Finite Group Databasebeta

← #11796032

Subgroups — #11796032

Order 1152.

534 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 74 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×M16×C3⋊D3C211yesmaximal, characteristic
2#10593762C212yesmaximal, complemented
3#10590201C212yesmaximal, complemented
4#10590180C212yesmaximal, complemented
5C22×C4×C3⋊D3C411yescharacteristic
6C2×C32×M16C411yescharacteristic
7C2×#3748C2211yescharacteristic
8M16×C3⋊D3—22no—
9M16×C3⋊D3—22no—
10C2×#3743C411yescharacteristic
11C2×#3743C2211yescharacteristic
12C2×C8×C3⋊D3C411yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14#63773C2214yescomplemented
15#63765—22no—
16#63764—22no—
17C2×D3×M16—62no—
18C23×C3⋊D3C811yescharacteristic
19C22×C32×C4C2×C411yescharacteristic
20C22×C3⋊Dic3C811yescharacteristic
21C2×C4×C3⋊D3—21no—
22C2×C4×C3⋊D3—21no—
23C2×C4×C3⋊D3—21no—
24C2×C4×C3⋊D3—21no—
25C2×C4×C3⋊D3C811yescharacteristic
26C2×C4×C3⋊D3C811yescharacteristic
27C2×C4×C3⋊D3C2×C411yescharacteristic
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C32×M16—22no—
30C2×C32×C8C2×C411yescharacteristic
31C2×C32×C8C2×C411yescharacteristic
32#3748—22no—
33C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
34C2×C3⋊(C3⋊C8)C2311yescharacteristic
35#3743—22no—
36#3743—22no—
37C8×C3⋊D3—21no—
38C8×C3⋊D3—21no—
39C8×C3⋊D3D412yes—
40C8×C3⋊D3D412yes—
41#3708—24no—
42C2×#349—91nomaximal, Sylow
43C22×C4×D3—62no—
44C2×C3×M16—22no—
45C2×#208—62no—
46D3×M16—68no—
47D3×M16—68no—
48C2×ΓL(1,𝔽25)—62no—
49C2×ΓL(1,𝔽25)—62no—
50C2×D3×C8—62no—
51C2×D3×C8—62no—
52C23×C32C2×C811yescharacteristic
53C22×C3⋊D3—21no—
54C22×C3⋊D3—21no—
55C22×C3⋊D3—42no—
56C22×C3⋊D3C2×C811yescharacteristic
57C22×C3⋊D3C2×C811yescharacteristic
58C2×C32×C4—21no—
59C2×C32×C4—21no—
60C2×C32×C4C2×C811yescharacteristic
61C2×C32×C4C22×C411yescharacteristic
62C2×C3⋊Dic3—21no—
63C2×C3⋊Dic3—21no—
64C2×C3⋊Dic3C2×C811yescharacteristic
65C2×C3⋊Dic3C2×C811yescharacteristic
66C4×C3⋊D3—21no—
67C4×C3⋊D3—21no—
68C4×C3⋊D3—21no—
69C4×C3⋊D3—21no—
70C4×C3⋊D3—21no—
71C4×C3⋊D3—21no—
72C4×C3⋊D3C22⋊C411yescharacteristic
73C4×C3⋊D3C22⋊C411yescharacteristic
74C4×C3⋊D3M1611yescharacteristic
75C4×C3⋊D3M1611yescharacteristic
76C32×C8—21no—
77C32×C8C22⋊C412yes—
78C3⋊(C3⋊C8)—21no—
79C3⋊(C3⋊C8)C2×D412yes—
80C22×M16—91no—
81C2×M32—92no—
82#349—92no—
83#349—92no—
84C23×D3—62no—
85C22×C3×C4—22no—
86C22×Dic3—62no—
87C2×C4×D3—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×C4×D3—62no—
91C2×C4×D3—64no—
92C2×C4×D3—64no—
93C2×C4×D3—64no—
94C2×C4×D3—64no—
95C3×M16—28no—
96C2×C3×C8—22no—
97C2×C3×C8—22no—
98#208—68no—
99C2×C3⋊C8—62no—
100C2×C3⋊C8—62no—
101ΓL(1,𝔽25)—68no—
102ΓL(1,𝔽25)—68no—
103D3×C8—64no—
104D3×C8—64no—
105D3×C8—64no—
106D3×C8—64no—
107C22×C32—21no—
108C22×C32—41no—
109C22×C32C22×C811yescharacteristic
110C2×C3⋊D3—22no—
111C2×C3⋊D3—21no—
112C2×C3⋊D3—42no—
113C2×C3⋊D3—42no—
114C2×C3⋊D3—41no—
115C2×C3⋊D3C22⋊C811yescharacteristic
116C2×C3⋊D3C22⋊C811yescharacteristic
117C32×C4—21no—
118C32×C4C2×C22⋊C411yescharacteristic
119C32×C4C2×M1611yescharacteristic
120C3⋊Dic3—21no—
121C3⋊Dic3C22⋊C811yescharacteristic
