Finite Group Databasebeta

← #81085

Subgroups — #81085

Order 384.

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

normal subgroups only

This group has 386 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#5734C211yesmaximal, characteristic, complemented
2#5551C211yesmaximal, characteristic, complemented
3C3×#476C211yesmaximal, characteristic, complemented
4#5080C211yesmaximal, characteristic, complemented
5C4×#213C211yesmaximal, characteristic, complemented
6#4863C212yesmaximal, complemented
7#4861C212yesmaximal, complemented
8#4846C211yesmaximal, characteristic, complemented
9#4838C211yesmaximal, characteristic, complemented
10#4784C212yesmaximal, complemented
11#4782C212yesmaximal, complemented
12#3354—31nomaximal, Sylow
13C2×#235—21no—
14C3×C4⋊Q8C2211yescharacteristic
15C3×C4×D4C2211yescharacteristic
16#947—22no—
17#938C2212yes—
18C2×#213C2211yescharacteristic
19#924—21no—
20C2×ΓL(1,𝔽25)C2212yes—
21#895—21no—
22#895C2212yes—
23#892—21no—
24#892C2212yes—
25D3×C4⋊C4C2212yes—
26#883—22no—
27C4×D12C2211yescharacteristic
28C4×D12C2211yescharacteristic
29#869C2211yescharacteristic
30C3×#106C2212yes—
31C3×C4⋊C8C2211yescharacteristic
32C3×#102C2212yes—
33#832C2211yescharacteristic
34#821C2212yes—
35(C2×D3)⋊C8C2212yes—
36#818C2212yes—
37#809C2211yescharacteristic
38#808C2212yes—
39#808C2212yes—
40#807C2211yescharacteristic
41C4×C3⋊C8C2211yescharacteristic
42#555—31no—
43#547—31no—
44#498—31no—
45#482—32no—
46#481—32no—
47#476D311yescharacteristic, complemented
48#474—31no—
49#469—32no—
50C4×D8—31no—
51#436—31no—
52#428—32no—
53C2×C3×Q8—21no—
54C2×C3×D4C2311yescharacteristic
55C22×C3×C4—21no—
56C2×#67—22no—
57#235—44no—
58C2×D12—22no—
59C2×D12D411yescharacteristic
60C2×D12C2311yescharacteristic
61C2×C4×D3—22no—
62C2×C4×D3—21no—
63C2×C4×D3C2312yes—
64C2×Dic6—21no—
65C2×C3×C8C2312yes—
66C3×C4⋊C4—21no—
67C3×C4⋊C4C2311yescharacteristic
68C3×C4⋊C4C2312yes—
69C3×C22⋊C4—21no—
70C3×C42C2311yescharacteristic
71#217—22no—
72#213—22no—
73(C2×D3)⋊C4—22no—
74(C2×D3)⋊C4—21no—
75(C2×D3)⋊C4—22no—
76(C2×D3)⋊C4D412yes—
77C4⋊Dic3—21no—
78C4⋊Dic3D411yescharacteristic
79C4⋊Dic3C2311yescharacteristic
80C4⋊Dic3C2312yes—
81Dic3⋊C4—22no—
82C4×Dic3—22no—
83C2×C3⋊C8C2311yescharacteristic
84C2×C3⋊C8C2311yescharacteristic
85ΓL(1,𝔽25)—24no—
86C2×#41—61no—
87C2×D8—31no—
88C2×M16—32no—
89C4⋊Q8—31no—
90C4⋊Q8C2×D311yescharacteristic
91#124—62no—
92#123—62no—
93C22⋊Q8—61no—
94#121—32no—
95#121—32no—
96#121—61no—
97C4×D4—31no—
98C4×D4—31no—
99C4×D4C2×D311yescharacteristic
100#117—32no—
101#117—61no—
102C2×C4⋊C4—32no—
103#107—32no—
104#107—31no—
105#106—32no—
106#106—32no—
107#106C2×D312yes—
108C4⋊C8C2×D311yescharacteristic
109#102—31no—
110#102—32no—
111#102—31no—
112#102C2×D312yes—
113C22⋊C8—32no—
114C4×C8—31no—
115C23×C3—21no—
116C22×D3—21no—
117C22×D3C2×D412yes—
118C3×Q8—81no—
119C3×D4—21no—
120C3×D4—21no—
121C2×C3×C4—22no—
122C2×C3×C4—21no—
123C2×C3×C4—42no—
