Finite Group Databasebeta

← #81690

Subgroups — #81690

Order 384.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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
1D3×C4⋊Q8C211yesmaximal, characteristic, complemented
2#5680C211yesmaximal, characteristic
3C3×#489C211yesmaximal, characteristic, complemented
4#5081C211yesmaximal, characteristic, complemented
5#5055C211yesmaximal, characteristic, complemented
6#4805C212yesmaximal, complemented
7#4793C212yesmaximal, complemented
8#4774C212yesmaximal
9#4761C212yesmaximal, complemented
10#4705C211yesmaximal, characteristic, complemented
11#4702C211yesmaximal, characteristic, complemented
12#3238—31nomaximal, Sylow
13C2×D3×Q8—21no—
14C3×C4⋊Q8C2211yescharacteristic
15C3×#124C2211yescharacteristic
16#946C2211yescharacteristic
17Q8×Dic3C2211yescharacteristic
18#944—21no—
19#938C2211yescharacteristic
20D4×Dic3C2211yescharacteristic
21D3×C4⋊C4—21no—
22D3×C4⋊C4C2212yes—
23#888—21no—
24#888C2212yes—
25#883—21no—
26#67⋊C4—21no—
27#879—21no—
28#877—21no—
29C42×D3C2211yescharacteristic
30#870C2211yescharacteristic
31#869C2211yescharacteristic
32C3×#103C2212yes—
33C3×#102C2212yes—
34C3×#97C2211yescharacteristic
35#835C2212yes—
36#832C2212yes—
37(C2×D3)⋊C8C2212yes—
38#818C2212yes—
39#817C2212yes—
40Dic3⋊C8C2212yes—
41#808C2212yes—
42#807C2212yes—
43#803C2211yescharacteristic
44C2×C4⋊Q8—31no—
45#529—31no—
46#501—31no—
47#501—31no—
48#489—31no—
49#489D311yescharacteristic, complemented
50#483—32no—
51#480—32no—
52#477—32no—
53#476—32no—
54#432—31no—
55C2×C3×Q8—21no—
56C2×C3×Q8C2311yescharacteristic
57C2×C3×D4C2311yescharacteristic
58C2×#67—21no—
59C22×Dic3—21no—
60D3×Q8—44no—
61C2×C4×D3—22no—
62C2×C4×D3D411yescharacteristic
63C2×C4×D3D411yescharacteristic
64C2×C4×D3C2311yescharacteristic
65C2×Dic6—21no—
66C2×Dic6—22no—
67C2×C3×C8C2312yes—
68C3×C4⋊C4—21no—
69C3×C4⋊C4C2312yes—
70C3×C22⋊C4—21no—
71C3×C22⋊C4—21no—
72C3×C42C2311yescharacteristic
73#217—21no—
74#217—21no—
75(C2×D3)⋊C4—21no—
76C4⋊Dic3—21no—
77C4⋊Dic3—21no—
78C4⋊Dic3C2311yescharacteristic
79C4⋊Dic3C2311yescharacteristic
80C4⋊Dic3C2312yes—
81Dic3⋊C4—21no—
82Dic3⋊C4—21no—
83Dic3⋊C4—21no—
84Dic3⋊C4—22no—
85Dic3⋊C4—22no—
86C4×Dic3—21no—
87C4×Dic3D411yescharacteristic
88C4×Dic3D411yescharacteristic
89C4×Dic3C2311yescharacteristic
90C2×C3⋊C8C2312yes—
91C22×Q8—61no—
92C4⋊Q8—32no—
93C4⋊Q8—31no—
94C4⋊Q8—61no—
95C4⋊Q8—61no—
96C4⋊Q8C2×D311yescharacteristic
97#126—61no—
98#125—31no—
99#124C2×D311yescharacteristic
100#123—61no—
101C22⋊Q8—31no—
102#121—31no—
103C4×Q8—31no—
104C4×D4—31no—
105C4×D4—61no—
106#117—61no—
107C2×C4⋊C4—32no—
108C2×C4⋊C4—61no—
109C2×C42—31no—
110#107—32no—
111#107—32no—
112#106—32no—
113#106—32no—
114C4⋊C8—32no—
115#103—32no—
116#103C2×D312yes—
117#102—32no—
118#102C2×D312yes—
119C22⋊C8—32no—
120#97—31no—
121#97C2×D311yescharacteristic
122C23×C3—21no—
123C22×D3C2×D411yescharacteristic
124C3×Q8—22no—
125C3×Q8—42no—
126C3×D4—22no—
127C2×C3×C4—21no—
128C2×C3×C4—22no—
