Finite Group Databasebeta

← #81586

Subgroups — #81586

Order 384.

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

normal subgroups only

This group has 396 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#5730C211yesmaximal, characteristic, complemented
2#5718C211yesmaximal, characteristic, complemented
3C3×#486C211yesmaximal, characteristic, complemented
4#5084C211yesmaximal, characteristic, complemented
5#5072C211yesmaximal, characteristic, complemented
6#4786C212yesmaximal, complemented
7#4785C212yesmaximal, complemented
8#4766C212yesmaximal, complemented
9#4764C212yesmaximal, complemented
10C4×D24C211yesmaximal, characteristic, complemented
11#4679C211yesmaximal, characteristic, complemented
12#3366—31nomaximal, Sylow
13C2×#237—21no—
14C3×C4⋊Q8C2211yescharacteristic
15C3×#127C2211yescharacteristic
16#946—22no—
17#940C2212yes—
18#939—22no—
19#938—21no—
20D4×Dic3C2212yes—
21C2×#213C2212yes—
22C2×D24C2211yescharacteristic
23#897—21no—
24#893C2212yes—
25D3×C4⋊C4—21no—
26#890C2212yes—
27C4×D12C2211yescharacteristic
28C4×D12C2211yescharacteristic
29C4×Dic6C2211yescharacteristic
30C3×#102C2212yes—
31C3×#102C2212yes—
32C3×C4×C8C2211yescharacteristic
33#832C2212yes—
34#821C2211yescharacteristic
35#821C2211yescharacteristic
36#818C2211yescharacteristic
37#815C2212yes—
38Dic3⋊C8C2212yes—
39#809C2212yes—
40#808C2212yes—
41C4⋊(C3⋊C8)C2211yescharacteristic
42#554—31no—
43#550—31no—
44#490—32no—
45#486D311yescharacteristic, complemented
46#478—32no—
47#476—31no—
48#459—31no—
49#459—32no—
50#446—31no—
51#442—32no—
52C4×D8—31no—
53C2×C3×Q8—21no—
54C2×C3×D4—21no—
55C2×C3×D4—21no—
56C2×C3×D4C2312yes—
57C2×#67—22no—
58C2×#67—22no—
59C22×Dic3—22no—
60#237—44no—
61C2×D12C2311yescharacteristic
62C2×D12C2311yescharacteristic
63C2×C4×D3—21no—
64C2×C4×D3—21no—
65C2×C4×D3—22no—
66C2×Dic6D411yescharacteristic
67C2×C3×C8C2311yescharacteristic
68C2×C3×C8C2311yescharacteristic
69C3×C4⋊C4—21no—
70C3×C4⋊C4C2312yes—
71C3×C42C2311yescharacteristic
72#217—22no—
73#213—24no—
74(C2×D3)⋊C4—21no—
75(C2×D3)⋊C4—21no—
76(C2×D3)⋊C4—22no—
77C4⋊Dic3—22no—
78C4⋊Dic3D411yescharacteristic
79C4⋊Dic3C2311yescharacteristic
80C4⋊Dic3C2311yescharacteristic
81Dic3⋊C4—22no—
82Dic3⋊C4D412yes—
83C4×Dic3C2312yes—
84C2×C3⋊C8C2312yes—
85D24—22no—
86C2×#41—61no—
87C2×D8—32no—
88C2×D8—31no—
89C4⋊Q8C2×D311yescharacteristic
90#127—32no—
91#127C2×D311yescharacteristic
92#125—32no—
93C22⋊Q8—61no—
94C22⋊Q8—62no—
95#121—61no—
96#121—62no—
97C4×Q8—31no—
98C4×D4—32no—
99C4×D4—32no—
100C4×D4—31no—
101C4×D4—31no—
102C2×C4⋊C4—61no—
103#107—31no—
104#106—32no—
105C4⋊C8—32no—
106C4⋊C8—31no—
107#102—32no—
108#102—31no—
109#102—31no—
110#102—32no—
111#102C2×D312yes—
112#102C2×D312yes—
113#97—32no—
114C4×C8C2×D311yescharacteristic
115C23×C3—22no—
116C22×D3—21no—
117C22×D3—21no—
118C3×Q8—81no—
119C3×D4—22no—
120C3×D4—22no—
121C3×D4—42no—
122C3×D4—81no—
123C2×C3×C4—22no—
124C2×C3×C4C2×D411yescharacteristic
125C2×C3×C4C2×D411yescharacteristic
126C2×C3×C4C2411yescharacteristic
