Finite Group Databasebeta

← #25081988

Subgroups — #25081988

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#19145517C211yesmaximal, characteristic, complemented
2#19144411C211yesmaximal, characteristic, complemented
3#19144044C211yesmaximal, characteristic
4#19143704C211yesmaximal, characteristic, complemented
5#19134028C212yesmaximal, complemented
6#19134021C212yesmaximal, complemented
7#19133942C212yesmaximal, complemented
8#19133935C212yesmaximal, complemented
9#19133367C211yesmaximal, characteristic, complemented
10C2×#14582646C211yesmaximal, characteristic, complemented
11C43×#1547C211yesmaximal, characteristic, complemented
12C2×#13063345—21no—
13C2×#13063325C2211yescharacteristic
14C4×#10621898C2211yescharacteristic
15#14583271C2212yes—
16#14583251C2212yes—
17#14583195—21no—
18#14583190—21no—
19#14583185C2212yes—
20#14583180C2212yes—
21#14583118—21no—
22#14583111—21no—
23#14583106C2211yescharacteristic
24#14583104—21no—
25#14583104—21no—
26#14583101C2211yescharacteristic
27#14583096C2211yescharacteristic
28#14583091C2211yescharacteristic
29#14583037—22no—
30#14583023C2212yes—
31#14582964C2212yes—
32C8×C22⋊D43—22no—
33#14582952C2211yescharacteristic
34#14582951—21no—
35#14582941—21no—
36C2×C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊C8×D43—21no—
38#14582901—21no—
39#14582895—21no—
40#14582649C2212yes—
41#14582649C2212yes—
42#14582646C2212yes—
43#14582646C2212yes—
44C43×#532C2211yescharacteristic
45C43×#423C2211yescharacteristic
46C2×C4⋊C8×C43C2211yescharacteristic
47C43×#332C2212yes—
48C43×#331C2212yes—
49C2×#10621898D411yescharacteristic
50C22×Dic86—21no—
51#13063345—44no—
52C2×#10621885—21no—
53C2×#10621883—21no—
54C2×#10621883—22no—
55C2×#10621883—22no—
56C2×#10621884—21no—
57C2×#10621882—21no—
58C22×C43⋊C8—21no—
59C2×C8×D43—22no—
60#13063325—21no—
61#13063325—21no—
62#13063325—21no—
63#13063325C2312yes—
64C4×Dic86D411yescharacteristic
65C4×Dic86C2311yescharacteristic
66C4×D172D411yescharacteristic
67C4×D172C2311yescharacteristic
68C4×C22⋊D43—21no—
69C4×C22⋊D43—21no—
70#13063284D411yescharacteristic
71#13063282—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C42×D43—21no—
75#13063259—22no—
76#13063257—22no—
77C4⋊(C43⋊C8)—21no—
78C4⋊(C43⋊C8)D411yescharacteristic
79C4⋊(C43⋊C8)D411yescharacteristic
80C4⋊(C43⋊C8)C2311yescharacteristic
81C4⋊(C43⋊C8)C2311yescharacteristic
82Dic43⋊C8—22no—
83#13063250—22no—
84#13063249—21no—
85#13063249—21no—
86#13063248—22no—
87#13063248—22no—
88#13063247—22no—
89#13063246—21no—
90#13063246—21no—
91C22⋊(C43⋊C8)D412yes—
92(C2×D43)⋊C8—22no—
93C4×C43⋊C8C2312yes—
94C8×Dic43—22no—
95C2×#41×C43—21no—
96C2×M16×C43—21no—
97C22×C8×C43—21no—
98C4⋊Q8×C43C2311yescharacteristic
99#127×C43C2311yescharacteristic
100#124×C43—21no—
101#121×C43—21no—
102#121×C43—21no—
103C4×D4×C43—21no—
104C4×D4×C43—21no—
105C2×C42×C43C2311yescharacteristic
106C4⋊C8×C43—21no—
107C4⋊C8×C43—21no—
108C4⋊C8×C43C2312yes—
109C4⋊C8×C43C2312yes—
110#41×C43—42no—
111#41×C43—42no—
112C2×Q8×C43—21no—
113C2×D4×C43—21no—
114C2×D4×C43—21no—
115C2×D4×C43—21no—
116C2×D4×C43—41no—
117C22×C4×C43—41no—
118C22×C4×C43C2×D411yescharacteristic
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43#4111yescharacteristic
121C2×C22⋊D43—21no—
122C22×Dic43—41no—
123#10621898—22no—
124#10621898SD1614yescomplemented
125C2×D172C2×D411yescharacteristic
126C2×C4×D43—21no—
127C2×C4×D43—21no—
128C2×C4×D43—21no—
129C2×Dic86—22no—
130C2×Dic86—41no—
131C2×Dic86—81no—
132C2×Dic86—81no—
