Finite Group Databasebeta

← #11777055

Subgroups — #11777055

Order 1152.

359 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 359 conjugacy classes of subgroups — too many to draw. Only its 100 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#10592384C211yesmaximal, characteristic
2#10590260C211yesmaximal, characteristic
3#10590256C211yesmaximal, characteristic
4C3×#4458C212yesmaximal, complemented
5#10589098C212yesmaximal, complemented
6#68573—32nomaximal
7C42×C3⋊D3C2211yescharacteristic
8C32×C4×C8C2211yescharacteristic
9#63647C412yes—
10#63641C412yes—
11C4×C3⋊(C3⋊C8)C2211yescharacteristic
12C3×C4⋊(C3⋊C8)C2212yes—
13C3×C4⋊(C3⋊C8)C2212yes—
14#63557—21no—
15#63557—21no—
16#63555—21no—
17#63553—21no—
18#4835—32no—
19#4833—32no—
20#4685—32no—
21#4685—61no—
22C3×#335—32no—
23#4480—32no—
24#4480—32no—
25#4458D312yescomplemented
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3Q811yescharacteristic
29C2×C32×C8C2×C412yes—
30C32×C42C2311yescharacteristic
31C4×C3⋊Dic3C2×C411yescharacteristic
32C4×C3⋊Dic3D411yescharacteristic
33C4×C3⋊Dic3Q811yescharacteristic
34C2×C3⋊(C3⋊C8)C2×C412yes—
35C2×C3×C3⋊C8—22no—
36C2×C3×C3⋊C8—22no—
37#1572—91noSylow
38C42×D3—32no—
39C42×D3—61no—
40C3×C4⋊C8—32no—
41C3×C4⋊C8—32no—
42C3×C4×C8—21no—
43C3×C4×C8C2×D312yes—
44(C2×D3)⋊C8—32no—
45(C2×D3)⋊C8—32no—
46(C2×D3)⋊C8—62no—
47(C2×D3)⋊C8—62no—
48(C2×D3)⋊C8—62no—
49#815—62no—
50Dic3⋊C8—32no—
51Dic3⋊C8—32no—
52Dic3⋊C8—62no—
53C8×Dic3—62no—
54C4⋊(C3⋊C8)C2×D312yes—
55C4⋊(C3⋊C8)C2×D312yes—
56C4×C3⋊C8—32no—
57C4×C3⋊C8—61no—
58C22×C3⋊D3C4⋊C411yescharacteristic
59C2×C32×C4C22×C411yescharacteristic
60C2×C32×C4C2×D411yescharacteristic
61C2×C32×C4C2×Q811yescharacteristic
62C2×C3⋊Dic3C4⋊C411yescharacteristic
63C2×C3⋊Dic3C4⋊C411yescharacteristic
64C2×C3⋊Dic3C4⋊C411yescharacteristic
65C4×C3⋊D3—22no—
66C4×C3⋊D3—22no—
67C4×C3⋊D3—41no—
68C32×C8—22no—
69C3⋊(C3⋊C8)—22no—
70C3×C3⋊C8—42no—
71C3×C3⋊C8—42no—
72#432—91no—
73#431—91no—
74#431—91no—
75#335—32no—
76#334—92no—
77C2×C4×D3—32no—
78C2×C4×D3—32no—
79C2×C4×D3—32no—
80C2×C4×D3—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C3×C8—22no—
84C2×C3×C8—62no—
85C2×C3×C8—62no—
86C2×C3×C8C4×D312yes—
87C2×C3×C8C4×D312yes—
88C3×C42—21no—
89C3×C42C22×D312yes—
90C4×Dic3—32no—
91C4×Dic3—32no—
92C4×Dic3—32no—
93C4×Dic3—61no—
94C4×Dic3—61no—
95C4×Dic3—61no—
96C2×C3⋊C8—22no—
97C2×C3⋊C8—22no—
98C2×C3⋊C8—32no—
99C2×C3⋊C8—32no—
100C2×C3⋊C8—62no—
101C22×C32C2×C4⋊C411yescharacteristic
102C2×C3⋊D3—21no—
103C2×C3⋊D3—21no—
104C2×C3⋊D3—21no—
105C32×C4—21no—
106C32×C4#13112yes—
107C32×C4#13512yes—
108C3⋊Dic3—21no—
109C3⋊Dic3—21no—
110C3⋊Dic3—21no—
