Finite Group Databasebeta

← #11796055

Subgroups — #11796055

Order 1152.

486 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 72 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×#64110C211yesmaximal, characteristic
2#10593762C212yesmaximal, complemented
3#10590201C212yesmaximal, complemented
4#10590180C212yesmaximal, complemented
5C2×#3828C411yescharacteristic
6C22×C32×C8C411yescharacteristic
7C2×#3748C2211yescharacteristic
8#64110—22no—
9#64110—22no—
10C2×#3743C411yescharacteristic
11C2×#3743C2211yescharacteristic
12C2×C8×C3⋊D3C411yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14#63773C2214yes—
15#63765—22no—
16#63764—22no—
17C2×#901—62no—
18C22×C32×C4C2×C411yescharacteristic
19C2×#638C811yescharacteristic
20C2×#638C811yescharacteristic
21#3828—22no—
22#3828—22no—
23C2×C4⋊(C3⋊D3)C811yescharacteristic
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×#634C811yescharacteristic
27C2×C32×C8—21no—
28C2×C32×C8—21no—
29C2×C32×C8C2×C411yescharacteristic
30C2×C32×C8C2×C411yescharacteristic
31#3748—22no—
32C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
33C2×C3⋊(C3⋊C8)C2311yescharacteristic
34#3743—22no—
35#3743—22no—
36C8×C3⋊D3—21no—
37C8×C3⋊D3—21no—
38C8×C3⋊D3D412yes—
39C8×C3⋊D3D412yes—
40#3708—24no—
41#2115—91nomaximal, Sylow
42C2×#235—62no—
43C22×C3×C8—22no—
44C2×#208—62no—
45#901—68no—
46#901—68no—
47C2×ΓL(1,𝔽25)—62no—
48C2×ΓL(1,𝔽25)—62no—
49C2×D3×C8—62no—
50C2×D3×C8—62no—
51C23×C32C2×C811yescharacteristic
52C22×C3⋊D3C2×C811yescharacteristic
53C22×C3⋊D3C2×C811yescharacteristic
54C2×C32×C4—21no—
55C2×C32×C4—21no—
56C2×C32×C4C2×C811yescharacteristic
57C2×C32×C4C22×C411yescharacteristic
58#638—22no—
59#638—22no—
60C2×C3⋊Dic3C2×C811yescharacteristic
61C2×C3⋊Dic3C2×C811yescharacteristic
62C4⋊(C3⋊D3)—22no—
63C4×C3⋊D3—21no—
64C4×C3⋊D3—21no—
65C4×C3⋊D3C22⋊C412yes—
66C4×C3⋊D3M1612yes—
67#634—22no—
68C32×C8—21no—
69C32×C8C22⋊C411yescharacteristic
70C32×C8C22⋊C411yescharacteristic
71C3⋊(C3⋊C8)—21no—
72C3⋊(C3⋊C8)C2×D412yes—
73C2×#131—91no—
74C2×M32—92no—
75#349—92no—
76#349—92no—
77C22×C3×C4—22no—
78C2×#67—62no—
79C2×#67—62no—
80#235—68no—
81#235—68no—
82C2×D12—62no—
83C2×C4×D3—62no—
84C2×C4×D3—62no—
85C2×Dic6—62no—
86C2×C3×C8—24no—
87C2×C3×C8—24no—
88C2×C3×C8—22no—
89C2×C3×C8—22no—
90#208—68no—
91C2×C3⋊C8—62no—
92C2×C3⋊C8—62no—
93ΓL(1,𝔽25)—68no—
94ΓL(1,𝔽25)—68no—
95D3×C8—64no—
96D3×C8—64no—
97D3×C8—64no—
98D3×C8—64no—
99C22×C32—21no—
100C22×C32—41no—
101C22×C32C22×C811yescharacteristic
102C2×C3⋊D3—21no—
103C2×C3⋊D3—41no—
104C2×C3⋊D3—41no—
105C2×C3⋊D3C22⋊C812yes—
106C32×C4—21no—
107C32×C4C2×C22⋊C411yescharacteristic
108C32×C4C2×M1611yescharacteristic
109C3⋊Dic3—21no—
