Finite Group Databasebeta

← #80464

Subgroups — #80464

Order 384.

338 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 117 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
2Q8×Dic6C211yesmaximal, characteristic, complemented
3C3×#462C211yesmaximal, characteristic, complemented
4#5185C212yesmaximal
5#5184C212yesmaximal, complemented
6#5079C211yesmaximal, characteristic, complemented
7C4×#215C211yesmaximal, characteristic
8#4842C211yesmaximal, characteristic
9#4831C211yesmaximal, characteristic, complemented
10#4794C212yesmaximal
11#4791C212yesmaximal, complemented
12#3369—31nomaximal, Sylow
13C2×C3×Q16C2212yes—
14C3×C4⋊Q8C2211yescharacteristic
15C3×C4×Q8C2211yescharacteristic
16#947C2212yes—
17Q8×Dic3C2212yes—
18Q8×Dic3C2212yes—
19C2×#215C2211yescharacteristic
20#898—22no—
21#897—21no—
22#892—21no—
23#888—22no—
24#888C2212yes—
25C4×D12C2211yescharacteristic
26#869—21no—
27#869C2211yescharacteristic
28C4×Dic6—21no—
29C4×Dic6C2211yescharacteristic
30C3×C4⋊C8C2211yescharacteristic
31C3×#103C2212yes—
32#835C2211yescharacteristic
33#835C2212yes—
34#835C2212yes—
35#821C2212yes—
36#817C2212yes—
37#815C2212yes—
38Dic3⋊C8C2212yes—
39#809C2211yescharacteristic
40#808C2211yescharacteristic
41C4×C3⋊C8C2211yescharacteristic
42Q82—31no—
43#556—31no—
44#489—32no—
45#487—31no—
46#476—31no—
47#475—32no—
48#464—32no—
49#462D311yescharacteristic, complemented
50#446—31no—
51#441—32no—
52C4×SD16—31no—
53C2×C3×Q8C2312yes—
54C2×C3×Q8C2311yescharacteristic
55C2×D12C2311yescharacteristic
56C2×C4×D3—21no—
57C2×Dic6—21no—
58C2×Dic6—22no—
59C2×Dic6D411yescharacteristic
60C3×Q16—24no—
61C2×C3×C8C2312yes—
62C3×C4⋊C4—21no—
63C3×C4⋊C4—21no—
64C3×C4⋊C4—21no—
65C3×C4⋊C4C2311yescharacteristic
66C3×C42—21no—
67C3×C42C2311yescharacteristic
68#215—22no—
69(C2×D3)⋊C4—21no—
70(C2×D3)⋊C4—22no—
71(C2×D3)⋊C4—22no—
72C4⋊Dic3—21no—
73C4⋊Dic3—22no—
74C4⋊Dic3—22no—
75C4⋊Dic3D411yescharacteristic
76C4⋊Dic3C2311yescharacteristic
77C4⋊Dic3C2312yes—
78Dic3⋊C4—22no—
79Dic3⋊C4D412yes—
80C4×Dic3—22no—
81C4×Dic3—22no—
82C4×Dic3C2312yes—
83C2×C3⋊C8C2311yescharacteristic
84C2×C3⋊C8C2311yescharacteristic
85C2×Q16C2×D312yes—
86C2×SD16—31no—
87C4⋊Q8—32no—
88C4⋊Q8—31no—
89C4⋊Q8—61no—
90C4⋊Q8—62no—
91C4⋊Q8C2×D311yescharacteristic
92#126—62no—
93#124—32no—
94C22⋊Q8—61no—
95C4×Q8—31no—
96C4×Q8—32no—
97C4×Q8—32no—
98C4×Q8—61no—
99C4×Q8C2×D311yescharacteristic
100C4×D4—31no—
101#117—61no—
102#106—32no—
103#106—31no—
104C4⋊C8—32no—
105C4⋊C8C2×D311yescharacteristic
106#103—31no—
107#103—32no—
108#103—32no—
109#103C2×D312yes—
110#102—32no—
111#102—31no—
112#97—32no—
113C4×C8—31no—
114C22×D3—21no—
115C3×Q8—21no—
116C3×Q8—22no—
117C3×Q8—22no—
