Finite Group Databasebeta

← #11787767

Subgroups — #11787767

Order 1152.

996 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 996 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C32×#568C211yesmaximal, characteristic, complemented
2#10596303C211yesmaximal, characteristic
3#10592939C211yesmaximal, characteristic, complemented
4#10592838C212yesmaximal, complemented
5#10589421C212yesmaximal, complemented
6#72021—34nomaximal
7C2×C32×#41C2211yescharacteristic
8C2×#3828C2211yescharacteristic
9C32×#131—24no—
10C2×C32×M16—22no—
11C2×C32×M16C2212yes—
12#64156C411yescharacteristic, complemented
13#64153C411yescharacteristic, complemented
14#64149C411yescharacteristic, complemented
15#64148—22no—
16#64145C411yescharacteristic, complemented
17C4×#638—22no—
18#64135C2212yes—
19C2×C4×C3⋊Dic3C2211yescharacteristic
20#63661—22no—
21#63652—24no—
22C3×#568D314yescomplemented
23#5832—34no—
24#5240—34no—
25#5139—38no—
26#4555—38no—
27C32×#41—22no—
28C32×#41—22no—
29C2×C32×Q8C2×C411yescharacteristic
30C2×C32×D4C2×C411yescharacteristic
31C2×C32×D4D412yes—
32C22×C32×C4D412yes—
33C22×C32×C4C2311yescharacteristic
34C2×#638—22no—
35C2×#638—21no—
36C22×C3⋊Dic3—21no—
37#3828—22no—
38#3828—22no—
39C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
40C2×C4×C3⋊D3—21no—
41C2×#634C2×C411yescharacteristic
42C32×M16—24no—
43C32×M16—22no—
44C32×M16D414yescomplemented
45C2×C32×C8—24no—
46C2×C32×C8—22no—
47#3757—22no—
48#3757—22no—
49#3752—22no—
50C4⋊(C3⋊Dic3)—22no—
51#3750—22no—
52C4×C3⋊Dic3—21no—
53C4×C3⋊Dic3—22no—
54C4×C3⋊Dic3C2×C411yescharacteristic
55C4×C3⋊Dic3C2×C411yescharacteristic
56#1884—91noSylow
57C2×C3×#41C2×D314yes—
58C2×#235—34no—
59C3×#131—216no—
60C2×C3×M16—28no—
61C2×C3×M16C2×D318yes—
62#947—34no—
63#944—34no—
64#940—34no—
65#939—68no—
66#936—34no—
67C4×#67—68no—
68#926—38no—
69C2×C4×Dic3—34no—
70#834—68no—
71#825—616no—
72C23×C32C22⋊C412yes—
73C23×C32C2×D411yescharacteristic
74C22×C3⋊D3—21no—
75C32×Q8—22no—
76C32×D4—24no—
77C32×D4—22no—
78C2×C32×C4—22no—
79C2×C32×C4—22no—
80C2×C32×C4C22⋊C412yes—
81C2×C32×C4C22×C411yescharacteristic
82C2×C32×C4C2×D412yes—
83C2×C32×C4C2×D411yescharacteristic
84C2×C32×C4#4112yes—
85#638—44no—
86#638—42no—
87C2×C3⋊Dic3—21no—
88C2×C3⋊Dic3—21no—
89C2×C3⋊Dic3—21no—
90C2×C3⋊Dic3—42no—
91C2×C3⋊Dic3—42no—
92C4⋊(C3⋊D3)—22no—
93C4×C3⋊D3—41no—
94C4×C3⋊D3—41no—
95#634—22no—
96C32×C8—24no—
97#568C3⋊D311yescharacteristic, complemented
98#532—91no—
99#421—92no—
100#410—91no—
101#339—92no—
102C3×#41—28no—
103C3×#41—28no—
104C2×C3×Q8C4×D314yes—
105C2×C3×D4C4×D314yes—
106C2×C3×D4D1218yes—
107C22×C3×C4#6718yes—
108C22×C3×C4C22×D314yes—
109C2×#67—68no—
110C2×#67—64no—
111C22×Dic3—64no—
112#235—68no—
113#235—68no—
114C2×D12—34no—
115C2×C4×D3—64no—
116C2×Dic6—34no—
117C3×M16—216no—
118C3×M16—28no—
119C3×M16#67116yescomplemented
120C2×C3×C8—216no—
121C2×C3×C8—28no—
122#217—68no—
123#217—68no—
124(C2×D3)⋊C4—68no—
125C4⋊Dic3—68no—
126Dic3⋊C4—68no—
127C4×Dic3—34no—
128C4×Dic3—34no—
129C4×Dic3—64no—
130C4×Dic3—68no—
131C22×C32—22no—
132C22×C32—41no—
133C22×C32—42no—
134C22×C32C2×C22⋊C411yescharacteristic
135C22×C32#12112yes—
136C2×C3⋊D3—42no—
137C2×C3⋊D3—41no—
138C32×C4—22no—
139C32×C4C4×D412yes—
140C32×C4#12011yescharacteristic
141C32×C4#12311yescharacteristic
142C3⋊Dic3—22no—
143C3⋊Dic3—41no—
144C3⋊Dic3—41no—
145C3⋊Dic3—82no—
146C2×#41—91no—
