Finite Group Databasebeta

← #11781607

Subgroups — #11781607

Order 1152.

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

normal subgroups only

This group has 546 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#10592775C211yesmaximal, characteristic, complemented
2#10592771C211yesmaximal, characteristic
3#10592545C211yesmaximal, characteristic, complemented
4#10592537C211yesmaximal, characteristic, complemented
5C32×#331C211yesmaximal, characteristic, complemented
6#10589348C211yesmaximal, characteristic, complemented
7#10589345C211yesmaximal, characteristic, complemented
8#68398—34nomaximal
9C32×#127C2211yescharacteristic
10C2×#3754—21no—
11C2×#3754—21no—
12C2×#3753—21no—
13C2×#3743—21no—
14C4×C4⋊(C3⋊D3)C2211yescharacteristic
15#64078C2211yescharacteristic
16C32×C4⋊C8C2211yescharacteristic
17C32×C4⋊C8C2211yescharacteristic
18#63659—21no—
19#63648—21no—
20#63647—21no—
21#63645—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24#5076—34no—
25#5072—34no—
26#4846—34no—
27#4838—34no—
28C3×#331D314yescomplemented
29#4482—34no—
30#4479—34no—
31C2×C32×D4—21no—
32C2×C32×D4—21no—
33C2×C32×D4—21no—
34C2×C4⋊(C3⋊D3)D411yescharacteristic
35C2×C4×C3⋊D3—21no—
36C2×#634—21no—
37C2×C32×C8—21no—
38C2×C32×C8—21no—
39C32×C42C2311yescharacteristic
40#3754—42no—
41#3754—42no—
42#3753—42no—
43#3752—21no—
44C4⋊(C3⋊Dic3)—21no—
45C4⋊(C3⋊Dic3)—21no—
46C4⋊(C3⋊Dic3)D411yescharacteristic
47C2×C3⋊(C3⋊C8)—21no—
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50#3743—42no—
51#1685—91noSylow
52C3×#127C2×D314yes—
53C2×#214—64no—
54C2×#214—64no—
55C2×#213—64no—
56C2×ΓL(1,𝔽25)—64no—
57C4×D12—34no—
58#869—34no—
59C3×C4⋊C8C2×D314yes—
60C3×C4⋊C8C2×D314yes—
61#832—64no—
62#821—64no—
63(C2×D3)⋊C8—64no—
64#818—64no—
65C4⋊(C3⋊C8)—34no—
66C4×C3⋊C8—34no—
67C23×C32—41no—
68C22×C3⋊D3—21no—
69C32×D4—41no—
70C32×D4—41no—
71C32×D4—41no—
72C32×D4—41no—
73C32×D4—81no—
74C2×C32×C4C2×D411yescharacteristic
75C2×C32×C4C2×D411yescharacteristic
76C2×C32×C4#4111yescharacteristic
77C2×C3⋊Dic3—21no—
78C2×C3⋊Dic3—41no—
79C4⋊(C3⋊D3)—21no—
80C4⋊(C3⋊D3)—21no—
81C4×C3⋊D3—41no—
82C4×C3⋊D3—41no—
83#634—41no—
84#634—41no—
85C32×C8—41no—
86C32×C8—41no—
87C3⋊(C3⋊C8)—21no—
88C3⋊(C3⋊C8)—41no—
89C3⋊(C3⋊C8)D812yescomplemented
90#492—91no—
91#474—91no—
92#459—91no—
93#436—91no—
94#335—91no—
95#332—91no—
96#331C3⋊D311yescharacteristic, complemented
97C2×C3×D4—24no—
98C2×C3×D4—24no—
99C2×C3×D4—24no—
100C2×D12—34no—
101C2×C4×D3—64no—
102C2×Dic6—64no—
103C2×C3×C8—24no—
104C2×C3×C8—24no—
105C3×C42C22×D314yes—
106#214—128no—
107#214—128no—
108#213—128no—
109(C2×D3)⋊C4—64no—
110C4⋊Dic3—34no—
111C4⋊Dic3—64no—
112C4⋊Dic3—64no—
113C2×C3⋊C8—34no—
114C2×C3⋊C8—34no—
115C2×C3⋊C8—64no—
116ΓL(1,𝔽25)—128no—
117C22×C32—81no—
118C22×C32—81no—
119C22×C32—81no—
120C22×C32#12111yescharacteristic
121C2×C3⋊D3—41no—
122C2×C3⋊D3—41no—
123C2×C3⋊D3—41no—
124C32×C4—21no—
125C32×C4C2×D811yescharacteristic
126C32×C4AGL(1,ℤ/8)11yescharacteristic
127C32×C4AGL(1,ℤ/8)11yescharacteristic
128C32×C4#13711yescharacteristic
129C3⋊Dic3—41no—