118C3×Q8#4112yes—
119C2×C3×C4—21no—
120C2×C3×C4—22no—
121C2×C3×C4—21no—
122C2×C3×C4C2×D411yescharacteristic
123C2×C3×C4C2×D411yescharacteristic
124C2×C3×C4C2411yescharacteristic
125C2×Dic3—21no—
126C2×Dic3—22no—
127C2×Dic3C2×D412yes—
128C2×Dic3C2×D412yes—
129D12—21no—
130D12—21no—
131C4×D3—42no—
132Dic6—22no—
133Dic6—82no—
134Dic6—81no—
135C3×C8—22no—
136C3⋊C8—21no—
137C3⋊C8—21no—
138C2×Q8—31no—
139C2×Q8—62no—
140C2×Q8—61no—
141C2×Q8C22×D312yes—
142C2×Q8C22×D311yescharacteristic
143C2×D4—31no—
144C22×C4—61no—
145Q16—24no—
146SD16—62no—
147C2×C8—31no—
148C2×C8—31no—
149C2×C8C22×D312yes—
150C4⋊C4—21no—
151C4⋊C4—21no—
152C4⋊C4—21no—
153C4⋊C4—31no—
154C4⋊C4—32no—
155C4⋊C4—32no—
156C4⋊C4—31no—
157C4⋊C4—62no—
158C4⋊C4—62no—
159C4⋊C4—62no—
160C4⋊C4—61no—
161C4⋊C4C22×D311yescharacteristic
162C22⋊C4—62no—
163C22⋊C4—62no—
164C22⋊C4—61no—
165C42—21no—
166C42—32no—
167C42—62no—
168C42—62no—
169C42C22×D311yescharacteristic
170C22×C3C22×D411yescharacteristic
171C2×D3—41no—
172C2×D3—41no—
173C2×D3—41no—
174C3×C4—22no—
175C3×C4—21no—
176C3×C4—42no—
177C3×C4—41no—
178C3×C4#13712yes—
179C3×C4C2×#4111yescharacteristic
180C3×C42−1+411yescharacteristic
181Dic3—22no—
182Dic3—22no—
183Dic3—41no—
184Dic3—42no—
185C23—61no—
186Q8—21no—
187Q8—22no—
188Q8—22no—
189Q8—62no—
190Q8—241no—
191Q8—242no—
192Q8#23712yes—
193D4—61no—
194D4—61no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—32no—
199C2×C4—32no—
200C2×C4—61no—
201C2×C4—62no—
202C2×C4—122no—
203C2×C4D3×D411yescharacteristic
204C2×C4D3×D411yescharacteristic
205C2×C4C23×D311yescharacteristic
206C8—22no—
207C8—61no—
208C8—61no—
209C2×C3#54811yescharacteristic
210C2×C3C2×#13711yescharacteristic
211C2×C3#57711yescharacteristic
212D3—81no—
213C22—121no—
214C22—121no—
215C22—121no—
216C22C2×D3×D411yescharacteristic
217C4—21no—
218C4—22no—
219C4—41no—
220C4—42no—
221C4—62no—
222C4—62no—
223C4—121no—
224C4—122no—
225C4#91812yes—
226C4C2×#23711yescharacteristic
227C4#101011yescharacteristic
228C3#336911yescharacteristic, complemented, Sylow
229C2—241no—
230C2#559811yescharacteristic
231C2C2×#91811yescharacteristic
232C2#577811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#462C2
socleC22×C3C22×D4
prime radicalC2×D12C23
hypercenter#462D3
hypocenterC3#3369
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. Q8×Dic6C2semidirect
3. C3×#462C2semidirect
5. #5184C2semidirect
6. #5079C2semidirect
9. #4831C2semidirect
11. #4791C2semidirect
49. #462D3semidirect
228. C3#3369semidirect

Maximal subgroups

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

subgroupindex
#57322
Q8×Dic62
C3×#4622
#51852
#51842
#50792
C4×#2152
#48422
#48312
#47942
#47912
#33693