Finite Group Databasebeta

← #11796041

Subgroups — #11796041

Order 1152.

354 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 69 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×#64283C211yesmaximal, characteristic
2#10596481C212yesmaximal, complemented
3#10593274C212yesmaximal, complemented
4#10593266C212yesmaximal, complemented
5C22×C4×C3⋊D3C411yescharacteristic
6C2×#3792C411yescharacteristic
7C2×#3792C2211yescharacteristic
8#64283—22no—
9#64283—22no—
10C2×#3788C411yescharacteristic
11C2×#3788C2211yescharacteristic
12C2×#3787C411yescharacteristic
13C2×#3787C2211yescharacteristic
14#64218C2214yescomplemented
15#64214—22no—
16#64213—22no—
17C23×C3⋊D3C811yescharacteristic
18C22×C32×C4C811yescharacteristic
19C22×C3⋊Dic3C2×C411yescharacteristic
20C2×C4×C3⋊D3—21no—
21C2×C4×C3⋊D3—21no—
22C2×C4×C3⋊D3—21no—
23C2×C4×C3⋊D3—21no—
24C2×C4×C3⋊D3C811yescharacteristic
25C2×C4×C3⋊D3C811yescharacteristic
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×C4×C3⋊D3C2×C411yescharacteristic
28#3792—22no—
29#3792—22no—
30C2×#622C2×C411yescharacteristic
31C2×#622C2×C411yescharacteristic
32C2×#622C2×C411yescharacteristic
33C2×#622C2311yescharacteristic
34#3788—22no—
35#3788—22no—
36#3787—21no—
37#3787—21no—
38#3787D412yes—
39#3787D412yes—
40#3771—24no—
41C2×#349—91nomaximal, Sylow
42C22×C4×D3—121no—
43C23×C32C2×C811yescharacteristic
44C22×C3⋊D3—21no—
45C22×C3⋊D3—21no—
46C22×C3⋊D3—42no—
47C22×C3⋊D3C2×C811yescharacteristic
48C22×C3⋊D3C2×C811yescharacteristic
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4C2×C811yescharacteristic
52C2×C32×C4C2×C811yescharacteristic
53C2×C3⋊Dic3—21no—
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3C2×C811yescharacteristic
56C2×C3⋊Dic3C22×C411yescharacteristic
57C4×C3⋊D3—21no—
58C4×C3⋊D3—21no—
59C4×C3⋊D3—21no—
60C4×C3⋊D3—21no—
61C4×C3⋊D3—21no—
62C4×C3⋊D3—21no—
63C4×C3⋊D3C22⋊C411yescharacteristic
64C4×C3⋊D3C22⋊C411yescharacteristic
65C4×C3⋊D3M1611yescharacteristic
66C4×C3⋊D3M1611yescharacteristic
67#622—21no—
68#622—21no—
69#622C22⋊C412yes—
70#622C2×D412yes—
71C22×M16—91no—
72C2×M32—92no—
73#349—92no—
74#349—92no—
75C23×D3—121no—
76C22×C3×C4—41no—
77C22×Dic3—121no—
78C2×C4×D3—121no—
79C2×C4×D3—121no—
80C2×C4×D3—121no—
81C2×C4×D3—121no—
82C2×C4×D3—122no—
83C2×C4×D3—122no—
84C2×C4×D3—122no—
85C2×C4×D3—122no—
86C22×C32—21no—
87C22×C32—41no—
88C22×C32C22×C811yescharacteristic
89C2×C3⋊D3—22no—
90C2×C3⋊D3—21no—
91C2×C3⋊D3—42no—
92C2×C3⋊D3—42no—
93C2×C3⋊D3—41no—
94C2×C3⋊D3C22⋊C811yescharacteristic
95C2×C3⋊D3C22⋊C811yescharacteristic
96C32×C4—21no—
97C32×C4C22⋊C811yescharacteristic
98C32×C4C22⋊C811yescharacteristic
99C3⋊Dic3—21no—
100C3⋊Dic3C2×C22⋊C411yescharacteristic
101C3⋊Dic3C2×M1611yescharacteristic
102C23×C4—91no—
103C2×M16—91no—
104C2×M16—91no—
105C2×M16—91no—
106C2×M16—91no—
107C2×M16—182no—
108C2×M16—182no—
109C22×C8—91no—
