Finite Group Databasebeta

← #78191

Subgroups — #78191

Order 384.

468 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 147 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×#887C211yesmaximal, characteristic
2C2×#887C211yesmaximal, characteristic
3C3×#400C211yesmaximal, characteristic
4#4985C211yesmaximal, characteristic
5#4979C211yesmaximal, characteristic
6#4656C211yesmaximal, characteristic
7#4654C212yesmaximal
8#4652C212yesmaximal
9#4650C211yesmaximal, characteristic
10#4647C212yesmaximal
11#4646C212yesmaximal
12#2581—31nomaximal, Sylow
13C22×Dic6C2211yescharacteristic
14C22×Dic6C2211yescharacteristic
15C2×C3×C4⋊C4C2211yescharacteristic
16C2×C3×C4⋊C4C2211yescharacteristic
17C2×C4⋊Dic3C2212yes—
18C2×Dic3⋊C4C2212yes—
19C2×Dic3⋊C4C2211yescharacteristic
20C2×Dic3⋊C4C2212yes—
21C2×Dic3⋊C4C2212yes—
22C2×Dic3⋊C4C2211yescharacteristic
23C2×C4×Dic3C2212yes—
24C2×C4×Dic3C2211yescharacteristic
25C2×C4×Dic3C2211yescharacteristic
26C2×C4×Dic3C2211yescharacteristic
27#887—24no—
28#887—24no—
29C3×#95C2212yes—
30C3×#95C2212yes—
31C3×#95C2211yescharacteristic
32C3⋊#95C2212yes—
33C3⋊#95C2212yes—
34C3⋊#95C2212yes—
35C3⋊#95C2212yes—
36C3⋊#95C2212yes—
37C3⋊#95C2211yescharacteristic
38C2×C4×Q8—31no—
39C2×C4×Q8—31no—
40#400—31no—
41#400D311yescharacteristic
42#395—31no—
43#395—31no—
44#391—32no—
45#389—32no—
46#387—32no—
47#387—32no—
48#382—31no—
49C22×C3×C4C2312yes—
50C22×C3×C4C2312yes—
51C22×C3×C4C2311yescharacteristic
52C22×C3×C4C2311yescharacteristic
53C22×C3×C4C2311yescharacteristic
54C22×Dic3C2312yes—
55C22×Dic3C2311yescharacteristic
56C22×Dic3C2311yescharacteristic
57C22×Dic3C2311yescharacteristic
58C22×Dic3C2312yes—
59C22×Dic3C2311yescharacteristic
60C2×Dic6—22no—
61C2×Dic6—22no—
62C2×Dic6—24no—
63C2×Dic6—22no—
64C2×Dic6Q814yescomplemented
65C3×C4⋊C4—22no—
66C3×C4⋊C4—22no—
67C4⋊Dic3—24no—
68Dic3⋊C4—22no—
69Dic3⋊C4—24no—
70Dic3⋊C4—22no—
71Dic3⋊C4—24no—
72Dic3⋊C4—24no—
73C4×Dic3—22no—
74C4×Dic3—24no—
75C4×Dic3—22no—
76C4×Dic3D414yes—
77C22×Q8—31no—
78C22×Q8—31no—
79C4×Q8—64no—
80C4×Q8—64no—
81C2×C4⋊C4—32no—
82C2×C4⋊C4—31no—
83C2×C4⋊C4—31no—
84C2×C4⋊C4—32no—
85C2×C4⋊C4—32no—
86C2×C4⋊C4—32no—
87C2×C4⋊C4C2×D311yescharacteristic
88C2×C4⋊C4C2×D311yescharacteristic
89C2×C42—31no—
90C2×C42—31no—
91C2×C42—31no—
92C2×C42—32no—
93#95—32no—
94#95—31no—
95#95—32no—
96#95—32no—
97#95—32no—
98#95—32no—
99#95C2×D311yescharacteristic
100#95C2×D312yes—
101#95C2×D312yes—
102C23×C3C2411yescharacteristic
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—22no—
106C2×C3×C4—21no—
107C2×C3×C4—22no—
108C2×C3×C4—22no—
109C2×C3×C4—22no—
110C2×C3×C4—22no—
