C43D411yescharacteristic
98C4×D4×C43—22no—
99C4×D4×C43—21no—
100C4×D4×C43—22no—
101C4×D4×C43—21no—
102C4×D4×C43D411yescharacteristic
103#117×C43—22no—
104#117×C43—21no—
105#117×C43D412yes—
106C2×C22⋊C4×C43—22no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C42×C43C2311yescharacteristic
110C24×C43—21no—
111#41×C43—81no—
112#41×C43—81no—
113C2×Q8×C43—22no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43—21no—
117C2×Q8×C43—41no—
118C2×Q8×C43—41no—
119C2×Q8×C43—81no—
120C2×Q8×C43—81no—
121C2×Q8×C43C22⋊C411yescharacteristic
122C2×Q8×C43C22⋊C412yes—
123C2×D4×C43—22no—
124C2×D4×C43—22no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43—41no—
128C2×D4×C43—41no—
129C2×D4×C43C22⋊C411yescharacteristic
130C2×D4×C43C22⋊C412yes—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×Dic43—41no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43—21no—
146C4⋊C4×C43—22no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—21no—
149C4⋊C4×C43—21no—
150C4⋊C4×C43—21no—
151C4⋊C4×C43—21no—
152C4⋊C4×C43C22⋊C412yes—
153C4⋊C4×C43C22⋊C412yes—
154C4⋊C4×C43C22⋊C411yescharacteristic
155C4⋊C4×C43C22⋊C411yescharacteristic
156C22⋊C4×C43—22no—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—22no—
159C22⋊C4×C43—22no—
160C22⋊C4×C43—22no—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—21no—
164C22⋊C4×C43—21no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—22no—
167C22⋊C4×C43—21no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—21no—
170C22⋊C4×C43—22no—
171C42×C43—22no—
172C42×C43—22no—
173C42×C43—21no—
174C42×C43C22×C411yescharacteristic
175C42×C43C2×D411yescharacteristic
176C42×C43C2×D411yescharacteristic
177C42×C43C2×D411yescharacteristic
178C4⋊Dic43—22no—
179C4⋊Dic43—41no—
180C4×Dic43—42no—
181#10621877—22no—
182#10621877—41no—
183C2×C43⋊C8—41no—
184C2×C43⋊C8—41no—
185C2×C43⋊C8—41no—
186C2×C43⋊C8—41no—
187C2×C43⋊C8—41no—
188C23×C43—22no—
189C23×C43—21no—
190C23×C43—41no—
191C23×C43—41no—
192C23×C43—81no—
193C23×C43—81no—
194C23×C43#12011yescharacteristic
195Q8×C43—42no—
196Q8×C43—41no—
197Q8×C43—41no—
198Q8×C43—41no—
199Q8×C43—41no—
200Q8×C43—41no—
201Q8×C43—81no—
202Q8×C43—82no—
203D4×C43—42no—
204D4×C43—41no—
205D4×C43—41no—
206D4×C43—41no—
207D4×C43—41no—
208D4×C43—41no—
209D4×C43—82no—
210D4×C43—82no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—22no—
217C2×C4×C43—21no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—21no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—81no—
225C2×C4×C43—82no—
226C2×C4×C43—82no—
227C2×C4×C43—82no—
228C2×C4×C43C2×C22⋊C411yescharacteristic
229C2×C4×C43C2×C22⋊C411yescharacteristic
230C2×C4×C43C2×C22⋊C411yescharacteristic
231C2×C4×C43#12011yescharacteristic
232C2×C4×C43#12011yescharacteristic
233C2×C4×C43#12011yescharacteristic
234C2×Dic43—42no—
235C2×Dic43—81no—
236C2×Dic43—81no—
237C43⋊C8—42no—
238C43⋊C8—81no—
239C43⋊C8—81no—
240#8511—431nomaximal, Sylow
241C22×C43—21no—
242C22×C43—21no—
243C22×C43—42no—
244C22×C43—41no—
245C22×C43—42no—
246C22×C43—41no—
247C22×C43—42no—
248C22×C43—41no—
249C22×C43—161no—
250C22×C43—161no—
251C22×C43#37911yescharacteristic
252C22×C43#45411yescharacteristic
253C22×C43#45611yescharacteristic
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—21no—
258C4×C43—21no—
259C4×C43—41no—
260C4×C43—42no—
261C4×C43—42no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—42no—
265C4×C43#45311yescharacteristic
266C4×C43#45511yescharacteristic
267Dic43—82no—
268#3561D4311yescharacteristic
269#1986—431no—
270#1983—431no—
271#1552—431no—
272#1527—431no—
273#1509—431no—
274#1483—431no—
275C2×C43—21no—
276C2×C43—21no—
277C2×C43—81no—
278C2×C43—82no—
279C2×C43#179211yescharacteristic
280C2×C43#179311yescharacteristic
281C2×C43#179411yescharacteristic
282#563Dic4312yescomplemented
283#562Dic4312yescomplemented
284#556—21no—
285#551—22no—
286D4×Q8—21no—
287#548—21no—
288#546—21no—
289#543—21no—
290#542—21no—
291#542—22no—
292#538—21no—
293#536—21no—
294#533C2×D4311yescharacteristic
295#529C2×D4311yescharacteristic
296C2×#124C2×D4311yescharacteristic
297#432—431no—
298C2×C4⋊C8—431no—
299C2×#103—861no—
300C2×#102—861no—
301C4×M16—431no—
302C4×C4⋊C4—431no—
303#339—862no—
304#332—861no—
305#332—861no—
306#329—862no—
307#328—861no—
308#327—861no—
309Q8⋊C8—861no—
310D4⋊C8—861no—
311C43#851111yescharacteristic, complemented, Sylow
312C2×#41—21no—
313C22×Q8—21no—
314C22×Q8C22⋊D4311yescharacteristic
315C22×D4C22⋊D4311yescharacteristic
316C2×M16—861no—
