Finite Group Databasebeta

← #25081987

Subgroups — #25081987

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#19144410C211yesmaximal, characteristic, complemented
3#19143706C211yesmaximal, characteristic, complemented
4#19134027C212yesmaximal, complemented
5#19134020C212yesmaximal, complemented
6#19133941C212yesmaximal, complemented
7#19133934C212yesmaximal, complemented
8#19133365C211yesmaximal, characteristic, complemented
9#19133272C211yesmaximal, characteristic, complemented
10C2×#14582644C211yesmaximal, characteristic, complemented
11C43×#3035C211yesmaximal, characteristic
12C2×#13063325C2211yescharacteristic
13#14583271C2212yes—
14#14583251C2212yes—
15#14583194—21no—
16#14583189—21no—
17#14583184C2212yes—
18#14583179C2212yes—
19#14583104—21no—
20#14583104—21no—
21#14583037—22no—
22Q8×C43⋊C8C2212yes—
23D4×C43⋊C8—22no—
24D4×C43⋊C8C2212yes—
25#14582952—21no—
26#14582952C2211yescharacteristic
27#14582942—21no—
28#14582923C2211yescharacteristic
29C2×C4⋊(C43⋊C8)—21no—
30C2×C4⋊(C43⋊C8)C2211yescharacteristic
31#14582900—21no—
32#14582649C2212yes—
33#14582649C2212yes—
34#14582645C2212yes—
35#14582644C2212yes—
36#14582644C2212yes—
37#14582643C2212yes—
38C2×#135×C43—21no—
39C43×#532C2211yescharacteristic
40C4×#41×C43C2211yescharacteristic
41C43×#464—21no—
42C43×#463—21no—
43C43×#462C2211yescharacteristic
44C43×#461C2211yescharacteristic
45C43×#460C2211yescharacteristic
46C43×#459C2211yescharacteristic
47C2×C4⋊C8×C43C2211yescharacteristic
48C43×#416—21no—
49C22×Dic86—21no—
50C2×#10621883—22no—
51C2×#10621883—22no—
52C2×#10621877—21no—
53C22×C43⋊C8—21no—
54C22×C43⋊C8—22no—
55#13063325—21no—
56#13063325—21no—
57#13063325—21no—
58#13063325C2312yes—
59C2×C4⋊Dic43—21no—
60C2×C4⋊Dic43—21no—
61#13063258—22no—
62#13063256—22no—
63C4⋊(C43⋊C8)—21no—
64C4⋊(C43⋊C8)—21no—
65C4⋊(C43⋊C8)—22no—
66C4⋊(C43⋊C8)D411yescharacteristic
67C4⋊(C43⋊C8)D411yescharacteristic
68C4⋊(C43⋊C8)C2312yes—
69C4⋊(C43⋊C8)C2312yes—
70#13063249—22no—
71#13063248—22no—
72#13063248—22no—
73#13063246—22no—
74C22⋊(C43⋊C8)—22no—
75C22⋊(C43⋊C8)D412yes—
76C4×C43⋊C8—22no—
77C4×C43⋊C8C2312yes—
78C2×#41×C43—21no—
79C2×#41×C43D411yescharacteristic
80#135×C43—44no—
81C2×Q16×C43—21no—
82C2×SD16×C43—21no—
83C2×SD16×C43—21no—
84C2×D8×C43—21no—
85C22×C8×C43—21no—
86C4⋊Q8×C43C2311yescharacteristic
87#127×C43C2311yescharacteristic
88#124×C43—21no—
89#121×C43—21no—
90#121×C43—21no—
91C4×Q8×C43D411yescharacteristic
92C4×Q8×C43C2311yescharacteristic
93C4×D4×C43—21no—
94C4×D4×C43—21no—
95C4×D4×C43—21no—
96C4×D4×C43—21no—
97C4×D4×C43D411yescharacteristic
98C4×D4×C43C2311yescharacteristic
99#117×C43—21no—
100#117×C43D411yescharacteristic
101C2×C42×C43—21no—
102C2×C42×C43C2311yescharacteristic
103C4⋊C8×C43—21no—
104C4⋊C8×C43C2311yescharacteristic
105C4⋊C8×C43C2311yescharacteristic
106#103×C43—21no—
107#103×C43—21no—
108#102×C43—21no—
109#102×C43—21no—
110#41×C43—22no—
111#41×C43—42no—
112#41×C43—42no—
113#41×C43SD1614yescomplemented
114C2×Q8×C43—21no—
115C2×Q8×C43C2×D411yescharacteristic
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—41no—
121C2×D4×C43C2×D411yescharacteristic
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—21no—
125C22×C4×C43—41no—
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43#4111yescharacteristic
129C22×Dic43—41no—
130C2×Dic86—22no—
131C2×Dic86—41no—
132C2×Dic86—81no—
133C2×Dic86—81no—
134Q16×C43—42no—
135SD16×C43—42no—
136SD16×C43—42no—
137D8×C43—42no—
138C2×C8×C43—21no—
139C2×C8×C43—21no—
140C2×C8×C43—42no—
141C4⋊C4×C43—21no—
142C4⋊C4×C43—21no—
143C4⋊C4×C43—21no—
144C4⋊C4×C43—21no—
145C4⋊C4×C43C2×D411yescharacteristic
146C4⋊C4×C43C2×D411yescharacteristic
