Finite Group Databasebeta

← #11799130

Subgroups — #11799130

Order 1152.

450 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 105 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×#510C211yesmaximal, characteristic
2#10592895C211yesmaximal, characteristic
3#10592894C211yesmaximal, characteristic
4#10592882C211yesmaximal, characteristic, complemented
5#10589431C211yesmaximal, characteristic, complemented
6#10589383C211yesmaximal, characteristic, complemented
7#10589377C211yesmaximal, characteristic, complemented
8#71520—34nomaximal
9C32×#135C2211yescharacteristic
10C2×C32×Q16C2211yescharacteristic
11#64157—21no—
12#64153—21no—
13C2×#3756—21no—
14C2×#3746C2211yescharacteristic
15C32×Q32—21no—
16C32×SD32—21no—
17C32×M32C2211yescharacteristic
18#63664—21no—
19#63656—21no—
20#63654—21no—
21#63646C2211yescharacteristic
22C8×C3⋊Dic3C2211yescharacteristic
23#63639C2211yescharacteristic
24C3×#510D314yes—
25#5196—34no—
26#5195—34no—
27#5183—34no—
28#4565—34no—
29#4517—34no—
30#4511—34no—
31C32×#41—21no—
32C2×C32×Q8—21no—
33C2×#634—21no—
34C32×Q16—21no—
35C32×Q16—21no—
36C32×Q16D411yescharacteristic
37C32×SD16—21no—
38C32×D8D411yescharacteristic
39C2×C32×C8C2311yescharacteristic
40#3756—41no—
41#3756—41no—
42#3750—42no—
43C4×C3⋊Dic3D411yescharacteristic
44#3748—21no—
45#3748—41no—
46C2×C3⋊(C3⋊C8)—41no—
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48#3746—21no—
49#3746—21no—
50C32×C16—21no—
51C3⋊(C3⋊C16)—21no—
52#2214—91noSylow
53C3×#135C2×D314yes—
54C2×C3×Q16C2×D314yes—
55#948—64no—
56#944—64no—
57C2×#216—64no—
58C2×Dic12—34no—
59C3×Q32—24no—
60C3×SD32—24no—
61C3×M32C2×D314yes—
62#837—64no—
63#829—64no—
64#827—64no—
65#819—34no—
66C8×Dic3—34no—
67#812—34no—
68C32×Q8—21no—
69C32×Q8—41no—
70C32×Q8—41no—
71C32×D4—21no—
72C32×D4—41no—
73C2×C32×C4—41no—
74C2×C32×C4—41no—
75C2×C32×C4C2×D411yescharacteristic
76C2×C3⋊Dic3—21no—
77C2×C3⋊Dic3—41no—
78#634—41no—
79#634—41no—
80C32×C8C2×D411yescharacteristic
81C32×C8#4111yescharacteristic
82C3⋊(C3⋊C8)—41no—
83C3⋊(C3⋊C8)D811yescharacteristic
84C3⋊(C3⋊C8)D811yescharacteristic
85#510—91no—
86#510C3⋊D311yescharacteristic
87#494—91no—
88#443—91no—
89#364—91no—
90#362—91no—
91#362—91no—
92C3×#41—24no—
93C2×C3×Q8—24no—
94C2×Dic6—64no—
95C3×Q16—24no—
96C3×Q16—24no—
97C3×Q16#6714yes—
98C3×SD16—24no—
99C3×D8#6714yes—
100C2×C3×C8C22×D314yes—
101#216—124no—
102#216—124no—
103Dic3⋊C4—128no—
104C4×Dic3—34no—
105#208—64no—
106#208—124no—
107C2×C3⋊C8—34no—
108C2×C3⋊C8—124no—
109Dic12—64no—
110Dic12—64no—
111C3×C16—24no—
112C3⋊C16—64no—
113C22×C32—41no—
114C22×C32AGL(1,ℤ/8)11yescharacteristic
115C32×C4—41no—
116C32×C4—81no—
117C32×C4#12111yescharacteristic
118C32×C4C2×D811yescharacteristic
119C3⋊Dic3—22no—
120C3⋊Dic3—81no—
121#135C2×C3⋊D311yescharacteristic
122C2×Q16—91no—
123C2×Q16—181no—
124C2×Q16C2×C3⋊D311yescharacteristic
125#131—181no—
126C4⋊Q8—181no—
127Q32—21no—
128Q32—181no—
129SD32—21no—
130SD32—181no—
131M32—91no—
132M32C2×C3⋊D311yescharacteristic
133#108—91no—
134#104—181no—
135C4×C8—91no—
136C3×Q8—24no—
137C3×Q8—44no—
138C3×Q8—44no—
139C3×D4—24no—
140C3×D4—44no—
141C2×C3×C4—44no—
142C2×C3×C4—44no—
143C2×C3×C4D3×D414yes—
144C2×Dic3—64no—
145C2×Dic3—124no—
146Dic6—124no—
147Dic6—124no—
148C3×C8#23714yes—
149C3×C8C2×#6714yes—
150C3⋊C8—34no—
151C3⋊C8—34no—
152C3⋊C8—124no—
153C2×C32—21no—
154C2×C32—81no—
155C2×C32#45911yescharacteristic
156#41—21no—
157C2×Q8—21no—
158C2×Q8—181no—
159Q16—21no—
160Q16—21no—
161Q16—181no—
162Q16—181no—
163Q16—361no—
164Q16—361no—
165Q16#63811yescharacteristic
166SD16—21no—
167D8#63811yescharacteristic
168M16—181no—
169M16—361no—
170C2×C8—91no—
171C2×C8—361no—
172C2×C8C22×C3⋊D311yescharacteristic
173C4⋊C4—362no—
174C42—91no—
175C16—21no—
176C16—181no—
177C22×C3—44no—
178C22×C3#91114yes—
179C3×C4—44no—
180C3×C4—84no—
181C3×C4D3×D814yes—
182C3×C4#93914yes—
183Dic3—68no—
184Dic3—244no—
185C32#221411yescharacteristic, complemented, Sylow
186Q8—21no—
187Q8—41no—
188Q8—41no—
189Q8—361no—
190Q8—361no—
191D4—21no—
192D4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—181no—
196C2×C4—361no—
197C2×C4D4×C3⋊D311yescharacteristic
198C8—91no—
199C8—91no—
200C8—361no—
201C8#383011yescharacteristic
202C8C2×#63811yescharacteristic
203C2×C3—24no—
204C2×C3—84no—
205C2×C3#515014yes—
206C22—41no—
207C22#6412011yescharacteristic
208C4—41no—
209C4—81no—
210C4—182no—
211C4—721no—
212C4D8×C3⋊D311yescharacteristic
213C4#6414811yescharacteristic
214C3#7152014yescomplemented
215C2—21no—
216C2—81no—
217C2#1059284911yescharacteristic
subgroupG/H
centerC2#10592849
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#510C2
socleC2×C32#459
prime radicalC32×#135C22
hypercenter#510C3⋊D3
hypocenterC32#2214
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
4. #10592882C2semidirect
5. #10589431C2semidirect
6. #10589383C2semidirect
7. #10589377C2semidirect
185. C32#2214semidirect
214. C3#71520semidirect

Maximal subgroups

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

subgroupindex
C32×#5102
#105928952
#105928942
#105928822
#105894312
#105893832
#105893772
#715203