Finite Group Databasebeta

← #11776220

Subgroups — #11776220

Order 1152.

556 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 60 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#10596139C211yesmaximal, characteristic
2#10593725C212yesmaximal, complemented
3#10590220C212yesmaximal, complemented
4#10590214C212yesmaximal, complemented
5C2×#3832C411yescharacteristic
6C2×#3830C411yescharacteristic
7C32×#124C411yescharacteristic
8#64153C2211yescharacteristic
9#64149C2211yescharacteristic
10#64093—22no—
11#64090—22no—
12#64084C411yescharacteristic
13C42×C3⋊D3C2211yescharacteristic
14#63779C2214yes—
15#63778—22no—
16C4×#622—22no—
17#5668—62no—
18C2×C32×Q8C2×C411yescharacteristic
19C2×C32×D4C2×C411yescharacteristic
20C2×#638—21no—
21C2×#638—22no—
22C22×C3⋊Dic3—21no—
23#3832—42no—
24#3830—42no—
25C2×C4⋊(C3⋊D3)—21no—
26C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
27C2×C4×C3⋊D3—21no—
28C2×C4×C3⋊D3C2×C411yescharacteristic
29C2×C4×C3⋊D3D412yes—
30C2×#634C2×C411yescharacteristic
31C2×#622—24no—
32C32×C22⋊C4—22no—
33C32×C42C2×C411yescharacteristic
34#3752—22no—
35#3750—22no—
36C4×C3⋊Dic3D412yes—
37C4×C3⋊Dic3C2311yescharacteristic
38#1543—91nomaximal, Sylow
39C2×#239—62no—
40C2×#237—62no—
41C3×#124—22no—
42#944—62no—
43#940—62no—
44#884—68no—
45#67⋊C4—68no—
46#875—62no—
47C42×D3—62no—
48C23×C32—21no—
49C22×C3⋊D3—21no—
50C22×C3⋊D3C22⋊C411yescharacteristic
51C32×Q8—41no—
52C32×D4—41no—
53C2×C32×C4—21no—
54C2×C32×C4C22⋊C412yes—
55C2×C32×C4C22×C411yescharacteristic
56#638—42no—
57#638—44no—
58C2×C3⋊Dic3—21no—
59C2×C3⋊Dic3—42no—
60C2×C3⋊Dic3C22⋊C411yescharacteristic
61C2×C3⋊Dic3C2×D412yes—
62C4⋊(C3⋊D3)—41no—
63C4⋊(C3⋊D3)—42no—
64C4×C3⋊D3—22no—
65C4×C3⋊D3—24no—
66C4×C3⋊D3—42no—
67#634—41no—
68#622—44no—
69#532—91no—
70#431—92no—
71#333—92no—
72#331—92no—
73C2×C3×Q8—22no—
74C2×C3×D4—22no—
75C2×#67—68no—
76C2×#67—64no—
77C22×Dic3—64no—
78#239—128no—
79#237—128no—
80C2×D12—62no—
81C2×D12—64no—
82C2×C4×D3—62no—
83C2×C4×D3—64no—
84C2×C4×D3—64no—
85C2×Dic6—62no—
86C3×C22⋊C4—28no—
87C3×C42—22no—
88(C2×D3)⋊C4—68no—
89Dic3⋊C4—68no—
90C4×Dic3—64no—
91C4×Dic3—62no—
92C22×C32—41no—
93C22×C32—42no—
94C22×C32C2×C22⋊C411yescharacteristic
95C2×C3⋊D3—21no—
96C2×C3⋊D3—22no—
97C2×C3⋊D3—41no—
98C2×C3⋊D3—42no—
99C32×C4—21no—
100C32×C4—22no—
101C32×C4—41no—
102C3⋊Dic3—41no—
103C3⋊Dic3#10012yes—
104C3⋊Dic3#13514yes—
105C2×#41—91no—
106C2×#41—91no—
107C4⋊Q8—91no—
108#127—91no—
109#124—91no—
110#124#15711yescharacteristic
111#121—182no—
112C4×D4—182no—
113C2×C42—91no—
114C4⋊C8—94no—
115C22⋊C8—182no—
116C4×C8—182no—
117C23×C3—24no—
118C22×D3—62no—
119C22×D3—64no—
120C3×Q8—44no—
121C3×D4—44no—
122C2×C3×C4—24no—
123C2×C3×C4—22no—
124C2×C3×C4—24no—
125#67—1216no—
126#67—128no—
127C2×Dic3—62no—
128C2×Dic3—64no—
129C2×Dic3—64no—
130C2×Dic3—128no—
131D12—124no—
132D12—128no—
133C4×D3—68no—
134C4×D3—128no—
135C4×D3—128no—
136Dic6—124no—
137C2×C32—81no—
138C2×C32C2×#10011yescharacteristic
139C2×C32#41612yes—
140C3⋊D3—41no—
141C3⋊D3—81no—
142#41—362no—
143#41—362no—
144C2×Q8—91no—
145C2×Q8C2×#15711yescharacteristic
146C2×D4—91no—
147C2×D4—181no—
148C2×D4—182no—
149C2×D4—181no—
150C2×D4C2×#15711yescharacteristic
151C22×C4—91no—
152C22×C4—92no—
153C22×C4—181no—
154C22×C4—181no—
155C2×C8—184no—
156C4⋊C4—182no—
157C22⋊C4—22no—
158C22⋊C4—182no—
159C42—91no—
160C42—92no—
161C42C2×#15711yescharacteristic
162C22×C3—22no—
163C22×C3—44no—
164C22×C3—48no—
165C2×D3—64no—
166C2×D3—124no—
167C2×D3—124no—
168C2×D3—128no—
169C3×C4—24no—
170C3×C4—44no—
171C3×C4—44no—
172Dic3—64no—
173Dic3—68no—
174Dic3—124no—
175C32#154311yescharacteristic, complemented, Sylow
176C23—21no—
177C23—91no—
178C23—181no—
179Q8—41no—
180Q8—361no—
181D4—41no—
182D4—361no—
183D4—362no—
184D4—364no—
185D4—362no—
186C2×C4—21no—
187C2×C4—92no—
188C2×C4—91no—
189C2×C4—182no—
190C2×C4—184no—
191C2×C4—181no—
192C2×C4—362no—
193C2×C4—362no—
194C2×C4C22⋊#15712yes—
195C2×C4C22×#15711yescharacteristic
196C8—364no—
197C2×C3—22no—
198C2×C3—24no—
199C2×C3—84no—
200D3—124no—
201D3—244no—
202C22—41no—
203C22—42no—
204C22—181no—
205C22—182no—
206C22—361no—
207C22—362no—
208C22C2×C22⋊#15711yescharacteristic
209C4—21no—
210C4—22no—
211C4—41no—
212C4—92no—
213C4—94no—
214C4—361no—
215C3—22no—
216C2—81no—
217C2—361no—
218C2—721no—
219C2#1059382511yescharacteristic
220C2#1059384112yes—
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#124C4
socleC22×C32C2×C22⋊C4
prime radical#10596139C2
cosocleC4×C3⋊Dic3C23
hypercenter#124#157
hypocenterC32#1543
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #10593725C2semidirect
3. #10590220C2semidirect
4. #10590214C2semidirect
175. C32#1543semidirect

Maximal subgroups

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

subgroupindex
#105961392
#105937252
#105902202
#105902142
#15439