147C22⋊C4×C43—21no—
148C22⋊C4×C43—21no—
149C22⋊C4×C43—21no—
150C22⋊C4×C43—41no—
151C22⋊C4×C43—41no—
152C42×C43—21no—
153C42×C43—21no—
154C42×C43—21no—
155C42×C43C2×D411yescharacteristic
156C42×C43C2×D411yescharacteristic
157C42×C43#4111yescharacteristic
158C42×C43C2411yescharacteristic
159#10621883—82no—
160#10621883—82no—
161C4⋊Dic43—22no—
162C4⋊Dic43—22no—
163C4⋊Dic43—41no—
164C4⋊Dic43—41no—
165#10621877—42no—
166C2×C43⋊C8—22no—
167C2×C43⋊C8—22no—
168C2×C43⋊C8—82no—
169C2×C43⋊C8—81no—
170C2×C43⋊C8C2×D412yes—
171C2×C43⋊C8C2×D412yes—
172C23×C43—21no—
173C23×C43—41no—
174C23×C43#12111yescharacteristic
175Q8×C43—21no—
176Q8×C43—41no—
177Q8×C43—41no—
178Q8×C43C2×SD1612yes—
179D4×C43—24no—
180D4×C43—21no—
181D4×C43—41no—
182D4×C43—41no—
183D4×C43—41no—
184D4×C43—41no—
185D4×C43—81no—
186D4×C43—82no—
187D4×C43C2×SD1612yes—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—24no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—81no—
199C2×C4×C43—82no—
200C2×C4×C43#12111yescharacteristic
201C2×C4×C43#12111yescharacteristic
202C2×C4×C43#12111yescharacteristic
203C2×C4×C43C2×SD1612yes—
204C2×C4×C43#13512yes—
205C2×C4×C43C22×D411yescharacteristic
206C2×C4×C43C22×D411yescharacteristic
207C2×C4×C43C2×#4111yescharacteristic
208C2×Dic43—42no—
209C2×Dic43—82no—
210Dic86—42no—
211Dic86—42no—
212Dic86—82no—
213C8×C43—41no—
214C8×C43—41no—
215C43⋊C8—22no—
216C43⋊C8—22no—
217C43⋊C8—42no—
218C43⋊C8—42no—
219#19408—431nomaximal, Sylow
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—22no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43—81no—
226C22×C43—81no—
227C22×C43—81no—
228C22×C43#46512yes—
229C22×C43C2×#12111yescharacteristic
230C4×C43—21no—
231C4×C43—22no—
232C4×C43—21no—
233C4×C43—21no—
234C4×C43—41no—
235C4×C43—41no—
236C4×C43—81no—
237C4×C43#46512yes—
238C4×C43C22×SD1611yescharacteristic
239C4×C43C2×#13511yescharacteristic
240C4×C43#57611yescharacteristic
241C4×C43#57711yescharacteristic
242Dic43—82no—
243#3206—431no—
244#3079—431no—
245#3035D4311yescharacteristic
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—42no—
256C2×C43—161no—
257C2×C43#304511yescharacteristic
258C2×C43C2×#46511yescharacteristic
259C2×C43#306911yescharacteristic
260C2×#135—21no—
261#532C2×D4311yescharacteristic
262C2×C4⋊Q8—431no—
263C4×#41C2×D4311yescharacteristic
264#492—432no—
265#487—432no—
266#477—861no—
267#476—861no—
268#475—432no—
269#474—432no—
270#464—21no—
271#463—21no—
272#462C2×D4311yescharacteristic
273#461—861no—
274#461—861no—
275#461C2×D4311yescharacteristic
276#460C2×D4311yescharacteristic
277#459C2×D4311yescharacteristic
278#448—862no—
279C8×Q8—432no—
280C8×D4—432no—
281C8×D4—862no—
282#431—431no—
283#431—861no—
284#428—861no—
285#423—431no—
286C2×C4⋊C8—431no—
287C2×C4⋊C8—861no—
288C2×C4⋊C8C2×D4311yescharacteristic
289#417—861no—
290#416—21no—
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×#41C22⋊D4311yescharacteristic
300C22×Q8—861no—
301#135—44no—
302C2×Q16—21no—
303C2×SD16—21no—
304C2×SD16—21no—
305C2×SD16—862no—
306C2×SD16—862no—
307C2×D8—21no—
308C2×M16—861no—
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×Q8C22⋊D4311yescharacteristic
322C4×Q8C22×D4311yescharacteristic
323C4×D4—21no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4C22⋊D4311yescharacteristic
328C4×D4C22×D4311yescharacteristic
329#117—21no—
330#117C22⋊D4311yescharacteristic
331C2×C4⋊C4—861no—
332C2×C4⋊C4—861no—
333C2×C42—21no—
334C2×C42C22×D4311yescharacteristic
335#107—862no—
336#106—862no—
337C4⋊C8—21no—
338C4⋊C8—431no—
339C4⋊C8—431no—
340C4⋊C8—432no—
341C4⋊C8—432no—
342C4⋊C8—862no—
343C4⋊C8—861no—
344C4⋊C8—861no—
