Finite Group Databasebeta

← #11861164

Subgroups — #11861164

Order 1152.

987 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594685C211yesmaximal, characteristic
2#10594670C212yesmaximal, complemented
3C4×#3743C211yesmaximal, characteristic, complemented
4C3×#4700C212yesmaximal, complemented
5#10590922C212yesmaximal, complemented
6#10590920C212yesmaximal, complemented
7#10590914C211yesmaximal, characteristic, complemented
8#10590393C212yesmaximal, complemented
9#10590389C212yesmaximal, complemented
10#79889—32nomaximal
11#64306C2212yes—
12C2×#3743C2211yescharacteristic
13C2×#3743C2211yescharacteristic
14C42×C3⋊D3C2211yescharacteristic
15C3×#904C2212yes—
16C3×#901C2214yescomplemented
17#63822C2212yes—
18#63818C2212yes—
19#63815C2214yescomplemented
20#63811C414yescomplemented
21#63804—24no—
22#63798C414yescomplemented
23D3×ΓL(1,𝔽25)—24no—
24C32×C4×C8C2211yescharacteristic, complemented
25#63642C2211yescharacteristic, complemented
26#63642C2211yescharacteristic, complemented
27C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
28C3×#819C2212yescomplemented
29C3×#805C2214yescomplemented
30#63578C2212yescomplemented
31#63568C2214yescomplemented
32#5768—32no—
33#5750—34no—
34C3×#443—32no—
35#5197—32no—
36#5145—34no—
37#4894—32no—
38#4893—32no—
39#4824—34no—
40D3×#104—34no—
41#4700D312yescomplemented
42C4×ΓL(1,𝔽25)—32no—
43C4×ΓL(1,𝔽25)—61no—
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3C2311yescharacteristic
46C3×#235C2314yes—
47#3811—22no—
48#3805—22no—
49#3802C2×C412yes—
50C4×D32—22no—
51#3798—22no—
52#3797C2×C412yes—
53#3796C2×C414yes—
54C2×C32×C8C2311yescharacteristic
55C2×C32×C8C2311yescharacteristic
56C32×C42C2311yescharacteristic
57C4×C3⋊Dic3—21no—
58C4×C3⋊Dic3C2311yescharacteristic
59C2×C3⋊(C3⋊C8)C2311yescharacteristic
60C2×C3⋊(C3⋊C8)C2311yescharacteristic
61#3743C2×C414yes—
62#3743D414yes—
63C3×#208C2314yes—
64C3×Dic12C2×C412yescomplemented
65C3×D24C2×C412yescomplemented
66C3×#204C2×C414yescomplemented
67C3×ΓL(1,𝔽25)—24no—
68C3×D3×C8—24no—
69#3718C2×C412yescomplemented
70#3715C2×C414yescomplemented
71#3713C2×C412yescomplemented
72#3712—22no—
73#3711—24no—
74#3710—22no—
75D3×C3⋊C8—24no—
76#2956—91noSylow
77D3×#41—34no—
78C3×#135—32no—
79C3×#131—34no—
80#950—34no—
81#948—34no—
82#918—34no—
83#915—34no—
84#914—34no—
85#911—34no—
86#907—34no—
87#907—64no—
88D3×M16—34no—
89D3×M16—64no—
90#904C2×D312yes—
91#901—64no—
92#901C2×D314yescomplemented
93C2×ΓL(1,𝔽25)—32no—
94C2×ΓL(1,𝔽25)—32no—
95C2×ΓL(1,𝔽25)—61no—
96C2×ΓL(1,𝔽25)—61no—
97C2×ΓL(1,𝔽25)—64no—
98C42×D3—32no—
99C42×D3—61no—
100C3×#108—32no—
101C3×#104—34no—
102C3×C4×C8—21no—
103C3×C4×C8C2×D312yescomplemented
104#837—34no—
105#825—34no—
106#822—34no—
107#819C2×D312yescomplemented
108#815—32no—
109#815—32no—
110#815—61no—
111#815—61no—
112#805C2×D314yescomplemented
113C4×C3⋊C8—32no—
114C4×C3⋊C8—61no—
115C22×C3⋊D3#4111yescharacteristic
116C2×D32—22no—
117C2×C32×C4—21no—
118C2×C32×C4C2411yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3#4111yescharacteristic
