Finite Group Databasebeta

← #25081985

Subgroups — #25081985

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144404C211yesmaximal, characteristic, complemented
2#19144044C211yesmaximal, characteristic
3#19143703C211yesmaximal, characteristic, complemented
4#19134022C212yesmaximal, complemented
5#19134015C212yesmaximal, complemented
6#19133940C212yesmaximal, complemented
7#19133933C212yesmaximal, complemented
8#19133366C211yesmaximal, characteristic, complemented
9#19133272C211yesmaximal, characteristic, complemented
10C2×#14582645C211yesmaximal, characteristic, complemented
11C43×#3206C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13C4×#10621898C2211yescharacteristic
14#14583191—21no—
15#14583186—21no—
16#14583181C2212yes—
17#14583176C2212yes—
18#14583118—21no—
19#14583111—21no—
20#14583106C2211yescharacteristic
21#14583101C2211yescharacteristic
22#14583096C2211yescharacteristic
23#14583091C2211yescharacteristic
24C8×Dic86C2212yes—
25C8×D172C2212yes—
26(C22⋊D43)⋊C8—22no—
27#14582951—21no—
28#14582939—21no—
29#14582923C2211yescharacteristic
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31C2×C4⋊(C43⋊C8)C2211yescharacteristic
32C4⋊C8×D43—21no—
33#14582898—21no—
34#14582895—21no—
35#14582650C2212yes—
36#14582650C2212yes—
37#14582645C2212yes—
38#14582645C2212yes—
39#14582645C2212yes—
40#14582643C2212yes—
41C43×#532C2211yescharacteristic
42C2×C4⋊Q8×C43C2211yescharacteristic
43C43×#492C2212yes—
44C43×#487C2212yes—
45C43×#461—21no—
46C43×#461—21no—
47C43×#448—22no—
48C43×#431C2211yescharacteristic
49C2×#10621898D411yescharacteristic
50#13063345—44no—
51C2×#10621885—21no—
52C2×#10621883—21no—
53C2×#10621884—21no—
54C2×#10621882—21no—
55C2×#10621877—21no—
56C22×C43⋊C8—21no—
57C22×C43⋊C8—21no—
58C2×C8×D43—22no—
59C4×Dic86D411yescharacteristic
60C4×Dic86C2311yescharacteristic
61C4×D172D411yescharacteristic
62C4×D172C2311yescharacteristic
63C4×C22⋊D43—21no—
64C4×C22⋊D43—21no—
65#13063284D411yescharacteristic
66#13063282—21no—
67C42×D43—21no—
68#13063258—22no—
69#13063256—22no—
70C4⋊(C43⋊C8)—21no—
71C4⋊(C43⋊C8)—21no—
72C4⋊(C43⋊C8)—21no—
73C4⋊(C43⋊C8)C2311yescharacteristic
74C4⋊(C43⋊C8)C2311yescharacteristic
75C4⋊(C43⋊C8)C2312yes—
76C4⋊(C43⋊C8)C2312yes—
77Dic43⋊C8—22no—
78#13063249—21no—
79#13063249—21no—
80#13063248—22no—
81#13063246—21no—
82#13063246—21no—
83#13063245—22no—
84(C2×D43)⋊C8—22no—
85C8×Dic43—22no—
86C2×#41×C43—21no—
87C22×Q8×C43—21no—
88C2×SD16×C43—22no—
89C2×SD16×C43—22no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43—21no—
92C4⋊Q8×C43—21no—
93C4⋊Q8×C43C2312yes—
94C4⋊Q8×C43C2311yescharacteristic
95#127×C43C2311yescharacteristic
96#124×C43—21no—
97#121×C43—21no—
98#121×C43—21no—
99C4×D4×C43—21no—
100C4×D4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C42×C43C2311yescharacteristic
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43D411yescharacteristic
106#103×C43—22no—
107#103×C43—22no—
108C22⋊C8×C43D412yes—
109C4×C8×C43C2312yes—
110#41×C43—42no—
111#41×C43—42no—
112C2×Q8×C43—22no—
113C2×Q8×C43—21no—
114C2×Q8×C43—41no—
115C2×Q8×C43—81no—
116C2×Q8×C43—81no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—41no—
121C22×C4×C43—41no—
122C22×C4×C43—41no—
123C22×C4×C43C2×D411yescharacteristic
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43#4111yescharacteristic
126C2×C22⋊D43—21no—
127#10621898—22no—
128#10621898SD1614yescomplemented
129C2×D172C2×D411yescharacteristic
130C2×C4×D43—21no—
131C2×C4×D43—21no—
132C2×C4×D43—21no—
133C2×Dic86C2×D411yescharacteristic
134SD16×C43—82no—
135SD16×C43—82no—
136C2×C8×C43C2×D412yes—
137C2×C8×C43C2×D412yes—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—22no—
140C4⋊C4×C43—22no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43—41no—
144C22⋊C4×C43—41no—
