Finite Group Databasebeta

← #81269

Subgroups — #81269

Order 384.

390 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 119 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#5600C211yesmaximal, characteristic
2C2×#887C211yesmaximal, characteristic, complemented
3C3×#480C211yesmaximal, characteristic
4#5040C211yesmaximal, characteristic
5#4971C211yesmaximal, characteristic, complemented
6#4877C212yesmaximal, complemented
7#4873C212yesmaximal, complemented
8#4767C212yesmaximal, complemented
9#4758C212yesmaximal, complemented
10#4739C211yesmaximal, characteristic, complemented
11#4718C211yesmaximal, characteristic, complemented
12#3108—31nomaximal, Sylow
13C22×Dic6C2211yescharacteristic
14C3×#121C2211yescharacteristic
15C2×C3×C4⋊C4C2211yescharacteristic
16#936C2211yescharacteristic
17#935—21no—
18D4×Dic3—21no—
19D4×Dic3C2211yescharacteristic
20C2×#214C2212yes—
21#924C2211yescharacteristic
22C2×Dic3⋊C4—21no—
23C2×C4×Dic3—21no—
24C2×C4×Dic3C2211yescharacteristic
25C2×Dic12C2212yes—
26#890C2211yescharacteristic
27#887—21no—
28#887—21no—
29#887C2211yescharacteristic
30#887C2212yes—
31#887C2212yes—
32#879—21no—
33#877—21no—
34C3×#107C2212yes—
35C3×#102C2212yes—
36C3×C22⋊C8C2211yescharacteristic
37#830C2211yescharacteristic
38#816C2212yes—
39Dic3⋊C8C2212yes—
40C8×Dic3C2212yes—
41#810C2212yes—
42#810C2212yes—
43#808C2212yes—
44#529—31no—
45C2×C4×Q8—31no—
46#483—31no—
47#480D311yescharacteristic
48#479—32no—
49#464—32no—
50#451—31no—
51#448—31no—
52C4×Q16—32no—
53C4×SD16—32no—
54#431—31no—
55C2×C3×D4—21no—
56C2×C3×D4C2311yescharacteristic
57C22×C3×C4—21no—
58C22×C3×C4C2311yescharacteristic
59C22×Dic3—21no—
60C22×Dic3—21no—
61C22×Dic3D411yescharacteristic
62C22×Dic3D411yescharacteristic
63C2×Dic6—21no—
64C2×Dic6—24no—
65C2×Dic6C2311yescharacteristic
66C2×Dic6C2312yes—
67C2×C3×C8C2312yes—
68C3×C4⋊C4—21no—
69C3×C4⋊C4C2312yes—
70C3×C4⋊C4C2311yescharacteristic
71C3×C22⋊C4—21no—
72#217—21no—
73#217—21no—
74#217—21no—
75#217—21no—
76#214—24no—
77C4⋊Dic3—21no—
78C4⋊Dic3C2311yescharacteristic
79Dic3⋊C4—21no—
80Dic3⋊C4—21no—
81Dic3⋊C4—21no—
82Dic3⋊C4—22no—
83Dic3⋊C4—22no—
84C4×Dic3—21no—
85C4×Dic3—22no—
86C4×Dic3—22no—
87C4×Dic3D411yescharacteristic
88C4×Dic3D411yescharacteristic
89C4×Dic3C2311yescharacteristic
90C4×Dic3C2311yescharacteristic
91C2×C3⋊C8C2312yes—
92Dic12—24no—
93C22×Q8—31no—
94C2×Q16—32no—
95C2×SD16—32no—
96#126—61no—
97#125—31no—
98#124—31no—
99#123—61no—
100C22⋊Q8—31no—
101#121C2×D311yescharacteristic
102C4×Q8—32no—
103C4×Q8—32no—
104C4×Q8—31no—
105C4×Q8—61no—
106C4×Q8—61no—
107C4×D4—31no—
108C4×D4—61no—
109#117—61no—
110C2×C4⋊C4—61no—
111C2×C4⋊C4C2×D311yescharacteristic
112C2×C42—31no—
113C2×C42—61no—
114#107C2×D312yes—
115#106—32no—
116C4⋊C8—32no—
117#103—32no—
118#103—32no—
119#103—32no—
120#102C2×D312yes—
121C22⋊C8—31no—
122C22⋊C8C2×D311yescharacteristic
123C4×C8—32no—
124C23×C3—21no—
125C23×C3C2×D411yescharacteristic
126C3×D4—22no—
127C3×D4—42no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130C2×C3×C4—21no—
