Finite Group Databasebeta

← #11771933

Subgroups — #11771933

Order 1152.

462 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 95 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#10592648C211yesmaximal, characteristic
2C32×#342C211yesmaximal, characteristic
3#10589391C211yesmaximal, characteristic
4#67492—34nomaximal
5C2×C32×C22⋊C4—21no—
6C2×C32×C22⋊C4C2211yescharacteristic
7C2×#3757—21no—
8C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
9C2×#3750—21no—
10#63658C411yescharacteristic, complemented
11#63657—21no—
12#4949—34no—
13C3×#342D314yes—
14#4525—34no—
15C24×C32D411yescharacteristic
16C22×C32×C4—41no—
17C22×C32×C4C2×C411yescharacteristic
18C22×C32×C4D411yescharacteristic
19C22×C3⋊Dic3—21no—
20C22×C3⋊Dic3—21no—
21C32×C22⋊C4—22no—
22C32×C22⋊C4—41no—
23C32×C22⋊C4—41no—
24#3757—42no—
25C4⋊(C3⋊Dic3)—41no—
26#3750—42no—
27C2×C3⋊(C3⋊C8)—41no—
28#1352—91noSylow
29C2×C3×C22⋊C4—24no—
30C2×C3×C22⋊C4C2×D314yes—
31C2×#217—64no—
32C2×C4⋊Dic3—34no—
33C2×Dic3⋊C4—64no—
34C3⋊#95—34no—
35#830—64no—
36C23×C32—21no—
37C23×C32—21no—
38C23×C32—41no—
39C23×C32—41no—
40C23×C32C22⋊C411yescharacteristic
41C23×C32SD1611yescharacteristic
42C23×C32Q1611yescharacteristic
43C2×C32×C4—21no—
44C2×C32×C4—21no—
45C2×C32×C4—41no—
46C2×C32×C4—41no—
47C2×C32×C4—42no—
48C2×C32×C4—81no—
49C2×C32×C4—81no—
50C2×C3⋊Dic3—22no—
51C2×C3⋊Dic3—41no—
52C2×C3⋊Dic3—41no—
53C2×C3⋊Dic3—41no—
54C2×C3⋊Dic3—41no—
55C2×C3⋊Dic3—41no—
56C3⋊(C3⋊C8)—81no—
57#399—91no—
58#342C3⋊D311yescharacteristic
59#323—91no—
60C24×C3#6714yes—
61C22×C3×C4—44no—
62C22×C3×C4C4×D314yes—
63C22×C3×C4D1214yes—
64C22×Dic3—64no—
65C22×Dic3—64no—
66C3×C22⋊C4—28no—
67C3×C22⋊C4—44no—
68C3×C22⋊C4—44no—
69#217—128no—
70C4⋊Dic3—124no—
71Dic3⋊C4—128no—
72C2×C3⋊C8—124no—
73C22×C32—21no—
74C22×C32—21no—
75C22×C32—21no—
76C22×C32—21no—
77C22×C32—41no—
78C22×C32—41no—
79C22×C32—41no—
80C22×C32—41no—
81C22×C32—81no—
82C22×C32#9911yescharacteristic
83C22×C32#10311yescharacteristic
84C22×C32#10411yescharacteristic
85C32×C4—41no—
86C32×C4—41no—
87C32×C4—82no—
88C3⋊Dic3—42no—
89C3⋊Dic3—81no—
90C2×C4⋊C4—91no—
91C2×C4⋊C4—181no—
92C2×C22⋊C4—21no—
93C2×C22⋊C4—181no—
94C2×C22⋊C4C2×C3⋊D311yescharacteristic
95C22⋊C8—181no—
96#95—91no—
97C23×C3—24no—
98C23×C3—24no—
99C23×C3—44no—
100C23×C3—44no—
101C23×C3(C2×D3)⋊C414yes—
102C23×C3#21414yes—
103C23×C3#21614yes—
104C2×C3×C4—24no—
105C2×C3×C4—24no—
106C2×C3×C4—44no—
107C2×C3×C4—44no—
108C2×C3×C4—48no—
109C2×C3×C4—84no—
110C2×C3×C4—84no—
111C2×Dic3—68no—
112C2×Dic3—124no—
113C2×Dic3—124no—
114C2×Dic3—124no—
115C2×Dic3—124no—
116C2×Dic3—124no—
117C3⋊C8—244no—
118C2×C32—21no—
119C2×C32—21no—
120C2×C32—41no—
121C2×C32—41no—
122C2×C32#32811yescharacteristic
123C2×C32#35211yescharacteristic
124C2×C32#35311yescharacteristic
125C24#63811yescharacteristic
126C22×C4—41no—
127C22×C4—181no—
128C22×C4—181no—
129C22×C4C4×C3⋊D311yescharacteristic
130C22×C4C4⋊(C3⋊D3)11yescharacteristic
131C2×C8—361no—
132C4⋊C4—361no—
133C4⋊C4—362no—
134C22⋊C4—22no—
135C22⋊C4—41no—
136C22⋊C4—41no—
137C22⋊C4—362no—
138C22×C3—24no—
139C22×C3—24no—
140C22×C3—24no—
141C22×C3—24no—
142C22×C3—44no—
143C22×C3—44no—
144C22×C3—44no—
145C22×C3—44no—
146C22×C3—84no—
147C22×C3#80514yes—
148C22×C3#80614yes—
149C22×C3#81014yes—
150C3×C4—44no—
151C3×C4—44no—
152C3×C4—88no—
153Dic3—128no—
154Dic3—244no—
155C32#135211yescharacteristic, complemented, Sylow
156C23—21no—
157C23—21no—
158C23—41no—
159C23—41no—
160C23#375211yescharacteristic
161C23#375411yescharacteristic
162C23#375611yescharacteristic
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—81no—
169C2×C4—81no—
170C2×C4—182no—
171C2×C4—361no—
172C2×C4—361no—
173C2×C4—361no—
174C2×C4—361no—
175C2×C4—361no—
176C8—721no—
177C2×C3—24no—
178C2×C3—24no—
179C2×C3—44no—
180C2×C3—44no—
181C2×C3#445214yes—
182C2×C3#447214yes—
183C2×C3#447414yes—
184C22—21no—
185C22—21no—
186C22—21no—
187C22—21no—
188C22—41no—
189C22—41no—
190C22—41no—
191C22—41no—
192C22—81no—
193C22#6363211yescharacteristic
194C22#6363311yescharacteristic
195C22#6363711yescharacteristic
196C4—41no—
197C4—41no—
198C4—82no—
199C4—362no—
200C4—721no—
201C3#6749214yescomplemented
202C2—21no—
203C2—21no—
204C2—41no—
205C2—41no—
206C2#1058931811yescharacteristic
207C2#1058933811yescharacteristic
208C2#1058934011yescharacteristic
subgroupG/H
centerC22#63633
commutatorC22×C32×C4C2×C4
FrattiniC2×C22⋊C4C2×C3⋊D3
FittingC32×#342C2
socleC22×C32#99
prime radicalC24×C32D4
cosocleC2×C32×C22⋊C4C22
hypercenter#342C3⋊D3
hypocenterC32#1352
LCSG ▷ C22×C32×C4 ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #342

Complements

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

NH ≅ G/Ntype
8. C2×C4⋊(C3⋊Dic3)C4semidirect
10. #63658C4semidirect
155. C32#1352semidirect
201. C3#67492semidirect

Maximal subgroups

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

subgroupindex
#105926482
C32×#3422
#105893912
#674923