Finite Group Databasebeta

← #11798965

Subgroups — #11798965

Order 1152.

510 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 107 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#10592854C211yesmaximal, characteristic, complemented
2C2×#63653C211yesmaximal, characteristic
3C2×#63627C211yesmaximal, characteristic, complemented
4#10592571C211yesmaximal, characteristic, complemented
5C32×#357C211yesmaximal, characteristic, complemented
6#10589367C211yesmaximal, characteristic, complemented
7#10589358C211yesmaximal, characteristic, complemented
8#69203—34nomaximal
9C2×C32×D8C2211yescharacteristic
10#64145—21no—
11C2×#3754—21no—
12C2×#3746C2211yescharacteristic
13C2×#3745C2211yescharacteristic
14#64102—21no—
15C2×C32×C16C2211yescharacteristic
16C32×#107C2211yescharacteristic
17#63653—22no—
18C8×C3⋊Dic3C2211yescharacteristic
19C2×C3⋊(C3⋊C16)C2211yescharacteristic
20#63636—21no—
21#63627—22no—
22#5155—34no—
23C2×#826—34no—
24C2×#800—34no—
25#4872—34no—
26C3×#357D314yescomplemented
27Dic3⋊C16—34no—
28#4492—34no—
29C2×C32×D4—21no—
30C2×C4⋊(C3⋊D3)—21no—
31C2×C4×C3⋊D3—41no—
32C2×#634—21no—
33C32×D8—21no—
34C32×D8—21no—
35C2×C32×C8C2311yescharacteristic
36C32×C4⋊C4—21no—
37#3757—41no—
38#3757—41no—
39#3754—42no—
40#3752—41no—
41C4×C3⋊Dic3D411yescharacteristic
42C2×C3⋊(C3⋊C8)D411yescharacteristic
43#3746—21no—
44#3746—21no—
45#3745—21no—
46#3745D412yes—
47C32×C16—21no—
48C3⋊(C3⋊C16)—21no—
49#2210—91noSylow
50C2×C3×D8C2×D314yes—
51#936—64no—
52C2×#214—64no—
53C2×Dic12—34no—
54C2×D24—34no—
55#893—64no—
56C2×C3×C16C2×D314yes—
57C3×#107C2×D314yes—
58#826—68no—
59C8×Dic3—34no—
60C2×C3⋊C16—34no—
61#809—64no—
62#800—68no—
63C23×C32—41no—
64C22×C3⋊D3—41no—
65C32×D4—41no—
66C32×D4—41no—
67C2×C32×C4—41no—
68C2×C32×C4C2×D411yescharacteristic
69C2×C3⋊Dic3—41no—
70C2×C3⋊Dic3D811yescharacteristic
71C2×C3⋊Dic3D811yescharacteristic
72C4⋊(C3⋊D3)—22no—
73C4⋊(C3⋊D3)—41no—
74C4×C3⋊D3—82no—
75#634—41no—
76#634—41no—
77C32×C8C2×D411yescharacteristic
78C32×C8#4111yescharacteristic
79C3⋊(C3⋊C8)—21no—
80C2×SD32—91no—
81C2×D16—91no—
82#495—91no—
83C4×D8—91no—
84C4⋊C16—91no—
85#358—91no—
86#357C3⋊D311yescharacteristic, complemented
87C2×C3×D4—24no—
88C2×D12—64no—
89C2×C4×D3—124no—
90C2×Dic6—64no—
91C3×D8—24no—
92C3×D8—24no—
93C2×C3×C8C22×D314yes—
94C3×C4⋊C4—24no—
95#217—124no—
96#217—124no—
97#214—128no—
98(C2×D3)⋊C4—124no—
99C4×Dic3—34no—
100C2×C3⋊C8—34no—
101Dic12—64no—
102Dic12—64no—
103D24—38no—
104D24—64no—
105C3×C16—24no—
106C3⋊C16—64no—
107C22×C32—81no—
108C22×C32—81no—
109C22×C32—81no—
110C22×C32C2×D811yescharacteristic
111C2×C3⋊D3—42no—
112C2×C3⋊D3—81no—
113C2×C3⋊D3—81no—
114C32×C4—81no—
115C32×C4#12111yescharacteristic
116C32×C4AGL(1,ℤ/8)11yescharacteristic
117C3⋊Dic3—21no—
