Finite Group Databasebeta

← #24988458

Subgroups — #24988458

Order 11008.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 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#19133107C211yesmaximal, characteristic, complemented
4#19133081C211yesmaximal, characteristic, complemented
5#19133029C211yesmaximal, characteristic, complemented
6#19133016C211yesmaximal, characteristic, complemented
7C43×#3518C211yesmaximal, characteristic
8#14582956C2211yescharacteristic
9#14582952C2211yescharacteristic
10C2×#13063252—21no—
11C4×#10621877C2211yescharacteristic
12#14582745C2211yescharacteristic
13#14582658—21no—
14#14582641—21no—
15#14582639—21no—
16#14582636—21no—
17#14582636—22no—
18#14582633—21no—
19Q8⋊(C43⋊C8)—22no—
20Q8⋊(C43⋊C8)—21no—
21D4⋊(C43⋊C8)—21no—
22Q82×C43C411yescharacteristic, complemented
23C43×#556—21no—
24C43×#556—22no—
25C43×#556—21no—
26C43×#556C411yescharacteristic, complemented
27C43×#555—21no—
28C43×#555C411yescharacteristic, complemented
29D4×Q8×C43C411yescharacteristic, complemented
30C43×#548—21no—
31C43×#542—22no—
32C43×#542—21no—
33C43×#533—21no—
34C43×#533C2211yescharacteristic
35C43×#529—21no—
36C43×#529C2211yescharacteristic
37C43×#519—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×C43D411yescharacteristic
53C22×Q8×C43—21no—
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—21no—
66#125×C43D411yescharacteristic
67#124×C43—22no—
68#124×C43—22no—
69#124×C43—22no—
70#124×C43—22no—
71#124×C43—21no—
72#124×C43D411yescharacteristic
73#123×C43—22no—
74#123×C43—21no—
75C22⋊Q8×C43—22no—
76C22⋊Q8×C43—22no—
77C22⋊Q8×C43—21no—
78C22⋊Q8×C43—21no—
79C22⋊Q8×C43—21no—
80C22⋊Q8×C43—22no—
81C22⋊Q8×C43D411yescharacteristic
82C22⋊Q8×C43D412yes—
83#121×C43—22no—
84#121×C43—21no—
85#121×C43—21no—
86#121×C43D411yescharacteristic
87C4×Q8×C43—22no—
88C4×Q8×C43—22no—
89C4×Q8×C43—22no—
90C4×Q8×C43—21no—
91C4×Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43C2×C411yescharacteristic
95C4×Q8×C43C2×C411yescharacteristic
96C4×Q8×C43D411yescharacteristic
97C4×Q8×C43D412yes—
98C4×D4×C43—22no—
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
106#117×C43—22no—
107#117×C43—22no—
108#117×C43—21no—
109#117×C43—21no—
110#117×C43—21no—
111#117×C43—21no—
112#117×C43—21no—
113#117×C43—21no—
114#117×C43D411yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#41×C43—22no—
118#41×C43—41no—
119C2×Q8×C43—22no—
120C2×Q8×C43—22no—
121C2×Q8×C43—21no—
122C2×Q8×C43—42no—
123C2×Q8×C43—42no—
124C2×Q8×C43C22⋊C411yescharacteristic
125C2×Q8×C43C22⋊C411yescharacteristic
126C2×Q8×C43C22⋊C412yes—
127C2×D4×C43—22no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43C22⋊C411yescharacteristic
131C2×D4×C43C22⋊C411yescharacteristic
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×Dic43—41no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—22no—
143C4⋊C4×C43—22no—
144C4⋊C4×C43—22no—
145C4⋊C4×C43—21no—
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—22no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43C22⋊C411yescharacteristic
157C4⋊C4×C43C22⋊C411yescharacteristic
158C4⋊C4×C43C22⋊C411yescharacteristic
159C4⋊C4×C43C22⋊C411yescharacteristic
160C4⋊C4×C43C22⋊C412yes—
161C22⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C22⋊C4×C43—21no—
167C22⋊C4×C43—21no—
168C22⋊C4×C43—21no—
169C22⋊C4×C43—21no—
170C22⋊C4×C43—21no—
171C22⋊C4×C43—21no—
172C22⋊C4×C43—22no—
173C22⋊C4×C43—21no—
174C22⋊C4×C43—21no—
175C42×C43—22no—
176C42×C43—22no—
177C42×C43—22no—