345C4⋊C8C22×D4311yescharacteristic
346C4⋊C8C22×D4311yescharacteristic
347#103—21no—
348#103—21no—
349#103—862no—
350#103—862no—
351#103—862no—
352#102—21no—
353#102—21no—
354#102—862no—
355C22⋊C8—432no—
356C22⋊C8—862no—
357C4×C8—432no—
358C4×C8—862no—
359#41—22no—
360#41—42no—
361#41—42no—
362#41#1062188314yescomplemented
363C2×Q8—21no—
364C2×Q8—862no—
365C2×Q8—3441no—
366C2×Q8—3441no—
367C2×Q8—1721no—
368C2×Q8C2×C22⋊D4311yescharacteristic
369C2×D4—21no—
370C2×D4—21no—
371C2×D4—21no—
372C2×D4—21no—
373C2×D4—41no—
374C2×D4C2×C22⋊D4311yescharacteristic
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—1721no—
380C22×C4D4×D4311yescharacteristic
381C22×C4#1062190011yescharacteristic
382C22×C4C2×C22⋊D4311yescharacteristic
383Q16—42no—
384SD16—42no—
385SD16—42no—
386SD16—3442no—
387SD16—3442no—
388D8—42no—
389M16—1722no—
390C2×C8—21no—
391C2×C8—21no—
392C2×C8—42no—
393C2×C8—432no—
394C2×C8—432no—
395C2×C8—862no—
396C2×C8—862no—
397C2×C8—3442no—
398C2×C8—3441no—
399C4⋊C4—21no—
400C4⋊C4—21no—
401C4⋊C4—21no—
402C4⋊C4—21no—
403C4⋊C4—862no—
404C4⋊C4—862no—
405C4⋊C4—1721no—
406C4⋊C4—1721no—
407C4⋊C4C2×C22⋊D4311yescharacteristic
408C4⋊C4C2×C22⋊D4311yescharacteristic
409C22⋊C4—21no—
410C22⋊C4—21no—
411C22⋊C4—21no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42D4×D4311yescharacteristic
418C42#1062190011yescharacteristic
419C42C2×C22⋊D4311yescharacteristic
420C42C23×D4311yescharacteristic
421C23—21no—
422C23—41no—
423C23#1306329711yescharacteristic
424Q8—21no—
425Q8—41no—
426Q8—41no—
427Q8—3442no—
428Q8—1722no—
429Q8—1722no—
430Q8C2×#1062188312yes—
431D4—24no—
432D4—21no—
433D4—41no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—81no—
438D4—82no—
439D4C2×#1062188312yes—
440C2×C4—21no—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—81no—
451C2×C4—82no—
452C2×C4—3442no—
453C2×C4—1722no—
454C2×C4#1306329711yescharacteristic
455C2×C4#1306329711yescharacteristic
456C2×C4#1306329711yescharacteristic
457C2×C4C2×#1062188312yes—
458C2×C4#1306334512yes—
459C2×C4C2×D4×D4311yescharacteristic
460C2×C4C22×C22⋊D4311yescharacteristic
461C2×C4C2×#1062190011yescharacteristic
462C8—41no—
463C8—41no—
464C8—862no—
465C8—862no—
466C8—1722no—
467C8—1722no—
468C22—21no—
469C22—21no—
470C22—22no—
471C22—41no—
472C22—41no—
473C22—81no—
474C22—81no—
475C22—81no—
476C22#1458312612yes—
477C22C2×#1306329711yescharacteristic
478C4—21no—
479C4—21no—
480C4—21no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—81no—
485C4—3442no—
486C4#1458312612yes—
487C4C22×#1062188311yescharacteristic
488C4C2×#1306334511yescharacteristic
489C4#1458370111yescharacteristic
490C4#1458370611yescharacteristic
491C2—22no—
492C2—42no—
493C2—161no—
494C2#1914413211yescharacteristic
495C2C2×#1458312611yescharacteristic
496C2#1914433411yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
Fitting, prime radicalC43×#3035C2
socleC22×C43C2×#121
hypercenter#3035D43
hypocenterC43#19408
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3035

Complements

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

NH ≅ G/Ntype
1. #19145517C2semidirect
2. #19144410C2semidirect
3. #19143706C2semidirect
4. #19134027C2semidirect
5. #19134020C2semidirect
6. #19133941C2semidirect
7. #19133934C2semidirect
8. #19133365C2semidirect
9. #19133272C2semidirect
10. C2×#14582644C2semidirect
113. #41×C43SD16semidirect
297. C43#19408semidirect
362. #41#10621883semidirect

Maximal subgroups

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

subgroupindex
#191455172
#191444102
#191437062
#191340272
#191340202
#191339412
#191339342
#191333652
#191332722
C2×#145826442
C43×#30352
#1940843