124C2×C3×C4C2×D411yescharacteristic
125C2×C3×C4C2×D411yescharacteristic
126C2×C3×C4C2411yescharacteristic
127#67—44no—
128C2×Dic3—21no—
129C2×Dic3—22no—
130C2×Dic3C2×D412yes—
131D12—22no—
132D12—21no—
133D12—21no—
134D12—82no—
135C4×D3—22no—
136C4×D3—22no—
137C4×D3—44no—
138C4×D3—42no—
139Dic6—42no—
140C3×C8—22no—
141C3⋊C8—21no—
142C3⋊C8#4112yescomplemented
143#41—124no—
144C2×Q8—21no—
145C2×Q8—61no—
146C2×D4—31no—
147C2×D4—31no—
148C2×D4—62no—
149C2×D4—62no—
150C2×D4C22×D311yescharacteristic
151C22×C4—21no—
152C22×C4—32no—
153C22×C4—62no—
154C22×C4—61no—
155D8—62no—
156M16—64no—
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—61no—
166C4⋊C4C22×D311yescharacteristic
167C4⋊C4C22×D312yes—
168C22⋊C4—21no—
169C22⋊C4—32no—
170C22⋊C4—62no—
171C22⋊C4—62no—
172C22⋊C4—62no—
173C22⋊C4—61no—
174C42—62no—
175C42C22×D311yescharacteristic
176C22×C3—41no—
177C22×C3—41no—
178C22×C3—41no—
179C22×C3C22×D411yescharacteristic
180C2×D3—22no—
181C2×D3—22no—
182C2×D3—22no—
183C2×D3—41no—
184C2×D3—41no—
185C2×D3—41no—
186C3×C4—21no—
187C3×C4—41no—
188C3×C4—42no—
189C3×C4AGL(1,ℤ/8)12yes—
190C3×C4C2×#4111yescharacteristic
191C3×C42−1+411yescharacteristic
192Dic3—22no—
193Dic3—42no—
194Dic3—41no—
195C23—21no—
196C23—32no—
197C23—61no—
198Q8—81no—
199Q8—122no—
200D4—21no—
201D4—21no—
202D4—62no—
203D4—61no—
204D4—61no—
205D4—124no—
206D4—242no—
207C2×C4—22no—
208C2×C4—21no—
209C2×C4—32no—
210C2×C4—42no—
211C2×C4—62no—
212C2×C4—62no—
213C2×C4—61no—
214C2×C4—62no—
215C2×C4—124no—
216C2×C4—122no—
217C2×C4D3×D411yescharacteristic
218C2×C4D3×D411yescharacteristic
219C2×C4C23×D311yescharacteristic
220C8—22no—
221C8—32no—
222C8—61no—
223C2×C3—81no—
224C2×C3#54711yescharacteristic
225C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
226C2×C3#57711yescharacteristic
227D3—42no—
228D3—81no—
229C22—41no—
230C22—41no—
231C22—41no—
232C22—62no—
233C22—62no—
234C22—62no—
235C22—121no—
236C22—121no—
237C22—121no—
238C22C2×D3×D411yescharacteristic
239C4—21no—
240C4—41no—
241C4—42no—
242C4—62no—
243C4—122no—
244C4—121no—
245C4#91412yes—
246C4#100711yescharacteristic
247C4D3×#4111yescharacteristic
248C3#335411yescharacteristic, complemented, Sylow
249C2—81no—
250C2—122no—
251C2—241no—
252C2#563111yescharacteristic
253C2C2×#91411yescharacteristic
254C2#577511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#476C2
socleC22×C3C22×D4
hypercenter#476D3
hypocenterC3#3354
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #5734C2semidirect
2. #5551C2semidirect
3. C3×#476C2semidirect
4. #5080C2semidirect
5. C4×#213C2semidirect
6. #4863C2semidirect
7. #4861C2semidirect
8. #4846C2semidirect
9. #4838C2semidirect
10. #4784C2semidirect
11. #4782C2semidirect
47. #476D3semidirect
142. C3⋊C8#41semidirect
248. C3#3354semidirect

Maximal subgroups

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

subgroupindex
#57342
#55512
C3×#4762
#50802
C4×#2132
#48632
#48612
#48462
#48382
#47842
#47822
#33543