Finite Group Databasebeta

← #80995

Subgroups — #80995

Order 384.

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

normal subgroups only

This group has 382 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#5721C211yesmaximal, characteristic, complemented
2#5553C211yesmaximal, characteristic
3C3×#474C211yesmaximal, characteristic, complemented
4#5088C211yesmaximal, characteristic, complemented
5C4×#214C211yesmaximal, characteristic, complemented
6#4891C212yesmaximal, complemented
7#4889C212yesmaximal, complemented
8#4848C211yesmaximal, characteristic, complemented
9#4831C211yesmaximal, characteristic, complemented
10#4764C212yesmaximal, complemented
11#4762C212yesmaximal, complemented
12#3368—31nomaximal, Sylow
13C2×#235—21no—
14C3×C4⋊Q8C2211yescharacteristic
15C3×C4×D4C2211yescharacteristic
16Q8×Dic3—21no—
17#944—21no—
18#940C2212yes—
19C2×#214C2211yescharacteristic
20#930—21no—
21C2×#204C2212yes—
22#893C2212yes—
23#890C2212yes—
24#889—22no—
25#887C2212yes—
26#884—22no—
27#874C2211yescharacteristic
28C4×Dic6C2211yescharacteristic
29C4×Dic6C2211yescharacteristic
30C3×#107C2212yes—
31C3×C4⋊C8C2211yescharacteristic
32C3×#102C2212yes—
33#832C2211yescharacteristic
34#821C2212yes—
35#815C2212yes—
36Dic3⋊C8C2212yes—
37#810C2211yescharacteristic
38#809C2212yes—
39#809C2212yes—
40#808C2211yescharacteristic
41C4×C3⋊C8C2211yescharacteristic
42#557—31no—
43#550—31no—
44#490—32no—
45#486—31no—
46#478—32no—
47#474D311yescharacteristic, complemented
48#460—31no—
49#460—32no—
50#446—31no—
51#440—32no—
52C4×SD16—31no—
53C2×C3×Q8—21no—
54C2×C3×D4C2311yescharacteristic
55C22×C3×C4—21no—
56C2×#67—22no—
57C2×#67—22no—
58#235—44no—
59C2×D12—21no—
60C2×D12—21no—
61C2×D12C2312yes—
62C2×C4×D3—22no—
63C2×Dic6D411yescharacteristic
64C2×Dic6C2311yescharacteristic
65C2×C3×C8C2312yes—
66C3×C4⋊C4—21no—
67C3×C4⋊C4C2311yescharacteristic
68C3×C4⋊C4C2312yes—
69C3×C22⋊C4—21no—
70C3×C42C2311yescharacteristic
71#214—22no—
72(C2×D3)⋊C4—22no—
73C4⋊Dic3—22no—
74C4⋊Dic3D411yescharacteristic
75C4⋊Dic3C2311yescharacteristic
76Dic3⋊C4—21no—
77Dic3⋊C4—22no—
78Dic3⋊C4—22no—
79Dic3⋊C4D412yes—
80C4×Dic3—21no—
81C4×Dic3—22no—
82C4×Dic3C2312yes—
83C2×C3⋊C8C2311yescharacteristic
84C2×C3⋊C8C2311yescharacteristic
85#204—24no—
86C2×#41—61no—
87C2×SD16—31no—
88C2×SD16—32no—
89C4⋊Q8—61no—
90C4⋊Q8C2×D311yescharacteristic
91#127—32no—
92#127—31no—
93#125—32no—
94#125—62no—
95#121—62no—
96#121—61no—
97C4×Q8—31no—
98C4×Q8—32no—
99C4×Q8—31no—
100C4×Q8—61no—
101C4×D4—32no—
102C4×D4C2×D311yescharacteristic
103#107C2×D312yes—
104#106—31no—
105C4⋊C8—32no—
106C4⋊C8C2×D311yescharacteristic
107#103—31no—
108#102—31no—
109#102—32no—
110#102—32no—
111#102—32no—
112#102C2×D312yes—
113#97—32no—
114C4×C8—31no—
115C23×C3—21no—
116C22×D3—22no—
117C3×Q8—42no—
118C3×D4—21no—
119C3×D4—21no—
120C2×C3×C4—22no—
121C2×C3×C4—21no—
122C2×C3×C4—42no—
123C2×C3×C4C2×D411yescharacteristic
124C2×C3×C4C2×D411yescharacteristic
