Finite Group Databasebeta

← #11776219

Subgroups — #11776219

Order 1152.

556 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 62 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#10596303C211yesmaximal, characteristic
2#10593801C212yesmaximal, complemented
3#10590220C212yesmaximal, complemented
4#10590214C212yesmaximal, complemented
5C2×C32×#41C411yescharacteristic
6C2×#3828C411yescharacteristic
7#64156C411yescharacteristic
8#64153C2211yescharacteristic
9#64149C2211yescharacteristic
10#64148—22no—
11#64145C411yescharacteristic
12C4×#638—22no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22⋊#622—22no—
15#63779C2214yes—
16C4×#622—22no—
17#5832—62no—
18C32×#41—42no—
19C2×C32×Q8C2×C411yescharacteristic
20C2×C32×D4—21no—
21C2×C32×D4C2×C411yescharacteristic
22C22×C32×C4—21no—
23C22×C32×C4C2×C411yescharacteristic
24C2×#638—21no—
25C2×#638—22no—
26C22×C3⋊Dic3D412yes—
27#3828—42no—
28C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
29C2×C4×C3⋊D3—21no—
30C2×#634C2×C411yescharacteristic
31C2×#622—24no—
32#3757—22no—
33#3752—22no—
34#3750—22no—
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D412yes—
37C4×C3⋊Dic3C2311yescharacteristic
38#1543—91nomaximal, Sylow
39C2×C3×#41—22no—
40C2×#235—62no—
41#947—62no—
42#944—62no—
43#940—62no—
44#939—68no—
45#936—62no—
46C4×#67—68no—
47C2×C4×Dic3—62no—
48C23×C32—21no—
49C23×C32C22⋊C411yescharacteristic
50C22×C3⋊D3—21no—
51C32×Q8—41no—
52C32×D4—41no—
53C32×D4—42no—
54C2×C32×C4—22no—
55C2×C32×C4—21no—
56C2×C32×C4—42no—
57C2×C32×C4C22⋊C411yescharacteristic
58C2×C32×C4C22×C411yescharacteristic
59#638—42no—
60#638—44no—
61C2×C3⋊Dic3—21no—
62C2×C3⋊Dic3—24no—
63C2×C3⋊Dic3C22⋊C412yes—
64C2×C3⋊Dic3C2×D412yes—
65C4⋊(C3⋊D3)—41no—
66C4×C3⋊D3—42no—
67#634—41no—
68#622—44no—
69#532—91no—
70#431—92no—
71#333—92no—
72#331—92no—
73C3×#41—48no—
74C2×C3×Q8—22no—
75C2×C3×D4—24no—
76C2×C3×D4—22no—
77C22×C3×C4—24no—
78C22×C3×C4—22no—
79C2×#67—68no—
80C2×#67—64no—
81C22×Dic3—64no—
82#235—128no—
83C2×D12—62no—
84C2×C4×D3—64no—
85C2×Dic6—62no—
86#217—68no—
87(C2×D3)⋊C4—68no—
88Dic3⋊C4—68no—
89C4×Dic3—64no—
90C4×Dic3—62no—
91C4×Dic3—62no—
92C22×C32—21no—
93C22×C32—22no—
94C22×C32—41no—
95C22×C32—42no—
96C22×C32C2×C22⋊C411yescharacteristic
97C2×C3⋊D3—41no—
98C2×C3⋊D3—42no—
99C32×C4—21no—
100C32×C4—41no—
101C32×C4#10012yes—
102C3⋊Dic3—22no—
103C3⋊Dic3—41no—
104C3⋊Dic3#13514yes—
105C2×#41—91no—
106C2×#41#15711yescharacteristic
107C4⋊Q8—91no—
108#127—91no—
109#124—91no—
110#124—91no—
111#121—182no—
112C4×D4—182no—
113C2×C42—91no—
114C4⋊C8—94no—
115C22⋊C8—182no—
116C4×C8—182no—
117C23×C3—24no—
118C23×C3—22no—
119C22×D3—64no—
120C3×Q8—44no—
121C3×D4—44no—
122C3×D4—48no—
123C2×C3×C4—28no—
124C2×C3×C4—24no—
125C2×C3×C4—22no—
126C2×C3×C4—22no—
127C2×C3×C4—48no—
128#67—1216no—
129#67—128no—
130C2×Dic3—64no—
131C2×Dic3—64no—
132C2×Dic3—64no—
133C2×Dic3—128no—
134D12—124no—
135C4×D3—128no—
136Dic6—124no—
137C2×C32—41no—
138C2×C32—81no—
139C2×C32C2×#10011yescharacteristic
140C2×C32#41612yes—
141C3⋊D3—81no—
142#41—42no—
143#41—362no—
144C2×Q8—91no—
145C2×Q8C2×#15711yescharacteristic
146C2×D4—21no—
147C2×D4—91no—
148C2×D4—182no—
149C2×D4—181no—
150C2×D4C2×#15711yescharacteristic
151C22×C4—21no—
152C22×C4—92no—
153C22×C4—181no—
154C22×C4C2×#15711yescharacteristic
155C2×C8—184no—
156C4⋊C4—182no—
157C22⋊C4—182no—
158C22⋊C4—182no—
159C42—91no—
160C42—91no—
161C42—92no—
162C22×C3—24no—
163C22×C3—22no—
164C22×C3—44no—
165C22×C3—48no—
166C22×C3—44no—
167C2×D3—124no—
168C2×D3—128no—
169C3×C4—24no—
170C3×C4—24no—
171C3×C4—44no—
172Dic3—68no—
173Dic3—124no—
174Dic3—124no—
175C32#154311yescharacteristic, complemented, Sylow
176C23—21no—
177C23—181no—
178C23C22⋊#15711yescharacteristic
179Q8—41no—
180Q8—361no—
181D4—41no—
182D4—42no—
183D4—361no—
184D4—364no—
185D4—362no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—42no—
189C2×C4—92no—
190C2×C4—92no—
191C2×C4—184no—
192C2×C4—181no—
193C2×C4—362no—
194C2×C4C22⋊#15711yescharacteristic
195C2×C4C22×#15711yescharacteristic
196C8—364no—
197C2×C3—24no—
198C2×C3—22no—
199C2×C3—44no—
200C2×C3—84no—
201D3—244no—
202C22—22no—
203C22—21no—
204C22—42no—
205C22—41no—
206C22—362no—
207C22—361no—
208C22C2×C22⋊#15711yescharacteristic
209C4—21no—
210C4—41no—
211C4—94no—
212C4—182no—
213C4—361no—
214C4#6378812yes—
215C3—22no—
216C2—41no—
217C2—81no—
218C2—721no—
219C2#1059384112yes—
220C2C2×#6378811yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC2×C32×#41C4
socleC22×C32C2×C22⋊C4
prime radical#10596303C2
cosocleC4×C3⋊Dic3C23
hypercenterC2×#41#157
hypocenterC32#1543
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10593801C2semidirect
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
#105963032
#105938012
#105902202
#105902142
#15439