111C2×C3×C4—24no—
112C2×C3×C4—22no—
113C2×C3×C4C2×D412yes—
114C2×C3×C4C2×Q812yes—
115C2×Dic3—21no—
116C2×Dic3—22no—
117C2×Dic3—21no—
118C2×Dic3—22no—
119C2×Dic3—22no—
120C2×Dic3—21no—
121C2×Dic3—22no—
122C2×Dic3—22no—
123C2×Dic3—22no—
124C2×Dic3—22no—
125C2×Dic3C2×D412yes—
126C2×Dic3C2×D412yes—
127C2×Dic3C2×Q812yes—
128C2×Dic3C2×Q812yes—
129C2×Dic3#4114yes—
130C2×Dic3#4112yes—
131Dic6—28no—
132Dic6—28no—
133C2×Q8—34no—
134C2×Q8—62no—
135C2×Q8—62no—
136C2×Q8—64no—
137C2×Q8—62no—
138C22×C4—31no—
139C22×C4—31no—
140C22×C4—31no—
141C22×C4—32no—
142C22×C4—32no—
143C22×C4—31no—
144C22×C4C22×D312yes—
145C22×C4C22×D312yes—
146C22×C4C22×D311yescharacteristic
147C22×C4C22×D311yescharacteristic
148C22×C4C22×D311yescharacteristic
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—62no—
152C4⋊C4—64no—
153C4⋊C4—64no—
154C4⋊C4—64no—
155C4⋊C4—64no—
156C4⋊C4—62no—
157C42—34no—
158C42—62no—
159C42—64no—
160C42—62no—
161C22×C3C22×D411yescharacteristic
162C22×C3C22×Q811yescharacteristic
163C22×C3C2×#4111yescharacteristic
164C22×C3C2×#4112yes—
165C22×C32−1+412yes—
166C3×C4—22no—
167C3×C4—22no—
168C3×C4—41no—
169C3×C4—42no—
170C3×C4—42no—
171Dic3—22no—
172Dic3—24no—
173Dic3—22no—
174Dic3—41no—
175Dic3—42no—
176Dic3C22⋊Q814yes—
177C23C23×D311yescharacteristic
178Q8—68no—
179Q8—68no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—24no—
189C2×C4—22no—
190C2×C4—32no—
191C2×C4—32no—
192C2×C4—32no—
193C2×C4—32no—
194C2×C4—32no—
195C2×C4—34no—
196C2×C4—62no—
197C2×C4—61no—
198C2×C4—62no—
199C2×C4—61no—
200C2×C4—62no—
201C2×C4—61no—
202C2×C4—62no—
203C2×C4—62no—
204C2×C4—62no—
205C2×C4—62no—
206C2×C4D3×D412yes—
207C2×C4D3×Q812yes—
208C2×C3C2×C22⋊Q811yescharacteristic
209C2×C3#52511yescharacteristic
210C2×C3#53611yescharacteristic
211C2×C3#55612yes—
212C2×C3#55712yes—
213C22C2×D3×D411yescharacteristic
214C22C2×D3×Q811yescharacteristic
215C22D3×#4112yes—
216C22D3×#4111yescharacteristic
217C22#101012yes—
218C4—22no—
219C4—22no—
220C4—34no—
221C4—41no—
222C4—42no—
223C4—42no—
224C4—64no—
225C4—62no—
226C4—62no—
227C4—121no—
228C4—122no—
229C3#258111yescharacteristic, complemented, Sylow
230C2D3×C22⋊Q811yescharacteristic
231C2#565611yescharacteristic
232C2#567511yescharacteristic
233C2#568512yes—
234C2#570212yes—
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#400C2
hypercenter#400D3
hypocenterC3#2581
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
64. C2×Dic6Q8semidirect
229. C3#2581semidirect

Maximal subgroups

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

subgroupindex
C2×#8872
C3×#4002
#49852
#49792
#46562
#46542
#46522
#46502
#46472
#46462
#25813