Finite Group Databasebeta

← #81621

Subgroups — #81621

Order 384.

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

normal subgroups only

This group has 350 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#5732C211yesmaximal, characteristic, complemented
2#5730C211yesmaximal, characteristic, complemented
3C3×#487C211yesmaximal, characteristic, complemented
4#5084C211yesmaximal, characteristic, complemented
5#5083C211yesmaximal, characteristic, complemented
6#4819C212yesmaximal
7#4800C212yesmaximal, complemented
8#4796C212yesmaximal, complemented
9#4788C212yesmaximal, complemented
10C4×D24C211yesmaximal, characteristic
11C8×Dic6C211yesmaximal, characteristic, complemented
12#3360—31nomaximal, Sylow
13C3×C4⋊Q8C2211yescharacteristic
14C3×C4⋊Q8C2211yescharacteristic
15#947C2212yes—
16#946—22no—
17Q8×Dic3C2212yes—
18C2×#215C2212yes—
19C2×D24C2211yescharacteristic
20#898—22no—
21#897—21no—
22#897—21no—
23#893C2212yes—
24#892—21no—
25D3×C4⋊C4—21no—
26#890C2212yes—
27C4×D12C2211yescharacteristic
28C4×D12C2211yescharacteristic
29C4×Dic6C2211yescharacteristic
30C3×#103C2212yes—
31C3×#103C2212yes—
32C3×C4×C8C2211yescharacteristic
33#835C2212yes—
34#821C2211yescharacteristic
35#821C2211yescharacteristic
36#818C2211yescharacteristic
37Dic3⋊C8C2212yes—
38C8×Dic3C2212yes—
39#809C2212yes—
40#808C2212yes—
41C4⋊(C3⋊C8)C2211yescharacteristic
42#556—31no—
43#554—31no—
44#488—32no—
45#487D311yescharacteristic, complemented
46#479—32no—
47#476—31no—
48#463—32no—
49#461—31no—
50C8×Q8—31no—
51C4×SD16—32no—
52C4×D8—31no—
53C2×C3×Q8—21no—
54C2×C3×Q8C2312yes—
55C2×D12C2311yescharacteristic
56C2×D12C2311yescharacteristic
57C2×C4×D3—21no—
58C2×C4×D3—21no—
59C2×C4×D3—22no—
60C2×Dic6D411yescharacteristic
61C2×C3×C8C2311yescharacteristic
62C2×C3×C8C2311yescharacteristic
63C3×C4⋊C4—21no—
64C3×C4⋊C4—21no—
65C3×C4⋊C4—21no—
66C3×C4⋊C4C2312yes—
67C3×C42C2311yescharacteristic
68#215—24no—
69(C2×D3)⋊C4—21no—
70(C2×D3)⋊C4—21no—
71(C2×D3)⋊C4—22no—
72(C2×D3)⋊C4—22no—
73(C2×D3)⋊C4—22no—
74C4⋊Dic3—22no—
75C4⋊Dic3—22no—
76C4⋊Dic3D411yescharacteristic
77C4⋊Dic3C2311yescharacteristic
78C4⋊Dic3C2311yescharacteristic
79Dic3⋊C4—22no—
80Dic3⋊C4D412yes—
81C4×Dic3—22no—
82C4×Dic3C2312yes—
83C2×C3⋊C8C2312yes—
84D24—22no—
85C2×SD16—32no—
86C2×D8—31no—
87C4⋊Q8C2×D311yescharacteristic
88C4⋊Q8C2×D311yescharacteristic
89#126—62no—
90#125—32no—
91#124—32no—
92C22⋊Q8—61no—
93C22⋊Q8—61no—
94C22⋊Q8—62no—
95C4×Q8—31no—
96C4×Q8—32no—
97C4×D4—32no—
98C4×D4—31no—
99C4×D4—31no—
100#117—61no—
101C2×C4⋊C4—61no—
102#107—31no—
103#106—32no—
104C4⋊C8—32no—
105C4⋊C8—31no—
106#103—32no—
107#103C2×D312yes—
108#103C2×D312yes—
109#102—31no—
110#102—31no—
111#102—32no—
112C4×C8—32no—
113C4×C8C2×D311yescharacteristic
114C22×D3—21no—
115C22×D3—21no—
116C3×Q8—22no—
117C3×Q8—22no—
118C3×Q8—81no—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