127#67—44no—
128#67—82no—
129C2×Dic3—21no—
130C2×Dic3—21no—
131C2×Dic3—44no—
132C2×Dic3C2×D412yes—
133C2×Dic3C2×D412yes—
134D12—21no—
135D12—21no—
136D12—21no—
137D12#4112yescomplemented
138C4×D3—42no—
139C4×D3—42no—
140C4×D3—82no—
141Dic6—22no—
142C3×C8—21no—
143C3×C8—21no—
144C3⋊C8—22no—
145#41—124no—
146C2×Q8—21no—
147C2×Q8—31no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—31no—
151C2×D4—31no—
152C2×D4—62no—
153C2×D4—62no—
154C2×D4C22×D312yes—
155C22×C4—62no—
156C22×C4—62no—
157C22×C4—61no—
158C22×C4—61no—
159D8—62no—
160D8—64no—
161C2×C8—32no—
162C2×C8C22×D311yescharacteristic
163C2×C8C22×D311yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—31no—
166C4⋊C4—32no—
167C4⋊C4—31no—
168C4⋊C4—31no—
169C4⋊C4—62no—
170C4⋊C4—62no—
171C4⋊C4C22×D312yes—
172C22⋊C4—62no—
173C22⋊C4—62no—
174C22⋊C4—61no—
175C22⋊C4—61no—
176C42—32no—
177C42C22×D311yescharacteristic
178C22×C3—42no—
179C22×C3—42no—
180C22×C3—42no—
181C22×C3C22×D411yescharacteristic
182C2×D3—22no—
183C2×D3—41no—
184C2×D3—41no—
185C2×D3—41no—
186C2×D3—41no—
187C2×D3—41no—
188C3×C4—21no—
189C3×C4—42no—
190C3×C4AGL(1,ℤ/8)12yes—
191C3×C4C2×#4111yescharacteristic
192C3×C42−1+411yescharacteristic
193Dic3—22no—
194Dic3—22no—
195Dic3—41no—
196Dic3—41no—
197C23—22no—
198C23—61no—
199C23—61no—
200Q8—62no—
201Q8—81no—
202D4—22no—
203D4—22no—
204D4—32no—
205D4—42no—
206D4—61no—
207D4—61no—
208D4—61no—
209D4—81no—
210D4—124no—
211D4—242no—
212C2×C4—22no—
213C2×C4—32no—
214C2×C4—32no—
215C2×C4—61no—
216C2×C4—61no—
217C2×C4—124no—
218C2×C4—122no—
219C2×C4—122no—
220C2×C4—242no—
221C2×C4D3×D411yescharacteristic
222C2×C4D3×D411yescharacteristic
223C2×C4C23×D311yescharacteristic
224C8—21no—
225C8—21no—
226C8—62no—
227C2×C3—82no—
228C2×C3#54811yescharacteristic
229C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
230C2×C3#57611yescharacteristic
231D3—42no—
232D3—81no—
233C22—42no—
234C22—42no—
235C22—42no—
236C22—62no—
237C22—121no—
238C22—121no—
239C22—121no—
240C22—121no—
241C22—121no—
242C22C2×D3×D411yescharacteristic
243C4—21no—
244C4—42no—
245C4—62no—
246C4—62no—
247C4—121no—
248C4—121no—
249C4#91412yes—
250C4D3×#4111yescharacteristic
251C4#101011yescharacteristic
252C3#336611yescharacteristic, complemented, Sylow
253C2—82no—
254C2—122no—
255C2—241no—
256C2#567711yescharacteristic
257C2#575711yescharacteristic
258C2C2×#91411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#486C2
socleC22×C3C22×D4
hypercenter#486D3
hypocenterC3#3366
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #5730C2semidirect
2. #5718C2semidirect
3. C3×#486C2semidirect
4. #5084C2semidirect
5. #5072C2semidirect
6. #4786C2semidirect
7. #4785C2semidirect
8. #4766C2semidirect
9. #4764C2semidirect
10. C4×D24C2semidirect
11. #4679C2semidirect
45. #486D3semidirect
137. D12#41semidirect
252. C3#3366semidirect

Maximal subgroups

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

subgroupindex
#57302
#57182
C3×#4862
#50842
#50722
#47862
#47852
#47662
#47642
C4×D242
#46792
#33663