Finite Group Databasebeta

← #11781323

Subgroups — #11781323

Order 1152.

498 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C32×#487C211yesmaximal, characteristic, complemented
2#10592786C211yesmaximal, characteristic
3#10592782C211yesmaximal, characteristic
4C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic, complemented
6#10589413C211yesmaximal, characteristic, complemented
7#10589323C211yesmaximal, characteristic, complemented
8#71232—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4⋊Q8C2211yescharacteristic
11C2×#3755—21no—
12C2×C8×C3⋊D3—21no—
13C4×C4⋊(C3⋊D3)C2211yescharacteristic
14C32×#103—21no—
15C32×#103—21no—
16C32×C4×C8C2211yescharacteristic
17#63662—21no—
18#63647—21no—
19#63636—21no—
20#63634—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#487D314yescomplemented
25#5087—34no—
26#5083—34no—
27C8×D12—34no—
28#4547—34no—
29#4547—34no—
30#4457—34no—
31C2×C32×Q8—21no—
32C2×C32×Q8—21no—
33C2×C4⋊(C3⋊D3)D411yescharacteristic
34C2×C4×C3⋊D3—21no—
35C2×C32×C8D411yescharacteristic
36C2×C32×C8D411yescharacteristic
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C4⋊C4—21no—
41C32×C42C2311yescharacteristic
42#3755—42no—
43#3752—21no—
44C4⋊(C3⋊Dic3)D411yescharacteristic
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48C8×C3⋊D3—42no—
49#1679—91noSylow
50C3×C4⋊Q8C2×D314yes—
51C3×C4⋊Q8C2×D314yes—
52C2×#215—64no—
53C2×D3×C8—64no—
54C4×D12—34no—
55C3×#103—24no—
56C3×#103—24no—
57C3×C4×C8C2×D314yes—
58#835—64no—
59(C2×D3)⋊C8—64no—
60#809—64no—
61#807—64no—
62C4⋊(C3⋊C8)—34no—
63C4⋊(C3⋊C8)—34no—
64C4⋊(C3⋊C8)—34no—
65C22×C3⋊D3—21no—
66C32×Q8—41no—
67C32×Q8—41no—
68C32×Q8—41no—
69C32×Q8—41no—
70C2×C32×C4—41no—
71C2×C32×C4—41no—
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4#4111yescharacteristic
75C2×C3⋊Dic3—21no—
76C4⋊(C3⋊D3)—21no—
77C4⋊(C3⋊D3)SD1612yes—
78C4×C3⋊D3—41no—
79C4×C3⋊D3—41no—
80C32×C8—21no—
81C32×C8—21no—
82C3⋊(C3⋊C8)—41no—
83C3⋊(C3⋊C8)—41no—
84C3⋊(C3⋊C8)—41no—
85#487C3⋊D311yescharacteristic, complemented
86#474—91no—
87#461—91no—
88C8×D4—91no—
89#334—91no—
90#332—91no—
91#332—91no—
92C2×C3×Q8—24no—
93C2×C3×Q8—24no—
94C2×D12—34no—
95C2×C4×D3—64no—
96C2×C3×C8#6714yes—
97C2×C3×C8#6714yes—
98C3×C4⋊C4—24no—
99C3×C4⋊C4—24no—
100C3×C4⋊C4—24no—
101C3×C4⋊C4—24no—
102C3×C42C22×D314yes—
103#215—128no—
104(C2×D3)⋊C4—64no—
105C4⋊Dic3—34no—
106C2×C3⋊C8—64no—
107C2×C3⋊C8—64no—
108C2×C3⋊C8—64no—
109D3×C8—128no—
110C22×C32#12111yescharacteristic
111C2×C3⋊D3—22no—
112C2×C3⋊D3—41no—
113C2×C3⋊D3—41no—
114C32×C4—21no—
115C32×C4—81no—
116C32×C4—81no—
117C32×C4C2×SD1611yescharacteristic
118C32×C4#13511yescharacteristic
119C32×C4#13511yescharacteristic
120C32×C4AGL(1,ℤ/8)11yescharacteristic
121C3⋊Dic3—41no—
122C2×SD16—181no—