131C2×C3×C4—42no—
132C2×C3×C4C2×D411yescharacteristic
133C2×C3×C4C2411yescharacteristic
134C2×Dic3—24no—
135C2×Dic3—22no—
136C2×Dic3—22no—
137C2×Dic3—22no—
138C2×Dic3—21no—
139C2×Dic3—21no—
140C2×Dic3—42no—
141C2×Dic3C2×D411yescharacteristic
142C2×Dic3C2×D411yescharacteristic
143C2×Dic3C2×D411yescharacteristic
144C2×Dic3C2×D411yescharacteristic
145Dic6—24no—
146Dic6—22no—
147Dic6—22no—
148Dic6#4114yes—
149C3×C8—22no—
150C3⋊C8—22no—
151C2×Q8—32no—
152C2×Q8—31no—
153C2×Q8—64no—
154C2×Q8—61no—
155C2×D4—21no—
156C2×D4C22×D311yescharacteristic
157C22×C4—21no—
158C22×C4—31no—
159C22×C4—31no—
160C22×C4—61no—
161C22×C4—61no—
162C22×C4C22×D311yescharacteristic
163Q16—64no—
164SD16—64no—
165C2×C8—32no—
166C2×C8C22×D312yes—
167C4⋊C4—21no—
168C4⋊C4—31no—
169C4⋊C4—62no—
170C4⋊C4—62no—
171C4⋊C4—61no—
172C4⋊C4—61no—
173C4⋊C4—61no—
174C4⋊C4—61no—
175C4⋊C4C22×D312yes—
176C4⋊C4C22×D311yescharacteristic
177C22⋊C4—21no—
178C22⋊C4—61no—
179C22⋊C4—61no—
180C22⋊C4—61no—
181C22⋊C4—61no—
182C42—31no—
183C42—31no—
184C42—31no—
185C42—31no—
186C42—62no—
187C42—62no—
188C42—61no—
189C22×C3—21no—
190C22×C3—21no—
191C22×C3—41no—
192C22×C3—41no—
193C22×C3—41no—
194C22×C3#13512yes—
195C22×C3C22×D411yescharacteristic
196C3×C4—21no—
197C3×C4—42no—
198C3×C4—41no—
199C3×C4C2×#4112yes—
200Dic3—24no—
201Dic3—21no—
202Dic3—21no—
203Dic3—21no—
204Dic3—41no—
205Dic3—41no—
206Dic3#13712yes—
207C23—21no—
208C23D3×D411yescharacteristic
209Q8—34no—
210Q8—64no—
211Q8—62no—
212Q8—62no—
213D4—22no—
214D4—42no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—31no—
219C2×C4—31no—
220C2×C4—31no—
221C2×C4—31no—
222C2×C4—42no—
223C2×C4—62no—
224C2×C4—64no—
225C2×C4—62no—
226C2×C4—62no—
227C2×C4—61no—
228C2×C4—61no—
229C2×C4—122no—
230C2×C4D3×D411yescharacteristic
231C2×C4C23×D311yescharacteristic
232C8—22no—
233C8—62no—
234C2×C3—22no—
235C2×C3—81no—
236C2×C3#52511yescharacteristic
237C2×C3C2×#13511yescharacteristic
238C2×C3C2×#13711yescharacteristic
239C22—21no—
240C22—21no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22#91212yes—
245C22C2×D3×D411yescharacteristic
246C4—21no—
247C4—32no—
248C4—42no—
249C4—41no—
250C4—64no—
251C4—61no—
252C4—61no—
253C4—61no—
254C4—121no—
255C4—121no—
256C4D3×#4112yes—
257C3#310811yescharacteristic, complemented, Sylow
258C2—22no—
259C2—81no—
260C2#565611yescharacteristic
261C2C2×#91211yescharacteristic
262C2D3×#13711yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#480C2
socleC22×C3C22×D4
prime radicalC3×#121C22
hypercenter#480D3
hypocenterC3#3108
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
2. C2×#887C2semidirect
5. #4971C2semidirect
6. #4877C2semidirect
7. #4873C2semidirect
8. #4767C2semidirect
9. #4758C2semidirect
10. #4739C2semidirect
11. #4718C2semidirect
257. C3#3108semidirect

Maximal subgroups

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

subgroupindex
#56002
C2×#8872
C3×#4802
#50402
#49712
#48772
#48732
#47672
#47582
#47392
#47182
#31083