Finite Group Databasebeta

← #11874971

Subgroups — #11874971

Order 1152.

1068 conjugacy classes of subgroups; only the 277 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 277 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#10596199C212yesmaximal
2C32×#500C211yesmaximal, characteristic, complemented
3#10592779C212yesmaximal, complemented
4#10592579C214yesmaximal
5#10592577C214yesmaximal, complemented
6C4×C8×C3⋊D3C211yesmaximal, characteristic
7#10592381C211yesmaximal, characteristic, complemented
8#81938—34nomaximal
9C32×C4⋊Q8C2212yes—
10#64155—22no—
11Q8×C3⋊Dic3—22no—
12C2×C8×C3⋊D3C2212yes—
13#64106—22no—
14#64101C2214yes—
15#64099C2214yes—
16#64096—22no—
17C42×C3⋊D3C2211yescharacteristic
18#64078C2212yes—
19C32×#107C2214yes—
20C32×C4×C8C2211yescharacteristic
21#63645C2214yes—
22C8×C3⋊Dic3C2212yes—
23#63635C2218yes—
24C4×C3⋊(C3⋊C8)C2211yescharacteristic
25#5728—38no—
26C3×#500D314yescomplemented
27#5080—38no—
28#4880—316no—
29#4878—316no—
30C4×D3×C8—34no—
31#4682—34no—
32C2×C32×Q8—22no—
33C2×C4×C3⋊D3D411yescharacteristic
34C2×C4×C3⋊D3D411yescharacteristic
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×#634—22no—
37C2×C32×C8C2312yes—
38C32×C4⋊C4—22no—
39C32×C4⋊C4C2314yes—
40C32×C42C2311yescharacteristic
41#3752—24no—
42C4⋊(C3⋊Dic3)—22no—
43C4⋊(C3⋊Dic3)—24no—
44C4⋊(C3⋊Dic3)C2314yes—
45#3750—24no—
46C4×C3⋊Dic3—24no—
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3C2311yescharacteristic
50C2×C3⋊(C3⋊C8)C2312yes—
51C8×C3⋊D3Q818yescomplemented
52#3160—91noSylow
53C3×C4⋊Q8C2×D318yes—
54#946—68no—
55Q8×Dic3—68no—
56C2×D3×C8—38no—
57#897—68no—
58#892—316no—
59#890—316no—
60#887—68no—
61C42×D3—34no—
62#869—38no—
63C3×#107C2×D3116yes—
64C3×C4×C8C2×D314yes—
65#818—316no—
66C8×Dic3—38no—
67#808—332no—
68C4×C3⋊C8—34no—
69C22×C3⋊D3C2×D411yescharacteristic
70C32×Q8—44no—
71C2×C32×C4—24no—
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4C2411yescharacteristic
75C2×C3⋊Dic3—24no—
76C2×C3⋊Dic3C2×D411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78C2×C3⋊Dic3C2×D411yescharacteristic
79C4×C3⋊D3—22no—
80C4×C3⋊D3—22no—
81C4×C3⋊D3C2×Q814yes—
82#634—44no—
83C32×C8C2×Q814yes—
84C3⋊(C3⋊C8)C2×Q814yes—
85#533—92no—
86#500—91no—
87#500C3⋊D311yescharacteristic, complemented
88#499—94no—
89#498—92no—
90#427—94no—
91C2×C4×C8—91no—
92C2×C3×Q8—28no—
93C2×C4×D3—34no—
94C2×C4×D3—34no—
95C2×C4×D3—34no—
96C2×Dic6—68no—
97C2×C3×C8C22×D318yes—
98C3×C4⋊C4—28no—
99C3×C4⋊C4C22×D3116yes—
100C3×C42C22×D314yes—
101(C2×D3)⋊C4—616no—
102C4⋊Dic3—316no—
103C4⋊Dic3—616no—
104C4⋊Dic3—68no—
105Dic3⋊C4—616no—
106C4×Dic3—34no—
107C4×Dic3—34no—
108C4×Dic3—34no—
109C4×Dic3—616no—
110C2×C3⋊C8—38no—
111D3×C8—332no—
112C22×C32C22×D411yescharacteristic
113C2×C3⋊D3—21no—
114C2×C3⋊D3—21no—
115C2×C3⋊D3C4⋊Q812yes—
