Finite Group Databasebeta

← #83848

Subgroups — #83848

Order 384.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×C3×SD16C211yesmaximal, characteristic, complemented
2#5816C211yesmaximal, characteristic, complemented
3#5798C211yesmaximal, characteristic, complemented
4C2×#932C211yesmaximal, characteristic
5#5225C211yesmaximal, characteristic, complemented
6#5165C214yesmaximal, complemented
7#5162C214yesmaximal, complemented
8#5113C211yesmaximal, characteristic, complemented
9#5102C211yesmaximal, characteristic, complemented
10#3042—31nomaximal, Sylow
11C22×C3×Q8C2211yescharacteristic
12C22×C3×D4C2211yescharacteristic
13C2×#235C2211yescharacteristic
14C2×C3×SD16—24no—
15C2×C3×SD16C2214yes—
16C22×C3×C8C2211yescharacteristic
17C2×#217—22no—
18#947C2212yescomplemented
19#946—22no—
20#944C2212yescomplemented
21D4×Dic3—22no—
22D4×Dic3C2214yes—
23C2×#214C2212yes—
24#932—24no—
25C2×#213C2212yes—
26#929—22no—
27#926C2211yescharacteristic
28#926C2211yescharacteristic
29C2×#208C2211yescharacteristic
30#835C2214yescomplemented
31#821C2212yescomplemented
32#816C2212yescomplemented
33Dic3⋊C8C2214yescomplemented
34C2×AGL(1,ℤ/8)—31no—
35C22×SD16D311yescharacteristic, complemented
36#536—31no—
37#518—31no—
38#463—34no—
39#461—34no—
40#424—31no—
41#419—31no—
42#416—31no—
43C24×C3—21no—
44C2×C3×Q8—21no—
45C2×C3×Q8—22no—
46C2×C3×Q8—22no—
47C2×C3×Q8C2312yes—
48C2×C3×D4—21no—
49C2×C3×D4—22no—
50C2×C3×D4D414yes—
51C2×C3×D4C2312yes—
52C22×C3×C4—21no—
53C22×C3×C4C2311yescharacteristic
54C2×#67—21no—
55C22×Dic3—24no—
56#235—22no—
57#235—22no—
58C2×D12C2311yescharacteristic
59C2×C4×D3—21no—
60C2×Dic6C2311yescharacteristic
61C3×SD16—28no—
62C2×C3×C8—22no—
63C2×C3×C8C2312yes—
64#217—21no—
65#217—24no—
66#217D412yes—
67#214—24no—
68#213—24no—
69(C2×D3)⋊C4—24no—
70C4⋊Dic3D412yes—
71C4⋊Dic3C2312yes—
72Dic3⋊C4—24no—
73C4×Dic3—21no—
74C4×Dic3C2312yes—
75#208—22no—
76C2×C3⋊C8C2312yes—
77C2×#41—31no—
78C22×Q8C2×D311yescharacteristic
79C22×D4C2×D311yescharacteristic
80AGL(1,ℤ/8)—64no—
81C2×SD16—24no—
82C2×SD16—32no—
83C2×SD16C2×D314yes—
84C2×D8—32no—
85C2×M16—31no—
86C22×C8C2×D311yescharacteristic
87C4⋊Q8—32no—
88#124—32no—
89#123—62no—
90C22⋊Q8—62no—
91C4×D4—34no—
92C4×D4—62no—
93#117—31no—
94#117—31no—
95C2×C22⋊C4—62no—
96C4⋊C8—34no—
97#103—34no—
98#103—32no—
99#102—32no—
100C23×C3—22no—
101C23×C3—24no—
102C23×C3—82no—
103C23×C3C2×D411yescharacteristic
104C22×D3—21no—
105C3×Q8—22no—
106C3×Q8—22no—
107C3×Q8—42no—
108C3×D4—24no—
109C3×D4—22no—
110C3×D4C2×D414yes—
111C2×C3×C4—22no—
112C2×C3×C4—42no—
113C2×C3×C4C2×D411yescharacteristic
114C2×C3×C4C2×D412yes—
115C2×C3×C4#4112yes—
116C2×C3×C4C2411yescharacteristic
117#67—42no—
118C2×Dic3—22no—
