Finite Group Databasebeta

← #11772904

Subgroups — #11772904

Order 1152.

200 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C3×#5056C211yesmaximal, characteristic
2#10589408C211yesmaximal, characteristic
3C3×#4541C211yesmaximal, characteristic
4#67782—31nomaximal
5#67543—31nomaximal
6C32×#124C2211yescharacteristic
7C3×#870C411yescharacteristic, complemented
8#63663—21no—
9C3×#835—21no—
10C3×#834—21no—
11C3×#832—21no—
12C3×C4×C3⋊C8C411yescharacteristic, complemented
13C3×#488—31no—
14#5056D311yescharacteristic
15C3×#354—31no—
16#4542—31no—
17#4542—31no—
18#4542—61no—
19#4541D311yescharacteristic
20C2×C32×Q8D411yescharacteristic
21C2×C32×D4D411yescharacteristic
22C32×C22⋊C4—41no—
23C32×C42C2×C411yescharacteristic
24#3748—41no—
25C3×#217—41no—
26C3×C4⋊Dic3—21no—
27C3×Dic3⋊C4—41no—
28C2×C3×C3⋊C8—21no—
29#1414—91noSylow
30C3×#125—31no—
31C3×#124—21no—
32C3×#124C2×D311yescharacteristic
33C3×#124C2×D311yescharacteristic
34#870Dic311yescharacteristic, complemented
35C3×#103—61no—
36C3×#102—61no—
37C3×#99—61no—
38C3×C4×C8—31no—
39#836—62no—
40#836—61no—
41#836—61no—
42#835—21no—
43#834—21no—
44#832—21no—
45C4×C3⋊C8Dic311yescharacteristic, complemented
46C23×C32—21no—
47C32×Q8—41no—
48C32×D4—41no—
49C2×C32×C4—21no—
50C2×C32×C4—21no—
51C2×C32×C4C22⋊C411yescharacteristic
52C2×C3×Dic3—41no—
53C2×C3×Dic3—81no—
54C3⋊(C3⋊C8)—81no—
55C3×C3⋊C8—41no—
56#488—31no—
57#355—91no—
58#354—31no—
59C2×C3×Q8—21no—
60C2×C3×Q8D1211yescharacteristic
61C2×C3×Q8#6711yescharacteristic
62C2×C3×D4—21no—
63C2×C3×D4#6711yescharacteristic
64C2×C3×D4#6711yescharacteristic
65C2×C3×C8—61no—
66C3×C4⋊C4—61no—
67C3×C4⋊C4—121no—
68C3×C22⋊C4—41no—
69C3×C22⋊C4—41no—
70C3×C22⋊C4—42no—
71C3×C22⋊C4—121no—
72C3×C42—21no—
73C3×C42C4×D311yescharacteristic
74C3×C42C2×Dic311yescharacteristic
75#217—41no—
76C4⋊Dic3—21no—
77Dic3⋊C4—41no—
78#208—122no—
79#208—121no—
80#208—121no—
81C2×C3⋊C8—21no—
82C22×C32—41no—
83C22×C32—81no—
84C22×C32#9911yescharacteristic
85C32×C4—21no—
86C32×C4—41no—
87C32×C4—41no—
88C3×Dic3—81no—
89C3×Dic3—161no—
90#125—31no—
91#124D3211yescharacteristic
92#103—61no—
93#102—61no—
94#101—181no—
95#99—61no—
96C4×C8—31no—
97C23×C3—21no—
98C23×C3—21no—
99C23×C3—41no—
100C3×Q8—41no—
101C3×Q8—41no—
102C3×Q8—81no—
103C3×D4—41no—
104C3×D4—41no—
105C3×D4—81no—
106C2×C3×C4—22no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—41no—
113C2×C3×C4—121no—
114C2×C3×C4—241no—
115C2×C3×C4(C2×D3)⋊C411yescharacteristic
116C2×C3×C4#21711yescharacteristic
117C2×Dic3—41no—
118C2×Dic3—81no—
119C3×C8—121no—
120C3⋊C8—41no—
121C3⋊C8—242no—
122C3⋊C8—241no—
123C3⋊C8—241no—
124C2×C32—21no—
125C2×C32—81no—
126C2×C32#35411yescharacteristic
127C2×Q8#62611yescharacteristic
128C2×D4#62511yescharacteristic
129M16—361no—
130C2×C8—61no—
131C4⋊C4—61no—
132C4⋊C4—121no—
133C22⋊C4—41no—
134C22⋊C4—121no—
135C42D3×Dic311yescharacteristic
136C22×C3—21no—
137C22×C3—41no—
138C22×C3—41no—
139C22×C3—81no—
140C22×C3—81no—
141C22×C3—81no—
142C22×C3—82no—
143C22×C3#80611yescharacteristic
144C22×C3#83411yescharacteristic
145C3×C4—21no—
146C3×C4—21no—
147C3×C4—41no—
148C3×C4—42no—
149C3×C4—41no—
150C3×C4—41no—
151C3×C4—41no—
152C3×C4—41no—
153C3×C4—81no—
154C3×C4—241no—
155C3×C4—481no—
156Dic3—81no—
157Dic3—161no—
158C32#141411yescharacteristic, complemented, Sylow
159C23—21no—
160Q8—41no—
161D4—41no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—121no—
165C2×C4—241no—
166C2×C4(C2×D3)⋊Dic311yescharacteristic
167C8—121no—
168C8—721no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3—41no—
173C2×C3—81no—
174C2×C3—81no—
175C2×C3—161no—
176C2×C3#447311yescharacteristic
177C2×C3#454111yescharacteristic
178C22—41no—
179C22—81no—
180C22#6358011yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—241no—
185C4—481no—
186C3—21no—
187C3#6754311yescharacteristic, complemented
188C3#6778211yescharacteristic, complemented
189C2—21no—
190C2—81no—
191C2#1058918011yescharacteristic
subgroupG/H
centerC2#10589180
commutatorC32×C42C2×C4
Frattini, hypercenter#124D32
Fitting, cosocleC32×#124C22
socleC2×C32#354
prime radicalC2×C32×D4D4
hypocenterC32#1414
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
7. C3×#870C4semidirect
12. C3×C4×C3⋊C8C4semidirect
34. #870Dic3semidirect
45. C4×C3⋊C8Dic3semidirect
158. C32#1414semidirect
187. C3#67543semidirect
188. C3#67782semidirect

Maximal subgroups

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

subgroupindex
C3×#50562
#105894082
C3×#45412
#677823
#675433