Finite Group Databasebeta

← #10593401

Subgroups — #10593401

Order 576.

402 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 45 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×#3802C211yesmaximal, characteristic
2C2×D32⋊C4C212yesmaximal, complemented
3C2×D32⋊C4C212yesmaximal, complemented
4#63883C211yesmaximal, characteristic, complemented
5#63781C211yesmaximal, characteristic, complemented
6C22×D32C2212yes—
7C22×#157C2212yes—
8C2×C4×C3⋊D3C2211yescharacteristic
9C2×C3×D12—21no—
10C2×#625—21no—
11C2×#624C2211yescharacteristic
12C2×#624C2211yescharacteristic
13#3802—24no—
14D32⋊C4—24no—
15D32⋊C4—24no—
16C3×Dic3⋊C4—21no—
17Dic3⋊Dic3—21no—
18C2×D3×D4—61no—
19D3×C4⋊C4—61no—
20C22×C3⋊D3C2311yescharacteristic
21C22×C3×D3—22no—
22C2×D32—22no—
23C2×D32—22no—
24C2×D32—22no—
25C2×D32—22no—
26C2×D32—22no—
27C2×D32D414yes—
28C2×#157—22no—
29C2×#157—22no—
30C2×#157—22no—
31C2×C32×C4D411yescharacteristic
32C2×C3⋊Dic3D411yescharacteristic
33C4×C3⋊D3—22no—
34C2×C3×Dic3—21no—
35C2×C3×Dic3—21no—
36C3×D12—24no—
37#625—24no—
38#624—21no—
39#624—22no—
40#624D412yescomplemented
41#394—91nomaximal, Sylow
42C23×D3—62no—
43C2×C3×D4—61no—
44C2×#67—62no—
45D3×D4—68no—
46C2×D12—21no—
47C2×C4×D3—61no—
48C2×C4×D3—61no—
49C2×C4×D3—61no—
50C2×C4×D3—61no—
51C3×C4⋊C4—61no—
52C4⋊Dic3—61no—
53Dic3⋊C4—21no—
54Dic3⋊C4—61no—
55C22×C32C2×D411yescharacteristic
56C2×C3⋊D3C2×D411yescharacteristic
57C2×C3⋊D3C2×D412yes—
58C2×C3⋊D3#4112yes—
59C2×C3⋊D3#4111yescharacteristic
60C2×C3×D3—24no—
61C2×C3×D3—42no—
62C2×C3×D3—42no—
63D32—24no—
64D32—24no—
65D32—42no—
66D32—42no—
67#157—42no—
68C32×C4—21no—
69C3⋊Dic3—21no—
70C3×Dic3—22no—
71C3×Dic3—41no—
72C22×D4—91no—
73C2×C4⋊C4—91no—
74C2×C22⋊C4—92no—
75C2×C22⋊C4—92no—
76#95—91no—
77C23×C3—62no—
78C22×D3—22no—
79C22×D3—64no—
80C22×D3—61no—
81C22×D3—61no—
82C22×D3—64no—
83C22×D3—122no—
84C22×D3—122no—
85C22×D3—122no—
86C22×D3—122no—
87C3×D4—64no—
88C2×C3×C4—21no—
89C2×C3×C4—21no—
90C2×C3×C4—61no—
91C2×C3×C4—61no—
92#67—68no—
93C2×Dic3—21no—
94C2×Dic3—21no—
95C2×Dic3—61no—
96C2×Dic3—61no—
97D12—24no—
98C4×D3—62no—
99C4×D3—62no—
100C4×D3—64no—
101C4×D3—122no—
102C4×D3—122no—
103C2×C32#12011yescharacteristic
104C2×C32#12111yescharacteristic
105C2×C32#12411yescharacteristic
106C3⋊D3#12112yes—
107C3⋊D3#12312yes—
108C3×D3—44no—
109C24—92no—
110C2×D4—61no—
111C2×D4—181no—
112C2×D4—184no—
113C22×C4—91no—
114C22×C4—91no—
115C22×C4—91no—
116C22×C4—92no—
117C4⋊C4—61no—
118C4⋊C4—181no—
119C22⋊C4—184no—
120C22⋊C4—184no—
121C22×C3—21no—
122C22×C3—21no—
123C22×C3—64no—
124C22×C3—122no—
125C22×C3—122no—
126C2×D3—24no—
127C2×D3—42no—
128C2×D3—42no—
129C2×D3—62no—
130C2×D3—61no—
131C2×D3—61no—
132C2×D3—62no—
133C2×D3—61no—
134C2×D3—62no—
135C2×D3—61no—
136C2×D3—62no—
137C2×D3—124no—
138C2×D3—124no—
139C2×D3—124no—
140C2×D3—124no—
141C3×C4—22no—
142C3×C4—41no—
143C3×C4—62no—
144C3×C4—121no—
145Dic3—22no—
146Dic3—41no—
147Dic3—62no—
148Dic3—121no—
149C32#39411yescharacteristic, complemented, Sylow
150C23—62no—
151C23—94no—
152C23—91no—
153C23—182no—
154C23—182no—
155C23—182no—
156C23—182no—
157C23—182no—
158D4—64no—
159D4—184no—
160C2×C4—61no—
161C2×C4—61no—
162C2×C4—92no—
163C2×C4—91no—
164C2×C4—182no—
165C2×C4—181no—
166C2×C4—182no—
167C2×C4—182no—
168C2×C4—182no—
169C2×C4—182no—
170C2×C4GO+(4,𝔽2)11yescharacteristic
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—21no—
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—124no—
178D3—44no—
179D3—62no—
180D3—62no—
181D3—62no—
182D3—62no—
183C22—64no—
184C22—92no—
185C22—91no—
186C22—91no—
187C22—92no—
188C22—122no—
189C22—122no—
190C22—184no—
191C22—184no—
192C22—362no—
193C22—362no—
194C22C2×GO+(4,𝔽2)11yescharacteristic
195C4—21no—
196C4—62no—
197C4—121no—
198C4—181no—
199C4—362no—
200C3—21no—
201C3—21no—
202C2—92no—
203C2—92no—
204C2—124no—
205C2#6422111yescharacteristic
206C2#6423011yescharacteristic
207C2#6424111yescharacteristic
subgroupG/H
center, FrattiniC22C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊D3C23
FittingC2×C32×C4D4
socleC22×C32C2×D4
prime radicalC2×#3802C2
hypercenterC2×C4GO+(4,𝔽2)
hypocenterC32#394
LCSG ▷ C22×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×D32⋊C4C2semidirect
3. C2×D32⋊C4C2semidirect
4. #63883C2semidirect
5. #63781C2semidirect
40. #624D4semidirect
149. C32#394semidirect

Maximal subgroups

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

subgroupindex
C2×#38022
C2×D32⋊C42
#638832
#637812
#3949