Finite Group Databasebeta

← #11783569

Subgroups — #11783569

Order 1152.

1236 conjugacy classes of subgroups; only the 301 normal subgroups are shown.

normal subgroups only

This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 301 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
1C2×C42×C3⋊D3C211yesmaximal, characteristic
2C2×#63647C212yesmaximal
3C2×#63642C212yesmaximal, complemented
4C32×#336C211yesmaximal, characteristic, complemented
5#10589390C211yesmaximal, characteristic, complemented
6#68600—34nomaximal
7C22×C4×C3⋊D3C412yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C22×C32×C8C2212yes—
10C2×C32×C42C2211yescharacteristic
11C2×C4×C3⋊Dic3C412yes—
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2212yes—
14C42×C3⋊D3—24no—
15#63647C418yescomplemented
16#63642—24no—
17C2×C42×D3—34no—
18C2×(C2×D3)⋊C8—38no—
19C2×#815—38no—
20C3×#336D314yescomplemented
21#4524—34no—
22C23×C3⋊D3C2×C411yescharacteristic
23C22×C32×C4C2×C412yes—
24C22×C32×C4C2311yescharacteristic
25C22×C3⋊Dic3C2×C411yescharacteristic
26C22×C3⋊Dic3C2×C412yes—
27C2×C4×C3⋊D3—24no—
28C2×C4×C3⋊D3—24no—
29C2×C4×C3⋊D3—22no—
30C2×C4×C3⋊D3—21no—
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—24no—
33C2×C4×C3⋊D3C2×C414yes—
34C2×C32×C8—22no—
35C2×C32×C8—22no—
36C2×C32×C8C2×C414yescomplemented
37C32×C42—22no—
38C4×C3⋊Dic3—24no—
39C4×C3⋊Dic3D414yes—
40C2×C3⋊(C3⋊C8)—22no—
41C2×C3⋊(C3⋊C8)—22no—
42C2×C3⋊(C3⋊C8)C2×C414yescomplemented
43#1749—91noSylow
44C22×C4×D3—34no—
45C22×C4×D3—38no—
46C22×C3×C8C2×D318yes—
47C2×C3×C42C2×D314yes—
48C2×C4×Dic3—34no—
49C2×C4×Dic3—38no—
50C22×C3⋊C8—38no—
51C42×D3—616no—
52(C2×D3)⋊C8—332no—
53#815—616no—
54C23×C32C22×C411yescharacteristic
55C22×C3⋊D3—21no—
56C22×C3⋊D3—21no—
57C22×C3⋊D3—22no—
58C22×C3⋊D3C4212yes—
59C22×C3⋊D3M1614yes—
60C2×C32×C4—22no—
61C2×C32×C4—22no—
62C2×C32×C4M1614yes—
63C2×C32×C4C22×C412yes—
64C2×C32×C4C2×D412yes—
65C2×C32×C4#4111yescharacteristic
66C2×C32×C4#4111yescharacteristic
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—22no—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3C4212yes—
72C2×C3⋊Dic3C22⋊C414yes—
73C4×C3⋊D3—216no—
74C4×C3⋊D3—24no—
75C4×C3⋊D3—24no—
76C32×C8—24no—
77C3⋊(C3⋊C8)—24no—
78C22×C42—91no—
79C2×C22⋊C8—92no—
80C2×#97—92no—
81#336—91no—
82#336C3⋊D311yescharacteristic, complemented
83C23×D3—34no—
84C22×C3×C4C4×D318yes—
85C22×C3×C4C22×D314yes—
86C22×Dic3—34no—
87C22×Dic3—38no—
88C2×C4×D3—316no—
89C2×C4×D3—616no—
90C2×C4×D3—616no—
91C2×C4×D3—616no—
92C2×C4×D3—68no—
93C2×C4×D3—64no—
94C2×C4×D3—64no—
95C2×C3×C8—28no—
96C2×C3×C8—28no—
97C2×C3×C8C4×D3116yescomplemented
98C3×C42—28no—
99C4×Dic3—316no—
100C4×Dic3—616no—
101C2×C3⋊C8—316no—
102C2×C3⋊C8—68no—
103C2×C3⋊C8—68no—
104C22×C32C2×C4211yescharacteristic
105C22×C32C2×C22⋊C411yescharacteristic
106C22×C32#11711yescharacteristic
107C22×C32C2×M1612yes—
108C22×C32C2×M1612yes—
109C2×C3⋊D3—22no—
110C2×C3⋊D3—22no—
111C2×C3⋊D3—24no—
112C2×C3⋊D3—24no—
113C2×C3⋊D3#9714yescomplemented
114C32×C4—24no—
115C32×C4C4×D412yes—
116C32×C4C4×D412yes—
117C3⋊Dic3—22no—
118C3⋊Dic3—24no—
119C23×C4—91no—
120C23×C4—92no—
121C22×C8—92no—
122C22×C8C2×C3⋊D312yes—
123C2×C42—91no—
124C2×C42—92no—
125C2×C42—184no—
126C2×C42C2×C3⋊D311yescharacteristic
