Finite Group Databasebeta

← #11776046

Subgroups — #11776046

Order 1152.

631 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 631 conjugacy classes of subgroups — too many to draw. Only its 116 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#10595948C211yesmaximal, characteristic
2C3×#4926C212yesmaximal, complemented
3#10589087C214yesmaximal, complemented
4#70811—32nomaximal
5C2×#3828C412yes—
6C2×C32×C42C2211yescharacteristic
7#64139—22no—
8#64084C2212yes—
9#64083C411yescharacteristic
10C4×C4⋊(C3⋊D3)—22no—
11#64078C411yescharacteristic
12C3×#830—22no—
13C3×C4⋊(C3⋊C8)—22no—
14C3×#803C2214yes—
15#5477—32no—
16#5477—61no—
17C3×#432—32no—
18#4926D312yescomplemented
19#4464—38no—
20C22×C32×C4C2×C411yescharacteristic
21C22×C32×C4D412yes—
22C2×#638—22no—
23#3828—44no—
24C2×C4⋊(C3⋊D3)—22no—
25C2×C4⋊(C3⋊D3)C2×C412yes—
26C2×C4×C3⋊D3—22no—
27C2×#634C2×C412yes—
28C32×C42C2×C411yescharacteristic
29C32×C42D412yes—
30C32×C42C2311yescharacteristic
31#3752—24no—
32C4⋊(C3⋊Dic3)—22no—
33C2×C3×C3⋊C8—24no—
34#1536—91noSylow
35C2×#235—34no—
36C2×#235—62no—
37C2×C3×C42—21no—
38C2×C3×C42C2×D312yes—
39#930—64no—
40#930—62no—
41#930—62no—
42#875—34no—
43#875—62no—
44#874—32no—
45#874—61no—
46C4×D12—64no—
47C4×D12—62no—
48C4×D12—62no—
49#869—32no—
50#869—61no—
51C3×C4⋊C8—62no—
52C3×C22⋊C8—62no—
53C3×#97—34no—
54#830—22no—
55C4⋊(C3⋊C8)—22no—
56#803C2×D314yes—
57C23×C32C22⋊C411yescharacteristic
58C22×C3⋊D3—22no—
59C2×C32×C4—22no—
60C2×C32×C4—42no—
61C2×C32×C4C22⋊C412yes—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C22×C411yescharacteristic
64C2×C32×C4C2×D412yes—
65#638—44no—
66C2×C3⋊Dic3—22no—
67C4⋊(C3⋊D3)—42no—
68C4⋊(C3⋊D3)—44no—
69C4×C3⋊D3—44no—
70#634—42no—
71C3×C3⋊C8—44no—
72#532—91no—
73#432—32no—
74#329—94no—
75C22×C3×C4—21no—
76C22×C3×C4—22no—
77C22×C3×C4C4×D312yes—
78C22×C3×C4D1212yes—
79C22×C3×C4#6712yes—
80C2×#67—64no—
81C2×#67—64no—
82#235—128no—
83#235—128no—
84C2×D12—34no—
85C2×D12—62no—
86C2×D12—64no—
87C2×D12—62no—
88C2×D12—62no—
89C2×C4×D3—64no—
90C2×C4×D3—64no—
91C2×Dic6—34no—
92C2×Dic6—62no—
93C2×C3×C8—64no—
94C3×C42—21no—
95C3×C42—22no—
96C3×C42—21no—
97C3×C42C4×D312yes—
98C3×C42D1212yes—
99C3×C42#6712yes—
100C3×C42C22×D312yes—
101(C2×D3)⋊C4—68no—
102(C2×D3)⋊C4—64no—
103(C2×D3)⋊C4—64no—
104C4⋊Dic3—64no—
105C4⋊Dic3—62no—
106C4⋊Dic3—62no—
107C2×C3⋊C8—24no—
108C22×C32—21no—
109C22×C32—22no—
110C22×C32C2×C22⋊C411yescharacteristic
111C2×C3⋊D3—42no—
112C2×C3⋊D3—44no—
113C32×C4—21no—
114C32×C4—22no—
115C32×C4—22no—
116C32×C4#10012yes—
117C3⋊Dic3—42no—
118C2×#41—92no—
119C4⋊Q8—91no—
120#127—91no—
121#124—92no—
122#121—182no—
123C4×D4—182no—
124C2×C42D3211yescharacteristic