118C3⋊Dic3—21no—
119C3⋊Dic3—81no—
120C2×Q16—91no—
121C2×SD16—181no—
122C2×D8—91no—
123C2×D8C2×C3⋊D311yescharacteristic
124#124—181no—
125C4×D4—181no—
126SD32—182no—
127D16—182no—
128C2×C16—91no—
129C2×C16C2×C3⋊D311yescharacteristic
130#107C2×C3⋊D311yescharacteristic
131#102—181no—
132C4×C8—91no—
133C23×C3—44no—
134C22×D3—124no—
135C3×D4—44no—
136C3×D4—44no—
137C2×C3×C4—44no—
138C2×C3×C4D3×D414yes—
139C2×Dic3—34no—
140C2×Dic3—34no—
141C2×Dic3—124no—
142D12—68no—
143D12—124no—
144C4×D3—248no—
145Dic6—124no—
146Dic6—124no—
147C3×C8#23514yes—
148C3×C8D3×D414yes—
149C3⋊C8—64no—
150C2×C32—161no—
151C2×C32#45911yescharacteristic
152C2×C32#50811yescharacteristic
153C2×C32#50911yescharacteristic
154C3⋊D3—82no—
155C2×Q8—181no—
156C2×D4—21no—
157C2×D4—181no—
158C22×C4—361no—
159Q16—181no—
160Q16—181no—
161SD16—362no—
162D8—21no—
163D8—21no—
164D8—92no—
165D8—181no—
166C2×C8—91no—
167C2×C8C22×C3⋊D311yescharacteristic
168C4⋊C4—21no—
169C22⋊C4—361no—
170C22⋊C4—361no—
171C22⋊C4—361no—
172C42—91no—
173C16—21no—
174C16—181no—
175C22×C3—84no—
176C22×C3—84no—
177C22×C3—84no—
178C22×C3D3×D814yes—
179C2×D3—128no—
180C2×D3—244no—
181C2×D3—244no—
182C3×C4—84no—
183C3×C4#88414yes—
184C3×C4#91414yes—
185Dic3—64no—
186Dic3—64no—
187Dic3—244no—
188C32#221011yescharacteristic, complemented, Sylow
189C23—41no—
190C23—361no—
191Q8—361no—
192Q8—361no—
193D4—41no—
194D4—41no—
195D4—182no—
196D4—361no—
197C2×C4—41no—
198C2×C4—91no—
199C2×C4—91no—
200C2×C4—361no—
201C2×C4—722no—
202C2×C4D4×C3⋊D311yescharacteristic
203C8—181no—
204C8#382811yescharacteristic
205C8D4×C3⋊D311yescharacteristic
206C2×C3—164no—
207C2×C3#478614yes—
208C2×C3#491114yes—
209C2×C3#491614yes—
210D3—248no—
211C22—81no—
212C22—81no—
213C22—81no—
214C22—362no—
215C22—721no—
216C22—721no—
217C22D8×C3⋊D311yescharacteristic
218C4—81no—
219C4—181no—
220C4—181no—
221C4—721no—
222C4#6409311yescharacteristic
223C4#6412311yescharacteristic
224C3#6920314yescomplemented
225C2—161no—
226C2—722no—
227C2#1059248511yescharacteristic
228C2#1059261011yescharacteristic
229C2#1059261511yescharacteristic
subgroupG/H
centerC22D8×C3⋊D3
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#357C2
socleC22×C32C2×D8
prime radicalC2×#63653C2
hypercenter#357C3⋊D3
hypocenterC32#2210
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
1. #10592854C2semidirect
3. C2×#63627C2semidirect
4. #10592571C2semidirect
5. C32×#357C2semidirect
6. #10589367C2semidirect
7. #10589358C2semidirect
26. C3×#357D3semidirect
86. #357C3⋊D3semidirect
188. C32#2210semidirect
224. C3#69203semidirect

Maximal subgroups

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

subgroupindex
#105928542
C2×#636532
C2×#636272
#105925712
C32×#3572
#105893672
#105893582
#692033