Finite Group Databasebeta

← #11886892

Subgroups — #11886892

Order 1152.

1428 conjugacy classes of subgroups; only the 217 normal subgroups are shown.

normal subgroups only

This group has 1428 conjugacy classes of subgroups — too many to draw. Only its 217 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596306C212yesmaximal, complemented
2#10596245C212yesmaximal, complemented
3C32×#453C211yesmaximal, characteristic, complemented
4#10592898C212yesmaximal, complemented
5#10592776C211yesmaximal, characteristic, complemented
6#10592772C211yesmaximal, characteristic, complemented
7#10592523C212yesmaximal, complemented
8#10592521C212yesmaximal, complemented
9#10592448C212yesmaximal, complemented
10#80282—34nomaximal
11C32×H(5,𝔽2)C2211yescharacteristic, complemented
12#64366C2212yescomplemented
13#64361C2211yescharacteristic, complemented
14C32×AGL(1,ℤ/8)C2212yescomplemented
15C32×#127C2211yescharacteristic, complemented
16#64159—22no—
17#64159C2212yes—
18#64158—22no—
19#64158C2212yescomplemented
20#64157C2212yescomplemented
21#64141—22no—
22#64141C2212yescomplemented
23C2×#3753—22no—
24C2×#3753C2212yescomplemented
25C2×#3753C2212yescomplemented
26#64125—22no—
27#64123—22no—
28#64120—22no—
29D8×C3⋊D3—22no—
30#64117C2212yescomplemented
31#64116C2212yescomplemented
32#64083C2211yescharacteristic, complemented
33C32×#104C2212yescomplemented
34C32×#100C2211yescharacteristic, complemented
35#63660C2211yescharacteristic, complemented
36#63650C2212yescomplemented
37#63649C2212yescomplemented
38#63632C2212yescomplemented
39C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
40#5835—38no—
41#5774—38no—
42C3×#453D314yescomplemented
43#5199—38no—
44#5077—34no—
45#5073—34no—
46#4824—38no—
47#4822—38no—
48#4749—38no—
49C32×#41—22no—
50C32×#41C2312yes—
51C2×C32×D4—22no—
52C2×C32×D4—41no—
53C2×C32×D4—41no—
54C2×C32×D4C2311yescharacteristic
55C2×C32×D4C2311yescharacteristic
56C2×#638—41no—
57#3832—22no—
58#3830—22no—
59D4×C3⋊D3—22no—
60D4×C3⋊D3—22no—
61D4×C3⋊D3—42no—
62#3828—22no—
63#3828C2312yes—
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)—41no—
66C2×C4⋊(C3⋊D3)C2312yes—
67C32×SD16—22no—
68C32×D8—22no—
69C32×M16C2312yes—
70C32×C42C2311yescharacteristic
71#3756D412yescomplemented
72#3755—22no—
73#3755D412yescomplemented
74#3754—22no—
75#3754D412yescomplemented
76#3753—22no—
77#3753—22no—
78#3753—22no—
79#3753—22no—
80#3753—22no—
81#3753—22no—
82#3753D412yescomplemented
83#3748—22no—
84#3748C2312yes—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87#3745—22no—
88#3744—22no—
89#3743—22no—
90C8×C3⋊D3—22no—
91#3292—91noSylow
92C3×H(5,𝔽2)C2×D314yescomplemented
93#1009—38no—
94#1004—34no—
95C3×AGL(1,ℤ/8)C2×D318yescomplemented
96C3×#127C2×D314yescomplemented
97#950—38no—
98#950—68no—
99#949—38no—
100#949—68no—
101#948—38no—
102#932—38no—
103#932—68no—
104C2×#213—38no—
105C2×#213—38no—
106C2×#213—68no—
107#916—68no—
108#914—68no—
109#911—68no—
110D3×D8—68no—
111#908—38no—
112#907—38no—
113#874—34no—
114C3×#104C2×D318yescomplemented
115C3×#100C2×D314yescomplemented
116#833—34no—
117#823—38no—
118#822—38no—
119#805—38no—
120C4×C3⋊C8—34no—
121C23×C32—21no—
122C23×C32—21no—
123C23×C32—41no—
124C22×C3⋊D3—22no—
125C22×C3⋊D3—41no—
126C22×C3⋊D3—42no—
127C32×Q8C2×D412yes—
128C32×D4—22no—
