Finite Group Databasebeta

← #11860712

Subgroups — #11860712

Order 1152.

866 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 866 conjugacy classes of subgroups — too many to draw. Only its 151 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
1C2×#64225C211yesmaximal, characteristic
2#10594606C212yesmaximal, complemented
3#10593748C211yesmaximal, characteristic, complemented
4#10593420C212yesmaximal, complemented
5#10593419C214yesmaximal, complemented
6C4×#3774C212yesmaximal, complemented
7#10593389C211yesmaximal, characteristic, complemented
8#10593363C212yesmaximal, complemented
9C2×#3802C2212yes—
10C2×#3788C2211yescharacteristic
11C2×#3787C2211yescharacteristic
12C2×#3774C2212yes—
13C2×#3774C2212yes—
14#64225C418yescomplemented
15#64101C2211yescharacteristic
16C3×#893—22no—
17D3×(C2×D3)⋊C4—24no—
18#63902C2214yescomplemented
19C4×#625C2214yescomplemented
20Dic3×D12—22no—
21#63874C2212yes—
22#63777C2212yescomplemented
23C4×#622C2212yescomplemented
24#63743C2211yescharacteristic, complemented
25#63743C2211yescharacteristic, complemented
26#63742C2212yescomplemented
27#63739C2214yescomplemented
28#63739C2214yescomplemented
29#5545—62no—
30C22×D32—22no—
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×C3×D12—22no—
33C2×C3×C4×D3—24no—
34C2×#625C2314yes—
35C2×D3×Dic3—24no—
36#3802—24no—
37#3802C2×C418yescomplemented
38C2×#622C2312yes—
39C2×#622C2311yescharacteristic
40C2×#622C2311yescharacteristic
41#3788—22no—
42#3787C2×C414yescomplemented
43#3774C2×C418yescomplemented
44#3774C2×C418yescomplemented
45C32×C4⋊C4D411yescharacteristic
46#3752D412yes—
47C4⋊(C3⋊Dic3)D411yescharacteristic
48C4×C3⋊Dic3C2312yes—
49C3×(C2×D3)⋊C4—24no—
50C3×C4×Dic3—22no—
51#3724C2312yes—
52#3724C2312yes—
53#3722—22no—
54(C2×D3)⋊Dic3—24no—
55#2948—91nomaximal, Sylow
56C2×D3×D4—62no—
57C3×C4×D4—62no—
58D4×Dic3—62no—
59C4×#67—64no—
60C2×(C2×D3)⋊C4—64no—
61#893—22no—
62#892—62no—
63#67⋊C4—64no—
64D3×C22⋊C4—64no—
65C4×D12—62no—
66#872—62no—
67C22×C3⋊D3C2×D411yescharacteristic
68C22×C3×D3—24no—
69C2×D32—28no—
70C2×D32—82no—
71C2×D32—82no—
72C2×C32×C4C2×D412yes—
73C2×C32×C4C2×D411yescharacteristic
74C2×C3⋊Dic3C2×D412yes—
75C2×C3⋊Dic3C2411yescharacteristic
76C4×C3⋊D3C22×C412yes—
77C4×C3⋊D3#4112yes—
78C2×C3×Dic3—22no—
79C2×C3×Dic3—22no—
80C3×D12—28no—
81C3×C4×D3—84no—
82#625—24no—
83#625C22×C418yes—
84D3×Dic3—84no—
85#622—22no—
86#622C22×C412yes—
87#622C22×C412yes—
88C22×D8—91no—
89#518—92no—
90#442—94no—
91C4×D8—92no—
92C4×D8—92no—
93#427—91no—
94#418—92no—
95#405—91no—
96C23×D3—64no—
97C2×C3×D4—62no—
98C22×C3×C4—64no—
99C2×#67—64no—
100C22×Dic3—64no—
101D3×D4—68no—
102D3×D4—68no—
103C2×D12—22no—
104C2×C4×D3—24no—
105C2×C4×D3—62no—
106C2×C4×D3—64no—
107C3×C4⋊C4—22no—
108C3×C22⋊C4—64no—
109C3×C42—62no—
110#217—64no—
111(C2×D3)⋊C4—24no—
112(C2×D3)⋊C4—64no—
113(C2×D3)⋊C4—62no—
114(C2×D3)⋊C4—62no—
115(C2×D3)⋊C4—64no—
116C4⋊Dic3—62no—
117Dic3⋊C4—62no—
118Dic3⋊C4—62no—
119C4×Dic3—22no—
120C4×Dic3—64no—
121C22×C32C22×D411yescharacteristic
122C2×C3⋊D3—21no—
123C2×C3⋊D3—21no—
124C2×C3⋊D3C4×D412yes—
125C2×C3×D3—28no—
126C2×C3×D3—44no—
127C2×C3×D3—44no—
128D32—88no—
129C32×C4—22no—
130C32×C4C4×D412yes—
131C3⋊Dic3—22no—
132C3⋊Dic3C23×C411yescharacteristic
133C3⋊Dic3C2×#4111yescharacteristic
134C3×Dic3—42no—
135C3×Dic3—42no—
136C22×D4—92no—
137C2×D8—92no—
138C2×D8—92no—