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—
189#10621877—22no—
190#10621877—41no—
191C2×C43⋊C8—41no—
192C2×C43⋊C8—41no—
193C2×C43⋊C8—41no—
194C23×C43—21no—
195C23×C43—21no—
196C23×C43#12011yescharacteristic
197Q8×C43—21no—
198Q8×C43—42no—
199Q8×C43—41no—
200Q8×C43—44no—
201Q8×C43—41no—
202Q8×C43—41no—
203Q8×C43—82no—
204Q8×C43#10412yes—
205D4×C43—21no—
206D4×C43—21no—
207D4×C43—42no—
208D4×C43—41no—
209D4×C43—81no—
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—21no—
219C2×C4×C43—21no—
220C2×C4×C43—22no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—42no—
225C2×C4×C43—44no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—81no—
229C2×C4×C43C2×C22⋊C411yescharacteristic
230C2×C4×C43C2×C22⋊C411yescharacteristic
231C2×C4×C43C2×C22⋊C411yescharacteristic
232C2×C4×C43#12011yescharacteristic
233C2×C4×C43#12011yescharacteristic
234C2×C4×C43#12011yescharacteristic
235C2×Dic43—42no—
236C2×Dic43—81no—
237C2×Dic43—81no—
238C43⋊C8—42no—
239C43⋊C8—81no—
240C43⋊C8—81no—
241#8413—431nomaximal, Sylow
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—21no—
245C22×C43—41no—
246C22×C43—41no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43#37911yescharacteristic
252C4×C43—21no—
253C4×C43—21no—
254C4×C43—21no—
255C4×C43—21no—
256C4×C43—21no—
257C4×C43—22no—
258C4×C43—41no—
259C4×C43—42no—
260C4×C43—41no—
261C4×C43—41no—
262C4×C43—41no—
263C4×C43—42no—
264C4×C43—41no—
265C4×C43C2×#10411yescharacteristic
266C4×C43#42111yescharacteristic
267Dic43—82no—
268#3518D4311yescharacteristic
269#1759—431no—
270#1529—431no—
271#1506—431no—
272#1500—431no—
273#1488—431no—
274#1485—431no—
275C2×C43—41no—
276C2×C43—81no—
277C2×C43—81no—
278C2×C43#178911yescharacteristic
279C2×C43#179411yescharacteristic
280C2×C43#179611yescharacteristic
281Q82Dic4311yescharacteristic, complemented
282#556—21no—
283#556—22no—
284#556—21no—
285#556Dic4311yescharacteristic, complemented
286#555—21no—
287#555Dic4311yescharacteristic, complemented
288D4×Q8Dic4311yescharacteristic, complemented
289#548—21no—
290#542—22no—
291#542—21no—
292#533—21no—
293#533C2×D4311yescharacteristic
294#529—21no—
295#529C2×D4311yescharacteristic
296#519—21no—
297C4×#41C2×D4311yescharacteristic
298#432—431no—
299#431—431no—
300C2×#104—861no—
301C4×M16—431no—
302#376—431no—
303#339—861no—
304#330—861no—
305#329—861no—
306#328—861no—
307#328—862no—
308#327—861no—
309Q8⋊C8—862no—
310Q8⋊C8—861no—
311D4⋊C8—861no—
312C43#841311yescharacteristic, complemented, Sylow
313C2×#41C22⋊D4311yescharacteristic
314C22×Q8—21no—
315C2×M16—861no—
316C4⋊Q8—22no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8C2×Dic4311yescharacteristic
321C4⋊Q8C2×Dic4311yescharacteristic
322#126—22no—
323#126—22no—
324#126—22no—
325#126—22no—
326#126—21no—
327#125—21no—
328#125C22⋊D4311yescharacteristic
329#124—22no—
330#124—22no—
331#124—22no—
332#124—22no—
333#124—21no—
334#124C22⋊D4311yescharacteristic
335#123—22no—
336#123—21no—
337C22⋊Q8—22no—
338C22⋊Q8—22no—
339C22⋊Q8—21no—
340C22⋊Q8—21no—
341C22⋊Q8—21no—
342C22⋊Q8—22no—
343C22⋊Q8C22⋊D4311yescharacteristic
344C22⋊Q8C22⋊D4312yes—
345#121—22no—
346#121—21no—
347#121—21no—
348#121C22⋊D4311yescharacteristic
349C4×Q8—22no—
350C4×Q8—22no—
351C4×Q8—22no—
352C4×Q8—21no—
353C4×Q8—21no—
354C4×Q8—21no—
355C4×Q8—21no—
356C4×Q8C2×Dic4311yescharacteristic
357C4×Q8C2×Dic4311yescharacteristic
358C4×Q8C22⋊D4311yescharacteristic
359C4×Q8C22⋊D4312yes—
360C4×D4—22no—
361C4×D4—21no—
362C4×D4—21no—
363C4×D4—21no—
