Finite Group Databasebeta

← #11874918

Subgroups — #11874918

Order 1152.

785 conjugacy classes of subgroups; only the 188 normal subgroups are shown.

normal subgroups only

This group has 785 conjugacy classes of subgroups — too many to draw. Only its 188 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#10594482C212yesmaximal
2C3⋊D3×#106C211yesmaximal, characteristic
3C3×#4858C212yesmaximal, complemented
4#10590871C212yesmaximal, complemented
5#10590685C211yesmaximal, characteristic
6C8×#624C211yesmaximal, characteristic
7#10590573C212yesmaximal
8#10590413C214yesmaximal, complemented
9D3×#499—32nomaximal
10C2×C8×C3⋊D3C2211yescharacteristic
11C4⋊C4×C3⋊D3C2212yes—
12C3×#890C2214yes—
13#63900—22no—
14#63900C2212yes—
15#63883—22no—
16C4×#624C2211yescharacteristic
17#63869C2214yes—
18#63847—24no—
19C2×#3710C2211yescharacteristic
20C32×#106C2211yescharacteristic
21#63644C2211yescharacteristic
22#63635C2212yes—
23C3×#817C2212yes—
24C3×C8×Dic3C2212yes—
25C3×#807C2214yes—
26#63575C2214yes—
27#63574C2212yes—
28Dic3×C3⋊C8C2212yes—
29D3×#125—34no—
30C3×#499—32no—
31#5065—34no—
32D3×#107—34no—
33#4878—34no—
34D3×#106—32no—
35D3×#106—32no—
36D3×#106—61no—
37#4858—32no—
38#4858D312yescomplemented
39C4×D3×C8—32no—
40#4683—32no—
41C2×C4×C3⋊D3—22no—
42C2×C4×C3⋊D3C2311yescharacteristic
43C2×#624—22no—
44C2×#624D412yes—
45C2×C32×C8C2311yescharacteristic
46C32×C4⋊C4C2312yes—
47C4⋊(C3⋊Dic3)C2312yes—
48#3750—22no—
49C2×C3⋊(C3⋊C8)C2311yescharacteristic
50C8×C3⋊D3Q814yes—
51C3×C4⋊Dic3—24no—
52C3×C4⋊Dic3C2314yes—
53C3×Dic3⋊C4—24no—
54C3×C4×Dic3C2312yes—
55C2×C3×C3⋊C8C2312yes—
56#3724—22no—
57#3724—24no—
58Dic3⋊Dic3—24no—
59Dic32D412yes—
60#3710Q814yes—
61C2×#499—91noSylow
62C3×#125—34no—
63C2×D3×C8—32no—
64C2×D3×C8—32no—
65C2×D3×C8—61no—
66D3×C4⋊C4—34no—
67D3×C4⋊C4—34no—
68D3×C4⋊C4—62no—
69D3×C4⋊C4—64no—
70D3×C4⋊C4—64no—
71#890—34no—
72#890C2×D314yes—
73#889—64no—
74#889—64no—
75C42×D3—32no—
76#870—34no—
77C3×#107—34no—
78C3×#106—21no—
79C3×#106—32no—
80C3×#106C2×D312yes—
81C3×C4×C8—32no—
82#818—34no—
83#817—32no—
84#817—61no—
85#817C2×D312yes—
86C8×Dic3—32no—
87C8×Dic3C2×D312yes—
88#808—34no—
89#808—34no—
90#808—62no—
91#807—34no—
92#807C2×D314yes—
93C4×C3⋊C8—32no—
94C22×C3⋊D3C2×D411yescharacteristic
95C2×C32×C4—22no—
96C2×C32×C4C2411yescharacteristic
97C2×C3⋊Dic3—22no—
98C2×C3⋊Dic3C2×D411yescharacteristic
99C4×C3⋊D3—44no—
100C4×C3⋊D3C2×Q812yes—
101C4×C3⋊D3C2×Q812yes—
102C2×C3×Dic3—24no—
103C2×C3×Dic3C2×D414yes—
104#624—24no—
105#624—44no—
106C32×C8C2×Q812yes—
107C3⋊(C3⋊C8)C2×Q812yes—
108C3×C3⋊C8C2×Q814yes—
109C2×#125—92no—
110#499—32no—
111#499—92no—
112#499—94no—
113C2×#107—92no—
114C2×#106—91no—
115C2×#106—91no—
116C2×C4×C8—91no—
117C2×C4×D3—32no—
118C2×C4×D3—34no—
119C2×C4×D3—61no—
120C2×C4×D3—64no—
121C2×C4×D3—64no—
122C2×C4×D3—122no—
123C2×C3×C8—21no—
124C2×C3×C8—32no—
125C2×C3×C8C22×D312yes—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—34no—
128C3×C4⋊C4—64no—
129C3×C4⋊C4—64no—
130C3×C4⋊C4C22×D314yes—
131C3×C42—32no—
132C4⋊Dic3—24no—
133C4⋊Dic3—34no—
134C4⋊Dic3—62no—
135C4⋊Dic3—64no—
136C4⋊Dic3C22×D314yes—
137Dic3⋊C4—24no—
138Dic3⋊C4—64no—
139Dic3⋊C4—64no—
140Dic3⋊C4—64no—
141Dic3⋊C4—64no—
142Dic3⋊C4—64no—