139C2×D8—98no—
140C2×M16—91no—
141C22×C8—91no—
142C4×D4—62no—
143C4×D4—94no—
144C4×D4—94no—
145C4×D4—182no—
146#117—92no—
147#117—91no—
148C2×C22⋊C4—184no—
149#107—91no—
150#107—91no—
151#106—92no—
152#102—94no—
153#102—94no—
154#97—92no—
155C4×C8—92no—
156C23×C3—64no—
157C22×D3—24no—
158C22×D3—62no—
159C22×D3—616no—
160C22×D3—244no—
161C22×D3—244no—
162C3×D4—68no—
163C2×C3×C4—22no—
164C2×C3×C4—24no—
165C2×C3×C4—62no—
166C2×C3×C4—62no—
167C2×C3×C4—244no—
168#67—68no—
169#67—68no—
170C2×Dic3—22no—
171C2×Dic3—22no—
172C2×Dic3—62no—
173C2×Dic3—64no—
174C2×Dic3—244no—
175D12—28no—
176C4×D3—64no—
177C4×D3—64no—
178C4×D3—84no—
179C4×D3—244no—
180C2×C32C2×C4×D411yescharacteristic
181C2×C32#57611yescharacteristic
182C2×C32#57611yescharacteristic
183C3⋊D3—22no—
184C3×D3—48no—
185C24—182no—
186C2×D4—62no—
187C2×D4—98no—
188C2×D4—94no—
189C2×D4—184no—
190C22×C4—64no—
191C22×C4—91no—
192C22×C4—184no—
193D8—98no—
194D8—98no—
195M16—182no—
196C2×C8—91no—
197C2×C8—91no—
198C2×C8—94no—
199C2×C8—92no—
200C4⋊C4—92no—
201C4⋊C4—92no—
202C4⋊C4—91no—
203C4⋊C4GO+(4,𝔽2)11yescharacteristic
204C22⋊C4—64no—
205C22⋊C4—92no—
206C22⋊C4—182no—
207C22⋊C4—184no—
208C42—62no—
209C42—92no—
210C22×C3—22no—
211C22×C3—68no—
212C22×C3—124no—
213C22×C3—124no—
214C2×D3—28no—
215C2×D3—44no—
216C2×D3—44no—
217C2×D3—64no—
218C2×D3—122no—
219C2×D3—122no—
220C2×D3—2416no—
221C3×C4—24no—
222C3×C4—44no—
223C3×C4—122no—
224C3×C4—122no—
225Dic3—42no—
226Dic3—42no—
227Dic3—62no—
228Dic3—62no—
229Dic3—124no—
230C32#294811yescharacteristic, complemented, Sylow
231C23—64no—
232C23—91no—
233C23—188no—
234C23—722no—
235C23—722no—
236D4—68no—
237D4—98no—
238D4—184no—
239C2×C4—62no—
240C2×C4—62no—
241C2×C4—91no—
242C2×C4—92no—
243C2×C4—92no—
244C2×C4—92no—
245C2×C4—244no—
246C2×C4—724no—
247C2×C4C2×GO+(4,𝔽2)12yes—
248C2×C4C2×GO+(4,𝔽2)11yescharacteristic
249C8—92no—
250C8—92no—
251C8—182no—
252C2×C3—22no—
253C2×C3—22no—
254C2×C3—22no—
255C2×C3—128no—
256D3—48no—
257D3—124no—
258C22—68no—
259C22—92no—
260C22—124no—
261C22—124no—
262C22—181no—
263C22—181no—
264C22—728no—
265C22C22×GO+(4,𝔽2)11yescharacteristic
266C4—22no—
267C4—91no—
268C4—91no—
269C4—122no—
270C4—122no—
271C4—182no—
272C4C4×GO+(4,𝔽2)12yes—
273C3—22no—
274C2—128no—
275C2—182no—
276C2C2×C4×GO+(4,𝔽2)11yescharacteristic
277C2#1059651411yescharacteristic
278C2#1059652211yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC3⋊Dic3C23×C4
FittingC32×C4⋊C4D4
socleC22×C32C22×D4
prime radicalC2×#64225C2
cosocleC2×C3⋊Dic3C24
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2948
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #10594606C2semidirect
3. #10593748C2semidirect
4. #10593420C2semidirect
5. #10593419C2semidirect
6. C4×#3774C2semidirect
7. #10593389C2semidirect
8. #10593363C2semidirect
14. #64225C4semidirect
18. #63902C22semidirect
19. C4×#625C22semidirect
22. #63777C22semidirect
23. C4×#622C22semidirect
24. #63743C22semidirect
25. #63743C22semidirect
26. #63742C22semidirect
27. #63739C22semidirect
28. #63739C22semidirect
37. #3802C2×C4semidirect
42. #3787C2×C4semidirect
43. #3774C2×C4semidirect
44. #3774C2×C4semidirect
230. C32#2948semidirect

Maximal subgroups

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

subgroupindex
C2×#642252
#105946062
#105937482
#105934202
#105934192
C4×#37742
#105933892
#105933632
#29489