Finite Group Databasebeta

← #11771393

Subgroups — #11771393

Order 1152.

469 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 469 conjugacy classes of subgroups — too many to draw. Only its 66 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#10592687C211yesmaximal, characteristic
2C3×#4528C212yesmaximal, complemented
3#67454—32nomaximal
4C22×C4⋊(C3⋊D3)C411yescharacteristic
5C2×C32×C4⋊C4C2211yescharacteristic
6C2×#3752—22no—
7C2×C4×C3⋊Dic3C411yescharacteristic
8C3×#830—22no—
9#4988—32no—
10#4988—61no—
11C3×#324—32no—
12#4528D312yescomplemented
13C23×C3⋊D3—21no—
14C22×C32×C4C2×C411yescharacteristic
15C22×C32×C4D412yes—
16C22×C3⋊Dic3—21no—
17C2×C4⋊(C3⋊D3)—21no—
18C2×C4⋊(C3⋊D3)—41no—
19C2×C4⋊(C3⋊D3)—41no—
20C2×C4⋊(C3⋊D3)C812yescomplemented
21C32×C4⋊C4—41no—
22#3752—44no—
23C4×C3⋊Dic3—41no—
24C2×C3×C3⋊C8—42no—
25#1318—91noSylow
26C22×D12—32no—
27C22×D12—61no—
28C2×C3×C4⋊C4—21no—
29C2×C3×C4⋊C4C2×D312yes—
30C2×(C2×D3)⋊C4—64no—
31C2×(C2×D3)⋊C4—62no—
32C2×(C2×D3)⋊C4—62no—
33C2×C4×Dic3—32no—
34C2×C4×Dic3—61no—
35C3×C22⋊C8—62no—
36#830—22no—
37C23×C32C22⋊C411yescharacteristic
38C22×C3⋊D3—22no—
39C22×C3⋊D3—42no—
40C22×C3⋊D3—42no—
41C22×C3⋊D3—41no—
42C22×C3⋊D3—41no—
43C2×C32×C4—21no—
44C2×C32×C4—21no—
45C2×C32×C4—22no—
46C2×C32×C4—42no—
47C2×C32×C4C2×C811yescharacteristic
48C2×C32×C4M1611yescharacteristic
49C2×C3⋊Dic3—22no—
50C2×C3⋊Dic3—41no—
51C2×C3⋊Dic3—41no—
52C4⋊(C3⋊D3)—42no—
53C4⋊(C3⋊D3)—42no—
54C3×C3⋊C8—82no—
55#390—91no—
56#324—32no—
57C23×D3—62no—
58C23×D3—62no—
59C22×C3×C4—21no—
60C22×C3×C4—22no—
61C22×C3×C4C4×D312yes—
62C22×C3×C4D1212yes—
63C22×C3×C4#6712yes—
64C22×Dic3—62no—
65C22×Dic3—62no—
66C2×D12—34no—
67C2×D12—62no—
68C2×D12—62no—
69C2×D12—62no—
70C2×D12—122no—
71C2×D12—122no—
72C2×D12—122no—
73C2×D12—122no—
74C2×C3×C8—122no—
75C3×C4⋊C4—42no—
76C3×C4⋊C4—42no—
77(C2×D3)⋊C4—124no—
78(C2×D3)⋊C4—124no—
79(C2×D3)⋊C4—128no—
80C4×Dic3—122no—
81C4×Dic3—122no—
82C2×C3⋊C8—42no—
83C22×C32—21no—
84C22×C32—21no—
85C22×C32C22⋊C811yescharacteristic
86C22×C32#9911yescharacteristic
87C22×C32#10011yescharacteristic
88C2×C3⋊D3—44no—
89C2×C3⋊D3—42no—
90C2×C3⋊D3—82no—
91C2×C3⋊D3—81no—
92C2×C3⋊D3—81no—
93C32×C4—21no—
94C32×C4—21no—
95C32×C4—42no—
96C3⋊Dic3—42no—
97C22×D4—91no—
98C2×C4⋊C4D3211yescharacteristic
99C2×C22⋊C4—182no—
100C2×C42—91no—
101C22⋊C8—62no—
102C23×C3—21no—
103C23×C3(C2×D3)⋊C412yes—
104C22×D3—64no—
105C22×D3—64no—
106C22×D3—124no—
107C22×D3—122no—
108C22×D3—122no—
109C22×D3—122no—
110C22×D3—122no—
111C22×D3—124no—
112C22×D3—122no—
113C22×D3—122no—
114C22×D3—122no—
115C22×D3—122no—
116C2×C3×C4—22no—
117C2×C3×C4—22no—
118C2×C3×C4—22no—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
