Finite Group Databasebeta

← #11776853

Subgroups — #11776853

Order 1152.

419 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 419 conjugacy classes of subgroups — too many to draw. Only its 118 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#10592532C211yesmaximal, characteristic
2C4×#3712C211yesmaximal, characteristic
3#10590331C211yesmaximal, characteristic
4C3×#4480C212yesmaximal, complemented
5#10589099C212yesmaximal, complemented
6#68528—32nomaximal
7C42×C3⋊D3C2211yescharacteristic
8C2×#3712C411yescharacteristic
9C2×#3712C411yescharacteristic
10C2×#3710—21no—
11C32×C4⋊C8C2211yescharacteristic
12#63647—21no—
13C8×C3⋊Dic3—21no—
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C3×C4⋊(C3⋊C8)C2212yes—
16C3×C4×C3⋊C8C2212yes—
17#63572—21no—
18#63555C412yes—
19#4833—32no—
20#4833—61no—
21D3×C4⋊C8—32no—
22C4×ΓL(1,𝔽25)—32no—
23C3×#334—32no—
24#4480D312yescomplemented
25#4479—32no—
26#4458—32no—
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3Q811yescharacteristic
30C2×C32×C8—21no—
31C32×C42C2311yescharacteristic
32C4×C3⋊Dic3C2×C411yescharacteristic
33C4×C3⋊Dic3D411yescharacteristic
34C4×C3⋊Dic3Q811yescharacteristic
35C2×C3⋊(C3⋊C8)—21no—
36C2×C3×C3⋊C8—22no—
37C2×C3×C3⋊C8C2×C412yes—
38C2×C3×C3⋊C8C2×C412yes—
39#3712—22no—
40#3712C814yescomplemented
41#3710—42no—
42#1565—91noSylow
43C2×ΓL(1,𝔽25)—32no—
44C2×ΓL(1,𝔽25)—32no—
45C2×D3×C8—62no—
46C42×D3—32no—
47C42×D3—61no—
48C3×C4⋊C8—21no—
49C3×C4⋊C8—32no—
50C3×C4⋊C8C2×D312yes—
51C3×C4×C8—32no—
52(C2×D3)⋊C8—62no—
53(C2×D3)⋊C8—62no—
54#815—32no—
55#815—32no—
56Dic3⋊C8—62no—
57C8×Dic3—62no—
58C8×Dic3—62no—
59C4⋊(C3⋊C8)—32no—
60C4⋊(C3⋊C8)—61no—
61C4⋊(C3⋊C8)C2×D312yes—
62C4×C3⋊C8C2×D312yes—
63C22×C3⋊D3C4⋊C411yescharacteristic
64C2×C32×C4C22×C411yescharacteristic
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4C2×Q811yescharacteristic
67C2×C3⋊Dic3C4⋊C411yescharacteristic
68C2×C3⋊Dic3C4⋊C411yescharacteristic
69C2×C3⋊Dic3C4⋊C411yescharacteristic
70C4×C3⋊D3—21no—
71C4×C3⋊D3—21no—
72C4×C3⋊D3—41no—
73C4×C3⋊D3C2×C812yes—
74C4×C3⋊D3M1612yes—
75C32×C8—41no—
76C3⋊(C3⋊C8)—41no—
77C3×C3⋊C8—22no—
78C3×C3⋊C8—42no—
79C3×C3⋊C8C2×C814yescomplemented
80#431—91no—
81C2×C4⋊C8—91no—
82C4×M16—91no—
83#335—92no—
84#334—32no—
85C2×C4×D3—32no—
86C2×C4×D3—32no—
87C2×C4×D3—32no—
88C2×C4×D3—61no—
89C2×C4×D3—61no—
90C2×C4×D3—61no—
91C2×C3×C8—22no—
92C2×C3×C8—22no—
93C2×C3×C8—32no—
94C2×C3×C8—32no—
95C2×C3×C8—62no—
96C3×C42—21no—
97C3×C42C22×D312yes—
98C4×Dic3—32no—
99C4×Dic3—32no—
100C4×Dic3—32no—
101C4×Dic3—61no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C2×C3⋊C8—22no—
105C2×C3⋊C8—62no—
106C2×C3⋊C8—62no—
107C2×C3⋊C8C4×D312yes—
108C2×C3⋊C8C4×D312yes—
109ΓL(1,𝔽25)—38no—
110ΓL(1,𝔽25)—64no—
111D3×C8—124no—
112C22×C32C2×C4⋊C411yescharacteristic
113C2×C3⋊D3—21no—
114C2×C3⋊D3—21no—
115C2×C3⋊D3C4⋊C812yes—
116C32×C4—21no—
117C32×C4C22×C811yescharacteristic
118C32×C4C2×M1611yescharacteristic
119C32×C4AGL(1,ℤ/8)11yescharacteristic
120C32×C4#13711yescharacteristic
121C3⋊Dic3—21no—
122C3⋊Dic3—21no—
