Finite Group Databasebeta

← #77785

Subgroups — #77785

Order 384.

540 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 171 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×#888C212yesmaximal
2C2×#888C211yesmaximal, characteristic
3C2×#887C211yesmaximal, characteristic
4C3×#398C211yesmaximal, characteristic
5#4983C211yesmaximal, characteristic
6#4981C211yesmaximal, characteristic
7#4976C212yesmaximal
8#4661C211yesmaximal, characteristic
9#4649C211yesmaximal, characteristic
10#4647C212yesmaximal
11#4646C212yesmaximal
12#2546—31nomaximal, Sylow
13C22×Dic6C2212yes—
14C22×Dic6C2211yescharacteristic
15C2×C3×C4⋊C4C2212yes—
16C2×C3×C4⋊C4C2211yescharacteristic
17C2×C3×C4⋊C4C2211yescharacteristic
18C2×C4⋊Dic3C2212yes—
19C2×C4⋊Dic3C2211yescharacteristic
20C2×Dic3⋊C4C2211yescharacteristic
21C2×Dic3⋊C4C2212yes—
22C2×Dic3⋊C4C2212yes—
23C2×Dic3⋊C4C2211yescharacteristic
24C2×Dic3⋊C4C2212yes—
25C2×Dic3⋊C4C2212yes—
26C2×C4×Dic3C2212yes—
27C2×C4×Dic3C2211yescharacteristic
28C2×C4×Dic3C2211yescharacteristic
29C2×C4×Dic3C2211yescharacteristic
30#888—28no—
31#888—24no—
32#887—24no—
33C3×#95C2212yes—
34C3×#95C2211yescharacteristic
35C3⋊#95C2212yes—
36C3⋊#95C2212yes—
37C3⋊#95C2212yes—
38C3⋊#95C2211yescharacteristic
39C2×C4⋊Q8—31no—
40C2×C4⋊Q8—32no—
41C2×C4×Q8—31no—
42#398—31no—
43#398—31no—
44#398—31no—
45#398D311yescharacteristic
46#391—32no—
47#389—32no—
48#389—32no—
49C4×C4⋊C4—31no—
50C22×C3×C4C2311yescharacteristic
51C22×C3×C4C2312yes—
52C22×C3×C4C2311yescharacteristic
53C22×C3×C4C2311yescharacteristic
54C22×C3×C4C2312yes—
55C22×Dic3C2311yescharacteristic
56C22×Dic3C2312yes—
57C22×Dic3C2311yescharacteristic
58C22×Dic3C2312yes—
59C22×Dic3C2311yescharacteristic
60C22×Dic3C2311yescharacteristic
61C2×Dic6—22no—
62C2×Dic6—22no—
63C2×Dic6—24no—
64C2×Dic6—24no—
65C2×Dic6—24no—
66C2×Dic6D414yes—
67C3×C4⋊C4—22no—
68C3×C4⋊C4—24no—
69C3×C4⋊C4—22no—
70C4⋊Dic3—22no—
71C4⋊Dic3—24no—
72Dic3⋊C4—22no—
73Dic3⋊C4—24no—
74Dic3⋊C4—22no—
75Dic3⋊C4—24no—
76Dic3⋊C4—24no—
77Dic3⋊C4Q818yescomplemented
78C4×Dic3—22no—
79C4×Dic3—22no—
80C4×Dic3—24no—
81C4×Dic3D414yes—
82C22×Q8—31no—
83C22×Q8—32no—
84C4⋊Q8—64no—
85C4⋊Q8—68no—
86C4×Q8—64no—
87C2×C4⋊C4—32no—
88C2×C4⋊C4—31no—
89C2×C4⋊C4—31no—
90C2×C4⋊C4—32no—
91C2×C4⋊C4—32no—
92C2×C4⋊C4—32no—
93C2×C4⋊C4—32no—
94C2×C4⋊C4—31no—
95C2×C4⋊C4C2×D311yescharacteristic
96C2×C4⋊C4C2×D312yes—
97C2×C4⋊C4C2×D311yescharacteristic
98C2×C42—31no—
99C2×C42—31no—
100C2×C42—31no—
101C2×C42—32no—
102#95—31no—
103#95—32no—
104#95—32no—
105#95—32no—
106#95C2×D311yescharacteristic
107#95C2×D312yes—
108C23×C3C2411yescharacteristic
109C2×C3×C4—22no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—22no—
113C2×C3×C4—22no—
114C2×C3×C4—21no—
115C2×C3×C4—22no—
116C2×C3×C4—22no—