130C3⋊Dic3—81no—
131C2×SD16—181no—
132C2×SD16—181no—
133C2×D8—181no—
134C2×M16—181no—
135C4⋊Q8—91no—
136#127C2×C3⋊D311yescharacteristic
137C4×D4—91no—
138#107—181no—
139C4⋊C8—91no—
140C4⋊C8C2×C3⋊D311yescharacteristic
141C4⋊C8C2×C3⋊D311yescharacteristic
142#102—181no—
143#102—181no—
144C22⋊C8—181no—
145C4×C8—91no—
146C23×C3—44no—
147C22×D3—64no—
148C3×D4—44no—
149C3×D4—44no—
150C3×D4—44no—
151C3×D4—44no—
152C3×D4—84no—
153C2×C3×C4#23514yes—
154C2×C3×C4D3×D414yes—
155C2×C3×C4D3×D414yes—
156C2×Dic3—64no—
157C2×Dic3—124no—
158D12—64no—
159D12—64no—
160C4×D3—124no—
161C4×D3—124no—
162Dic6—124no—
163Dic6—124no—
164C3×C8—44no—
165C3×C8—44no—
166C3⋊C8—38no—
167C3⋊C8—64no—
168C3⋊C8—124no—
169C2×C32—161no—
170C2×C32#45911yescharacteristic
171C2×C32#46811yescharacteristic
172C2×C32#47111yescharacteristic
173C3⋊D3—81no—
174C2×Q8—181no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—91no—
179C22×C4—181no—
180SD16—362no—
181SD16—362no—
182D8—362no—
183M16—362no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—91no—
187C2×C8—91no—
188C2×C8—181no—
189C4⋊C4—91no—
190C4⋊C4—181no—
191C4⋊C4—181no—
192C22⋊C4—181no—
193C42C22×C3⋊D311yescharacteristic
194C22×C3—84no—
195C22×C3—84no—
196C22×C3—84no—
197C22×C3#88414yes—
198C2×D3—124no—
199C2×D3—124no—
200C2×D3—124no—
201C3×C4—24no—
202C3×C4D3×D814yes—
203C3×C4#91114yes—
204C3×C4#91414yes—
205C3×C4#91514yes—
206Dic3—124no—
207Dic3—244no—
208C32#168511yescharacteristic, complemented, Sylow
209C23—41no—
210C23—181no—
211Q8—361no—
212Q8—361no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217D4—81no—
218D4—181no—
219D4—181no—
220C2×C4—181no—
221C2×C4—361no—
222C2×C4—361no—
223C2×C4—361no—
224C2×C4#382811yescharacteristic
225C2×C4D4×C3⋊D311yescharacteristic
226C2×C4D4×C3⋊D311yescharacteristic
227C8—41no—
228C8—41no—
229C8—92no—
230C8—181no—
231C8—361no—
232C2×C3—164no—
233C2×C3#474814yes—
234C2×C3#478014yes—
235C2×C3#478614yes—
236D3—244no—
237C22—81no—
238C22—81no—
239C22—81no—
240C22—361no—
241C22—361no—
242C22—361no—
243C22#6409311yescharacteristic
244C4—21no—
245C4—361no—
246C4—721no—
247C4D8×C3⋊D311yescharacteristic
248C4#6412011yescharacteristic
249C4#6412311yescharacteristic
250C4#6412411yescharacteristic
251C3#6839814yescomplemented
252C2—161no—
253C2—721no—
254C2#1059244711yescharacteristic
255C2#1059247911yescharacteristic
256C2#1059248511yescharacteristic
subgroupG/H
centerC22#64093
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#331C2
socleC22×C32#121
prime radical#10592771C2
hypercenter#331C3⋊D3
hypocenterC32#1685
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #10592775C2semidirect
3. #10592545C2semidirect
4. #10592537C2semidirect
5. C32×#331C2semidirect
6. #10589348C2semidirect
7. #10589345C2semidirect
28. C3×#331D3semidirect
89. C3⋊(C3⋊C8)D8semidirect
96. #331C3⋊D3semidirect
208. C32#1685semidirect
251. C3#68398semidirect

Maximal subgroups

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

subgroupindex
#105927752
#105927712
#105925452
#105925372
C32×#3312
#105893482
#105893452
#683983