129C32×D4—22no—
130C32×D4—22no—
131C32×D4—42no—
132C32×D4—82no—
133C32×D4C2×D412yes—
134C2×C32×C4—21no—
135C2×C32×C4—22no—
136C2×C32×C4—41no—
137C2×C32×C4C2411yescharacteristic
138#638—22no—
139#638—42no—
140#638—42no—
141C2×C3⋊Dic3—41no—
142C4⋊(C3⋊D3)—22no—
143C4⋊(C3⋊D3)—22no—
144C4⋊(C3⋊D3)—42no—
145C4⋊(C3⋊D3)—82no—
146C4⋊(C3⋊D3)C2×D412yes—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—42no—
149#634C2×D412yes—
150C32×C8—22no—
151C3⋊(C3⋊C8)—22no—
152C3⋊(C3⋊C8)C2×D412yes—
153C3⋊(C3⋊C8)C2×D412yes—
154#576—92no—
155#576—92no—
156#493—91no—
157#472—92no—
158#472—92no—
159#453—91no—
160#453—92no—
161#453C3⋊D311yescharacteristic, complemented
162#443—92no—
163C3×#41—28no—
164C3×#41C22×D318yes—
165C2×C3×D4—28no—
166C2×C3×D4—44no—
167C2×C3×D4—44no—
168C2×C3×D4C22×D314yes—
169C2×C3×D4C22×D314yes—
170C2×#67—124no—
171#239—68no—
172#237—68no—
173D3×D4—68no—
174D3×D4—68no—
175D3×D4—128no—
176#235—38no—
177#235—68no—
178C2×D12—38no—
179C2×D12—68no—
180C2×D12—124no—
181C3×SD16—28no—
182C3×D8—28no—
183C3×M16C22×D318yes—
184C3×C42C22×D314yes—
185#216—38no—
186#215—38no—
187#215—68no—
188#214—38no—
189#214—68no—
190#213—38no—
191#213—68no—
192#213—68no—
193#213—68no—
194#213—68no—
195#213—68no—
196#213—68no—
197#208—38no—
198#208—68no—
199C2×C3⋊C8—38no—
200C2×C3⋊C8—68no—
201D24—68no—
202#204—68no—
203ΓL(1,𝔽25)—68no—
204D3×C8—68no—
205C22×C32—22no—
206C22×C32—41no—
207C22×C32—41no—
208C22×C32—81no—
209C22×C32—81no—
210C22×C32—161no—
211C22×C32H(5,𝔽2)11yescharacteristic
212C2×C3⋊D3—22no—
213C2×C3⋊D3—42no—
214C2×C3⋊D3—82no—
215C2×C3⋊D3—161no—
216C2×C3⋊D3—162no—
217C32×C4—22no—
218C32×C4—22no—
219C32×C4C22×D412yes—
220C3⋊Dic3—22no—
221H(5,𝔽2)—92no—
222H(5,𝔽2)—91no—
223H(5,𝔽2)C2×C3⋊D311yescharacteristic, complemented
224AGL(1,ℤ/8)—92no—
225AGL(1,ℤ/8)—92no—
226AGL(1,ℤ/8)—92no—
227AGL(1,ℤ/8)—182no—
228AGL(1,ℤ/8)—182no—
229AGL(1,ℤ/8)—182no—
230AGL(1,ℤ/8)—182no—
231AGL(1,ℤ/8)C2×C3⋊D312yescomplemented
232#135—92no—
233#135—182no—
234#135—182no—
235C2×D8—92no—
236C2×D8—92no—
237C2×D8—182no—
238C2×D8—182no—
239#131—92no—
240#131—92no—
241#127—91no—
242#127C2×C3⋊D311yescharacteristic, complemented
243#108—92no—
244#104—92no—
245#104C2×C3⋊D312yescomplemented
246#100—91no—
247#100—92no—
248#100C2×C3⋊D311yescharacteristic, complemented
249C4×C8—91no—
250C23×C3—24no—
251C23×C3—24no—
252C23×C3—44no—
253C22×D3—68no—
254C22×D3—124no—
255C22×D3—128no—
256C3×Q8D3×D418yes—
257C3×D4—28no—
258C3×D4—28no—
259C3×D4—28no—
260C3×D4—48no—
261C3×D4—88no—
262C3×D4D3×D418yes—
263C2×C3×C4—24no—
264C2×C3×C4—28no—
265C2×C3×C4—44no—
266C2×C3×C4C23×D314yes—
267#67—68no—
268#67—128no—
269#67—128no—
270C2×Dic3—124no—
271D12—38no—
272D12—68no—
273D12—68no—
274D12—128no—
275D12—248no—
276C4×D3—68no—
277C4×D3—128no—
278Dic6—38no—
279C3×C8—28no—
280C3⋊C8—38no—
281C3⋊C8—38no—
282C3⋊C8—68no—
283C2×C32—21no—
284C2×C32—42no—
285C2×C32—81no—
286C2×C32—81no—
287C2×C32D4211yescharacteristic
288C3⋊D3—42no—
289C3⋊D3—82no—
290#41—22no—
291#41—92no—
292#41—182no—
293#41—182no—
294#41—182no—
295#41C22×C3⋊D312yes—
296C2×D4—22no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—92no—
300C2×D4—182no—
301C2×D4—182no—
302C2×D4—182no—
303C2×D4—361no—
304C2×D4—362no—
305C2×D4—361no—
306C2×D4C22×C3⋊D311yescharacteristic
307C2×D4C22×C3⋊D311yescharacteristic
