Finite Group Databasebeta

← #11776930

Subgroups — #11776930

Order 1152.

417 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 417 conjugacy classes of subgroups — too many to draw. Only its 112 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
1C4×C8×C3⋊D3C211yesmaximal, characteristic
2#10590260C212yesmaximal
3C3×#4458C212yesmaximal, complemented
4#10589098C212yesmaximal, complemented
5#68570—32nomaximal
6C2×C8×C3⋊D3C411yescharacteristic
7C2×C8×C3⋊D3C411yescharacteristic
8C42×C3⋊D3C2211yescharacteristic
9C32×C4×C8C2211yescharacteristic
10C8×C3⋊Dic3C411yescharacteristic
11C8×C3⋊Dic3C411yescharacteristic
12C4×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×C4⋊(C3⋊C8)C2214yes—
14#63557—22no—
15#63555—22no—
16#4835—34no—
17C4×D3×C8—32no—
18C4×D3×C8—61no—
19C3×#335—32no—
20#4480—34no—
21#4458D312yescomplemented
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3Q811yescharacteristic
25C2×C32×C8C2×C411yescharacteristic
26C2×C32×C8C2×C411yescharacteristic
27C32×C42C2311yescharacteristic
28C4×C3⋊Dic3C2×C411yescharacteristic
29C4×C3⋊Dic3D411yescharacteristic
30C4×C3⋊Dic3Q811yescharacteristic
31C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
32C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
33C8×C3⋊D3—22no—
34C8×C3⋊D3—22no—
35C2×C3×C3⋊C8—24no—
36#1568—91noSylow
37C2×D3×C8—32no—
38C2×D3×C8—32no—
39C2×D3×C8—61no—
40C2×D3×C8—61no—
41C42×D3—32no—
42C42×D3—61no—
43C3×C4⋊C8—34no—
44C3×C4×C8—21no—
45C3×C4×C8C2×D312yes—
46(C2×D3)⋊C8—64no—
47#815—64no—
48C8×Dic3—32no—
49C8×Dic3—32no—
50C8×Dic3—61no—
51C8×Dic3—61no—
52C4⋊(C3⋊C8)C2×D314yes—
53C4×C3⋊C8—32no—
54C4×C3⋊C8—61no—
55C22×C3⋊D3C4⋊C411yescharacteristic
56C2×C32×C4C22×C411yescharacteristic
57C2×C32×C4C2×D411yescharacteristic
58C2×C32×C4C2×Q811yescharacteristic
59C2×C3⋊Dic3C4⋊C411yescharacteristic
60C2×C3⋊Dic3C4⋊C411yescharacteristic
61C2×C3⋊Dic3C4⋊C411yescharacteristic
62C4×C3⋊D3—22no—
63C4×C3⋊D3—21no—
64C4×C3⋊D3—21no—
65C4×C3⋊D3—22no—
66C32×C8—21no—
67C32×C8M1612yes—
68C3⋊(C3⋊C8)—21no—
69C3⋊(C3⋊C8)M1612yes—
70C3×C3⋊C8—44no—
71#432—92no—
72C2×C4×C8—91no—
73#335—32no—
74#334—92no—
75C2×C4×D3—32no—
76C2×C4×D3—32no—
77C2×C4×D3—32no—
78C2×C4×D3—61no—
79C2×C4×D3—61no—
80C2×C4×D3—61no—
81C2×C3×C8—21no—
82C2×C3×C8—21no—
83C2×C3×C8—64no—
84C2×C3×C8C4×D312yes—
85C2×C3×C8C4×D312yes—
86C3×C42—21no—
87C3×C42C22×D312yes—
88C4×Dic3—32no—
89C4×Dic3—32no—
90C4×Dic3—32no—
91C4×Dic3—61no—
92C4×Dic3—61no—
93C4×Dic3—61no—
94C2×C3⋊C8—24no—
95C2×C3⋊C8—32no—
96C2×C3⋊C8—32no—
97C2×C3⋊C8—61no—
98C2×C3⋊C8—61no—
99D3×C8—64no—
100D3×C8—64no—
101D3×C8—64no—
102D3×C8—64no—
103C22×C32C2×C4⋊C411yescharacteristic
104C2×C3⋊D3—21no—
105C2×C3⋊D3—21no—
106C2×C3⋊D3#10812yes—
107C32×C4—21no—
108C32×C4C2×M1611yescharacteristic
109C32×C4C2×M1611yescharacteristic
110C32×C4#13512yes—