143Dic3⋊C4—122no—
144C4×Dic3—34no—
145C4×Dic3C22×D312yes—
146C2×C3⋊C8—32no—
147C2×C3⋊C8—61no—
148C2×C3⋊C8C22×D312yes—
149D3×C8—38no—
150D3×C8—38no—
151D3×C8—64no—
152C22×C32C22×D411yescharacteristic
153C2×C3⋊D3C4⋊Q812yes—
154C2×C3⋊D3#13514yes—
155C32×C4—42no—
156C32×C4C22×Q811yescharacteristic
157C32×C4C22×Q811yescharacteristic
158C3⋊Dic3—42no—
159C3⋊Dic3C4⋊Q812yes—
160C3×Dic3—24no—
161C3×Dic3—44no—
162C22×C8—91no—
163C22×C8—91no—
164#125—34no—
165#125—94no—
166#125—184no—
167C2×C4⋊C4—92no—
168C2×C4⋊C4—92no—
169C2×C4⋊C4—182no—
170C2×C4⋊C4—182no—
171C2×C42—91no—
172#107—34no—
173#107—94no—
174#106—32no—
175#106—92no—
176#106—91no—
177#106—92no—
178#106D3211yescharacteristic
179C4×C8—32no—
180C4×C8—92no—
181C22×D3—32no—
182C22×D3—61no—
183C2×C3×C4—24no—
184C2×C3×C4—21no—
185C2×C3×C4—34no—
186C2×C3×C4—42no—
187C2×C3×C4—64no—
188C2×C3×C4C23×D312yes—
189C2×Dic3—24no—
190C2×Dic3—32no—
191C2×Dic3—61no—
192C2×Dic3—64no—
193C2×Dic3—122no—
194C2×Dic3D3×D414yes—
195C4×D3—34no—
196C4×D3—34no—
197C4×D3—62no—
198C4×D3—62no—
199C4×D3—68no—
200C4×D3—128no—
201C4×D3—128no—
202C4×D3—244no—
203C3×C8—22no—
204C3×C8—34no—
205C3×C8D3×Q814yes—
206C3⋊C8—34no—
207C3⋊C8—62no—
208C3⋊C8D3×Q814yes—
209C2×C32C2×C4⋊Q811yescharacteristic
210C2×C32C2×#13512yes—
211C3⋊D3#49914yescomplemented
212C22×C4—92no—
213C22×C4—91no—
214C22×C4—182no—
215C22×C4—182no—
216C2×C8—32no—
217C2×C8—94no—
218C2×C8—91no—
219C2×C8—94no—
220C2×C8C2×D3211yescharacteristic
221C4⋊C4—34no—
222C4⋊C4—64no—
223C4⋊C4—64no—
224C4⋊C4—92no—
225C4⋊C4—182no—
226C4⋊C4—184no—
227C4⋊C4—184no—
228C4⋊C4—182no—
229C4⋊C4C2×D3212yes—
230C42—32no—
231C42—92no—
232C22×C3—21no—
233C22×C3C2×D3×D412yes—
234C2×D3—34no—
235C2×D3—38no—
236C2×D3—62no—
237C2×D3—64no—
238C3×C4—21no—
239C3×C4—21no—
240C3×C4—44no—
241C3×C4—64no—
242C3×C4—82no—
243C3×C4—124no—
244C3×C4C2×D3×Q812yes—
245C3×C4C2×D3×Q812yes—
246Dic3—24no—
247Dic3—34no—
248Dic3—44no—
249Dic3—62no—
250Dic3—124no—
251Dic3—242no—
252C32C2×#49911yescharacteristic, complemented, Sylow
253C23—91no—
254C2×C4—22no—
255C2×C4—34no—
256C2×C4—64no—
257C2×C4—91no—
258C2×C4—92no—
259C2×C4—92no—
260C2×C4—184no—
261C2×C4—182no—
262C2×C4—364no—
263C2×C4—364no—
264C2×C4C22×D3211yescharacteristic
265C8—34no—
266C8—92no—
267C8#379712yes—
268C2×C3—21no—
269C2×C3—22no—
270C2×C3D3×C4⋊Q812yes—
271C2×C3D3×#13514yes—
272D3—38no—
273D3—64no—
274C22—92no—
275C22—94no—
276C22D32×D411yescharacteristic
277C4—42no—
278C4—64no—
279C4—92no—
280C4—124no—
281C4—362no—
282C4C2×#379711yescharacteristic
283C4D32×Q811yescharacteristic
284C3—21no—
285C3D3×#49912yescomplemented
286C2—94no—
287C2#1059437411yescharacteristic
288C2#1059474712yes—
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#106C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#106D32
hypocenterC32C2×#499
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
3. C3×#4858C2semidirect
4. #10590871C2semidirect
8. #10590413C2semidirect
38. #4858D3semidirect
211. C3⋊D3#499semidirect
252. C32C2×#499semidirect
285. C3D3×#499semidirect

Maximal subgroups

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

subgroupindex
#105944822
C3⋊D3×#1062
C3×#48582
#105908712
#105906852
C8×#6242
#105905732
#105904132
D3×#4993