147C2×#41C2×C3⋊D311yescharacteristic
148#131—24no—
149C2×M16—22no—
150C2×M16C2×C3⋊D312yes—
151C4⋊Q8—91no—
152#127—91no—
153#124—91no—
154#124—91no—
155#121—182no—
156C4×D4—182no—
157#117—92no—
158C2×C42—91no—
159#104—184no—
160#99—182no—
161C23×C3(C2×D3)⋊C418yes—
162C23×C3C2×D1214yes—
163C22×D3—64no—
164C3×Q8—28no—
165C3×D4—216no—
166C3×D4—28no—
167C2×C3×C4—28no—
168C2×C3×C4—28no—
169C2×C3×C4(C2×D3)⋊C418yes—
170C2×C3×C4C2×C4×D314yes—
171C2×C3×C4#23518yes—
172C2×C3×C4C2×#6718yes—
173C2×C3×C4C2×#6714yes—
174#67—1216no—
175#67—128no—
176C2×Dic3—64no—
177C2×Dic3—64no—
178C2×Dic3—64no—
179C2×Dic3—128no—
180C2×Dic3—128no—
181D12—68no—
182C4×D3—124no—
183C4×D3—124no—
184Dic6—68no—
185C3×C8—216no—
186C2×C32—21no—
187C2×C32—22no—
188C2×C32—42no—
189C2×C32#38611yescharacteristic
190C3⋊D3—81no—
191#41—22no—
192#41—22no—
193#41—182no—
194#41—182no—
195C2×Q8—91no—
196C2×Q8C4×C3⋊D311yescharacteristic
197C2×D4—91no—
198C2×D4—182no—
199C2×D4—181no—
200C2×D4C4×C3⋊D311yescharacteristic
201C2×D4C4⋊(C3⋊D3)12yes—
202C22×C4—181no—
203C22×C4—181no—
204C22×C4#63812yes—
205C22×C4C22×C3⋊D311yescharacteristic
206M16—24no—
207M16—22no—
208M16#63814yescomplemented
209C2×C8—24no—
210C2×C8—22no—
211C4⋊C4—182no—
212C4⋊C4—182no—
213C22⋊C4—182no—
214C22⋊C4—182no—
215C22⋊C4—182no—
216C42—91no—
217C42—91no—
218C42—181no—
219C42—182no—
220C22×C3—28no—
221C22×C3—44no—
222C22×C3—48no—
223C22×C3C2×(C2×D3)⋊C414yes—
224C22×C3#93018yes—
225C2×D3—128no—
226C2×D3—124no—
227C3×C4—28no—
228C3×C4C4×#6718yes—
229C3×C4#92914yes—
230C3×C4#95314yes—
231Dic3—68no—
232Dic3—124no—
233Dic3—124no—
234Dic3—248no—
235C32#188411yescharacteristic, complemented, Sylow
236C23—181no—
237C23#375212yes—
238C23C2×C4⋊(C3⋊D3)11yescharacteristic
239Q8—22no—
240Q8—182no—
241D4—24no—
242D4—22no—
243D4—182no—
244D4—364no—
245D4—362no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—181no—
249C2×C4—181no—
250C2×C4—181no—
251C2×C4—362no—
252C2×C4—361no—
253C2×C4—361no—
254C2×C4—362no—
255C2×C4#375212yes—
256C2×C4C2×C4×C3⋊D311yescharacteristic
257C2×C4#382812yes—
258C2×C4C2×#63812yes—
259C2×C4C2×#63811yescharacteristic
260C8—24no—
261C2×C3—24no—
262C2×C3—28no—
263C2×C3—48no—
264C2×C3#521314yes—
265D3—244no—
266C22—22no—
267C22—41no—
268C22—42no—
269C22—362no—
270C22—361no—
271C22C2×#375211yescharacteristic
272C22#6413912yes—
273C4—22no—
274C4—182no—
275C4—361no—
276C4—361no—
277C4—722no—
278C4C4×#63812yes—
279C4#6413811yescharacteristic
280C4#6416211yescharacteristic
281C3#7202114yescomplemented
282C2—21no—
283C2—22no—
284C2—42no—
285C2—721no—
286C2#1059291211yescharacteristic
subgroupG/H
centerC4#64162
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#568C2
socleC2×C32#386
prime radical#10596303C2
cosocleC22×C32×C4C23
hypercenter#568C3⋊D3
hypocenterC32#1884
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
1. C32×#568C2semidirect
3. #10592939C2semidirect
4. #10592838C2semidirect
5. #10589421C2semidirect
12. #64156C4semidirect
13. #64153C4semidirect
14. #64149C4semidirect
16. #64145C4semidirect
22. C3×#568D3semidirect
44. C32×M16D4semidirect
97. #568C3⋊D3semidirect
119. C3×M16#67semidirect
208. M16#638semidirect
235. C32#1884semidirect
281. C3#72021semidirect

Maximal subgroups

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

subgroupindex
C32×#5682
#105963032
#105929392
#105928382
#105894212
#720213