Finite Group Databasebeta

← #79935

Subgroups — #79935

Order 384.

348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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#5585C211yesmaximal, characteristic
2#5567C211yesmaximal, characteristic, complemented
3C3×C8×Q8C211yesmaximal, characteristic, complemented
4#4851C211yesmaximal, characteristic, complemented
5#4848C211yesmaximal, characteristic
6#4847C212yesmaximal, complemented
7#4845C212yesmaximal, complemented
8C4×Dic12C211yesmaximal, characteristic, complemented
9#4697C212yesmaximal, complemented
10#4694C211yesmaximal, characteristic
11C4×#204C212yesmaximal, complemented
12#3365—31nomaximal, Sylow
13C3×C4×Q8C2211yescharacteristic
14#947—21no—
15#944—21no—
16C2×Dic12C2211yescharacteristic
17C2×#204C2212yes—
18#894—22no—
19#893—21no—
20#889—22no—
21#887—21no—
22#875C2212yes—
23#874C2211yescharacteristic
24C4×D12C2212yes—
25#870C2212yes—
26#869C2211yescharacteristic
27C4×Dic6C2212yes—
28C4×Dic6C2211yescharacteristic
29C4×Dic6C2211yescharacteristic
30C3×C4⋊C8C2212yes—
31C3×C4⋊C8C2211yescharacteristic
32C3×C4×C8C2212yes—
33C3×C4×C8C2211yescharacteristic
34#821C2212yes—
35#821C2212yes—
36#821C2212yes—
37#818C2211yescharacteristic
38#817C2212yes—
39#816C2211yescharacteristic
40#816C2211yescharacteristic
41#816C2212yes—
42#559—31no—
43#557—31no—
44#488—32no—
45#486—31no—
46#478—32no—
47#475—31no—
48#464—32no—
49#460—31no—
50C8×Q8D311yescharacteristic, complemented
51C4×Q16—31no—
52C4×SD16—32no—
53C2×C3×Q8D411yescharacteristic
54C2×D12—21no—
55C2×D12—21no—
56C2×D12C2312yes—
57C2×C4×D3—22no—
58C2×Dic6—21no—
59C2×Dic6C2311yescharacteristic
60C2×Dic6C2311yescharacteristic
61C2×C3×C8C2311yescharacteristic
62C2×C3×C8C2312yes—
63C2×C3×C8C2311yescharacteristic
64C3×C4⋊C4D411yescharacteristic
65C3×C4⋊C4D412yes—
66C3×C42C2311yescharacteristic
67C3×C42C2312yes—
68(C2×D3)⋊C4—22no—
69(C2×D3)⋊C4—22no—
70(C2×D3)⋊C4—22no—
71C4⋊Dic3—21no—
72C4⋊Dic3C2311yescharacteristic
73C4⋊Dic3C2312yes—
74C4⋊Dic3C2311yescharacteristic
75Dic3⋊C4—21no—
76Dic3⋊C4—22no—
77Dic3⋊C4—21no—
78Dic3⋊C4—22no—
79Dic3⋊C4—22no—
80C4×Dic3—22no—
81C4×Dic3—21no—
82C4×Dic3—21no—
83Dic12—22no—
84#204—24no—
85C2×Q16—31no—
86C2×SD16—32no—
87C4⋊Q8—31no—
88C4⋊Q8—61no—
89#127—31no—
90#125—32no—
91#125—62no—
92#124—32no—
93#124—61no—
94#123—62no—
95C4×Q8—32no—
96C4×Q8—31no—
97C4×Q8—31no—
98C4×Q8—61no—
99C4×Q8C2×D311yescharacteristic
100C4×D4—32no—
101C4×D4—61no—
102#107—31no—
103#106—32no—
104C4⋊C8C2×D311yescharacteristic
105C4⋊C8C2×D312yes—
106#103—31no—
107#103—31no—
108#103—32no—
109#102—32no—
110#102—32no—
111#102—32no—
112C4×C8C2×D312yes—
113C4×C8C2×D311yescharacteristic
114C22×D3—22no—
115C3×Q8—22no—
116C2×C3×C4C2×D412yes—
117C2×C3×C4C2×D411yescharacteristic
118C2×C3×C4C2×D412yes—
119C2×C3×C4C2×D411yescharacteristic