317C22×C8—861no—
318C4⋊Q8—21no—
319C4⋊Q8—22no—
320C4⋊Q8C22⋊D4311yescharacteristic
321C4⋊Q8C22⋊D4311yescharacteristic
322#126—22no—
323#126—22no—
324#126—22no—
325#126—21no—
326#125C2×Dic4311yescharacteristic
327#125C2×Dic4312yes—
328#124—21no—
329#124—22no—
330#124—22no—
331#124—21no—
332#124—21no—
333#124C2×Dic4312yes—
334#124C2×Dic4311yescharacteristic
335#124C22⋊D4312yes—
336#123—22no—
337#123—22no—
338#123—21no—
339#123—22no—
340#123—22no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—21no—
344C22⋊Q8—22no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8C22⋊D4311yescharacteristic
352#121—21no—
353#121—22no—
354#121—22no—
355#121C22⋊D4311yescharacteristic
356#120—22no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8C22⋊D4311yescharacteristic
361C4×D4—22no—
362C4×D4—21no—
363C4×D4—22no—
364C4×D4—21no—
365C4×D4C22⋊D4311yescharacteristic
366#117—22no—
367#117—21no—
368#117C22⋊D4312yes—
369C2×C4⋊C4—861no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C42—861no—
374C2×C42C22×D4311yescharacteristic
375C4⋊C8—861no—
376C4⋊C8—861no—
377C4⋊C8—861no—
378#103—1722no—
379#102—1722no—
380C22⋊C8—861no—
381#97—861no—
382#97—861no—
383C4×C8—861no—
384#95—861no—
385C24—21no—
386#41—81no—
387#41—81no—
388C2×Q8—22no—
389C2×Q8—21no—
390C2×Q8—21no—
391C2×Q8—21no—
392C2×Q8—41no—
393C2×Q8—41no—
394C2×Q8—81no—
395C2×Q8—81no—
396C2×Q8C22⋊Dic4311yescharacteristic
397C2×Q8C22⋊Dic4312yes—
398C2×D4—21no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—21no—
402C2×D4—41no—
403C2×D4—41no—
404C2×D4C22⋊Dic4311yescharacteristic
405C2×D4C22⋊Dic4312yes—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—1721no—
412C22×C4C2×C22⋊D4311yescharacteristic
413C22×C4C2×C22⋊D4311yescharacteristic
414C22×C4C2×C22⋊D4311yescharacteristic
415M16—862no—
416M16—1721no—
417C2×C8—1721no—
418C2×C8—1721no—
419C2×C8—1721no—
420C2×C8—1721no—
421C2×C8—1721no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—862no—
435C4⋊C4—1721no—
436C4⋊C4C22⋊Dic4312yes—
437C4⋊C4C22⋊Dic4312yes—
438C4⋊C4C22⋊Dic4311yescharacteristic
439C4⋊C4C22⋊Dic4311yescharacteristic
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—21no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C42—22no—
456C42—22no—
457C42—21no—
458C42—1722no—
459C42C22×Dic4311yescharacteristic
460C42C2×C22⋊D4311yescharacteristic
461C42C2×C22⋊D4311yescharacteristic
462C42C2×C22⋊D4311yescharacteristic
463C23—22no—
464C23—21no—
465C23—41no—
466C23—41no—
467C23—81no—
468C23—81no—
469C23#1306329411yescharacteristic
470Q8—42no—
471Q8—41no—
472Q8—41no—
473Q8—41no—
474Q8—41no—
475Q8—41no—
476Q8—81no—
477Q8—82no—
478D4—42no—
479D4—41no—
480D4—41no—
481D4—41no—
482D4—41no—
483D4—41no—
484D4—82no—
485D4—82no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—81no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4—3441no—
504C2×C4—3441no—
505C2×C4—1722no—
506C2×C4C2×C22⋊Dic4311yescharacteristic
507C2×C4C2×C22⋊Dic4311yescharacteristic
508C2×C4C2×C22⋊Dic4311yescharacteristic
509C2×C4#1306329411yescharacteristic
510C2×C4#1306329411yescharacteristic
511C2×C4#1306329411yescharacteristic
512C8—3441no—
513C8—3441no—
514C8—1722no—
515C22—21no—
516C22—21no—
517C22—41no—
518C22—42no—
519C22—41no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—161no—
524C22—161no—
525C22#1458275511yescharacteristic
526C22#1458307211yescharacteristic
527C22#1458308211yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—21no—
533C4—41no—
534C4—42no—
535C4—42no—
536C4—41no—
537C4—41no—
538C4—42no—
539C4—3442no—
540C4#1458306711yescharacteristic
541C4#1458307711yescharacteristic
542C2—21no—
543C2—21no—
544C2—82no—
545C2—81no—
546C2#1913454911yescharacteristic
547C2#1913455411yescharacteristic
548C2#1913455911yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3561C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3561D43
hypocenterC43#8511
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3561

Complements

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

NH ≅ G/Ntype
1. #19135540C2semidirect
2. #19135528C2semidirect
3. #19133295C2semidirect
4. #19133193C2semidirect
5. #19133120C2semidirect
6. #19133008C2semidirect
22. C43×#563C4semidirect
23. C43×#562C4semidirect
282. #563Dic43semidirect
283. #562Dic43semidirect
311. C43#8511semidirect

Maximal subgroups

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

subgroupindex
#191355402
#191355282
#191332952
#191331932
#191331202
#191330082
C43×#35612
#851143