133C2×Dic86C2×D411yescharacteristic
134M16×C43—42no—
135C2×C8×C43—22no—
136C2×C8×C43—22no—
137C2×C8×C43—81no—
138C4⋊C4×C43—21no—
139C4⋊C4×C43—21no—
140C22⋊C4×C43—41no—
141C22⋊C4×C43—41no—
142C42×C43C2×D411yescharacteristic
143C42×C43C2×D411yescharacteristic
144C42×C43#4111yescharacteristic
145C42×C43C2411yescharacteristic
146C22⋊Dic43—21no—
147#10621885—42no—
148#10621884—42no—
149#10621883—42no—
150#10621883—82no—
151#10621883—82no—
152#10621882—42no—
153(C2×D43)⋊C4—21no—
154(C2×D43)⋊C4—21no—
155C4⋊Dic43—22no—
156C4⋊Dic43—22no—
157C4⋊Dic43—41no—
158C4⋊Dic43—41no—
159C4⋊Dic43C2×D411yescharacteristic
160C4⋊Dic43C2×D411yescharacteristic
161Dic43⋊C4—21no—
162Dic43⋊C4—21no—
163C4×Dic43—21no—
164C4×Dic43—21no—
165C4×Dic43—21no—
166C2×C43⋊C8—21no—
167C2×C43⋊C8—21no—
168C2×C43⋊C8—42no—
169C2×C43⋊C8C2×D412yes—
170C2×C43⋊C8C2×D412yes—
171C8×D43—82no—
172C23×C43—41no—
173C23×C43#12111yescharacteristic
174C22×D43—21no—
175Q8×C43—41no—
176Q8×C43—41no—
177D4×C43—41no—
178D4×C43—41no—
179D4×C43—41no—
180D4×C43—41no—
181D4×C43—81no—
182D4×C43—82no—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—82no—
188C2×C4×C43#12111yescharacteristic
189C2×C4×C43#12111yescharacteristic
190C2×C4×C43#12111yescharacteristic
191C2×C4×C43C2×SD1612yes—
192C2×C4×C43#13512yes—
193C2×C4×C43C22×D411yescharacteristic
194C2×C4×C43C22×D411yescharacteristic
195C2×C4×C43C2×#4111yescharacteristic
196C22⋊D43—24no—
197C2×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—42no—
201C2×Dic43—82no—
202D172—21no—
203D172C2×SD1612yes—
204C4×D43—24no—
205C4×D43—41no—
206C4×D43—41no—
207C4×D43—81no—
208Dic86—21no—
209Dic86—42no—
210Dic86—42no—
211Dic86—82no—
212Dic86C2×SD1612yes—
213C8×C43—42no—
214C8×C43—42no—
215C43⋊C8—22no—
216C43⋊C8—22no—
217C43⋊C8—41no—
218C43⋊C8—41no—
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—81no—
234C4×C43#46512yes—
235C4×C43C22×SD1611yescharacteristic
236C4×C43C2×#13511yescharacteristic
237C4×C43#57611yescharacteristic
238C4×C43#57711yescharacteristic
239Dic43—22no—
240Dic43—41no—
241Dic43—41no—
242Dic43—82no—
243#3206—431no—
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#1547D4311yescharacteristic, complemented
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⋊Q8—431no—
263C4×#41—431no—
264#492—432no—
265#487—432no—
266#477—861no—
267#476—861no—
268#475—432no—
269#474—432no—
270#464—861no—
271#463—861no—
272#462—431no—
273#461—431no—
274#461—861no—
275#461—861no—
276#460—431no—
277#459—431no—
278#448—862no—
279C8×Q8—432no—
280C8×D4—432no—
281C8×D4—862no—
282#431—431no—
283#431—861no—
284#428—861no—
285#423C2×D4311yescharacteristic
286C2×C4⋊C8—431no—
287C2×C4⋊C8—861no—
288C2×C4⋊C8C2×D4311yescharacteristic
289#417—861no—
290#416—861no—
291#334—432no—
292#334—432no—
293#332—432no—
294#332—432no—
295#332C2×D4312yes—
296#331C2×D4312yes—
297C43#1940811yescharacteristic, complemented, Sylow
298C2×#41—21no—
299C2×#41—431no—
300C22×Q8—861no—
301#135—1724no—
302C2×Q16—861no—
303C2×SD16—862no—
304C2×SD16—862no—
305C2×SD16—861no—
306C2×SD16—861no—
307C2×D8—861no—
308C2×M16—21no—
309C22×C8—21no—
310C22×C8—862no—
311C22×C8—861no—
312C4⋊Q8—432no—
313C4⋊Q8—861no—
314C4⋊Q8—861no—
315C4⋊Q8—861no—
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—861no—
332C2×C4⋊C4—861no—
333C2×C42—861no—
334C2×C42C22×D4311yescharacteristic
335#107—862no—
336#106—862no—
337C4⋊C8—21no—
338C4⋊C8—21no—
339C4⋊C8—431no—
340C4⋊C8—431no—
341C4⋊C8—431no—
342C4⋊C8—431no—
343C4⋊C8—862no—
344C4⋊C8—861no—
345C4⋊C8C22×D4312yes—