120C2×C3×C4C2411yescharacteristic
121C2×Dic3—21no—
122C2×Dic3—21no—
123C2×Dic3—22no—
124C2×Dic3—21no—
125C2×Dic3—21no—
126D12—22no—
127D12—22no—
128D12—42no—
129D12—81no—
130C4×D3—82no—
131Dic6—21no—
132Dic6—21no—
133Dic6—21no—
134Dic6—42no—
135Dic6#4112yes—
136C3×C8—22no—
137C3×C8—21no—
138C3×C8—21no—
139C2×Q8—31no—
140C2×Q8—31no—
141C2×Q8—61no—
142C2×Q8D1211yescharacteristic
143C2×D4—32no—
144C2×D4—61no—
145C2×D4—61no—
146C22×C4—62no—
147Q16—62no—
148SD16—64no—
149C2×C8C22×D311yescharacteristic
150C2×C8C22×D311yescharacteristic
151C2×C8C22×D312yes—
152C4⋊C4—32no—
153C4⋊C4—31no—
154C4⋊C4—31no—
155C4⋊C4—61no—
156C4⋊C4—61no—
157C4⋊C4—62no—
158C4⋊C4—62no—
159C4⋊C4—62no—
160C4⋊C4—61no—
161C4⋊C4D1211yescharacteristic
162C4⋊C4D1212yes—
163C22⋊C4—62no—
164C22⋊C4—62no—
165C22⋊C4—62no—
166C42—61no—
167C42—62no—
168C42—61no—
169C42C22×D312yes—
170C42C22×D311yescharacteristic
171C22×C3C22×D411yescharacteristic
172C2×D3—42no—
173C2×D3—42no—
174C2×D3—42no—
175C3×C4—22no—
176C3×C4—22no—
177C3×C4—21no—
178C3×C4#13512yes—
179C3×C4C2×#4111yescharacteristic
180C3×C42−1+411yescharacteristic
181Dic3—22no—
182Dic3—41no—
183Dic3—42no—
184Dic3—41no—
185Dic3—41no—
186C23—62no—
187Q8—22no—
188Q8—32no—
189Q8—61no—
190Q8—61no—
191Q8—61no—
192Q8—122no—
193D4—62no—
194D4—62no—
195D4—122no—
196D4—241no—
197C2×C4—61no—
198C2×C4—61no—
199C2×C4—61no—
200C2×C4—61no—
201C2×C4—62no—
202C2×C4—242no—
203C2×C4C2×D1212yes—
204C2×C4C2×D1212yes—
205C2×C4C2×D1211yescharacteristic
206C2×C4C2×D1211yescharacteristic
207C2×C4C23×D311yescharacteristic
208C8—21no—
209C8—22no—
210C8—21no—
211C2×C3#54811yescharacteristic
212C2×C3C2×#13511yescharacteristic
213C2×C3#57711yescharacteristic
214D3—82no—
215C22—122no—
216C22—122no—
217C22—122no—
218C22C22×D1211yescharacteristic
219C4—22no—
220C4—22no—
221C4—21no—
222C4—62no—
223C4—122no—
224C4—121no—
225C4—121no—
226C4—121no—
227C4#90412yes—
228C4#100711yescharacteristic
229C4D3×#4111yescharacteristic
230C3#336511yescharacteristic, complemented, Sylow
231C2—242no—
232C2#557611yescharacteristic
233C2C2×#90411yescharacteristic
234C2#575111yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×C8×Q8C2
socleC22×C3C22×D4
prime radical#874C22
hypercenterC8×Q8D3
hypocenterC3#3365
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×Q8 ◁ C8×Q8

Complements

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

NH ≅ G/Ntype
2. #5567C2semidirect
3. C3×C8×Q8C2semidirect
4. #4851C2semidirect
6. #4847C2semidirect
7. #4845C2semidirect
8. C4×Dic12C2semidirect
9. #4697C2semidirect
11. C4×#204C2semidirect
50. C8×Q8D3semidirect
230. C3#3365semidirect

Maximal subgroups

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

subgroupindex
#55852
#55672
C3×C8×Q82
#48512
#48482
#48472
#48452
C4×Dic122
#46972
#46942
C4×#2042
#33653