121C4×C3⋊D3—42no—
122C4×C3⋊D3C22×C412yes—
123C4×C3⋊D3C2×D412yes—
124C3×#67—24no—
125C3×D12C22×C414yes—
126C3×C4×D3—24no—
127C3×Dic6C22×C414yes—
128#627—22no—
129#626—24no—
130#625—22no—
131#624—22no—
132D3×Dic3—24no—
133C32×C8C22×C412yes—
134C32×C8C2×D412yes—
135C3⋊(C3⋊C8)C22×C412yes—
136C3⋊(C3⋊C8)C2×D412yes—
137C3×C3⋊C8—24no—
138#575—91no—
139#568—92no—
140#444—92no—
141#444—92no—
142#443—32no—
143#443—92no—
144#430—91no—
145C2×#104—92no—
146C4×M16—91no—
147C3×#41—34no—
148#239—34no—
149D3×Q8—34no—
150#237—34no—
151#237—64no—
152D3×D4—34no—
153D3×D4—64no—
154#235—64no—
155#235C22×D314yes—
156C2×C4×D3—32no—
157C2×C4×D3—61no—
158C2×C4×D3—64no—
159C2×C4×D3—62no—
160C2×C4×D3—62no—
161C3×Q16—32no—
162C3×SD16—34no—
163C3×D8—32no—
164C3×M16—34no—
165C3×M16—64no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—64no—
169C2×C3×C8C22×D312yes—
170C2×C3×C8C22×D312yes—
171C3×C42—21no—
172C3×C42C22×D312yes—
173#216—34no—
174#215—34no—
175#214—34no—
176#213—34no—
177C4×Dic3—32no—
178C4×Dic3—61no—
179C4×Dic3—62no—
180C4×Dic3—62no—
181#208—64no—
182#208C22×D314yes—
183C2×C3⋊C8—32no—
184C2×C3⋊C8—32no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—64no—
188Dic12C4×D312yescomplemented
189D24C4×D312yescomplemented
190#204C4×D314yescomplemented
191ΓL(1,𝔽25)—24no—
192ΓL(1,𝔽25)—34no—
193ΓL(1,𝔽25)—34no—
194ΓL(1,𝔽25)—34no—
195ΓL(1,𝔽25)—34no—
196ΓL(1,𝔽25)—64no—
197ΓL(1,𝔽25)—64no—
198ΓL(1,𝔽25)—64no—
199ΓL(1,𝔽25)—64no—
200D3×C8—24no—
201D3×C8—64no—
202D3×C8—64no—
203C22×C32C2×#4111yescharacteristic
204C2×C3⋊D3—41no—
205C2×C3⋊D3C4×D412yes—
206C2×C3×D3—24no—
207D32—82no—
208C32×C4—22no—
209C32×C4C23×C411yescharacteristic
210C32×C4C22×D411yescharacteristic
211C3⋊Dic3—41no—
212C3⋊Dic3C4×D412yes—
213C3×Dic3—24no—
214C2×#41—92no—
215#137—94no—
216AGL(1,ℤ/8)—94no—
217#135—32no—
218#135—92no—
219#131—34no—
220#131—94no—
221#131—184no—
222C2×M16—91no—
223C2×M16—91no—
224C2×M16—92no—
225C2×M16—184no—
226C2×C42—91no—
227#108—32no—
228#108—92no—
229#104—34no—
230#104—94no—
231#97—91no—
232#97—91no—
233C4×C8—91no—
234C4×C8D3211yescharacteristic, complemented
235C22×D3—32no—
236C22×D3—61no—
237C22×D3—64no—
238C3×Q8—34no—
239C3×D4—34no—
240C3×D4—64no—
241C2×C3×C4—22no—
242C2×C3×C4—22no—
243C2×C3×C4—21no—
244C2×C3×C4—64no—
245C2×C3×C4C23×D312yes—
246#67—24no—
247#67—64no—
248#67—64no—
249C2×Dic3—32no—
250C2×Dic3—61no—
251C2×Dic3—64no—
252C2×Dic3—62no—
253C2×Dic3—62no—
254D12—64no—
255D12C2×C4×D314yes—
256C4×D3—24no—
257C4×D3—34no—
258C4×D3—34no—
259C4×D3—62no—
260C4×D3—62no—
261C4×D3—64no—
262C4×D3—64no—
263C4×D3—124no—
264C4×D3—124no—
265Dic6—64no—
266Dic6C2×C4×D314yes—
267C3×C8—22no—
268C3×C8—22no—
269C3×C8—64no—
270C3×C8C2×C4×D312yes—
271C3×C8C2×C4×D312yes—
272C3×C8D3×D412yes—
273C3×C8D3×D412yes—
274C3⋊C8—24no—
275C3⋊C8—34no—
276C3⋊C8—34no—
277C3⋊C8—62no—
278C3⋊C8—62no—
279C2×C32—21no—
280C2×C32C2×C4×D411yescharacteristic
281C3⋊D3—22no—
282C3×D3—44no—
283#41—34no—
284#41—94no—
285#41—182no—
286#41—182no—
287C2×Q8—92no—