123C3⋊Dic3C4⋊C812yes—
124C2×M16—91no—
125C2×M16—91no—
126C22×C8—181no—
127C2×C42—91no—
128C4⋊C8—32no—
129C4⋊C8—91no—
130C4⋊C8—181no—
131C4⋊C8D3211yescharacteristic
132C22⋊C8—181no—
133#97—92no—
134C4×C8—32no—
135C4×C8—181no—
136C22×D3—32no—
137C22×D3—61no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4C2×C4×D312yes—
142C2×C3×C4D3×D412yes—
143C2×C3×C4D3×Q812yes—
144C2×Dic3—32no—
145C2×Dic3—32no—
146C2×Dic3—32no—
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C4×D3—34no—
151C4×D3—34no—
152C4×D3—62no—
153C4×D3—62no—
154C4×D3—62no—
155C4×D3—62no—
156C4×D3—121no—
157C4×D3—121no—
158C4×D3—122no—
159C4×D3—122no—
160C3×C8—34no—
161C3×C8—42no—
162C3×C8—42no—
163C3×C8—62no—
164C3×C8—122no—
165C3⋊C8—22no—
166C3⋊C8—42no—
167C3⋊C8—122no—
168C3⋊C8—122no—
169C3⋊C8D3×C814yescomplemented
170C2×C32C2×C4⋊C811yescharacteristic
171C2×C32#42811yescharacteristic
172C2×C32#43011yescharacteristic
173C3⋊D3—22no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—91no—
177M16—94no—
178M16—182no—
179C2×C8—21no—
180C2×C8—32no—
181C2×C8—32no—
182C2×C8—62no—
183C2×C8—181no—
184C2×C8—362no—
185C42—91no—
186C42—91no—
187C42—91no—
188C42C2×D3211yescharacteristic
189C22×C3—21no—
190C22×C3D3×C4⋊C412yes—
191C2×D3—34no—
192C2×D3—62no—
193C2×D3—62no—
194C2×D3—62no—
195C2×D3—121no—
196C2×D3—121no—
197C3×C4—22no—
198C3×C4—21no—
199C3×C4—21no—
200C3×C4—21no—
201C3×C4—21no—
202C3×C4—41no—
203C3×C4C2×D3×C812yes—
204C3×C4D3×M1612yes—
205C3×C4#91412yes—
206C3×C4#91512yes—
207Dic3—34no—
208Dic3—62no—
209Dic3—62no—
210Dic3—62no—
211Dic3—62no—
212Dic3—121no—
213C32#156511yescharacteristic, complemented, Sylow
214C23—91no—
215C2×C4—91no—
216C2×C4—92no—
217C2×C4—92no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—181no—
221C2×C4—181no—
222C2×C4—361no—
223C2×C4#379711yescharacteristic
224C2×C4C4×D3211yescharacteristic
225C2×C4#381111yescharacteristic
226C8—34no—
227C8—41no—
228C8—62no—
229C8—122no—
230C8—361no—
231C2×C3—21no—
232C2×C3—21no—
233C2×C3—21no—
234C2×C3D3×C4⋊C812yes—
235C2×C3#486112yes—
236C2×C3#489312yes—
237D3—64no—
238D3—122no—
239C22—92no—
240C22—181no—
241C22—181no—
242C22#6388311yescharacteristic
243C4—21no—
244C4—92no—
245C4—181no—
246C4—181no—
247C4D32×C811yescharacteristic
248C4#6379111yescharacteristic
249C4#6393111yescharacteristic
250C4#6394111yescharacteristic
251C3—21no—
252C3#6852812yescomplemented
253C2—182no—
254C2#1059058411yescharacteristic
255C2#1059065811yescharacteristic
256C2#1059097411yescharacteristic
subgroupG/H
centerC2×C4#3811
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC32×C42C23
hypercenterC4⋊C8D32
hypocenterC32#1565
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. C3×#4480C2semidirect
5. #10589099C2semidirect
24. #4480D3semidirect
40. #3712C8semidirect
79. C3×C3⋊C8C2×C8semidirect
169. C3⋊C8D3×C8semidirect
213. C32#1565semidirect
252. C3#68528semidirect

Maximal subgroups

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

subgroupindex
#105925322
C4×#37122
#105903312
C3×#44802
#105890992
#685283