116C32×C4—44no—
117C32×C4#13512yes—
118C32×C4#13512yes—
119C32×C4C22×Q812yes—
120C3⋊Dic3—21no—
121C3⋊Dic3—21no—
122C3⋊Dic3—44no—
123C3⋊Dic3C4⋊Q812yes—
124C22×C8—92no—
125C4⋊Q8—92no—
126C4⋊Q8C2×C3⋊D312yes—
127#125—94no—
128C22⋊Q8—182no—
129C22⋊Q8—182no—
130C4×Q8—182no—
131C4×Q8—182no—
132#117—94no—
133C2×C42—91no—
134#107—94no—
135#107C2×C3⋊D314yes—
136#106—98no—
137C4×C8—92no—
138C4×C8—91no—
139C4×C8C2×C3⋊D311yescharacteristic
140C22×D3—34no—
141C3×Q8—416no—
142C2×C3×C4—216no—
143C2×C3×C4D3×D414yes—
144C2×C3×C4D3×D414yes—
145C2×C3×C4C23×D314yes—
146C2×Dic3—34no—
147C2×Dic3—34no—
148C2×Dic3—34no—
149C2×Dic3—616no—
150C4×D3—316no—
151C4×D3—68no—
152C4×D3—68no—
153Dic6—1216no—
154C3×C8D3×Q8116yes—
155C3⋊C8—316no—
156C2×C32C2×C4⋊Q811yescharacteristic
157C2×C32C2×#13511yescharacteristic
158C2×C32C2×#13511yescharacteristic
159C3⋊D3—22no—
160C2×Q8—22no—
161C2×Q8—182no—
162C22×C4—91no—
163C22×C4—91no—
164C22×C4—91no—
165C2×C8—92no—
166C2×C8—98no—
167C2×C8C22×C3⋊D312yes—
168C4⋊C4—22no—
169C4⋊C4—94no—
170C4⋊C4—184no—
171C4⋊C4—184no—
172C4⋊C4—182no—
173C4⋊C4C22×C3⋊D314yes—
174C22⋊C4—184no—
175C42—91no—
176C42—91no—
177C42—91no—
178C42—184no—
179C42C22×C3⋊D311yescharacteristic
180C22×C3C2×D3×D414yes—
181C2×D3—38no—
182C2×D3—64no—
183C2×D3—64no—
184C3×C4—416no—
185C3×C4#91218yes—
186C3×C4#91918yes—
187C3×C4C2×D3×Q818yes—
188Dic3—38no—
189Dic3—64no—
190Dic3—64no—
191Dic3—1216no—
192C32#316011yescharacteristic, complemented, Sylow
193C23—91no—
194Q8—44no—
195Q8—364no—
196C2×C4—24no—
197C2×C4—91no—
198C2×C4—94no—
199C2×C4—91no—
200C2×C4—91no—
201C2×C4—182no—
202C2×C4—182no—
203C2×C4—184no—
204C2×C4D4×C3⋊D311yescharacteristic
205C2×C4D4×C3⋊D311yescharacteristic
206C2×C4C23×C3⋊D311yescharacteristic
207C8—94no—
208C8Q8×C3⋊D314yes—
209C2×C3D3×C4⋊Q814yes—
210C2×C3C2×#91214yes—
211C2×C3C2×#91914yes—
212D3—68no—
213C22—92no—
214C22—181no—
215C22—181no—
216C22C2×D4×C3⋊D311yescharacteristic
217C4—44no—
218C4—92no—
219C4—181no—
220C4—181no—
221C4—364no—
222C4#6412112yes—
223C4#6412812yes—
224C4C2×Q8×C3⋊D312yes—
225C3#8193814yescomplemented
226C2—182no—
227C2C3⋊D3×C4⋊Q811yescharacteristic
228C2C2×#6412111yescharacteristic
229C2C2×#6412811yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#500C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#500C3⋊D3
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
2. C32×#500C2semidirect
3. #10592779C2semidirect
5. #10592577C2semidirect
7. #10592381C2semidirect
26. C3×#500D3semidirect
51. C8×C3⋊D3Q8semidirect
87. #500C3⋊D3semidirect
192. C32#3160semidirect
225. C3#81938semidirect

Maximal subgroups

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

subgroupindex
#105961992
C32×#5002
#105927792
#105925792
#105925772
C4×C8×C3⋊D32
#105923812
#819383