145C22⋊C4×C43—41no—
146C42×C43C2×D411yescharacteristic
147C42×C43C2×D411yescharacteristic
148C42×C43#4111yescharacteristic
149C42×C43C2411yescharacteristic
150C22⋊Dic43—21no—
151#10621885—42no—
152#10621884—42no—
153#10621883—42no—
154#10621882—42no—
155(C2×D43)⋊C4—21no—
156(C2×D43)⋊C4—21no—
157C4⋊Dic43C2×D411yescharacteristic
158C4⋊Dic43C2×D411yescharacteristic
159Dic43⋊C4—21no—
160Dic43⋊C4—21no—
161C4×Dic43—21no—
162C4×Dic43—21no—
163C4×Dic43—21no—
164#10621877—42no—
165C2×C43⋊C8—22no—
166C2×C43⋊C8—22no—
167C2×C43⋊C8—21no—
168C2×C43⋊C8—21no—
169C2×C43⋊C8—42no—
170C2×C43⋊C8—81no—
171C8×D43—82no—
172C23×C43—41no—
173C23×C43#12111yescharacteristic
174C22×D43—21no—
175Q8×C43—41no—
176Q8×C43—41no—
177Q8×C43—42no—
178Q8×C43—42no—
179Q8×C43—82no—
180D4×C43—41no—
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—81no—
185D4×C43—82no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—42no—
191C2×C4×C43—82no—
192C2×C4×C43—82no—
193C2×C4×C43#12111yescharacteristic
194C2×C4×C43#12111yescharacteristic
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43C2×SD1612yes—
197C2×C4×C43#13512yes—
198C2×C4×C43C22×D411yescharacteristic
199C2×C4×C43C22×D411yescharacteristic
200C2×C4×C43C2×#4111yescharacteristic
201C22⋊D43—24no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205D172—21no—
206D172C2×SD1612yes—
207C4×D43—24no—
208C4×D43—41no—
209C4×D43—41no—
210C4×D43—81no—
211Dic86—21no—
212Dic86C2×SD1612yes—
213C8×C43—22no—
214C8×C43—22no—
215C43⋊C8—41no—
216C43⋊C8—41no—
217C43⋊C8—42no—
218C43⋊C8—42no—
219#19408—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—81no—
223C22×C43—81no—
224C22×C43—81no—
225C22×C43#46512yes—
226C22×C43C2×#12111yescharacteristic
227C2×D43—22no—
228C2×D43—41no—
229C2×D43—41no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—21no—
233C4×C43—82no—
234C4×C43—81no—
235C4×C43#46512yes—
236C4×C43C22×SD1611yescharacteristic
237C4×C43C2×#13511yescharacteristic
238C4×C43#57611yescharacteristic
239C4×C43#57711yescharacteristic
240Dic43—22no—
241Dic43—41no—
242Dic43—41no—
243#3206D4311yescharacteristic, complemented
244#3079—431no—
245#3035—431no—
246#2988—431no—
247#1680—432no—
248#1679—432no—
249#1666—432no—
250#1665—432no—
251#1570—431no—
252#1547—431no—
253C2×#332—431no—
254C2×C43—22no—
255C2×C43—161no—
256C2×C43#304511yescharacteristic
257C2×C43C2×#46511yescharacteristic
258C2×C43#306911yescharacteristic
259D43—42no—
260C2×#135—861no—
261#532C2×D4311yescharacteristic
262C2×C4⋊Q8C2×D4311yescharacteristic
263C4×#41—431no—
264#492C2×D4312yes—
265#487C2×D4312yes—
266#477—861no—
267#476—861no—
268#475—432no—
269#474—432no—
270#464—861no—
271#463—861no—
272#462—431no—
273#461—21no—
274#461—21no—
275#461—431no—
276#460—431no—
277#459—431no—
278#448—22no—
279C8×Q8—432no—
280C8×D4—432no—
281C8×D4—862no—
282#431—861no—
283#431C2×D4311yescharacteristic
284#428—861no—
285#423—431no—
286C2×C4⋊C8—431no—
287C2×C4⋊C8—431no—
288C2×C4⋊C8—861no—
289#417—861no—
290#416—861no—
291#334—432no—
292#334—432no—
293#332—432no—
294#332—432no—
295#332—432no—
296#331—432no—
297C43#1940811yescharacteristic, complemented, Sylow
298C2×#41—21no—
299C2×#41—431no—
300C22×Q8—21no—
301#135—1724no—
302C2×Q16—861no—
303C2×SD16—22no—
304C2×SD16—22no—
305C2×SD16—861no—
306C2×SD16—861no—
307C2×D8—861no—
308C2×M16—861no—
309C22×C8—861no—
310C22×C8—861no—
311C22×C8—862no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8C22×D4312yes—
316C4⋊Q8C22×D4311yescharacteristic
317#127C22×D4311yescharacteristic
318#124—21no—
319#121—21no—
320#121—21no—
321C4×Q8—431no—
322C4×Q8—431no—
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—431no—
326C4×D4—431no—
327C4×D4—861no—
328C4×D4—861no—
329#117—431no—
330#117—861no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C42—861no—