117C2×C3×C4—22no—
118C2×C3×C4—22no—
119C2×C3×C4C2×D412yes—
120C2×C3×C4C2×D412yes—
121C2×C3×C4C2×Q814yes—
122C2×Dic3—22no—
123C2×Dic3—21no—
124C2×Dic3—21no—
125C2×Dic3—22no—
126C2×Dic3—21no—
127C2×Dic3—22no—
128C2×Dic3—22no—
129C2×Dic3—22no—
130C2×Dic3—22no—
131C2×Dic3C2×D412yes—
132C2×Dic3C2×D412yes—
133C2×Dic3C2×D412yes—
134C2×Dic3C2×D412yes—
135C2×Dic3C2×Q814yes—
136C2×Dic3C2×Q814yes—
137C2×Dic3#4112yes—
138Dic6—28no—
139Dic6—48no—
140C2×Q8—34no—
141C2×Q8—62no—
142C2×Q8—62no—
143C2×Q8—64no—
144C2×Q8—64no—
145C2×Q8—64no—
146C22×C4—31no—
147C22×C4—31no—
148C22×C4—32no—
149C22×C4—31no—
150C22×C4—31no—
151C22×C4—32no—
152C22×C4C22×D311yescharacteristic
153C22×C4C22×D312yes—
154C22×C4C22×D311yescharacteristic
155C22×C4C22×D311yescharacteristic
156C22×C4C22×D312yes—
157C4⋊C4—22no—
158C4⋊C4—24no—
159C4⋊C4—22no—
160C4⋊C4—38no—
161C4⋊C4—62no—
162C4⋊C4—64no—
163C4⋊C4—64no—
164C4⋊C4—64no—
165C4⋊C4—62no—
166C4⋊C4—64no—
167C4⋊C4—62no—
168C42—34no—
169C42—62no—
170C42—62no—
171C42—64no—
172C22×C3C22×D411yescharacteristic
173C22×C3C22×D411yescharacteristic
174C22×C3C22×Q812yes—
175C22×C3C2×#4111yescharacteristic
176C22×C32−1+412yes—
177C3×C4—22no—
178C3×C4—22no—
179C3×C4—24no—
180C3×C4—42no—
181C3×C4—41no—
182Dic3—22no—
183Dic3—24no—
184Dic3—42no—
185Dic3—41no—
186Dic3#12114yes—
187Dic3C4⋊Q814yescomplemented
188C23C23×D311yescharacteristic
189Q8—68no—
190Q8—128no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—32no—
202C2×C4—32no—
203C2×C4—32no—
204C2×C4—34no—
205C2×C4—32no—
206C2×C4—32no—
207C2×C4—34no—
208C2×C4—62no—
209C2×C4—61no—
210C2×C4—61no—
211C2×C4—62no—
212C2×C4—61no—
213C2×C4—62no—
214C2×C4—62no—
215C2×C4—62no—
216C2×C4—62no—
217C2×C4D3×D412yes—
218C2×C4D3×D412yes—
219C2×C4D3×Q814yes—
220C2×C3C2×#12111yescharacteristic
221C2×C3C2×C4⋊Q811yescharacteristic
222C2×C3#53611yescharacteristic
223C2×C3D4×Q812yes—
224C2×C3#55712yes—
225C22C2×D3×D411yescharacteristic
226C22C2×D3×D411yescharacteristic
227C22C2×D3×Q812yes—
228C22D3×#4111yescharacteristic
229C22#101012yes—
230C4—24no—
231C4—22no—
232C4—22no—
233C4—34no—
234C4—34no—
235C4—41no—
236C4—42no—
237C4—64no—
238C4—62no—
239C4—121no—
240C4—122no—
241C3#254611yescharacteristic, complemented, Sylow
242C2D3×#12111yescharacteristic
243C2#563212yes—
244C2#564811yescharacteristic
245C2#568512yes—
246C2D3×C4⋊Q811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, prime radical, cosocleC23×C3C24
FittingC3×#398C2
hypercenter#398D3
hypocenterC3#2546
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
77. Dic3⋊C4Q8semidirect
187. Dic3C4⋊Q8semidirect
241. C3#2546semidirect

Maximal subgroups

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

subgroupindex
C2×#8882
C2×#8872
C3×#3982
#49832
#49812
#49762
#46612
#46492
#46472
#46462
#25463