Finite Group Databasebeta

← #25070901

Subgroups — #25070901

Order 11008.

1156 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145781C212yesmaximal, complemented
2#19140293C211yesmaximal, characteristic, complemented
3#19133632C212yesmaximal, complemented
4#19133615C212yesmaximal, complemented
5#19133598C212yesmaximal, complemented
6#19133581C212yesmaximal, complemented
7#19133103C212yesmaximal, complemented
8#19132929C211yesmaximal, characteristic, complemented
9C43×#3449C211yesmaximal, characteristic
10C2×#13063317C2211yescharacteristic, complemented
11#14583305—22no—
12#14583263—22no—
13#14583215C2214yescomplemented
14#14583210C2214yescomplemented
15#14583199—24no—
16#14582956C2212yescomplemented
17#14582838C2211yescharacteristic, complemented
18#14582835C2211yescharacteristic
19#14582829C2211yescharacteristic, complemented
20#14582824C2211yescharacteristic
21#14582794—21no—
22#14582793—21no—
23#14582783—21no—
24#14582772—21no—
25#14582745C2211yescharacteristic, complemented
26#14582633C2214yescomplemented
27#14582633C2214yescomplemented
28#14582625C2212yescomplemented
29#14582623C2212yes—
30C22×#41×C43—21no—
31C43×#537—21no—
32C43×#537C2212yes—
33C43×#536—22no—
34C43×#535—22no—
35C43×#534—21no—
36C43×#534C2212yes—
37C43×#532—21no—
38C43×#532C2212yes—
39C43×#525—24no—
40C2×#117×C43C2211yescharacteristic
41#13063317—22no—
42#13063317—22no—
43C2×C4⋊Dic43C2311yescharacteristic
44C2×C4⋊Dic43C2311yescharacteristic
45C2×Dic43⋊C4—21no—
46C2×Dic43⋊C4—21no—
47C2×Dic43⋊C4—21no—
48C2×Dic43⋊C4—21no—
49C2×C22⋊Dic43—21no—
50C2×C22⋊Dic43—21no—
51C2×C4×Dic43—21no—
52#13063258—24no—
53#13063256—24no—
54C4⋊(C43⋊C8)—22no—
55#13063246—24no—
56#13063246—24no—
57C22⋊(C43⋊C8)C2314yes—
58#13063236—22no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95—21no—
62C43⋊#95—21no—
63C43⋊#95—21no—
64C43⋊#95C2311yescharacteristic
65C43⋊#95C2311yescharacteristic
66C2×#41×C43—22no—
67C2×#41×C43—22no—
68C2×#41×C43—22no—
69C2×#41×C43—22no—
70C2×#41×C43—44no—
71C2×#41×C43—44no—
72C22×Q8×C43—21no—
73C22×D4×C43—21no—
74C22×D4×C43—22no—
75C23×C4×C43—22no—
76C23×C4×C43D411yescharacteristic
77C4⋊Q8×C43—21no—
78C4⋊Q8×C43D412yes—
79#127×C43—21no—
80#127×C43D412yes—
81#124×C43—22no—
82#124×C43—22no—
83#123×C43—24no—
84#123×C43—24no—
85C22⋊Q8×C43—24no—
86C22⋊Q8×C43—24no—
87#121×C43—24no—
88#121×C43—24no—
89#121×C43—22no—
90#121×C43—22no—
91#121×C43—22no—
92#121×C43C2314yes—
93#120×C43—24no—
94#120×C43—24no—
95C4×D4×C43—22no—
96C4×D4×C43—22no—
97C4×D4×C43—22no—
98C4×D4×C43D414yes—
99#117×C43—22no—
100#117×C43—22no—
101C2×C4⋊C4×C43D411yescharacteristic
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C22⋊C4×C43D411yescharacteristic
104C2×C22⋊C4×C43C2311yescharacteristic
105C2×C42×C43D411yescharacteristic
106C2×C42×C43C2311yescharacteristic