119C2×Dic3—21no—
120C2×Dic3—84no—
121C2×Dic3C2×D414yes—
122D12—21no—
123D12—21no—
124C4×D3—42no—
125Dic6—21no—
126Dic6—21no—
127C3×C8—22no—
128C3⋊C8—22no—
129C24—21no—
130#41—62no—
131#41—62no—
132C2×Q8—21no—
133C2×Q8—22no—
134C2×Q8—22no—
135C2×Q8—31no—
136C2×Q8C22×D312yes—
137C2×D4—21no—
138C2×D4—22no—
139C2×D4—31no—
140C2×D4—61no—
141C2×D4#6714yes—
142C2×D4C22×D312yes—
143C22×C4—21no—
144C22×C4—64no—
145C22×C4—61no—
146C22×C4C22×D311yescharacteristic
147SD16—28no—
148SD16—64no—
149D8—64no—
150M16—62no—
151C2×C8—22no—
152C2×C8—32no—
153C2×C8C22×D312yes—
154C4⋊C4—32no—
155C4⋊C4—32no—
156C4⋊C4—64no—
157C22⋊C4—32no—
158C22⋊C4—64no—
159C22⋊C4—64no—
160C22⋊C4—61no—
161C42—32no—
162C42—61no—
163C22×C3—22no—
164C22×C3—24no—
165C22×C3—44no—
166C22×C3—84no—
167C22×C3#12112yes—
168C22×C3C22×D411yescharacteristic
169C2×D3—41no—
170C2×D3—42no—
171C3×C4—42no—
172C3×C4#12112yes—
173C3×C4C22×D411yescharacteristic
174C3×C4C2×#4111yescharacteristic
175Dic3—24no—
176Dic3—41no—
177Dic3—42no—
178C23—22no—
179C23—24no—
180C23—61no—
181C23—82no—
182C23D3×D411yescharacteristic
183Q8—22no—
184Q8—22no—
185Q8—42no—
186Q8—61no—
187Q8—61no—
188D4—24no—
189D4—22no—
190D4—61no—
191D4—61no—
192D4—122no—
193D4C2×#6714yes—
194C2×C4—22no—
195C2×C4—34no—
196C2×C4—42no—
197C2×C4—62no—
198C2×C4—61no—
199C2×C4—122no—
200C2×C4—244no—
201C2×C4D3×D411yescharacteristic
202C2×C4#23712yes—
203C2×C4C2×#6712yes—
204C2×C4C23×D311yescharacteristic
205C8—22no—
206C8—62no—
207C2×C3—22no—
208C2×C3—44no—
209C2×C3C2×#12111yescharacteristic
210C2×C3#57712yes—
211D3—81no—
212C22—22no—
213C22—24no—
214C22—44no—
215C22—84no—
216C22—122no—
217C22—121no—
218C22#93912yes—
219C22C2×D3×D411yescharacteristic
220C4—42no—
221C4—64no—
222C4—122no—
223C4—121no—
224C4#93912yes—
225C4C2×#23711yescharacteristic
226C4C22×#6711yescharacteristic
227C3#304211yescharacteristic, complemented, Sylow
228C2—22no—
229C2—44no—
230C2—241no—
231C2#576212yes—
232C2C2×#93911yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC22×C3×SD16C2
socleC22×C3C22×D4
prime radicalC2×#932C2
hypercenterC22×SD16D3
hypocenterC3#3042
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×C3×SD16C2semidirect
2. #5816C2semidirect
3. #5798C2semidirect
5. #5225C2semidirect
6. #5165C2semidirect
7. #5162C2semidirect
8. #5113C2semidirect
9. #5102C2semidirect
18. #947C22semidirect
20. #944C22semidirect
30. #835C22semidirect
31. #821C22semidirect
32. #816C22semidirect
33. Dic3⋊C8C22semidirect
35. C22×SD16D3semidirect
227. C3#3042semidirect

Maximal subgroups

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

subgroupindex
C22×C3×SD162
#58162
#57982
C2×#9322
#52252
#51652
#51622
#51132
#51022
#30423