Finite Group Databasebeta

← #81082

Subgroups — #81082

Order 384.

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

normal subgroups only

This group has 364 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#5563C211yesmaximal, characteristic, complemented
3C3×#476C211yesmaximal, characteristic, complemented
4#5078C211yesmaximal, characteristic, complemented
5C4×#213C211yesmaximal, characteristic, complemented
6#4866C212yesmaximal, complemented
7#4860C212yesmaximal, complemented
8#4842C211yesmaximal, characteristic, complemented
9#4834C211yesmaximal, characteristic, complemented
10#4779C212yesmaximal, complemented
11#4775C212yesmaximal, complemented
12#3341—31nomaximal, Sylow
13C3×C4⋊Q8C2211yescharacteristic
14C3×C4×D4C2211yescharacteristic
15#947—22no—
16#938C2212yes—
17C2×#213C2211yescharacteristic
18#930—21no—
19#926—21no—
20C2×D3×C8C2212yes—
21#895—21no—
22#895C2212yes—
23#892—21no—
24#892C2212yes—
25#892C2212yes—
26#885—22no—
27C4×D12C2211yescharacteristic
28C4×D12C2211yescharacteristic
29#869C2211yescharacteristic
30C3×#106C2212yes—
31C3×C4⋊C8C2211yescharacteristic
32C3×#102C2212yes—
33#832C2211yescharacteristic
34#821C2212yes—
35(C2×D3)⋊C8C2212yes—
36#817C2212yes—
37#809C2211yescharacteristic
38#807C2212yes—
39#807C2211yescharacteristic
40#807C2212yes—
41C4×C3⋊C8C2211yescharacteristic
42#555—31no—
43#555—31no—
44#500—31no—
45#482—32no—
46#482—32no—
47#476—31no—
48#476D311yescharacteristic, complemented
49#466—32no—
50C4×D8—31no—
51C8×D4—31no—
52#427—32no—
53C2×C3×Q8—21no—
54C2×C3×D4C2311yescharacteristic
55C22×C3×C4—21no—
56C2×#67—22no—
57C2×D12—22no—
58C2×D12D411yescharacteristic
59C2×D12C2311yescharacteristic
60C2×C4×D3—21no—
61C2×C4×D3C2312yes—
62C2×Dic6—21no—
63C2×C3×C8C2312yes—
64C3×C4⋊C4—21no—
65C3×C4⋊C4C2312yes—
66C3×C4⋊C4C2311yescharacteristic
67C3×C22⋊C4—21no—
68C3×C42C2311yescharacteristic
69#217—22no—
70#213—22no—
71(C2×D3)⋊C4—22no—
72(C2×D3)⋊C4—22no—
73(C2×D3)⋊C4—21no—
74(C2×D3)⋊C4—22no—
75(C2×D3)⋊C4D412yes—
76C4⋊Dic3—21no—
77C4⋊Dic3D411yescharacteristic
78C4⋊Dic3C2312yes—
79C4⋊Dic3C2311yescharacteristic
80C4×Dic3—22no—
81C4×Dic3—22no—
82C2×C3⋊C8C2311yescharacteristic
83C2×C3⋊C8C2311yescharacteristic
84D3×C8—24no—
85C2×D8—31no—
86C22×C8—32no—
87C4⋊Q8—31no—
88C4⋊Q8C2×D311yescharacteristic
89#124—62no—
90#124—62no—
91#121—32no—
92#121—32no—
93#121—61no—
94#121—61no—
95C4×D4—31no—
96C4×D4—31no—
97C4×D4C2×D311yescharacteristic
98#117—32no—
99#117—32no—
100#117—61no—
101#117—61no—
102#107—31no—
103#107—32no—
104#107—32no—
105#106—32no—
106#106C2×D312yes—
107C4⋊C8C2×D311yescharacteristic
108#102—31no—
109#102—32no—
110#102—31no—
111#102C2×D312yes—
112C22⋊C8—32no—
113C4×C8—31no—
114C23×C3—21no—
115C22×D3—21no—
116C22×D3C2×D412yes—
117C3×Q8—81no—
118C3×D4—21no—
119C3×D4—21no—
120C2×C3×C4—21no—
121C2×C3×C4—22no—
122C2×C3×C4—42no—
123C2×C3×C4C2×D411yescharacteristic