123C22×C8—181no—
124C4⋊Q8C2×C3⋊D311yescharacteristic
125C4⋊Q8C2×C3⋊D311yescharacteristic
126C4×D4—91no—
127#107—181no—
128C4⋊C8—91no—
129C4⋊C8—91no—
130C4⋊C8—91no—
131#103—21no—
132#103—21no—
133#103—181no—
134#102—181no—
135C22⋊C8—181no—
136C4×C8C2×C3⋊D311yescharacteristic
137C22×D3—64no—
138C3×Q8—44no—
139C3×Q8—44no—
140C3×Q8—44no—
141C3×Q8—44no—
142C2×C3×C4—44no—
143C2×C3×C4—44no—
144C2×C3×C4D3×D414yes—
145C2×C3×C4#23714yes—
146C2×C3×C4C2×#6714yes—
147C2×Dic3—64no—
148D12—38no—
149D12—64no—
150C4×D3—124no—
151C4×D3—124no—
152C3×C8—24no—
153C3×C8—24no—
154C3⋊C8—124no—
155C3⋊C8—124no—
156C3⋊C8—124no—
157C2×C32#46311yescharacteristic
158C2×C32#46511yescharacteristic
159C2×C32#47311yescharacteristic
160C3⋊D3—42no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×D4—91no—
164C22×C4—181no—
165SD16—362no—
166C2×C8—181no—
167C2×C8—181no—
168C2×C8—181no—
169C2×C8—362no—
170C2×C8#63811yescharacteristic
171C2×C8#63811yescharacteristic
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—91no—
177C22⋊C4—181no—
178C42C22×C3⋊D311yescharacteristic
179C22×C3#93814yes—
180C2×D3—68no—
181C2×D3—124no—
182C2×D3—124no—
183C3×C4—24no—
184C3×C4—84no—
185C3×C4—84no—
186C3×C4D3×SD1614yes—
187C3×C4#91614yes—
188C3×C4#94914yes—
189C3×C4#95014yes—
190Dic3—124no—
191C32#167911yescharacteristic, complemented, Sylow
192C23—181no—
193Q8—41no—
194Q8—41no—
195Q8—41no—
196Q8—41no—
197D4—92no—
198D4—181no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—181no—
202C2×C4—361no—
203C2×C4—361no—
204C2×C4D4×C3⋊D311yescharacteristic
205C2×C4#383011yescharacteristic
206C2×C4C2×#63811yescharacteristic
207C8—21no—
208C8—21no—
209C8—361no—
210C8—361no—
211C8—361no—
212C2×C3#505714yes—
213C2×C3#517114yes—
214C2×C3#519214yes—
215D3—128no—
216C22—182no—
217C22—361no—
218C22—361no—
219C22#6414711yescharacteristic
220C4—21no—
221C4—81no—
222C4—81no—
223C4—361no—
224C4SD16×C3⋊D311yescharacteristic
225C4#6412511yescharacteristic
226C4#6415811yescharacteristic
227C4#6415911yescharacteristic
228C3#7123214yescomplemented
229C2—362no—
230C2#1059275611yescharacteristic
231C2#1059287011yescharacteristic
232C2#1059289111yescharacteristic
subgroupG/H
centerC22#64147
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#487C2
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#487C3⋊D3
hypocenterC32#1679
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. C32×#487C2semidirect
5. #10589413C2semidirect
6. #10589413C2semidirect
7. #10589323C2semidirect
24. C3×#487D3semidirect
85. #487C3⋊D3semidirect
191. C32#1679semidirect
228. C3#71232semidirect

Maximal subgroups

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

subgroupindex
C32×#4872
#105927862
#105927822
C8×C4⋊(C3⋊D3)2
#105894132
#105893232
#712323