129C2×C3×C4C2×D411yescharacteristic
130C2×C3×C4C2×D411yescharacteristic
131C2×C3×C4C2411yescharacteristic
132#67—42no—
133C2×Dic3—21no—
134C2×Dic3—21no—
135C2×Dic3—22no—
136C2×Dic3—42no—
137C2×Dic3C2×D411yescharacteristic
138C2×Dic3C2×D411yescharacteristic
139C2×Dic3C2×D411yescharacteristic
140C4×D3—22no—
141C4×D3—22no—
142C4×D3—22no—
143C4×D3—44no—
144Dic6—44no—
145Dic6—42no—
146C3×C8—22no—
147C3⋊C8—22no—
148C2×Q8—21no—
149C2×Q8—62no—
150C2×Q8—61no—
151C2×Q8—124no—
152C2×Q8C22×D311yescharacteristic
153C2×D4—61no—
154C2×D4C22×D311yescharacteristic
155C22×C4—31no—
156C22×C4—31no—
157C22×C4—31no—
158C22×C4—62no—
159C22×C4—61no—
160C2×C8—32no—
161C2×C8C22×D312yes—
162C4⋊C4—21no—
163C4⋊C4—32no—
164C4⋊C4—31no—
165C4⋊C4—31no—
166C4⋊C4—62no—
167C4⋊C4—62no—
168C4⋊C4—61no—
169C4⋊C4—61no—
170C4⋊C4—61no—
171C4⋊C4—61no—
172C4⋊C4—61no—
173C4⋊C4C22×D312yes—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—61no—
177C22⋊C4—61no—
178C22⋊C4—61no—
179C42—31no—
180C42—31no—
181C42—31no—
182C42—61no—
183C42C22×D311yescharacteristic
184C22×C3—41no—
185C22×C3—41no—
186C22×C3—41no—
187C22×C3C22×D411yescharacteristic
188C2×D3—21no—
189C2×D3—21no—
190C2×D3AGL(1,ℤ/8)12yes—
191C3×C4—21no—
192C3×C4—21no—
193C3×C4—41no—
194C3×C4—42no—
195C3×C42−1+412yes—
196Dic3—21no—
197Dic3—21no—
198Dic3—42no—
199Dic3—41no—
200Dic3—41no—
201Dic3#13712yes—
202C23—21no—
203C23—31no—
204Q8—22no—
205Q8—42no—
206Q8—122no—
207Q8—124no—
208D4—22no—
209D4—122no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—31no—
213C2×C4—31no—
214C2×C4—31no—
215C2×C4—62no—
216C2×C4—62no—
217C2×C4—62no—
218C2×C4—61no—
219C2×C4—61no—
220C2×C4—62no—
221C2×C4—122no—
222C2×C4—124no—
223C2×C4D3×D411yescharacteristic
224C2×C4D3×D411yescharacteristic
225C2×C4C23×D311yescharacteristic
226C8—22no—
227C8—62no—
228C2×C3—81no—
229C2×C3#53611yescharacteristic
230C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
231C2×C3C2×#13711yescharacteristic
232D3—22no—
233C22—32no—
234C22—41no—
235C22—41no—
236C22—41no—
237C22—61no—
238C22—61no—
239C22C2×D3×D411yescharacteristic
240C4—21no—
241C4—21no—
242C4—32no—
243C4—41no—
244C4—42no—
245C4—61no—
246C4—61no—
247C4—122no—
248C4—121no—
249C4—121no—
250C4#101012yes—
251C3#323811yescharacteristic, complemented, Sylow
252C2—62no—
253C2—81no—
254C2#567511yescharacteristic
255C2D3×AGL(1,ℤ/8)11yescharacteristic
256C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#489C2
socleC22×C3C22×D4
prime radical#938C22
hypercenter#489D3
hypocenterC3#3238
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. D3×C4⋊Q8C2semidirect
3. C3×#489C2semidirect
4. #5081C2semidirect
5. #5055C2semidirect
6. #4805C2semidirect
7. #4793C2semidirect
9. #4761C2semidirect
10. #4705C2semidirect
11. #4702C2semidirect
49. #489D3semidirect
251. C3#3238semidirect

Maximal subgroups

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

subgroupindex
D3×C4⋊Q82
#56802
C3×#4892
#50812
#50552
#48052
#47932
#47742
#47612
#47052
#47022
#32383