122C3⋊Dic3C22⋊C811yescharacteristic
123C23×C4—91no—
124C2×M16—91no—
125C2×M16—91no—
126C2×M16—91no—
127C2×M16—182no—
128C2×M16—182no—
129C2×M16#15711yescharacteristic
130C22×C8—91no—
131C22×C8—91no—
132M32—94no—
133M32—182no—
134C2×C16—182no—
135C23×C3—22no—
136C22×D3—62no—
137C22×D3—62no—
138C22×D3—64no—
139C22×D3—64no—
140C22×D3—128no—
141C2×C3×C4—24no—
142C2×C3×C4—24no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—64no—
148C2×Dic3—64no—
149C4×D3—62no—
150C4×D3—62no—
151C4×D3—62no—
152C4×D3—62no—
153C4×D3—64no—
154C4×D3—64no—
155C4×D3—64no—
156C4×D3—64no—
157C4×D3—64no—
158C4×D3—64no—
159C3×C8—24no—
160C3×C8—24no—
161C3⋊C8—64no—
162C3⋊C8—64no—
163C2×C32—21no—
164C2×C32—41no—
165C2×C32C2×C22⋊C811yescharacteristic
166C3⋊D3—21no—
167C3⋊D3—41no—
168C3⋊D3#34912yescomplemented
169C24—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—181no—
176C22×C4—181no—
177C22×C4—181no—
178C22×C4—181no—
179C22×C4C2×#15711yescharacteristic
180M16—22no—
181M16—182no—
182M16—182no—
183M16—182no—
184C2×C8—91no—
185C2×C8—92no—
186C2×C8—92no—
187C2×C8—91no—
188C2×C8—181no—
189C2×C8—181no—
190C2×C8C2×#15711yescharacteristic
191C2×C8C2×#15711yescharacteristic
192C16—184no—
193C22×C3—24no—
194C22×C3—22no—
195C22×C3—44no—
196C2×D3—62no—
197C2×D3—62no—
198C2×D3—68no—
199C2×D3—64no—
200C2×D3—128no—
201C2×D3—128no—
202C2×D3—124no—
203C3×C4—24no—
204C3×C4—22no—
205C3×C4—22no—
206Dic3—62no—
207Dic3—62no—
208Dic3—64no—
209C32C2×#34911yescharacteristic, complemented, Sylow
210C23—91no—
211C23—91no—
212C23—181no—
213C23—181no—
214C23—362no—
215C23#378711yescharacteristic
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—91no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—91no—
224C2×C4—181no—
225C2×C4—181no—
226C2×C4—181no—
227C2×C4—181no—
228C2×C4—181no—
229C2×C4—181no—
230C2×C4—181no—
231C2×C4—181no—
232C2×C4#378711yescharacteristic
233C2×C4C22×#15711yescharacteristic
234C8—21no—
235C8—92no—
236C8—181no—
237C8C22⋊#15712yes—
238C2×C3—24no—
239C2×C3—22no—
240C2×C3—44no—
241D3—64no—
242D3—64no—
243D3—124no—
244C22—21no—
245C22—41no—
246C22—91no—
247C22—91no—
248C22—182no—
249C22—181no—
250C22—361no—
251C22—362no—
252C22—362no—
253C22C2×#378711yescharacteristic
254C4—21no—
255C4—91no—
256C4—91no—
257C4—181no—
258C4#6428311yescharacteristic
259C4C2×C22⋊#15711yescharacteristic
260C3—22no—
261C2—21no—
262C2—41no—
263C2—92no—
264C2—181no—
265C2—361no—
266C2#1059380011yescharacteristic
subgroupG/H
centerC4C2×C22⋊#157
commutatorC22×C32C22×C8
FrattiniC2×C4C22×#157
FittingC2×C32×M16C4
socleC2×C32C2×C22⋊C8
prime radicalC23×C3⋊D3C8
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC2×M16#157
hypocenterC32C2×#349
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C8 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10593762C2semidirect
3. #10590201C2semidirect
4. #10590180C2semidirect
14. #63773C22semidirect
168. C3⋊D3#349semidirect
209. C32C2×#349semidirect

Maximal subgroups

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

subgroupindex
C2×M16×C3⋊D32
#105937622
#105902012
#105901802
C2×#3499