110C3⋊Dic3C22⋊C812yes—
111C2×#41—91no—
112#131—182no—
113#131—182no—
114C2×M16—91no—
115C2×M16—91no—
116C2×M16—91no—
117C22×C8—91no—
118C22×C8—91no—
119C22×C8#15711yescharacteristic
120M32—94no—
121M32—182no—
122C2×C16—182no—
123C23×C3—22no—
124C22×D3—62no—
125C22×D3—62no—
126C2×C3×C4—24no—
127C2×C3×C4—24no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130#67—68no—
131#67—68no—
132C2×Dic3—62no—
133C2×Dic3—62no—
134D12—68no—
135C4×D3—64no—
136C4×D3—64no—
137C4×D3—64no—
138C4×D3—64no—
139Dic6—68no—
140C3×C8—24no—
141C3×C8—22no—
142C3×C8—22no—
143C3⋊C8—64no—
144C3⋊C8—64no—
145C2×C32—21no—
146C2×C32—41no—
147C2×C32C2×C22⋊C811yescharacteristic
148C3⋊D3—22no—
149C3⋊D3—41no—
150#41—182no—
151#41—182no—
152C2×Q8—91no—
153C2×D4—91no—
154C2×D4—91no—
155C2×D4—91no—
156C22×C4—91no—
157C22×C4—91no—
158C22×C4C2×#15711yescharacteristic
159M16—182no—
160M16—182no—
161M16—182no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—91no—
165C2×C8—92no—
166C2×C8—92no—
167C2×C8—91no—
168C2×C8—181no—
169C2×C8—181no—
170C2×C8C2×#15711yescharacteristic
171C2×C8C2×#15711yescharacteristic
172C16—184no—
173C22×C3—24no—
174C22×C3—22no—
175C22×C3—44no—
176C2×D3—64no—
177C2×D3—64no—
178C2×D3—124no—
179C2×D3—124no—
180C3×C4—24no—
181C3×C4—22no—
182C3×C4—22no—
183Dic3—64no—
184Dic3—64no—
185C32#211511yescharacteristic, complemented, Sylow
186C23—91no—
187C23—91no—
188C23#378711yescharacteristic
189Q8—182no—
190D4—182no—
191D4—182no—
192D4—182no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—91no—
196C2×C4—92no—
197C2×C4—92no—
198C2×C4—91no—
199C2×C4—181no—
200C2×C4—181no—
201C2×C4#378711yescharacteristic
202C2×C4C22×#15711yescharacteristic
203C8—21no—
204C8—92no—
205C8—181no—
206C8C22⋊#15711yescharacteristic
207C8C22⋊#15711yescharacteristic
208C2×C3—24no—
209C2×C3—22no—
210C2×C3—44no—
211D3—124no—
212D3—124no—
213C22—21no—
214C22—41no—
215C22—92no—
216C22—181no—
217C22—361no—
218C22—361no—
219C22C2×#378711yescharacteristic
220C4—21no—
221C4—92no—
222C4—181no—
223C4#6428311yescharacteristic
224C4C2×C22⋊#15711yescharacteristic
225C3—22no—
226C2—21no—
227C2—41no—
228C2—182no—
229C2—361no—
230C2#1059380011yescharacteristic
subgroupG/H
centerC8C22⋊#157
commutatorC22×C32C22×C8
FrattiniC2×C4C22×#157
FittingC22×C32×C8C4
socleC2×C32C2×C22⋊C8
prime radicalC2×#3828C4
cosocleC2×C3⋊(C3⋊C8)C23
hypercenterC22×C8#157
hypocenterC32#2115
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10593762C2semidirect
3. #10590201C2semidirect
4. #10590180C2semidirect
185. C32#2115semidirect

Maximal subgroups

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

subgroupindex
C2×#641102
#105937622
#105902012
#105901802
#21159