127C22⋊C8—98no—
128#97—184no—
129C23×C3C2×C4×D314yes—
130C22×D3—38no—
131C22×D3—316no—
132C22×D3—64no—
133C22×D3—64no—
134C22×D3—68no—
135C2×C3×C4—28no—
136C2×C3×C4—28no—
137C2×C3×C4ΓL(1,𝔽25)116yes—
138C2×C3×C4C2×C4×D318yes—
139C2×C3×C4D3×D418yes—
140C2×C3×C4#23714yes—
141C2×C3×C4#23914yes—
142C2×Dic3—38no—
143C2×Dic3—316no—
144C2×Dic3—64no—
145C2×Dic3—64no—
146C2×Dic3—68no—
147C2×Dic3—68no—
148C4×D3—664no—
149C4×D3—616no—
150C4×D3—616no—
151C3×C8—216no—
152C3⋊C8—616no—
153C2×C32C4×C22⋊C411yescharacteristic
154C2×C32C2×#9711yescharacteristic
155C2×C32C4×M1611yescharacteristic
156C2×C32#40712yes—
157C2×C32#43212yes—
158C3⋊D3—24no—
159C24—91no—
160C22×C4—91no—
161C22×C4—92no—
162C22×C4—94no—
163C22×C4—184no—
164C22×C4—184no—
165C22×C4—184no—
166C22×C4—182no—
167C22×C4—181no—
168C22×C4—181no—
169C22×C4C4×C3⋊D312yes—
170C22×C4C22×C3⋊D311yescharacteristic
171C2×C8—22no—
172C2×C8—22no—
173C2×C8—94no—
174C2×C8—182no—
175C2×C8—182no—
176C2×C8C4×C3⋊D314yescomplemented
177C42—22no—
178C42—94no—
179C42—184no—
180C22×C3C42×D314yes—
181C22×C3D3×C22⋊C414yes—
182C22×C3#89214yes—
183C22×C3C2×ΓL(1,𝔽25)18yes—
184C22×C3D3×M1618yes—
185C2×D3—316no—
186C2×D3—68no—
187C2×D3—68no—
188C2×D3—616no—
189C2×D3—616no—
190C3×C4—216no—
191C3×C4#67⋊C418yes—
192C3×C4#89318yes—
193Dic3—68no—
194Dic3—616no—
195C32#174911yescharacteristic, complemented, Sylow
196C23—92no—
197C23—94no—
198C23—181no—
199C23—181no—
200C23—182no—
201C23C2×C4×C3⋊D311yescharacteristic
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—92no—
205C2×C4—94no—
206C2×C4—1816no—
207C2×C4—181no—
208C2×C4—181no—
209C2×C4—182no—
210C2×C4—182no—
211C2×C4—184no—
212C2×C4—184no—
213C2×C4#374314yes—
214C2×C4C2×C4×C3⋊D312yes—
215C2×C4D4×C3⋊D312yes—
216C2×C4#383011yescharacteristic
217C2×C4#383211yescharacteristic
218C8—24no—
219C8—184no—
220C2×C3#466614yes—
221C2×C3C4×ΓL(1,𝔽25)14yes—
222C2×C3D3×#9714yes—
223C2×C3#472618yes—
224C2×C3#483518yes—
225D3—616no—
226C22—94no—
227C22—184no—
228C22—182no—
229C22—182no—
230C22—184no—
231C22C42×C3⋊D311yescharacteristic
232C22C22⋊C4×C3⋊D311yescharacteristic
233C22#6410111yescharacteristic
234C22C2×#374312yes—
235C22M16×C3⋊D312yes—
236C4—24no—
237C4—182no—
238C4—184no—
239C4#6409012yes—
240C4#6410212yes—
241C3#6860014yescomplemented
242C2—184no—
243C2#1059236511yescharacteristic
244C2C4×#374311yescharacteristic
245C2C3⋊D3×#9711yescharacteristic
246C2#1059242512yes—
247C2#1059253412yes—
subgroupG/H
center, FrattiniC22×C4C22×C3⋊D3
commutatorC22×C32C2×C42
FittingC32×#336C2
socleC23×C32C22×C4
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C32×C4C23
hypercenter#336C3⋊D3
hypocenterC32#1749
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
3. C2×#63642C2semidirect
4. C32×#336C2semidirect
5. #10589390C2semidirect
15. #63647C4semidirect
20. C3×#336D3semidirect
36. C2×C32×C8C2×C4semidirect
42. C2×C3⋊(C3⋊C8)C2×C4semidirect
82. #336C3⋊D3semidirect
97. C2×C3×C8C4×D3semidirect
113. C2×C3⋊D3#97semidirect
176. C2×C8C4×C3⋊D3semidirect
195. C32#1749semidirect
241. C3#68600semidirect

Maximal subgroups

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

subgroupindex
C2×C42×C3⋊D32
C2×#636472
C2×#636422
C32×#3362
#105893902
#686003