Finite Group Databasebeta

← #81042

Subgroups — #81042

Order 384.

326 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 115 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#5721C211yesmaximal, characteristic
2#5567C211yesmaximal, characteristic
3C3×#475C211yesmaximal, characteristic
4#5093C211yesmaximal, characteristic
5C4×#216C211yesmaximal, characteristic
6#4857C212yesmaximal
7#4853C212yesmaximal
8#4849C211yesmaximal, characteristic
9#4831C211yesmaximal, characteristic
10#4797C212yesmaximal
11#4795C212yesmaximal
12#3374—31nomaximal, Sylow
13C3×C4⋊Q8C2211yescharacteristic
14C3×C4×Q8C2211yescharacteristic
15Q8×Dic3—21no—
16#944—21no—
17#944C2212yes—
18C2×#216C2211yescharacteristic
19C2×Dic12C2212yes—
20#890C2212yes—
21#889—22no—
22#889—22no—
23#887C2212yes—
24#887C2212yes—
25#870—21no—
26#869C2211yescharacteristic
27C4×Dic6—21no—
28C4×Dic6C2211yescharacteristic
29C4×Dic6C2211yescharacteristic
30C3×#106C2212yes—
31C3×C4⋊C8C2211yescharacteristic
32C3×#103C2212yes—
33#835C2211yescharacteristic
34#816C2212yes—
35#815C2212yes—
36Dic3⋊C8C2212yes—
37#810C2211yescharacteristic
38#810C2212yes—
39#810C2212yes—
40#807C2211yescharacteristic
41C4×C3⋊C8C2211yescharacteristic
42#557—31no—
43#557—31no—
44#491—32no—
45#487—31no—
46#479—32no—
47#475D311yescharacteristic
48#462—31no—
49#462—32no—
50#446—31no—
51#441—32no—
52C4×Q16—31no—
53C2×C3×Q8—21no—
54C2×C3×Q8C2311yescharacteristic
55C2×Dic6D411yescharacteristic
56C2×Dic6C2312yes—
57C2×Dic6C2311yescharacteristic
58C2×C3×C8C2312yes—
59C3×C4⋊C4—21no—
60C3×C4⋊C4—21no—
61C3×C4⋊C4C2311yescharacteristic
62C3×C4⋊C4C2312yes—
63C3×C42—21no—
64C3×C42C2311yescharacteristic
65#216—22no—
66C4⋊Dic3—21no—
67C4⋊Dic3—21no—
68C4⋊Dic3—22no—
69C4⋊Dic3D411yescharacteristic
70C4⋊Dic3C2311yescharacteristic
71Dic3⋊C4—21no—
72Dic3⋊C4—22no—
73Dic3⋊C4—22no—
74Dic3⋊C4—22no—
75Dic3⋊C4—22no—
76Dic3⋊C4—22no—
77Dic3⋊C4D412yes—
78C4×Dic3—21no—
79C4×Dic3—22no—
80C4×Dic3—22no—
81C4×Dic3C2312yes—
82C2×C3⋊C8C2311yescharacteristic
83C2×C3⋊C8C2311yescharacteristic
84Dic12—24no—
85C2×Q16—31no—
86C2×Q16—32no—
87C4⋊Q8—32no—
88C4⋊Q8—31no—
89C4⋊Q8—61no—
90C4⋊Q8C2×D311yescharacteristic
91#125—32no—
92#125—61no—
93#125—62no—
94#125—62no—
95C4×Q8—31no—
96C4×Q8—32no—
97C4×Q8—32no—
98C4×Q8—31no—
99C4×Q8—61no—
100C4×Q8—61no—
101C4×Q8C2×D311yescharacteristic
102#107—31no—
103#106C2×D312yes—
104C4⋊C8—32no—
105C4⋊C8C2×D311yescharacteristic
106#103—31no—
107#103—32no—
108#103—31no—
109#103—32no—
110#103—32no—
111#103C2×D312yes—
112#97—32no—
113C4×C8—31no—
114C3×Q8—21no—
115C3×Q8—21no—
116C3×Q8—42no—
117C2×C3×C4—21no—
118C2×C3×C4—22no—
119C2×C3×C4—21no—
120C2×C3×C4C2×D411yescharacteristic
121C2×C3×C4C2×D411yescharacteristic
122C2×C3×C4C2411yescharacteristic
123C2×Dic3—21no—
124C2×Dic3—21no—
125C2×Dic3—22no—
126C2×Dic3C2×D412yes—
127C2×Dic3C2×D412yes—
128Dic6—22no—
129Dic6—21no—
130Dic6—22no—
131Dic6—22no—
132Dic6#4112yes—
133C3×C8—22no—
134C3⋊C8—21no—
135C3⋊C8—21no—
136C2×Q8—21no—
137C2×Q8—31no—
138C2×Q8—31no—
139C2×Q8—32no—
140C2×Q8C22×D311yescharacteristic
141Q16—64no—
142Q16—62no—
143C2×C8—31no—
144C2×C8—31no—
145C2×C8C22×D312yes—
146C4⋊C4—21no—
147C4⋊C4—21no—
148C4⋊C4—31no—
149C4⋊C4—32no—
150C4⋊C4—31no—
151C4⋊C4—62no—
152C4⋊C4—62no—
153C4⋊C4—62no—
154C4⋊C4—62no—
155C4⋊C4—62no—
156C4⋊C4—62no—
157C4⋊C4—61no—
158C4⋊C4—61no—
159C4⋊C4—61no—
160C4⋊C4C22×D312yes—
161C4⋊C4C22×D311yescharacteristic
162C42—21no—
163C42—32no—
164C42—62no—
165C42—62no—
166C42—61no—
167C42C22×D311yescharacteristic
168C22×C3C22×D411yescharacteristic
169C3×C4—21no—
170C3×C4—41no—
171C3×C4—42no—
172C3×C4—41no—
173C3×C4#13712yes—
174C3×C4C2×#4111yescharacteristic
175C3×C42−1+411yescharacteristic
176Dic3—22no—
177Dic3—22no—
178Dic3—22no—
179Dic3—42no—
180Dic3—41no—
181Q8—21no—
182Q8—21no—
183Q8—32no—
184Q8—42no—
185Q8—62no—
186Q8—61no—
187Q8—62no—
188Q8—62no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—32no—
193C2×C4—32no—
194C2×C4—61no—
195C2×C4—61no—
196C2×C4—62no—
197C2×C4D3×D411yescharacteristic
198C2×C4D3×D411yescharacteristic
199C2×C4C23×D311yescharacteristic
200C8—22no—
201C8—61no—
202C8—61no—
203C2×C3#54811yescharacteristic
204C2×C3C2×#13711yescharacteristic
205C2×C3#57811yescharacteristic
206C22C2×D3×D411yescharacteristic
207C4—21no—
208C4—41no—
209C4—42no—
210C4—41no—
211C4—62no—
212C4—62no—
213C4—62no—
214C4—122no—
215C4—121no—
216C4#91512yes—
217C4#100711yescharacteristic
218C4D3×#4111yescharacteristic
219C3#337411yescharacteristic, complemented, Sylow
220C2#563311yescharacteristic
221C2C2×#91511yescharacteristic
222C2#577911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#475C2
socle, prime radicalC22×C3C22×D4
hypercenter#475D3
hypocenterC3#3374
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
219. C3#3374semidirect

Maximal subgroups

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

subgroupindex
#57212
#55672
C3×#4752
#50932
C4×#2162
#48572
#48532
#48492
#48312
#47972
#47952
#33743