346C4⋊C8C22×D4312yes—
347#103—862no—
348#103—862no—
349#103—861no—
350#103—861no—
351#103—862no—
352#102—861no—
353#102—861no—
354#102—862no—
355C22⋊C8—432no—
356C22⋊C8—862no—
357C4×C8—432no—
358C4×C8—862no—
359#41—42no—
360#41—42no—
361#41—434no—
362#41—862no—
363C2×Q8—21no—
364C2×Q8—431no—
365C2×Q8—862no—
366C2×Q8—3441no—
367C2×Q8—3441no—
368C2×Q8—1721no—
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—41no—
373C2×D4—431no—
374C2×D4—861no—
375C22×C4—41no—
376C22×C4—861no—
377C22×C4—861no—
378C22×C4—861no—
379C22×C4—1721no—
380C22×C4#1062189811yescharacteristic
381C22×C4D4×D4311yescharacteristic
382C22×C4D4×D4311yescharacteristic
383Q16—1722no—
384SD16—3442no—
385SD16—3442no—
386SD16—1722no—
387SD16—1722no—
388D8—1722no—
389M16—42no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—81no—
393C2×C8—432no—
394C2×C8—432no—
395C2×C8—861no—
396C2×C8—861no—
397C2×C8—3442no—
398C2×C8—1722no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—431no—
402C4⋊C4—431no—
403C4⋊C4—861no—
404C4⋊C4—861no—
405C4⋊C4—862no—
406C4⋊C4—862no—
407C4⋊C4—1721no—
408C4⋊C4—1721no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—861no—
412C22⋊C4—861no—
413C22⋊C4—861no—
414C42—861no—
415C42—861no—
416C42—861no—
417C42#1062189811yescharacteristic
418C42D4×D4311yescharacteristic
419C42D4×D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—41no—
422C23—861no—
423C23#1306329811yescharacteristic
424Q8—41no—
425Q8—41no—
426Q8—432no—
427Q8—861no—
428Q8—3442no—
429Q8—1722no—
430Q8—1722no—
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—82no—
445C2×C4—861no—
446C2×C4—864no—
447C2×C4—861no—
448C2×C4—861no—
449C2×C4—3441no—
450C2×C4—3442no—
451C2×C4—1722no—
452C2×C4—1721no—
453C2×C4—1721no—
454C2×C4#1306329811yescharacteristic
455C2×C4#1306329811yescharacteristic
456C2×C4#1306329811yescharacteristic
457C2×C4SD16×D4312yes—
458C2×C4#1306334412yes—
459C2×C4C2×D4×D4311yescharacteristic
460C2×C4C2×D4×D4311yescharacteristic
461C2×C4C2×#1062189811yescharacteristic
462C8—42no—
463C8—42no—
464C8—862no—
465C8—862no—
466C8—1721no—
467C8—1721no—
468C22—21no—
469C22—21no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22—862no—
474C22—1721no—
475C22—1721no—
476C22#1458312712yes—
477C22C2×#1306329811yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—81no—
482C4—862no—
483C4—3442no—
484C4—1721no—
485C4—1721no—
486C4#1458312712yes—
487C4C2×SD16×D4311yescharacteristic
488C4C2×#1306334411yescharacteristic
489C4#1458370311yescharacteristic
490C4#1458370811yescharacteristic
491C2—22no—
492C2—161no—
493C2—1722no—
494C2#1914413311yescharacteristic
495C2C2×#1458312711yescharacteristic
496C2#1914433511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1547C2
socleC22×C43C2×#121
prime radical#19144044C2
hypercenter#1547D43
hypocenterC43#19408
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1547

Complements

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

NH ≅ G/Ntype
1. #19145517C2semidirect
2. #19144411C2semidirect
4. #19143704C2semidirect
5. #19134028C2semidirect
6. #19134021C2semidirect
7. #19133942C2semidirect
8. #19133935C2semidirect
9. #19133367C2semidirect
10. C2×#14582646C2semidirect
11. C43×#1547C2semidirect
124. #10621898SD16semidirect
252. #1547D43semidirect
297. C43#19408semidirect

Maximal subgroups

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

subgroupindex
#191455172
#191444112
#191440442
#191437042
#191340282
#191340212
#191339422
#191339352
#191333672
C2×#145826462
C43×#15472
#1940843