107C24×C43—22no—
108C24×C43C2×D411yescharacteristic
109#41×C43—48no—
110#41×C43—48no—
111#41×C43—44no—
112#41×C43—44no—
113#41×C43—44no—
114#41×C43—44no—
115C2×Q8×C43—22no—
116C2×Q8×C43—22no—
117C2×Q8×C43—44no—
118C2×D4×C43—24no—
119C2×D4×C43—22no—
120C2×D4×C43—22no—
121C2×D4×C43—22no—
122C2×D4×C43—22no—
123C2×D4×C43—22no—
124C2×D4×C43—24no—
125C2×D4×C43—44no—
126C2×D4×C43—44no—
127C2×D4×C43—44no—
128C2×D4×C43C2×D414yes—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—22no—
132C22×C4×C43—24no—
133C22×C4×C43—22no—
134C22×C4×C43—24no—
135C22×C4×C43—22no—
136C22×C4×C43—48no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C4⋊C4×C43—22no—
148C4⋊C4×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—22no—
152C4⋊C4×C43C2×D414yes—
153C22⋊C4×C43—24no—
154C22⋊C4×C43—24no—
155C22⋊C4×C43—22no—
156C22⋊C4×C43—24no—
157C22⋊C4×C43—22no—
158C22⋊C4×C43—24no—
159C42×C43—21no—
160C42×C43—21no—
161C42×C43C2×D412yes—
162C42×C43C2×D412yes—
163C22⋊Dic43—42no—
164C22⋊Dic43—42no—
165C4⋊Dic43—22no—
166C4⋊Dic43—22no—
167Dic43⋊C4—42no—
168Dic43⋊C4—41no—
169Dic43⋊C4—41no—
170Dic43⋊C4—42no—
171Dic43⋊C4—42no—
172C4×Dic43—42no—
173C2×C43⋊C8—24no—
174C23×C43—21no—
175C23×C43—21no—
176C23×C43—24no—
177C23×C43—41no—
178C23×C43—41no—
179C23×C43—44no—
180C23×C43—82no—
181C23×C43—82no—
182C23×C43AGL(1,ℤ/8)12yes—
183C23×C43C22×D411yescharacteristic
184Q8×C43—44no—
185Q8×C43—44no—
186D4×C43—44no—
187D4×C43—44no—
188D4×C43—44no—
189D4×C43—48no—
190D4×C43—44no—
191D4×C43—44no—
192D4×C43—82no—
193D4×C43—82no—
194D4×C43—82no—
195C2×C4×C43—24no—
196C2×C4×C43—24no—
197C2×C4×C43—21no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—24no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—48no—
207C2×C4×C43—48no—
208C2×C4×C43—44no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43#12011yescharacteristic
212C2×C4×C43#12011yescharacteristic
213C2×C4×C43#12012yes—
214C2×C4×C43AGL(1,ℤ/8)12yes—
215C2×C4×C43C22×D412yes—
216C2×Dic43—22no—
217C2×Dic43—41no—
218C2×Dic43—41no—
219C2×Dic43—41no—
220C2×Dic43—41no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C43⋊C8—44no—
229#18339—431nomaximal, Sylow
230C22×C43—21no—
231C22×C43—21no—
232C22×C43—22no—
233C22×C43—42no—
234C22×C43—41no—
235C22×C43—41no—
236C22×C43—44no—
237C22×C43—44no—
238C22×C43—44no—
239C22×C43—81no—
240C22×C43—88no—
241C22×C43C2×#12011yescharacteristic
242C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
243C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
244C4×C43—21no—
245C4×C43—22no—
246C4×C43—21no—
247C4×C43—22no—
248C4×C43—22no—
249C4×C43—44no—
250C4×C43—41no—
251C4×C43—41no—
252Dic43—42no—
253Dic43—81no—
254Dic43—81no—
255Dic43—81no—
256#3449D4311yescharacteristic
257#3234—432no—
258#2611—431no—
259#1616—432no—
260#1613—432no—
261#1610—432no—
