Finite Group Databasebeta

← #11771822

Subgroups — #11771822

Order 1152.

406 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 30 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#10592921C211yesmaximal, characteristic
2#10590208C211yesmaximal, characteristic, complemented
3#10590203C211yesmaximal, characteristic, complemented
4C22×C32×D4C411yescharacteristic
5C2×#3792—21no—
6C2×#3757—21no—
7C2×#3757—21no—
8C2×#3750C2211yescharacteristic
9C22⋊#622—21no—
10#63658C411yescharacteristic
11#5222—62no—
12C24×C32—21no—
13C2×C32×D4—41no—
14C2×C32×D4—42no—
15C22×C32×C4C2×C411yescharacteristic
16C22×C3⋊Dic3—21no—
17C22×C3⋊Dic3D411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19#3792—22no—
20#3792—41no—
21C2×#622—41no—
22C2×#622—41no—
23#3757—42no—
24#3757—41no—
25#3757—41no—
26#3750—41no—
27#1345—91nomaximal, Sylow
28C22×C3×D4—22no—
29C2×#217—64no—
30C2×#217—64no—
31C2×Dic3⋊C4—62no—
32C3⋊#95—62no—
33C23×C32—22no—
34C23×C32—41no—
35C23×C32—41no—
36C23×C32—41no—
37C23×C32—41no—
38C23×C32—41no—
39C23×C32—41no—
40C23×C32C22⋊C411yescharacteristic
41C32×D4—42no—
42C32×D4—42no—
43C2×C32×C4—21no—
44C2×C32×C4—41no—
45C2×C3⋊Dic3—21no—
46C2×C3⋊Dic3—21no—
47C2×C3⋊Dic3—21no—
48C2×C3⋊Dic3—41no—
49C2×C3⋊Dic3—41no—
50C2×C3⋊Dic3—41no—
51C2×C3⋊Dic3—41no—
52C2×C3⋊Dic3D811yescharacteristic
53C2×C3⋊Dic3SD1611yescharacteristic
54#622—42no—
55#622—81no—
56#394—91no—
57#343—91no—
58#324—91no—
59C24×C3—24no—
60C2×C3×D4—44no—
61C2×C3×D4—48no—
62C22×C3×C4—22no—
63C22×Dic3—62no—
64C22×Dic3—62no—
65C22×Dic3—64no—
66#217—124no—
67#217—124no—
68#217—128no—
69Dic3⋊C4—124no—
70C22×C32—21no—
71C22×C32—21no—
72C22×C32—42no—
73C22×C32—42no—
74C22×C32—42no—
75C22×C32—81no—
76C22×C32—81no—
77C22×C32—81no—
78C22×C32—81no—
79C22×C32#9911yescharacteristic
80C22×C32#10211yescharacteristic
81C22×C32#10411yescharacteristic
82C32×C4—41no—
83C3⋊Dic3—21no—
84C3⋊Dic3—21no—
85C3⋊Dic3—41no—
86C3⋊Dic3—81no—
87C22×D4#15711yescharacteristic
88C2×M16—181no—
89C2×C4⋊C4—91no—
90C2×C22⋊C4—181no—
91C2×C22⋊C4—181no—
92C22⋊C8—181no—
93#95—91no—
94C23×C3—28no—
95C23×C3—22no—
96C23×C3—44no—
97C23×C3—44no—
98C23×C3—44no—
99C23×C3—44no—
100C23×C3—44no—
101C23×C3—44no—
102C3×D4—48no—
103C3×D4—48no—
104C2×C3×C4—24no—
105C2×C3×C4—44no—
106C2×Dic3—62no—
107C2×Dic3—62no—
108C2×Dic3—122no—
109C2×Dic3—122no—
110C2×Dic3—122no—
111C2×Dic3—124no—
112C2×Dic3—124no—
113C2×Dic3—124no—
114C2×Dic3—124no—
115C2×C32—21no—
116C2×C32—21no—
117C2×C32—82no—
118C2×C32#32711yescharacteristic
119C2×C32AΣL(1,𝔽16)11yescharacteristic
120C2×C32#35511yescharacteristic
121C24—21no—
122C2×D4—41no—
123C2×D4—42no—
124C22×C4—91no—
125C22×C4—91no—
126C22×C4—181no—
127C22×C4C2×#15711yescharacteristic
128M16—182no—
129M16—361no—
130C2×C8—361no—
131C2×C8—361no—
132C4⋊C4—361no—
133C22⋊C4—361no—
134C22⋊C4—361no—
135C22⋊C4—362no—
136C22×C3—24no—
137C22×C3—24no—
138C22×C3—22no—
139C22×C3—22no—
140C22×C3—22no—
141C22×C3—48no—
142C22×C3—48no—
143C22×C3—48no—
144C22×C3—84no—
145C22×C3—84no—
146C22×C3—84no—
147C22×C3—84no—
148C3×C4—44no—
149Dic3—122no—
150Dic3—122no—
151Dic3—242no—
152Dic3—244no—
153C32#134511yescharacteristic, complemented, Sylow
154C23—22no—
155C23—41no—
156C23—41no—
157C23—41no—
158C23—41no—
159C23—41no—
160C23—41no—
161C23C22⋊#15711yescharacteristic
162D4—42no—
163D4—42no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—181no—
169C2×C4—181no—
170C2×C4—181no—
171C2×C4—361no—
172C2×C4—361no—
173C2×C4—361no—
174C2×C4—361no—
175C8—362no—
176C8—721no—
177C2×C3—24no—
178C2×C3—24no—
179C2×C3—22no—
180C2×C3—22no—
181C2×C3—22no—
182C2×C3—88no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—81no—
189C22—81no—
190C22—81no—
191C22—81no—
192C22#6378211yescharacteristic
193C22#6378311yescharacteristic
194C22#6378611yescharacteristic
195C4—41no—
196C4—181no—
197C4—181no—
198C4—361no—
199C4—721no—
200C3—22no—
201C2—21no—
202C2—21no—
203C2—82no—
204C2#1059020911yescharacteristic
205C2#1059021211yescharacteristic
206C2#1059022311yescharacteristic
subgroupG/H
centerC22#63786
commutatorC22×C32×C4C2×C4
FrattiniC22×C4C2×#157
Fitting, prime radicalC22×C32×D4C4
socleC22×C32#99
cosocleC2×#3750C22
hypercenterC22×D4#157
hypocenterC32#1345
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #10590208C2semidirect
3. #10590203C2semidirect
153. C32#1345semidirect

Maximal subgroups

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

subgroupindex
#105929212
#105902082
#105902032
#13459