110C22×C8—91no—
111M32—94no—
112M32—182no—
113C2×C16—182no—
114C23×C3—41no—
115C22×D3—121no—
116C22×D3—121no—
117C22×D3—122no—
118C22×D3—122no—
119C22×D3—128no—
120C2×C3×C4—42no—
121C2×C3×C4—42no—
122C2×C3×C4—41no—
123C2×C3×C4—41no—
124C2×Dic3—121no—
125C2×Dic3—121no—
126C2×Dic3—122no—
127C2×Dic3—122no—
128C4×D3—121no—
129C4×D3—121no—
130C4×D3—121no—
131C4×D3—121no—
132C4×D3—122no—
133C4×D3—122no—
134C4×D3—122no—
135C4×D3—122no—
136C4×D3—122no—
137C4×D3—122no—
138C2×C32—21no—
139C2×C32—41no—
140C2×C32C2×C22⋊C811yescharacteristic
141C3⋊D3—21no—
142C3⋊D3—41no—
143C3⋊D3#34912yescomplemented
144C24—91no—
145C22×C4—91no—
146C22×C4—91no—
147C22×C4—91no—
148C22×C4—91no—
149C22×C4—91no—
150C22×C4—181no—
151C22×C4—181no—
152C22×C4—181no—
153C22×C4—181no—
154C22×C4AGL(1,𝔽9)11yescharacteristic
155M16—182no—
156M16—182no—
157M16—182no—
158M16—182no—
159C2×C8—92no—
160C2×C8—91no—
161C2×C8—92no—
162C2×C8—91no—
163C2×C8—91no—
164C2×C8—91no—
165C2×C8—181no—
166C2×C8—181no—
167C16—184no—
168C22×C3—42no—
169C22×C3—44no—
170C22×C3—41no—
171C2×D3—121no—
172C2×D3—121no—
173C2×D3—122no—
174C2×D3—124no—
175C2×D3—124no—
176C2×D3—128no—
177C2×D3—128no—
178C3×C4—42no—
179C3×C4—41no—
180C3×C4—41no—
181Dic3—121no—
182Dic3—121no—
183Dic3—122no—
184C32C2×#34911yescharacteristic, complemented, Sylow
185C23—91no—
186C23—91no—
187C23—181no—
188C23—181no—
189C23—362no—
190C23C2×AGL(1,𝔽9)11yescharacteristic
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—91no—
196C2×C4—91no—
197C2×C4—91no—
198C2×C4—91no—
199C2×C4—181no—
200C2×C4—181no—
201C2×C4—181no—
202C2×C4—181no—
203C2×C4—181no—
204C2×C4—181no—
205C2×C4—181no—
206C2×C4—181no—
207C2×C4C2×AGL(1,𝔽9)11yescharacteristic
208C2×C4C2×AGL(1,𝔽9)11yescharacteristic
209C8—92no—
210C8—92no—
211C8—181no—
212C8—181no—
213C2×C3—42no—
214C2×C3—44no—
215C2×C3—41no—
216D3—122no—
217D3—122no—
218D3—124no—
219C22—21no—
220C22—41no—
221C22—91no—
222C22—91no—
223C22—182no—
224C22—181no—
225C22—361no—
226C22—362no—
227C22—362no—
228C22C22×AGL(1,𝔽9)11yescharacteristic
229C4—21no—
230C4—91no—
231C4—91no—
232C4—181no—
233C4C22⋊AGL(1,𝔽9)11yescharacteristic
234C4C22⋊AGL(1,𝔽9)11yescharacteristic
235C3—41no—
236C2—21no—
237C2—41no—
238C2—92no—
239C2—181no—
240C2—361no—
241C2C2×C22⋊AGL(1,𝔽9)11yescharacteristic
subgroupG/H
centerC4C22⋊AGL(1,𝔽9)
commutatorC22×C32C22×C8
FrattiniC22C22×AGL(1,𝔽9)
FittingC22×C32×C4C8
socleC2×C32C2×C22⋊C8
prime radicalC23×C3⋊D3C8
cosocleC2×#622C23
hypercenterC22×C4AGL(1,𝔽9)
hypocenterC32C2×#349
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. #10596481C2semidirect
3. #10593274C2semidirect
4. #10593266C2semidirect
14. #64218C22semidirect
143. C3⋊D3#349semidirect
184. C32C2×#349semidirect

Maximal subgroups

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

subgroupindex
C2×#642832
#105964812
#105932742
#105932662
C2×#3499