262#1607—432no—
263#1505—432no—
264#1464—431no—
265C2×C43—21no—
266C2×C43—21no—
267C2×C43—42no—
268C2×C43—84no—
269C2×C43#300311yescharacteristic
270C2×C43#301811yescharacteristic
271C2×C43#302811yescharacteristic
272C22×#41—21no—
273#537—21no—
274#537C2×D4312yes—
275#536—22no—
276#535—22no—
277#534—21no—
278#534C2×D4312yes—
279#532—21no—
280#532C2×D4312yes—
281C2×#125—431no—
282#525—24no—
283C2×#117C2×D4311yescharacteristic
284#501—862no—
285#490—862no—
286#481—434no—
287#480—434no—
288#478—864no—
289#432—432no—
290#400—431no—
291#399—431no—
292#398—431no—
293#397—431no—
294#389—861no—
295#388—861no—
296#387—861no—
297#385—861no—
298#376—431no—
299#327—434no—
300#327—434no—
301#324—432no—
302#323—432no—
303C43#1833911yescharacteristic, complemented, Sylow
304C2×#41—22no—
305C2×#41—22no—
306C2×#41—22no—
307C2×#41—22no—
308C2×#41—44no—
309C2×#41—44no—
310C22×Q8—21no—
311C22×D4—21no—
312C22×D4—22no—
313C23×C4—22no—
314C23×C4C22⋊D4311yescharacteristic
315C4⋊Q8—21no—
316C4⋊Q8C22⋊D4312yes—
317#127—21no—
318#127C22⋊D4312yes—
319#125—862no—
320#125—862no—
321#124—22no—
322#124—22no—
323#123—24no—
324#123—24no—
325C22⋊Q8—24no—
326C22⋊Q8—24no—
327#121—24no—
328#121—24no—
329#121—22no—
330#121—22no—
331#121—22no—
332#121C22×D4314yes—
333#120—24no—
334#120—24no—
335C4×D4—22no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4C22⋊D4314yes—
339#117—22no—
340#117—22no—
341C2×C4⋊C4—431no—
342C2×C4⋊C4—431no—
343C2×C4⋊C4—861no—
344C2×C4⋊C4—861no—
345C2×C4⋊C4—861no—
346C2×C4⋊C4—861no—
347C2×C4⋊C4C22⋊D4311yescharacteristic
348C2×C4⋊C4C22×D4311yescharacteristic
349C2×C22⋊C4—861no—
350C2×C22⋊C4—861no—
351C2×C22⋊C4C22⋊D4311yescharacteristic
352C2×C22⋊C4C22×D4311yescharacteristic
353C2×C42—861no—
354C2×C42C22⋊D4311yescharacteristic
355C2×C42C22×D4311yescharacteristic
356#107—864no—
357#106—864no—
358C4⋊C8—862no—
359#102—864no—
360#102—864no—
361C22⋊C8—434no—
362#97—862no—
363#95—431no—
364#95—431no—
365#95—861no—
366#95—861no—
367#95—861no—
368#95—861no—
369#95—861no—
370C24—22no—
371C24C2×C22⋊D4311yescharacteristic
372#41—48no—
373#41—48no—
374#41—44no—
375#41—44no—
376#41—44no—
377#41—44no—
378C2×Q8—22no—
379C2×Q8—22no—
380C2×Q8—44no—
381C2×D4—24no—
382C2×D4—22no—
383C2×D4—24no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—22no—
387C2×D4—22no—
388C2×D4—44no—
389C2×D4—44no—
390C2×D4—44no—
391C2×D4C2×C22⋊D4314yes—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—22no—
398C22×C4—24no—
399C22×C4—48no—
400C22×C4—861no—
401C22×C4—861no—
402C22×C4—861no—
403C22×C4—861no—
404C22×C4C2×C22⋊D4311yescharacteristic
405C22×C4C2×C22⋊D4311yescharacteristic
406C22×C4C2×C22⋊D4311yescharacteristic
407C22×C4C2×C22⋊D4311yescharacteristic
408C22×C4C2×C22⋊D4311yescharacteristic
409C22×C4C23×D4311yescharacteristic
410C2×C8—864no—
411C4⋊C4—22no—
