Finite Group Databasebeta

← #80959

Subgroups — #80959

Order 384.

374 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 125 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#5727C211yesmaximal, characteristic, complemented
2#5543C211yesmaximal, characteristic, complemented
3C3×#474C211yesmaximal, characteristic, complemented
4#5080C211yesmaximal, characteristic, complemented
5C4×#213C211yesmaximal, characteristic
6#4891C212yesmaximal, complemented
7#4876C212yesmaximal, complemented
8#4842C211yesmaximal, characteristic, complemented
9#4831C211yesmaximal, characteristic, complemented
10#4785C212yesmaximal
11#4761C212yesmaximal, complemented
12#3384—31nomaximal, Sylow
13C2×D3×Q8—21no—
14C3×C4⋊Q8C2211yescharacteristic
15C3×C4×D4C2211yescharacteristic
16#946—21no—
17D4×Dic3C2212yes—
18C2×#213C2211yescharacteristic
19C2×C4⋊Dic3—21no—
20#924—21no—
21#896—22no—
22#893C2212yes—
23#890C2212yes—
24#888C2212yes—
25#878—22no—
26C4×D12C2211yescharacteristic
27#869C2211yescharacteristic
28C4×Dic6C2211yescharacteristic
29C3×#107C2212yes—
30C3×C4⋊C8C2211yescharacteristic
31C3×#102C2212yes—
32#832C2211yescharacteristic
33#821C2212yes—
34#817C2212yes—
35#815C2212yes—
36Dic3⋊C8C2212yes—
37#809C2211yescharacteristic
38#808C2212yes—
39#808C2212yes—
40#807C2211yescharacteristic
41C4×C3⋊C8C2211yescharacteristic
42#554—31no—
43D4×Q8—31no—
44#501—32no—
45#498—31no—
46#478—32no—
47#476—31no—
48#476—32no—
49#474D311yescharacteristic, complemented
50#446—31no—
51#442—32no—
52C4×D8—31no—
53C2×C3×Q8—21no—
54C2×C3×D4C2311yescharacteristic
55C22×C3×C4—21no—
56C22×Dic3—22no—
57D3×Q8—44no—
58C2×D12C2311yescharacteristic
59C2×C4×D3—21no—
60C2×C4×D3—22no—
61C2×Dic6—22no—
62C2×Dic6—21no—
63C2×Dic6D411yescharacteristic
64C2×C3×C8C2312yes—
65C3×C4⋊C4—21no—
66C3×C4⋊C4C2311yescharacteristic
67C3×C4⋊C4C2312yes—
68C3×C22⋊C4—21no—
69C3×C42C2311yescharacteristic
70#217—22no—
71#213Q814yescomplemented
72(C2×D3)⋊C4—21no—
73(C2×D3)⋊C4—22no—
74C4⋊Dic3—21no—
75C4⋊Dic3—22no—
76C4⋊Dic3D411yescharacteristic
77C4⋊Dic3C2311yescharacteristic
78C4⋊Dic3C2312yes—
79Dic3⋊C4—22no—
80Dic3⋊C4—22no—
81Dic3⋊C4D412yes—
82C4×Dic3C2312yes—
83C2×C3⋊C8C2311yescharacteristic
84C2×C3⋊C8C2311yescharacteristic
85C22×Q8—61no—
86C2×D8—31no—
87C4⋊Q8—32no—
88C4⋊Q8—31no—
89C4⋊Q8C2×D311yescharacteristic
90#125—32no—
91C22⋊Q8—62no—
92C22⋊Q8—62no—
93C22⋊Q8—61no—
94C22⋊Q8—61no—
95C4×Q8—31no—
96C4×D4—32no—
97C4×D4—32no—
98C4×D4—31no—
99C4×D4C2×D311yescharacteristic
100C2×C4⋊C4—61no—
101#107—31no—
102#107C2×D312yes—
103#106—32no—
104#106—32no—
105#106—32no—
106C4⋊C8—32no—
107C4⋊C8C2×D311yescharacteristic
108#102—31no—
109#102—32no—
110#102—31no—
111#102C2×D312yes—
112#97—32no—
113C4×C8—31no—
114C23×C3—21no—
115C22×D3—21no—
116C3×Q8—42no—
117C3×D4—21no—
118C3×D4C2×Q812yescomplemented
119C2×C3×C4—21no—
120C2×C3×C4—22no—
121C2×C3×C4—42no—
122C2×C3×C4C2×D411yescharacteristic
123C2×C3×C4C2×D411yescharacteristic