334C2×C42C22×D4311yescharacteristic
335#107—862no—
336#106—862no—
337C4⋊C8—432no—
338C4⋊C8—432no—
339C4⋊C8—431no—
340C4⋊C8—431no—
341C4⋊C8—862no—
342C4⋊C8—861no—
343C4⋊C8—861no—
344C4⋊C8—861no—
345C4⋊C8C22⋊D4311yescharacteristic
346C4⋊C8C22⋊D4311yescharacteristic
347#103—22no—
348#103—22no—
349#103—862no—
350#103—861no—
351#103—861no—
352#102—862no—
353#102—861no—
354#102—861no—
355C22⋊C8—862no—
356C22⋊C8C22⋊D4312yes—
357C4×C8—862no—
358C4×C8C22×D4312yes—
359#41—42no—
360#41—42no—
361#41—434no—
362#41—862no—
363C2×Q8—21no—
364C2×Q8—22no—
365C2×Q8—41no—
366C2×Q8—81no—
367C2×Q8—81no—
368C2×Q8—431no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4—431no—
374C2×D4—861no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—861no—
378C22×C4—861no—
379C22×C4—861no—
380C22×C4D4×D4311yescharacteristic
381C22×C4#1062190011yescharacteristic
382C22×C4C2×C22⋊D4311yescharacteristic
383Q16—1722no—
384SD16—82no—
385SD16—82no—
386SD16—1722no—
387SD16—1722no—
388D8—1722no—
389M16—1722no—
390C2×C8—862no—
391C2×C8—861no—
392C2×C8—861no—
393C2×C8—862no—
394C2×C8—3442no—
395C2×C8—3441no—
396C2×C8—1722no—
397C2×C8C2×C22⋊D4312yes—
398C2×C8C2×C22⋊D4312yes—
399C4⋊C4—22no—
400C4⋊C4—21no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—431no—
406C4⋊C4—431no—
407C4⋊C4—861no—
408C4⋊C4—861no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—861no—
412C22⋊C4—861no—
413C22⋊C4—861no—
414C42—861no—
415C42—861no—
416C42—861no—
417C42D4×D4311yescharacteristic
418C42#1062190011yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—41no—
422C23—861no—
423C23#1306329611yescharacteristic
424Q8—41no—
425Q8—41no—
426Q8—42no—
427Q8—42no—
428Q8—82no—
429Q8—432no—
430Q8—861no—
431D4—41no—
432D4—41no—
433D4—41no—
434D4—41no—
435D4—81no—
436D4—82no—
437D4—432no—
438D4—864no—
439D4—861no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—82no—
446C2×C4—82no—
447C2×C4—861no—
448C2×C4—864no—
449C2×C4—861no—
450C2×C4—861no—
451C2×C4—3441no—
452C2×C4—1721no—
453C2×C4—1721no—
454C2×C4#1306329611yescharacteristic
455C2×C4#1306329611yescharacteristic
456C2×C4#1306329611yescharacteristic
457C2×C4SD16×D4312yes—
458C2×C4#1306334612yes—
459C2×C4C2×D4×D4311yescharacteristic
460C2×C4C22×C22⋊D4311yescharacteristic
461C2×C4C2×#1062190011yescharacteristic
462C8—22no—
463C8—22no—
464C8—1721no—
465C8—1721no—
466C8—1722no—
467C8—1722no—
468C22—21no—
469C22—21no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—862no—
474C22—1721no—
475C22—1721no—
476C22#1458312512yes—
477C22C2×#1306329611yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—82no—
482C4—81no—
483C4—862no—
484C4—1721no—
485C4—1721no—
486C4#1458312512yes—
487C4C2×SD16×D4311yescharacteristic
488C4C2×#1306334611yescharacteristic
489C4#1458370211yescharacteristic
490C4#1458371011yescharacteristic
491C2—22no—
492C2—161no—
493C2—1722no—
494C2#1914413011yescharacteristic
495C2C2×#1458312511yescharacteristic
496C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#3206C2
socleC22×C43C2×#121
prime radical#19144044C2
hypercenter#3206D43
hypocenterC43#19408
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3206

Complements

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

NH ≅ G/Ntype
1. #19144404C2semidirect
3. #19143703C2semidirect
4. #19134022C2semidirect
5. #19134015C2semidirect
6. #19133940C2semidirect
7. #19133933C2semidirect
8. #19133366C2semidirect
9. #19133272C2semidirect
10. C2×#14582645C2semidirect
11. C43×#3206C2semidirect
128. #10621898SD16semidirect
243. #3206D43semidirect
297. C43#19408semidirect

Maximal subgroups

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

subgroupindex
#191444042
#191440442
#191437032
#191340222
#191340152
#191339402
#191339332
#191333662
#191332722
C2×#145826452
C43×#32062
#1940843