288C2×D4—92no—
289C2×D4—182no—
290C22×C4—91no—
291C22×C4—181no—
292C22×C4—182no—
293Q16—32no—
294Q16—92no—
295SD16—34no—
296SD16—94no—
297D8—32no—
298D8—92no—
299M16—34no—
300M16—64no—
301M16—94no—
302M16—94no—
303M16—182no—
304M16—184no—
305C2×C8—64no—
306C2×C8—91no—
307C2×C8—91no—
308C2×C8—182no—
309C2×C8—184no—
310C2×C8C2×D3211yescharacteristic
311C2×C8C2×D3211yescharacteristic
312C42—91no—
313C42—181no—
314C42C2×D3211yescharacteristic
315C22×C3—21no—
316C22×C3—64no—
317C22×C3D3×#4112yes—
318C2×D3—24no—
319C2×D3—34no—
320C2×D3—62no—
321C2×D3—122no—
322C2×D3—122no—
323C2×D3—244no—
324C3×C4—24no—
325C3×C4—24no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—64no—
329C3×C4C22×C4×D312yes—
330C3×C4C2×D3×D412yes—
331Dic3—24no—
332Dic3—34no—
333Dic3—62no—
334Dic3—122no—
335Dic3—122no—
336C32#295611yescharacteristic, complemented, Sylow
337C23—91no—
338C23—182no—
339Q8—34no—
340Q8—182no—
341D4—34no—
342D4—64no—
343D4—184no—
344D4—182no—
345C2×C4—21no—
346C2×C4—64no—
347C2×C4—91no—
348C2×C4—92no—
349C2×C4—92no—
350C2×C4—182no—
351C2×C4—184no—
352C2×C4—181no—
353C2×C4—362no—
354C2×C4C22×D3211yescharacteristic
355C8—64no—
356C8—92no—
357C8—92no—
358C8C4×D3212yes—
359C8#380212yes—
360C2×C3—22no—
361C2×C3—22no—
362C2×C3—21no—
363C2×C3—124no—
364C2×C3C4×D3×D412yes—
365D3—44no—
366D3—64no—
367D3—122no—
368C22—64no—
369C22—92no—
370C22—361no—
371C22—722no—
372C22#6430611yescharacteristic
373C4—22no—
374C4—64no—
375C4—92no—
376C4—361no—
377C4C2×C4×D3211yescharacteristic
378C4C2×#380211yescharacteristic
379C3—21no—
380C3#7988912yescomplemented
381C2—21no—
382C2—124no—
383C2—182no—
384C2C4×#380211yescharacteristic
subgroupG/H
centerC4C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC2×C32C2×C4×D4
prime radical#10594685C2
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32#2956
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #10594670C2semidirect
3. C4×#3743C2semidirect
4. C3×#4700C2semidirect
5. #10590922C2semidirect
6. #10590920C2semidirect
7. #10590914C2semidirect
8. #10590393C2semidirect
9. #10590389C2semidirect
16. C3×#901C22semidirect
19. #63815C22semidirect
20. #63811C4semidirect
22. #63798C4semidirect
24. C32×C4×C8C22semidirect
25. #63642C22semidirect
26. #63642C22semidirect
27. C4×C3⋊(C3⋊C8)C22semidirect
28. C3×#819C22semidirect
29. C3×#805C22semidirect
30. #63578C22semidirect
31. #63568C22semidirect
41. #4700D3semidirect
64. C3×Dic12C2×C4semidirect
65. C3×D24C2×C4semidirect
66. C3×#204C2×C4semidirect
69. #3718C2×C4semidirect
70. #3715C2×C4semidirect
71. #3713C2×C4semidirect
92. #901C2×D3semidirect
103. C3×C4×C8C2×D3semidirect
107. #819C2×D3semidirect
112. #805C2×D3semidirect
188. Dic12C4×D3semidirect
189. D24C4×D3semidirect
190. #204C4×D3semidirect
234. C4×C8D32semidirect
336. C32#2956semidirect
380. C3#79889semidirect

Maximal subgroups

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

subgroupindex
#105946852
#105946702
C4×#37432
C3×#47002
#105909222
#105909202
#105909142
#105903932
#105903892
#798893