121C2×C3×C4—22no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—42no—
125C2×C3×C4—42no—
126C2×C3×C4—42no—
127C2×C3×C4—44no—
128C2×C3×C4D3×C812yes—
129C2×C3×C4ΓL(1,𝔽25)12yes—
130C2×Dic3—64no—
131C2×Dic3—64no—
132C2×Dic3—122no—
133C2×Dic3—122no—
134C2×Dic3—122no—
135C2×Dic3—122no—
136D12—124no—
137D12—124no—
138D12—124no—
139D12—124no—
140C3×C8—242no—
141C3⋊C8—82no—
142C2×C32—21no—
143C2×C32—21no—
144C2×C32#32311yescharacteristic
145C2×C32#35311yescharacteristic
146C2×C32#35511yescharacteristic
147C3⋊D3—82no—
148C24—181no—
149C2×D4—92no—
150C2×D4—181no—
151C2×D4—361no—
152C2×D4—361no—
153C22×C4—181no—
154C22×C4#62411yescharacteristic
155C22×C4#62612yes—
156C2×C8—122no—
157C4⋊C4—41no—
158C22⋊C4—364no—
159C42—361no—
160C22×C3—22no—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—22no—
164C22×C3—21no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3#80612yes—
168C22×C3(C2×D3)⋊C812yes—
169C22×C3#82312yes—
170C2×D3—124no—
171C2×D3—128no—
172C2×D3—124no—
173C2×D3—124no—
174C2×D3—124no—
175C2×D3—244no—
176C2×D3—242no—
177C2×D3—242no—
178C2×D3—242no—
179C2×D3—242no—
180C2×D3—242no—
181C2×D3—242no—
182C3×C4—22no—
183C3×C4—22no—
184C3×C4—22no—
185C3×C4—22no—
186C3×C4—42no—
187C3×C4—42no—
188C3×C4—82no—
189Dic3—124no—
190Dic3—124no—
191C32#131811yescharacteristic, complemented, Sylow
192C23—182no—
193C23—362no—
194C23—362no—
195C23—361no—
196C23—361no—
197C23#372211yescharacteristic
198D4—362no—
199D4—362no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—42no—
204C2×C4—182no—
205C2×C4—361no—
206C2×C4—361no—
207C2×C4#371011yescharacteristic
208C2×C4#371211yescharacteristic
209C8—242no—
210C2×C3—22no—
211C2×C3—22no—
212C2×C3—22no—
213C2×C3—22no—
214C2×C3—21no—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3#446812yes—
218C2×C3#447412yes—
219C2×C3#447712yes—
220D3—244no—
221D3—244no—
222C22—21no—
223C22—21no—
224C22—364no—
225C22—362no—
226C22—722no—
227C22—721no—
228C22—721no—
229C22#6355711yescharacteristic
230C22#6355911yescharacteristic
231C22#6358111yescharacteristic
232C4—21no—
233C4—21no—
234C4—42no—
235C4—362no—
236C3—21no—
237C3#6745412yescomplemented
238C2—21no—
239C2—21no—
240C2—722no—
241C2#1058914611yescharacteristic
242C2#1058917911yescharacteristic
243C2#1058918311yescharacteristic
subgroupG/H
centerC22#63581
commutatorC2×C32×C4C2×C8
Frattini, hypercenterC2×C4⋊C4D32
Fitting, cosocleC2×C32×C4⋊C4C22
socleC22×C32#99
prime radicalC22×C4⋊(C3⋊D3)C4
hypocenterC32#1318
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4528C2semidirect
12. #4528D3semidirect
20. C2×C4⋊(C3⋊D3)C8semidirect
191. C32#1318semidirect
237. C3#67454semidirect

Maximal subgroups

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

subgroupindex
#105926872
C3×#45282
#674543