111C2×C42—91no—
112C4⋊C8—32no—
113C4⋊C8—32no—
114C4⋊C8—92no—
115C22⋊C8—92no—
116C22⋊C8—181no—
117C22⋊C8—181no—
118#97—181no—
119C4×C8—91no—
120C4×C8—181no—
121C4×C8D3211yescharacteristic
122C22×D3—32no—
123C22×D3—61no—
124C2×C3×C4—21no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4C2×C4×D312yes—
128C2×C3×C4D3×D412yes—
129C2×C3×C4D3×Q812yes—
130C2×Dic3—32no—
131C2×Dic3—32no—
132C2×Dic3—32no—
133C2×Dic3—61no—
134C2×Dic3—61no—
135C2×Dic3—61no—
136C4×D3—64no—
137C4×D3—62no—
138C4×D3—62no—
139C4×D3—62no—
140C4×D3—62no—
141C4×D3—122no—
142C4×D3—122no—
143C4×D3—122no—
144C3×C8—22no—
145C3×C8—22no—
146C3×C8—42no—
147C3×C8—122no—
148C3×C8—122no—
149C3⋊C8—42no—
150C3⋊C8—42no—
151C3⋊C8—62no—
152C3⋊C8—62no—
153C3⋊C8—122no—
154C2×C32#42411yescharacteristic
155C2×C32#42711yescharacteristic
156C2×C32#43011yescharacteristic
157C3⋊D3—41no—
158C22×C4—91no—
159C22×C4—91no—
160C22×C4—91no—
161C2×C8—62no—
162C2×C8—62no—
163C2×C8—92no—
164C2×C8#62412yes—
165C42—91no—
166C42—91no—
167C42—91no—
168C42C2×D3211yescharacteristic
169C22×C3—21no—
170C22×C3D3×C4⋊C412yes—
171C2×D3—62no—
172C2×D3—62no—
173C2×D3—62no—
174C2×D3—62no—
175C2×D3—121no—
176C2×D3—121no—
177C3×C4—22no—
178C3×C4—22no—
179C3×C4—22no—
180C3×C4—22no—
181C3×C4#90112yes—
182C3×C4#90712yes—
183C3×C4#91212yes—
184C3×C4#91912yes—
185Dic3—62no—
186Dic3—62no—
187Dic3—62no—
188Dic3—62no—
189Dic3—121no—
190Dic3—121no—
191C32#157211yescharacteristic, complemented, Sylow
192C23—91no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—91no—
196C2×C4—182no—
197C2×C4—182no—
198C2×C4—361no—
199C2×C4#379711yescharacteristic
200C2×C4#380211yescharacteristic
201C2×C4C2×#62411yescharacteristic
202C8—22no—
203C8—122no—
204C8—122no—
205C8—182no—
206C2×C3—21no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3#483912yes—
210C2×C3#488012yes—
211C2×C3#489312yes—
212D3—122no—
213D3—122no—
214C22—181no—
215C22—181no—
216C22—181no—
217C22#6390011yescharacteristic
218C4—21no—
219C4—181no—
220C4—181no—
221C4—181no—
222C4#6381012yes—
223C4#6381712yes—
224C3—21no—
225C3#6857312yescomplemented
226C2—361no—
227C2#1059033211yescharacteristic
228C2#1059071411yescharacteristic
229C2#1059091411yescharacteristic
subgroupG/H
centerC2×C4#3802
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1572
LCSG ▷ C2×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×#4458C2semidirect
5. #10589098C2semidirect
25. #4458D3semidirect
191. C32#1572semidirect
225. C3#68573semidirect

Maximal subgroups

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

subgroupindex
#105923842
#105902602
#105902562
C3×#44582
#105890982
#685733