125C2×C3×C4C2411yescharacteristic
126#67—44no—
127#67—82no—
128C2×Dic3—21no—
129C2×Dic3—21no—
130C2×Dic3C2×D412yes—
131C2×Dic3C2×D412yes—
132D12—22no—
133D12—22no—
134D12—42no—
135D12—81no—
136C4×D3—44no—
137Dic6—22no—
138Dic6—21no—
139Dic6#4112yescomplemented
140C3×C8—22no—
141C3⋊C8—21no—
142C3⋊C8—21no—
143#41—124no—
144C2×Q8—21no—
145C2×Q8—31no—
146C2×Q8—31no—
147C2×D4—32no—
148C2×D4—62no—
149C2×D4—62no—
150C2×D4—61no—
151C2×D4—61no—
152C2×D4C22×D311yescharacteristic
153C22×C4—21no—
154C22×C4—62no—
155SD16—64no—
156SD16—62no—
157C2×C8—31no—
158C2×C8—31no—
159C2×C8C22×D312yes—
160C4⋊C4—21no—
161C4⋊C4—31no—
162C4⋊C4—32no—
163C4⋊C4—31no—
164C4⋊C4—62no—
165C4⋊C4—62no—
166C4⋊C4—62no—
167C4⋊C4—61no—
168C4⋊C4C22×D312yes—
169C4⋊C4C22×D311yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—62no—
172C42—32no—
173C42—62no—
174C42—61no—
175C42C22×D311yescharacteristic
176C22×C3—41no—
177C22×C3—41no—
178C22×C3—41no—
179C22×C3C22×D411yescharacteristic
180C2×D3—42no—
181C2×D3—42no—
182C2×D3—42no—
183C3×C4—21no—
184C3×C4—41no—
185C3×C4—42no—
186C3×C4AGL(1,ℤ/8)12yes—
187C3×C4C2×#4111yescharacteristic
188C3×C42−1+411yescharacteristic
189Dic3—22no—
190Dic3—22no—
191Dic3—22no—
192Dic3—41no—
193C23—21no—
194C23—62no—
195Q8—32no—
196Q8—42no—
197Q8—62no—
198Q8—61no—
199D4—21no—
200D4—21no—
201D4—62no—
202D4—62no—
203D4—124no—
204D4—122no—
205D4—241no—
206D4—242no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—32no—
210C2×C4—32no—
211C2×C4—42no—
212C2×C4—61no—
213C2×C4—61no—
214C2×C4—124no—
215C2×C4D3×D411yescharacteristic
216C2×C4D3×D411yescharacteristic
217C2×C4C23×D311yescharacteristic
218C8—22no—
219C8—61no—
220C8—61no—
221C2×C3—81no—
222C2×C3#54811yescharacteristic
223C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
224C2×C3#57711yescharacteristic
225D3—82no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—122no—
230C22—122no—
231C22—122no—
232C22C2×D3×D411yescharacteristic
233C4—21no—
234C4—41no—
235C4—42no—
236C4—62no—
237C4—62no—
238C4—62no—
239C4—121no—
240C4#91112yes—
241C4#100711yescharacteristic
242C4D3×#4111yescharacteristic
243C3#336811yescharacteristic, complemented, Sylow
244C2—81no—
245C2—242no—
246C2#563311yescharacteristic
247C2C2×#91111yescharacteristic
248C2#577811yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#474C2
socleC22×C3C22×D4
prime radical#5553C2
hypercenter#474D3
hypocenterC3#3368
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. #5721C2semidirect
3. C3×#474C2semidirect
4. #5088C2semidirect
5. C4×#214C2semidirect
6. #4891C2semidirect
7. #4889C2semidirect
8. #4848C2semidirect
9. #4831C2semidirect
10. #4764C2semidirect
11. #4762C2semidirect
47. #474D3semidirect
139. Dic6#41semidirect
243. C3#3368semidirect

Maximal subgroups

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

subgroupindex
#57212
#55532
C3×#4742
#50882
C4×#2142
#48912
#48892
#48482
#48312
#47642
#47622
#33683