Finite Group Databasebeta

← #10593319

Subgroups — #10593319

Order 576.

278 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 47 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
1#64306C211yesmaximal, characteristic
2C2×C4⋊#157C211yesmaximal, characteristic, complemented
3#63818C211yesmaximal, characteristic, complemented
4#63730C212yesmaximal, complemented
5#63729C212yesmaximal, complemented
6C22×#157—21no—
7C2×C4×C3⋊D3C2211yescharacteristic
8C3×#235—21no—
9#3811—21no—
10#3805C412yescomplemented
11#3802C2211yescharacteristic
12C4×D32—21no—
13#3798C412yescomplemented
14#3797C2211yescharacteristic
15#3796—21no—
16C4⋊#157—21no—
17C4⋊#157C2212yes—
18C3×#208—21no—
19#3712—21no—
20#3710C2212yes—
21D3×#41—61no—
22D3×M16—61no—
23C22×C3⋊D3D411yescharacteristic
24C2×D32—21no—
25C2×#157—22no—
26C2×#157—42no—
27C2×C32×C4D411yescharacteristic
28C2×C3⋊Dic3C2×C411yescharacteristic
29C4×C3⋊D3C2×C411yescharacteristic
30C4×C3⋊D3D411yescharacteristic
31C4×C3⋊D3D411yescharacteristic
32C4×C3⋊D3C2311yescharacteristic
33C3×#67—22no—
34C3×D12—21no—
35C3×C4×D3—22no—
36C3×Dic6—21no—
37#627C2×C412yescomplemented
38#626—22no—
39#625C2×C412yescomplemented
40#624—21no—
41D3×Dic3—22no—
42C3×C3⋊C8—22no—
43#417—91nomaximal, Sylow
44C3×#41—61no—
45#239—61no—
46D3×Q8—61no—
47#237—62no—
48#237—61no—
49D3×D4—61no—
50D3×D4—62no—
51#235—21no—
52#235—62no—
53C2×C4×D3—61no—
54C2×C4×D3—61no—
55C2×C4×D3—62no—
56C3×M16—61no—
57#208—21no—
58ΓL(1,𝔽25)—62no—
59D3×C8—62no—
60C22×C32C22⋊C411yescharacteristic
61C2×C3⋊D3—21no—
62C2×C3⋊D3—21no—
63C2×C3⋊D3C22⋊C411yescharacteristic
64C2×C3⋊D3C2×D411yescharacteristic
65C2×C3×D3—22no—
66D32—41no—
67D32—41no—
68#157—42no—
69C32×C4C22⋊C411yescharacteristic
70C32×C4C2×D411yescharacteristic
71C3⋊Dic3C22⋊C411yescharacteristic
72C3⋊Dic3C22×C411yescharacteristic
73C3×Dic3—22no—
74C2×#41—91no—
75C2×M16—91no—
76C2×C4⋊C4—91no—
77#103—92no—
78#102—92no—
79C22×D3—61no—
80C22×D3—61no—
81C22×D3—62no—
82C3×Q8—61no—
83C3×D4—61no—
84C3×D4—62no—
85C2×C3×C4—21no—
86C2×C3×C4—21no—
87C2×C3×C4—62no—
88#67—22no—
89#67—62no—
90#67—62no—
91C2×Dic3—61no—
92C2×Dic3—61no—
93C2×Dic3—62no—
94D12—21no—
95D12—62no—
96C4×D3—22no—
97C4×D3—61no—
98C4×D3—61no—
99C4×D3—61no—
100C4×D3—61no—
101C4×D3—61no—
102C4×D3—61no—
103C4×D3—61no—
104C4×D3—61no—
105C4×D3—62no—
106C4×D3—62no—
107Dic6—21no—
108Dic6—62no—
109C3×C8—62no—
110C3⋊C8—22no—
111C2×C32—21no—
112C2×C32C2×C22⋊C411yescharacteristic
113C3⋊D3—21no—
114C3⋊D3AGL(1,ℤ/8)11yescharacteristic
115C3⋊D3#13711yescharacteristic
116C3×D3—42no—
117#41—61no—
118#41—92no—
119#41—92no—
120#41—181no—
121C2×Q8—91no—
122C2×D4—91no—
123C2×D4—181no—
124C22×C4—91no—
125C22×C4—181no—
126C22×C4—181no—
127M16—61no—
128M16—181no—
129C2×C8—92no—
130C4⋊C4—92no—
131C4⋊C4—181no—
132C22×C3—21no—
133C22×C3—21no—
134C22×C3—62no—
135C2×D3—22no—
136C2×D3—61no—
137C2×D3—61no—
138C2×D3—61no—
139C2×D3—61no—
140C2×D3—121no—
141C2×D3—121no—
142C2×D3—121no—
143C2×D3—121no—
144C2×D3—122no—
145C2×D3—122no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4—21no—
149C3×C4—21no—
150C3×C4—62no—
151Dic3—22no—
152Dic3—61no—
153Dic3—61no—
154Dic3—61no—
155Dic3—61no—
156C32#41711yescharacteristic, complemented, Sylow
157C23—91no—
158C23—181no—
159Q8—61no—
160Q8—92no—
161D4—62no—
162D4—61no—
163D4—92no—
164D4—182no—
165C2×C4—62no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—181no—
172C2×C4—182no—
173C2×C4—182no—
174C2×C4—362no—
175C2×C4GO+(4,𝔽2)11yescharacteristic
176C8—62no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—41no—
180C2×C3—41no—
181C2×C3—122no—
182D3—42no—
183D3—61no—
184D3—61no—
185D3—61no—
186D3—61no—
187D3—121no—
188D3—121no—
189C22—62no—
190C22—91no—
191C22—91no—
192C22—181no—
193C22—181no—
194C22—361no—
195C22—361no—
196C22D32⋊C411yescharacteristic
197C4—62no—
198C4—91no—
199C4—91no—
200C4—362no—
201C4D32⋊C411yescharacteristic
202C4C2×GO+(4,𝔽2)11yescharacteristic
203C3—21no—
204C3—21no—
205C2—21no—
206C2—91no—
207C2—91no—
208C2—122no—
209C2—181no—
210C2C2×D32⋊C411yescharacteristic
subgroupG/H
centerC2C2×D32⋊C4
commutatorC3⋊Dic3C22×C4
FrattiniC4C2×GO+(4,𝔽2)
FittingC2×C32×C4D4
socleC2×C32C2×C22⋊C4
prime radical#64306C2
cosocleC4×C3⋊D3C23
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#417
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#157C2semidirect
3. #63818C2semidirect
4. #63730C2semidirect
5. #63729C2semidirect
10. #3805C4semidirect
13. #3798C4semidirect
37. #627C2×C4semidirect
39. #625C2×C4semidirect
156. C32#417semidirect

Maximal subgroups

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

subgroupindex
#643062
C2×C4⋊#1572
#638182
#637302
#637292
#4179