364C4×D4—21no—
365C4×D4C2×Dic4311yescharacteristic
366C4×D4C2×Dic4311yescharacteristic
367C4×D4C22⋊D4311yescharacteristic
368#117—22no—
369#117—22no—
370#117—21no—
371#117—21no—
372#117—21no—
373#117—21no—
374#117—21no—
375#117—21no—
376#117C22⋊D4311yescharacteristic
377C2×C42—21no—
378C2×C42—861no—
379C2×C42C22×D4311yescharacteristic
380C4⋊C8—861no—
381C4⋊C8—861no—
382#104—864no—
383C22⋊C8—861no—
384C22⋊C8—861no—
385#97—861no—
386#97—861no—
387C4×C8—861no—
388C4×C8—861no—
389#95—861no—
390#95—861no—
391#41—22no—
392#41—41no—
393C2×Q8—22no—
394C2×Q8—22no—
395C2×Q8—21no—
396C2×Q8—42no—
397C2×Q8—42no—
398C2×Q8C22⋊Dic4311yescharacteristic
399C2×Q8C22⋊Dic4311yescharacteristic
400C2×Q8C22⋊Dic4312yes—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4C22⋊Dic4311yescharacteristic
405C2×D4C22⋊Dic4311yescharacteristic
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
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—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4C22⋊Dic4311yescharacteristic
436C4⋊C4C22⋊Dic4311yescharacteristic
437C4⋊C4C22⋊Dic4311yescharacteristic
438C4⋊C4C22⋊Dic4311yescharacteristic
439C4⋊C4C22⋊Dic4312yes—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—21no—
447C22⋊C4—21no—
448C22⋊C4—21no—
449C22⋊C4—21no—
450C22⋊C4—21no—
451C22⋊C4—21no—
452C22⋊C4—21no—
453C22⋊C4—21no—
454C42—22no—
455C42—22no—
456C42—22no—
457C42—21no—
458C42—21no—
459C42—21no—
460C42—21no—
461C42—22no—
462C42—862no—
463C42—1721no—
464C42C22×Dic4311yescharacteristic
465C42C2×C22⋊D4311yescharacteristic
466C42C2×C22⋊D4311yescharacteristic
467C42C2×C22⋊D4311yescharacteristic
468C23—21no—
469C23—21no—
470C23#1306329411yescharacteristic
471Q8—21no—
472Q8—42no—
473Q8—41no—
474Q8—44no—
475Q8—41no—
476Q8—41no—
477Q8—82no—
478Q8#1306325212yes—
479D4—21no—
480D4—21no—
481D4—42no—
482D4—41no—
483D4—81no—
484D4—82no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—22no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—44no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—81no—
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—21no—
518C22—41no—
519C22—41no—
520C22—41no—
521C22—41no—
522C22—41no—
523C22—41no—
524C22#1458275511yescharacteristic
525C4—21no—
526C4—22no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—21no—
531C4—42no—
532C4—41no—
533C4—41no—
534C4—42no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—3442no—
539C4C2×#1306325211yescharacteristic
540C4#1458291611yescharacteristic
541C2—41no—
542C2—81no—
543C2—81no—
544C2#1913453911yescharacteristic
545C2#1913455911yescharacteristic
546C2#1913457011yescharacteristic
subgroupG/H
centerC22#14582755
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3518C2
socleC22×C43#379
cosocleC2×C42×C43C23
hypercenter#3518D43
hypocenterC43#8413
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3518

Complements

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

NH ≅ G/Ntype
1. #19134405C2semidirect
2. #19133202C2semidirect
3. #19133107C2semidirect
4. #19133081C2semidirect
5. #19133029C2semidirect
6. #19133016C2semidirect
22. Q82×C43C4semidirect
26. C43×#556C4semidirect
28. C43×#555C4semidirect
29. D4×Q8×C43C4semidirect
281. Q82Dic43semidirect
285. #556Dic43semidirect
287. #555Dic43semidirect
288. D4×Q8Dic43semidirect
312. C43#8413semidirect

Maximal subgroups

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

subgroupindex
#191344052
#191332022
#191331072
#191330812
#191330292
#191330162
C43×#35182
#841343