412C4⋊C4—22no—
413C4⋊C4—22no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—862no—
417C4⋊C4—862no—
418C4⋊C4—1722no—
419C4⋊C4—1721no—
420C4⋊C4—1721no—
421C4⋊C4—1722no—
422C4⋊C4—1722no—
423C4⋊C4C2×C22⋊D4314yes—
424C22⋊C4—24no—
425C22⋊C4—24no—
426C22⋊C4—22no—
427C22⋊C4—24no—
428C22⋊C4—22no—
429C22⋊C4—24no—
430C22⋊C4—1722no—
431C22⋊C4—1722no—
432C42—21no—
433C42—21no—
434C42—1722no—
435C42C2×C22⋊D4312yes—
436C42C2×C22⋊D4312yes—
437C23—21no—
438C23—21no—
439C23—24no—
440C23—41no—
441C23—41no—
442C23—44no—
443C23—82no—
444C23—82no—
445C23#1306335112yes—
446C23C22×C22⋊D4311yescharacteristic
447Q8—44no—
448Q8—44no—
449D4—44no—
450D4—44no—
451D4—44no—
452D4—48no—
453D4—44no—
454D4—44no—
455D4—82no—
456D4—82no—
457D4—82no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—24no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—48no—
470C2×C4—48no—
471C2×C4—44no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—862no—
475C2×C4—1721no—
476C2×C4—1721no—
477C2×C4—1721no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4—1721no—
481C2×C4—1721no—
482C2×C4—1721no—
483C2×C4—1721no—
484C2×C4—1721no—
485C2×C4—1721no—
486C2×C4#1306329411yescharacteristic
487C2×C4#1306329411yescharacteristic
488C2×C4#1306329412yes—
489C2×C4#1306335112yes—
490C2×C4C22×C22⋊D4312yes—
491C8—1724no—
492C22—21no—
493C22—21no—
494C22—22no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—44no—
499C22—44no—
500C22—44no—
501C22—81no—
502C22—88no—
503C22C2×#1306329411yescharacteristic
504C22C2×#1306335111yescharacteristic
505C22C2×#1306335111yescharacteristic
506C4—22no—
507C4—22no—
508C4—21no—
509C4—22no—
510C4—21no—
511C4—41no—
512C4—41no—
513C4—44no—
514C4—3441no—
515C4—3441no—
516C4—3441no—
517C4—1722no—
518C2—21no—
519C2—21no—
520C2—42no—
521C2—84no—
522C2#1914382211yescharacteristic
523C2#1914394411yescharacteristic
524C2#1914400111yescharacteristic
subgroupG/H
centerC22C2×#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC43×#3449C2
socleC22×C43C2×#120
hypercenter#3449D43
hypocenterC43#18339
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #19145781C2semidirect
2. #19140293C2semidirect
3. #19133632C2semidirect
4. #19133615C2semidirect
5. #19133598C2semidirect
6. #19133581C2semidirect
7. #19133103C2semidirect
8. #19132929C2semidirect
10. C2×#13063317C22semidirect
13. #14583215C22semidirect
14. #14583210C22semidirect
16. #14582956C22semidirect
17. #14582838C22semidirect
19. #14582829C22semidirect
25. #14582745C22semidirect
26. #14582633C22semidirect
27. #14582633C22semidirect
28. #14582625C22semidirect
303. C43#18339semidirect

Maximal subgroups

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

subgroupindex
#191457812
#191402932
#191336322
#191336152
#191335982
#191335812
#191331032
#191329292
C43×#34492
#1833943