111C3⋊Dic3—21no—
112C3⋊Dic3—21no—
113C3⋊Dic3—21no—
114C22×C8—91no—
115C22×C8—91no—
116C2×C42—91no—
117C4⋊C8—34no—
118C22⋊C8—182no—
119#97—182no—
120C4×C8—91no—
121C4×C8—91no—
122C4×C8—91no—
123C4×C8D3211yescharacteristic
124C22×D3—32no—
125C22×D3—61no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4C2×C4×D312yes—
130C2×C3×C4D3×D412yes—
131C2×C3×C4D3×Q812yes—
132C2×Dic3—32no—
133C2×Dic3—32no—
134C2×Dic3—32no—
135C2×Dic3—61no—
136C2×Dic3—61no—
137C2×Dic3—61no—
138C4×D3—64no—
139C4×D3—62no—
140C4×D3—62no—
141C4×D3—64no—
142C4×D3—64no—
143C4×D3—62no—
144C4×D3—62no—
145C4×D3—62no—
146C4×D3—62no—
147C3×C8—22no—
148C3×C8—22no—
149C3×C8—22no—
150C3×C8—124no—
151C3×C8ΓL(1,𝔽25)14yes—
152C3⋊C8—34no—
153C3⋊C8—44no—
154C3⋊C8—62no—
155C3⋊C8—62no—
156C3⋊C8—62no—
157C2×C32#42311yescharacteristic
158C2×C32#42711yescharacteristic
159C2×C32C2×#10811yescharacteristic
160C3⋊D3—22no—
161C22×C4—91no—
162C22×C4—91no—
163C22×C4—91no—
164C2×C8—64no—
165C2×C8—91no—
166C2×C8—91no—
167C2×C8—182no—
168C2×C8—182no—
169C2×C8#62411yescharacteristic
170C2×C8#62411yescharacteristic
171C42—91no—
172C42—91no—
173C42—91no—
174C42C2×D3211yescharacteristic
175C22×C3—21no—
176C22×C3D3×C4⋊C412yes—
177C2×D3—34no—
178C2×D3—62no—
179C2×D3—62no—
180C2×D3—62no—
181C2×D3—62no—
182C2×D3—62no—
183C3×C4—22no—
184C3×C4—22no—
185C3×C4—22no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4C2×ΓL(1,𝔽25)12yes—
189C3×C4D3×M1612yes—
190C3×C4#91212yes—
191C3×C4#91912yes—
192Dic3—62no—
193Dic3—62no—
194Dic3—62no—
195Dic3—62no—
196Dic3—62no—
197Dic3—62no—
198C32#156811yescharacteristic, complemented, Sylow
199C23—91no—
200C2×C4—91no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—182no—
204C2×C4—182no—
205C2×C4—181no—
206C2×C4—181no—
207C2×C4#379711yescharacteristic
208C2×C4#380211yescharacteristic
209C2×C4C2×#62411yescharacteristic
210C8—21no—
211C8—92no—
212C8—124no—
213C8—181no—
214C8#371212yes—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—21no—
218C2×C3#483712yes—
219C2×C3#488012yes—
220C2×C3D3×#10812yes—
221D3—64no—
222D3—64no—
223C22—92no—
224C22—181no—
225C22—181no—
226C22#6390011yescharacteristic
227C4—21no—
228C4—181no—
229C4—181no—
230C4—181no—
231C4#6381012yes—
232C4#6381811yescharacteristic
233C4C2×#371211yescharacteristic
234C3—21no—
235C3#6857012yescomplemented
236C2—182no—
237C2#1059034011yescharacteristic
238C2#1059071411yescharacteristic
239C2#1059091311yescharacteristic
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#1568
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
3. C3×#4458C2semidirect
4. #10589098C2semidirect
21. #4458D3semidirect
198. C32#1568semidirect
235. C3#68570semidirect

Maximal subgroups

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

subgroupindex
C4×C8×C3⋊D32
#105902602
C3×#44582
#105890982
#685703