308Q16—92no—
309SD16—22no—
310SD16—92no—
311SD16—92no—
312SD16—182no—
313SD16—182no—
314SD16—182no—
315D8—22no—
316D8—92no—
317D8—182no—
318D8—182no—
319D8—182no—
320D8—182no—
321D8—182no—
322D8—182no—
323D8—182no—
324M16—92no—
325M16—182no—
326M16—182no—
327M16C22×C3⋊D312yes—
328C2×C8—92no—
329C2×C8—182no—
330C2×C8—182no—
331C42C22×C3⋊D311yescharacteristic
332C22×C3—28no—
333C22×C3—44no—
334C22×C3—44no—
335C22×C3—84no—
336C22×C3—84no—
337C22×C3—164no—
338C22×C3#100414yes—
339C2×D3—68no—
340C2×D3—128no—
341C2×D3—248no—
342C2×D3—484no—
343C2×D3—488no—
344C3×C4—28no—
345C3×C4—28no—
346C3×C4C2×D3×D418yes—
347Dic3—68no—
348C32#329211yescharacteristic, complemented, Sylow
349C23—21no—
350C23—21no—
351C23—41no—
352C23—182no—
353C23—362no—
354C23—361no—
355Q8—92no—
356Q8D4×C3⋊D312yes—
357D4—22no—
358D4—22no—
359D4—22no—
360D4—42no—
361D4—82no—
362D4—92no—
363D4—182no—
364D4—182no—
365D4—182no—
366D4—362no—
367D4—362no—
368D4—362no—
369D4—722no—
370D4D4×C3⋊D312yes—
371C2×C4—21no—
372C2×C4—22no—
373C2×C4—41no—
374C2×C4—182no—
375C2×C4—362no—
376C2×C4—361no—
377C2×C4C23×C3⋊D311yescharacteristic
378C8—22no—
379C8—92no—
380C8—92no—
381C8—182no—
382C2×C3—24no—
383C2×C3—48no—
384C2×C3—84no—
385C2×C3—84no—
386C2×C3#559014yes—
387D3—128no—
388D3—248no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—81no—
393C22—81no—
394C22—161no—
395C22—182no—
396C22—362no—
397C22—722no—
398C22—1442no—
399C22—1441no—
400C22#6436111yescharacteristic
401C4—22no—
402C4—22no—
403C4—182no—
404C4C2×D4×C3⋊D312yes—
405C3#8028214yescomplemented
406C2—21no—
407C2—42no—
408C2—81no—
409C2—81no—
410C2—362no—
411C2—722no—
412C2#1059606111yescharacteristic
subgroupG/H
centerC2#10596061
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#453C2
socleC2×C32D42
hypercenter#453C3⋊D3
hypocenterC32#3292
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #10596306C2semidirect
2. #10596245C2semidirect
3. C32×#453C2semidirect
4. #10592898C2semidirect
5. #10592776C2semidirect
6. #10592772C2semidirect
7. #10592523C2semidirect
8. #10592521C2semidirect
9. #10592448C2semidirect
11. C32×H(5,𝔽2)C22semidirect
12. #64366C22semidirect
13. #64361C22semidirect
14. C32×AGL(1,ℤ/8)C22semidirect
15. C32×#127C22semidirect
19. #64158C22semidirect
20. #64157C22semidirect
22. #64141C22semidirect
24. C2×#3753C22semidirect
25. C2×#3753C22semidirect
30. #64117C22semidirect
31. #64116C22semidirect
32. #64083C22semidirect
33. C32×#104C22semidirect
34. C32×#100C22semidirect
35. #63660C22semidirect
36. #63650C22semidirect
37. #63649C22semidirect
38. #63632C22semidirect
39. C4×C3⋊(C3⋊C8)C22semidirect
42. C3×#453D3semidirect
71. #3756D4semidirect
73. #3755D4semidirect
75. #3754D4semidirect
82. #3753D4semidirect
92. C3×H(5,𝔽2)C2×D3semidirect
95. C3×AGL(1,ℤ/8)C2×D3semidirect
96. C3×#127C2×D3semidirect
114. C3×#104C2×D3semidirect
115. C3×#100C2×D3semidirect
161. #453C3⋊D3semidirect
223. H(5,𝔽2)C2×C3⋊D3semidirect
231. AGL(1,ℤ/8)C2×C3⋊D3semidirect
242. #127C2×C3⋊D3semidirect
245. #104C2×C3⋊D3semidirect
248. #100C2×C3⋊D3semidirect
348. C32#3292semidirect
405. C3#80282semidirect

Maximal subgroups

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

subgroupindex
#105963062
#105962452
C32×#4532
#105928982
#105927762
#105927722
#105925232
#105925212
#105924482
#802823