125C4⋊C8—62no—
126C22⋊C8—62no—
127#97—34no—
128C23×C3—21no—
129C23×C3(C2×D3)⋊C412yes—
130C22×D3—64no—
131C22×D3—64no—
132C2×C3×C4—24no—
133C2×C3×C4—24no—
134C2×C3×C4—22no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—22no—
138C2×C3×C4—42no—
139C2×C3×C4—42no—
140C2×C3×C4—44no—
141C2×C3×C4(C2×D3)⋊C412yes—
142C2×C3×C4(C2×D3)⋊C412yes—
143C2×C3×C4(C2×D3)⋊C412yes—
144C2×C3×C4C2×C4×D312yes—
145C2×C3×C4C2×D1212yes—
146C2×C3×C4C2×#6712yes—
147#67—128no—
148#67—128no—
149C2×Dic3—64no—
150C2×Dic3—64no—
151D12—124no—
152D12—128no—
153D12—124no—
154D12—124no—
155D12—124no—
156C4×D3—128no—
157C4×D3—128no—
158Dic6—124no—
159Dic6—124no—
160C3×C8—124no—
161C3⋊C8—44no—
162C2×C32—41no—
163C2×C32C2×#10011yescharacteristic
164C2×C32#42112yes—
165C3⋊D3—82no—
166#41—364no—
167C2×Q8—92no—
168C2×D4—92no—
169C2×D4—182no—
170C2×D4—182no—
171C22×C4—182no—
172C22×C4#62411yescharacteristic
173C22×C4#62612yes—
174C2×C8—64no—
175C4⋊C4—182no—
176C22⋊C4—184no—
177C42#62411yescharacteristic
178C42#62612yes—
179C42C2×D3211yescharacteristic
180C22×C3—22no—
181C22×C3—22no—
182C22×C3—22no—
183C22×C3—22no—
184C22×C3—21no—
185C22×C3—42no—
186C22×C3C2×(C2×D3)⋊C412yes—
187C2×D3—124no—
188C2×D3—128no—
189C2×D3—124no—
190C2×D3—124no—
191C2×D3—124no—
192C3×C4—22no—
193C3×C4—24no—
194C3×C4—22no—
195C3×C4—22no—
196C3×C4—22no—
197C3×C4—22no—
198C3×C4—22no—
199C3×C4—22no—
200C3×C4—42no—
201C3×C4#82314yes—
202Dic3—124no—
203Dic3—124no—
204C32#153611yescharacteristic, complemented, Sylow
205C23—182no—
206C23#372211yescharacteristic
207Q8—362no—
208D4—362no—
209D4—364no—
210D4—364no—
211C2×C4—22no—
212C2×C4—42no—
213C2×C4—182no—
214C2×C4—364no—
215C2×C4#372212yes—
216C2×C4#372211yescharacteristic
217C2×C4C2×#62411yescharacteristic
218C2×C4C2×#62612yes—
219C8—124no—
220C2×C3—21no—
221C2×C3—22no—
222C2×C3—42no—
223C2×C3—42no—
224C2×C3#500512yes—
225C2×C3C2×#82312yes—
226C2×C3#513912yes—
227D3—244no—
228D3—244no—
229C22—21no—
230C22—22no—
231C22—362no—
232C22—364no—
233C22C2×#372211yescharacteristic
234C4—21no—
235C4—22no—
236C4—22no—
237C4—362no—
238C4#6355912yes—
239C3—21no—
240C3#7081112yescomplemented
241C2—41no—
242C2—722no—
243C2C2×#6355911yescharacteristic
244C2#1059111312yes—
subgroupG/H
centerC22C2×#3722
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#10595948C2
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1536
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4926C2semidirect
3. #10589087C2semidirect
18. #4926D3semidirect
204. C32#1536semidirect
240. C3#70811semidirect

Maximal subgroups

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

subgroupindex
#105959482
C3×#49262
#105890872
#708113