124C2×C3×C4C2×D411yescharacteristic
125C2×C3×C4C2411yescharacteristic
126#67—82no—
127C2×Dic3—21no—
128C2×Dic3—22no—
129C2×Dic3C2×D412yes—
130D12—22no—
131D12—21no—
132D12—21no—
133D12—82no—
134C4×D3—22no—
135C4×D3—22no—
136C4×D3—42no—
137Dic6—81no—
138C3×C8—22no—
139C3⋊C8—21no—
140C3⋊C8#4112yes—
141C2×Q8—21no—
142C2×Q8—61no—
143C2×D4—31no—
144C2×D4—31no—
145C2×D4—62no—
146C2×D4—62no—
147C2×D4C22×D311yescharacteristic
148C22×C4—21no—
149C22×C4—32no—
150C22×C4—61no—
151D8—62no—
152C2×C8—31no—
153C2×C8—31no—
154C2×C8—64no—
155C2×C8C22×D312yes—
156C4⋊C4—21no—
157C4⋊C4—31no—
158C4⋊C4—31no—
159C4⋊C4—32no—
160C4⋊C4—61no—
161C4⋊C4C22×D311yescharacteristic
162C4⋊C4C22×D312yes—
163C22⋊C4—21no—
164C22⋊C4—32no—
165C22⋊C4—62no—
166C22⋊C4—62no—
167C22⋊C4—62no—
168C22⋊C4—62no—
169C22⋊C4—61no—
170C42—62no—
171C42—62no—
172C42C22×D311yescharacteristic
173C22×C3—41no—
174C22×C3—41no—
175C22×C3—41no—
176C22×C3C22×D411yescharacteristic
177C2×D3—22no—
178C2×D3—22no—
179C2×D3—22no—
180C2×D3—41no—
181C2×D3—41no—
182C2×D3—41no—
183C3×C4—21no—
184C3×C4—41no—
185C3×C4—42no—
186C3×C4#13512yes—
187C3×C4C2×#4111yescharacteristic
188C3×C42−1+411yescharacteristic
189Dic3—22no—
190Dic3—41no—
191Dic3—42no—
192C23—21no—
193C23—32no—
194C23—61no—
195Q8—81no—
196Q8—241no—
197D4—21no—
198D4—21no—
199D4—62no—
200D4—61no—
201D4—61no—
202D4—242no—
203D4—242no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—32no—
207C2×C4—42no—
208C2×C4—62no—
209C2×C4—62no—
210C2×C4—61no—
211C2×C4—62no—
212C2×C4—122no—
213C2×C4D3×D411yescharacteristic
214C2×C4D3×D411yescharacteristic
215C2×C4C23×D311yescharacteristic
216C8—22no—
217C8—32no—
218C8—61no—
219C2×C3—81no—
220C2×C3#54711yescharacteristic
221C2×C3C2×#13511yescharacteristic
222C2×C3#57611yescharacteristic
223D3—42no—
224D3—81no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—62no—
229C22—62no—
230C22—62no—
231C22—121no—
232C22—121no—
233C22—121no—
234C22C2×D3×D411yescharacteristic
235C4—21no—
236C4—41no—
237C4—42no—
238C4—62no—
239C4—121no—
240C4—122no—
241C4#91612yes—
242C4#100711yescharacteristic
243C4D3×#4111yescharacteristic
244C3#334111yescharacteristic, complemented, Sylow
245C2—81no—
246C2—122no—
247C2—241no—
248C2#563111yescharacteristic
249C2C2×#91611yescharacteristic
250C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#476C2
socleC22×C3C22×D4
hypercenter#476D3
hypocenterC3#3341
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. #5563C2semidirect
3. C3×#476C2semidirect
4. #5078C2semidirect
5. C4×#213C2semidirect
6. #4866C2semidirect
7. #4860C2semidirect
8. #4842C2semidirect
9. #4834C2semidirect
10. #4779C2semidirect
11. #4775C2semidirect
48. #476D3semidirect
244. C3#3341semidirect

Maximal subgroups

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

subgroupindex
#57342
#55632
C3×#4762
#50782
C4×#2132
#48662
#48602
#48422
#48342
#47792
#47752
#33413