121C2×C3×C4C2×D411yescharacteristic
122C2×C3×C4C2×D411yescharacteristic
123C2×C3×C4C2411yescharacteristic
124C2×Dic3—21no—
125C2×Dic3—21no—
126C2×Dic3C2×D412yes—
127C2×Dic3C2×D412yes—
128D12—21no—
129D12—21no—
130D12—21no—
131D12#4112yes—
132C4×D3—42no—
133C4×D3—42no—
134C4×D3—82no—
135Dic6—22no—
136C3×C8—21no—
137C3×C8—21no—
138C3⋊C8—22no—
139C2×Q8—21no—
140C2×Q8—31no—
141C2×Q8C22×D312yes—
142C2×D4—31no—
143C2×D4—31no—
144C22×C4—62no—
145C22×C4—61no—
146C22×C4—61no—
147SD16—64no—
148D8—62no—
149C2×C8—32no—
150C2×C8C22×D311yescharacteristic
151C2×C8C22×D311yescharacteristic
152C4⋊C4—21no—
153C4⋊C4—21no—
154C4⋊C4—21no—
155C4⋊C4—31no—
156C4⋊C4—32no—
157C4⋊C4—31no—
158C4⋊C4—31no—
159C4⋊C4—62no—
160C4⋊C4—62no—
161C4⋊C4—62no—
162C4⋊C4C22×D312yes—
163C22⋊C4—62no—
164C22⋊C4—62no—
165C22⋊C4—62no—
166C22⋊C4—61no—
167C22⋊C4—61no—
168C42—32no—
169C42—62no—
170C42C22×D311yescharacteristic
171C22×C3C22×D411yescharacteristic
172C2×D3—22no—
173C2×D3—41no—
174C2×D3—41no—
175C2×D3—41no—
176C2×D3—41no—
177C2×D3—41no—
178C3×C4—21no—
179C3×C4—42no—
180C3×C4—42no—
181C3×C4#13512yes—
182C3×C4C2×#4111yescharacteristic
183C3×C42−1+411yescharacteristic
184Dic3—22no—
185Dic3—22no—
186Dic3—41no—
187Dic3—41no—
188C23—61no—
189C23—61no—
190Q8—22no—
191Q8—22no—
192Q8—62no—
193Q8—81no—
194D4—32no—
195D4—61no—
196D4—61no—
197D4—61no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—32no—
201C2×C4—32no—
202C2×C4—61no—
203C2×C4—61no—
204C2×C4—122no—
205C2×C4—122no—
206C2×C4—242no—
207C2×C4D3×D411yescharacteristic
208C2×C4D3×D411yescharacteristic
209C2×C4C23×D311yescharacteristic
210C8—21no—
211C8—21no—
212C8—62no—
213C2×C3#54811yescharacteristic
214C2×C3C2×#13511yescharacteristic
215C2×C3#57711yescharacteristic
216D3—42no—
217D3—81no—
218C22—62no—
219C22—121no—
220C22—121no—
221C22—121no—
222C22—121no—
223C22—121no—
224C22C2×D3×D411yescharacteristic
225C4—21no—
226C4—42no—
227C4—42no—
228C4—62no—
229C4—62no—
230C4—121no—
231C4—121no—
232C4#91912yes—
233C4D3×#4111yescharacteristic
234C4#101011yescharacteristic
235C3#336011yescharacteristic, complemented, Sylow
236C2—122no—
237C2—241no—
238C2#567711yescharacteristic
239C2#576211yescharacteristic
240C2C2×#91911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#487C2
socleC22×C3C22×D4
prime radicalC2×D24C22
hypercenter#487D3
hypocenterC3#3360
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #5732C2semidirect
2. #5730C2semidirect
3. C3×#487C2semidirect
4. #5084C2semidirect
5. #5083C2semidirect
7. #4800C2semidirect
8. #4796C2semidirect
9. #4788C2semidirect
11. C8×Dic6C2semidirect
45. #487D3semidirect
235. C3#3360semidirect

Maximal subgroups

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

subgroupindex
#57322
#57302
C3×#4872
#50842
#50832
#48192
#48002
#47962
#47882
C4×D242
C8×Dic62
#33603