Finite Group Databasebeta

← #11780549

Subgroups — #11780549

Order 1152.

419 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 419 conjugacy classes of subgroups — too many to draw. Only its 70 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#10593868C211yesmaximal, characteristic, complemented
2#10592770C211yesmaximal, characteristic
3C3×#5071C212yesmaximal
4#10589089C211yesmaximal, characteristic, complemented
5#10589088C212yesmaximal, complemented
6#71250—32nomaximal
7C32×#127C2211yescharacteristic
8#64079C2211yescharacteristic
9C3×#870C2212yes—
10#63847—22no—
11#63846—22no—
12#63845—22no—
13#63659—22no—
14#63630C2211yescharacteristic
15C3×#832—22no—
16C3×#832—22no—
17C3×#803C2212yes—
18C3⋊#564—32no—
19C3×#490—32no—
20#5071—32no—
21#5071—61no—
22#5071D312yes—
23#4543—32no—
24#4465—32no—
25#4465—32no—
26C2×C32×D4—21no—
27C2×C32×D4—22no—
28C32×C42C2311yescharacteristic
29C4⋊(C3⋊Dic3)D412yes—
30#3750—22no—
31C2×C3⋊(C3⋊C8)—21no—
32C3×C4⋊Dic3D412yes—
33C3×C4⋊Dic3D412yes—
34C3×Dic3⋊C4—22no—
35C3×Dic3⋊C4—22no—
36C2×C3×C3⋊C8—22no—
37#3724—22no—
38Dic3⋊Dic3—22no—
39Dic3⋊Dic3—22no—
40Dic32—22no—
41#1658—91noSylow
42C3×#127—21no—
43C3×#127C2×D312yes—
44C3×#125—32no—
45#890—62no—
46#890—62no—
47#889—62no—
48#889—62no—
49#889—62no—
50#889—62no—
51#870—32no—
52#870—61no—
53#870C2×D312yes—
54C3×#102—62no—
55C3×#102—62no—
56C3×#97—32no—
57#832—22no—
58#832—22no—
59#832—62no—
60#832—62no—
61#832—64no—
62#803—32no—
63#803—61no—
64#803C2×D312yes—
65C23×C32—41no—
66C32×D4—42no—
67C32×D4—44no—
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4C2×D412yes—
70C2×C3⋊Dic3—22no—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73C3⋊(C3⋊C8)—41no—
74C3×C3⋊C8—42no—
75#564—91no—
76#490—32no—
77#490—91no—
78#330—91no—
79#330—92no—
80C2×C3×D4—22no—
81C2×C3×D4—22no—
82C2×C3×D4—22no—
83C2×C3×D4—22no—
84C2×C3×D4—42no—
85C2×C3×C8—62no—
86C3×C4⋊C4—32no—
87C3×C4⋊C4—32no—
88C3×C4⋊C4—62no—
89C3×C4⋊C4—62no—
90C3×C42—21no—
91C3×C42C22×D312yes—
92C4⋊Dic3—32no—
93C4⋊Dic3—32no—
94C4⋊Dic3—62no—
95C4⋊Dic3—62no—
96C4⋊Dic3—62no—
97C4⋊Dic3#6712yes—
98C4⋊Dic3#6712yes—
99Dic3⋊C4—22no—
100Dic3⋊C4—22no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104Dic3⋊C4—62no—
105Dic3⋊C4—62no—
106Dic3⋊C4—62no—
107Dic3⋊C4—122no—
108C4×Dic3—62no—
109C4×Dic3—62no—
110C2×C3⋊C8—22no—
111C2×C3⋊C8—62no—
112C2×C3⋊C8—62no—
113C22×C32—81no—
114C22×C32—82no—
115C22×C32#12011yescharacteristic
116C32×C4—21no—
117C32×C4—22no—
118C3⋊Dic3—42no—
119C3×Dic3—42no—
120C3×Dic3—42no—
121#127D3211yescharacteristic
122#125—32no—
123#125—91no—
124#125—182no—
125#125—182no—
126#125—182no—
127#102—62no—
128#102—62no—
129#102—182no—
130#97—32no—
131#97—91no—
132C23×C3—42no—
133C23×C3—42no—
134C3×D4—44no—
135C3×D4—44no—
136C3×D4—44no—
137C3×D4—44no—
138C3×D4—84no—
139C2×C3×C4—22no—
140C2×C3×C4—21no—
141C2×C3×C4—62no—
142C2×C3×C4—62no—
143C2×C3×C4D3×D412yes—
144C2×C3×C4D3×D412yes—
145C2×C3×C4C2×#6712yes—
146C2×Dic3—22no—
147C2×Dic3—22no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150C2×Dic3—122no—
151C3×C8—122no—
152C3⋊C8—42no—
153C3⋊C8—122no—
154C3⋊C8—122no—
155C2×C32—161no—
156C2×C32#45411yescharacteristic
157C2×C32#45412yes—
158C2×D4—22no—
159C2×D4—21no—
160C2×C8—62no—
161C2×C8—181no—
162C4⋊C4—32no—
163C4⋊C4—32no—
164C4⋊C4—62no—
165C4⋊C4—62no—
166C4⋊C4—92no—
167C4⋊C4—182no—
168C4⋊C4—182no—
169C4⋊C4—182no—
170C4⋊C4—182no—
171C42—182no—
172C42C2×D3211yescharacteristic
173C22×C3—21no—
174C22×C3—82no—
175C22×C3—84no—
176C22×C3—82no—
177C22×C3—82no—
178C22×C3—82no—
179C22×C3#93712yes—
180C3×C4—22no—
181C3×C4—22no—
182C3×C4—22no—
183C3×C4—22no—
184C3×C4—42no—
185C3×C4—122no—
186C3×C4—122no—
187Dic3—42no—
188Dic3—42no—
189Dic3—122no—
190Dic3—122no—
191Dic3—242no—
192C32#165811yescharacteristic, complemented, Sylow
193C23—41no—
194D4—42no—
195D4—44no—
196C2×C4—62no—
197C2×C4—62no—
198C2×C4—182no—
199C2×C4D3×#6712yes—
200C2×C4#381111yescharacteristic
201C8—122no—
202C8—361no—
203C2×C3—21no—
204C2×C3—22no—
205C2×C3—162no—
206C2×C3—162no—
207C2×C3#506212yes—
208C2×C3#520112yes—
209C2×C3#520112yes—
210C22—81no—
211C22—82no—
212C22#6398311yescharacteristic
213C4—21no—
214C4—22no—
215C4—122no—
216C4—122no—
217C4—362no—
218C3—21no—
219C3#7125012yescomplemented
220C2—161no—
221C2#1059152411yescharacteristic
222C2#1059152512yes—
subgroupG/H
centerC22#63983
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
Fitting, prime radicalC32×#127C22
socleC22×C32#120
hypercenter#127D32
hypocenterC32#1658
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10593868C2semidirect
4. #10589089C2semidirect
5. #10589088C2semidirect
192. C32#1658semidirect
219. C3#71250semidirect

Maximal subgroups

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

subgroupindex
#105938682
#105927702
C3×#50712
#105890892
#105890882
#712503