Finite Group Databasebeta

← #11781329

Subgroups — #11781329

Order 1152.

498 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 119 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#10592786C211yesmaximal, characteristic
2#10592778C211yesmaximal, characteristic, complemented
3#10592540C211yesmaximal, characteristic
4#10592533C211yesmaximal, characteristic
5C32×#332C211yesmaximal, characteristic, complemented
6#10589352C211yesmaximal, characteristic, complemented
7#10589346C211yesmaximal, characteristic, complemented
8#68444—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C2×#3744—21no—
11C2×C8×C3⋊D3—21no—
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13#64078C2211yescharacteristic
14C32×C4⋊C8C2211yescharacteristic
15C32×C4⋊C8C2211yescharacteristic
16#63662—21no—
17#63662—21no—
18#63647—21no—
19#63643—21no—
20#63636—21no—
21#63634—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#5087—34no—
25#5079—34no—
26#4841—34no—
27#4834—34no—
28C3×#332D314yescomplemented
29#4486—34no—
30#4480—34no—
31C2×C32×Q8—21no—
32C2×C4⋊(C3⋊D3)D411yescharacteristic
33C2×C4×C3⋊D3—21no—
34C2×#634—21no—
35C2×C32×C8—21no—
36C2×C32×C8—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C42C2311yescharacteristic
40#3752—21no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)D411yescharacteristic
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)D411yescharacteristic
46C2×C3⋊(C3⋊C8)D411yescharacteristic
47#3744—42no—
48C8×C3⋊D3—42no—
49#1679—91noSylow
50C3×C4⋊Q8C2×D314yes—
51C2×#204—64no—
52C2×D3×C8—64no—
53C4×D12—34no—
54#869—34no—
55C3×C4⋊C8C2×D314yes—
56C3×C4⋊C8C2×D314yes—
57#835—64no—
58#835—64no—
59(C2×D3)⋊C8—64no—
60#816—64no—
61#809—64no—
62#807—64no—
63C4⋊(C3⋊C8)—34no—
64C4×C3⋊C8—34no—
65C22×C3⋊D3—21no—
66C32×Q8—41no—
67C32×Q8—41no—
68C2×C32×C4—41no—
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C32×C4#4111yescharacteristic
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—41no—
74C4⋊(C3⋊D3)—21no—
75C4⋊(C3⋊D3)SD1612yes—
76C4×C3⋊D3—41no—
77C4×C3⋊D3—41no—
78#634—41no—
79#634—41no—
80C32×C8—41no—
81C32×C8—41no—
82C3⋊(C3⋊C8)—21no—
83C3⋊(C3⋊C8)—21no—
84C3⋊(C3⋊C8)—41no—
85#487—91no—
86#474—91no—
87#461—91no—
88C8×D4—91no—
89#334—91no—
90#332—91no—
91#332C3⋊D311yescharacteristic, complemented
92C2×C3×Q8—24no—
93C2×D12—34no—
94C2×C4×D3—64no—
95C2×Dic6—64no—
96C2×C3×C8—24no—
97C2×C3×C8—24no—
98C3×C4⋊C4—24no—
99C3×C4⋊C4—24no—
100C3×C42C22×D314yes—
101(C2×D3)⋊C4—64no—
102C4⋊Dic3—34no—
103C4⋊Dic3—64no—
104C4⋊Dic3—64no—
105C2×C3⋊C8—34no—
106C2×C3⋊C8—34no—
107C2×C3⋊C8—64no—
108#204—128no—
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×C4C2×SD1611yescharacteristic
117C32×C4#13511yescharacteristic
118C32×C4#13511yescharacteristic
119C32×C4AGL(1,ℤ/8)11yescharacteristic
120C3⋊Dic3—41no—
121C3⋊Dic3—81no—
122C2×SD16—181no—
123C22×C8—181no—
124C4⋊Q8—91no—
125C4⋊Q8C2×C3⋊D311yescharacteristic
126C4×D4—91no—
127#107—181no—
128C4⋊C8—91no—
129C4⋊C8C2×C3⋊D311yescharacteristic
130C4⋊C8C2×C3⋊D311yescharacteristic
131#103—181no—
132#103—181no—
133#103—181no—
134#102—181no—
135C22⋊C8—181no—
136C4×C8—91no—
137C22×D3—64no—
138C3×Q8—44no—
139C3×Q8—44no—
140C2×C3×C4—44no—
141C2×C3×C4#23514yes—
142C2×C3×C4D3×D414yes—
143C2×C3×C4D3×D414yes—
144C2×Dic3—64no—
145C2×Dic3—124no—
146D12—38no—
147D12—64no—
148C4×D3—124no—
149C4×D3—124no—
150Dic6—124no—
151Dic6—124no—
152C3×C8—44no—
153C3×C8—44no—
154C3⋊C8—64no—
155C3⋊C8—64no—
156C3⋊C8—124no—
157C2×C32#46311yescharacteristic
158C2×C32#46511yescharacteristic
159C2×C32#47311yescharacteristic
160C3⋊D3—42no—
161C2×Q8—21no—
162C2×Q8—181no—
163C2×D4—91no—
164C22×C4—181no—
165SD16—362no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—91no—
169C2×C8—91no—
170C2×C8—181no—
171C2×C8—362no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—91no—
175C4⋊C4—181no—
176C4⋊C4—181no—
177C22⋊C4—181no—
178C42C22×C3⋊D311yescharacteristic
179C22×C3#88414yes—
180C2×D3—68no—
181C2×D3—124no—
182C2×D3—124no—
183C3×C4—24no—
184C3×C4—84no—
185C3×C4#91114yes—
186C3×C4D3×SD1614yes—
187C3×C4#91614yes—
188C3×C4#91914yes—
189Dic3—124no—
190Dic3—244no—
191C32#167911yescharacteristic, complemented, Sylow
192C23—181no—
193Q8—41no—
194Q8—41no—
195Q8—361no—
196Q8—361no—
197D4—92no—
198D4—181no—
199C2×C4—41no—
200C2×C4—181no—
201C2×C4—361no—
202C2×C4—361no—
203C2×C4—361no—
204C2×C4#382811yescharacteristic
205C2×C4D4×C3⋊D311yescharacteristic
206C2×C4D4×C3⋊D311yescharacteristic
207C8—41no—
208C8—41no—
209C8—181no—
210C8—181no—
211C8—361no—
212C2×C3#475514yes—
213C2×C3#478714yes—
214C2×C3#480714yes—
215D3—128no—
216C22—182no—
217C22—361no—
218C22—361no—
219C22#6409311yescharacteristic
220C4—21no—
221C4—81no—
222C4—361no—
223C4—721no—
224C4#6412011yescharacteristic
225C4SD16×C3⋊D311yescharacteristic
226C4#6412511yescharacteristic
227C4#6412811yescharacteristic
228C3#6844414yescomplemented
229C2—362no—
230C2#1059245411yescharacteristic
231C2#1059248611yescharacteristic
232C2#1059250611yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#332C2
socleC22×C32#121
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#332C3⋊D3
hypocenterC32#1679
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #10592778C2semidirect
5. C32×#332C2semidirect
6. #10589352C2semidirect
7. #10589346C2semidirect
28. C3×#332D3semidirect
91. #332C3⋊D3semidirect
191. C32#1679semidirect
228. C3#68444semidirect

Maximal subgroups

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

subgroupindex
#105927862
#105927782
#105925402
#105925332
C32×#3322
#105893522
#105893462
#684443