124C2×C3×C4C2411yescharacteristic
125C2×Dic3—21no—
126C2×Dic3—22no—
127C2×Dic3—82no—
128C2×Dic3C2×D412yes—
129C2×Dic3C2×D412yes—
130D12—21no—
131D12C2×Q812yes—
132C4×D3—44no—
133C4×D3—42no—
134Dic6—22no—
135Dic6—44no—
136Dic6—81no—
137C3×C8—22no—
138C3⋊C8—21no—
139C3⋊C8C2×Q812yescomplemented
140C2×Q8—21no—
141C2×Q8—31no—
142C2×Q8—62no—
143C2×Q8—61no—
144C2×Q8—124no—
145C2×D4—31no—
146C2×D4C22×D311yescharacteristic
147C22×C4—21no—
148C22×C4—62no—
149C22×C4—62no—
150C22×C4—61no—
151D8—34no—
152C2×C8—31no—
153C2×C8—31no—
154C2×C8C22×D312yes—
155C4⋊C4—21no—
156C4⋊C4—31no—
157C4⋊C4—32no—
158C4⋊C4—32no—
159C4⋊C4—31no—
160C4⋊C4—62no—
161C4⋊C4—62no—
162C4⋊C4—62no—
163C4⋊C4—61no—
164C4⋊C4C22×D311yescharacteristic
165C4⋊C4C22×D312yes—
166C22⋊C4—21no—
167C22⋊C4—62no—
168C22⋊C4—62no—
169C22⋊C4—61no—
170C42—32no—
171C42C22×D311yescharacteristic
172C22×C3—22no—
173C22×C3—41no—
174C22×C3—41no—
175C22×C3C22×D411yescharacteristic
176C2×D3—22no—
177C2×D3—41no—
178C2×D3—41no—
179C3×C4—21no—
180C3×C4—42no—
181C3×C4—41no—
182C3×C4AGL(1,ℤ/8)12yes—
183C3×C4C22×Q811yescharacteristic
184C3×C42−1+411yescharacteristic
185Dic3—22no—
186Dic3—22no—
187Dic3—41no—
188Dic3—42no—
189C23—21no—
190C23—61no—
191Q8—42no—
192Q8—62no—
193Q8—124no—
194Q8—241no—
195D4—21no—
196D4—32no—
197D4—61no—
198D4D3×Q812yescomplemented
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—32no—
202C2×C4—32no—
203C2×C4—42no—
204C2×C4—62no—
205C2×C4—61no—
206C2×C4—124no—
207C2×C4—122no—
208C2×C4—242no—
209C2×C4D3×D411yescharacteristic
210C2×C4D3×D411yescharacteristic
211C2×C4C23×D311yescharacteristic
212C8—22no—
213C8—32no—
214C8—61no—
215C2×C3—42no—
216C2×C3D4×Q811yescharacteristic
217C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
218C2×C3#57711yescharacteristic
219D3—42no—
220C22—22no—
221C22—41no—
222C22—41no—
223C22—62no—
224C22—121no—
225C22—121no—
226C22C2×D3×D411yescharacteristic
227C4—21no—
228C4—41no—
229C4—42no—
230C4—62no—
231C4—62no—
232C4—121no—
233C4—122no—
234C4#91112yes—
235C4C2×D3×Q811yescharacteristic
236C4#101011yescharacteristic
237C3#338411yescharacteristic, complemented, Sylow
238C2—42no—
239C2—122no—
240C2#563211yescharacteristic
241C2C2×#91111yescharacteristic
242C2#577811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#474C2
socleC22×C3C22×D4
prime radicalC2×#213C22
hypercenter#474D3
hypocenterC3#3384
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #5727C2semidirect
2. #5543C2semidirect
3. C3×#474C2semidirect
4. #5080C2semidirect
6. #4891C2semidirect
7. #4876C2semidirect
8. #4842C2semidirect
9. #4831C2semidirect
11. #4761C2semidirect
49. #474D3semidirect
71. #213Q8semidirect
118. C3×D4C2×Q8semidirect
139. C3⋊C8C2×Q8semidirect
198. D4D3×Q8semidirect
237. C3#3384semidirect

Maximal subgroups

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

subgroupindex
#57272
#55432
C3×#4742
#50802
C4×#2132
#48912
#48762
#48422
#48312
#47852
#47612
#33843